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Planetary2D User`s Manual

1. 1 06 F 7 Tangential disp Uy in 1 08H 1 12 1 1 1 1 1 1 1 0 0 002 0 004 0 006 0 008 0 01 0 012 0 014 0 016 0 018 Time secs Figure 9 2 Graph showing the pinion bearing tangential displacement against time for dynamic analysis The tangential displacement at each instant of time is given in Column no 3 of the PINIONIBRGRES DAT file 140 Running a dynamic case x 10 5 8 5 85 n 59r 1 n 2 N 2 _5 95 4 o 6 _ 6 05 6 1 1 1 0 1 2 3 4 5 6 7 8 9 Time secs Figure 9 3 Graph showing the housing moments against time for dynamic analysis The moment about the Z axis for each time instant is given in column no 13 of the HOUSINGRES DAT file 9 17 Analysis and Results 141 9 17 1 Calculating the Dynamic load factor A graph of timestep against dynamic loads obtained from the file LOADS DAT is shown in Figure 9 4 The LOADS DAT file has row for each instant of time The first column contains the time Ea
2. PE TIE SOLMETHOD B STATIC NTIMESTEPS 5551515 DELTATIME 0 0001742000 ogee STARTSPEEDFACTOR n 0000000000 000 ID EDT 1 0000000000 ce ce ce ce e e ce ce e 4 I D eleme ra D m 25 sl al al 2 gt E m SI Fl n m m3 gt sof 9 m m s 81 Iv s ISPLITPOSTPROCFILE s ELI AME posterac dat NSTEPSWRITE Po MELELEH z Figure 6 4 The setup menu 67 68 Running an Analysis Chapter 7 Pre and Post processing The PREPROC command in the main menu leads to the pre processing menu shown in Fig ure 7 1 The POSTPROC command leads to the dialog box shown in Figure 7 2 where Multyx asks for the name of the post processing data file created in the analysis step When a valid name is entered the post processing menu shown in Figure 7 3 comes up The pre processing menu and the post processing menu are used to make drawings of the sys The CLEAR command clears the graphics screen The DRAWBODIES draws all the selected bodies using the current view settings The DRAWBODIES command does not clear the screen before it makes the drawing In the post processing menu the FIRST POSN PREVPOSN NEXTPOSN and LAST
3. 75 7 4 The NUMBER command 78 7 5 The TOOTHLOAD 78 7 6 The CONTACT 82 7 7 TOOTHLDHIST command 84 7 8 SUBSURFACE command 84 7 9 The GRIDLDHIST command 8T 1 10 The GRIDPRHIST command 2 9 EGRE 87 7 11 The SEPBEFHIST command 91 7 12 SEPAFTHIST command 91 7 13 The SEARCHSTRESS command 95 7 14 The POINTSTRESS command 95 7 15 The PATTERN command 101 1 46 The AUDIT command i Gace ee AREER EAA 102 7 17 The BODYDEFLECTION command 104 7 18 The BODYREACTION command 104 7 19 The BRGDEFORMN command 108 7 20 The BRGREACTION command 108 Pre and Post processing using IglassViewer 113 8 1 Generating an Iglass for preprocessing 113 MS MEDU x ccr 116 8 21 Finite element mesh 116 8 2 2 Cutting plane s s s aiya 9e RUE ee ee REESE 116 8 2 8 Selecting the time 116 8 2 4 Reference frames s esd ck sx 119 8 9 Th
4. Palette Mode POSITIVE 1 5 0334 004 1 2583e 004 3 3975e 003 8 4938 002 0 0000 000 Pick 3 2189e 003 _ Background Load 006645 Contact Pressure 2 2111 005 5 5277 004 1 4925 004 3 7312 003 0 0000e 000 Contact Pressure Scale 0 0 Figure 8 16 The iglass postprocessing attribute menu Attribute NONE Figure 8 17 The attribute switch Palette Mode POSITIVE 5 0334 004 1 2583 004 3 3975 003 8 4938 002 0 0000 000 3 2189 003 Figure 8 18 The palette switch 124 Pre and Post processing using IglassViewer Figure 8 19 Finite element mesh so as to find the stress at a nodal point E CE EET WI To tt mmmummi m Oton cole Contre Figure 8 20 The background color popup window switch 8 5 Features specific to iglass post processing 125 Contact Pressure 2 2111 005 5 527 7e 004 1 4925 004 3 7312 003 0 0000 000 Contact Pressure Scale Figure 8 21 The Contact pattern menu 126 Pre and Post processing using Iglass Viewer Chapter 9 Running a dynamic case Using the Planetary2D program for running dynamic cases is one of the most important appli cations of the Planetary2D analysis package Bearing reactions and H
5. 0 500 1000 1500 2000 2500 3000 3500 4000 Freq Hz Figure 9 10 Plot showing a narrow range of tangential component frequency response of pin ionl in the planetary system in the dynamic state transient response is in column no 2 of the PINIONIBRGRES DAT file 9 18 Applying the 2D Planetary program for modal analysis 151 3 5 2 5 Disp 1 5 0 700 800 900 1000 1100 1200 1300 1400 1500 1600 Freq Hz Figure 9 11 Plot showing the response near the second multiple of the mesh frequency for the tangential component of deformation of the pinionl bearing transient response is in column no 2 of the PINIONIBRGRES DAT file 152 Running a dynamic case Uy in Figure 9 12 Plot showing the mode shape at pinionl in the planetary system in the dynamic state at 574 05Hz 9 18 Applying the 2D Planetary program for modal analysis 153 x 10 Uy in 2 3 2 1 0 1 2 3 Figure 9 13 Plot showing the mode shape at the sun gear in the planetary system in the dynamic state at 574 05Hz 154 Running a dynamic case Appendix Tooth Mesh Templates The finite element meshes in the Planetary2D package are created with very little input from the user The user does not need to provide any of the node numbering and element connectivity information
6. 26 Pinion error Men ouo 24 6 x E Cy eee V 4 A SN EA 28 Pinion angular position menu 22 28 Pin positioB error Menus soes RU b OE Ro ONUS RT RECS 30 Pinion lumped parameters 33 Bearing menu parameters s ex 2 9 ox Romo ov Rd e deg 33 error Menus i05 so oo RR we we bee hd ba 4 6 37 Thickness errof Men sese e wx b Y 38 Parameters describing the tooth profile for pinion 41 Rayleigh damping parameters for 43 Linear tip modification parameters 47 Quadratic tip modification parameters 47 Tabular profile modification parameters 48 Rim data parameters s ss soe 9 es sor n SS eR 51 Spline data parameters x o oo obo robo 57 Carrier data parameters 222229 x 59 Common buttons in Iglass pre and postprocessing window 117 5 2256 ee dee 128 System level ddd dh seep bie ae Sa a 128 Pinion angular position data 128 Data describing the tooth profile for pinion 129 Quadratic tip modification data 129 Bearing menu parameters si d a Th i t le a RA S 129 Pinion Rim data asta __
7. 76 An example of a drawing made in the post processing mode using the exaggeration Commands ed ou ae 9 9 3 0 BH Oe REESE SG 4 77 The NUMBER menu ee sesa 544 78 Tooth numbering superimposed on a sun gear drawing using the NUMBER com MONG y saaa OSE Ee Ve ee Be eh ee So Se eS 79 The TOOTHLOAD menu 80 The toothload vs time graph generated by the TOOTHLOAD menu 81 The CONTACT mentse ues bee AAAS Y EC m e hee RB 82 The tooth contact pressure vs time graph generated by the CONTACT menu 83 The TOOTHLDHIST menu deae ee ee 84 The tooth load histogram generated by the TOOTHLDHIST menu 85 SUBSURFACE menu 2 86 The GRIDLDHIST menu 8T The gridload histogram generated by the GRIDLDHIST menu 88 The GRIDPRHIST menu o oses hrs 89 The gridload histogram generated by the GRIDPRHIST menu 90 The SEPBEEHIST menu x xr ORO RI 91 The histogram of grid separation before contact generated by the SEPBEFHIST d A xc e RC DR a 76 86 92 The SEPAFTHIST menus ee 93 The histogram of grid separation after contact generated by the SEPAFTHIST TH DUL ji te et
8. ee 137 9 17 1 Calculating the Dynamic load factor 141 Applying the 2D Planetary program for modal analysis 144 A Tooth Mesh Templates 155 vi CONTENTS List of Figures 11 The 2D planetary 2 2 1 The computer programs in the Planetary2D analysis package 6 2 2 The menu presented to the user by Guide 7 Aanulti body system vv be Peon 10 3 2 Reference frame degrees 11 3 3 The reference frames set up for a 2D planetary gear set shown at time t 0 12 3 4 Bearing connections in the multi body 13 3 0 Bearing T8668 4 ala RR RR GRRE S He 5 RU 13 3 6 Bearing deformation 0 2 14 Bearing reaction pos ook S vo boe do Queso EUR SE X 14 3 8 Ihe nain ment io sos s o on bono ee e 16 4 1 Planetary2D user 18 4 2 An integer data entry box les 19 4 3 An floating point data entry box 19 4 4 An boolean data entry box 19 4 5 An string data entry oo 2 2 19 4 6 switch type data entry box 20 5 1 The EDIT menu 2222 y RR RARO eee 23 5 2 The system data men sses
9. FIXED AHIDDENREMOVE ELEMENTS COLORS RESOLUTION 1 21 1 0 0000000000 000 Figure 7 5 The view menu in pre processing mode 7 2 View parameters EXIT QUIT WINDOW AUTOWINDOVV VIEWPORT XPROJECTION YPROJECTION ZPROJECTION ISOMETRIC LEFTROTATE 0000000 UPROTATE 0000000000000 000 DOWNROTATE 0000000000000 000 000000 0 0 COWROTATE 0 0000000000 00 00 Feo o 7 HIDDENREMOVE 2 OUTLINE 2 ELEMENTS 3 COLORS Ce RESOLUTION 1 E LOADS 8 6000000000000 0 0 CONTOURS Figure 7 6 The view menu post processing mode Pre and Post processing QUIT WINDOW AUTOWINDOW IEWPORT XPROJECTION YPROJECTION ZPROJECTION ISOMETRIC LEFTROTATE 10000 0 02 RIGHTROTATE 0 0 UPROTATE 000 DOWNROTATE pomo 000 00 CCwR TATE 0 0000000000 000 REFFRAME Feo o ES FIXED m HIDDENREMOVE v sl OUTLINE ELEMENTS s COLORS RESOLUTION LOADS LOADSCALE 6001000000 Contours Figure 7 7 The view menu in post processing mode with the LOADS option enabled 7 3 The DRAWBODIES command 75 7 3 The DRAWBODIES command After an appropriate view and objects have been selected the DRAWBODIES command in the pre and post processing menu
10. In multi body contact analysis the term body is used to refer to an object that is capable of rigid body motion and interacts with other bodies through surface contact and bearing connections There is a special body called the fixed body which refers to ground Figure 3 1 shows a typical multi body system In a 2D Planetary system the sun gear pinions and the ring gear are all treated as separate bodies The sun pinion and the pinion ring interaction is through contact The spider or the carrier supports the planet shafts The pinions revolve around the central axis while rotating along their own axes at the same time much like planets revolve around the sun The interaction between the carrier and the pinion shafts is also through contact 3 3 Reference frames Each of the bodies in the system has a reference frame to which it is rigidly attached The reference frame has 6 rigid body type degrees of freedom three translation components Uz Uy and U and three rotation components 9 0 and and 6 Figure 3 2 In addition to the body reference frames there is a special reference frame called the fixed reference frame that is considered as ground and does not move It is used as the reference for defining the locations of all other reference frames Figure 3 3 shows how the pinion sun ring and carrier reference frames are set up relative to the fixed reference frame for a 2D planetary gear set at time t 0 The fixed
11. QUTPUTTOFILE Iv 8 FILENAME output txt APPEND ME Figure 7 35 The BODYDEFLECTION menu 7 17 The BODYDEFLECTION command The BODYDEFLECTION command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 35 This menu is used to generate a graph of a component of the rigid body type motion of a body as a function of time as shown in Figure 7 36 The six components of motion that can be graphed are the translation motions uz uy and uz and the three rotation components and 0 These components are calculated in the reference frame attached to the body The rotation components are displayed in Radians 7 18 The BODYREACTION command The BODYREACTION command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 37 This menu is used to generate a graph of a component of the body frame reaction as a function of time as shown in Figure 7 38 The six force components that can be graphed are the three forces Fy Fy and the three moments and Mz These components are calculated in the reference frame attached to the body The moments are computed about origin of this reference frame 7 18 The BODYREACTION command 105 8 8 8 8 8 8 1 3 4 8 8 E 8 a 8 3 8 5 Y E 8 5 8 8 8 8 g 8 8 8 E 8 8 8 5 8 8 8 2 4 8
12. The SETUP command is used to set up an analysis The SEPTOL DSPROF and NPROF DIVS menu can be accessed through the SETUP panel The FEPROBES SURFGAGES and LOADSENSORS commands are used to control the data created by the analysis The POSTPROC command is used to graphically inspect the results of the analysis 16 Figure 3 8 The main menu Preliminaries 4 The Graphical User Interface Planetary2D s user interface is presented by Guide in graphical form as shown in Figure 4 1 Planetary2D sends out a stream of informational error and warning messages to the user These messages are separated by Guide and presented in separate windows as shown The user activates these message windows by hitting the appropriate Error Information or Warning tab Graphical information sent by PlanetaryZD is directed to a graphics window 4 1 Menu command items In the example shown in Figure 2 2 the large buttons such as those labeled EXIT QUIT OPTIONS LOADSESSION EDIT send commands to Planetary2D when hit by the user In response to the command Planetary2D might carry out an action as in the case of the LOAD SESSION command or lead the user to a different menu as in the case of the EDIT command Moving the mouse over a button without depressing it will cause Guide to momentarily pop up a balloon a tool tip containing a short description of the use of that button The tool tips can be disabled by
13. Vs Uy for the sun gear is shown in Figure 9 13 Using this graph you can predict the motion of the sun gear in the Planetary system in the dynamic state An example of a MATLAB program for plotting a graph of Uy Vs Uy for Pinionl is shown below Time Step Dt pi 2 of steps N 30 114 arrays containing t and X t for i 0 N 1 t it1 Dt i end Radial displacement Ux 3 367e 6 cos 2 pi 574 05 t 1 3418 Tangential displacement Uy 6 282e 6 cos 2 pi 574 05 t 1 8201 plot Ux Uy 146 Running a dynamic case 6 2 5 Disp 1 5 0 0 5 1 1 5 2 2 5 3 Freq Hz 4 Figure 9 6 Plot showing the radial component frequency response of pinionl the planetary system in the dynamic state transient response is in column no 2 of the PINIONIBRGRES DAT file Table 9 19 Displacement values in the radial direction for a critical frequency of 574 05 Hz for the pinions Body member Phase Pinion 7 6426 7 3 2792 6 3 367 6 1 3418 Pinion2 2 5407 6 2 5428 6 3 5946e 6 2 3558 Pinion3 5 0789 7 3 139e 6 3 1798e 6 1 7312 Pinion4 2 2697 6 2 6768 6 3 5095e 6 0 8675 Sun 1 2569 6 2 6292 6 2 9142e 6 1 1249 9 18 Applying the 2D Planetary program for modal analysis 147 x10 25 Disp in 0 5 4 A HER 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Freq Hz Figure 9 7 Plot sh
14. 0 0000000000e 000 4 4 0 1000000000 0 1323000000 14 5000000000 Figure 5 26 The Spline data menu 55 Building Model 56 VIGLOOU HLOOL 198590 ANITdS VIG2IHNNI 1145440 WTA OT ANI TdS HIONTISNIIdS HIMA WNA VIANA VIG3SILO0 mim 7 IHOIHH ANITdS Figure 5 27 Ring gear spline geometry 5 14 Ring data Table 5 15 Spline data parameters Item Description CONTACTTYPE ANGULARPLAY NSPLINES Switch Whether contact condi tions are enforced on both sides of the spline or just one side Float Amount of play deg al lowed to the ring gear due to clearance at the splines Integer Number of splines in the rim gear diameter EVENLYSPACED Boolean Whether splines are ANGLEFIRST NWIDTH NHEIGHT WIDTH HEIGHT PRESSANGLE evenly spaced Float Angular position of the first spline Integer Number of elements NWIDTH across the span as shown in Figure 5 27 Integer Number of elements NHEIGHT across the span as shown in Figure 5 27 Float Spline width Float Spline height Float Spline pressure angle 57 58 EXIT QUIT BEARING 2 E mb 0 0 T A 0 0000000000e 000 an IE 0 0000000000e 000 RIGID Iv 8 LUMPMASS 100 0000000000 ECE LUMPMOMINERTIA 1000 0000000000 noses LUMPALPHA 0 0000000000 000 Figure 5 28 The carrier menu 5
15. 8 contact at Ti Figure 7 27 The histogram of grid separation after contact generated by the SEPAFTHIST menu 7 13 The SEARCHSTRESS command 95 7 13 The SEARCHSTRESS command The SEARCHSTRESS command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 28 This menu is used to locate the most critical stresses in the system The COMPONENT box is used to select the stress component of interest Available choices are MAXPPLSTRESS the maximum principal normal stress 1 MINPPLSTRESS the min imum principal normal stress 53 MAXSHEAR the maximum shear stress and VON MISES the Von Mises octahedral shear stress Depending on selection in the XAXIS box the stress can be displayed as a function of time TIME profile SPROF face TFACE or depth DEPTH The stress values are computed over a range of time steps specified by BEGINSTEP and ENDSTEP teeth specified by TOOTHBEGIN and TOOTHEND location along the profile specified by SPROFBEGIN SPROFEND and NUMSPROF location along the face specified by TFACEBEGIN TFACEEND and NUMTFACE and depth specified by DEPTHBEGIN DEPTHEND and NUMDEPTH If the number of teeth defined by TOOTHBEGIN and TOOTHEND is 7 or less and if the SEPTEETH box is checked then a separate graph is drawn for each tooth Otherwise a single graph is drawn showing the most critical stress among all the teeth in the range File output is contr
16. 8 8 8 s 8 8 8 3 5 8 8 8 3 8 5 0 003000 Figure 7 36 The graph generated by the BODYDEFLECTION menu 106 Pre and Post processing COMPONENT BEGINSTEP 1 ENDSTEP SEL D bI Iv 8 FILENAME pape rrrr output tx Figure 7 37 The BODYREACTION menu 7 18 The BODYREACTION command 107 MZ Range 8 452300E 004 4 058760E 004 Peak to Peak 4 393540E 004 0 003000 0 004000 0 005000 0 006000 0 007000 0 008000 0 009000 0 010000 0 011000 0 002000 0 001000 0 000000 30000 000000 40000 000000 0000 000000 60000 000000 70000 000000 80000 000000 90000 000000 Figure 7 38 The graph generated by the BODYREACTION menu 108 Pre and Post processing BEARING PINIONTBRG x BEGINSTEP 1 ELELEE ENDSTEP 1 SEXE D P TET hd BUTPUTTOFILE v si FILENAME 00020200 APPEND Figure 7 39 The BRGDEFORMN menu 7 19 The BRGDEFORMN command The BRGDEFORMN command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 39 This menu is used to generate a graph of a component of the bearing deformation as a function of time as shown in Figure 7 40 The six components of motion that can be graphed are the 3 translation motions uz uy and uz and the three rotation components and 0 of bearing race 1 with respect to bearing race 2 The componen
17. 8 8 8 8 3 8 3 a 700 000000 600 000000 500 000000 400 000000 300 000000 200 000000 100 000000 0 000000 100 000000 Figure 7 42 The graph generated by the BRGREACTION menu 112 Post processing 8 Pre and Post processing using Iglass Viewer IglassViewer is a very powerful tool for pre and postprocessing gear models and results Sev eral features have been added to the Multyx program so as to enhance the compatability with IglassViewer Thus it can be considered as a program which enables the user to view pre and postprocessing files generated by an external code Note that the IglassViewer graphics window is independent of the guide graphics window The advantage of using IglassViewer over guide program for pre and postprocessing is that it is more faster efficient and more simple to operate Also you can visualise the models in their dynamic mode which is not possible using the Guide program Following sections gives a detailed explanation of the procedure for creating the pre and postprocessing iglass files and also the various functions associated with the iglass program 8 1 Generating an Iglass file for preprocessing The GENIGLASSFILE command in Figure 7 1 will lead to a menu shown in Figure 8 1 using which you can generate a preprocessing file for Iglass The filename is specified in the IGLASS FILENAME menu The time at which the user wan
18. ES E 52 zd zi Em Ex np ofm lt tv 11015 a a a n B E OUTPUTTOFILE FILENAME s 21 1 s 0 000000e 000 4 800000 001 1 0 000000 000 0 000000 000 0000000000 000 0 0000000000e 000 0000000000 000 Iv e output txt APPEND M e Figure 7 28 The SEARCHSTRESS menu 7 14 The POINTSTRESS command 0 006000 0 007000 0 008000 0 009000 0 005000 0 002000 0 003000 0 004000 0 001000 8 g 5 g Max Ppl no 0 000000 50000 000000 40000 000000 30000 000000 20000 000000 10000000000 0 000000 Figure 7 29 The graph of root stress vs time generated by the SEARCHSTRESS menu 97 processing Pre and Post 98 00000070 000000 0 000000 07 000000 01 0000000 BSS IL f TA VAANS 1 INOINId uo 000000 00001 00000070 000000700001 000000 0000 00000 0000 000000 0000 lt Figure 7 30 The graph of root stress vs profile generated by the SEARC
19. MEMBER PINION bs TOOTHBEGIN fi SEL D DP ET TOOTHEND 15 lt 1210120 BEGINSTEP Do g SIX DPI 5 ENDSTEP SIX DIST COLORS contours NN MINPRESS 40000 0000000000 MAXPRESS 420000 0000000000 LEECH DELTAPRESS 40000 0000000000 PELE SMOOTH Ll eT Figure 2 2 The menu presented to the user by Guide 2 2 Planetary2D Software Package Installation of the software package on windows plat form The procedure for installing the software analysis package on windows 95 98 NT platforms is as follows Get the self extracting file setup exe from Ansol Advanced numerical solutions either by email ftp or on a floppy If you are using an ftp client make sure that the setup exe file is downloaded when ftp is in binary mode Before installing anything make sure that there are no previous copies of guide exe multyx exe or calyx exe in your path If these files are present then you either have to move the old programs elsewhere or change the path so that they don t conflict with the new programs Now you are all set to install the software package Close all the other programs and run setup exe It will ask you questions about where to install the program and where to keep the working directory After you answer these questions it will display the Computer ID and ask for a licence key Copy the Computer ID and click the button skip or install key
20. QUIT START CLEAR SURFACEPAIR PINION1_SURFACE1_SUN_SURF MEMBER PINION1 TIMESTEP 5 D P TET Z HISTCOLOR BLACK AUTOSCALE 2 QUTPUTTOFILE Iv 8 FILENAME 0 output txt APPEND ME Figure 7 17 The TOOTHLDHIST menu 7 7 The TOOTHLDHIST command The TOOTHLDHIST command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 17 This menu is used to generate a histogram of tooth loads at the different teeth in the pinion or gear at a particular time step The SURFACEPAIR item selects the surface pair and the MEMBER parameter selects one of the two bodies in this pair The time step number is selected by the TIMESTEP item If the AUTOSCALE box is checked then the vertical scale is automatically computed Otherwise the user can specify a maximum load value to be used for scaling the vertical axis The color of the histogram is specified in the HISTCOLOR item An example of a tooth load histogram is shown in Figure 7 18 7 8 The SUBSURFACE command The SUBSURFACE command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 19 This menu is used to generate a graph of subsurface stresses vs depth under the most critical point in the contact zone at a given timestep The items TOOTHBEGIN and TOOTHEND are used to select a range of surface instances tooth numbers There can be at most 7 teeth in this range The items DEPTHBEGIN and DEPTHEND
21. but the accuracy of results computed by such almost singular stiffness matrices is questionable Our approach has been to attach a reference frame to each individual component and to carry out the finite element computations for each individual component separately in its own reference frame As long as each finite element mesh is sufficiently well constrained to its reference frame the stiffness matrices are well behaved The free mechanisms in the system can be modeled by allowing the reference frames to move freely The contact solver used is based the Revised Simplex Solver This Solver is commonly used to solve quadratic programming problems It can take into account any free mechanisms in the system while computing the contact loads System Kinematics The nominal position of each individual gear in the system changes with time The nominal positions of the components are determined by the kinematics of the system The kinematics of the system affects the nominal sliding velocities and inertial loads It is very difficult to include this kinematic information into the finite element programs currently available We have built a special purpose programming language into the software in order to specify the details of the kinematics of each component in the system Important details such as the kinematic effect of assembly errors runout and misalignments are easy to apply using this approach Large number of degrees of freedom For a system
22. 0 005000 0 004000 0 003000 HE 0002000 3 0 001000 B 2 z 2 B 5 0 000000 Tooth Load on 4000 000000 000 000000 2000 000000 1000 000000 0 000000 Figure 7 14 The toothload vs time graph generated by the TOOTHLOAD menu 81 82 SURFACEPAIR MEMBER TOOTHBEGIN Pre and Post processing PINION1_SURFACE1_SUN_SURF PINION 35 2 v T TOOTHEND 2 Hanana BEGINSTEP OS b bI ENDSTEP T SPROFBEGIN 00000000 SPROFEND 8000000 TFACEBEGIN 70000000 TFACEEND nomeo Iv 8 FILENAME PPEND 8 gt mp 5 ES fes m LE 5 output txt Figure 7 15 The CONTACT menu 7 6 The CONTACT command The CONTACT command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 15 This menu is used to generate a graph of contact pressure vs time The SURFACEPAIR item selects the contact surface pair for which the pressure is of interest Each surface pair has two contacting memb
23. 1 Tooth amp v Gear Rim 1 Sector Gear with rim Figure 8 9 Iglass preprocessing Bodies menu 120 Pre and Post processing using Iglass Viewer 8 4 Post processing using iglass The GENIGLASSFILE command in Figure 7 3 leads to the generate iglass file menu shown in Figure 8 10 post processing in iglass BEGINSTEP and ENDSTEP menus shown in Figure 8 10 define the range for which you want to check for results Note that these menus are independent of the GOTOPOSN menu shown in Figure 7 3 An example of an iglass post processing window is shown in Figure 8 11 R X 5 EXIT QUIT SELECT IGLASSFILENAME IGLASS DAT BEGINSTEP 1 amp ENDSTEP ELLEN z POPUPIGLASS START Figure 8 10 The generate iglass file menu for post processing 8 5 Features specific to iglass post processing The position switch shown in Figure 8 12 is used to run the simulation of the model in the post processing iglass window You can look at the simulation at a particular time step by dragging the slider along the scale The Defmn deformation slider shown in Figure 8 13 is used to view the deformed shaped of the gear bodies The Rigid and the F E Defl shows the rigid body deflection and the finite element deflection of the bodies The magnification scale of deformation can be adjusted using the slider The load slider shown in Figure 8 14 is used to look for the load patterns on a tooth over the
24. 4 The setup menu Figure 6 4 shows the analysis setup menu accessed by using the SETUP command at the main menu The parameters SEPTOL NPROFDIVS NFACEDIVS and DSPROF are the grid spec ification parameters The variable SEPTOL controls the maximum separation between mating surfaces Surfaces separated by more than this distance are not considered in the contact anal ysis NPROFDIVS parameter contols the number of contact cells that will be used to cover the contact zone between the gear teeth DSPROFSUN and DSPROFRING control the width of the contact zone in local surface units at the pinion sun and pinion ring interfaces respec tively The initial state of the system can be specified as the undeformed state by enabling the ZEROINITIAL flag The time at which to start the analysis is specified in the INITIALTIME box If the ZEROINITIAL flag is not checked then a restart file has to be specified from which the deformed state and the value of time will be loaded The analysis time is divided into a user specified number NRANGES of time ranges The time step DELTATIME solution method SOLMETHOD and the number of time steps NTIMESTEPS can be specified separately for each time range It is possible to control the operating speed in each time range by specifying a speed factor at the beginning of the range A speed factor of 1 0 implies that the system is at its nominal speed The speed factor at the end of a time range is the same as the speed factor at t
25. 9 5 9 6 The Pinion bearing data The RIGIDRACE box for the Pinion bearing is not checked that means the inner diameter of the Pinion is not rigid Table 9 6 gives the details of the Pinion bearing data menu 9 7 The Pinion Rim data Table 9 7 shows the data for the Pinion rim Table 9 6 Bearing menu parameters Item Description CIRCORDER 4 BRGFILE pinion brg 130 Running a dynamic case Table 9 7 Pinion Rim data Item Description MESHFILENAME pinionrim msh RIMDIA 3 0668 NRADIAL 2 NCIRCULAR 128 ELEMTYPE LINEAR CIRCORDER 4 Table 9 8 Data describing the tooth profile for sun gear Item Description NTEETH 27 DIAMPITCH 8 85 THICKNESS 0 176 HOBTIPRAD 0 04256 OUTERDIA 3 309 ROOTDIA 2 7775 INNERDIA 2 25 YOUNGSMOD 3 004e7 POISSON 0 3 DENSITY 7 112 4 ALPHA 4 79e2 BETA 1 4 7 MESHFILE sun msh TEMPLATE MEDIUM TPL 9 8 The Sun gear data Do not select the rim option for the Sun gear The values of LUMPMASS LUMPMOMINERTIA and LUMPALPHA are all 0 0 for this example Also we do not apply the spacing errors for the Sun gear in this problem The inner diameter of the Sun is assumed to behave like a rigid cylinder Also the Sun gear has a bearing Table 9 8 shows the Sun gear tooth data 9 9 The Sun tooth modification We apply the tabular profile modification on the sun gear tooth for this example problem The modification values are given in Table 9 9 9 10 The Ring gear data Select the SPLINEO
26. If TOOTHBEGIN is greater than TOOTHEND then the range wraps around the last tooth of the surface This means that if suppose the model has 27 teeth and you specify the TOOTHBEGIN parameter as 25 and the TOOTHEND parameter as 3 then it will select the range as 25 26 27 1 2 and 3 This range must contain 7 teeth or less BEGINSTEP and ENDSTEP are used to select a range of time steps for which results have been stored in the post processing file Figure 7 14 shows a graph of tooth load vs time generated by the TOOTHLOAD command The OUTPUTFILENAME item is used to write the tooth load data into an ASCII file The name of the ASCII file is entered into the item OUTPUTFILENAME If the APPEND box is checked and if this file already exists then the data is appended at the end of the file Otherwise a new file is created 7 5 The TOOTHLOAD command 79 M gt Se x 4 5 D 4 gt Figure 7 12 Tooth numbering superimposed on a sun gear drawing using the NUMBER com mand 80 Pre and Post processing EXIT QUIT START CLEAR SURFACEPAIR PINION1_SURFACE1_SUN_SURF v MEMBER PINION TOOTHBEGIN 665 IE DD TE BEGINSTEP a4 ELELEE ENDSTEP 11 2 FILENAM 7 APPEND 2 Figure 7 13 The TOOTHLOAD menu 7 5 The TOOTHLOAD command pe 0 006000
27. Multyx It also has post processing and data extraction code to help the user extract the results of analysis from Calyz Multyx and Calyx are designed as portable code and can run on any system that supports standard In order to keep it portable Multyx s menu system is command line based and does not use any of the GUI features such as buttons windows or mouse interaction The following dialog shows some of the command line interface of Multyz gt 1 MultyX v 1 06 Copyright Advanced Numerical Solutions Dec 21 2000 MultyX gt post ok patt MultyX PostProc 1 11 Pattern HELP MENU Show menu Show menu HELP Show menu EXIT Return to main menu QUIT Return to main menu START Draw the contact pattern CLEAR Clear the graphics page SURFACEPAIR Surface pair Currently PINION1_SURFACE1_SUN_SURFACE1_ MEMBER Member Currently PINION1 TOOTHBEGIN 20 Tooth no or instance no of surface TOOTHEND 2 Tooth no or instance no of surface 6 Planetary2D Software Package Windows 95 98 NT 2000 Server running any O S System User Graphical Mesh Generator Contact amp Finite User Interface amp Post Processing Element Analysis Figure 2 1 The computer programs in the Planetary2D analysis package BEGINSTEP 1 Time Roll angle step at which to begin search ENDSTEP 11 Time Roll angle step at which to end search COLORS Whether to render the model in color Enabled CONTOURS Whether to draw pressure cont
28. SIDE1 and SIDE2 as shown in Figures 5 10 and 5 11 Side Side 1 2 Figure 5 11 The tooth and side numbering scheme for the ring gear 36 Building a Model 5 6 Spacing error menu The SPACEERR command in Figure 5 8 leads to the Spacing error menu shown in Figure 5 12 The spacing error is an angular amount by which the two surfaces of individual tooth on the individual pinion can be rotated from their nominal positions This value is in radians and corresponds to a positive rotation of the tooth surface about the pinion z axis following the right hand rule SIDE1 and SIDE2 are the two sides of each tooth If you click any of these it will lead you to a separate submenu as shown in Figure 5 13 Table 5 7 explains the parameters in the Spacing error menu SIDE1 SIDE2 Figure 5 12 The Spacing error menu NPINIONS 4 ananas PINION 4 id 35 T a 1 T 0000000000 000 Figure 5 13 The Spacing error submenu 5 7 Thickness errors 37 Table 5 7 Spacing error menu Item Description NPINIONS Integer Number of pinions in the system PINION Integer Pinion number for which data presently is being displayed NTEETH Integer Number of teeth on the pinion TOOTH Integer The tooth number on the pinion SIDE1 Float Spacing error on SIDE1 of individual teeth of the pinion 5 7 Thickness errors The THICKERROR command in Figure 5 8 leads to the thickness error menu shown i
29. SSS Ge wee ws eee we 25 5 3 Sun and ring gear assembly errors 27 5 4 The pinion assembly 29 55 The Pinionrunout Men ae 4 99 9 30 5 6 Angposnpinion 30 5 7 Pinposn rror iment ce ok e 44 mare a 09 e 4m y EEE 31 5 8 The Pinion main ment uuo Rene RR Bono p EU eR d eod 32 5 9 The Bearing y Lidia eR RR RR OS 64 nant dea 34 5 10 The tooth and side numbering scheme for the pinion and sun gear 35 5 11 The tooth and side numbering scheme for the ring gear 35 5 12 The Spacing errormenu 2 0 36 5 13 The Spacing error submenu s x aesaad padda ma d oa elate ae aaie N 36 5 14 The Thickness error mien s s eoe a aa ER es 37 5 15 The tooth data menu for the pinion gear 39 5 16 Diameter definitions for an external gear 40 5 17 Frequency Response of aSDOF system 44 5 18 The tooth modification menu 2 2 46 5 19 Linear tip Gri 99 8 5 Bus 47 viii 5 20 5 21 5 22 5 23 5 24 5 25 5 26 5 27 5 28 7 11 7 12 7 13 7 14 7 15 7 16 7 17 7 18 7 19 7 20 7 21 7 22 7 23 7 24 7 25 7 26 7 27 7 28 7 29 7 30 7 31 7 32 7 33 LIST OF FIGUR
30. bearing race are inter related through a stiffness matrix The six degrees of freedom are the three translation degrees of freedom Uz Uy and U and three rotation degrees of freedom 0 and 0 The degrees of freedom represent the motion of race 1 relative to 2 The components are measured in the reference frame attached to race 2 as shown in Figure 3 6 The bearing may also generate internal reaction forces and moments The six components of bearing reaction Figure 3 7 consist of three forces Fy Fy and F and the three moments M and M Again these reactions are those exerted by race 1 on race 2 The components are computed in the reference frame of race 2 14 Preliminaries X2 RU Y2 m _ 2 Figure 3 6 Bearing deformation Figure 3 7 Bearing reaction 3 5 Contact solver contact modelling and grid specification 15 3 5 Contact solver contact modelling and grid specifica tion At each time step the unknown contact loads have to be determined by a Contact Algorithm Calyx poses the contact problem in the form of a quadratic programming problem and then uses the Revised simplex algorithm to efficiently solve the unknown loads The advantage of this technique is that convergence is excellent and there is a mathematical proof of convergence Calyx carries out a search over all possible combinations of instances of all specified surface pairings to determine which surface instanc
31. contact grid cells in the unloaded and undeformed state Figure 7 25 shows an example of a histogram of separation in the unloaded state Negative separation values are possible in this histogram 7 12 The SEPAFTHIST command The SEPAFTHIST command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 26 This menu is used to generate a histogram of the distribution of normal separation over individual contact grid cells in the loaded and deformed state Figure 7 27 shows an example of a histogram of separation in the loaded state These sepa ration values must be either zero or positive 92 Pre Post processing dth 35 7 500000E 004 Range 2 472058E 004 2 043032E 004 Each Div 1 000000E 004 To ontact at Tim Separation before c Figure 7 25 The histogram of grid separation before contact generated by the SEPBEFHIST menu 7 12 The SEPAFTHIST command EXIT QUIT START CLEAR Te PiNiON1 SURFACE1 SUN SURF v MEMBER TOOTHBEGIN TOOTHEND TIMESTEP DUTPUTTOFLE Figure 7 26 The SEPAFTHIST menu 93 94 Post processing 8 8 8 a 2 5 8 3 3 amp 8 8 E
32. does it read data from the new file Data is written to the session file through the SAVESESSION command Data can be loaded from an existing session file using the LOADSESSION command The QUIT command terminates the program without saving any data in the session file The EXIT command first writes data to the session file and then terminates the program All data entry occurs in a hierarchy of submenus accessed through the EDIT command on this main menu After data entry is completed the GENERATE command may be used to generate the model At this point a consistency check is carried out If any errors or inconsistencies are detected in the user s inputs then error messages are displayed and the model is not generated If the program detects something that it thinks is questionable but is still able to proceed then it displays warning messages but proceeds with generating the model The REPORT command is used to generate an ASCII file called report txt describing all the inputs the user has supplied to the program The PREPROC command allows the user to graphically inspect the latest model If the user has changed some parameters after the last GENERATE action then the PREPROC command detects this and calls the GENERATE command itself You can select the bodies for which you want to check for results in the SELECT menu in the PREPROC panel The selected bodies can be visualized in the graphics region by clicking on the DRAWBODIES button
33. due Bo a amp ae 94 SEARCHSTRESS menu 96 The graph of root stress vs time generated by the SEARCHSTRESS menu 97 The graph of root stress vs profile generated by the SEARCHSTRESS menu 98 POINTSTRESS menu 99 The graph of root stress vs time generated by the POINTSTRESS menu 100 he PATTERN menis bak be EE Mew a Bee ee a 101 LIST OF FIGURES ix 7 34 7 35 7 36 7 37 7 38 7 39 7 40 7 41 7 42 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 8 11 8 12 8 13 8 14 8 15 8 16 8 17 8 18 8 19 8 20 8 21 9 1 9 2 9 3 9 4 9 5 9 6 9 7 The AUDIT ment So a 2004 4 0445544 4449 44 S44 LEGG EH 103 The BODYDEFLECTION menu 104 The graph generated by the BODYDEFLECTION menu 105 The BODYREACTION menu 106 The graph generated by the BODYREACTION menu 107 BRGDEFORMN menu ee ee 108 The graph generated by the BRGDEFORMN menu 109 The BRGREACTION menu 110 The graph generated by the BRGREACTION menu 111 The generate Iglass menu 114 An example of Iglass preprocessing window 115 Iglass preprocessing view menu 116 Finite element mesh model
34. especially useful in pre and post processing of complicated models with a large number of internal gears The cutting plane can be selected along the ve and ve X and Z axes Using the button below the cutplane switch you can select the cutting plane at various points along the axis chosen by the cut plane switch option 8 2 3 Selecting the time step User can visualise the model at a particular timestep in iglass pre processing using the Position slider shown in Figure 8 6 Each position corresponds to the DELTATIME selected in the generate iglass file menu The corresponding time can be seen in the Time item shown in Figure 8 7 8 2 View menu Table 8 1 Common buttons in Iglass pre and postprocessing window Button l 9 Purpose Zoom In Zoom Out Move the model upwards If Spin is turned OFF Move the model downwards If Spin is turned OFF Move the model towards right If Spin is turned OFF Move the model towards left If Spin is turned OFF Rotate the model upwards If Spin is turned ON Rotate the model downwards If Spin is turned ON Rotate the model towards right If Spin is turned ON Rotate the model towards left If Spin is turned ON Rotate the model clockwise If Spin is turned ON Rotate the model counterclock wise If Spin is turned ON View the model in an isometric view View the model in the Y 7 plane View the model in the X 7 plane View the model in
35. frame is located with its origin coinciding with the center of the carrier The pinion sun ring and carrier 10 Preliminaries Figure 3 1 A multi body system reference frames have their origins at their centers of rotation At time t 0 the sun ring and carrier X Y axes are parallel to the corresponding axes of the fixed reference frame Manufacturing and assembly errors applied to the system might perturb the location of these reference frames slightly from their nominal location In their nominal location the origin of the sun and ring gears coincide with the origins of the fixed and carrier frames 3 3 Reference frames 11 Ux Thetay X 25 Theta Uz Figure 3 2 Reference frame degrees of freedom 12 Preliminaries o ORIGIN p PINION r RING s SUN Figure 3 3 The reference frames set up for a 2D planetary gear set shown at time t 0 3 4 Bearings 13 Bearing 1 Bearing 2 Ground Figure 3 4 Bearing connections in the multi body model Y Race 2 Figure 3 5 Bearing races 3 4 Bearings In a multi body system bodies can also interact through bearings Figure 3 4 Bearings are treated as a stiffness connection between two bearing races Figure 3 5 Each race has an attached reference frame The race is treated as a rigid body and the six degrees of freedom of the first bearing race and the six degrees of freedom of the second
36. frequency response function for a single degree of freedom system is as follows 1 ren E 1 r 46212 5 6 44 Building Model stati 1 Dynamic Factor X X A T 1 r 1 n r2 0 1 1 1 1 1 1 1 1 0 0 2 0 4 0 6 0 8 1 122 1 4 1 6 1 8 2 Normalized Frequency omega Figure 5 17 Frequency Response of a SDOF system where r Q u is ratio of the excitation frequency to the natural frequency and F K is the static deflection Figure 5 17 shows the frequency response of a sdof system At resonance the response is controlled purely by damping The width of the peak depends on the damping ratio The damping ratio can be estimated as follows Let r1 1 and r2 be the frequencies where the dynamic deflection level is less than the peak value by a factor of n that is z 2 Two estimates of the damping ratio is obtained as 1 LL 5 7 75 oat 2 8 2 5 8 24 n r2 The system damping ratio is is the average value of the above two estimates eO ae co e 2 5 9 2 Modal Damping Ratio Measurement The modal damping ratio based on viscous damping model at various system natural frequen cies is computed from the measured frequency response function driving point compliance The dynamic displacement response at dof k due to force at dof 7 is given as Tk Ui Uij Q B where the su
37. his support and encouragement Sandeep Vijayakar Hilliard OH Samir Abad Hilliard OH February 2003 1 Introduction Planetary gear systems yield several advantages over conventional parallel shaft gear systems They produce high speed reductions in compact spaces greater load sharing higher torque to weight ratio diminished bearing loads and reduced noise and vibration They are used in automobiles helicopters aircraft engines heavy machinery and a variety of other applications Despite their advantages noise induced by the vibration of planetary gear system remains a key concern In helicopter for example cabin noise exceeding 100db is directly traceable to the last stage planetary gear mounted to the cabin Dynamic response calculations of Planetary gears have received considerably less research attention than single mesh gear pairs The purpose of this work is to demonstrate the ap plication of Planetary2D program for static and dynamic problems The analytical technique used to design the software package combines a unique semi analytical finite element approach with detailed contact modeling at the tooth mesh This approach was specifically developed to examine the mechanics of precisely machined contacting elastic bodies such as gears The semi analytical finite element approach does not require a highly refined mesh at the contacting tooth surfaces This dramatically reduces the computational eff
38. in which the total number of gear teeth is about 200 the total number of finite element degrees of freedom can be extremely large This is so even with the finite element model refined only as much as is necessary for the far field solution The total number of finite element degrees of freedom is approximately proportional to the total number of teeth The amount of CPU time and memory needed to run a dynamic analysis with such a large degree of freedom would make it impractical We have resorted to using a hierarchical representation of the system in which the system is built from many substructures with each substructure in turn being composed of many substructures The processes of stiffness decomposition and load vector back substitution now become very complex and involve multiple recursive traversals of the substructure hierarchy However it is now possible to keep CPU requirements within practical limits Convergence of conditions at contact interfaces Poor convergence of contact conditions at interfaces is one of the biggest problems caused by using a general non linear solver to solve a problem with contact constraints The constraints imposed by the contact between mating surfaces are essentially linear inequality constraints When a general purpose non linear solver is used to solve this problem convergence is not guaranteed and if it does occur it is usually very slow The Revised Simplex solver that we use provides a guarantee of co
39. later It will proceed with the installation and will install 3 icons under Start Programs 2DPlanetary Analysis Send the Computer ID via email to support ansol com and we will send you the Licence Key If you forget to copy the Computer ID run the icon Start Programs 2DPlanetary Analysis Register and copy it again Click on the skip button After you receive the Licence Key from Ansol run Start Programs 2DPlanetary Anal ysis Register again and paste the Licence Key in the respective box Now click on the button Install Licence Key Now you are all set to run the analysis Start the program by using the icon Start Programs 2DPlanetary Analysis 2D Planetary Chapter 3 Preliminaries The previous chapter gave an overview of the software architecture This chapter provides some information to help you get up and running with the program 3 1 System of units Any system of units can be used provided that all the inputs provided by the user are in consistent with this system of units The user is free to choose any units for force time and length All the inputs should then be in units that are consistent with this choice For example if the user chooses Kgf as the unit for force seconds as the unit for time and cm as the unit for length then the input torque should be in Kgf cm the Youngs modulus in Kgf cm the Diametral pitch in 1 cm and the mass density in Kg f 5 cm Outputs will also appear in consistent units 3 2 Bodies
40. list as shown in Figure 4 6 4 7 Commonly occurring buttons The data entry dialog boxes use a few small buttons as short cuts for common tasks as shown in the Table 4 1 Some of these buttons may be disabled depending upon the particular item and its value Table 4 1 Common buttons Button Purpose s Select the minimum allowable value si Decrement the value by 1 wj Select the default value Increment the value by 1 gt Select the maximum allowable value el Accept the value just typed in xj Discard the value just typed in Get additional information 4 Change the current graphics page Q Q Q Change the zoom level lt Refresh the graphics page 4 8 Graphics 21 4 8 Graphics Guide directs the graphical output from Planetary2D to a graphics window The graphics are stored as separate pages A new page is started when Planetary2D clears the graphics screen The user can move between screens using the 4 buttons on the toolbar Double clicking anywhere in the graphics window with the left mouse button or dragging the mouse in the graphics window with the left button depressed lets you zoom in To zoom out double click with the right mouse button The buttons on the toolbar can also be used to zoom in zoom out and to return to the original view By default the graphics are refreshed automatically when necessary However this behaviour can be undesirable if the graphi
41. range of time step selected in the BEGINSTEP and ENDSTEP menus The magnification scale of loading can be adjusted using the slider The directions of the bearing forces and moments can be visualised using the Brg Fre and Brg Mom sliders shown in Figure 8 15 The magnification scale of the forces and the moments can be adjusted using the respective sliders The Attribs menu is shown in Figure 8 16 The attribute menu shown in Figure 8 17 is used to check for contours for different component of results The available options are DISPLVEC TOR MAXPPLNORMAL S2PPLNORMAL MINPPLNORMAL MAXSHEAR VONMISES and ERRORESTIMATE The DISPLVECTOR will pop up a component switch using which the contour for displacement vector in the X Y and Z directions can be displayed MAXP PLNORMAL S2PPLNORMAL MINPPLNORMAL MAXSHEAR VONMISES menus show their respective stress contours The ERRORESTIMATE menu is used to display the stress error estimate This error estimate is computed from the magnitude of the inter element stress discontinuity 8 5 Features specific to iglass post processing 121 IGLASS DAT 1 xl View Bodies Attribute MAXPPLNORMAL Palette Mode POSITIVE 1 2972 005 3 2430 004 8 75 2 003 2 1890e 003 0 0000 000 0 0000e 000 Load Pn Contact Pressure 6 4956 005 1 6239 005 4 3845 004 1 0961 004 0 0000 00
42. the View DisableToolTips item in the Guide main menu 18 The Graphical User Interface Guide 2Dplanetary Figure 4 1 Planetary2D user interface 4 2 Integer menu items 19 4 2 Integer menu items RESOLUTION 1 0101211 Figure 4 2 An integer data entry box Integer data items are entered through a dialog box of the kind shown in Figure 4 2 The current value appears in a box in the dialog box If the value of the data item is undefined then the box appears blank 4 3 Floating point menu items EXAGGERATION 0 000000 000 EEE Figure 4 3 An floating point data entry box Floating point data is entered through the dialog box shown in Figure 4 3 4 4 Boolean menu items HIDDENREMOVE s Figure 4 4 An boolean data entry box Boolean data items are those that can only take a YES NO or TRUE FALSE type of value Their value is set by checking or clearing the box as shown in Figure 4 4 4 5 String menu items SESFILENAME meses 022020 Figure 4 5 An string data entry box String data items contain ASCII strings The dialog box shown in Figure 4 5 allows the user to enter string type data 20 The Graphical User Interface 4 6 Switch type menu items BACKCOLOR GT Figure 4 6 An switch type data entry box The last kind of data item is of the switch type This item can be switched between a fixed set of valid choices The choice is made through a drop down
43. 0 Contact Pressure Scale a Figure 8 11 An example of an iglass post processing window The colors for minimum and maximum stress contours can be controlled using the palette mode menu shown in Figure 8 18 A POSITIVE mode will align the scale from 0 minimum stress to a maximum positive value maximum stress A NEGATIVE mode will align the scale from 0 to a negative value The BOTH type mode will align the scale from the maximum negative value minimum stress to a maximum positive value maximum stress So as to find the stress at a node double click on the gear body The finite element nodes are now visible as shown in figure 8 19 Clicking once on the node will show the stress at that nodal point in the pick item of the Palette menu Double clicking on the Background button will popup the Color window shown in Fig ure 8 20 using which you can change the background color of the iglass graphics window The Contact pattern menu shown in Figure 8 21 is used to view the contact pressure pattern on the contacting surfaces The EXIT button will take you out of the iglass post processing window 122 Pre and Post processing using IglassViewer E Figure 8 12 The position slider Figure 8 13 The deformation slider Figure 8 14 The load slider Figure 8 15 The bearing forces and moments sliders 8 5 Features specific to iglass post processing 123 View Bodies Attribs
44. 00 Figure 5 24 The Sun bearing menu 53 54 Building a Model QUIT TOOTH SPACEERR RIMDATA SPLINEDATA SPLINEOPTION 2 RIMOPTION Iv 2 CIRCORDER 2 y Figure 5 25 The Ring data menu 5 14 Ring data The RING command in the EDIT menu Figure 5 1 leads to the ring data menu shown in Figure 5 25 If the SPLINEOPTION is checked SPLINEDATA comand will show up in the ring menu Figure 5 25 Ring gear splines will be modeled if you check this option These splines are on the outer diameter on the ring gear Click on the SPLINEDATA button to access its menu Figure 5 26 Table 5 15 explains the parameters in the SPLINEDATA menu If you do not select the SPLINEOPTION then a menu called RIGIDOUTERDIA pops up If you check this option then the rim outer diameter is modeled as a rigid body If the RIMOPTION is selected then a separate finite element model will be generated between the rim diameter of the ring gear and the outer diameter RIMDATA pops up if the RIMOPTION box is checked Click on the RIMDATA command Figure 5 25 to access the rim data menu The ring rim parameters are similar to the pinion rim parameters The TOOTH menu and the SPACEERR menu for the Ring data are similar to those in the PINION menu 5 14 Ring data EXIT QUIT CONTACTTYPE ANGULARPLAY LEH NSPLINES 4 lt gt ET DOUBLESIDED 0 0740000000 50 EVENLYSPACED PRESSANGLE IL D ET jv 2
45. 000000000 1 4000000000e 007 gt pinion msh m n 22 aa MEDIUM TPL ES mE m Figure 5 15 The tooth data menu for the pinion gear 5 8 Modelling the tooth profile The TOOTH command in Figure 5 8 leads to the tooth data menu shown in Figure 5 15 Ta ble 5 9 describes the parameters required for modelling the pinion tooth In this table C M and K are the damping mass and stiffness matrices Figure 5 16 shows the details of the various diameters definitions for an external gear The Mesh file contains element connectivity and geometry information This file is created by the program The complete path of the file should be entered if the file is not to be created in the current directory The file extension should also be provided The Template file contains element connectivity information The complete path of the file should be entered if the file is not in the current directory The file extension should also be provided There are several pre built template files The element numbering used in the pre built template files is described in Appendix A Medium tpl Figure A 1 is the most commonly used template file for mesh generation Very good stress predictions in the root region are obtained 40 Diameter Figure 5 16 Diameter definitions for an external gear Building a Model 5 8 Modelli
46. 004 Ran Load at T Pre and Post processing poth 1 oth 35 To Figure 7 21 The gridload histogram generated by the GRIDLDHIST menu 7 10 The GRIDPRHIST command CLEAR SURFACEPAIR PINION1 SURFACE1 SUN SURF MEMBER PINION TOOTHBEGIN 05 IX DP TTE TOOTHEND 1 TIMESTEP OUTPUTTOFILE Iv 2 AID output txt APPEND 2 Figure 7 22 The GRIDPRHIST menu 89 90 0 000000E 000 2 969799E 005 Each Div 1 000000E 005 me 7 500000E 004 Range Contact Pressure at Ti Pre and Post processing ooth 1 oth 35 To Figure 7 23 The gridload histogram generated by the GRIDPRHIST menu 7 11 The SEPBEFHIST command 91 SURFACEPAIR PINION1 SURFACE SUN SURF v MEMBER PINION TOOTHBEGIN SI DP TIST TOOTHEND 4 IE gt bp pL TIMESTEP SEL D bp i OUTPUTTOFILE Iv 2 FILENAME oun tit APPEND Figure 7 24 The SEPBEFHIST menu 7 11 The SEPBEFHIST command The SEPBEFHIST command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 24 This menu is used to generate a histogram of the distribution of normal separation over individual
47. 130 Data describing the tooth profile for sun gear 130 Tabular profile modification data for the Sun gear tooth 131 Data describing the tooth profile for Ring gear 131 Tabular profile modification data for the Ring gear tooth 132 Spline data for the Ring gear 132 Rim data parameters for the ring 133 Cartier data onie nee bb Seed da Gere ae GR 9S RAO EY 133 Setup MENU i ERS RE 4 136 Surface gage data for extracting the plot shown in Figure9 1 138 Load sensor data for extracting the plot shown in Figure 94 142 Tooth load data for extracting the plot shown in Figure 9 5 142 xii LIST OF TABLES 9 19 Displacement values in the radial direction for a critical frequency of 574 05 Hz lor tbe PIMOS 4 3 4 woe E de dos eg 146 9 20 Displacement values in the tangential direction for a critical frequency of 574 05 Hz for the pitons 30 9 20H33 Pp d ses dram cece 147 Preface The Planetary2D computer program has been under development for many years and is finally available for use by the gearing community We have received active support and encouragement from many people We would especially like to thank Timothy Krantz of the Army Research Laboratory at the NASA Glenn Research Center for
48. 15 Carrier data The CARRIER command in the EDIT menu Figure 5 1 leads to the CARRIER menu shown in Figure 5 28 Table 5 16 explains the terms associated with the CARRIER menu If you set the RIGID box in the Carrier menu then the Carrier is modeled as a rigid body otherwise it will be modeled using a stiffness matrix If you set the BEARING flag in the Carrier menu then the Carrier has a bearing and a bearing file name has to be provided Otherwise the Carrier can be made to float or can be constrained Building a Model 5 15 Carrier data Table 5 16 Carrier data parameters Item Description BEARING BRGFILE CONSTRAINT RIGID STFFILE LUMPMASS Boolean Whether the carrier has a bearing String Bearing file name if car rier has a bearing Switch Whether the carrier is floating or is fixed Boolean Whether the carrier is modeled as a rigid body String Stiffness file name for the carrier Float Additional lump mass at carrier center LUMPMOMINERTIA Float Lumped polar moment of LUMPALPHA inertia Jz at the carrier center Float Damping constant alpha for the lumped mass 59 60 Building a Model 6 Running an Analysis The analysis is started by using STARTANAL command of Figure 3 8 Before starting an analysis sensor locations have to be set up to measure stress and loads in the model This is done through the SURFGAGES FEPROBES and LOADSENSORS com mands in the main menu Fig
49. 4 916252665 01 0 0 15046 945761 0 0 15046 945761 62 36947675 4 787355666 01 0 0 01 0 0 01 0 0 01 Total mass damping force UE Total contact force Uf Total bearing force Total reaction force tf mo 0 0 16200 m 0 0 16200 5 613287613 013 1 296740493 013 01 0 0 3 637978807 0121 0 0 3 637978807 0121 Residual force error 7 16 The AUDIT command 103 EXIT QUIT START CLEAR SELECT BEGINSTEP 1 OE Ea oe ENDSTEP 11 I PST H z OUTPUTTOFILE 8 FILENAME APPEND Figure 7 34 The AUDIT menu The forces and moments are broken down into contact forces bearing forces internal forces mass and damping forces and reaction forces The reaction forces are the forces exerted by the reference frame constraints Two values for the moments are displayed In the above example mo refers to the moments computed about the origin of the sun gear m stands for the moment computed about the origin of the fixed reference frame The moments about the fixed reference frame are more useful in comparing the action and reaction acting on different bodies Regardless of the origin about which the moments are computed the X Y and Z components of each force and moment always refer to the fixed reference frame 104 and Post processing EXIT QUIT START CLEAR BODY m SUN COMPONENT THETAZ M BEGINSTEP fi LLELLE ENDSTEP 11 5 sI I D T3 T3
50. 9 11 The Ring gear tooth modification The tabular profile modification is applied on the ring tooth for this problem The values are given in the Table 9 11 9 12 The Spline data for the Ring gear For this example problem we have evenly spaced the splines over the circumference of the Ring gear Table 9 12 shows the spline data for the ring gear 9 13 The Ring gear rim data Table 9 13 shows the Ring gear rim data 9 14 The Carrier data The carrier for this problem is modeled as a rigid body and it has a bearing Bearing file name is provided in the BRGFILE box The data related to the carrier menu is shown in the Table 9 14 9 14 The Carrier data 133 Table 9 13 Rim data parameters for the ring gear Item Description MESHFILENAME RIMDIA NRADIAL NCIRCULAR CIRCORDER ringrim msh 11 675 2 256 32 Table 9 14 Carrier data Item Description BRGFILE LUMPMASS LUMPMOMINERTIA LUMPALPHA carrier brg 100 134 Running a dynamic case 9 15 Calculating the time step for dynamic problems Let ws Angular speed of the Sun gear in rad sec Angular speed of the Carrier in rad sec Angular speed of the Pinion gear in rad sec Angular speed of the Ring gear in rad sec RPM Speed of the sun gear in RPM RPM Speed of the carrier in RPM RPM Speed of the pinion in RPM Speed of the ring gear in RPM Ns Number of teeth on the sun gear Number of teeth on the pinion gear
51. EEE MAXPRESS 0 000000 000 5151218 22 DELTAPRESS 0 000000 000 EEEE aid SMOOTH Iv 2 IGRID sl Iv 2 FILENAME t output tx APPEND 2 Figure 7 33 The PATTERN menu 7 15 The PATTERN command The PATTERN command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 33 This menu is used to create a drawing of the contact pattern on a tooth The surface is selected by specifying the body in the BODY box and a surface in the SUR FACE box A range of teeth with up to 7 teeth is selected through the TOOTHBEGIN and TOOTHEND items The range of time steps is specified by the BEGINSTEP and ENDSTEP items The contact pattern can be displayed in color if the COLORS box is checked or with contour lines if the CONTOURS box is checked contact pattern cannot be generated for a Planetary2D gear set since it does not have any thickness The contact pattern drawing is not three dimensional It is a projection of the contact surface in the r z coordinate plane If the SMOOTH box is checked then the contact pressures will be smoothed by fitting a polynomial surface to the raw data 102 Pre and Post processing 7 16 The AUDIT command Frequently the user needs to obtain the force and moment balance for the individual bodies in the system The AUDIT command of the post processing menu Figure 7 3 generates an equilibrim audit of all the for
52. ES Quadratic tip 48 Tabular tip modification ssi lt s aa d ie dee 49 The menu for specifying rim data for pinion 50 The SUN test 254 454 Rare 52 Sun bearing menu i499 woe RA PEOR OO Roe Rok oy RR P y Ro 53 The Ring data gqnenu 432933 game eee ee 54 Th Spline data menus q qna 642 0999939499995 55 Ring gear spline 56 The carrier menu o 244465 Ru om ded su 58 Theistrface gage Ment eee vv ORES Sa o GE 63 The finite element probe menu 64 The load sensor mieni 6 44 WRK Sq 65 Thesetup ment Pep ee SO Noe Goad 67 The pre processing menu 69 The post processing file name dialog box 70 The post processing 70 The body selection mMenu osa ace Eun aa 5845 71 The view menu in pre processing 72 The view menu in post processing 73 The view menu in post processing mode with the LOADS option enabled 74 An example of a drawing made in the post processing mode 75 An example of a drawing made in the post processing mode
53. HSTRESS menu 7 14 The POINTSTRESS command BODY SUN 2 SURFACE SURFACE1 hz TOOTHBEGIN 27 5201219 TOOTHEND 2 lt 800000e 001 E 0 0000000000 000 REFDIRECTION semF 21 0 0000000000e 000 OUTPUTTOFILE Iv 3 FILENAME APPEND M il Figure 7 31 The POINTSTRESS menu 99 100 Post processing E E a FE gt LoT rl p E cH 8 Ber eI 8 8 E m 1 LP 8 C LL I TT HL g g 8 E 5 5 y Figure 7 32 The graph of root stress vs time generated by the POINTSTRESS menu 7 15 The PATTERN command 101 SURFACEPAIR PINION1 SURFACET SUN SURF MEMBER PINION TOOTHBEGIN OSG P EET TOOTHEND 5 ED D b DI fi BEGINSTEP 1 ENDSTEP OE 2 oes COLORS 2 CONTOURS 2 MINPRESS 0 000000 000 E
54. NOUTSUN Float Orientation angle Deg high point of runout error for Sun MAGAXISERRRING Float Magnitude of Ring axis er ror ANGAXISERRRING Float Orientation angle Deg of the axis error for Ring MAGRUNOUTRING Float Magnitude of high point of runout error for Ring ANGRUNOUTRING Float Orientation angle Deg high point of runout error for Ring BACKSIDECONTACT Boolean Check for back side con tact 5 1 System level data 27 SUN RING PITCH CIRCLE OF SUN OR CIRCLE ANGRUNOUTSUN RING MAGRUNOUTSUN RING CENTER OF SUN OR RING BEARING MAGAXISERRSUN RING ANGAXISERRSUN RING CENTER CARRIER Figure 5 3 Sun and ring gear assembly errors 28 Building Model Table 5 2 Pinion runout error menu Item Description NUMPINIONS Integer Number of pinions in the system PINIONNO Integer Pinion number for which data presently is being displayed MAGNITUDE Float Magnitude of high point of runout error for individual pin ions ANGLE Float Orientation Angle Deg of the high point of runout error for individual pinions Table 5 3 Pinion angular position menu Item Description NUMPINIONS Integer Number of pinions in the system PINIONNO Integer Pinion number for which data presently is being displayed ANGPOSNPINION Float Nominal Angle Deg po sition for the pinion 5 2 System sub menus There are three submenus in the SYSTEM panel PINIONRUNOUT Fi
55. Ng Number of teeth on the ring gear Time Step Teycle Tooth Cycle time Nsteps number of steps per tooth cycle The following relationships are used to determine the time step required for dynamic cases Ws wp We wn We NR 27 2m 2T Teycle 1 ws Wp wc NR 60 60 60 Teycle RPM steps 9 16 The setup menu 135 9 16 The setup menu For the example problem we assume that the system is starting from an undeformed state The analysis is divided in to 3 ranges The purpose of using 3 ranges is to minimize initial transients The first range is the Static range when the input speed is 0 00 The second range is dynamic when the input speed increases from 0 r p m to 1623 r p m The ramping from minimum speed to maximum speed is controlled by the STARTSPEEDFACTOR parameter The STARTSPEED FACTOR for range 1 and range 2 is 0 0 The third step is again dynamic when the input member Sun gear for this example maintains a constant speed of 1623rpm The STARTSPEEDFAC TOR for range 3 is 1 00 The solution method for the Static range is STATIC and that for the dynamic ranges we use the NEWMARK method For this problem we run the analysis for about 3000 steps steps for range 3000 For so many steps normally the
56. POSN commands allow the user to move from one time step saved in the post processing file to another Entering a position number directly tem and its components in the GOTOPOSN box takes the user directly to that time step EXIT CLEAR SELECT VIEW DRAW BODIES NUMBER GENIGLASSFILE Figure 7 1 The pre processing menu 70 Pre and Post processing postproc dat Figure 7 2 The post processing file name dialog box Figure 7 3 The post processing menu 7 1 Selecting bodies 71 7 1 Selecting bodies The object selection menu which appears when the SELECT command is invoked from the pre and post processing menus is shown in Figure 7 4 The objects that should be drawn are selected from this menu PrePro Oh EXIT QUIT SUN Iv 2 CARRIER Iv 2 RING Iv 2 HOUSING BB 10 BY PINION PINION Iv 2 PINION Figure 7 4 The body selection menu 7 2 View parameters The VIEW menu controls the appearance of the drawings In the pre processing view menu shown in Figure 7 5 the user can enter any value of time into the TIME box The next drawing will show the system as it would appear at this instant of time The resolution level controls the degree of detail with which the drawing is made The ELEMENTS checkbox controls whether or not the individual finite elements should be drawn The COLORS option controls whether or not the bodies will be filled with
57. PTION splines will be modeled and the RIMOPTION separate finite element model will be generated between the Rim dia of the Ring gear and the Outer dia Select the default value 32 for the CIRCORDER item We do not apply any Spacing errors for the ring gear tooth in this example problem Table 9 10 shows the ring gear tooth data 9 10 The Ring gear data 131 Table 9 9 Tabular profile modification data for the Sun gear tooth Item Description NROLLS ROLLNO ROLLANGLE MAGNITUDE ROLLNO ROLLANGLE MAGNITUDE ROLLNO ROLLANGLE MAGNITUDE ROLLNO ROLLANGLE MAGNITUDE Table 9 10 Data describing the tooth profile for Ring gear Item Description NTEETH 99 DIAMPITCH 9 1428 PRESSANGLE 20 19 THICKNESS 0 123 FILLETRAD 5 8 2 MINORDIA 10 69 ROOTDIA 11 18 OUTERDIA 11 85 YOUNGSMOD 3 004e7 POISSON 0 3 DENSITY 7 112 4 ALPHA 4 79e2 BETA 1 4e 7 MESHFILE ring msh TEMPLATE MEDIUM TPL 182 Running a dynamic case Table 9 11 Tabular profile modification data for the Ring gear tooth Item Description NROLLS 3 ROLLNO 1 ROLLANGLE 20 63 MAGNITUDE 0 00 ROLLNO 2 ROLLANGLE 19 16 MAGNITUDE 8 4 ROLLNO 3 ROLLANGLE 18 84 MAGNITUDE 1 05 3 Table 9 12 Spline data for the Ring gear Item Description CONTACTTYPE DOUBLESIDED ANGULARPLAY 7 4 2 NSPLINES 50 ANGLEFIRST 0 0 ELEMTYPE LINEAR NWIDTH 4 NHEIGHT 4 WIDTH 0 1 HEIGHT 0 1323 PRESSANGLE 14 5
58. Planetary2D User s Manual Advanced Numerical Solutions Hilliard OH April 25 2006 Contents Preface 1 Introduction 2 Planetary2D Software Package 2 1 Planetary2D analysis package 2 2 Installation of the software package on windows platform Preliminaries dSystenbof UMS DS de ULL x 0 2 I BOGIGS coss e vete rer RR SE Bo a ane RU UR TRAN UU BL 9 9 Reference frames 2225 2 2 4 RUE SUR 3 4 Bearings it cu ee ub dob SAS d AG 3 5 Contact solver contact modelling and grid specification 2 0 Mente RUE The Graphical User Interface 4 l Menu command items TRU RU S 4 2 Integer menu items 3 5 m9 kokoes o3 a 3 08 3 3 4 3 Floating point menu 4 4 Boolean menu items soro ee bade ee ee x RR RR X Strine MenW GEMS ae DU SE 4 6 Switch type menu items AT Commonly occurring buttons s s siara a 4 8 24 4 a8 ae da a hehe RR ewe eo ee 4 Building a Model 5 1 system level data 53km bb OE p RO ae Ee x 5 2 System sub menus 5 3 Pinion data 0 4 Bearings excl
59. R PINION1 TOOTHBEGIN I p TIMESTEP 11 E ide biel FILENAME 0000200 APPEND Oa Figure 7 20 GRIDLDHIST menu 7 9 The GRIDLDHIST command The GRIDLDHIST command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 20 This menu is used to generate a histogram of the distribution of contact load over individual contact grid cells This figure is useful in determining whether the contact grid cell has been properly sized and whether it has adequate resolution The SURFACEPAIR item selects the surface pair and the MEMBER parameter selects one of the two bodies in this pair The items TOOTHBEGIN and TOOTHEND are used to select a range of surface instances tooth numbers There can be at most 7 teeth in this range The item TIMESTEP selects a time step number Figure 7 21 shows an example of a grid load histogram 7 10 The GRIDPRHIST command The GRIDPRHIST command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 22 This menu is used to generate a histogram of the distribution of contact pressure over individual contact grid cells This command is very similar to the GRIDLDHIST command The only difference is that it uses contact pressure instead of contact load Figure 7 23 shows an example of a grid pressure histogram 88 ige 0 000000E 000 3 836496E 002 Each Div 1 000000E 002 ime 7 500000E
60. RFACEPAIR PINIONI SURFACEI SUN SURFACEI MEMBER SUN TOOTHBEGIN 1 TOOTHEND 1 BEGINSTEP ENDSTEP 11 9 17 Analysis and Results 143 2 909233E 003 Tooth 1 of SUN at time 5 421010E 020 0 000200 0 000000 0 000200 0 000400 0 000600 0 000800 0 001000 0 001200 0 000400 on surface pair PINIONI_SURFACE1_SUN_SURFACE1 0 000600 Tooth Load 0 000800 2910 000000 900 000000 2880 000000 2870 000000 2860 000000 850 000000 Figure 9 5 Graph showing the static tooth load against time using the TOOTHLOAD command 144 Running a dynamic case 9 18 Applying the 2D Planetary program for modal anal ysis Following is the detailed procedure which demonstrates the application of the Planetary2D pro gram for calculating the modes for the pinion Use the PINIONnBRGRES DAT files for data analysis related to the pinions The Uy com ponent column no 2 gives the radial displacement and the component column no 3 gives the tangential displacement You can either use excel or MATLAB to calculate the fourier transform fft of or Uy values This gives us the frequency response of the pinion If X t X to i 1 At i 1 is the time domain response of a particular component of a system then the fft of X will yield X X f X i where Af 1 N At Half of these points lie below the Nyquist frequency NAf 2 and half lie above The frequency response data f for i gt N 2 are usually d
61. S LUMPMOMINERTIA and LUMPALPHA are all 0 0 Table 9 4 shows the data related to the Pinion tooth We have not applied any Spacing errors for the pinion 128 Table 9 1 Physical units English Physical quantity Running a dynamic case Metric Engg units LENGTH in mm TIME secs secs ANGLE deg or rad deg or rad MASS Ibf s in kg MOMENT OF INERTIA Ibf s in kg mm STIFFNESS Ibf in N mm SPEED RPM RPM TORQUE Ibf in N mm YOUNGS MODULUS Ibf in N mm DENSITY Ibf s in kg mm LOAD Ibf N STRESSES psi N mm Table 9 2 System level data Item Description NUMPINIONS 4 CENTERDIST 3 5 INPUT SUN TORQUEINPUT 1 62e4 RPMINPUT 1 623e3 RPMRING 0 0 Table 9 3 Pinion angular position data Item Description NUMPINIONS PINIONNO ANGPOSNPINION 9 5 The Pinion tooth modification 129 Table 9 4 Data describing the tooth profile for pinion Item Description NTEETH 35 DIAMPITCH 8 85 THICKNESS 0 163 HOBTIPRAD 0 018 OUTERDIA 4 13 ROOTDIA 3 60 INNERDIA 2 90 YOUNGSMOD 3 004e7 POISSON 0 3 DENSITY 7 112e 4 ALPHA 4 79e2 BETA 1 4e 7 MESHFILE pinion msh TEMPLATE MEDIUM TPL Table 9 5 Quadratic tip modification data Item Description ROLLQUADTIPMOD 12 MAGQUADTIPMOD 1 00e 4 9 5 The Pinion tooth modification We apply the Quadratic Tip Modification on the Pinion tooth for this example problem The modification values are given in the Table
62. an double 5 1 System level data QUIT PINIONRUNOUT PINPOSNERROR NUMPINIONS P TET ANGPOSNPINION CENTERDIST 3 5000000000 INPUT SUN TORQUEINPUT fs200 0000000000 T 1623000000000 00 0000000000000 0 0 0 0000000000 000 0 0000000000000 ANGAXISERRSUN 000 MAGRUNDUTSUN 0000 ANGRUNDUTSUN 000 MAGAXISERARING 0 0000000000e 000 00 2 ANGAXISERRRING MAGRUNDUTRING 00020 ANGRUNDUTRING 10 BACKSIDECONTACT Eze 2 2 2 oles Hele gt nH ja Slats 12116 a e Figure 5 2 The system data menu 25 Building a Model Table 5 1 System configuration parameters Item Description NUMPINIONS Integer Number of pinions in the system CENTERDIST Float The operating center dis tance INPUT Switch Which body is the power input choices available are SUN CARRIER and RING TORQUEINPUT Float The torque at the input member RPMINPUT Float Input speed in RPM RPMRING Float The speed of the Ring in RPM If INPUT RING RPMCARRIER Float The speed of the Carrier in RPM If INPUT RING MU Float The coefficient of Coulomb friction MAGAXISERRSUN Float Magnitude of Sun axis er ror ANGAXISERRSUN Float Orientation angle Deg of the axis error for Sun MAGRUNOUTSUN Float Magnitude of high point of runout error for Sun ANGRU
63. as the body then there are only two surfaces SPLINESURF1 and SPLINESURF2 When there are multiple copies of a surface on a body each individual copy of that surface is called an instance of that surface and is given a unique instance number In the case of gear tooth surfaces the instance number is the same as the tooth number The parameters TOOTHBEGIN and TOOTHEND define a range of teeth over which the gages will be placed The reading of the gage is the stress at the most critical tooth If the value of TOOTHBEGIN is greater than TOOTHEND then the search range will wrap around the last tooth There are two parameters that identify a point on a surface We refer to these two parameters as S which varies in the profile direction and T which varies in the face width direction In a 2D model the parameter T is ignored The profile parameter S increases from fillet to the tip on Side 1 of a tooth and from the tip to the fillet on Side 2 as shown in Appendix A The parameters SPROFBEGIN and SPROFEND 62 Running an Analysis define a range over which the stress will be calculated These are in surface local units as shown in Appendix A The GAGE will read out the critical value of stress in this range The NUMSPROF parameter controls how many search points should be used over this range The face width range parameters TFACEBEGIN TFACEEND and NUMTFACE are ignored for 2D models The DEPTHBEGIN DEPTHEND and NUMDEPTH parameters extend the search
64. aspect ratio 5 9 Rayleigh Damping Model 43 Table 5 10 Rayleigh damping parameters for steel Material a l sec sec Steel 479 1 2 07 5 9 Rayleigh Damping Model The Rayleigh Damping model assumes that the damping matirx for a finite element is is related to the mass matrix M and the stiffness matrix K by a linear relationship C aM BK 5 1 a has units of 1 sec and 8 has units of sec The relationship between the Rayleigh damping model and the equivalent viscous damping model is obtained by from a single degree of free system by comparing the two equivalent damping models kr f t 5 2 Comparing the two damping models yields lun Bu 2 Bw 5 3 Wn In a general multi degree of freedom system if the damping ratios are measured at a number of system natural frequencies w the paramters for the Rayleigh damping model can be computed using a least squares approach 26 wi 262 w 2 TEE 26 v i B j On 26 ios Wn 14 5 55 Equation 5 5 is solved to compute a and Least squares solution is used if the values of damping ratio in Equation 5 5 are measured at more than two different natural frequencies In general Equation 5 5 is solved in the regular sense by measuring the damping ratio at two natural frequencies of the system Table 5 10 shows a and 8 for steel 5 9 1 Modal Damping Ratio SDOF system The displacement
65. bly errors Building a Model NUMPINIONS n PINIONNO 4 2 IIb b T5 z MAGNITUDE 0 0000000000e 000 ECE ANGLE 0 0000000000 000 Figure 5 5 The Pinionrunout menu NUMPINIONS FM 2 ELELEE gt PINION 4 EELEE z ANGPOSNPINION 271 4290000000 EECH Figure 5 6 The Angposnpinion menu Table 5 4 Pin position error menu Item Description NUMPINIONS Integer Number of pinions in the system PINIONNO Integer Pinion number for which data presently is being displayed MAGNITUDE Float Magnitude of pin position error for individual pinions ANGLE Float Orientation Angle Deg for the pin position error for in dividual pinions 5 2 System sub menus NUMPINIONS ganana PINIONNO 4 2 nanana MAGNITUDE 0 0000000000 000 TEE TT ANGLE 0 0000000000 00 0020 ANGLE 0 0000000000 000 Figure 5 7 The Pinposnerror menu 31 32 Building a Model 5 3 Pinion data The PINION command in the EDIT menu Figure 5 1 leads to the Pinion menu shown in Figure 5 8 The three terms Lumped mass Lumped moment of inertia and Lump alpha are explained in Table 5 5 TOOTH SPACEERR RIMDATA BEARING THICKERROR BMOPUON ee 0 0000000000 000 Figure 5 8 The Pinion main menu There are five submenus in the Pinion menu BEARING SPACEERR THICKERR TOOTH and RIMDATA If the RIMOPTION flag in the PINION menu is set then a separate
66. ces and moments acting on each body Figure 7 34 shows the AUDIT sub menu The list of bodies for which this audit is to be generated is selected through a sub menu accessed through the SELECT button in this menu The range if time steps is specified in the BEGINSTEP and ENDSTEP boxes The START button then displays the audit statement in the Information window It can also be sent to an ASCII file by using the OUTPUTTOFILE FILENAME and APPEND boxes A sample equilibrium audit for the sun is shown below Time 0 00025 Body no 1 SUN Origin at 0 0 0 Contact forces Exerted by PINION1 Total f 1099 798249 2462 388408 0 mo 0 0 3740 488587 m 0 0 3740 488587 Exerted by PINION2 Total f 2431 622595 1159 733387 0 mo 0 0 3736 616789 m 0 0 3736 616789 Exerted by PINION3 Total f 1120 528974 2489 569011 0 mo 0 0 3775 141985 m 0 0 3775 141985 Exerted by PINION4 Total f 2474 940612 1191 830242 0 mo 0 0 3794 698401 m 0 0 3794 698401 Total contact force f 64 04874165 4 916252665 0 mo 0 0 15046 94576 m 0 0 15046 94576 Bearing forces SUNBRG f 62 36947675 4 787355666 0 mo 0 0 0 m 0 0 0 Total bearing force f 62 36947675 4 787355666 0 mo 0 0 0 m 0 0 0 Total internal force inertial press body f 891078848 015 8 351416196 015 01 mo 0 3 0 0 7 478249975e 007 0 0 7 478249975e 007 1 6792649 0 1288969982 01 0 0 1153 0542381 0 0 1153 0542381 64 04874165
67. ch subsequent column contains the reading for one load sensor Table 9 17 shows the data for a load sensor so as to obtain the plot shown in Figure 9 4 So as to obtain the plot of static loads against time a STATIC analysis is performed on the same planetary gear set Figure 9 5 shows a plot of static load against time using the TOOTHLOAD command The TOOTHLOAD data used to extract this plot is given in Table 9 18 Using the static and dynamic load values you can calculate the dynamic load factor a term very commonly used in the gear industry to predict dynamic stresses from static values D ic Height Dynamic Load Factor 5 ae 9 1 Static Height For the present example the Dynamic Load Factor 3514 50 1 208 4000 T T T T 3500 3000 2500 r 4 2000 F 4 Tooth loads Ibf 1500 j 1000 F 500 F JEU it 0 0 052 0 054 0 056 0 058 0 06 0 062 0 064 0 066 0 068 0 07 Time s Figure 9 4 Graph showing the dynamic tooth load against time The plot is obtained using the load values from column nos 6 10 11 and 12 from the LOADS DAT file 142 Running a dynamic case Table 9 17 Load sensor data for extracting the plot shown in Figure 9 4 Item Description NLOADSENSORS 11 LOADSENSOR 5 SURFPAIR PINION1 SURFACEI SUN SURFACEI MEMBER SUN TOOTH 1 FILENAME LOADS DAT Table 9 18 Tooth load data for extracting the plot shown in Figure 9 5 Item Description SU
68. ch subsequent column contains the readout of an individual probe 6 2 Finite element probes SUN m SURFACED 000000000 000 ine 51 1000000 00000000 0000000 0 02 10000000 0000 GAGES DAT The surface gage menu 63 64 Running an Analysis ZETA 40 5 1 SUN 1 000000 7 1 000000 7 0000000000000 20 MAXPPLNORMAL r PROBES DAT Figure 6 2 The finite element probe menu 6 3 Load sensors 65 LOS Doo EXIT QUIT NLOADSENSORS I bier LOADSENSOR 5 IE DPI SURFPAIR PiNION1 SURFACE1 SUN sURF v MEMBER SUN mom uu FILENAME LOADS DAT Figure 6 3 The load sensor menu 6 3 Load sensors Load sensors are used to measure the contact loads generated at the contact surfaces Figure 6 3 shows the load sensor menu used to set up the sensors The SURFPAIR item selects the contact surface pair for which the contact load is of interest Each surface pairing has two contacting members or bodies The MEMBER parameter selects one of these two bodies and the TOOTH item selects the individual surface instance number within that body The outputs of all the sensors are put into a file called LOADS DAT This file has one row for each instant of time The first column contains the time Each subsequent column contains the reading of one load sensor 6
69. color In pre processing mode all bodies are painted Gray The OUTLINE box controls whether or not an outline drawing of the body will be made The view menu in post processing mode Figure 7 6 has a few additional parameters There is a CONTOURS option to draw stress contours If the COLORS or CONTOURS option is selected then the menu also asks for the values of the lowest contour level MINSTRESS and the highest contour level MAXSTRESS The colors used in the drawing are based on the stress level If the CONTOURS option is checked then the command DELTASTRESS will appear in the menu You can specify the spacing between the stress contours using this parameter If the LOADS option is selected then the contact loads acting on the components will be drawn using the scale factor entered in the LOADSCALE box Figure 7 7 If the LOADS option is not checked Figure 7 6 then an additional box EXAGGERA TION appears where an exaggeration factor can by entered for deformed geometry plots An exaggeration factor of 0 0 will draw the bodies in their undeformed state 72 Pre and Post processing EXIT QUIT WINDOW AUTOWINDOW VIEWPORT XPROJECTION YPROJECTION ZPROJECTION ISOMETRIC LEFTROTATE 0 0000000000 000 RIGHTROTATE ENTM 0 0000000000 000 UPROTATE 0 0000000000 000 DOWNROTATE UT 0 0000000000e 000 CWROTATE 0 0000000000 000 0 0000000000 000 REFFRAME pi
70. cs are very complex This auto refresh behavior can be toggled using the View EnableAutoRefresh and View DisableAutoRefresh commands If auto refresh is disabled then the user can ask to refresh the graphics using the lt button It is possible to save a sequence of graphics pages in a metafile a MET file using the File SaveReplayFile command This file can later be replayed in Guide using the File ReplayGraphicsFile command The graphics currently displayed can be saved in Windows Metafile format a WMF file by using the File SaveWindowsMetafile command This WMF file can subsequently be loaded by another application such a word processor An encapsulated PostScript file a EPS file can be created by using the File CreateEPSFile command This command creates an EPS file containing only the visible part of the current graphics page Parts of the page that are not visible because of the zoom level will be cropped from the EPS file The Edit Copy command will copy the graphics in Windows Metafile format onto the clip board Graphics pages can be printed by using the File Print command on Guide s main menu 22 The Graphical User Interface 5 Building Model All the parameters that describe the Planetary gear set are entered in the sub menus of the EDIT menu Click EDIT in the main menu to access the EDIT submenus Figure 5 1 shows the EDIT menu In the EDIT menu and in all sub menus under it the QUIT command ta
71. define a depth range and NUMDEPTH specifies the number of points over this range Very close to the surface the subsurface stresses have a large error because of the concentrated nature of the load So DEPTHBEGIN should never be set to zero The stress component is selected in the COMPONENT box Options available are MAXP PLNORMAL the maximum principal normal stress s1 MINPPLNORMAL the minimum principal normal stress 53 MAXSHEAR the maximum shear stress Tmar and VONMISES the Von Mises octahedral shear stress sym A subsurface vs depth graph is not possible for a Planetary2D gear set 7 8 The SUBSURFACE command 85 surface pair PINION1_SURFACE1_SUN_SURFACE1 Load on 1600 0 1400 0 1200 0 1000 0 800 0 600 400 0 2000 o Figure 7 18 The tooth load histogram generated by the TOOTHLDHIST menu 86 EXIT QUIT START CLEAR SURFACEPAIR MEMBER TOOTHBEGIN TOOTHEND OEE aoe ee TIMESTEP OE Ga oe DEPTHBEGIN DEPTHEND LELEH NUMDEPTH 1 2 b Pre and Post processing PINION1 SURFACE1 SUN SURF PINION x 35 2 2 1 z 0 0000000000e 000 0 0000000000e 000 1 z 5 OUTPUTTOFILE 2 FILENAME output txt APPEND Iv El Figure 7 19 The SUBSURFACE menu 7 9 The GRIDLDHIST command 87 SL D EXIT QUIT START CLEAR SURFACEPAIR PINION1 SURFACE1 SUN SURF MEMBE
72. e 9 1 Graph showing the dynamic maximum principal normal stresses 81 and minimum principal normal stresses s3 against time for the fillet surface of the sun gear measured by Surfage Gage 1 The results are obtained from the file GAGES DAT 188 Running a dynamic case Table 9 16 Surface gage data for extracting the plot shown in Figure 9 1 Item Gage 1 BODY SUN SURFACE FILLET 1 TOOTHBEGIN 1 TOOTHEND 1 SPROFBEGIN 0 00 SPROFEND 15 00 NUMSPROF 51 TFACEBEGIN 0 00 TFACEEND 0 00 NUMTFACE 1 DEPTHBEGIN 0 00 DEPTHEND 0 00 NUMDEPTH 1 DISTMIN 0 005 FILENAME GAGES DAT The dynamic analysis should attain a steady state behavior after some time This can be checked for using the pinion bearing reaction plots as shown in the Figure 9 2 This plot shows the pinion bearing tangential displacement against time The data for the plot is obtained from the PINIONIBRGRES DAT file The file contains the results for Pinionl Bearing It has one row for each instant of time analyzed The first column contains the time The third column will give the tangential displacement for Pinionl Reaction forces transmitted in the Housing can be checked using the housing bearing reaction plots A plot of timestep against housing moments is shown in Figure 9 3 Column no 13 in the HOUSINGRES DAT file gives the moment about the Z axis for each time instant 9 17 Analysis and Results 139 0 98 T T T 1 02r 4 1 04 H
73. e Bodies ment a 119 8 4 Post processing using iglass ee 120 8 5 Features specific to iglass post processing 120 Running a dynamic case 127 9 1 Whe EDIT neni s ionene ii Bee Gs Re os Rh 127 9 2 System level data 127 9 3 The Angular position data 2 127 9 4 The o 8 a ae BOR EO SRS Ek oe ad 127 9 5 The Pinion tooth modification 129 9 6 Pinion bearing data 4 22 1 399 D Ee 129 9 7 Pinion Rim datas kot SG tanw e v9 ERG Sw we rg 129 CONTENTS 9 8 9 9 9 10 9 11 9 12 9 13 9 14 9 15 9 16 9 17 9 18 The Sun geardata 4449 99x tiad tiaa eae ead 5 2 130 Sun tooth modification 130 Whe Ring gear data s o sat q wicie 130 The Ring gear tooth modification ss aa 132 The Spline data for the Ring 132 The Ring gear rin data Leics sw bo e ARS hare eRe RR dia 132 The Cartier daba x 4 4 amp X ME b deae ROB AS PAS Leeds 132 Calculating the time step for dynamic 134 Nei 20 itn SUP 135 Analysis and Results
74. e RIMDATA command in the pinion data menu Figure 5 8 leads to the rimdata menu shown in Figure 5 22 Table 5 14 explains the rim data parameters for the pinion There are three types of element types you can use to generate the pinion rim mesh Linear Quadratic and Cubic The mesh file contains the element connectivity and geometry information This file is created by the program The complete path of the file should be entered if the file is not to be created in the current directory The file extension should also be provided Changing the rim diameter affects the aspect ratio of the elements The standard template files are designed to create the best aspect ratio when RIMDIA 2 ROOTDIA OUTERDIA The deformation of the rim at the interface between the tooth and rim model is expressed as a Fourier series If the pinion bearing race is modeled as a flexible cylinder then the bearing race is modeled using the Fourier shape functions in the circular direction The CIRCORDER variable specifies the order of the Fourier series in the circular direction 5 11 Modelling the rim Table 5 14 Rim data parameters Item Description MESHFILENAME String Mesh file name for pinion RIMDIA NRADIAL NCIRCULAR ELEMTYPE CIRCORDER rim Float Rim diameter of the pinion rim Integer ments in the rim Integer ments in rection in Number of finite ele the radial direction in Number of finite ele the circumferential di the ri
75. ee ae Y 5 0 Tooth numbering i5 a x 3303 3 89 ES 5 6 Spacing bit Thickness hob eee 844 e RR ROS 5 8 Modelling the tooth profile 5 9 Rayleigh Damping Model 5 9 1 Modal Damping Ratio SDOF system 5 9 2 Modal Damping Ratio Measurement 5 10 Surface modifications assisi a komm mom RR Re 4 54 Modelling the riM YER Se 5 12 oun pear datas 666 Gk Be wD 3 53 d x xiii 17 17 19 19 19 19 20 20 21 CONTENTS 5 13 S n gear beArlHgs 1444664 FG GEESE LEELA Gee dS 52 De Aime fe bp Bee A Of 54 5 15 Carrier data ana da ob ES Ct eee a ee eee Re 58 Running an Analysis 61 6 1 Surface 305 E eR PS Ue Rx a ee x EA EET 61 6 2 Finite element probes 62 6 3 Load sensors 4 4 ana Go ee eae ee ae eR ES hon eee eee e ded 65 04 Thessetup mend 52122224 ove eee beh eee ne eer hand eee ds 65 6 5 Other output 66 Pre and Post processing 69 Gl Selecting bodies a we SA RS y ye RRR EU P o 71 7 2 View parameters ss 4 4 4 0 4444 4444 bb o RUE P Sa eh dee ad 71 7 3 DRAWBODIES command
76. ers or bodies The MEMBER parameter selects one of these two bodies and the TOOTHBEGIN and TOOTHEND items select a range of instance numbers or tooth numbers within that body If TOOTHBEGIN is greater than TOOTHEND then the range wraps around the last tooth of the surface This range must contain 7 teeth or less The items SPROFBEGIN SPROFEND TFACEBEGIN and TFACEEND are used to restrict the search to a part of the contact surface Contact occurring outside this range is not considered for display in this graph You dont need to enter any value for TFACEBEGIN and TFACEEND for a 2D planetary gear set Figure 7 16 shows a graph of tooth contact pressure vs time over the surface of the pinion tooth 7 6 The CONTACT command 83 8 5 2 5 E Contact Pressure on surface pair PINION1_SURFACE1 Time Figure 7 16 600000 000000 500000 000000 200000 000000 100000 000000 The tooth contact pressure vs time graph generated by the CONTACT menu 84 and Post processing PostPro aothLdHi
77. es could make contact To eliminate very widely separated surface instances from further analysis it uses a parameter called the separation tolerance or SEPTOL in Multyx The value of this parameter is specified by the user and is in units of distance If two surfaces are separated by more than this distance the pair of surfaces are discarded for further analysis Each two dimensional surface is parameterized by a parameter s which varies from 0 at one end of the surface to a maximum value say n at the other end of the surface During contact analysis Calyx finds the point on the surface that is most likely to make contact and then lays a contact grid around the point The grid is placed at equal intervals of s away from the most likely point of contact This width of each grid cell is specified by the user It is called DSPROF in Multyx The number of such patches laid out on either side of the most likely point of contact can also be specified in the configuration file and is called NPROFDIVS in Multyx 3 6 The main menu The Planetary2D package is started by clicking on an icon created during the installation process After the Planetary2D package is started the main menu shown in Figure 3 8 comes up All user provided data is saved in a file called the session file The name of this session files can be changed by typing the name in the SESFILENAME box Changing the file name does not actually write the data to the new file nor
78. finite ele ment model will be generated between the RIMDIA of the pinion and the inner diameter 5 4 Bearings The BEARING command in Figure 5 8 leads to the Bearing data menu shown in Figure 5 9 Table 5 6 explains the parameters in the Bearing menu If the rigid race box is checked then the inner diameter of the pinion is treated as a rigid cylinder This rigid cylinder will be attached through a 6 x 6 stiffness matrix and damping matrix to a race on the carrier Otherwise its deformation is expressed using a Fourier series expansion in the circular direction The stiffness and the damping matrices of the bearing are read in from an existing input data file The name of the file should be entered in to the BRGFILE box The contents of a sample bearing file are shown below 000000 1 0e7 00000 1 0 7 0000 000000 000 0 0e9 0 0 0000 0 0e9 0 5 4 Bearings 33 Table 5 5 Pinion lumped parameters Item Description LUMPMASS Float Lumped mass added at the center of the pinion in addition to the mass of the tooth and rim model LUMPMOMINERTIA Float Lumped polar moment of inertia Jz added at the center of the pinion in addition to the Jz of the tooth and rim model LUMPALPHA Float The damping constant for the lumped mass and moment of inertia Table 5 6 Bearing menu parameters Item Description RIGIDRACE Boolean Whether the bearing race is a rigid cylinder CIRCORDER Integer Fourier series order in the circular d
79. gure 5 5 and Table 5 2 ANGPOSNPINION Figure 5 6 and Table 5 3 PINPOSNERROR Figure 5 7 and Ta ble 5 4 In the PINIONRUNOUT submenu you can enter the number of pinions using the NUMPIN IONS command Enter the pinion number for which the data is presently being displayed in the PINIONNO box For the PINIONRUNOUT panel the MAGNITUDE variable defines the magnitude of the high point of runout errors for individual pinions while the ANGLE variable defines the orientation of the same at time t 0 In the ANGPOSNPINION panel the ANGPOSNPINION variable defines the nominal an gular position of the pinion Ideally this angular position would be an integer multiple of 360 NTEETHSUN NTEETHRING The position of the pinion pin or the bearing can be moved by a small amount from the ideal position as shown in Figure 5 4 This pin position error is modelled using the PINPOSNERR command the SYSTEM menu In the PINPOSNERR panel the MAGNITUDE variable defines the magnitude of the pin position error for individual pinions while the ANGLE variable defines the orientation of the same for individual pinions The value of zero for this angle implies that the error is in the radial direction 5 2 System sub menus 29 PINION PITCH CIRCLE OF PINION H CIRCLE ANGRUNOUT MAGRUNOUT CENTER OF BEARING OR PIN MAGPINERR ANGPINERR CENTERDIST ANGPOSNPINION CENTER OF CARRIER Figure 5 4 The pinion assem
80. he beginning of the next time range The speed at the end of the last range is always assumed 1 0 The speed is assumed to vary as a linear function of time within a time range 66 Running an Analysis The torque in a time range can be controlled by setting the STARTTORQUEFACTOR and ENDTORQUEFACTOR for each range Again a factor of 1 0 means that the system is operating at its nominal torque The torque is assumed to vary as a linear function of time within a time range The SAVEPERIODICALLY option saves the state of the system in a restart file after every NSTEPSSAVE number of steps The state is saved in the restart file named in the SAVEFILE NAME box This restart file can be used to restart another analysis The OUTPUTRESTART option saves the state of the system in a restart file at the end of the analysis The file named in the OUTPUTFILENAME box is used This file can also be used to start a subsequent analysis Finally a finite element post processing data file can be emitted once every NSTEPSWRITE number of time steps by enabling the POSTPROCWRITE option The file used is selected in the POSTFILENAME box The post processing file can be used subsequently to make drawings and stress contour diagrams of the deformed system 6 5 Other output files Several tabular output files are created during the analysis The displacements and reaction forces generated by the reference frames of the individual bodies in the system are saved in data file
81. hed for each time instant or that the finite element mesh be highly refined over its entire surface area Both these alternatives lead to unacceptably high computational costs Our approach has been to use the finite element models only to compute relative deformation and stresses for points that are away from the contact RING Figure 1 1 The 2D planetary gear set SUN Introduction PINION zones For points within the contact zone we use semi analytical techniques to compute the relative deformations and stresses The near field semi analytical solution and the far field finite element solutions are matched at a matching surface Such a model is significantly difficult to program on a computer but once implemented can provide much better resolution without using a highly refined finite element mesh Rigid body degrees of freedom in the planetary system In multi mesh gear systems like planetary transmissions there are many rigid body degrees of freedom or mechanisms that are constrained only by the contact conditions This means that if a non linear finite element code with gap elements is used then the incremental stiffness matrices become singular Most commercial codes don t work when this happens Some manupalations are commonly used such as adding imaginary linear and torsional springs to make the system stiffness matrices non singular The spring stiffness can be made small
82. ic tip modification parameters Item Description QUADTIPMOD Boolean Whether to apply the quadratic tip modfn ROLLQUADTIPMOD Float Roll angle Deg at start of the quadratic tip modfn MAGQUADTIPMOD Float Magnitude of the quadratic tip modfn 48 Building a Model QUADRATIC TIP MODIFICATION Modification ve Material removed MAGQUADTIPMOD Roll Angle Root Tip TIP ROLLQUADTIPMOD Figure 5 20 Quadratic tip modification Table 5 13 Tabular profile modification parameters Item Description TABLEPROFMOD Boolean Whether to use a profile modfn table NROLLS Integer The number roll angles used in the profile modfn table ROLLNO Integer The roll angle number in the profile modfn table ROLLANGLE Float Vector indexed by IROLL Roll angle in the profile modfn table MAGNITUDE Float Vector indexed by IROLL Magnitude of modification in the profile modfn table 5 10 Surface modifications TABULAR PROFILE MODIFICATION Modification ve Material removed MAGNITUDE m m m m y 0 1 Roll Angle Root Tip ROLLANGLE Figure 5 21 Tabular tip modification 49 50 Building Model MESHFILENAME 00000 RIMDIA 0560000 0 0 RIMDIA _ 3 0868000000 NRADIAL 2 NCIRCULAR 128 EELEE ELEMTYPE LINEAR CIRCORDER 4 2 2 Figure 5 22 menu for specifying data for pinion 5 11 Modelling the rim Th
83. inionl in the plan etary system in the dynamic state transient response is in column no 3 of the PINIONIBRGRES DAT file 9 10 Plot showing a narrow range of tangential component frequency response of pin ionl in the planetary system in the dynamic state transient response is in column no 2 of the PINIONIBRGRES DAT 9 11 Plot showing the response near the second multiple of the mesh frequency for the tangential component of deformation of the pinionl bearing transient response is in column no 2 of the PINIONIBRGRES DAT file 9 12 Plot showing the mode shape at pinionl in the planetary system in the dynamic State at 57405 co v E i bs 9 13 Plot showing the mode shape at the sun gear in the planetary system in the dynamic state at 574 0502 i 5 oe Y REGEM The MEDIUM TPL template file A 2 The FINEROOT TPL template file The FINEST TPL template fille A A The THINRIM TPL template List of Tables 4 1 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5 11 5 12 5 13 5 14 5 15 5 16 8 1 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 9 10 9 11 9 12 9 13 9 14 9 15 9 16 9 17 9 18 Common buttons aaa 2562 46200 9952255952 RY REE EE 20 System configuration parameters
84. irection BRGFILE String Bearing file name for pin ion bearing O O O gt lt Oo O cO gt Oo Inside the bearing file the first line in this file must always have 6 zeroes This line is assigned for future use The next 12 lines contain the 626 stiffness and 6 x 6 damping matrices The last line contains zero This is a flag intended for future use The 6x6 matrices correspond to the 6 degrees of freedom of bearing race 1 relative to bearing race 2 as measured in the race 2 reference frame The six degrees of Freedom are the three translations in the X Y and Z directions and the three rotations about the X Y and Z directions For the Pinion bearing the X direction is always in the radial direction pointing from the carrier axis to the pinion axis The Y axis points in the tangential direction 34 EXIT QUIT gum RIGIDRACE 21 CIRCORDER 4 5 oannaam z ETE Figure 5 9 The Bearing menu Building a Model 5 5 Tooth numbering 35 5 5 Tooth numbering Each individual tooth of the Pinion Sun and Ring gear is assigned a tooth number Figure 5 10 shows the numbering scheme used for the Pinion and Sun gear Figure 5 11 shows the numbering scheme used for the Ring gear Side 2 Side 1 Figure 5 10 The tooth and side numbering scheme for the pinion and sun gear The two sides of each tooth are labelled
85. iscarded The first point X4 is proportional to the mean response gt The data obtained for the last range of the dynamic analysis when the speed is constant is normally used to plot the frequency response So for the present example problem 3000 since for the last step is 3000 An example of MATLAB program for plotting the frequency response Figure 9 6 amp Figure 9 9 and calculating the critical frequency value for Pinionl is shown below Time Step Dt 1 742e 5 No of steps N 3000 cd C Planetary2D load PINION1BRGRES DAT x1 PINION1BRGRES 1001 4000 1 x2 PINION1BRGRES 1001 4000 2 Df f 1 N Dt for i 1 N f i i 1 Df end Obtain X f FFT of known signal x t Fourier transform of U x X fft x2 N 2 N Plotting the frequency response plot f 1 N 2 abs X 1 N 2 plot f 2 N 2 abs X 2 N 2 Z Zooming in to catch the peak response plot abs X 2 1000 plot abs X 2 500 plot abs X 25 35 Afrequency 31 ans 574 0528 Response X 31 ans 7 6426e 007 3 2792 0061 Absolute value of the peak response abs X 31 ans 3 3671 006 Real part of the peak response 9 18 Applying the 2D Planetary program for modal analysis 145 real X 31 ans 7 6426e 007 Imaginary part of the peak response imag 31 ans 3 2792 006 APhase angle angle X 31 ans 1 3418 The frequency distribution using
86. kes the user back to the parent menu after discarding all changes made in the sub menu and all sub menus under it The EXIT command takes the user back to the parent without discarding changes There are five submenus under the EDIT menu SYSTEM PINION SUN RING and CARRIER The SYSTEM command leads to a menu for entering the system level data The PINION SUN RING and CARRIER commands lead to their respective data specific submenus EXIT QUIT SYSTEM PINION SUN RING CARRIER Figure 5 1 The EDIT menu 24 Building Model 5 1 System level data The SYSTEM command in the EDIT menu of Figure 5 1 leads to the SYSTEM menu shown in Figure 5 2 The parameters in this menu are summarized in Table 5 1 You can specify the number of pinions in the planetary system using the NUMPINIONS option The default value is 4 CENTERDIST is the operating center distance This should always be a positive value INPUT switch selects which one of the SUN RING and CARRIER acts as the input for power The torque and the angular speed directions of the input member are the same They are opposite for a member where power is exiting the system In order to completely specify the kinematics speed of one more member other than the input member is required TORQUEINPUT is the torque at the input member always postive RPMINPUT is the speed of the input member sign follows the right hand rule about the z axis RPMRING is the speed of the ring sign follo
87. m Switch Element type to be used for pinion rim Integer Fourier series order in the circular d irection 51 52 Building a Model EXIT QUIT BEARING TOOTH SPACEERR RIMOPTION LUMPMASS 0 0000000000 000 LUMPMOMINERTIA 7 0000000000000 Doge LUMPALPHA 0 0000000000 000 Doge ii Figure 5 23 The Sun gear menu 5 12 Sun gear data The SUN command in the EDIT menu Figure 5 1 leads us to the sun data menu as shown in Figure 5 23 The SUN menu is similar to the PINION menu except that there are no Thickness error inputs If the RIMOPTION flag is set then a separate finite element model will be generated between the Rim Dia of the Sun gear and the inner dia 5 13 gear bearings The Bearing menu for the Sun gear is shown in Figure 5 24 The menu is similar to the Pinion bearing menu except for the BEARING command which is not there in the pinion bearing menu If this BEARING flag is set then the sun has a bearing and a bearing file has to be provided Otherwise the Sun can be made to float or can be constrained The CONSTRAINT switch if the Bearing box is not checked decides whether the sun is allowed to float or is held at its axis The SPACEERR TOOTH and the RIMDATA menus for the sun gear are similar to those for the pinion 5 13 Sun gear bearings RIGIDRACE Iv 2 BEARING s BEL 0 o000000000e 000 FY Hoes 0 0000000000 0
88. mmation index 7 goes from mode 1 to mode n The modal vectors U are normalized with respect to the mass matrix is the k th element of the the i th modal vector The driving 5 9 Rayleigh Damping Model 45 point compliance k is guarenteed to have an antiresonance between two resonances since the numerator terms are always positive and the denominator terms are of opposing signs when the excitation frequency is between two resonances The driving point compliance of a gear is measured from an impulse test The modal damping ratio of each mode is computed based on the sharpness of the peak at the natural frequency using Equations 5 7 5 8 and 5 9 Once the modal damping ratio for a number of system modes are computed Equation 5 5 is used to determine the parameters for the Rayleigh damping model 46 Building a Model EXIT QUIT LINEARTIPMOD 21 ROLLLINEARTIPMOD 17112 MAGLINEARTIPMOD 0 0000000000 000 TECE i 5 IgUADTIPMOD 21 ROLLQUADTIPMOD 12 0000000000 ECEE MAGQUADTIPMOD 0 0001000000 TABLEPROFMOD 2 NROLLS 3 2 5211219 5 ROLLNO 3 ELELEE z ROLLANGLE 32 5900000000 ECEE MAGNITUDE 0 0008000000 Figure 5 18 The tooth modification menu 5 10 Surface modifications The MODFN command in the tooth data menu Figure 5 15 leads to the menu shown in Fig ure 5 18 This menu is used to specify surface modifications Three simple surface modifcations ca
89. n Fig ure 5 14 The thickness error is the amount by which the circular tooth thickness at the pitch circle of a particular pinion is more than the nominal amount A different thickness error can be prescribed for each pinion The thickness error is applied to the tooth by rotating the contact surfaces about the pitch circle center Table 5 8 explains all the thickness error parameters EXIT QUIT NUMPINIONS 4 lt gt PINION 4 ice THICKERROR aooo Figure 5 14 The Thickness error menu 38 Table 5 8 Thickness error menu Item Description NUMPINIONS Integer Number of pinions in the system PINIONNO Integer Pinion number for which data presently is being displayed THICKERROR Float Thickness error in individ ual pinions Building a Model 5 8 Modelling the tooth profile 39 MODFN 35 2 E m zi SEL D Db ET 8 8571 400000 9 TEs 24 6034000000 Be D 210 m E DE be m E 0 1630000000 0 0180000000 a 5 WS 41332000000 OF up Eie gt 3 6000000000 E 4 D CX Bi BE a 2 3000000000 LS uid 3 0040000000e 007 E 0 3000000000 e e 0 0007112000 E lt Done eS ALPHA 473 0
90. n be specified directly in this menu linear tip modification quadratic tip relief and tabular surface modification Linear tip modification is applied using the parameters shown in Table 5 11 and Figure 5 19 The modification magnitude is a linear function of the involute roll angle Positive value for the magnitude of linear tip modfn indicates removal of material Quadratic tip modification is applied using the parameters shown in Table 5 12 and Fig ure 5 20 The modification magnitude is a quadratic function of the involute roll angle A positive value for the magnitude implies removal of material Tabular surface modification is applied using the parameters shown in Table 5 13 and Fig ure 5 21 A table of roll angle and modification values will be used to describe the profile modification The profile modification is linearly interpolated between the roll angle values A positive value for magnitude indicates removal of material 5 10 Surface modifications 47 Table 5 11 Linear tip modification parameters Item Description LINEARTIPMOD Boolean Whether to apply the linear tip modfn ROLLLINEARTIPMOD Float Roll angle Deg at start of the linear tip modfn MAGLINEARTIPMOD Float Magnitude of the linear tip modfn LINEAR TIP MODIFICATION Modification ve Material removed MAGLINEARTIPMOD Roll Angle Root Tip TIP ROLLLINEARTIPMOD Figure 5 19 Linear tip modification Table 5 12 Quadrat
91. nerate Iglass file menu 8 1 Generating an Iglass file for preprocessing 115 IGLASS DAT Bodies Finite Element Mesh Cutaway Time 00000 Reference Frame zl Figure 8 2 An example of an Iglass preprocessing window 116 Pre and Post processing using Iglass Viewer View Bodies Attibs Perspective Finite Element Mesh Cutaway BAN X Position Time 100000 Reference Frame FIXED Figure 8 3 Iglass preprocessing view menu 8 2 View menu The View menu is shown in Figure 8 3 Table 8 1 shows the common tasks performed by some of the buttons displayed in the Iglass window Apart from all the features shown in Table 8 1 you can also rotate the model using the left mouse button Drag the left mouse button in the direction you want to rotate the model in the iglass graphics window Also the model can be moved in the graphics window in any directions you want using the right mouse button Drag the right mouse button in the direction you want to move the model in the iglass graphics window 8 2 1 Finite element mesh The finite element mesh model can be visualised if the Finite Element Mesh item is selected Figure 8 4 shows the finite element mesh model of the gear bodies in iglass preprocessing 8 2 2 Cutting plane Using the cutting plane switch shown in Figure 8 5 you can visualise the model along a section This feature is
92. ng the tooth profile Table 5 9 Parameters describing the tooth profile for pinion Item Description NTEETH Integer The number of teeth on pinion DIAMPITCH Float Diametral pitch of the pin ion PRESSANGLE Float Pressure angle deg of the pinion THICKNESS Float Transverse thickness of the pinion tooth HOBTIPRAD Float Tip radius of the hob used to generate the pinion OUTERDIA Float Outer diameter of the pin ion tooth ROOTDIA Float Root diameter of the pin ion tooth INNERDIA Float Inner diameter of the pin ion rim YOUNGSMOD Float Young s modulus for the pinion POISSON Float Poisson s ratio of the pin ion DENSITY Float Density of the pinion ALPHA Float Value of alpha in the equa tion alpha M beta BETA Float Value of beta in the equa tion C alpha M beta K MESHFILE String Mesh file name for pinion TEMPLATE String Template file name for pinion 42 Building a Model using this file since higher order elements are used in that region For convergence studies use the finer template files Figure A 2 and A 3 The element shapes generated by these template files are optimal when the difference OUTERDIA ROOTDIA is approximately same as the difference ROOTDIA RIMDIA If this is not possible when RIMDIA is too large a special template file called THINRIM tpl Figure A 4 has to be used This template generates fewer elements in order to maintain an adequate
93. nvergence within a predetermined number of iterations Furthermore ill posed contact problems can be detected even before the solution process is started The solver is specifically designed for the linear inequality type constraints found in contact problems Introduction 2 Planetary2D Software Package This chapter explains the various features of the Planetary2D software package 21 Planetary2D analysis package Calyx is a powerful contact analysis code capable of analyzing a variety of contact problems including 2D and 3D dynamic and static analysis of systems such as gears compressors and brakes Because Calyx has to be capable of handling a variety of problems it communicates with the outside world through a programming language The programming language interface of Calyx brings flexibility at the expense of ease of use Such an interaction is appropriate for an advanced user but not for a gear design engineer In order to address this issue the program Multyx is used is capable of commu nicating with the user through an easy to use menu based interface It translates the user s commands into the appropriate programming language statements and sends them on to Calyz A typical user does not even need to know that Calyx is running in the background In addition to the user interface Multyx also has built in model generators The Planetary 2D models described in this manual are all generated by
94. o output stresses at a particular point when its element number and local coordinates are known The Element numbering used in the gear tooth finite element meshes is shown in Appendix A Figure 6 2 shows the finite element probe input menu The BODY parameter selects the particular body or component to be probed Each body can have many finite element meshes The MESH parameter selects which finite element mesh should be probed There may be many copies or instances of the finite element mesh Each copy is given an instance number In the case of a gear tooth mesh this instance number is the same as the tooth number The TOOTH parameter selects the instance number The ELEM parameter selects the finite element number within the mesh The XI ETA and ZETA values are the local coordinates within the finite element XI ETA and ZETA vary between 1 and 1 over the element Appendix A shows the orientation of the local coordinate axes for each finite element in the various mesh templates The COMPONENT parameter selects which stress component should be measured by the probe Available options are Maximum principal normal stress 81 minimum principal normal stress s3 maximum shear stress Tmar Won Mises octahedral shear stress Sym and the displacement magnitude The data measured by the finite element probes is written to a file called PROBES DAT The data file has a row for each time instant The first column contains the value of time Ea
95. of the gear bodies 118 The cutting plane switch eee 118 T h position slide uiua 118 The time si aos Po WIE vow eee aaa dd ben 118 The reference frame switchs usc aa an GO ee ea eG 119 Iglass preprocessing Bodies 119 The generate iglass file menu for post processing 120 An example of iglass post processing window 121 The position slider s sse s om s x RE 44444444440 Rev amp 122 The deformation slider 122 The load Slider sugs kobe he De eee eee ee kd bee 122 The bearing forces and moments 5 122 The iglass postprocessing attribute menu 123 Theattribute switches ed qu eA cee a E ee Wwe RE ebb ed ger 123 The palette switch o o haw A aan ee Sado SSS 123 Finite element mesh so as to find the stress at a nodal point 124 The background color popup window switch 000 124 The Contact pattern menu s eee a ee 125 Graph showing the dynamic maximum principal normal stresses 51 and min imum principal normal stresses s3 against time for the fillet surface of the sun gear measured by Surfage Gage 1 The results are obtained from the file GAGHS DAT s 408 W p
96. olled by the OUTPUTTOFILE FILENAME and APPEND items Fig ure 7 29 shows stress as a function of time Figure 7 30 shows stress as a function of profile 7 14 The POINTSTRESS command The POINTSTRESS command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 31 This menu is used to track normal stresses in a specific direction at a specific point on a surface The surface is selected by specifying the body in the BODY box and a surface in the SUR FACE box range of teeth with up to 7 teeth is selected through the TOOTHBEGIN and TOOTHEND items A profile and face location on this surface is specified through the SPROF and TFACE parameters The direction is specified by an angle in the item ANGLE This angle is the angle between the normal direction of interest and the profile direction if the REFDIRECTION option is SPROF The angle is measured using the right hand rule about the outward normal to the surface The range of time steps is specified by the BEGINSTEP and ENDSTEP items File output is controlled by the OUTPUTTOFILE FILENAME and APPEND items Figure 7 32 shows an example of the graph generated by this menu 96 m z EL E Pre Post processing MAXPPLSTRESS TIME SUN gt SURFACE1 2 212 2 68 Bed sis 5 lt gt BE e E 2163 t m
97. ort and allows calculation of the dynamic response at a sufficient number of time steps to study the response in the frequency domain In contrast the need for extremely refined gear tooth meshes limits conventional finite element analysis to static analysis and free body eigen solutions Experimental measurement of planetary gear dynamic response under operating conditions is difficult due to limited access and multiple moving bodies The Planetary2D analysis package provides a more accurate and comprehensive study of planetary gear dynamic response than is reasonably possible or has been conducted with conventional finite element analysis A typical Planetary2D gear set is shown in Figure 1 1 Contact pair analysis of a planetary gear set is difficult for general purpose finite element software for many reasons Size of the contact zone The width of the contact zone in typical gearing applications is two orders of magnitude smaller than the dimensions of the gear teeth themselves In order to model the contact conditions with sufficient accuracy a general purpose non linear finite element program needs to have a large number of nodes a very fine mesh inside the contact zone To run such a contact model the fine mesh in the contact zone has to transition into a much coarser mesh over the rest of the gear The location of the contact zone however changes as the gears move This means that either the gear finite element model should be re mes
98. ournal for Numerical Methods in Engineering vol 24 pp 1461 1477 1987 Edge effects in gear tooth contact S Vijayakar ASME 7 International Power Transmis sions Gearing Conference San Diego October 1996 162 BIBLIOGRAPHY 15 Vibration Measurements on Planetary Gears of Aircraft Turbine Engines Botman AIAA Journal vol 17 no 5 1980 16 Dynamic Tooth Loads in Epicyclic Gears Cunliffe J D Smith and Welbourn J Eng Ind Trans ASME May 1974
99. ours Enabled MINPRESS 4 000000E 004 Level of lowest press contour MAXPRESS 4 200000E 005 Level of highest press contour DELTAPRESS 4 000000 004 Spacing between press contours SMOOTH FALSE Whether to smooth the pressure contours OUTPUTTOFILE Whether to write data to file Disabled MultyX PostProc 1 20 Pattern gt START Guide is a program that provides a Graphical User Interface GUI to Guide trans lates each of Multyx s dialogs and presents them to the user in a graphical form The command line menu described above is presented to the user as shown in Figure 2 2 In addition Guide provide the user with convenient ways of viewing the graphics and helps the user convert the graphics into Microsoft formats and into Encapsulated PostScript EPS files Although Guide enhances the friendliness of Multyz it is not required the features of Multyx can be accessed without Guide The connection between Guide and Multyx is based on the TCP IP telnet protocol when they are running on different computers When running on the same computer they communicate through named pipes Guide is a heavy user of advanced operating system features including GUI support multi threading support and inter process communication support Guide now runs on Windows 95 98 NT 2000 systems only 2 1 Planetary2D analysis package ee PostProc UL Patter QUIT START CLEAR SURFACEPAIR PINION1_SURFACE1_SUN_SURF
100. ousing reaction plots can be extremely useful in accurately designing the gears for various applications An example of running a dynamic case is explained in this section User can initially use this example to get acquainted with running dynamic applications using the Planetary2D analysis package 9 1 The EDIT menu All the data describing the model is entered in the submenus of the EDIT menu The user is free to choose any units for force time and length Note that all the inputs should then be in units that are consistent with this choice The data for the example problem is given in English units The outputs will also appear in English units Table 9 1 shows the English and SI units for common physical quantities Tables 9 2 through 9 14 show the data used for the dynamic example problem The names of the bearing files and the mesh files given in this example can be changed according to the choice of the user Note that the working directory must have all the file names provided by the user in the edit menu 9 2 The System level data Table 9 2 shows the 2D Planetary system level data Use the default values for the items not shown in the table 9 3 The Angular position data Table 9 3 shows the angular position data for the pinion PINIONNO item gives the pinion number and the ANGPOSNPINION item gives the nominal angular position of the respective pinions 9 4 The Pinion data Select the Rim option for the pinion The values of LUMPMAS
101. owing a narrow range of radial component frequency response of pinionl in the planetary system in the dynamic state transient response is in column no 2 of the PIN IONIBRGRES DAT file Table 9 20 Displacement values in the tangential direction for a critical frequency of 574 05 Hz for the pinions Body member Phase Pinion 1 550 6 6 0878 6 6 282 6 1 8201 Pinion2 8 8757e 6 4 1427 6 9 7949e 6 0 4367 Pinion3 3 8233 6 3 0933 6 4 9179 6 2 4613 Pinion4 3 4846 6 7 1558 6 7 9591 6 2 0240 Sun 4 8865 6 4 8401 6 6 8778 6 2 3610 148 Running a dynamic case 3 5 T T T T T T 2 5 Disp 1 5 0 5 a 0 1 0 100 200 300 400 500 600 700 800 900 1000 Freq Hz Figure 9 8 Plot showing the response near the first multiple of mesh frequency for the radial component of deformation of the pinionl bearing transient response is in column no 2 of the PINIONIBRGRES DAT file 9 18 Applying the 2D Planetary program for modal analysis 149 x 10 3 5 T 2 5 Disp in 1 5 0 0 5 1 1 5 2 2 5 3 Freq Hz 10 Figure 9 9 Plot showing the tangential component frequency response of pinionl in the planetary system in the dynamic state transient response is in column no 3 of the PINIONIBRGRES DAT file 150 Running a dynamic case 3 5 2 5 Disp 1 5 5
102. postprocessing file size goes beyond 2 Gigabytes which may be too large So generally we do not write the postprocessing file while running dynamic cases unless it is for less than 100 steps So do not check the POSTPROCWRITE box Also most of the results are extracted using Surface gages FE probes and bearing files All the other parameters related to the setup menu are given in Table 9 15 For the dynamic example problem RPM 1623 r p m 0 r p m 27 99 Nsteps for first Static range 1 00 Nsteps for second Dynamic range 1000 Nsteps for third Dynamic range 3000 Using the above data and the formulas Teycle 1 742E 3 secs Time step For 100 steps per tooth cycle 1 742E 5 secs Tooth meshing frequency 1 Teycte 574 05 Hz Running a dynamic case Table 9 15 Setup menu Item Description SEPTOL 3e 3 NPROFDIVS 3 DSPROFSUN 0 2 DSPROFRING 0 2 INITIALTIME 0 0 NRANGES 3 RANGE 1 SOLMETHOD STATIC NTIMESTEPS 1 DELTATIME 1 742E 5 STARTSPEEDFACTOR 0 0 STARTTORQUEFACTOR 1 0 ENDTORQUEFACTOR 1 0 RANGE 2 SOLMETHOD NEWMARK NTIMESTEPS 1000 DELTATIME 1 742E 5 STARTSPEEDFACTOR 0 0 STARTTORQUEFACTOR 1 0 ENDTORQUEFACTOR 1 0 RANGE 3 SOLMETHOD NEWMARK NTIMESTEPS 3000 DELTATIME 1 742E 5 STARTSPEEDFACTOR 1 0 STARTTORQUEFACTOR 1 0 ENDTORQUEFACTOR 1 0 NSTEPSAVE 500 SAVEFILENAME restper dat OUTPUTFILENAME restout dat 9 17 Analysis and Results 137 9 17 Analysis and Re
103. range to a number NUMDEPTH of points ranging in depth from DEPTHBEGIN to DEPTHEND below the surface This is an expensive computation and should not be used unless necessary The surface gage will measure the stress at the critical depth The depth is in physical length units Because finite element stresses computed very close to the highly concentrated contact loads can have a large amount of error we need a way to screen out points that are too close The parameter DISTMIN is the minimum allowed distance of a stress calculation point from a contact point Stresses will not be calculated at any point whose distance from a contact point is less than this value This distance is in physical length units During the analysis all the surface gage readings are written to a file called GAGES DAT Each row in this file corresponds to a time instant The first column in the file contains the value of the time The remaining columns contain the readings of the surface gages There are four columns of data for each gage The first column for a gage contains the critical maximum principal normal stress 81 over its search range The second column contains the value of the critical minimum principal normal stress s3 The third column contains the critical maximum shear stress Tmax and the fourth column contains the critical Von Mises shear stress Sym The columns are separated by tabs 6 2 Finite element probes Finite Element Probes can be used t
104. s Figures 7 1 and 7 3 will generate a drawing Figures 7 8 and 7 9 show examples of drawings generated by Multyx in the post processing mode Figure 7 10 shows a drawing made in the post processing mode using the exaggeration factor Figure 7 8 An example of a drawing made in the post processing mode 76 Pre and Post processing Figure 7 9 An example of a drawing made in the post processing mode 7 3 The DRAWBODIES command i amp E 3 Figure 7 10 An example of a drawing made in the post processing mode using the exaggeration command 77 78 and Post processing 7 4 The NUMBER command The NUMBER command in the pre and post processing menus Figures 7 1 and 7 3 lead to the numbering menu shown in Figure 7 11 This menu is used to generate tooth and surface numbering as shown in Figure 7 12 BODY SUN TOOTHBEGIN Do z TOOTHEND po a LEELEE START Figure 7 11 The NUMBER menu 7 5 The TOOTHLOAD command The TOOTHLOAD command in the post processing menu Figure 7 3 leads to the menu shown in Figure 7 13 This menu is used to generate a graph of tooth load vs time The SURFACE PAIR item selects the contact surface pair for which the load is of interest Each surface pair has two contacting members or bodies The MEMBER parameter selects one of these two bodies and the TOOTHBEGIN and TOOTHEND items select a range of instance numbers or tooth numbers within that body
105. s during analysis These data files are named after the bodies The file PINION1RES DAT contains the results for the pinionl SUNRES DAT contains results for the sun Similarly CARRIERRES DAT contains the results for the carrier Each data file has one row for each instant of time analyzed The first column contains the time The next 6 columns contain the six components of reference frame deflection uz uy Uz Oy and 0 The last 6 columns contain the 6 components of reference frame reaction Fy Fy Fz My and The deformation and reaction forces generated in each bearing are also saved in data files dur ing analysis These data files are named after the bearings For example the file PINION1BRGRES DAT contains the results for the pinionl bearing SUNBRGRES DAT contains results for the sun bearing And CARRIERBRGRES DAT contains the results for the carrier bearing Each data file has one row for each instant of time analyzed The first column contains the time The next 6 columns con tain the six components of bearing deformation uz uy Uz Oz and 0 The last 6 columns contain the 6 components of bearing reaction Fr Fy Fz Mz My M 6 5 Other output files EXIT QUIT SEPTOL 0 0030000000 NPROFDIVS yg bP i DSPROFSUN 0 2000000000 noses DSPROFRING 0 2000000000 EROINITIAL INITIALTIME 0 0000000000 000 ECE a NRANGES eee
106. sults Before starting an analysis sensor locations have to be set up to measure stresses and loads in the model User should place the surface gages feprobes and load sensors at appropriate locations depending upon the requirement of results Once the sensors are set up click on the generate model button to check for any errors or warnings If there are none then click on the STARTANAL button to start the analysis The Planetary2D analysis package creates files like PINIONnBRGRES DAT SUNBRGRES DAT HOUSINGRES DAT GAGES DAT FEPROBES DAT LOADS DAT etc after the analysis is complete All these files are created in the working directory Figure 9 1 shows the plot of maximum principal normal stress for the fillet surface on the sun gear using the data from GAGES DAT The information for the Surface gage whose output is shown in Figure 9 1 is de scribed in Table 9 16 Each row in the file GAGES DAT corresponds to a time instant The first column in the file contains the value of time The remaining columns contain the data for the surface gages There are 4 columns of data for each gage So as to obtain the plot shown in the figure we have used the data from the first critical maximum principal normal stress and the second critical minimum principal normal stresses column for Gage no 1 x 10 51 53 51 53 psi 2r 4 4 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 Time secs Figur
107. the X Y plane 118 Pre and Post processing using Iglass Viewer Figure 8 4 Finite element mesh model of the gear bodies Cutaway Cut Plane IL Figure 8 5 The cutting plane switch Position Figure 8 6 The position slider Time 2 000000 Figure 8 7 The time menu 8 3 The Bodies menu 119 Reference Frame Figure 8 8 The reference frame switch 8 2 4 Reference frames The default reference frame is the FIXED reference frame All the bodies appear to move when observed from the FIXED frame The model will align itself to this reference frame when the iglass window pops up The reference frame can be aligned to a body member using the reference frame switch shown in Figure 8 8 If you select the SUN as the reference frame the reference frame origin will coincide with the origin of the Sun gear The Sun gear will appear stationary when observed from the SUN reference frame and rest of the bodies orbits around it If the PINION option is selected then the reference frame origin aligns itself to the origin of the pinion 8 3 The Bodies menu The Bodies menu is shown in Figure 8 9 The body member can be turned on or off by clicking on the member name in the Bodies menu User can view the tooth and the rim sector separately for each gear body View Bodies Aniibs System S PINION amp v Pinion 1 Tooth Pinion Rim 1 Sector Pinion with rim e H GEAR v Gear
108. the absolute values can be plotted using the abs command as shown in the program You can plot the frequency response using the real and imaginary values by using the commands real and imag respectively The phase angle can be calculated using the angle command e By narrowing down the frequency plot Figure 9 7 amp 9 10 you can measure the frequency at which the amplitude the maximum For this example problem critical frequencies came out to 574 05 H z 1148 1082 and 4018 4Hz Figure 9 8 amp 9 11 Critical frequency in this case is either the tooth meshing frequency or a multiple of tooth meshing frequency e Table 9 19 and 9 20 shows the data obtained from the frequency response plot for the radial and the tangential displacement components for all the pinions Using this data the absolute values in radial direction 0 and tangential direction Uy for Pinionl are 2 9142e 06 and 6 282e 06 respectively e The equation defining the relationship between the displacement and frequency is given by Us Acos 27ft where A absolute value of radial displacement and is the phase angle radians in the radial direction For different values of t you will get a set of values for Uz Similarly tangential component U can be calculated using the data from Table 9 20 A graph of Vs 7 for Pinionl is shown in Figure 9 12 Using this graph you can predict the motion of Pinion in the Planetary system in the dynamic state A graph of
109. thods in Engineering vol 31 pp 525 545 1991 Nonlinear and dynamic programming G Hadley Addison Wesley Publishing company 1964 Linear programming George Hadley Addison Wesley 1962 Linear and Combinatorial Programming Katta G Murty John Wiley 1976 ISBN 0 471 57370 1 Linearization of multibody frictional contact problems 5 Vijayakar Busby Houser Computers and Structures vol 29 no 4 pp 569 576 1987 Natural Frequency Spectra and Vibration Modes of Planetary Gears Jian Lin and Robert Parker 1998 ASME Design Engineering Technical Conference September 1998 Atlanta Georgia Gear Dynamics Experiments Part I Characterization of Forced Response Blankenship and Kahraman ASME 7 International Power Transmissions and Gearing Conference San Diego October 1996 Gear Dynamics Experiments Part II Effect of Involute Contact Ratio Blankenship and Kahraman ASME 7 International Power Transmissions and Gearing Conference San Diego October 1996 Gear Dynamics Experiments Part Effect of Involute Tip Relief Blankenship and Kahra man ASME 7 International Power Transmissions and Gearing Conference San Diego October 1996 The use of boundary elements for the determination of the geometry factor Vijayakar and Houser 1986 AGMA Fall Technical Meeting Paper no 86 10 Finite element analysis of quasi prismatic structures S Vijayakar H Busby and D Houser International J
110. to the model generator This information is read by the program from pre existing files called template files Figures A 1 through A 4 show the element connectivity and element numbering scheme used in the four standard templates The orientation of the element coordinate system is indicated by the notch in one of the corners of each element The range of the surface profile coordinate 5 for the two contact surfaces is also shown 156 Tooth Mesh Templates Element Coordinates Side 2 Side 1 Figure 1 The MEDIUM TPL template file 157 Element Coordinates Side 2 Figure A 2 The FINEROOT TPL template file 158 Tooth Mesh Templates Element Coordinates Side 2 Figure A 3 The FINEST TPL template file 159 Element Coordinates Side 2 Figure A 4 The THINRIM TPL template file 160 Tooth Mesh Templates Bibliography 10 11 12 13 14 Planetary Gear Train Ring Gear and Support Structure Investigation Mark Valco Ph D Dissertation Cleveland State University 1992 Gear Tooth Stress Measurements of Two Helicopter Planetary Stages Krantz T L NASA Technical Memorandum 105651 AVSCOM Technical Report 91 C 038 1992 A combined surface integral and finite element solution for a three dimensional contact problem 5 Vijayakar International Journal for Numerical Me
111. ts are measured bearing race 2 reference frame The rotation components are displayed in Radians 7 20 The BRGREACTION command The BRGREACTION command of the post processing menu Figure 7 3 leads to the menu shown in Figure 7 41 This menu is used to generate a graph of a component of the bearing reaction as a function of time as shown in Figure 7 42 The six force components that can be graphed are the forces Fy and F7 and the three moments and Mz These components are the forces and moments exerted by race 1 on race 2 The components are calculated in the race 2 reference frame The moments are about the origin of race 2 7 20 The BRGREACTION command 109 0 008000 0 009000 0 010000 0 011000 nge 4 682480E 006 1 338010E 004 Peak to Peak 1 291 185 004 UX Ran 0 002000 0 003000 0 004000 0 005000 0 006000 0 007000 0 001000 0 000000 0 000140 0 000100 0 000080 0 000060 0 000040 0 000020 0 000000 Figure 7 40 The graph generated by the BRGDEFORMN menu 110 Pre and Post processing BEARING COMPONENT BEGINSTEP SIE D pP ET ENDSTEP 11 deb Piet OUTPUTTOFILE Iv 2 FILENAME APPEND 2 PINIONIBRG Figure 7 41 The BRGREACTION menu 7 20 The BRGREACTION command 8 E a 8 5 5 2 8 E E E 8 3 2 s 5 E Y a E 5 x 8 8 E 8 3 8
112. ts to visualise the model can be specified in the TIME menu The user can also visualise the model at a sequence of time steps by entering the number of steps in the NTIMESTEPS menu DELTATIME menu is the value of time increment between successive writes to the iglass file The POPUPIGLASS menu if turned on will automatically open up the Iglass graphical window after the Igass file is generated If it is not turned on only the data file for iglass will be created and iglass will have to be started manually Using the SELECT menu in Figure 8 1 the user can select the bodies to be displayed in the Iglass graphical window Click on the START button in Figure 8 1 to generate the Iglass preprocessing file After the file is generated and if the POPUPIGLASS menu is turned on a separate Iglass window will open showing the reference axes and the gear bodies selected in the SELECT menu An example of the Iglass preprocessing window for a planetary system is shown in Figure 8 2 As shown in Figure it has 3 menus View Bodies and Attributes The Attributes menu is used more commonly in the postprocessing mode The Exit button in each menu will close the Iglass graphics window Pre and Post processing using Iglass Viewer QUIT SELECT IGLASSFILENAME Ee DELTATIME 0 0000000000 000 00 NTIMESTEPS 1 lt DEDI POPUPIGLASS Iv 2 START Figure 8 1 The ge
113. u S 137 Graph showing the pinion bearing tangential displacement against time for dy namic analysis The tangential displacement at each instant of time is given in Column no 3 of the PINIONIBRGRES DAT fil 139 Graph showing the housing moments against time for dynamic analysis The moment about the Z axis for each time instant is given in column no 13 of the HOUSINGRES DAT 140 Graph showing the dynamic tooth load against time The plot is obtained using the load values from column nos 6 10 11 and 12 from the LOADS DAT file 141 Graph showing the static tooth load against time using the TOOTHLOAD com mandi Beale GLE REE 143 Plot showing the radial component frequency response of pinionl in the plane tary system in the dynamic state transient response is in column no 2 of the PINIONIBRGRES DAT file 146 Plot showing a narrow range of radial component frequency response of pinionl in the planetary system in the dynamic state transient response is in column no 2 of the PINIONIBRGRES DAT 147 LIST OF FIGURES 9 8 Plot showing the response near the first multiple of mesh frequency for the radial component of deformation of the pinion1 bearing transient response is in column no 2 of the PINIONIBRGRES DAT 9 9 Plot showing the tangential component frequency response of p
114. ure 3 8 Additional analysis parameters and settings are controlled through the SETUP command 6 1 Surface gages A surface gage is used to measure the critical stress along tooth surfaces The reading of each gage is the most critical stress measured over a user defined range of teeth profile face and depth along a specific surface Figure 6 1 shows the Surface Gage setup menu The number of gages NGAGES has to be entered first Then the gage number for a particular gage can be entered into the GAGE box and the gage information can be typed into the remaining boxes For each gage the BODY item selects which of the individual components in the system the gage is attached to There is a switch provided to select the individual component For a planetary gear set the bodies are the Sun the Ring the individual Pinions the Housing if splines are used and the Carrier After the Body is selected the surface on which the gage should be attached should be se lected The sun and pinion gear teeth typically have four surfaces SURFACE and SURFACE2 cover the entire involute and fillet areas of the two sides Side 1 and Side 2 respectively of the teeth FILLET1 and FILLET2 cover only the fillet region of Side 1 and Side 2 respec tively If the ring gear is selected as the body then there are two more surfaces you can select SPLINESURF1 and SPLINESURF 2 which are the two sides of the spline teeth on the ring gear diameter If the housing is selected
115. ws the right hand rule about the z axis and RPMCARRIER is the speed of the carrier sign follows the right hand rule about the z axis If RING is the INPUT then the system menu asks for RPMINPUT and RPMCARRIER If the INPUT member is SUN or CARRIER then the system menu asks for RPMINPUT and RPMRING The axis of the carrier is assumed to be the origin for the fixed reference frame Ideally the SUN and the RING gear axes coincide with this origin However an assembly error could cause them to be non coincident These assembly errors are shown in Figure 5 3 MAGAXISERRSUN and MAGAXISERRRING variables define the magnitude of the sun axis error and ring axis error respectively ANGAXISERRSUN and ANGAXISERRRING vari ables define the orientation of the axis error for sun and ring respectively The value of zero for this angle implies that the error is along the x axis of the fixed reference frame at time t 0 MAGRUNOUTSUN and MAGRUNOUTRING variables define the magnitude of the high point of runout error for the sun and ring respectively ANGRUNOUTSUN and ANGRUNOUTRING variables define the orientation of the high point of runout error for the sun and ring respectively at t 0 A value of zero for this angle implies that the error is along the x axis of the fixed reference frame at t 0 If the BACKSIDECONTACT flag is set then the backside of the teeth will be checked for contact This flag should be used sparingly because it will cause CPU time to more th

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