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Universal Mechanism 5.0 8-1 Chapter 8. Simulation of railway vehicles

1. Edit subsystern General Position Identifiers Identifier WES Number of degrees of freedom p Cc Inertia parameters Mass 1500 Moments of inertia x lz 1200 l aoo Added mass 2 N Wheelseet Name Wheelseetl 4 bE rz Radius 0 525 n Pegg eee or eee Semibase 0 79 m wheelset C t Axle length 2 2 n ES Gear Edit subsystem Bouble Eee 045 General Position Identifiers Position Y 0 55 Translation Image f Simple C Fine x weel E z 0 525 z Fig 8 6 Wheelset parameters The following parameters are available on the inspector window Fig 8 6 Name of the subsystem e g Wheelset1 Identifier of the subsystem set of Latin letters and digits e g Wset1 The identifier is used for access to the identifiers of the wheelset while programming in the UM environment The identifier should be unique within the object Number of degrees of freedom Sect 8 2 3 1 Structure of subsystem Wheelset Further parameters of the wheelset Radius of the running circle Sect 8 2 3 2 Semibase of the wheelset Sect 8 2 3 2 Other parameters in the inspector window allow the user to modify the wheelset image Axle length increases or decreases the length of the axle image Gear for a traction wheelset adds a simplified image of a gear double if necessary as well as the corresponding radius of the gear and its position on the axle Image Simple Fine di
2. Equivalent contact angle parameter Nominal contact angle 2 9 Maximal displacement rm 6 50 Contact angle for flange degrees 70 00 Contacte 0r 35 0 H Fig 8 100 Choice of a creep forces calculation method and its parameters A method for computation of creep forces Sect 8 4 3 2 can be chosen on the Rail wheel Contact Creep forces tab e Simplified Parameters of the simplified model of rail wheel contact are shown in Fig 8 100 see 8 4 1 3 Simplified contact geometry Equivalent conicity and contact angle parameter equivalent conicity A contact angle parameter nominal contact angle degrees is the value of the contact angle for non shifted wheelset maximal lateral shift of a wheel relative to the rail y start of two point conntact mm contact angle on flange by two point contact 8 degrees Contact 2 Y Z coordinates of flange contact by two point contact in the rail coordi nate system y z mm Remark Mueller s method is used for computation of creep forces Model of creep forces Simplified C FastSima Mueller C Minov s model C FastSim C Nonellipt Exponent m 2 3 fa WA Fig 8 101 Mueller s model e Mueller See Sect 8 4 3 2 1 Mueller s method for the details The only parameter is m the de fault value is 3 Universal Mechanism 5 0 8 82 Chapter 8 Simulation of railway vehicles Model of creep forces Simplified C FastSima Mueller M
3. Kiev Nauk dumka 1989 240 p in Russian 2 J J Kalker and J Piotrowski Some New Results in Rolling Contact Vehicle System Dy namics 18 1989 3 Kik W Piotrowski J A Fast Approximate Method to Calculate Normal Load at Contact be tween Wheel and Rail and Creep Forces During Rolling Proceedings of 2nd mini conf Contact Mechanics and Wear of Rail Wheel Systems 1996 P 52 61 4 K L Johnson Contact Mechanics Cambridge University Press 1985
4. The user may compute any vertical or horizontal irregularity within this function Input position longitudinal coordinate for which the irregularities are computed Output Result returns function value If the return value is equal to 1 the programmed values will be taken into account otherwise they are ignored Universal Mechanism 5 0 8 62 Chapter 8 Simulation of railway vehicles LeftZ RightZ vertical irregularities of the left and right rails in meters LeftY RightY horizontal irregularities of the left and right rails in meters derLeftZ derRightZ derivatives of vertical irregularities of the left and right rails w r t longitu dinal coordinate derLeftY derRightY derivatives of horizontal irregularities of the left and right rails w r t lon gitudinal coordinate Irregularities computed in the function are added with those assigned to rails from files If it is necessary to take into account the programmed irregularities only the No rregularities way file should be assigned to the corresponding rails Fig 8 72 Slump Consider a separate irregularity of the Slump type Fig 8 72 The irregularity of the left rail and its derivative are defined by the formulae h A fi oos ma 2 L T in T x XQ 2L L xE xo xo T L 9 Here H L x are the depth and length of the slump as well as the start position along the track Let the same irregularity for the right rail be moved along the tr
5. r65new rpf new Russian rail R65 with running surface radius 500mm r65_300n rpf new Russian rail R65 with running surface radius 300mm r65o0ld13 rpf R65 with 13mm lateral wear r65o0ld15 rpf R65 with 15mm lateral wear r50 rpf new Russian rail R50 Several new and worn rail profiles UIC60 Universal Mechanism 5 0 8 72 Chapter 8 Simulation of railway vehicles Object simulation inspector Solver Identifiers Initial conditions Object variables Rail w heel VA Information Tools SHAT Track Frohiles Contact Fictt cars Forces Wheels Ralls Addit parameters Lett rail E umg bns A orb Sne rp Right rail D Sum40 bins F Wn pris E Snew rpt Profile wear process Rail profiles in control port a Control points left rai Control points right ral Integration Fig 8 87 Assignment of rail profiles and creation of wheel profile list Use the I buttons to assign profiles for the left and right rails Fig 8 87 Note Rail profiles assigned here are not used if the rail profile evolution mode is switch ed on Sect Rail profile evolution along the track Universal Mechanism 5 0 8 73 Chapter 8 Simulation of railway vehicles 8 5 2 3 2 Assignment of wheel profiles Object simulation inspector Solver Identifiers Initial conditions Object variables Rall w heel va Information Tools GH Ao Track Profiles Contact Fict cars Forces Wheels
6. Forces Speed Wheels Rails Addit parameters Difference in radii Contact options VWheelsets Deviation of radii mri Fig 8 109 Difference in running circle radii of Wheelset 1 Difference in running circles radii dr difference in running circles radii of the left and right wheel of a wheelset Sect Wheelset geometry in millimeters are set on the Rail Wheel Profiles Addit parameters Difference in radii The parameter is assigned to the right wheels It is positive 1f the left radius is greater than the right one In the case shown in Fig 8 109 the running circle radius of the right wheel of Wheelset 1 is decreased on 3 mm in comparison with the left wheel 8 5 2 7 2 Parameters of contact geometry computation Object simulation inspector Solver Identifiers Initial conditions S H Track Protiles Contact Fict vehicles Forces Profile files Wheels Evolution of rail profile Addit parameters Difference in radii Contact parameters Jump parameter in criterion 0 01 of two point contact rm M rotation of wheel profile on off I Thin out profile points Thin out step size mm fi Integration Fig 8 110 Additional parameters for contact geometry computations When worn profiles defined by a set of points are created some problems with the con tact geometry computations might appear Let us consider some of these problems as well as their solving with the help of paramet
7. e Vertical track macro geometry is taken into account A macro geometry file can include any number of curves tangents switches variable friction conditions along the track as well a an arbitrary vertical profile Use the Tool Create macrogeometry menu command or the button to start the win dow where the track is described JA Tangent L 10 CurvelLeft R 300 H 0 0 Tangent L 120 CurvelLeft R 300 H 0 0 Cy nl lt lt nn Fig 8 73 Marcogeometry window The upper part of the window is used for description of the track geometry in the hori zontal plane e To add a section click on the ey button and select the section type in the menu Add tangent AGG Curve Add switch Fig 8 74 Adding section menu Universal Mechanism 5 0 8 64 Chapter 8 Simulation of railway vehicles e To edit the section parameters double click on the corresponding line of the sec tion list or select the line and press Enter z Length 10 00 Friction coefficient 0 25 Apply Cancel Fig 8 75 Parameters of a tangent section e Tangent section window contains values of section length and coefficient of fric tion xl Type of curve i Lef C Right S 200 P2 feo R 300 0 09 dy foo Friction coefficients Outer rail Inner rail Flange Transient section forthe sige friction from fao to fan degrees Apply Cancel Fig 8 76 Window with curve parameters e Curve parameter w
8. 0 195 336 3 I amp l gt 0 025 sliding I 1 4 9 0 025 E where k is the ratio of the force to its maximal value vo is the vehicle speed m s y is the stiff ness of the third section of the curve s m The stiffness y depends of the speed vo as in the table vokmh 5 520 20 40 40 120 aooo T 09 06 05 o Creep forces are computed according to the formulas Fy f N k F F F F E E 62 E Remark In case of a two point contact the flange friction forces are computed as for pure sliding 8 4 3 3 Non elliptical contact model Taking into account that the bodies in contact are quasi identical i e material properties of wheel and rail are the same the contact problem can be divided into two independent ones the normal contact problem and the tangential contact problem Normal Contact Problem According to 3 an approximate contact patch is defined in the following way The wheel and the rail are considered as a body of revolution and a cylindric al surface respectively The surfaces are intersected in a depth 6 as rigid bodies fig 8 60 The function u x y specifies the interpenetration of the surfaces at the point x y It satisfies the linearized equation 2 u x y 5 z x y z y 5g thO 8 4 where z x y is the function which specifies the distance between the points of the bodies for 0 R is the wheel radius at the contact point A y is the dista
9. 8 4 1 2 computing the vertical rail deflection Az the angle B and B for the two point contact The second part of the rail deflection Ay is computed from the geometrical conditions Forces Ry R are computed according to Eq 8 1 The normal force N for a one point contact is obtained from Eq 8 2 in the case of a two point contact the normal reactions N and N2 are computed from Eq 8 3 4 The new value of the deflection Ay is computed and stored for the next iterations 8 4 3 2 Algorithms for computing creep forces X Fig 8 57 Creepages spin and creep forces Modern models of tangential forces in a wheel rail contact are based on nonlinear depen dencies of the general form BoE Nee OP F P N S 55y gt 9 p Here the following notations are used F Fy are the longitudinal and lateral creep forces lying in the tangential plane of the rail N is the normal force in the contact Sx Sy are the longitudinal and lateral creepages Q is the spin pis a set of geometrical parameters characterizing rail and wheel profiles e g curva tures of contact surfaces in the case of the FASTSIM algorithm Universal Mechanism 5 0 8 47 Chapter 8 Simulation of railway vehicles As it is known the creepages and the spin satisfy the following relations Ex Vzy V Sy Vvy vo p v0 where v V are the corresponding component of sliding velocity at the contact point on the Y wheel relative to th
10. 8 5 1 1 Creation of wheel and rail profiles my Curve editor Di um bint RW pri stwagnw wpt t lol x iy u K K TE TEE T el m 5 69 21 69 21 69 3 57059 on DOPOD Ca I ee tf Wheel C Rail 94 18 F Fig 8 62 Editor of curves for creation of profiles Wheel and rail profiles are located in the bin rw prf directory in form of separate files with extension wpf wheels and rpf rails The profiles are described in special systems of coordinates Sect 8 2 3 2 8 3 1 1 with the help of a special tool which is available in the UM Similation program by clicking the Tools Create wheel rail profile the Ctr P hot key or the T button on the tool panel Creation of new profiles and modification of old ones are made with the help of the Curve editor Fig 8 62 Detailed description of the editor can be found in Chapt 3 Sect Object constructor Curve editor Creation of new profiles is possible in two mod es e input as a set of points with successive spline approximation e input of profiles as a set of line segments and circle arcs The second type of the profile description is used mainly for new standard profiles Universal Mechanism 5 0 8 54 Chapter 8 Simulation of railway vehicles 8 5 1 1 1 Input as a set of points with successive spline approximation i P i 4e 42 em Fig 8 63 Input as a set of points Use either list of points in the left par
11. Animation window and in Chapt 4 Sect Animation window in the Simulation module Universal Mechanism 5 0 8 96 Chapter 8 Simulation of railway vehicles In addition to standard functions visualization of rails and slippers is available for rail way vehicles the Show gauge check in the Rail Wheel Track Macrogeometry tab of the object simulation inspector 8 5 3 3 Contact animation window The Contact animation window is a special animation window for visualization of rela tive positions of rail and wheel profiles as well as rail wheel interaction forces while simulation of a vehicle dynamics Use the Tools Contact animation menu command the button on the tool panel or the Ctrl N hot key to call the window Parameters of the contact animation are located in the bottom of the window These pa rameters allow the user to turn on off visualization of contact forces change vector scales and profile positioning horizontal or vertical manner Pointing the mouse cursor at a vector allows the user to get its current value Clicking the vertical positioning circles switch on off profiles corresponding to one of wheelsets tacl Animation of rail wheel contact m x TTOTTE BS leoedd J l P Animation of rail wheel contact x rome gt Parameters of vector animator Oinenieton Parameters of vector animation Orientation i Animation of torcas ENI oF horizonta
12. Ay Fig 8 43 Since the angle Aa is small the following nonlinear relation takes place YwO F Yw Zy yy Aa or Yw Ywo Zw w Aa To solve this nonlinear equation relative to y direct iterations 0 Yw Yw0 gt yil ypo toy Ja i 0 1 2 could be used As it is known direct iterations converge if the condition Bw no dy y takes place Since Aa lt lt 1 this condition is always valid for real profiles lt 1 Finally the coordinate z o 1s computed from the formula Zwo AZ YwAa t Zy and the value of minimized function 8z y is evaluated In this way the algorithm allows us to compute a pair of points and the distance between them The main advantage of the algorithms is its simplicity reliability and independence on smoothness of profiles Computing the minimal value 62Z is executed according to he following algorithm Consider a sequence of values of coordinate y with a contact step size h 1 mm Scat aI and select the points with the minimal value 6z After that the process is repeated near the found point with smaller step size 0 1mm 8 4 1 2 Computing tables of contact points As it 1s already mentioned computation of tables of contact geometry information is ex ecuted before start of the simulation if the rail profile does not change along the track This in formation is obtained in dependence on the wheel profile position relative to the rail profile UM Universal Mechanism 5 0 8 3
13. Fails Addit parameters Set of whell profile Se Osun 0 bin or newlocor wpt dum bina prh dmetidi wot Lett wheel Right wheel Hewlocow wpf Hewlocow wor i newlocow wpf Assign to all newlocow wpf dmetiso wpf Integration Fig 8 88 Assignment profiles to separate wheels UM database of wheel profiles includes the following files newlocow wpf new Russian locomotive wheel newwagonw wpt new Russian freight car wheel dmeti30 wpf new DMETI profile new and worn wheel profiles S1002 wpf Assignment of wheel profiles has two stages At the first stage a list of wheel profile is created Fig 8 87 The list should include at least one profile The S button on the pop up menu is used to add a profile to the list To assign profiles from the list to the wheels open the Rail wheel Profiles wheels tab Fig 8 88 call the pop up menu by clicking the right mouse button and select a profile to assign it to all the wheels if different profiles should be assigned to different wheels double click on the necessary wheel by the left mouse button and change the profile until the desired profile name appears 8 5 2 3 3 Rail profile evolution along the track To describe a changing the profile of the left or and right rail along the track Sect 8 3 1 1 the following points should be used Create the list of profiles with the Rail Wheel Profiles Profile files Rail tab The list is c
14. iy y paa a4 m o h lt Fe dy mE 3 o n y RV ry e The normal contact force is calculated as b q N ff p x y dxdy k u x y dxdy k 2f a h y a Bp dy 8 10 C C b Using Equations 8 9 8 10 the following nonlinear equation are obtained A a a h yja id SE i eR i 21 v y ata y a pes is 10 Jee z E y o 8 11 b The solution of Equation 8 11 is the interpenetration 6 Taking into account that o lt the approximate contact patch is found and then using equation 8 10 the proportionality factor k 1s calculated Substituting the value of k in equation 8 8 the distribution of the nor mal pressure over the contact area is obtained Tangential contact problem The FASTSIM algorithm which was adapted for non elliptical contact area was used to solve the tangential contact problem To determine the value of flexibility an equivalent ellipse such that the area of the non elliptic contact patch is equal to the area of the ellipse was calculated The semi axis of the ellipse in the rolling direction is set equal to the maximal half length of the non elliptical patch Universal Mechanism 5 0 8 52 Chapter 8 Simulation of railway vehicles 8 4 3 4 Coefficient of friction in wheel rail contact UM uses both variable and constant coefficients of friction in contacts of the wheel and rail Two main coefficients of friction are introduced for each of two rails The
15. 1w hA z Motor 1a zero velocities jie 1 VMAS Drive shaft 1a Coord From input dat File Message d U LIM message INITTIGL MESSAGE Integration Message Close Fig 8 25 Fixation of coordinates and creation of fixation file Fixation of a coordinate means that the coordinate and its time derivative velocity can not be changed during computation of initial values of coordinates and velocities The fixation file contains the list of fixed coordinates Thus in the case of locomotive VL8O0 it is necessary to fix coordinates of wheelsets corresponding to rotation of wheelsets about the lateral axis joint coordinates in joints JW SetRotat as well as coordinates in revolute joints setting rotation of mo tor casings about wheelset axes joints jMotor in the figure The fixation file is created in the simulation module on the Initial conditions Coordinates tab of the object simulation inspec tor Fig 8 25 Click on the upper button Message After this action the program automatically computes angular velocities of wheelsets as well as longitudinal velocities of some of bodies e g car body This stage of creation of fixation is not necessary but it allows the user to see the current values of wheelset angular velocities which must be fixed Fix the necessary coordinates by clicking on cells of the table column marked by the image on the top Save fixation in the file with name of the model in the directory of the mode
16. 36700F r2 20113 28 1934238 34 152547 12 115867 7 92245 5995 roor fa 4 Cure Curves ial Ci Ira Tal Ci ral UF Cancel esss nn nd nie ns nN A ns 25 9 261000 Fig 8 21 Total traction force versus unit speed Universal Mechanism 5 0 8 17 Chapter 8 Simulation of railway vehicles In our example the traction torque is defined by the set of force speed curves where the force is the total traction force of the unit Fig 8 21 The curves are described in the sequence corres ponding to the throttle position number 1 N The following parameters should be set for additional description of the element Fig 8 20 left o Curve identifier the identifies which numerical 0 N sets the throttle position and selects on of the curve zero value of the identifier means zero torque It is strongly recommended to use the trottle_position identified which automates the recognition of the identifier when the locomotive is included in a train 3D model o Factor X the factor should differ from unity if abscissa in Fig 8 20 is not angular velocity of the rotor e g the unit speed It should be also used when the drive shaft rotates in the negative direction i e the corresponding joint velocity is negative In the example in Fig 8 20 the expression 0 625 4 19 rotation_sign is used for the factor which first convert the rotor angular velocity to the vehicle speed 0 625 is the wheel radius 4 19 is the
17. Computation of initial angular velocities by fixation file Use of gearing makes setting the correct initial angular velocities of some bodies Neglect ing this requirement lead to large forces in drive system to lifting wheels from rails at the begin ning of simulation On of the main tool for automatic computation 1f initial angular velocities more precisely joint velocities is the creation by the user of a so called fixation file which prompt to the program which velocities must be kept without change by computation of initial values To illustrate the fixation of a coordinate consider the drive system of one of the wheelset of locomotive VL80 with the axle hung suspension of motor Due to the gearing the following eq uation takes place Oy o Om where is the angular velocity of the wheelset rotation is the angular velocity of the mo tor casing relative to the wheelset base is the angular velocity of the rotor relative to the mo tor casing i is the gear ratio It is clear that this equation does not have a unique solution The program cannot automatically choose which of three angular velocities should be computed from this expression and may choose any of them Often this leads to false solution either the motor casing has an angular velocity equal to the wheelset rotation velocity multiplied by the gear ratio or all angular velocities are zeroes The fixation file allows the program to solve the equation corr
18. Functional for UM Loco module Mean value of three four minimums or maximums All functional work according to the same algorithms with some minor differences Firstly the list of local extremums are created Local minimums are taken for _3Min Mean and 4Min Mean local maximums are taken for _3Min_ Mean _3Max_ Mean 3Max Zero 4Max Mean and 4Max Zero The win _3Max_Mean dow of 1 20 of the length of realization is used during creating the list of _3Max_ Zero local extremums Two adjacent extremums are added into a list of extre _4Min_Mean mums if only plot intersects the abscissa axis for functional with Zero _4Max Mean postfix or mean value for functional with Mean postfix between these _4Max Zero extremums Otherwise the only extremum is chosen Then 3 or 4 extre mums maximum minimum extremums are extracted For the _4Min Mean 4Max Mean and 4Max Zero functional the smal lest biggest one is deleted Then the mean value for the rest extremums are calculated as a results of the functional Ride Comfort G Ride comfort factor for horizontal direction according to Russian ex a USSR standard 24 050 16 85 R Ride comfort factor for vertical direction according to Russian exUSSR Ride_Comfort_V Standard 24 050 16 85 Universal Mechanism 5 0 8 99 Chapter 8 Simulation of railway vehicles References 1 Mathematical modeling vibrations of railway vehicles V F Ushkalov at al V F Ushkalov Ed AS USSR Inst of techn mech
19. N sin B4 0 8 2 R N cosB Fy sin By 0 Analogous equations are valid for a two point contact R Fi cosp N sin By Fp cosBy Na sin Bg 0 3 3 R N cosy Fy sin By N3 cosp Fh sin B3 0 Here B B gt are the angles between the normal to the rail at contact and the axis perpendicular to the track Eq 8 2 for a one point contact and 8 3 for a two point contact are complicated sys tems of nonlinear algebraic equations relative to unknown deflections of the rail and normal reactions N N gt Consider the main ideas for their solving not going into details l Position of the wheel as well as the rail shift due to irregularities gauge widening and cant are known by the computing the contact problem the only unknown are deflections Ay Az and their time derivatives Note that the vertical deflection Az is not an independent varia ble because when the lateral Ay delfection is known the value of Az can be obtained from the geometry of the contact This value is equal to the value 6z Sect 8 4 1 1 Calculation of the rail deflections and contact forces is an iterative process Iterations include two cycles internal end external The internal iterations are used for solving equations 8 2 8 3 for known values of tangential forces lateral creep forces External iterations calculate creep forces Values of creep forces on the previous integration step are used as initial ap pr
20. Re HH Left axlebox ea axlebox Fig 8 16 Visual components of UMLoco module Axle boxes can be added by visual components e Open the UMLoco tab of the visual component lists e Click on the axlebox button then click somewhere on the grid for a temporary location of the axlebox e Assign a revolute joint using either method above or the visual component 2 of the joint In the last case connection points of vector type corresponding to the joint location should be created for the wheelset base These points are automatically presented if the wheelset is added as a visual component 8 2 5 Modeling linear springs of primary and secondary suspension The following types of force elements are used for modeling both linear and nonlinear springs e Special force element Spring The element is used for modeling linear springs with identical shear stiffness Mathematic model of the element is described in Chapt 2 Sect Special forces Spring Generalized linear force element Examples of description and or usage Chapt 7 Sect Models of Springs Model samples Rail vehicles ac4 Chapt 8 Sect Springs e Generalized linear force element The element allows modeling both the same springs as the previous one and more complicated or simplified cases e g when the shear stiffness is not identical in different directions It can be used also for modeling bilinear springs Universal Mechanism 5 0 8 14 Chapter 8 Simulation of railway v
21. Y 8 2 7 1 2 Traction torque Universal Mechanism 5 0 8 16 Chapter 8 Simulation of railway vehicles Mame iDrive shat yma Sy Body Bod Type amp Rotational Geometry Description Joint force Le 4 Joint torque m List of forces sBirct shFro2 TERETE Name Poing Th List of forces sBfrc shFro2 Type fle List of characteristics BEE oe C ie i i Type are Expression Force Number of lines 11 aad Description of fore Curve Pascal C expression F F s vt EA throttle position C identifier P Example l l Becton 0 62574 19 rotation E cstiff 4 0 cdiss y amplsin om t Factor r ftraction_to_torque n F traction_torque rotation_sign P Fig 8 20 Setting traction torque Driving torque is introduced as a joint torques in the revolute joint connecting the drive shaft with the motor casing Fig 8 20 It is recommended to use the List of forces type of the joint torque The list contains two elements The first element of the List of characteristics type stands for modeling the torque value depending on the rotor angular velocity for different posi tions of the throttle The second element of the Expression type includes a parameterized ex pression and can be used for direct setting the traction torque if the locomotive model is in cluded in a 3D model of a train Curve editor THATS ke Ck BEM Be Lire yu KE Pile Es ee i ee 56395 47 458415 63
22. adding the number of a wheelset and the left or r right for wheel identification For instance the YWContact l_ r identifier of a variable coordinate Y of the first contact point in SC of the rail profiles Y Wheel Contact 1 is obtained Universal Mechanism 5 0 8 91 Chapter 8 Simulation of railway vehicles from the standard identifiers of the type YWContact and corresponds to the right wheel of Wheelset 1 If one variable for a separate wheel is created the used may change both the identifier and the comment in a standard manner However if a group of variables is created standard identifiers and comments are assigned automatically Identifier FIRST CONTACT POINT One point contact or contact on the running surface by two point contact Fig 8 56 Creep x Creeply Longitudinal and lateral creepages Sy the variables are used for com puting creep forces Sect 8 4 3 2 Spinl Spin The variables are used for computing creep forces by FASTSIM Sect 8 4 3 2 Module of the creepage vector d EZ FCreeplx FCreeply Longitudinal and lateral creep forces Sect 8 4 3 2 The lateral creep force corresponds to the F force in Fig 8 56 Unit N Normal force N Fig 8 56 Unit N Betal Contact angle angle B between the N and the Z axis of the track SC Fig 8 56 Unit rad The angle is positive for inclination of the normal forces inward the track YWContact1 Coordinates y later
23. coefficient vee iw External gearing Ey Special fo ae E Friction angle 22 767 a ty Gearing A Gearing angle 3 eae m Fig 8 23 Gering force element description A special force of the Gearing type is used for modeling the gearing The force element con nects the rotational part of the wheelset the WSetRotat body as the first body and the drive shaft as the second body The following parameters specify the force element o Attachment points are coordinates of bull gear and pinion centers in system of coor dinates of the wheelset and rotor o Axes of rotation are unit vectors 0 1 0 o Gear ration is the bull gear radius divided by the pinion radius Universal Mechanism 5 0 8 19 Chapter 8 Simulation of railway vehicles o Clearance is the value of possible teeth clearance due to wear m o Damping and stiffness coefficients characterize the drive system compliance re duced to the gear teeth o The External gearing key must be checked Fig 8 24 Visualization of the gearing force element Switch the animation window mode to the visualization of a single element by the but ton to control the correctness of geometrical parameters of the element Red vectors in the win dow correspond to the gear axes and red circles shows the central gear circles Fig 8 24 Remark Use of gearing force elements requires creation of fixation file or setting con straints for initial velocities see below 8 2 7 1 4
24. coordi nates of the rail profile Y Z SCR Sect 8 3 1 1 Fig 8 43 Introduce a new SC SCRO YoZo which origin coincides with the origin of SCR The Zo axis is perpendicular to the track plane as if the inclination angle a 9 is zero The SCR Y Z is inclined on a relative to SCRO Position of SCW system of coordinates of the wheel profile Sect 8 2 3 2 Y Zy relative to SCRO is de fined by coordinates of the origin Ay Az and the angle Aa Coordinates in Fig 8 43 are posi tive All angles are considered to be small Universal Mechanism 5 0 8 34 Chapter 8 Simulation of railway vehicles It is necessary to find a pair of points on the profiles which have the same Y coordinate in SCRO and the minimal difference in Z coordinate in SCRO min z min zy 7 zro Obviously the solution does not depend on Az Let us start with the algorithm for computing the value 0Z Zw0 ZrO for two points having the same Y coordinates in SCRO The coordinate y of a point on the rail profile in SCR Y Z has a given value We should compute the coordinates y z of the cor responding point on the wheel profile in SCW as well as 6z Firstly here are the coordinates of the point on the rail profile in SCRO Yro Yr t zr y oro gt ZrO lt r VrOr0 gt where z 1s the coordinate of the point in SCR Then a point on the wheel profile with coordinates y and z in SCW should be found which has the following abscissa in SCRO ypo y g
25. files in the model directory or in the bin rw directory 8 5 2 6 3 Plotting and visualization of forces Esa Wizard of variables a X Contact F All forces Joint force Track SC Coordinates Angular var Reaction F Linear war Railway Linear F User Expression Identifier special F Uservars scalar varales Index of array Uservars 1 1007 i102 A Fy lt y Longitudinal force component Fy1 a Fx Fy Fig 8 105 Variables corresponding to in train forces The UserVars array elements with standard numbers 1101 1106 Fxl Fyl Fz1 Fx2 Fy2 Fz2 are used to create variables corresponding to force components Use the Tools Wi zard of variables menu command to open the window for creating variables Open the UserVars tab and set the necessary number of the element variable name and co9mment and click the button to send the variable into the container Fig 8 105 Universal Mechanism 5 0 8 85 Chapter 8 Simulation of railway vehicles J Orientation Grid d Rotation style i _ Background color Ef Perspective Smoothing Window parameters Modes of body images r Position of list of vectors Scale of vectors Set GO Car body Information about Car body Add J Show forces for Car body Camera follows Car body Save animation Coordinate system tu Simplified drawing Fig 8 106 Visualization of forces for Car Body in animation window To visualize the forc
26. ro value of this coordinate corresponds to the wheelset center location of the SCO origin To add all other wheelsets use the operation of copying the described first wheelset by clicking the ze button change the name and identifier of the new wheelset change the longitudinal position and other parameters if necessary Visual adding a wheelset tt4 Wheelset with 6 d o f Wheelset with 7 d o f Fig 8 8 Visual components of UMLoco module The UMLoco tab of the component lists is used for visual adding wheelsets Fig 8 8 The advantage of the visual adding automatic full parameterization of the wheelset model as well as adding of connection points of the vector type for visual creation of axlebox revolute joints Universal Mechanism 5 0 8 10 Chapter 8 Simulation of railway vehicles 8 2 4 Modeling axle boxes Sometimes axle boxes are not included in vehicle models as separate bodies Sect 8 2 3 1 and the bogie frame is connected directly with the base of the wheelset the first body of the wheelset as a subsystem In this case graphic images of axle boxes can be introduced to make the vehicle model more realistic The images of the axle boxes are assigned to the base of the wheelset non rotating part of the wheelset In other cases introduction of axle boxes as separate rigid bodies is necessary to make the model correct Some of these cases are listed below e Non symmetric attachment and different
27. the track The cant function in S curve takes into account the length of the tangent section between the curves the L1 section is ignored only 3 In case of S curve the cant function is valid for both of the curves not for the first one In particular it means that the cant value entered in the H2 edit box is ignored To set a constant cant back the user should delete all points in the list in How to model the motion in a left curve Track type Tangent S Curve Profile Curve Switch First section second section L1 fo Le oO Pit foooo1 Pet fo s1 oon R1 fioooooof Piz 000001 dvi fo Lo 10 00003 vg dye jo 01 300 12 947557 Fig 8 96 Trick left curve as S curve S curve can be readily used for simulation of motion in a left curve 1f lengths correspond ing to the first right curve are small cant is zero and the radius is large Track type Tangent S Curve Profile Curve Switch Movement Facing C Trailing Lett switch Switch RES 1 11 Tangent section fio 00 Fig 8 97 Parameters of a switch Universal Mechanism 5 0 8 79 Chapter 8 Simulation of railway vehicles e Switch Use the amp I button to open a swt file with the switch parameters see Sect 8 5 1 4 Cre ation of files with switch parameters Other parameters allow the user to simulate both facing and trailing movements in left and right switches Fig 8 98 The Tangent section pa
28. 1 Creation of wheel and rail profiles ssensseenssensseesseessersserssserssersserssersssrsssrsssesssessserssersserss 8 53 8 5 1 1 1 Input as a set of points with successive spline approximation ccceccccsesecceeeeceeseeeaeeeeaenes 8 54 8 5 1 1 2 Input of profiles as a set of line segments and circle arcs osnnesenssonnseesseessseesseesserssersseess 8 55 8 5 1 2 Creation of track irregularities c cece ceecccsesccceneeceeeeecaeeeceeeeecseseeeeeeeeeeeeseneessesessensessesessaeeess 8 55 8 5 1 2 1 Creation of files with irregularities snenesennsonnseesssessseessersseesserssesssersseressesssersseesseesseesseee 8 56 8 5 1 2 2 Programming irregularities in the Control file cece ceecccescecseeeceeneeeaesecseeeeseeeeaeeeeaenes 8 61 8 5 1 3 Creation of macro geometry files 20 0 ecccceecccceeeeccenececeeeeeseeeesenecseeeeeeeeeseneesseeeeeeeseeseneeesanes 8 63 8 5 1 4 Creation of files with switch parameters ccccccccsscccseeeeceeeeeseeeecseseeseneecaeseesenseeseseessanessanes 8 67 8 5 2 Setting parameters of railway vehicle dynamics simulation cece eee cccseeccceeeeeeseeeeeeeeeaeeeceeneeeeuees 8 68 Universal Mechanism 5 0 8 2 Chapter 8 Simulation of railway vehicles 8 5 2 1 Solyer and its parameters Use of JACODIANS sgsccssasssnssisratencsnaniiastibvotowstaasesactit yet awedangusactsushemataasaione 8 68 8 5 2 2 Modes of lone nudinial TOUOM O8 VENICIC 6250 cisncssapssasac
29. 2 7 Some features of development of locomotive models Features of locomotive models are traction systems 8 2 7 1 Model of traction Fig 8 17 Model of one unit of VL80 electric locomotive Simplified modeling of traction motors and wheel driving systems are necessary for rea lization of traction mode Specific features of the model depend on a type of the drive system Universal Mechanism 5 0 8 15 Chapter 8 Simulation of railway vehicles Here we consider the axle hung traction motors taking the VL80 locomotive as an example Fig 8 17 8 2 7 1 1 Bodies and joints Fig 8 18 Subsystems bogie and wheel motor assembly Model of one unit of the locomotive includes two subsystems bogie which contain two subsystems wheel motor assembly each Traction system is realized within the wheel motor assembly subsystem ss Sy Q Fig 8 19 Bodies motor and reducer casings and drive shaft Model of the wheel motor assembly contains a wheelset two axle boxes motor and re ducer casings as one rigid body rotor with two pinions drive shaft Fig 8 19 as well as primary suspension force elements All the suspension force elements are described as external ones the External second body and have the autodetection attribute on Motor casing is connected to the wheelset base by a revolute joint Another revolute joint connects the rotor with the motor casing Joint axes are parallel to the lateral axis
30. 5 Chapter 8 Simulation of railway vehicles allows two kinds of pairs of profiles profiles with one point contact only and profiles with poss ible two point contact Fig 8 44 Fig 8 44 Pairs of profiles allowing two point contact left and one point contact only right In a one point contact mode the contact point position depends on the lateral shift Ay and the angle Aa Fig 8 43 Coordinates of the contact point correspond to the profile point with the minimal distance in the vertical direction Sect 8 4 1 1 Thus the table contains coordinates of the contact point in SCR and SCW for a discrete set of variables Ay Ao z I 1 Ny J 1 Na with a proper step size of discretization Computation of one point contact is realized according to the algorithm in Sect 8 4 1 1 Here we consider some features of computing a two point contact nO ne Fig 8 45 Types of contact for a pair of profiles allowing two point contact one point contact two point contact and creeping up Fix the value Aq and give the maximal value of the lateral displacement Fig 8 45 left In this position of the profile we have obviously a one point contact Now decrease Ay without changing Aa 1e shift the wheel profile to the left There exists some critical value of the lateral coordinate Ay for which a two point contact occurs if the profiles allow it Fig 8 45 center Further decreasing Ay does not change coordinates of contact points the rail pr
31. Department of Applied Mechanics Bryansk State Technical University UM Loco is an extension of UM aimed at simulation of dynamics of railway vehicles locomotives cars trains In addition to the standard UM configuration it includes the following items Wheelset as a standard subsystem Automatic calculation of wheel rail contact forces according to various models of creep forces Mueller model FastSim Non Hertzian contact model etc Specialized graphical interface for animation of contact forces Interface for creating rail and wheel profiles and track irregularities Interface for setting curve and switch parameters Standard list of variables which characterize wheel rail interaction creepages total normal and creep forces in wheel rail contacts angle of attack wear factors etc more than 30 variables for each of the vehicles wheels Database of profiles and track irregularities Database of subsystems wheels motor blocks bogies models of various vehicles UM Loco allows the user to calculate the critical speed of a vehicle to analyze 3D dynamics of a vehicle or a train in time domain on straight track or curves with without irregularities to analyze vehicle dynamics in dependence on wheel and rail profiles to include 3D vehicles in a train model to create multivariant projects for scanning the vehicle train dynamics depending on any pa rameters to compute natural frequencies and modes eigenvalues and eig
32. Fig 8 94 the cant value can be assigned for the outer rail by two different ways Universal Mechanism 5 0 8 78 Chapter 8 Simulation of railway vehicles The first method is used if the cant value is positive and constant in steady part of the curve and increases decreases uniformly in the transients In this case the numeric cant value should be set directly in the boxes H1 H2 The second method is used if the conditions of the first one do not take place e g when the cant value is not constant in the steady curve The variable cant value along the track both for the first right and for the second left curves is set by the El button in the right hand side of the H1 box Fig 8 93 Fig 8 94 The curve editor appears and the cant value m versus curve distance can be a by a sequence of the points Fig 8 95 After that the box looks like Al Profile Fig 8 95 The user should take into account the following important remarks concerning usage of the variable cant value 1 The cant function should be always zero at tangent sections of the track before the first right curve between the curves after the second curve Violation of this requirement leads to discontinuities in the vertical rail position 2 The cant function starts since begin of the first transient section and does not include the tangent section before the curve For example the point 0 0 in Fig 8 95 corresponds to the start of the curve not to the start of
33. IC Points Condition ORRERI Type pE C O ses Oy Lmin fo 0 Lminf200 00 Sumber of harmonics a000 WA Compute Fig 8 70 Standard SPD of FRA e Spectrum FRA With this option the user can generate irregularities by SPD corresponding to USA stan dards Six option of the track condition allow generating irregularities of different quality from very bad track 1 to very good track 6 The Lmin and Lmax parameters specify the minimal and the maximal length of irregularity in the realization m It is possible to generate different realizations for left end right rails both for vertical and horizontal irregularities To create two files for vertical irregularities of the left and right rails select the Z option in the Type group which denotes a SPD for a half sum of the vertical irregularities of the left and right rails generate realization by the Compute button and add it to the resultant irregularity by the 1 button select the Z option in the Type group which denotes a SPD for a half difference of the ver tical irregularities of the left and right rails generate realization by the Compute button and add it to the resultant irregularity by the 1 button keeping Factor 1 Fig 8 71 save the result to file for the left rail Resultant profile HO Length fiona otep 0 1 Profile components spectrum spectrum Half sum Fig 8 71 Resultant profile containing two realizations remove or switch off the seco
34. Pere reer eee ey TTT TTT TT eT oT TCT EC Te Ce ee Tr eT eens remem es a la ocr aie Pn Cae eI Beane ae plicit aia cadens Fig 8 50 Function E y for pairs of profiles in Fig 8 47 8 48 Universal Mechanism 5 0 8 40 Chapter 8 Simulation of railway vehicles The contact angle parameter is used for linear approximation of the function E y on the interval Ay of the lateral shift of the wheelset E y P A The formula similar to the equivalent conicity is used for evaluation of for y E y dy LO dy 0 ZEY E Simplified geometry of contact The following simplified formulas are used for evaluation of wheel radii at contacts and for contact angles depending on the lateral shift of the wheelset in terms of the equivalent conici ty and contact angle parameter LAs ENA Y r 2EY Ey a i Pr Pos at AR aa Here y y are lateral shifts of the left and right wheels relative to the corresponding rails which are in general different due to the elastic deflections of rails If the lateral shift of a wheel towards the rail is greater than some given value y a double contact takes place The contact point position on the side of the rail is specified by the coordinates of in the SCr y z and the contact angle 8 The longitudinal contact overswing is computed according to the results of the previous section The longitudinal and lateral creepages in the contact point on the r
35. Universal Mechanism 5 0 8 1 Chapter 8 Simulation of railway vehicles 8 SIMULATION OF RAILWAY VEHICLES IN UM 0 ee cece cece eee ee ee eeeeeeneeeeseeesenseenseeeeoneseneees 8 3 Subs General MPOFMAUON ss sssini de esnnis susnnans dassesudsenscbescuvendedsensaecSeesencd sesactsadeebedadsans 8 3 8 2 Creating railway vehicle models x0 scccssscssssscssssossssccssssovesccossesccessconsssccesesocessccssesocessscssesosesssossesooess 8 4 S2ale Typeol Object Railway Vehicle sisiicaicncwssnntawvenodexssinanicnawenaienaeiesewnnd Ea EE ERE EEEE EEEE 8 4 622 Base coordinale Syst eee ne Renee tines nee EE err ent etn E E rem tree ee nen Te etre eet tenn ere ete 8 4 A NV CONSE E E erodes canescens E E T A E E E ET 8 5 8 2 3 1 Str cture of subsystem Wheelset si aesicstnsndaeiesiediarnsietibainnateaid nanan nann a 8 5 8 2 3 2 IVY Ta SS comely tec sr EE cee aed act ego E O EEE atemapleesnienes 8 6 8 2 3 3 Adding wheelsets and changing their parameters cccsececcseeeceesecceeeeeeeeeeeeesecseneeeseeeeseneesees 8 7 Sak Modelim ie DOCE aan ne nnn were tener ere Treen eee ee rear ere Tren Tne EEE 8 10 8 2 4 1 Axle boxes as massless graphic images os xcrsusanedninuanennacnmnwhwneaeredanaeetnn apennunnentnmnanemimunaetannats 8 10 8 2 4 2 Axle DOr as aieia DOY ereere E 8 12 8 2 5 Modeling linear springs of primary and secondary suspension ssseesseesseesseesssessserssersserssersseess 8 13 5 20 Modelme dampers trahon TOUS
36. about materials the wheel and rail deflections at contacting points are equal thus 2 0 0 But in reality the bodies at contact cannot interpenetrate and deflections occur so the interpenetration region encloses the contact patch if the influence function is unidirectional Granting this fact the bodies are interpenetrated in the depth 6 lt 6 Figure 3 To find the normal pressure distribution p x y in the contact area the elastic Winkler foundation model 4 1 e the assumption about proportionality between stress and interpenetra tion u x y was used So the distribution of the normal pressure is set as p x y k u x y 8 8 where k is a proportionality factor In UM rail track model the rail is considered as a massless body on a visco elastic foun dation and the normal force N at the contact point is available from the solution of rail equili brium equations The interpenetration of the bodies is only used to compute the normal pressure distribution and the approximate contact patch and its small value can be neglected in the dy namic equations Thus the normal force depends on the quite small vertical and lateral stiffness of the rail track system and this model is not stiff Using Equations 8 4 8 8 the interpenetration in the case of single zone in the contact patch is Universal Mechanism 5 0 8 51 Chapter 8 Simulation of railway vehicles 03g b a 5 20 0 0 8 9
37. ack in the longitudinal direction on dx relatively to the left rail It is supposed that all of these four parameters are included in the list of identifiers of the corresponding UM model Chapt 3 Sect Basic elements of constructor function TrackProfile position real_ var LeftZ RightZ Lefty RightY derLeftzZ derRightZ derLeftY derRightY real_ integer begin Result 1 LeftY 0 Rigat 0 derLeftY 0 derRightY 0 J irreg larities for the left rail it position gt pzAll ll x 0 and positions pzZzAll 1 x0 _pzA1l11 1 L then begin lerea 0 5 pPZAlLIl A 1 cos pi position pzAld 1 x07 _pzAll 1 L Ger Lertea2 0 5 pL _pZAll 11 ea Ssin ol position pPZALL 1 x0 7 _pzA1l11 1 L _pzAl11l1 1 L end else begin LeftZ 0 derLeftZ 0 end irreg larities for the right rail af OS1tLON gt pPZALL 1 x0tdx and posiation lt _pzAll 1 xO Universal Mechanism 5 0 8 63 Chapter 8 Simulation of railway vehicles PZ2ALI eter 207 Fol Te So then begin Right U 0 _pPZALL 1 H 1 c05 PL1 Position pzAll is xK0 _pzAl1 1 dx a L derRight 4Zs 0 5 p1 _pZAll ll A sin pi position pzAll iLl x0 PAlla 7 Ala i pA LL end else begin Rigatar U derRightZ 0 end end 8 5 1 3 Creation of macro geometry files The macro geometry files mcg are used in the following cases e Track macro geometry differs from tangent section curve S curve or switch
38. acting on the wheel along axes of the track system of coordi nates Sect 8 3 1 3 Longitudinal lateral and vertical forces D ratio W R Dynamic ratio on the rail wheel level The value is computed according to the formula F F 9 Fro gt where Fis the total vertical force in the track SC F is the static load for a wheel dyTrack dzTrack Horizontal and vertical rail irregularities at the wheel position Path Path passing since start of simulation The variable is used for plotting oth er variables in dependence on the path Universal Mechanism 5 0 8 94 Chapter 8 Simulation of railway vehicles 8 5 3 1 2 Kinematic characteristics relative to track system of coordinates Kinematical variables of bodies especially in the case of use the inertial SCO Sect Base coordinate system should be often projected on the track system of coordinates TSC Sect Track system of coordinates Note that axes of the TSC and SCO in a straight track are parallel and projections of vectors on these SC are the same Ere Wizard of variables El amp fwagondpb 2 Basel 2 Car body a Bogie gp Boqied BIE Car body Contact F All forces Type i Coordinate Acceleration Ang veloc Velocity C Angles C Ang accel Lomponen ic x 2 ee rx Car bodyytrack lt y Coordinates of point 0 0 0 of body Car body lt n W Fig 8 112 Kinematic characteristics of bodies in the track SC Use the Track SC tab of the Wizard of
39. al and z vertical of the contact point in SC of the ZWContact1 wheel profile Sect 8 2 3 2 Unit m XRContact1 Coordinates y lateral and z vertical of the contact point in SC of the rail YRContact1 profile Sect 8 3 1 1 Unit m ZRContact1 Zlifting Vertical lifting the wheel running surface for profiles allowing a two point contact Fig 8 45 left Unit m Mwear1 Awear 1 Flanges wear factors for a one point contact of for the running surface con Swear tact in the two point contact power work and specific work The factor are computed according to formulae M wear FixVix MyViy the scalar product of the flange creep force and the sliding velocity at the contact unit W t Awear M weardt unit J 0 Swear Awegr S where S is the path unit J m Area of the contact patch Unit m Maximal pressure in the contact Unit Pa SECOND POINT CONTACT Flange contact for profiles allowing a two point contact Fig 8 56 right Creep2x Creep2y Longitudinal and lateral creepages amp the variables are used for com puting creep forces Sect 8 4 3 2 Spin2 Spin The variables are used for computing creep forces by FASTSIM Sect 8 4 3 2 Universal Mechanism 5 0 8 92 Chapter 8 Simulation of railway vehicles Module of the creepage vector J E x Fcreep2x Fcreep2y Longitudinal and lateral creep forces Sect 8 4 3 2 The lateral creep force corr
40. ar file Ctl Read fram text file Lay off variable as abscissa Lay off time as abscissa Fig 8 113 Plotting variables versus the path Drag the Path variable into he graphical window list Select the variable and click the right mouse button Click the Lay off variable as abscissa in the pop up menu e Use of Path variable in list of calculated variables Process parameters Objectvariables Solver statistics Accelerations Comment ayvikysop track Acceleration of point 0 0 0 of body Ky az kysoptrack Acceleration of point 0 0 0 of body Ky Fath Vehicle path fram the simulation start Lay off as absch fa Fath vehicle path from the simulation start t Fig 8 114 Setting dependence of calculated variables on the path It is strongly recommended that list of object variables for a railway vehicle always con tains the Path variable If it does not include this variable add it to the list before simulation of scanning the object in a standard manner Chapt 4 Sect Assignment and usage of a list of auto matically calculates variables To get dependence of computed variables on the path after the simulation drag it into the box Lay off as abscissa After that all the variables dragged from the list into the graphic windows tables processors etc are processed in dependence on the path 8 5 3 2 Animation window General information about usage of animation windows can be found in Chapt 3 Sect
41. ate starting with zero value The second column should contain the irregularities e g 0 0 0 05 0 011 0 10 0 021 To input this data with the help of the clipboard Delete all previously added points Copy data into clipboard from any text editor in a standard manner Activate the curve editor by the mouse and paste the data from the clipboard Ctrl V or Shift Insert hot keys Spline approximation can be applied to the data selection of spectrum FRA UIC Points spectrum none IY Circular frequency Sumber of harmonics a000 WA Compute e Spectrum Points Universal Mechanism 5 0 8 58 Chapter 8 Simulation of railway vehicles Track irregularities can be generated according to specified SPD spectral power density function The Rice Pearson algorithm is used to generate the irregularity functions according to the formula M x nAs gt 2S mAq A cos mA nAt p mAa m 0 Where As is the irregularity step size m M is the total number of harmonics in the sum S a is the SPD function m osc m Aq is the frequency increment osc m or rad m mAq is the phase uniformly distributed on interval 7z z The SPD can be function of frequency measured both in rad m circular frequency and in oscillation m Use the Circular frequency check box to specify the necessary type Consider generation of irregularities be the SPD function shown in Fig 8 67 Open the curve editor by the button and s
42. ates of the contact point on the rail in SCR Ny y M are the projections on the normal to the rail profile at the contact point at the latest step Ny N are some empirical criterion numbers e g ny 20mm n 0 5 Thus the two point contact is considered to be found if the contact coordinate on the rail profile changes by a large jump and the new coordinate of the contact point lies on the side of the rail After confirmation of the fact that the state of the two point contact is crossed the inter val y j 1 j 1s discretized on small subintervals about 0 0001 mm and the critical value is defined more exactly Ay j To model the process of creeping up the wheel the computation is continued for Ay gt Ay F The computations are repeated for other values of the angle Aq The contact tables contain coordinates of contact points for various values Aa Ay as well as the critical values of the lateral shift yh for each value of the angle Aa Computation of two point contact geometry assumes evaluation of a wheel overswing Xc 1 e the longitudinal coordinate of the flange contact for nonzero value of the angle of attack y UM uses an approximate analytic expression for the value of this parameter To get it consider a simplified geometrical model of the flange rail contact Fig 8 46 In this model the side surface of the rail near the contact is replaced by a plane with the same normal and the flange is re pla
43. bad_1000_y way 2 Good UIC track generated by SPD function 1000 m length The irregularity group file is uic_good_1000 uic_good_1000_zleft way uic_good_1000_zright way uic_good_1000_y way The Nolrregularities way file is used if a rail has no irregularities or the user programs the irregularities in the control file The Rail Wheel Track Irregularities Parameters tab is used for assignment of irregu larities from files To set both the vertical Z and the horizontal Y irregularities to the left and right rails use the corresponding amp button Fig 8 91 Use the S button on the inspector and on the tool bar to visualize the chosen irregularities The rreg ularity group contains buttons which are used for read and write groups of four files For example the user created four files with irregularities assigns them to the track as above After that he save names of files in a group file tig by the fd button and can assign later the whole group by the amp button without opening all of them separately The Factor Y and Factor Z parameters are used for increasing or decreasing the both as signed and computed in the control file irregularities For example if the Y factor is 0 7 the de creasing the horizontal irregularities come to 30 In addition the standard rail inclination amp in radians and the standard gauge widening m in the ideal straight track Ay should be set on this tab Sect 8 3 1 1 Universal Mechan
44. ced by a circle with a radius equal to the wheel radius at the contact SP Fig 8 46 Simplified model of the flange contact for computing a overswing Universal Mechanism 5 0 8 37 Chapter 8 Simulation of railway vehicles Let y be the angle of attack is the angle defining the flange contact with the overswing The value can be found from the condition that the tangent to the flange circle at contact is perpendicular to the plane normal n 0 1 1 z a The unit tangent vector in SC of the wheelset base is set by the following expression T r cos 0 7 sin o where r is the wheel radius at the flange contact Introducing the direct cosine matrix corresponding to the angle of attack cosy siny O Ajj siny cosy 0J 0 0 1 yields the following orthogonal condition n Aoyt 0 or taking into account that angles y and are small NpyY N O For small angles the overswing can be found as x np which results in the final for mula Xe ky k Fynpy Nng Universal Mechanism 5 0 8 38 Chapter 8 Simulation of railway vehicles 8 4 1 3 Simplified contact geometry Equivalent conicity and contact angle parameter Sometimes it is important tot analyze the behavior of a vehicle depending on the wheel rail profile wear level without exact profiles curves and taking into account on the impor tant notions of equivalent conicity and contact angle parameter Consider definitions of these parameters Equivalen
45. ces Not stiff Dampery TL DampervlR Dampery c Dampery R Fig 8 81 Switching on off evaluation of Jacobian matrices for force elements Note Use of the Jacobian matrices and other recommendations are useful if they allow increas ing the solver stability or decreasing CPU time The user should optimize these parameters by studying the model behavior 8 5 2 2 Modes of longitudinal motion of vehicle Track Profiles Contact Forces Speed Longitudinal motion mode Profile i y const C y Fig 8 82 Longitudinal motion modes Modes of longitudinal motion of vehicle are set on the Speed tab of the inspector e Neutral In this mode the initial speed value is set by the vO identifier The speed decreases due to re sistance forces Longitudinal mation mode Neutral Profile ununnnnnnnununnnnn v Speed control parameters Body Body Print fo OOO 0 000 fi 050 Amplifier fi godong Fig 8 83 Constant speed mode Universal Mechanism 5 0 8 70 Chapter 8 Simulation of railway vehicles e v const Constant speed mode The nearly constant value of the vehicle speed is supported automati cally by the longitudinal force F k v v0 where vO is the desired speed v is the current speed and k is the amplifier The force is ap plied to a body selected by the user usually to the car body to a point which coordinates should be set in the body fixed system of coordinates Fig 8 83 Usually th
46. contain constant values of coefficients of the rail running surface f and on its inward side fs If a coefficient of friction is variable along the track click the corresponding button to describe the function with the help of the Curve editor Chapt 3 Sect Object constructor Curve editor Finally the angles B 8 which define section with different coefficients of friction in the lateral direction for f f should be set in the two lower edit boxes 8 5 2 6 Setting in train forces Use the Rail Wheel Forces tab specify in train forces acting on the vehicles Fig 8 104 8 5 2 6 1 Setting forces and attachment points Track Profiles Contact Forces Speed On Function of path From the fron Body Car body Foint E fo oag fi OO0 Fx Fy LAR fre me From the rear Body Car body y Paint 5 fo O00 Ii OO0 Fx Fy Latytre Fz Fig 8 104 Window for specifying longitudinal forces Forces can be obtained from experiments or from UM Train module the module for analysis of longitudinal train dynamics Both front and rear forces can be applied to a vehicle or to a group of vehicles Each of the forces is specified by the following sets of data e Body which the force is applied to as a role this is a car body e Force application point Coordinates X are Y set in the body fixed SC whereas the Z coordinate is set from the rail head level e Files with force component description The force is descr
47. d vertical directions u is the coefficient of friction B is the flange contact angle If gt 5 then the value 5 is accepted The value 5 is set if there is no contact between a wheel and a rail a full separation The motion is safe if A gt 1 2 CSafetyRefined Refined derailment quotient Russian version _ F tgp u F uw tgB 1 Differs from in coefficient u which is less than coefficient of friction and computed as Universal Mechanism 5 0 8 93 Chapter 8 Simulation of railway vehicles where f is the lateral creep force in the flange contact and N is the cor responding normal force Less conservative than the Nadal criterion Usually 2 gt CSafetyFx Fy CsafetyFx N Variants of Refined derailment quotient Russian version F tgp Hr F tep Uy F Mp tgB l F Uytg l Coefficients are computed according to formulas r Hay H H Fy Fy F y Forces included in these formulas are F F_sin B F cos B N F cos P F sin P where the mines sign corresponds to the left wheel Less conservative than the Nadal criterion Usually 4 Ay gt 4 Nadal Derailment quotient san jr Q where the mines sign corresponds to the left wheels The value 0 is set if there is no contact between a wheel and a rail a full separation Weinstock Derailment criterion proposed by Weinstock Less conservative than the Nadal criterion Total forces
48. deal straight section The geometry of rails in an ideal straight section includes profiles of rail distance between centers of heads of rails rail inclination Different profiles can be assigned to the left and right rails The rail profile can be changed with the distance along the track Sect Rail profile evo lution along the track To do this enter a set of profiles as well as positions of each along the track Let profiles RI and R2 have positions S1 and S2 2 gt S1 Then the program computes an intermediate profile R S for every necessary position S S 1 S 2 as a linear interpolation of profiles R1 and R2 such as R S1 R1 R S2 R2 A rail profile in UM should be determined in a special system of coordinates SCR Fig 8 31 SCR origin is located at the profile top on its symmetry axis 1 e the profile curve passes though the origin The abscissa axis y 1s perpendicular to the rail profile axis and di rected inside the track The ordinate axis z is directed upwards Unit for profile data is millime ter Fig 8 31 System of coordinates of rail Lateral position of rails in an ideal straight section is set by the standard track widening Ay relative to the wheelset base Fig 8 32 L L Ay 2 9 Universal Mechanism 5 0 8 26 Chapter 8 Simulation of railway vehicles where L is the distance between the rail head centers L wheel base distance between running circles Sect 8 2 3 3 In
49. e boxes il i N 4 e Finally select the Wset body in the list of bodies the base of the wheelset Sect 8 2 3 1 and assign to it the created image Fig 8 11 WSet WSetRotat Mame Weet at is a Co Es Object A Object Oriented paints Vectors oo subsystems Parameters Points a ae To element S usnik qo BB os Avle boxes ite a Bodies No Axle bowes Mineria parameters i ZS WoetRotat ai Joints Fig 8 11 Selection of the Wset body in the list and assignment of an image Close subsystem oubs Cancel Fig 8 12 Close subsystem window e Close editing the wheelset subsystem by clicking the Accept button of the close subsys tem window or use the X button and confirm the acceptance of the modifications As a result the wheelset image will look like Fig 8 13 Fig 8 13 Wheelset with fictitious axle boxes Of course the image of the axle boxes cannot be assigned to the rotating part of the wheelset because this will lead to the corresponding rotation of the image during simulations Universal Mechanism 5 0 8 12 Chapter 8 Simulation of railway vehicles 8 2 4 2 Axle box as a rigid body If an axle box should be considered as a separate body the user should use the following instructions 1 Do not open the wheelset for editing Modify the object containing the wheelset as an in cluded subsystem 2 Create a new graphic object for the axle box ima
50. e curve centerline at the position of the vehicle body Universal Mechanism 5 0 8 5 Chapter 8 Simulation of railway vehicles center of mass X coordinate of the vehicle body center of mass is equal to the length of the tra versed path by the car body if its initial X coordinate is zero Description of models in Input module does not differ for both the SCO because they coin cide at t 0 Use of the inertial SCO is recommended in the following cases for models with several vehicles train for running in sharp curves The inertial SCO is automatically assigned in the case of switches and a track with an arbi trary macro geometry which can include several curves See Sect 8 5 2 4 2 Input track macro geometry parameters We consider an element of the vehicle model as a left one left wheel left spring etc if it has a positive Y coordinate 1 e if the element is on the left to the motion direction 8 2 3 Wheelset 3 x Fig 8 2 Wheelset degrees of freedom 8 2 3 1 Structure of subsystem Wheelset A wheelset is a UM standard subsystem Two types of wheelset with different number of degrees of freedom are available The model of wheelset with 6 d o f includes two bodies two joints and a wheelset im age Fig 8 2 The first body presents the base of the wheelset with 5 degrees of freedom This body lacks for the rotation around wheelset axle The standard name of the base is Wset The second body with the standard na
51. e point lies on the coupling level the longitudinal coordinate of the point is not important is the body is rigid Longitudinal motion mode Neutral y const Speed control parameter Body Body Paint 0 000 fo O00 fi 050 Amplifier fi dodda Speed profil oul StS Lreateedit need profil Abscissa type Time Distance Data input edit Points F Fig 8 84 Speed profile mode e Profile The vehicle speed is controlled according to a dependence on a time or distance the Abscis sa type group The force control force is similar to that in the previous mode v const A curve editor is available by the button for setting the speed profile Fig 8 85 The al buttons are used for reading previously created profiles and for saving the current curve Remark If initial speed is zero dependence of the speed on time must be used not on dis tance I lolx mA TTS dk CH Be Line yu KE 75 199 Fig 8 85 Example vehicle speed graph is dependence on time Universal Mechanism 5 0 8 71 Chapter 8 Simulation of railway vehicles e v 0 Longitudinal motion mode C Neutral Longitudinal motion mode Neutral Profile Profile e y C veconst je y Fix wheelset degrees of freedom Fix wheelset degrees of freedom x i a a lx Vy way v az Fig 8 86 Parameters of zero speed mode Degrees of freedom of wheelsets are not blocked left and blocked right C v
52. e rail vg is the longitudinal velocity of the wheelset is the projection of the wheel angular velocity on the normal to the rail at the contact point Models of the creep forces are used both for the one point and for the two point contact The following algorithms for computing the creep forces are available with UM 8 4 3 2 1 Mueller s method Mueller s method is the simplest one for computation of the creep forces according to the following analytic expressions 1 6 82 P 0 001N k P 235 P 2 4 0 01P 1000k 7 li K 6 fip Fy Cyl Fy Se gl Thus the model is very simple In particular forces do not depend on the spin If the two point contact is presented forces at the flange contact are computed as simple friction forces in the sliding mode Some advantage of the algorithm consists in its simplicity The disadvantage is its lower accuracy especially for a one point flange contact where the spin is not small Fy 8 4 3 2 2 FastSim FASTSIM is the well known and the most frequently used algorithm for creep forces by Kalker 2 It takes into account both the spin and the geometry of the contact surfaces The algo rithm is used for calculation of creep forces both for one and two point contacts Consider some features of the algorithm which are important for its understanding and a correct usage FASTSIM requires the following parameters and variables for computation of the creep fo
53. e sneanaaaasioasasnsasacssapeneandacdnwessapesmansacsuenanaauans 8 69 8 5 2 3 Assionment of rail and wheel profiles scannctibasacnnasapasaceccunietesaaniabansemintevaatonuadncasuoteapniueasendenecenaies 8 71 Soa ASe OF Ta DON ES oenar E 8 71 Des ASS Enmen OF WIELD ONIES mermisinin E 8 73 8 3 2 33 ath promlic evolution along the A Ci acceniaiicscunictcasaniaicuaraunticwssniepcuenieiatenanmiaidsersienesennimieumenuetes 8 73 8 5 2 4 DG a UES oso E E E E EE EE E A A A T E 8 75 8 5 2 4 1 Assignment of track irregularities and rail geometry parameters gauge rail inclination 8 75 8 5 2 4 2 Input track macro geometry parameters tangent curve S curve switch profile 8 76 S 0 24 5 Track SUMMMESS ANd dampni sesaran E Ea AEE Ea NE NE EEEa 8 80 8 5 2 4 4 Programming elastic and damping track parameters cccccccseecccneseeeeeeeceesecsenceeseeeeaeneees 8 80 8 5 2 5 Parameters for computation of rail wheel contact forces ssensssessseessersseesssrsseesssesssessseess 8 81 8 5 2 6 SCHE Mee TR OCE oc aes weer cde oth we ween sr lec EE EE EE EE E 8 83 8 5 2 6 1 Setting forces and attachment POIts cccccseccccseecceeeecceeeeccenceeseseeeeneeeaeeeceeneesseseesaneesaenes 8 83 8 5 2 6 2 Creating files with force description cccecccsescccseecceeeccaeseccencecsuseeseuseeseseesesessuseeesnsesaages 8 84 8 5 2 6 3 Plotting and visualization Of FOPCES cecccceccccsesccceeccceeecseeecsenee
54. e vectors in animation window move the mouse cursor to the car body click the right mouse button and select the Show forces for Name of Body popup menu command Fig 8 106 It the forces are invisible by the simulation either the force application coordinates are not correct or scale factor for forces is too large In the last case use the Scale of vectors command of the popup menu to decrease the scale factor Fig 8 106 8 5 2 6 4 Example of in train forces Consider lateral forces applied to the front and rear couplers Fig 8 107 The forces are zero on the first 50 m of the vehicle motion then they grow uniformly to 3000N on the interval from 50m to 70 m The forces are constant till 150m and decreases uniformly on the 20m inter val The front force is positive the rear one is negative Fig 8 107 Lateral forces versus distance Open the window for development of files with irregularities by the Tools Create track irregularities menu command open the Points tab and start the curve editor by the J button Universal Mechanism 5 0 8 86 Chapter 8 Simulation of railway vehicles m Curve editor cE OK Cancel I 189 2300 Sa F Fig 8 108 Force description by points Add 6 points by the er button and set their coordinates as in Fig 8 108 Optimize the Close the editor by the OK button and save the result in a file by the lower button 41 Re name the file extension manually to frc instead of way Let us consider a
55. econst Zero velocity mode This mode is used when e the vehicle equilibrium is not computed automatically by the el button or e the equilibrium is computed not quite correctly e g when dry fiction is presented in the model e oscillation under harmonic loads are analyzid In the last case the blocking of several degrees of freedom of wheelsets could be useful lon gitudinal and lateral motions X Y as well as rotations about the lateral and vertical axes aY aY To block a degree of freedom check the corresponding box Coordinates of the nearly equilibrium position computed in this mode can be used as 1in1 tial values in simulation with non zero speed The following steps are necessary for this o Run the simulation until the transient processes disappear Save finish values of coordinates in file by the Save button in the pause mode Open the Initial conditions tab of the inspector Read coordinate values by the amp button O oO O Set zero velocity values by the ll button 8 5 2 3 Assignment of rail and wheel profiles The Rail Wheel Profiles tab of the inspector is used for assignment profiles to the rail and wheels References to files the assigned profiles are stored in a vehicle configuration file rwc The button on the inspector of on the program tool bar let the user to view the as signed profiles 8 5 2 3 1 Assignment of rail profiles UM database of rail profiles includes the following files
56. ectly Namely if change of angular velocities of wheelset and casing is forbidden or the corresponding coordinates are fixed the program automatically selects the only velocity to be changed and compute it according to the current values of angular velocities of wheelset and casing Of course the casing initial angular velocity must be zero Universal Mechanism 5 0 8 20 Chapter 8 Simulation of railway vehicles Object simulation inspector Solver Identifiers Initial conditions Object variables Flailheel katin Information Tools Coordinates Constraints for initials ho vie 1 16 D 1 mm Ph mi Pail Hi D 1 DJ Ph Mi j Ph n J 7 D 1 Ooo J Lo i D mm ro oo cT co oC CO Bo co oO oO co co oOo oOo oa 0 amp fe pee Coordinate Velocity Comment 0 0 Bogie 1w bMA1 Leaf spring A la 0 Bogie 1 MAT Motor 1a 134 113242251 Bogie 1w MA Drive shaft 1a 20 Bogie 1w MAT Wheelset i Set Tc 0 Bogie 1w MAT Wheelset h Set 2c 0 Bogie 1w bAT Wheelset W S eat ac 0 Bogie 1 Whi Wheelset jw Set 4a 0 Bogie 1h Wheelset i Set Ba 32 0079337114 Bogie 1w MA1 Wwheelset W S etA otat 1a wee l w MAZ Set Aslebox L la je 1 WMA WS et_Aslebox A 1a je 1 WMA Leaf spring L 1a Save Fixation Read Fixation Galeulation of quabernion je 1 WMA2 jLeaf spring A 1a TE zero coordinates jie
57. eep force FCreeply Lateral creep force hl Normal force Betal Angle between the track normal and the normi WContactl Coordinate of contact point in SC of wheel pi Z Contact Coordinate 4 of contact point in SC of wheel pr sRAContact Coordinate of contact pointin SC of rail el d 4 ywContect _2r 2q Coordinate Y of contact point in ol of wheel p H w Contactl_ 11 wContact ir w Contact 2 wContactl sr Fig 8 111 Variables for rail wheel contacts To create one variable corresponding to one of the wheel the wheel should be selected in the list located in the left part of the wizard For example selection of the wset 1 left item cor responds to the choice of the left wheel wheelset 1 Note The wheelsets are numbering 1 2 1s ordered according to the decreasing their longitudinal coordinate To create a group of variables the All wheels All left wheels and All right wheels items are used Fig 8 111 shows an example when the four variables in the container are created by a single click on the wheels item were selected only two variables YWContactl_Ir and YWContactI_2r correspond ing to the right wheels were created by the A type of a variable is selected in a list located in the right part of the wizard The first column of the list contains standard identifiers of types An identifier of a variable is constructed from the identifier of the corresponding type by
58. ehicles Mathematic model of the element is described in Chapt 2 Sect Generalized linear force element Examples of description and or usage Chapt 7 Sect Models of Springs Model samples Rail vehicles Manchester benchmarks Vehicle1 Model samples Rail vehicles wedgetest e Bipolar force element The element can be used for modeling both linear and nonlinear springs which produce force directed along the element attachment points Mathematic model of the element is described in Chapt 2 Sect Bipolar force element Examples of description and or usage Model samples Rail vehicles Manchester benchmarks Vehicle1 Model samples Rail vehicles WManchester benchmarks Vehicle2 General recommendations models should be created near the equilibrium state at zero values of object coordinates stationary values of vertical loads should be set for springs set the lower body as the first attachment body of a vertical spring and the upper as the second one in this case the stationary vertical force is positive 8 2 6 Modeling dampers traction rods As a rule bipolar force elements are used for modeling dampers and traction rods Mathematic model of the element is described in Chapt 2 Sect Bipolar force element Examples of description and or usage Model samples Rail vehicles Manchester benchmarks Vehicle1 Model samples Rail vehicles WManchester benchmarks Vehicle2 Model samples Rail vehicles ac4 8
59. enforms as well as root locus of linearized equations of motion to create hybrid rigid elastic models of vehicles Simulation of vehicle dynamics is performed in time domain by means of numeric inte gration of automatically generated differential or differential algebraic equations of motion UM Loco allows the user to create fully parameterized models of vehicles Geometrical inertia force parameters may be specified using identifiers and symbolic expressions The para meterization of model is the base for its optimization More general information about use of UM for simulation can be found in the Power Point presentation at http umlab ru download docs eng umloco zip 33Mb with animations Below in the current chapter we consider some features of description of a railway ve hicle in UM as well as some useful notions and special utilities Universal Mechanism 5 0 8 4 Chapter 8 Simulation of railway vehicles 8 2 Creating railway vehicle models User creates UM models of railway vehicles similar to any other multibody systems see Chapt 3 The vehicle is considered as a system of rigid or flexible bodies connected by means of joints and force elements Usually a model of a railway vehicle contains the following rigid bo dies vehicle body frames of bogies wheelsets axle boxes often can be removed from the model etc In the case of a locomotive motor model consists often of two bodies a motor case and a rotor See the UMLoco_
60. equal to the torque value The last identifier should be expressed in terms of the total traction force as traction_torque traction_force ftraction_to_torque It is strongly recommended to use the traction_force identifier for the total traction force to au tomate its detection if the locomotive is included in a train 3D model Finally it is recommended to introduce the identifier n_throttle_positions with numeric value equal to the number of the throttle positions The identifier should be added to the identifi er list of the locomotive model not in the subsystems 8 2 7 1 3 Gearing Model of a gearing is the necessary part of the drive system Universal Mechanism 5 0 8 18 Chapter 8 Simulation of railway vehicles Radius Semibase Arle length Ad n W Gear W Double E Object Radius 0 45 ii A Object Position r 0 55 Imag Simple Fine Fig 8 22 Adjustment of the wheelset image To add bull gears to the wheelset image open the wheelset subsystem parameters in the object inspector check the Gear key and if necessary Double key as well as set the gear radius 0 45m in the figure and location on the axle 0 55m in the figure x Nene Searet HF 2 Body Body Wheelset W S ethic Drive shaft Type E Gearing Attachment point WwSetRotat N Drive shaft K Axes of rotatia Wi et otd asis 0 1 0 Gear ratio Clearance Damping coefficient dreductor C Stiffness
61. ers in the Rail Wheel Profiles Addit parameters Con tact parameters tab e Jump parameter in criterion of two point contact Universal Mechanism 5 0 8 89 Chapter 8 Simulation of railway vehicles The parameter is used in the procedure of computing contact coordinates for verifying the fact of a two point contact see the n parameter in Sect Computing tables of contact points Sometimes variation of this parameter can improve the detection of two point contact e Key X rotation of wheel profile on off Sometimes worn profiles of a wheel and rail are in a very close contact near the flange region so that a small relative rotations Aa of the profiles about the longitudinal X axis may cause a big jump in coordinates of contact points or transfer from profiles with one point contact only to the profiles which allow a two point contact and back Such cases lead usually to large jumps in values of contact forces and to divergence of solvers of equations of motion To stabil ize the simulation switching off the variation of the contact positions in dependence on the Aa angle is useful very often see Sect Computing tables of contact points Switching off the key means that the coordinates for Aa 0 are used e Key Thin out profile points A very small abscissa step size in defining profiles as well as the absence of profile smoothing leads to violation of continuity of contact point positions in dependence on lateral displacements and rela
62. eseseeseneeeseeeeseneesseseeeansesaanes 8 84 8220k Example ol Imra TONCO Soenen a De wenn ant ett a re ree gt ee etre erm Sere earn ee 8 85 8 5 2 7 Additional contact parameters sis iccccwnasetsavesddvanavece saecesadundueaintadernudeadsieeadtaawesulvadsvandbraweandoasdeavem 8 88 5 3 2 Difference in running circles radii esis dcensveaxivae baw enndenaex ent hanaencdeanaseatnnuesndvabsneudbaneeaniiaaweeuwia 8 88 8 5 2 7 2 Parameters of contact geometry COMPULALION ccccceeeccceecccececeesecseeeeseneeeseseceseseeesneeeaenes 8 88 8 5 3 Tools for visualization and analysis of railway vehicle CyYMaMICs ccseccceseeecesecceneeceeeeeceeeeeaanes 8 90 8 5 3 1 MONTE Tares Ol iG le Al On OL VATA ECS aoa A EEEE EE 8 90 Sool Rail WheelComtack Varia DICS 55 ccncdsaacreadenscoasnsmanereseesiuseeceasexsconsmannonamtacoueraepadesteastiguctesseceoncat 8 90 8 5 3 1 2 Kinematic characteristics relative to track system Of COOrdINALES ccccceeccceeeeceeeeeeeeeeeaeees 8 94 Orel URS OL FAVA AON EA E EE 8 94 8 9 32 PAIE OTR WY IIA i A A T EA A A A T A A A OT 8 95 8 5 3 3 BoE A Gy OY E A A A T EA A EAA OS 8 96 8 5 3 4 Comac paci ima O ie 8 97 8 5 3 5 Tane DOCE 5 O e EE E E 8 98 PRS HS 1 SS mierea REA AEA EAN AEAN REENER 8 99 Universal Mechanism 5 0 8 3 Chapter 8 Simulation of railway vehicles 8 Simulation of railway vehicles in UM 8 1 General information Program package Universal Mechanism UM has been developed at the
63. esponds to the F force in Fig 8 56 Unit N Normal force N3 Fig 8 56 Unit N Beta2 Contact angle angle B between the N and the Z axis of the track SC Fig 8 56 Unit rad The angle is positive for inclination of the normal forces inward the track YWContact2 Coordinates y lateral and z vertical of the contact point in SC of the wheel profile Sect 8 2 3 2 Unit m XRContact2 Coordinates y lateral and z vertical of the contact point in SC of the rail YRContact2 profile Sect 8 3 1 1 Unit m ZRContact2 N2y Guiding force projection of XN on y axis of the track SC Ny Mwear2 Awear2 Flanges wear factors for a two point contact power work and specific Swear2 work The factor are computed according to formulae M wear F2xV2x F2yV2y the scalar product of the flange creep force N sin B where the mines is set for the left wheel and the sliding velocity at the contact unit W t Awear M weardt unit J 0 Swear Awegr S Where S is the path unit J m Area of the contact patch Unit m Maximal pressure in the contact Unit Pa GENERAL VARIABLES Variables are not directly connected with one of the contact point Csafety Derailment quotient Russian version For a wheel with the two point contact is computed according to the formula F uteB 1 where F F are the total forces acting on the wheel from the rail in the lateral an
64. ffer in image discretization level Universal Mechanism 5 0 8 9 Chapter 8 Simulation of railway vehicles ee lt q So lt L ST Mn k call Fig 8 7 Images of wheelset Changing geometric parameters of the wheelset results in automatic changing its image Fig 8 7 Note An image is automatically assigned to the wheelset if the following files are avail able with UM bin graph rwsimple umi simple image bin graph rwfine umi fine image Use the Edit subsystem button Fig 8 6 to change inertia parameters or to modify the image e g to add images of axle boxes This button opens the subsystem as a multibody sys tem in a separate constructor where the necessary modifications of the wheelset such as changing parameters or renaming elements can be done in a usual manner see Chapt 3 Chapt 9 Use the Position tab Fig 8 6 to specify the longitudinal and vertical position of the wheelset If the object is a bogie the lateral position is set relative to the SC of the bogie If the object is a vehicle the lateral position is set relative to the corresponding SC Position of the wheelset can be parameterized 1 e specified by a simplified symbolic expression Chapt 3 Sect Simplified constant symbolic expression Set the z coordinate of the wheelset equal to the wheel radius to locate the origin of SCO at the rail head level Sect 8 2 2 Base coordinate system Ze
65. first one 1s the coefficient of friction on the rail running surface f the second one on the inward rail side f These coefficients are numeric constants or functions of the longitudinal coordinates along the track f x f x If the coefficients for a given longitudinal position have different values i e f f the coefficient of friction is considered as a variable one on the rail profile in the lateral direction Br Coefficient of teiot Fr F Transient section N Coefficient of friction fs Fig 8 61 Changing the coefficient of friction along the rail profile As a result the profile is divided into three parts Fig 8 61 The first one is the running surface with a constant coefficient f The second part is the inward side of the rail with the coefficient f Finally a transient section between the previous two parts there the coefficient changes continuously from f to f The transition is linear in the angle B To divide the profile on these sections the angles B B should be set Dependences of the coefficient of friction on the longitudinal coordinate allow the user to model e g an oil stain on a rail Different values of the coefficient on the running surface of the rail and on its side are used mainly for modeling lubrications in curves Universal Mechanism 5 0 8 53 Chapter 8 Simulation of railway vehicles 8 5 Simulation of railway vehicles 8 5 1 Tools for preparing simulation process
66. for R1 e g P11 0 01 S1 0 01 P12 0 01 R1 100000 Universal Mechanism 5 0 8 27 Chapter 8 Simulation of railway vehicles Transient sections are formed by a cubic parabola The curvature in transitions changes according approximately linear law Fig 8 33 On macro geometry of curve Growths and decreases of the cant at transient sections are linear It is possible to smooth the vertical junctions at ends of the transition by arc of circle Additional widening dy of track in a curve 1s proposed automatically dy 10 mm for R e 300 350 dy 15 mm for R lt 300m The widening is realized as symmetric lateral shift of both the rails on a half of the widening The widening on transient sections is the linear function of the position The user may set own widening See Sect Input track macro geometry parameters Let us introduce a number of designations for curve parameters computed by UM X s Y s equation for a curve s is the arc coordinate length along the curve y s angle between the X axis and the tangent to the curve p s curvature radius So traveled path Consider running of a vehicle in a curve when the non inertial SCO is used Sect 8 2 2 Let Wo be the angular velocity and the angular acceleration of SC relative to the vertical axis a be acentrifugal acceleration The following relations take place Oy V p so amp V x s0 a V7 p so Here x is the derivative of the curvatu
67. frame WHAT wheelset Reference frame what Wiheelset Reduction port WSetR ota F T H Object Type of descriptio pU A Object f Expression File E Subsystems H Images Force H Bodies ee E i Joints po a bostes FT E Linear forces Moment Hg ontact forces DO H les T Forces Jat yerepe braking_force 40 625 F Aee COo i F Fig 8 30 Setting braking torque for locomotive VL80 Such a moment should be added for each of the wheelsets using the T force element Fig 8 30 The first body in this element is the bogie frame the second one is the rotational part of the wheelset WSetRotat and the reference body must be the base of the wheelset It is an error if the reference body is BaseO The same model can be used in case of brake disks If unilateral brake blocks are used the force element must contain in addition a vertical force equal to the braking force the user should take care of the signs of torque and force The signs depend both on direction of rotation of the wheelset and on position of the brake block relative to the wheelset Universal Mechanism 5 0 8 25 Chapter 8 Simulation of railway vehicles 8 3 Rail track 8 3 1 Track geometry Track geometry includes the following components geometry of rails in an ideal straight section track gauge inclination of rail rail pro files macro geometry of curves track irregularities 8 3 1 1 Geometry of rails in an i
68. g the differential equations by the explicit Euler method Thus CPU expenses are of order mxn operations and depend on the discretization level 8 4 3 2 3 FastSim analytic FASTSIM_A is our semi analytic modification of the classical FASTSIM algorithm For a slice it was found an exact solution of the FASTSIM governing differential equations in the adhesion area of the contact patch and an approximate analytic solution for differential algebraic equations in the sliding area The solution was implemented in UM as FASTSIM_A FASTSIM Analytic procedure The number of operation for computing creep forces 1s proportional to the number of slices m The procedure for n 10 1s at least two times faster than FASTSIM and gives quite similar numeric results for computing creep forces in case of moderate spin values lt 0 5 8 4 3 2 4 Minov s model U 00 Oe OS 004 00S Ue 00 a Fig 8 59 Sticking coefficient versus creep in the Minov s model Universal Mechanism 5 0 8 49 Chapter 8 Simulation of railway vehicles The method is used in simulation of locomotive in traction modes and based on experimental dependence of sticking friction force on lateral creep Fig 8 59 K D Minov supposed an ana lytic approximation for this curve consisting of three sections 1 0 lt amp lt 0 0014 linear section of elastic sliding k 359 61178 2 0 0014 lt I amp l lt 0 025 nonlinear section of elastic sliding 350 E 0 155
69. g to the angular velocity of the wheelset more precise ly the derivative of the angle of rotation about the wheels axis this is the joint veloc ity in the joint jWSetRotat Universal Mechanism 5 0 8 23 Chapter 8 Simulation of railway vehicles o Open the Expression tab of the wizard Add an operation by the x button multipli cation o Set the wheelset angular velocity by the mouse as the fist operand enter the number 4 19 negative by the clipboard as the second operand o Set the variable name instead of the default value Expression o Send the variable into container by the F button and drag it into the constraint cell Fig 8 26 e When all the constraints are specified save them in a file in the object directory If con straint file has the name of the object the default value the constraints are automatical ly loaded at each load of the object in the simulation module Constraints are used at computation of initial conditions right before the start of the simulation process e To verify the correctness of the constraints open the Initial conditions Coordinates tab of the inspector run the upper command Message and compute the initial values by the button Compare the computed values of velocities with the desired ones 8 2 7 2 Support of braking mode Simulation of braking process is discussed in the user s manual chapter 15 devoted to the longitudinal train dynamics Here we consider only adding to a
70. ge In the simplest case the standard 1m age bin graph axlebox img could be used read it by using the amp button on the tool pan el 3 Add a new body for the axle box rename it assign the image a set inertia parameters If the axle box has one rotational degree of freedom relative to the axle it is enough to set the moment of inertia relative to the Y axis l jAxle Box R Axle box R n Mame j4xle Box R je rza Name JAxle box F ap BP 5 a a Wet Ah Set Axte BoxR Comments Rotational Oriented paints Vectors we SEU ai JEL lo WA Parameters Foin EY Description Joint force oe ae ool Rotation ial Create joint Translational 6 dot General Quaternion L d r atic axis 0 1 0 Y Axle Box R axis r 0 1 0 Y Fig 8 14 Adjustment of a joint to the right axle box 4 Adjust a joint to the axle box by the amp button Fig 8 14 If the axle box has one rotational degree of freedom relative to the axle the rotational joint should be assigned After that change the first body base of the wheelset instead of the BaseQ set axis of rotation 0 1 0 about Y axis for each of the bodies set the axle box position on the axle expression yaxle_box in Fig 8 14 for the right axle box Universal Mechanism 5 0 8 13 Chapter 8 Simulation of railway vehicles Fig 8 15 Wheelset with the right axle box Visual adding an axlebox
71. gear ratio second makes the velocity value positive by the rotation_sign identifier if the rotor rotates in negative direction Thus the rotation_sign should be 1 if the drive shaft rotates positive ly and 1 in the opposite case see Remark 2 in Sect 8 2 7 1 4 Computation of initial angular velocities by fixation file Factor Y the factor should differ from unity if the ordinate in Fig 8 20 is not an torque ap plied to the drive shaft e g the total traction force of the unit It should be also used when the drive shaft rotates in the negative direction i e the corresponding joint velocity is negative In the example in Fig 8 20 the expression ftraction_to_torque rotation_sign is used The ftrac tion_to_torque multiplier converts the total traction force into the torque on the rotor for a single motor In our case this identifier defined by the following expression ftraction_to_torque 1 4 0 625 4 19 4 1s the number of wheelsets 0 625 is the wheel radius 4 19 is the gear ratio The rotation_sign multiplier makes the sign of the torque equal to that of the joint velocity which corresponds to the traction mode Now consider the direct setting the traction torque which is necessary if the locomotive is included in the train 3D model see Fig 8 20 The torque is set by the expression trac tion_torque rotation_sign where the rotation_sign factor takes into account the rotor rotation direction and the traction_torque identifier is
72. geometry 1 e computing locations of contact points for a definite position of a wheelset 2 computation of kinematical characteristics at contacts creepages and spins rail ve locities 3 computation of normal forces and creep forces at contacts according to geometrical and kinematical parameters As it 1s shown below these problems are not solved independently a general iterative procedure is necessary 8 4 1 Algorithms for wheel rail contact geometry To make computation of contact points faster and more reliable two main ideas are rea lized Firstly if rail profile does not change along the track Sect 8 3 1 1 computation of contact points is executed once for given rail and wheel profiles before the simulation start UM creates tables of contact coordinates for different relative positions of the wheel profile relative to the rail profile lateral displacement and rotation about the longitudinal direction By simulation the coordinates of contacts are interpolated with the help of these data Secondly computation of contact points on the profiles is based on a procedure which computes the nearest point between two curves These algorithms proved to be very fast and re liable and do not depend on smoothness of the curves 8 4 1 1 Algorithm for computation of nearest points between two profiles Fig 8 43 Relative position of profiles Let us consider an arbitrary position of the wheel profile relative to the system of
73. gse pdf file with detailed information about process of a rail vehicle model description 8 2 1 Type of object Railway Vehicle To get an UM model of a vehicle the user should create a new UM object by clicking the File New object menu item After that set its type railway vehicle on the Object tab of the inspector In this case the standard UM subsystem Wheelset becomes available the standard identifier vO for initial speed of the vehicle is added to the list of identifiers 8 2 2 Base coordinate system Base coordinate system SCO BaseQ is the system of coordinate in which the object is described and simulated For railway vehicle the SCO satisfies the following requirements Z axis is directed vertically upwards X axis is horizontal along direction of motion at the vehicle initial position SCO origin is usually located either at the level of the rail head or at the wheelset axes level at their ideal initial position Y Yy Fig 8 1 Reference frames During the simulation the user can optionally choose two different types of SCO non inertial system of coordinates inertial system of coordinates These types of reference frames differ while curving only Fig 8 1 The inertial SCO is fixed OXY in Fig 8 1 The non inertial SCO oxy in Fig 8 1 coincides with the inertial one at the initial state but when the vehicle runs in curve the X axis rolls without sliding in horizontal plane So X axis 1s always tangential to th
74. he pro gramming in the Control File Chapt 5 The following procedure in the Control file is used for programming the track parameters function TrackStiffness position real_ var cLeftZ cRightZ cLeftY cRightY dLeftZ dRightZ dLeftY dRightY real_ integer begin Result 0 end Input position longitudinal coordinate for which the irregularities are computed Output Result return function value If the return value is 1 the programmed values will be taken into account otherwise they are ignored cLeftZ cRightZ vertical stiffness of the left and right rails in N m cLeftY cRightY lateral stiffness of the left and right rails in N m dLeftZ dRightZ vertical damping coefficient of the left and right rails in Ns m dLeftY dRightY lateral damping coefficient of the left and right rails in Ns m Note 1 If the function returns 1 parameters entered in Fig 8 99 are ignored except the cases in the Note 2 Note 2 Zero values of stiffness cLeftZ cRightZ cLeftY cRightY are ignored and replaced by values from entered in Fig 8 99 Universal Mechanism 5 0 8 81 Chapter 8 Simulation of railway vehicles 8 5 2 5 Parameters for computation of rail wheel contact forces Track Profiles Contact Forces Speed Creep forces Friction Wear model Model of creep forces Simplified C FastSima Mueller Minov s model C FastSim C Nonellipt Frotile parameters Equivalent conicity
75. ibed by three components in the body fixed SC To set a component a preliminary created frc file should be selected by the S buttons Fig 8 104 File format description can be found in the next section Use the On key foe switch on off the forces If the Function of path key is on the forces are functions of the distance else they are functions of time If files do not assign to some components of forces they are zeroes The Ej button is used for plotting the assigned functions All the assigned data is stored in the configuration file rwc Two methods are used to delete the file assignment Locate the text cursor in the box with the name of file and press Delete Use the popup menu of the text box Universal Mechanism 5 0 8 84 Chapter 8 Simulation of railway vehicles 8 5 2 6 2 Creating files with force description Components of forces in Sect 8 5 2 6 1 should be preliminary described in binary files fre The force should be given in N as a function of distance or time A force file contains suc cessive force values with step size 0 1m 0 1s starting from zero distance time Single binary format is used for fore values 4 byte floating point numbers It is recommended to use the window for development of track irrtegularities which uses the save format of files way Sect 8 5 1 2 Creation of track irregularities After creating the file its extention should be renamed to frc instead of way It is recommended to store
76. ies Generalized coordinates are not introduced for the rail and its lateral and vertical deflections must be computed from the equilibrium equations The following assumptions take place deflections of a rail for different wheelsets are independent and can be computed sepa rately deflections of the left and right rails are independent rail deflections include independent lateral Ay vertical Az deflections Fig 8 55 which are parallel to the corresponding SC of the track rail roll is not considered the rail as a linear force element both in the lateral and vertical directions the lateral dissipation is taken into account for two point contact mode only Fig 8 55 Rail as massless force element Let Cy Cz be the lateral and the vertical stiffness of the rail d yd z be the corresponding damping constants Forces acting on the rail due to the deflections are the following Ry cyAy dyAy R c Az d AZ Because the rail has no mass these forces must be balanced by contact forces acting on the rail from the wheel The contact forces acting on the wheel for one and two point contacts are shown in Fig 8 56 Longitudinal forces are not shown 1n this figure 8 1 Universal Mechanism 5 0 8 45 Chapter 8 Simulation of railway vehicles Fig 8 56 Forces acting on wheel at one and two point contacts Equilibrium equations for one point contact written in SC of the track are Ry F cosB
77. indow includes Sect Macro geometry of curve type of curve left or right geometric parameters of the curve lengths of transient sections P1 P2 length of steady curve section S radius R cant of outer rail H as well as additional gauge widening in curve dY coefficients of friction on running surfaces of outer and inner rails on the inward side of the outer rail flange as well as angles 8 which specify the transient prom the coefficients of friction on the running surface f and of the rail inward side f if f f Sect 8 4 3 4 Coefficient of friction in wheel rail contact Universal Mechanism 5 0 8 65 Chapter 8 Simulation of railway vehicles lol x my Switch parameters 4 Res 1711 Geometry Rail overhang mm 2764 0 Gauge mm 1520 Initial angle rrac r 9400 Switch angle mrad 90 6602 Radius of point RO im 1300 000 Radius of switch Aim 1300 000 Switch width for RO trim 75 0 Frog tail length rim 4045 0 Full switch length mi 34 862 Theoretical length rm 28 048 Computed tangent section mm 3285 0 Movement Facing C Trailing Lett switch Coefficient of frictian 0 250 Cancel Fig 8 77 Switch parameters e Switch parameter window includes values of Sect 8 3 1 3 Switch geometry q stock rail overhang gauge p initial angle a switch angle Ro radius of point R radius of switch b switch deviation for Ro
78. inov s model FastSim C Nonellipt Contact parameters Elasticity modulus 200 ooo 000000 Foisson s ratio oso Number of strips jo Number of elements 0o Fig 8 102 FastSim and FastSimA model parameters e FastSim FastSimA See Sect 8 4 3 2 2 8 4 3 2 3 for description of the models e Minov s model Computation of creep forces according to empirical analytic expressions The model 1s used for simulation of locomotives in traction mode See Sect 8 4 3 2 4 Minov s model Model of creep forces Simplified C FastSima Mueller C Minov s model C FastSim i Nonellipt Contact parameters Elasticity modulus 200 000 000000 Foisson s ratio foa Number of strips jo Number of elements 0 Embedding coefficient foaoo000 O e Nonelliptic contact This model is usually used by evaluation of wheel and rail wear evolution The Rail wheel Contact Friction tab is used for setting the friction in the wheel rail contact Creep forces Friction Lett rail tread 0 2 Lett rail flange 0 33 Right rail tread 0 33 Right rail flange 0 33 Transient section for side friction from fao to fan degrees Fig 8 103 Setting coefficients of friction See Sect Coefficient of friction in wheel rail contact for the detailed information about the coefficient of friction Universal Mechanism 5 0 8 83 Chapter 8 Simulation of railway vehicles The four upper edit boxed in Fig 8 103
79. ions by the Variable profile key Fig 8 89 Example Fig 8 89 show creation of sequence of profiles for the outer rail of a right curve with the following parameters Sect Macro geometry of curve LO 10m P11 50m 1 200m P12 50m The new profile r65new Fig 8 90 is used at straight sections At the first 50 m transition sec tion from 10m to 60m the new profile is transformed to the worn one r65old In the steady curve from 60m to 260m the profile does not change At the second 50 m transition from 260m to 310m the profile is transformed from the worn to the new one Universal Mechanism 5 0 8 75 Chapter 8 Simulation of railway vehicles 8 5 2 4 Track parameters 8 5 2 4 1 Assignment of track irregularities and rail geometry pa rameters gauge rail inclination Track Profiles Contact Forces Speed lrreqularities Parameters Macrogeometry Stiffness Track type lreg qroup Even Uneven gt H Let rail 2 D UM40_WORK bin rw uic c Right rail A D UM40_WORK bin rw uic c Left rail v7 D UM4l_WORK bin rw uic Right rail 7 DAUM40_WORK binirwAuic e r factor po Z factor po Rail inclination i ooo Gauge widening ooo Fig 8 91 Track irregularities and parameters Several files with track irregularities are delivered with UM 1 Bad UIC track generated by SPD function 1000 m length The irregularity group file is uic_bad_1000 uic_bad_1000_zleft way uic_bad_1000_zright way uic_
80. is the joint coordinate v x is the first time derivative of the joint coordinate joint velocity The right hand sides are arbitrary expressions created with the wizard of variables see Chapt 4 Sect Wizard of variables The following steps create a new constraint e Add arow to the table of constraints by the button e Open the wizard of variables by the Tools Wizard of variables menu command or by then button on the tool panel Universal Mechanism 5 0 EB 3 Wizard of variables 8 22 Chapter 8 Simulation of railway vehicles El vien T forces Bipolar F Linear F Uzer Expression Identifier E r Lar body Special F Contact F All forces Joint force Track SC a Poor Coordinates Angular war Reaction F Linear war R alway W118 E Pe Bogle frame si p WAT Selected coordinate lag M Set_Aslebox L we S ge MSet_Aslebox A a geet _ ype of varia DA y ee Coordinate Velocity Acceleration Hg Motor oe iDrive shaft 2 bee EY 118 fp Dp wheelset oe PE WHAZ H gt Bogie 2 v1 18 sE First denvative of coordinate 19 subsystem 1 i k Po Fig 8 27 Creation of variable velocity of drive shaft rotation relative to the motor casing e Create a variable corresponding to joint velocity for setting the initial value open the Bee Wizard of variables Coordinates tab select the necessary joint coordinate in the list located in the right pa
81. ism 5 0 8 76 Chapter 8 Simulation of railway vehicles Use the Even parameter of the Track type group to simulation a vehicle in the ideal sec tion of curve If this case the irregularities are ignored Use the Uneven parameter of the Track type group to take the irregularities into account See also Track irregularities Creation of files with irregularities Programming irregularities in the Control file References to files the assigned irregularities are stored in a vehicle configuration file TWC 8 5 2 4 2 Input track macro geometry parameters tangent curve S curve switch profile Track Profiles Contact Forces Speed lrreqularities Parameters Macroqeometry stiffness V Track image C S Curve C Profile Curve C Switch Fig 8 92 Macro geometry types Use the Rail Wheel Track Macrogeometry tab of the inspector to set the track macro geometry The Track type parameter specifies the current track e Tangent Motion in a tangent section of unlimited length lrreqularities Parameters Macroqgeometry stiffness Track image Track type Tangent SCurve Profile Curve Switch First section L1 fio F11 fso ol 200 Rl 300 H1 0 03 Elz fso dy jo 01 L 310 Vo 1294756 Smoothing 8 00 Inertial SCO Fig 8 93 Right curve parameters e Right curve Fig 8 93 Motion in a right curve including a tangent section before the curve L1 transien
82. ists wheel left and rail right profiles located in the standard di rectory lt Path to UM gt bin rw prrf responding part of the container select one of two menu commands without sorting adds pro files to the end of the list and open the file with the help of he standard dialog window Selection of a pair of profiles To select a pair of analyzed profiles select them in the lists by the mouse Fig 8 51 and click the Read button on the top of the window Analysis results The following results are available with the tool Universal Mechanism 5 0 8 42 Chapter 8 Simulation of railway vehicles Read Type of contact 4 Cleararn6 1 mm Fig 8 52 Type of contact and clearance on a side Type of contact one or two point contact Fig 8 52 Clearance on a side is the lateral shift of the wheel relative to the rail which lead to the double contact for profiles allowing two point contact Fig 8 52 Equivalent conicity and contact angle paran eter X RAS mm eai Interval mm 6 20 Equivalent ban Equivalent contact 2540 conicity ss angle parameter ene Compute GK Fig 8 53 Equivalent conicity and contact angle parameter Equivalent conicity and contact angle parameter Sect 8 4 1 3 The parameters are computed for given values of the standard deviation of the lateral shift RMS mm and averag ing interval Fig 8 53 The following graphic information is available depending on the
83. ius of point R radius of switch b switch deviation for Ro m frog tail length d track spacing R radius behind frog The parameters define fully the switch geometry and some additional parameters in Fig 8 40 like L full switch length L theoretical length K tangent section before frog UMS5S0O includes the standard R65 1 11 and R65 1 9 switches The user can create files with any switch parameters 8 3 1 4 Track system of coordinates A track system of coordinate is introduced for each body i of the vehicle TSK Its origin W coincides with the projection of the body center of mass on the ideal central axis of the track The abscissa axis x is the tangent to the ideal track centerline The ordinate axis y lies in the track plane on the left to the motion direction Fig 8 41 TCSi axes in presence of a cant A cant of the outer rail A Fig 8 41 gives the rotation of the track plane on the angle _ h Q arcsin r TSC is used for calculation of some dynamic performances of the vehicle in curves Sect Kine matic characteristics relative to track system of coordinates Universal Mechanism 5 0 8 32 Chapter 8 Simulation of railway vehicles 8 3 1 5 Track irregularities Vertical and horizontal irregularities of rails are stored in unformatted files way and as signed to rails before the simulation in the Simulation Module Step size of the irregularities is 0 1 m Sect 8 5 1 2 If horizon
84. l the default file name and path If the first item of this list is executed click on the button to compute the ini tial velocities and to verify the correctness of the fixation angular velocities of rotors must be computed Universal Mechanism 5 0 8 21 Chapter 8 Simulation of railway vehicles Remark 1 For some types of traction motor suspension e g in case of quill drive the fixation file is not sufficient for computation of all necessary initial velocities In such cases ad ditional constraints on initial velocities must be used see the next section of the manual Remark 2 The sign of the rotor angular velocity i e the sign of the corresponding joint velocity obtained from Fig 8 25 should be used for specifying the rotation_sign identifier value see Sect Traction torque 8 2 7 1 5 Computation of initial angular velocities by constraints for initial values Object simulation inspector Fail heel katri Informatior Tools Solver Identifiers Initial conditions Object variables Coordinate Constraints for initials led l Vi Set om ViS et om Vi S et3 omi Wi Set om Integration Fig 8 26 Tools for setting constraints for initial values Constraints for initial values are an alternative of the fixation file and give opportunities to some additional potential for setting initial values A constraint is an equation of one of the following two types xj Xj vi Vi where x
85. l i Animation of forces MONI horizontal Scale 170 0 ENim of variceal Scale fi7o 0 HA EMm vertical Fig 8 115 Direction of motion in the animation window Universal Mechanism 5 0 8 97 Chapter 8 Simulation of railway vehicles 8 5 3 4 Contact patch animation Use the Tools Contact patch menu command or the button on the tool bar to call the contact patch animation window Only one contact patch for a wheel is presented in the window even if a two point contact takes place The patch is presented either for the single contact point or for the contact on the running surface in the case of a two point contact The user can optionally watch the follows e elliptic contact patch FASTSIM and FASTSIM_A e vector of creep forces e adhesion dark color and sliding light color regions within the patch FASTSIM and FASTSIM_A e distribution of contact stresses within the contact patch FASTSIM and FASTSIM_A lojxj Wheelsets Wob a OWS6 TENER cir a ree FER EEEN i MSE Soe ee PStos EEE HA EE bert PEEEEREN iEPEETEl Mittirey HLEN k o aL a Sliding z me regions a G 2 _ Pa tr D A i E z aan Sere EnS A l i EEEE ESEE iFeserzi peed Bio ed Steere F e a Ae a Quit Fig 8 1 16 Contact patches while curving Universal Mechanism 5 0 8 98 Chapter 8 Simulation of railway vehicles 8 5 3 5 Table processor The following functional are added along with UM Loco module
86. lent conicity is com puted to fit the nonlinear RRD by a linear function on the Ay interval Often Ay is the shift of the wheelset corresponding to the start of the flange contact The normal distribution Universal Mechanism 5 0 8 39 Chapter 8 Simulation of railway vehicles is used in Eq 1 in the current UM version The default value of the standard deviation is o 2 5 mm Differentiating Eq 1 with respect to A yields the formula for the equivalent conicity as Ay of O Arly ay a 2 2 i f y y dy Contact angle parameter sy i i eb St a lt a Si Si SON Su mes Ss ip tel ay ea a a ag a ly a cece A lw ly Sk ln Yala aa Ti ah a Yip ea a iy a mG eal sath i Ji a it eid Simi ai Nh aa th a a a am ss Fig 8 49 Contact angle Contact angle B is the angle between the normal to the profiles at the contact point and the perpendicular to the track plane which is vertical for tangent sections Fig 8 49 The designation P y B y are introduced for the contact angles of the left and right wheels depending on the wheelset shift If the left and right pairs of profiles are equal the value B 0 B 0 B corresponds to the contact angle for symmetric position of the wheelset The dependence p Za p L E y 7 5 on the lateral shift is used for definition of the contact angle parameter Here L is the distance between the wheelset rolling radii Fig 8 6 PreeTrTeT TTT CTE TTT CT TTT TCE Te Lee eee er Ceres
87. m frog tail length d track spacing R radius behind frog The parameters define fully the switch geometry and some additional parameters Lp full switch length L theoretical length K tangent section before frog Additional parameters direction of motion facing trailing type of switch left or right coefficient of friction Universal Mechanism 5 0 8 66 Chapter 8 Simulation of railway vehicles Fig 8 78 Switch geometry parameters Use the buttons in the bottom part of he window to create the vertical profile of the track Double click of the line of the list to edit the section length and inclination Universal Mechanism 5 0 8 67 Chapter 8 Simulation of railway vehicles 8 5 1 4 Creation of files with switch parameters To create or edit a file with switch parameters use the Tools Switch menu command or the nl button _ o x Geometry Rail overhang mm 2764 0 Gauge mm 1520 Initial angle mrad r 9400 switch angle mrad 40 bee 300 000 Radius of switch R tm 300 000 Switch width for RO tron 75 0 Frog tail length rim 4045 0 Radius of point RO rm Track spacing rm 5 000 Radius behind trog gmi 300 000 Full switch length ir 34 862 Theoretical length rm 28 048 Computed tangent section mm 3285 0 Fig 8 79 Switch window parameters Use the amp bel buttons to read data from swt file or to save data The upper text box contains the name of the switch
88. me WSetRotat is a gyrostat It has only one degree of freedom relative to the base rotation about the axle It is known that equations of motion of the base plus gyrostat completely coincide with equations of motion of a one body with six degrees of freedom The goal of introducing the two bodies for one wheelset is as follows it allows avoid ing the introduction of axle boxes as separate bodies and reduces considerably CPU expenses while simulation of the vehicle dynamics Really it is impossible to attach linear force elements that are usually used for the modeling the primary suspension springs dampers guides etc di rectly to rotating wheelset with 6 d o f axle boxes are necessary In contrary it is possible to attach these elements to the wheelset base it does not rotate about the axle and the axle boxes can be omitted in the model The coordinates of the wheelset are numbered in the following sequence Fig 8 2 1 transition X 2 transition Y 3 transition Z Universal Mechanism 5 0 8 6 Chapter 8 Simulation of railway vehicles 4 rotation Z 5 rotation X 6 rotation Y Wheelset with 7 d o f is used sometimes in models of locomotives or wheelsets with freely rotating wheels In comparison with the above model the 7 degree of freedom is intro duced as the rotation of the right wheel with respect to the left one This degree of freedom al lows the user to take into account the torsional axle co
89. mpliance The wheelset model consists of three bodies and three joints The user should enter the joint force for the third joint j7WSe tRightWheel which describes the torsional stiffness and damping of the axle The user should set a value of the moment of inertia of the right wheel WSetRightWheel about the symmetry axis as well Subsystems of wheelsets can be corrected in a usual way but anyway it is not recom mended to change the sequence of rotations All wheelsets are added to the model of the vehicle as included subsystems 8 2 3 2 Wheelset geometry N K Fig 8 3 Geometrical parameters of wheelset Geometrical properties of a wheelset are fully set with the following data Fig 8 3 8 4 wheelset semibase L 2 running circle radius r reduction of running circles radii dr tread wheel profiles for the left and right wheels which should be given in a special coor dinate system of profile The first two parameters are specified in the Input module as the parameters of the stan dard subsystem wheelset The difference in running circles radii is the difference of the left and the right running circles radii e g due to wear This parameter is calculated according to the formula dr 1 Universal Mechanism 5 0 8 7 Chapter 8 Simulation of railway vehicles where 7 7 are the running circles of the left and right wheel respectively The dr parameter is positive if the left radius is greater than the right o
90. n alternative method for adding points which is highly useful if the force description includes many points The polygon should be presented by two columns in any text editor The first column corresponds to the abscissa distance or time the second one con tains the force values 0 0 50 0 70 30000 150 30000 170 0 180 0 Copy data into the clipboard by Ctrl C and paste into the curve editor Fig 8 108 by Ctrl V In this manner large data can be converted into the necessary format in the case when forces are obtained from experiment or from simulation of longitudinal train dynamics with UM Train In the last case the corresponding variable should be save in a text file from a graphic window single profile 7 OF fA Factor Hi M Autocorrection of length otart fo Finish s00 Track From file Slump spectrum Expression Points Points Paints G Universal Mechanism 5 0 8 87 Chapter 8 Simulation of railway vehicles To create a file with the force having the reverse sign set 1 minus unit in the Factor box send the plot to the upper part of the window by the button save it by Id and rename the extension The created files can be immediately assigned to the force components Fig 8 104 and used in simulation process Universal Mechanism 5 0 8 88 Chapter 8 Simulation of railway vehicles 8 5 2 7 Additional contact parameters 8 5 2 7 1 Difference in running circles radii Track Frotiles Contact
91. nce between the points of pro files in x 0 plane Edge of the approximate contact patch is determined as a line of intersection of the sur faces fig 8 60 The dependence of the intersection line on the lateral coordinate 1s a y 6 J2R 8 h y 8 5 Universal Mechanism 5 0 8 50 Chapter 8 Simulation of railway vehicles The roots y of the equation 5 h y 8 6 determine the length of the patch along the lateral axes The number of separate zones of the contact is equal to a half of the number of the roots So the contact area is a function of the surfaces of the contacting bodies and the interpe netration 6 Since the surfaces are always given functions we have the only unknown value 6 y Rolling direction Fig 8 60 Wheel rail contact The materials of the bodies are assumed to be homogeneous isotropic and elastic Since the size of the contact patch is small in comparison to the characteristic sizes of wheel and rail the contact stress does not depend on the shape of the contacting bodies distant from the contact patch In this case the contacting bodies can be considered as elastic half spaces By using the half space method the value of 6 can be estimated The deflection at point 0 0 can be found with the help of the Boussinesq s influence function as _l v ep psy 0 0 I ety dxdy 8 7 where p x y 1s the distribution of the normal pressure C contact area According to the as sumption
92. nd part of the resultant profile corresponding to the difference in the irregularities of the left and right rails Universal Mechanism 5 0 8 61 Chapter 8 Simulation of railway vehicles Resultant profile EO Length j1o00 otep 0 1 Profile components spectrum Spectrum spectrum gt ICO a E SOC single profile OF fA Factor Autocorrection of length subtract the half difference realization from the resultant irregularity by the button setting Factor 1 save the result to file for the right rail Horizontal irregularities are generated in the same manner selection of spectrum C Points Condition te Bad C Good Type e 2 i Lin fo 0 Lminf200 00 Sumber of harmonics a000 A Compute e Spectrum UIC With this option the user can generate irregularities by SPD corresponding to UIC stan dards Track conditions are of good or bad quality Generation process for vertical irregularities is similar to that for the FRA standards Note that horizontal irregularities in this case are equal for the left and right rails 8 5 1 2 2 Programming irregularities in the Control file Control file is the main tool for the user programming in UM environment Chapt 5 The control file for railway vehicles contains the following function function TrackProfile position real_ var LeftZ RightZ Lefty RightY derLeftZ derRightdZ derLeftY derRightY real_ integer begin Result 0 end
93. ne If dr is nonzero the radii 4 7 are equal to n r rn r dr 1 e the left radius is always equal to the value specified in the Input module Profiles are chosen from the UM database or created by the user with a special tool in the Simulation module Sect 8 5 1 1 Creation of wheel and rail profiles Let us introduce the notion of system of coordinate of a trade wheel profile Fig 8 4 SCW The SCW origin is located at point K on the running circle Fig 8 3 and corresponds to the middle point of the profile along abscissa The abscissa axis y is parallel to the wheelset axle and is directed towards the flange Z axis is vertical Coordinates of the profile points are set in mm Fig 8 4 System of coordinates of a tread wheel profile 8 2 3 3 Adding wheelsets and changing their parameters E S Object 2 ia F Object E E subs yoia nn E Contact forces Jat General forces ar suse ension Fg Special forces pA Connections Fig 8 5 Adding the first wheelset to a vehicle or bogie To add wheelsets WS to the model of a railway vehicle the Subsystems item of the ele ment list is used To create the first wheelset make sure that the object type is the railway vehicle Sect 8 2 1 add a new subsystem by clicking the button Fig 8 5 Choose the type of the subsystem wheelset Universal Mechanism 5 0 8 8 Chapter 8 Simulation of railway vehicles Wheelsetl Mame wheelset aF AF ake wheelset
94. ofile will move to the left together with the wheel profile This mode of the two point contact can dis appear in two different ways Firstly the wheel will move to the right and the flange contact dis appears Fig 8 45 left Secondly the contact on the running surface disappears the corres ponding normal force becomes zero and the wheel goes to the creeping up state Fig 8 45 right This mental experiment is the base of an algorithm for computing the two point contact Let us start discussions of the algorithm Universal Mechanism 5 0 8 36 Chapter 8 Simulation of railway vehicles Choose intervals for possible values of the Aa Ay coordinates with a definite reserve Aa E Admin Abmax Ay AYmin AY max and introduce a homogeneous discretization of the intervals VN and N are numbers of subinter vals Now for each fixed value Aa j 1 Natl compute coordinates of contact point on the running surface according to Sect 8 4 1 1 successively decreasing the lateral shift Ay iI Ny 1 1 If the profiles allow the two point contact the position of the contact point for some Ay will change by a large enough jump This fact means that the flange contact occurs inside the latest change of Ay Denote this value of Ay as Ay Two conditions formalize the notion of a large enough jump and give a criterion of passing through the two point contact Yri Yr i 1 7 Ny gt Ny y Np 2 gt Nn where y j j 1 are the successive coordin
95. oint computation process and to violation of continuity the contact point coordinate Note 2 The I J button is used for plotting the smoothed profile curvature which is used by com putation of creep forces with the help of FASTSIM procedure 8 5 1 1 2 Input of profiles as a set of line segments and circle arcs e cicle YKE a Line DN crc Vv Type 8 4 PapSplinet 10 93 445 0 Wheel C Rail Cluit 82 33 5 E Fig 8 65 Creation of profile as a set of line sections and circle arcs To create a profile as a set of line segments and circle arcs 1 Set coordinates of end points of line segments and arcs as a broken line from the left to the right increasing abscissa 2 Select by the mouse a section of a sequence of sections which should be replaced by cir cle arcs and set the Circle item as the type of sections Fig 8 65 3 Save the profile with the help of the 1 button on the toolbar of the editor 8 5 1 2 Creation of track irregularities There exist two ways how to create track irregularities in UM as files using programming in the Control file of the model Use of files with irregularities is the main method At the same time programming of the irregularities in some cases is more effective because it allows parameterizing some irregularity parameters such as height length etc In its turn the parameterization allows scanning dynamic properties of a vehicle in dependence on the irregulari
96. option selected in the Draw group Position shows the contact point for different values of the wheel shift relative to the rail dY as well as small wheel rotation angle relative to the longitudinal axis dA Fig 8 51 To changle values of dY mm and dA degrees use either track bars or direct input in the text boxes After direct input in a text box use the Enter key to redraw the contact The angle changes from 1 4 to 1 4 degrees Fig 8 54 All contacts of a pair of profiles Universal Mechanism 5 0 8 43 Chapter 8 Simulation of railway vehicles All contacts contacts on rail and wheel profiles for different values of lateral shift are connected by segments The thick segment corresponds to the current value of the shift RRD option draws the rolling radius difference curve Sect 8 4 1 3 dY Y Y coordinates of contact point on rail and wheel profiles in SC of the corresponding pro file depending on the lateral wheel shift Beta contact angle versus lateral wheel shift Fig 8 49 BL BR 2 L 2 plot of the function P B p L Ly used in computation of contact angle parameter Sect 8 4 1 3 Universal Mechanism 5 0 8 44 Chapter 8 Simulation of railway vehicles 8 4 3 Contact forces 8 4 3 1 Method for computation of rail deflections and contact force A rail is considered in UM as a massless force element This means both stiffness and damping of the rail is taken into account but not the inertia propert
97. optional parameter See the previous section as well as Sect 8 3 1 3 Switch geometry for more details Universal Mechanism 5 0 8 68 Chapter 8 Simulation of railway vehicles 8 5 2 Setting parameters of railway vehicle dynamics simulation Here we suppose that the model of a vehicle is ready for simulation and it is already loaded in the Simulation module Parameters of modeling a railway vehicle are set with the help of the Object Simulation Inspector which is called by means of the Analysis Simulation menu command the Ctrl F9 hot key the gt button of the tool bar A considerable part of the parameters can be set in a standard manner Chapt 4 Sect Preparing for integration Here we consider some features of the parameters setting for a railway vehicle 8 5 2 1 Solver and its parameters Use of Jacobians Object simulation inspector Railay ree oy Information Tools solver Identifiers Initial conditions Object variables Msssunsnsnononununonanannnnnansnansnnnnnnnnnnunununununnnsnnnnnnnnnnnnnnnnanununnnannnsnnunnninnnn solver Type of solving EREE C Null Space Method C ABM Bose fe R 3 Method e Range space Metho Gear ae Simulation time LA step size for animation and data storage j0 006 Error tolerance 4E 0006 Computation of Jacobian V Block diagonal Jacobian Jacobian for wheel rail forces Fig 8 80 Solver parameters Here we consider parameters in the Solver tab of the inspec
98. ot of the separate irregularity in the bottom graphic window always starts with zero O The Finish parameter sets the length of the current irregularity More exactly the length is the difference between the finish and the start parameter values Consider types of separate irregularities e Analytic expression the Formula tab Set an analytic expression f x in the Function of irregularity edit box and press the Enter button or click 21 button Standard functions can be used in the expression Chapt 3 Sect Standard functions and constants Standard expressions can be assigned from the pull down list as well e Slump Create a special and often used irregularity Set its position and length using the Start and Finish parameters e From file Here an already created file of irregularities way can be read To do this use the I button A part of the irregularity which length and position is determined by the Start and Finish parame ter may be added to the resultant track profile e Points Here an irregularity is created as a set of points defined with the help of the curve editor Chapr 3 Sect Object constructor Curve editor To call the editor click the f button In par ticular here the user can convert an irregularity given in a text format into UM format For this purpose the irregularity should be open in any text editor in a two column format The first col umn should contain abscissa values in meters 1 e the longitudinal coordin
99. other words the standard track widening is the lateral distance between the origins of two profile frames wheel and rail at ideal symmetric position of the wheelset Fig 8 32 On standard track widening Further expression for the widening S h L Ay r 4 2 where S is the gauge A width of the rail head Default value is Ay 0 003m Rail inclination 1s the angle between the rail profile axis of symmetry and the vertical in an ideal straight track Unit for angle is radian The angle is positive for inclination inside the track Default value is a9 0 05 rad 8 3 1 2 Macro geometry of curve The following types of curves are available in UM Fig 8 33 right curve S curve a right curve followed by a left one left curve can be obtained as a S curve with a very short right curve section The following designations are used for the S curve in Fig 8 33 LO straight section before the curve P11 first transition for the right curve S1 length steady curve RI radius of steady curve H1 cant for the outer rail P12 second transition for the right curve dy additional gauge widening in curve L length of a straight section between the right and the left curves for S curves only Other parameters for the second part of the S curve have quite the same meaning Note To get a left curve small values should be set for P11 S1 P12 zero value for H1 and a large value
100. oximations Thus the contact computation looks like this internal cycle of iterations com putes lateral deflection of the rail and normal force forces in contact contacts the lateral creep forces are taken from the previous step After that the new values of creep forces are computed When the new values differ from the previous ones more than an error tolerance the external iterations start and equations 8 2 8 3 are solved for corrected values of creep forces Consider some features of realization of internal iterations 1 Lateral deflection Ay is the sum of two components Ay Ayy Ay Universal Mechanism 5 0 8 46 Chapter 8 Simulation of railway vehicles The first component corresponds to the rail deflection by forces at the first contact point the second one differs from zero by the two point contact and results from the forces at the flange contact M2 F2 2 The previous value of the Ay variable is used as the initial value for iterative solving the equilibrium equations Iterations make the value more accurate 3 Each of the iterations includes Evaluation of the wheel profile position relative to the rail Ay Aqa according to the known data position of the wheel irregularities gauge widening etc These parame ters are used for determination of the contact type one or two point as well as for in terpolation of coordinates of the contact point or points with the help of the prelimi nary computed tables Sect
101. pecify four points on the SPD curve Note that this example illustrates the sequence of steps of the process and cannot be used as a realization of irregularities by simulation of rail vehicles 4m Curve editor PAT qh Hae hes 5 x ine SKE i Te lf 2 24 5E 6 Fig 8 67 SPD function as a sequence of points Set parameters like in Fig 8 68 and add the function to the resultant profile by the T but ton and save in to a file by clicking the 4 button in the top of the window Universal Mechanism 5 0 8 59 Chapter 8 Simulation of railway vehicles Making of a track profile 4 _ ol x Resultant profile f Length 2000 otep 0 1 Profile components spectrum single profile T tq Factor i Autocorrectian of length start fo Finish 2000 Expression Foints From file Slump Spectrum Track Selection of spectrum FRA CC UIC Points spectrum Faints 4 Circular frequency Sumber of harmonics 3000 A Compute Fig 8 68 Track irregularity generation window Reverse transformation of the irregularity to SPD function with the Statistics tool Tools Statistics menu command or the button is shown in Fig 8 69 m N 0 002 Fig 8 69 SPD function of generated irregularities Remark If necessary use the Factor value to convert irregularities in mm Universal Mechanism 5 0 8 60 Chapter 8 Simulation of railway vehicles selection of spectrum FRA C U
102. rameter sets the length of a tangent section before the switch c d Fig 8 98 Facing a b and trailing c d movements in left and right switches Track type Tangent S Curve Profile Curve Switch Macrogeometry file C Program FilessUM Sotware Labb bini restre es Use the I button to open a mcg file with the track macro geometry parameters see Sect 8 5 1 3 Creation of macro geometry files In this case of the track the motion in inertial SCO is always used e Profile Universal Mechanism 5 0 8 80 Chapter 8 Simulation of railway vehicles 8 5 2 4 3 Track stiffness and damping Irregularities Macrogeometry stifness Vertical stiffness faa 000000 Vertical damping jaopoog O Lateral stifness faooooo Lateral damping fooooo Fig 8 99 Track stiffness and damping parameters Stiffness and damping coefficients of the track for a wheel are here equal for the left and right rail and constant along the track Stiffness is measured in N m damping coefficient in Ns m The default values are given in Fig 8 99 See also 8 3 2 Elastic dissipative and inertia properties of track 8 4 3 Contact forces Method for computation of rail deflections and contact force 8 5 2 4 4 Programming elastic and damping track parameters To get track stiffness and damping which is variable in the longitudinal direction as well as set different values of these parameters for the left and right rail the user should use t
103. rces Rail and wheel material properties which are supposed to be equal elasticity modulus and Poisson ratio set by the user Current geometric characteristics of the contact point principal curvatures of the contact surfaces computed by the program The normal force N in the contact computed by the program This data is used by FASTSIM to compute the semi axes of the elliptic contact patch according to the Hertz theory Current values of the longitudinal and lateral x y creepages and spin computed by the program Universal Mechanism 5 0 8 48 Chapter 8 Simulation of railway vehicles aL bb Rolling direction Fig 8 58 Discretization of the contact ellipse According to this data FASTSIM solves a system of differential equations in the adhe sion area of the contact patch or a system of differential algebraic equations in the sliding area of the contact patch relative to tangential stresses For this purpose the contact ellipse is divided into a number of narrow slices of the same width In turn each slice is divided into n elements of equal length within one slice Fig 8 58 Number of slices m and elements n is set by the user The default values are 10 To compute the creep forces and to obtain adhesion and sliding areas of the patch FASTSIM solves the above equations for each of the slice successively In fact the discretiza tion on elements gives the constant step size for numeric solvin
104. re of the curve The following inertia force and inertia moment are taken into account for every body when the non inertial SCO is used F mla F xe M f Je where m J are the mass and moment of inertia of a body relative to the vertical axis xo is the longitudinal position of the body center of gravity relative to the vehicle body CG Note that the angular acceleration is non zero at transitions only Universal Mechanism 5 0 8 28 Chapter 8 Simulation of railway vehicles Fig 8 34 Inertia force for the non inertial SCO Consider an example of a S curve for the following parameters Lo 10m p 70m 8 150m R 300m pi2 60m h 0 09m L 10m p21 50m s2 140m R2 330m p22 70m h2 0 1m Fig 8 35 Angle between rail and X axis Fig 8 36 Curvature Fig 8 37 Derivative of the curvature Universal Mechanism 5 0 8 29 Chapter 8 Simulation of railway vehicles Fig 8 38 Gauge widening Fig 8 39 Cant for outer rail Universal Mechanism 5 0 8 30 Chapter 8 Simulation of railway vehicles 8 3 1 3 Switch geometry Fig 8 40 Geometric parameters of a switch Motion in left and right switches are implemented in UM The basic geometric parame ters of a switch are shown in Fig 8 40 The following parameters are used for description of the switch q stock rail overhang p initial angle Universal Mechanism 5 0 8 31 Chapter 8 Simulation of railway vehicles a switch angle Ro rad
105. reated by adding and deleting of existing files Use the B amp buttons or the pop up menu to add and delete profiles Use Rail Wheel Profiles Profile files Evolution of rail profile tab to set a sequence of profiles R the track as well as their positions along the track S Sect 8 3 1 1 i 1 2 Universal Mechanism 5 0 8 74 Chapter 8 Simulation of railway vehicles Add profiles to the sequence with the help of the pop up menu After that set the posi tions Fig 8 89 Object simulation inspector katri Informatior Tools Solver Identifiers Initial conditions Object variables Fail heel SHAT Track Frofiles Contact Fict cars Forces Wheels Ralls Addit parameters Lett rail D Sum4 bin WAT oriew rot a Aight rail D Sum40 bin R WATT oriew rot E W Profile wear process Rail profiles in control point FO Nurd 0 bin Aw or rbonew rt d umd 4 Opin orb Sold06 rpt a Control points lett ral Control points right rat DWuma OS bnt Aw or boriew rot AL D uma Obin Aw prir borew rot 350 100 d um40 bina or rE Sold08 rot 300 d umg binira prir bSold06 ppt a50 Dum bin A epr rE onew rot 0 D Aum40 bins A v prir bore rpt D ume OS bins A e pri bore rpt p 4d Cum 4O bin Rewi prf re snew fpr Pelete dsiuntO bina orr re Sold08 ror Er Edit coordinate Enters Fig 8 89 Creation of sequence of profiles along the track Switch on the mode of the profile evolut
106. rs at the top have the following functions O Button 1 is used for saving the profile in a file O Button O clears the resultant profiles removes all components O Parameter Length sets the length of the data along the track Tabs in the right bottom part are used for creation separate irregularities of different types The corresponding plot is located in the left bottom part of the window Fig 8 66 Buttons and parameters at the top have the following functions O Button V adds the current separate irregularity to the resultant track profile O Button 4 saves the current separate irregularity to file O Buttons O clears the current separate irregularity O Parameter Factor the current separate irregularity is added in the resultant one it is multiplied by this factor Consider an example The user wants to convert some irregularity Universal Mechanism 5 0 8 57 Chapter 8 Simulation of railway vehicles in text format data into UM format Let the data be given in meters The tool with the help of the Points tab can accept the irregularity However the factor 1000 should be set before add ing the data to the resultant profiles to convert it in millimeters O The Autocorrection of length check box if it is on the length of the resultant profile is automatically increased to match the adding separate irregularity O The Start parameter shows where the separate irregularity begins when added to the resultant profile Note that the pl
107. rt A but of the wizard Set the variable type Velocity and send in to the container by the ton Fig 8 27 Drag the variable by the mouse and drop it into the left cell of the co constraint data row Fig 8 26 Ea ze Wizard of variables ab J sin Jit SpecialF ContactF Allforces Joint force Track SC a veo T forces Bipolar LinearF User Expression Identifier 3 i Ee iCar body SpecialF ContactF Allforces Joint force Track SC ra y Coordinates Angular var Reaction F Linear var Railway y Bogie 1 Coordinates Angular var Reaction F Linear var Railway T orces BipolarF LinearF User Expression Identifier amp Bogie frame wat Selected coordinate iwWSet_Axlebox L 1 24 iwSet_Axebox R j Leaf spring L Type of variable C Coordinate Velocity C Acceleration Fig 8 28 Creation of variables angular velocity of wheelset and computed value of drive shaft angular velocity Create a variable corresponding to the desired value of the velocity and set it in the right cell of the constraint row Consider an example Let the rotor angular velocity is equal to the wheelset angular velocity multiplied by the gear ratio 4 19 It is necessary to take into account the wheelset and the rotor rotate in opposite directions 1 e the joint veloci ties have different signs o Create a variable correspondin
108. s sissirnrnraisen iarann roadenn NEn E ENE 8 14 8 2 7 Some features of development of locomotive models ssenssoesseesssessseesserssersseessersssreserssserssersseres 8 14 8 2 7 1 MoC EOT ACO eioen ea E EEEE EEE E E E A 8 14 SeT Bod mae ee E E E E 8 15 oe rA O O E a E E E E E 8 15 oer O E EA EEE 8 17 8 2 7 1 4 Computation of initial angular velocities by fixation file eccccececccseeeeeeeeseesecneneeeenes 8 19 8 2 7 1 5 Computation of initial angular velocities by constraints for initial values cccceeseeeeeeees 8 21 8 2 7 2 Support of braking mode ssennseesssessserssersssrssersseesssesssersserssersserosersssesseersserssersserssersseesseeo 8 23 83s Rail rack csacsi aia aE AEAEE E AAA 8 25 8d Track geome y eee E eaae E E E EEEE EENE NEE 8 25 8 3 1 1 Geometry of rails in an ideal straight section ssenssoesssesssessserssersserssersssesssrsseerssersserssersseres 8 25 8 3 1 2 Macro pcom y Ol CUVE etcetera ect E E EEEN 8 26 8 3 1 3 SA aera ete mg E E EE EE E 8 30 8 3 1 4 Track systemi of coordinates useina ore raed tener E EESE EE EEN EE EEEN DEE AEE 8 31 8 3 1 5 Track reola S o EEEE EE E E A E E 8 32 8 3 2 Elastic dissipative and inertia properties of track ccccceccccsseeecceeeceenceeaeeeeseneecseeecseneessecesanseesanes 8 32 Se W bheckralcontici eiis a a a a 8 33 8 4 1 Algorithms for wheel rail contact geometry ssenssensseesssersserssserssersserssersserssersserssersseesseesssess
109. sses 8 33 8 4 1 1 Algorithm for computation of nearest points between two profiles cccccceeeeeeeeeeeeeeeeeneees 8 33 8 4 1 2 COMMU TIS Tals OinC OM ACE PONI acacaacomsacasedanananataataaunsnas E imc 8 34 8 4 1 3 Simplified contact geometry Equivalent conicity and contact angle parametet 0066 8 38 542 FOOL TOP analysis Ol Pails OF PEOMNCS sson a TEE 8 41 8 4 3 OTE E E C8 EEA E E N E E E E O O A E 8 44 8 4 3 1 Method for computation of rail deflections and contact force cccccceececseeecceeseceeeeeeeeseeseneees 8 44 8 4 3 2 Algorithms for compu ne crep 1OLCES sess cess incsisnsnsaetae seganalsannoasadnayswcsnapeneundaatnwensapusmansanspmeanamnins 8 46 Beem zal JETER S MCI OC ie sccntasancnoasacimacancataiataceomatengaiansetesacuoteape tmntsaadenceisametnasaucd mies sancionaieacamerennaans 8 47 oka Tye ee E E sean ccioasazaninsaancetmasisanetucetaac A E 8 47 ee 25 P SIA A VNC a E E A 8 48 ee i o STO gt E A T E A A E E TT 8 48 8 4 3 3 Non elliptical contact model ccccccsescccceseccneeeeesceceeeeceeneesecesensecseeeeeenseeeseeeeseesessesesseneess 8 49 8 4 3 4 Coefficient of friction in wheel rail contact esseeeeseeesseeessseesssersseresssressserssseresseresssresseeees 8 52 5 5 Simulation of railway VENCE S saisis Na eR a EAE 8 53 8 5 1 Tools for preparing simulation Process cccccseccccsecccesecceneecseeeecaeeeeseneecaeseeseneeeseeeeseeesseneesanseesanes 8 53 8 5 1
110. stiffness of a pair of springs connected with the axle box e Non symmetric attachment of traction rods for traction wheelset e Lateral gaps in axle box assembly for some locomotives with 3 axle bogies 8 2 4 1 Axle boxes as massless graphic images Let us consider how we can add images of axle boxes without adding them as rigid bo dies A simplified standard image for an axle box can be obtained from the file bin graph axlebox img Make the following actions with a wheelset already added to the object e Run modification of the subsystem by clicking the Edit subsystem button fig 8 6 e Read image of the left axlebox from the bin graph axlebox img file by the amp button on the tool panel Rename the image e g Axlebox L e Copy the image of the left axlebox rotate it on 180 degrees about the vertical axis and rename the copy Axlebox R Name axleboxes ap aP E Description Go position ao Go Type ED GO z F ar r Parameters GE position Element i a graphic object AxleBox L Fig 8 9 Graphic element of GO type e Create a new graphic object with two graphic elements of GO type assign images of the axle boxes to the elements Fig 8 9 Set lateral locations of the axleboxes and rename the image The result if shown in Fig 8 10 Universal Mechanism 5 0 8 11 Chapter 8 Simulation of railway vehicles _ lt gt a Pe Fig 8 10 Image of fictitious axl
111. t conicity Consider a pair of rail wheel profiles in a contact When the wheel profile shifts in the lateral direction on distance y the contact point change its position of the profile curves Let Ar y Ar y be changes in radii if the left and right wheels The value Ar Ar Ar is noted as the Rolling Radius Difference RRD and its plot in dependence on the lateral shift is used for evaluation of the equivalent conicity of a pair of profiles scceeteeececereebcoeeceteccee rw beteascnoscesenoneeoheasGemepen EREE AT E E E EE EET T E E E E S E Fig 8 47 A pair of new profiles R65 and Russian wagon wheel left the corresponding RRD right aeaa aeaa a aa PSS OS SSE SA a aaa aaa aaa aa aaa Puc 8 48 A Pair of profiles R65 and DMetI left the corresponding RRD right For the new R65 and wagon wheel profile the RRD 1f a straight line in the region of one point contact The tangent of the line inclination angle is equal to the double wheel profile conic ity A 1 20 Fig 8 47 Really the wheel profile function is r rtay r nHn Ay and Ar 2Ay For worn of curved profiles the RRD curve is non linear even for small shifts of the wheelset Fig 8 48 In this case the notion of equivalent conicity A 1s introduced as a mean value for a definite lateral shift of the wheelset Ay according to the formula min f y Ar y 24 y dy 1 where f if the distribution function for the lateral shift y Thus the equiva
112. t of the editor window or clipboard for input of a profile as a set of points The points must be ordered from the left to the right according to in crease their abscissa The unit for data is millimeter For input from the clipboard points should be written as a text in two columns The first column contains abscissa values the second one the ordinate values 68 9 11 7 66 4 8 88 63 9 6 98 61 4 6 48 58 9 5 99 To set points from the clipboard Clear the editor Copy the new data to the clipboard from any text editor in a standard manner Activate the curve editor by the mouse and paste data from the clipboard Ctrl V or Shift Insert When all the points are set into the editor select the curve by dragging the mouse and set the Be ta spline approximation Fig 8 64 Save the profile with the help of the I button on the toolbar of the editor lol x my Curve editor Di um bint RAA pri Dmetizo wpt F Beta spline w uy y KE gee Geta spline e ae EE et 11 7 L 566 4 8 88 6 58 Wheel C Rail 78 21 Z Fig 8 64 Selection of curve and setting the approximation Universal Mechanism 5 0 8 55 Chapter 8 Simulation of railway vehicles Note 1 It is not recommended to use step size for abscissa less that 1 mm Otherwise the first derivative plot might look as a saw button Y and the curvature plot might have large overfalls button E Such cases may lead to deterioration of the contact p
113. t sec tions P11 P12 steady curve of radius R1 and length S1 a positive cant for the outer rail and Universal Mechanism 5 0 8 77 Chapter 8 Simulation of railway vehicles an additional widening in the curve dY1 All parameters of the curve including the additional widening dy should be set in meters See Sect 8 3 1 2 Macro geometry of curve for more details The L is equal to the full length of the curve including the tangent section L1 The V is equal to the vehicle speed m s in case of zero value of the uncompensated acceleration The Smoothing parameter is used for smoothing the vertical junctions at ends of the tran sition by arc of circle The parameter here sets the meters length of the smoothed section The Jnertial SCO check box allows the user to run the simulation either in the inertial checked or non inertial unchecked system of coordinate Sect Base coordinate system Track type C Tangent 5 Curve Curve C Switch First section Second section L1 fio F11 fso ol 200 Rl 300 H1 0 03 He 0 09 Ple fso Pee fso dy jo 01 dye jo 01 L 310 L350 Woo 1294756 Woo 12 947557 Fig 8 94 Parameters of S curve e S Curve S curve is a combination of a right curve followed by the left curve HEH nate dk Cs fel o ie z KE Cancel 230 141 7 Fig 8 95 Cant versus track distance Features of setting cant values In case of motion in a right curve and in S curve Fig 8 93
114. tal irregularities lead to excessively narrowed gauge and a simultaneous contact of two flanges of a wheelset takes place the program sends a message about the error and stops the simulation Long raise or and lowering of the track should be realized as irregularities It is possible to program user s irregularities in the Control File 8 5 1 2 2 Note To avoid a force jump while going up the begin of an irregularity the irregularity is set to zero on the first ten meters and a growth is considered on the next 20 meters be a mul tiplier which increases linearly from 0 to 1 As an example consider an irregularity of a constant height of 1 mm In the reality the irregularity in Fig 8 42 will be applied This is valid for file ir regularity only and not for the programmed one Fig 8 42 T an er ee 8 3 2 Elastic dissipative and inertia properties of track Elastic and dissipative properties of a track are taken into account by introducing linear stiffness and linear damping for rails in vertical and lateral directions The user can introduce variable stiffness and damping along the way using programming in the Control File Inertia properties of the track can be taken into account by usage added masses in the ver tical and lateral directions for wheelset bases Universal Mechanism 5 0 8 33 Chapter 8 Simulation of railway vehicles 8 4 Wheel rail contact Three main parts of contact computation can be pointed out 1 contact
115. tive rotations of profiles see Sect Computing tables of contact points and Creation of wheel and rail profiles If the key is checked the step size is decreased up to the value which is set as the Thin out step size parameter The step default value is 1mm Universal Mechanism 5 0 8 90 Chapter 8 Simulation of railway vehicles 8 5 3 Tools for visualization and analysis of railway vehicle dynamics 8 5 3 1 Some features of creation of variables General information about creation and usage of variables as well as lists of variables can be found in Chapt 4 Sect Variables Wizard of variables List of variables Here we consider variables which concern dynamics of railway vehicles exclusively 8 5 3 1 1 Rail wheel contact variables To get variables describing contacts between a rail and a wheel use the Railway tab of the Wizard of Variables For detailed information about the Wizard see Chapt 4 Sect Wizard of variables Eee Wizard of variables X Ene Wheel Special F All forces Joint force Trackse vE All wheels Coordinates Angular var Reaction F Linear var ee All left wheels Railway Bipolar F ser Expression Identifier 3 iia All right wheels i B weet right Comments B weet lett FIRST CONTACT POINT 2 ve weet 2 right creep x Longitudinal creepage B weet 2 lett creeply Lateral creepage spin spin in the first contact point creep Full creepage FCreep x Longitudinal cr
116. tor Fig It is recommended to use the Park solver with an error tolerance value about 1 10 1 107 The recommended step size for animations and data storage is 0 02 0 005 sec If the integration process does not con verge i e a beard is observed for some variable plots mainly for accelerations Computation of Jacobian should be used or the accuracy should be increased right up to disappearance of the beard Note that increasing the accuracy corresponds to decreasing the Error tolerance para meter Use of the Jacobians allows a considerable decreasing the CPU expenses in the following cases Small speed of the vehicle less than 8 10 m s in this case both the Computation of Jaco bian and Jacobian for rail wheel forces boxes must be checked The model contains stiff force element which description contains large stiffness and or damping coefficients contacts bump stops etc This may lead to large frequencies or damping level If computation of Jacobians is on simulation process can be often made faster by Use of block diagonal Jacobians Universal Mechanism 5 0 8 69 Chapter 8 Simulation of railway vehicles Switching of computation of Jacobians of non stiff forces such as suspension springs or dampers on the Tools Forces tab of the Object Simulation Inspector Fig 8 81 Object simulation inspector solver Identifiers Initial conditions Object variables RailWheel xva Information Tools Test For
117. ty parameters Universal Mechanism 5 0 8 56 Chapter 8 Simulation of railway vehicles 8 5 1 2 1 Creation of files with irregularities lol x my Making of a track profile Resultant profile H Length zoo Step fo Frofile components M Chum bin uniizht g m abs sinfe pr yl 2 54 a gt il Ranges are not used single profile iT tq Factor f i Autocorrection of length o Finish foo start Formula Points From file Slump Ranges are not used Fig 8 66 Tool for creation of irregularities Files with irregularities way are stored in the Din rw directory A file contains values of irregularities in meters with the constant step size 0 1 m in the single format 4 byte floating point numbers A new file of irregularities is created with a special tool which is available in the Simu lation module by clicking the Tools Create track irregularities menu command Within this tool the longitudinal coordinate is measured in meters but the irregularities in millimeters Let us consider the structure of the tool and the meaning of its parts The resultant profile of irregularities is plotted in the top part of the tool window It is created as a sum of separate irregularities of various types The list of components is located in the left top part of the window Fig 8 66 Deleting an element of the list removes the corres ponding component from the resultant irregularity Buttons and paramete
118. unning surface are computed by the formulas y _ V Sx m where V 9 V o are the longitudinal and lateral components of velocities of the point on the wheel profile corresponding to the running circle v is the longitudinal velocity of the wheelset enter Remark The Mueller s method of creep force computation is used in case of simplified geometry of contact see Sect 8 4 3 2 1 Mueller s method Universal Mechanism 5 0 8 41 Chapter 8 Simulation of railway vehicles 8 4 2 Tool for analysis of pairs of profiles w Analysis of pairs of profiles l o x Dra Read ge 0 0 ra hel Eie osion C RRD ee C All contacts wo BL BR 2 5 2 31 56 8 9 manchesterrl rpt manchesteny wpf manchesterrr rpt manchestenvrwpt ro rot newlocow wot newweg rw wpf rbSald1 3 rpt 1002 wot ICO vor rpt 510021 wept ICBO 1 pt o1002r_1awwot Cb Onew rot s1002worn wpot UICbOr_1 pt s1002wornd wot Fig 8 51 Profile analysis window The tool for analysis of profiles is available in the simulation program for the current val ues of the track gauge and rail inclination Sect 8 25 Geometry of rails in an ideal straight sec tion 8 5 2 4 1 Assignment of track irregularities and rail geometry parameters gauge rail incli nation Use the Tools Analysis of pairs of profiles menu command or the button on the tool panel to open the window Container with profiles The container contains l
119. variables to get any kinematic variable in projec tion of the TSC Fig 8 112 To create the variable e Select a body in the list in the left part of the wizard e Select the type of variable a linear variable Cartesian coordinates velocity or accelera tion or an angular variable angles angular velocity and angular acceleration e Set a point in SC of the body which coordinate velocity or acceleration should be com puted if a linear variable is selected e Set an axis of the TSC for projection For lateral component of acceleration either an uncompensated acceleration or a usual acceleration is selected Fig 8 112 8 5 3 1 3 Use of Path variable The Path variable is created on the Railway tab of the wizard of variables It denotes the distance passed by the vehicle since start the simulation This variable has the standard identifier which should not be modified by the user Using this variable simulation results obtained for railway vehicles running with different speed can be easily compared Consider variants of the variable usage e Use of Path variable in graphic windows Universal Mechanism 5 0 8 95 Chapter 8 Simulation of railway vehicles Ih Plots Vi ayiKysoeftrack ME acz Kysoe track Path Vehicle pat Options Edit Delete Del Copy to clipboard Ctl c Copy to active MS Excel book Cil E Filter Ctrl F Copy as static variables Ctirl 5 Save as text file Ctrl T Save as t
120. vehicle model both car and locomotive force elements which allow converting the braking force computed in the train module to the moments and forces acting between bodies of the rail vehicle Using UM the user could realize a detailed model of mechanical part of the braking system but here we consider a simplified force model which is quite precise in many cases Brake Block Meel Brake Block Fig 8 29 Bilateral brake blocks Let the total braking force for the vehicle is set by an identifier It is recommended to use for this purpose the standard identifier braking_force to automate the process of its recogni tion in the train 3D models Consider bilateral brake blocks which are pressed symmetrically against the wheel tread Fig 8 29 It is assumed also that all the wheelsets of the vehicle produce equal braking forces In this case the brake force for each of the wheelsets can be realized by tor que acting from the bogie frame on the wheelset opposite to its rotation braking_force Nw Rw rye Nw yaco KoslecHbIx nap Rw payuyc Kosteca The sign is set if the wheelset forward motion corresponds to the negative angular velocity it is possible often if a subsystem including the wheelset is rotated on 180 degrees about the vertical axis see the sign of angular velocity of the wheelset in Fig 8 25 Universal Mechanism 5 0 8 24 Chapter 8 Simulation of railway vehicles amebak a i Comment Body Body Bogie

Universal Mechanism 5.0 8-1 Chapter 8. Simulation of railway vehicles

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