DYNACAM USER MANUAL - Norton Associates Engineering
Contents
1. Creating a Cam 5 mm M M Input Data SVAJ BUlOon rli ii ad POLY MONON FUNCT ONS sacs ssi o mr eil ck e paa n e pee Padi a UR Spline FUNGOS Back to the Input Screen se Continuily CHECK SClOON ici SIZING fhe COM iii ti DIQWING o y y X Exporting Cam ii iii 19 Analysis Kinetostatic Analysis Dynamit Andys da 20 Eg gg 23 Fourier Transform FFI did ad ala AR 24 A A sia ates dad sia a pa bd id pud bed id bd aba cd ba ana E na naa RA 25 Fourbar Linkage Follower Train sccscessecsesescessscrsessscessssscesseceusssscesseseceusecesusecavenseseusecaveneecesensnse Fourbar Slider Follower Train Sixbar Linkage Follower Train eese esee ee estate tnn nana than atat rca Siba Slider FOllOWer TON a tata LINKAGE Plot SCIOON DeL Nue Els Lo a Importing Measured Cam Data Torque COMPENSATION Cams uso AAA 33 ipn 34 A 34 2 6 12 06 1 25 PM DYNACAM USER MANUAL Robert L Norton P E Copyright 2006 All rights reserved INTRODUCTION DYNACAM is acam design and analysis program intended for use by engineers and other professionals who are knowledgeable in the art and science of cam design It is assumed2. TORQUE COMPENSATION CAMS Dynacam can calculate an exact torque compensation cam that will if used in conjunc tion with the original cam reduce the torque oscillation in the shaft to the residual damp ing in the system This feature is accessed from the Dynamics screen After calculating the force and torque a checkbox at lower right can be clicked to bring up the screen shown in Figure A 23 To use this a mass spring constant and preload must be chosen for the compensation cam s follower train and these data typed into the boxes at upper left These values do not need to be the same as the primary cam s though they can be This uses a 4th order adaptive step Runge Kutta method to solve the ODE The solver control parameters can be changed at lower left The percent reduction of torque is returned in the left panel and the compensating torque curve plotted below that of the original or primary cam The example shown in the figure has a 99 94 reduction The method used is theoretically exact The error is due to numerical roundoff in the calcu lations Leaving this screen causes a recalcuation of the cam profile to make this counter torque cam The original cam torque function is saved and can be plotted against the compensator and an error function seen However the cam profile buckets are overwrit Eten D P Comp Now co xl Original cam torque Coro Spang mo Follower properties Tprime
3. Coro Flos 50 b torne h 9 x Cam Angle Deg Boh we Conr Stet Step a e Vin Step ODE solver b settings ni 142 Compensating cam torque T comp asoci Cam Angle Deg Deagn 1 1211 2006 cial Cause ect Cay f Biton chek tes FIGURE A 23 Torque Compensation Cam screen in Dynacam Dynacam_Manual PM7 33 6 12 06 1 26 PM 34 Dynacam_Manual PM7 DYNACAM USER MANUAL ten so that the compensation cam profile can be exported in the normal manner for man ufacture A warning box will appear on the Home screen when a compensation cam is stored in memory OTHER All the data calculated at each stage is saved and becomes available for plotting print ing or exporting to disk See General Program Operation for information on New Open Save Save As Plot Print Units and Quit functions REFERENCES 1 Norton L Cam Design and Manufacturing Handbook Industrial Press New York 2002 2 Norton R L Design of Machinery 3ed McGraw Hill New York 2004 34 6 12 06 1 26 PM ROBERT L NORTON 35 A angle to roller 26 B Spline 13 plotting 16 barrel cam contour 18 pressure angle 18 radii of curvature 18 base circle 18 C Calculate button 18 cam vs machine zero 19 cartesian plot 8 coefficient of fluctuation 20 of friction 20 conjugate cam 19 continuity
4. 7 cam rotation Cam follower Change E Gi cam type Follower motion Translating follower Change data appear follower here type A Keyway location Oscillating follower arm data Mate Wile irae posti e tort 5570 l e Dero dran Click here to calculate pressure angle radius of curvature and contour FIGURE A 8 Size Cam screen from DYNACAM for a radial cam with oscillating roller follower copying it to the clipboard or printing it to the printer with the appropriate buttons This will bring up the Continuity Check screen Continuity Check Screen This screen provides a visual check on the continuity of the cam design at the segment interfaces The values of each function at the beginning and end of each segment are grouped together for easy viewing The fundamental law of cam design requires that the S V and A functions be continuous This will be true if the boundary values for those functions shown grouped as pairs are equal If this is not true then a warning dialog box will appear when the Next button is clicked It displays any errors between adjacent seg ments in both absolute and percentage terms You must decide if any errors indicated are significant or due only to computational roundoff error Cancel will return you to the Input Data screen to correct the problem and OK will take you to the Home screen Sizing the Cam Once the S V A J functions have been defined to your satisfaction it rem
5. About Menu The About pulldown menu on the Home screen will display a splash screen containing information on the edition and revision of your copy of the program The Disclaimer and Registration form can also be accessed from this menu Exiting a Program Choosing either the Quit button or Quit on the File pulldown menu on the Home screen will exit the program If the current data has not been saved since it was last changed it will prompt you to save the model using an appropriate suffix In all cases it will ask you to confirm that you want to quit If you choose yes the program will terminate and any unsaved data will be gone at that point Note that the Home Screen lacks a check box at its upper right corner that is sometimes used to exit a program This omission is deliberate in order to force you to do a normal exit via the Quit command which cleans up on the way out and shuts down the graphics server that is running in the background If the graphics server is left running it may crash the system when other programs are later run Dynacam Manual PM7 11 6 12 06 1 25 PM 11 12 DYNACAM USER MANUAL Support Please notify the author of any bugs via email to norton designofmachinery com or norton wpi edu CREATING A CAM The Home Screen Initially only the SVAJ and Quit buttons are active on the Home screen Typically you will start a cam design with the SVAJ button but for a quick look at a cam as drawn by the progr
6. Itis used only to identify plots data files and printouts so they can be grouped if necessary at a later date When the Next button on the Title screen is clicked the Home screen appears The Home Screen All program actions start and end at the Home screen which has several pulldown menus and buttons File New Open Save Save As Units About Plot Print Quit These are described below 4 6 12 06 1 25 PM ROBERT L NORTON General User Actions Possible Within the Program The program is constructed to allow operation from the keyboard or the mouse or with any combination of both input devices Selections can be made either with the mouse or if a button is highlighted showing a dotted square within the button the Enter key will activate the button as if it had been clicked with the mouse Text boxes are provided where you need to type in data These have a yellow background Double clicking on a text box will select its contents In general what you type in any text box is not accept ed until you hit the Enter key or move off that box with the Tab key or the mouse This allows you to retype or erase with no effect until you leave the text box You can move between available input fields with the Tab key and back up with Shift Tab on most screens If you are in doubt as to the order in which to input the data on any screen try using the Tab key as it will take you to each needed entry field in a sensible order You can the
7. among four cardinal positions The prime circle radius base circle for a flat follower roller radius if any and cutter radius can be typed into their respective boxes For a translating follower its offset and angle of translation versus the positive x axis can be specified For an oscillating follower the lo cation of the arm pivot and the length and rotation direction of the arm must be provided When a change is made to any of these parameters the schematic image of cam and follower is updated Select the Calculate button to compute the cam size parameters and the cam con tour For barrel cams a summary of the max and min pressure angles and radii of curva ture appears Next returns you to the Home Screen Barrel cam contours cannot be dis played as they are three dimensional The cam contour is now ready for export A dia log box appears with instructions on exporting the cam contour data for manufacturing Drawing the Cam For radial cams the cam contour is displayed on the Draw Cam screen after calculation as shown in Figure A 9 This screen allows the prime or base circle and if translating the offset to be changed further Cam rotation direction can also be changed here and 18 6 12 06 1 26 PM ROBERT L NORTON the cam contour will be recalculated and redisplayed Changes to other parameters can be accomplished via the Back button which returns you to the Size Cam screen The maximum and minimum pressure angles
8. and radii of curvature are shown in the right side bar For more information on these parameters select the Show Summary radio but ton at the lower right This will change the cam image to a summary of pressure angle and radius of curvature information The Show Cam radio button will redraw the cam contour Selecting the Show Conjugate radio button computes and displays the conju gate of the cam previously shown In the cam profile drawing a curved arrow indicates the direction of cam rotation The initial position of a translating roller follower at cam angle 0 is shown as a filled circle with rectangular stem and of a flat faced follower as a filled rectangle Any ec centricity shows as a shift up or down of the roller follower with respect to the X axis through the cam center The smallest circle on the cam centerline represents the cam shaft and its keyway is shown as a solid dot The larger circle is the base circle The prime circle is not drawn The default image shows the inner cam surface Check boxes above the image al low the outer surface the track of the follower or the cutter path around the cam to be displayed instead When the follower path is shown the pitch curve is drawn through the locus of the roller follower centers The check box labeled Cam vs Machine Zero phase shifts the cam contour to ma chine zero and redisplays it In the case of an oscillating arm follower the cam contour is reoriented to put the keyw
9. bal coordinates of O4 must be defined Link 4 has two branches the one labeled 4 and shown in black that connects link 3 to O4 and the one labeled 4a in color that connects to link 5 at 745 The angle between branches 4 and 4a which are part of the same link must be defined also Offset is the perpendicular distance between the axis of slid ing and the pivot O2 The Slider Angle is the angle between the global X axis and the axis of sliding reer t we IN Un cache e Ringe 2 Mods Choose circuit Com Choose circuit for1234 Coord for1456 Offset is the perpendicular distance from the slider Link lengths axis to the pivot O5 Link length 5 Co are Slider angle is the angle between the slider axis Warton Arzodataz and the X axis here 90 Design Ma 1 02 11 2006 at 122241 Current angle Fis Model Dirag thesldertoimove Click the arrow to move the linkage continuously FIGURE A 19 Input Data screen for a Sixbar Slider cam follower train Dynacam_Manual PM7 29 6 12 06 1 26 PM 30 Can have two or four plots per screen Select Function Select Link Select Function Select Link FIGURE A 20 DYNACAM USER MANUAL Note that is possible to input a set of linkage data that is impossible to solve as the links may not be able to connect if their lengths are not compatible An error message will appear when the calculation is done if this is the case Once calculated the
10. copy and paste it into another document for your records You will only be able to reconstruct it later by again defining the BCs and recalculating the polynomial Spline Functions If any of your segments specified a Spline motion clicking the Calc button will bring up the same Boundary Condition screen shown in Figure A 6 that is used for polynomial functions These are defined in exactly the same way as described for polynomials in the preceding section Once you finish selecting boundary conditions for your spline and hit the Next but ton it takes you to the Spline Function screen shown in Figure A 7 This screen shows the current segment the number of boundary conditions that were selected and requires you to choose a spline order between 4 and the number of boundary conditions previ ously selected It then displays the total number of spline knots used and the number of those available for distribution as interior knots It also calculates the spline functions and displays their 5 V A J functions for the default assumption of evenly spaced interior knots The current locations of the knots in degrees are displayed in the right side bar The shape of the spline can be manipulated as described in Chapter 5 of reference 1 by moving the interior knots around There are several ways to do this One is to select a knot with its radio button in the right side bar and type the angle to move it to in the yellow box Alternatively you may sel
11. of linkage data that is impossible to solve as the links may not be able to connect if their lengths are not compatible An error message will appear when the calculation is done if this is the case Once calculated the linkage can be animated by using the Step button to advance it one cam increment at a time or by dragging the slider bar at the bottom of the screen to left or right A motion simula tion can be obtained by holding down the arrows at the ends of the slider bar ONAL AM Plon Profeewnmal Edon 1 Norton Copyright 2006 Humano 0 Rev 21 G Com Current angle Choose circuit Pine Slider angle is the angle between the slider axis and the X axis here zero 10 006 Link lengths E 3000 1000 y X Slider Ange Offset is the perpendicular distance from the slider axis to the pivot O5 ET 27778 ET EA TT Drag the slider to move the linkage Click the arrow to move the linkage continuously FIGURE A 17 Input Data screen for a Fourbar Slider cam follower train Dynacam_Manual PM7 27 6 12 06 1 26 PM 28 Linkage type Choose circuit for1234 Link lengths Drag the slider to move the linkage FIGURE A 18 Type Dit dto rear 12 C Fosta DYNACAM USER MANUAL The Plot Func button takes you to the Linkage Plot screen described below The Mass Prop button goes to the Mass Properties screen also described below Si
12. of polar plots showing just the vec tors just the envelope of the path of the vector tips or both A plot that connects the tips of the vectors with a line its envelope is sometimes called a hodograph SIEHE NICE Dis cM NIMM Hartos 19198 Select Pict Cite Double click Plot type on any item icon in this list Aligned Choose any puts plots Charter oc aed al four items in proper and their phase components annotated from these does not drop down lists Local coord system only is available These boxes show what for some will be variables plotted FIGURE A 3 Click here to see the plots WE Click here to select a variable for plot The PlotSelect screens are common to all programs this shows one of four styles of PlotSelect screens Dynacam_Manual PM7 9 6 12 06 1 25 PM 10 DYNACAM USER MANUAL SELECTING PLOT VARIABLES Choosing any one of the four plot types from the Plot Type screen brings up a Plot Select screen that is essentially the same in all pro grams See Figure A 3 As with the Print Select screen two arrangements for select ing the functions to be plotted are provided Preset Formats and Mix and Match The former provides preselected collections of functions and the latter allows you to select up to four functions from those available on the pulldown menus In some cases you will also have to select the component of the function desired 1 x m
13. same way as the LNCS y at point A that is it travels with point B but remains parallel to the world coordinate sys tem X Y at all times LOCAL COORDINATES The coordinate system y also travels with point as its origin but is embedded in link 4 and rotates with that link continuously changing its ori entation with respect to the global coordinate system X Y making itan LRCS Each link has such an LRCS but not all are shown in Figure A 13 The Local choice in the Coordi nate System panel uses the LRCS for each link to allow the plotting and printing of the tangential and radial components of acceleration or force on a link This is of value if for example a bending stress analysis of the link is wanted The dynamic force components perpendicular to the link due to the product of the link mass and tangential acceleration will create a bending moment in the link The radial component will create tension or compression PLOTTING Once your selections are made and are shown in the cyan boxes at the lower right of the Plot Select screen the Next button will become available Clicking it will bring up the plots that you selected Figure A 4 shows examples of the four plot types available From this Plot screen you may copy to the clipboard for pasting into another application or dump the Plot screen to a printer The Select Another button re turns you to the previous Plot Select screen Next returns you to the Home screen The
14. that the user knows how to determine whether a cam design is good or bad and whether it is suitable for the application for which it is intended The program will calculate the kinematic and dynamic data associated with any cam design but cannot substitute for the engineering judgment of the user The cam theory and mathematics on which this pro gram is based are shown in reference 1 Please consult it for explanations of the theory and mathematics involved The authors and publishers are not responsible for any damages that may re sult from the use or misuse of these programs Dynacam is one member of a family of programs by this author that share a com mon kernel for the overhead actions such as printing plotting etc In this manual you will sometimes see references such as these programs will which means that these features are common to the family DYNACAM also can generate files for export to sev eral of these programs e g FOURBAR SIXBAR SLIDER GENERAL INFORMATION Hardware Requirements These programs need a Pentium or better processor DYNACAM is large and uses signif icant computer resources A minimum of 128M of RAM is desirable DYNACAM may require that all other applications be shut off in order to run in a computer with other wise insufficient memory A CD ROM drive is needed as is a hard disk drive Operating System Requirements These custom programs are written in Microsoft Visual Basic 6 0 and work on a
15. will lead you through the steps needed to input all data as indicated by the circled numbers in Figure 5 On a blank Input screen Tab first to the Cam Omega box in the upper left corner 1 and type in the speed of the camshaft in rpm Tab again or mouse click if you prefer to the Number of Segments box 2 and type in any number desired between and 20 That number of rows will immediately become visible on the screen Tab or click to the Delta Theta pulldown 3 and select one of the offerings on the menu No other values than those shown may be used Next select either Translating or Oscillating for the follower motion 4 The Starting Angle box 5 allows any value to be typed to represent the machine angle on the timing diagram at which you choose to begin the first segment of your cam i e where you choose cam zero Unless the timing diagram places machine zero within a motion event this can be left as zero making cam zero the same as machine zero the default If machine zero is within a motion rise or fall you cannot start the cam design at that point Also you should always start at the beginning of a motion not at or in a dwell The External Force check box and the Motion Force option buttons 6 are provid ed for situations in which the cam follower is subjected to a substantial external force during operation such as in a compactor mechanism Checking this box temporarily converts the cam design program into
16. 2 cam revolu tions and displays the results in plots of displacement error s x x x and x along with their extreme values The data is saved only for the second revolution in order to dis card the effects of any numerical convergence start up transients The center bar shows 6 12 06 1 26 PM integration of the torque curve at left For single or multiple cams on same shaft 0 lt value lt 1 to generate flywheel torque curve DYNACAM USER MANUAL 1 DOF models 22 D YNACAM be Morton Cope 2001 Industrial models Automotive models FIGURE A 11 Select Dynamic Model screen in program DYNACAM Model type Mass properties spring constants and damping Polydyne calculation Eng Tre Runge Kutta solver parameters We dun am FIGURE A 12 Dynamic Modeling screen in program Dynacam Dynacam_Manual PM7 22 E Car aga Degi tee s C Cony Puts Donar Model 2 DOF models Follower error s x Follower displacement x Follower velocity x Follower acceleration x 6 12 06 1 26 PM ROBERT L NORTON calculated values of the system natural frequencies natural periods and various dynam ic ratios as described in of reference 1 Clicking the Next button at this point returns you to the Home screen POLYDYNE AND SPLINEDYNE CALCULATION The Select Dynamic Model screen provides a check box to make a polydyne or spli
17. Dynacam_Manual PM7 DYNACAM USER MANUAL Robert L Norton P E Copyright 2006 Robert L Norton All Rights Reserved Norton Associates Engineeering 46 Leland Road Norfolk MA 02056 USA http www designofmachinery com Contact info designofmachinery com 1 6 12 06 1 25 PM Dynacam_Manual PM7 Contents A T n 3 Generol uiia rx Rok DA EIA 3 BRE TER 3 Operating System Requirements 1 11 ndice iria 3 lanea tegere MW C 3 Installing fhe Soffwatre rccte tiit dread acea rece 4 WOW 10 950 This MANU Mete 4 Progr Oper OD ici 4 NAAA 4 TNE 0 e 4 General User Actions Possible Within the Program 5 Uo MN ii 5 Examples 5 Creating New Saving and Opening Files File 5 Copying Screens to Clipboard or Printer COPY 6 Printing to Screen Printer and Disk Files Print Button esee 6 Plotting Data Plot ii 7 Wai m 11 Exiting a PODA 11 Support _
18. In the latter case the cam contour will be modified to account for the linkage geometry The geometry of the follower arm as defined on the Size Cam screen is automati cally imported to all linkage screens thus defining the location of link two s ground piv ot versus the cam center The global coordinate system origin is at the cam center in all cases and the orientation is as previously defined on the Size Cam screen Dynacam does only a kinematic analysis of the linkage train calculating only angu lar displacements velocities and accelerations of all the links These can be plotted in Dynacam Mass properties of the links can be entered on a separate screen but these are not used for dynamic calculations in this program They are used only for the lumped model approximations on the Dynamics and Vibration screens Rather the linkage ge ometry and mass data along with all the cam SVA data can be exported in a text file that DYNALAM Plus Professional Erit by RA Morten Copyraght 2008 Release 9 0 2 1 2 Fourbar linkage Sixbar linkage Fourbar slider Sixbar slider FIGURE A 15 Linkage Selection screen in Dynacam Dynacam_Manual PM7 25 6 12 06 1 26 PM 26 Linkage type Choose circuit Link lengths Ture Froude C wt subs Cen im C End Esvector DYNACAM USER MANUAL in turn can be imported into a linkage analysis program such as Fourbar Sixbar or Slid er for further analysis T
19. YSALAM Pus Professional dita by RA Morten Copyright 2008 Release 90 Rev 2 8 2 0 00 Current angle Choose circuit for 1456 Click the arrow to move the linkage continuously Input Data screen for a Sixbar Linkage cam follower train Dynacam_Manual PM7 28 6 12 06 1 26 PM ROBERT L NORTON 29 by dragging the slider bar at the bottom of the screen to left or right A motion simula tion can be obtained by holding down the arrows at the ends of the slider bar The Plot Func button takes you to the Linkage Plot screen described below The Mass Prop button goes to the Mass Properties screen also described below Sixbar Slider Follower Train Figure A 19 shows the input screen for a sixbar slider linkage The Linkage Modes de fine the kinematic circuits of each stage of the linkage which can independently be ei ther open or crossed as desired For a definition of these terms see reference 2 The Angle to Roller parameter defines the included angle between the kinematic link 2 and the arm radius to the roller The link lengths are always defined as the pin to pin dis tances of each link Link numbering is standardized with link 1 always the ground link link 2 the link directly driven by the cam and pivoted to ground link 3 a floating coupler or connecting rod link 4 a rocker pivoted to ground at that connects the two couplers link 5 the second coupler and link 6 the output slider running against ground The glo
20. a force time function design program in which the shape of the force time or force angle function can be defined as if it were a cam dis placement function with units of force instead of length When calculated the force data is stored for later superposition on the follower s dynamic forces due to motion When External Force is checked a dialog box pops up with further information on how to use it Another Tab should put your cursor in the box for the Beta segment duration an gle of segment 1 7 Type any desired angle in degrees Successive Tabs will take you to each Beta box to type in the desired angles The Betas must of course sum to 360 degrees If they do not a warning will appear As you continue to Tab or click your mouse in the appropriate box if you prefer you will arrive at the boxes for Motion selection 8 These boxes offer a pulldown se If you intend to do any lection of Rise Fall Poly Dwell and Spline You may select from the pulldown menus dynamic analysis of your with the mouse or you can type the first letter of each word to select it Rise fall and follower train within dwell have obvious meanings The Poly choice indicates that you wish to create a cus tomized polynomial function for that segment and this will later cause a new screen to ell die numerical appear on which you will define the order and boundary conditions of your desired poly differential equation solver nomial function Th
21. ag or angle PLOT ALIGNMENT Some of the Plot Select screens offer a choice of two further plot style variants labeled Aligned and Annotated The aligned style places multiple plots in exact phase relationship one above the other The annotated style does not align the plots but allows more variety in their display such as fills and grids The data displayed are the same in each case ee Pss Clm by Into Caper TI mm mes mb Cl m by A rm gr c One to four plots superposed in one window d Single polar plot FIGURE A 4 The four styles of plots available in all programs sidebar information is different in each program Dynacam Manual PM7 10 6 12 06 1 25 PM ROBERT L NORTON COORDINATE SYSTEMS For particular variables in some programs a choice of co ordinate system is provided for display of vector information in plots The Coordinate System panel on the Plot Select screen will become active when one of these variables is selected Then either the Global or Local button can be clicked It defaults to Global GLOBAL COORDINATES The Global choice in the Coordinate System panel refers all angles to the XY axes of Figure A 14 For polar plots the vectors shown with the Glo bal choice actually are drawn in a local nonrotating coordinate system LNCS that re mains parallel to the global system such as x4 y at point A and y2 at point in Fig ure A 13 The LNCS y at point behaves in the
22. ains to size the cam and determine its pressure angles and radii of curvature This is done from the Size Cam screen shown in Figure A 8 which is accessible from the button of that name on the Home screen The Size Cam screen allows the cam rotation direction and follower Dynacam_Manual PM7 17 6 12 06 1 26 PM 18 Change cam rotation Cam phasing Primary cam conjugate cam or data Change animation speed FIGURE A 9 DYNACAM USER MANUAL Change cam contour display Core Rotes C Cw cow Con Orega 20054 Cu a Theta 1 de Cim Enos Dye Aj Machine Zero Korun e ot Can Stent arge wp Show Con O Sew Sun Show Coupe Speed Si Fent ro Cun Sue Duis Prive Podu Cam and 4000 2 follower Fon di fora y radii J n Offset Mi Pe 149 9 Pressure Tas ms angles and 134 radii of 33 n bi curvature MARIO Cun Theta 0 9 Feira Con CEN Linkage screen Animate cam Prnt For Draw Cam screen from DYNACAM for a radial cam with oscillating roller follower Dynacam Manual PM7 type flat or roller to be set The cam type radial barrel or linear and follower motion translating or oscillating can also be selected The cam start angle cam zero as chosen on the S V A J screen is shown and a drop down box allows the keyway location versus ma chine zero to be selected
23. am one of the examples under the Example pulldown menu can be selected and it will draw a cam profile If you activate one of these examples when you return from the Cam Profile screen you will find all the other buttons on the Home screen to be ac tive We will address each of these buttons in due course below Input Data SVAJ Button Much of the basic data for the cam design is defined on the Input screen shown in Figure 5 which is activated by selecting the SVAJ button on the Home screen When you open this screen for the first time it will be nearly blank with only one segment s row visible Note that the built in examples can also be accessed from this form at its upper right corner If you had selected an example cam from the pulldown menu on the Home screen making the Input screen nonblank please now select the Clear All button on the Input screen to zero all the data and blank the screen in order to better follow the pre Pull down for examples 1 You 5 plot or print 2 E each T I segment s 8 NE E data to i E inspect results as 4 _ you go 5 Select Select Click Calc these these 6 for each 9 segment FIGURE A 5 S V A J input screen for program DYNACAM Dynacam_Manual PM7 12 6 12 06 1 25 PM ROBERT L NORTON 13 sentation below We will proceed with the explanation as if you were typing your data into an initially blank Input screen If you use the Tab key it
24. ay at the selected o clock position For a translating follow er the follower is kept in a fixed orientation along the x axis and the keyway rotated to the correct relative position These phase shifts incorporate the start angle follower an gle and keyway location The magenta radial lines that form pieces of pie within the base circle represent the segments of the cam If the cam turns counterclockwise the radial lines are numbered clockwise around the circumference and vice versa The Next button returns you to the Home Screen The cam profile is now ready for export Whether the Show Cam or Show Conjugate radio button was selected when Next was clicked determines which of those two cam contours will be the one exported So to generate cutter data for a pair of conjugate cams requires sequential calculation and ex port of their respective data to files The state of the Inner Surface Outer Surface radio buttons at the time Next was clicked also dictates which cam surface will be exported Generating both cam surfaces also requires sequential calculation and export of data Only one set of cam surface contour data is stored in memory at a time The cam profile for a radial cam can be displayed at any time from the Home screen with the Draw Cam button So for creation of multiple cam surfaces or conjugates of radial cams it is only necessary to revisit the Draw Cam screen without resizing the cam Clicking Next on the Draw Cam screen returns
25. check 17 coordinate systems 10 copying to clipboard 6 creating new files 5 D Draw Cam screen 18 drawing the cam 18 dynamic forces 24 Dynamics button 20 screen 21 examples 5 exporting cam contour 19 SVA data 26 external force 13 24 F follower angle 18 arm 18 dynamics 20 21 23 offset 18 oscillating 18 translating 18 weight 24 Fourier transform 24 screen 24 Dynacam_Manual PM7 35 Index friction torque 20 fundamental law 17 H hardware requirements 3 hodograph 9 home screen 4 how to use this manual 4 importing measured cam data 31 inner surface outer surface 19 Input Data 12 installing the software 4 J journal diameter 20 K kinetostatic forces 23 L linkage 25 fourbar 26 fourbar slider 27 plot screen 30 sixbar 28 sixbar slider 29 M mass properties 25 button 27 screen 31 motion force option 13 N number of segments maximum allowed 13 O ODE solver 21 offset 18 opening a file 6 operating system requirements 3 P Plot Func button 27 plotting data 7 cartesian plots 8 polar plots 8 polar plot 8 polydyne 23 polynomial 13 coefficients 16 completing 16 solution method 15 polynomial functions 15 16 pressure angle 17 prime circle 18 printing 6 program operation 4 Q quitting the program 11 radii of curvature 17 roller radius 18 running the program 4 saving data 6 Select Dynamic Model screen 21 Show Cam 19 Show Conjugate 19 sizing
26. e Spline choice indicates that you wish to create a customized B will fail to converge Spline function for that segment and this will later cause a set of new screens to appear because when started on a on which you will define the boundary conditions order and knot locations of your de dwell it cannot make any sired B Spline function progress with its comput tions If you do not intend The next set of choices that you will Tab or mouse click to are the Program pull to do any dynamic downs 9 These provide a menu of standard cam functions such as Modified Trape B lysis shame on you but zoid Modified Sine and Cycloid as well as a large number of specialized functions as e You can start the cam described in reference 1 Also included are portions of functions such as the first and Dynacam_Manual PM7 13 6 12 06 1 25 PM 14 Start here Input no of boundary conditions for this segment Hint use Tab key to move to next box FIGURE A 6 DYNACAM USER MANUAL second halves of cycloids and simple harmonics that can be used to assemble piecewise continuous functions for special situations The standard double dwell polynomials 3 4 5 and 4 5 6 7 as well as a symmetrical single dwell 3 4 5 6 rise fall function are pro vided as menu picks though they can also be created with a Poly choice and subsequent definition of their boundary conditions After you have selected the desired Pro
27. ect a knot with its radio button and then click the mouse on any one of the SVAJ plots at any location that you want that knot to move to A shortcut for picking a knot is to Shift Click near the knot you want to activate and this will select its radio button for you Then a Click will move that selected knot Note that because knots must be in ascending order it will refuse to violate their order if you request an inappropriate knot location The plots and extreme values will update imme diately unless you unchecked the Autocalc On box at upper right If you are making a large number of knot changes turning off Autocalc will speed the process by suppress ing the screen updates It may also avoid tripping error messages engendered by a poor initial distribution of multiple knots until you can get them more or less where you want them before allowing it to recalculate the splines The back button returns you to the Boundary Condition screen if you wish to change them The Show Splines button will display the basis functions that make up the B Splines Plot Functions returns the B Spline plots Next returns you to the Input Screen Back to the Screen Completing a polynomial or spline function returns you to the Input screen When all segments have been calculated select the Next button on the Input screen perhaps after 16 6 12 06 1 26 PM ROBERT L NORTON 17 das Winder IL Menton Copright 2001 Change
28. es and operate in a consistent way For exam ple all printing and plotting functions are selected from identical screens common to all programs Opening and saving files are done identically in all programs These com mon operations will be discussed in this section independent of the particular program Later sections will address the unique features and operations of each program Running the Program At start up a splash screen appears that identifies the program name version revision number and revision date Click the button labeled Start or press the Enter key to run the program A Disclaimer screen next appears that defines the registered owner and al lows the printing of a registration form if the software is as yet unregistered A registra tion form can be accessed and printed from this screen The next screen the Title screen allows the input of any user and or project identi fication desired This information must be provided to proceed and is used to identify all plots and printouts from this program session The second box on the Title screen al lows any desired file name to be supplied for storing data to disk This name defaults to Modell and may be changed at this screen and or when later writing the data to disk The third box allows the typing of a starting design number for the first design This design number defaults to 1 and is automatically incremented each time you change the basic design during this program session
29. forces FIGURE A 13 Stress analysis screen in program DYNACAM Dynacam_Manual PM7 23 6 12 06 1 26 PM 23 Dynamic Force Radius of curvature Principal normal stress Maximum shear stress 24 Select segment Select function Select harmonics FIGURE A 14 DYNACAM USER MANUAL be supplied but are defaulted to steel for both The appropriate algorithm for surface stress will be used based on the earlier choice of flat or roller follower as described in Chapter 12 of reference 1 If a roller follower is used then you must specify it as cy lindrical or crowned and provide the relevant dimensional information A box is provid ed for the input of a follower weight force if applicable If an external force function was calculated on the 5 V A J form then the check box to include it will become avail able and it can be included or excluded from the stress calculation as desired The calculate button creates and displays the maximum normal and maximum shear stress in cam and follower at each point around the cam and also shows the dynamic force and cam radius of curvature used in the calculation Next returns you to the Home screen Fourier Transform FFT The Fourier transform of any function calculated within DYNACAM and the other pro grams can be formed by pulling down the menu labeled FFT on the Home screen Fig ure A 14 shows the Fourier Transform screen Any one cam segment or the entire cam can be se
30. ge Plot screen in Dynacam Dynacam Manual PM7 30 6 12 06 1 26 PM ROBERT L NORTON OYWACAM Plon Profane Edition by 1 Mortos Copyright 2006 Reinaru LO Rev 21 Ur Diet 05 Kor Pivot tempe lo 05 in Prost Now of Link 02 0025 Mon vs 05 0025 0 04125 0055 006875 0085 Efectos Mara 1 al Enea Mact 2 el End E tector Single Efecte Mars of Follower Use tg ados Une Morton Associates Design ho 1 Stress 00 679 5 3 T 00 11 2006 193230 Fie Mode FIGURE A 21 Mass Properties screen in Dynacam Mass Properties Screen Figure A 21 shows the Mass Properties screen The CG locations and mass properties of each link may be entered here Proper units must be used The stiffness parameters for each link can also be entered When calculated this screen will compute the effec tive mass and effective spring values for the dynamic models in the program these data will be automatically transferred to those screens The raw data will be exported to the linkage files for import to other programs IMPORTING MEASURED CAM DATA Sometimes one needs to reverse engineer an existing cam for which there may be no data available on its design or mathematical functions If a cam profile has been measured with reasonable accuracy those data can be imported to Dynacam and it will fit an inter polating function to approximate the cam s displaceme
31. gram functions for each segment you will Tab or Click to the Position Start and End boxes 10 Start in this context refers to the beginning displacement position for the follower in the particular segment and End for its final position You may begin at the top or bottom of the displacement hill as you wish but be aware that the position values of the follower must be in a range from zero to some positive value over the whole cam In other words you cannot include any anticipated base or prime circle radius in these position data These position values represent the excursion of the so called 5 diagram displacement of the cam and cannot include any prime circle information which will be input later Note that if you selected a translating follower then the displacement values are defined in length units but if you chose an oscillating follower they must be in degrees As each row s segment s input data are completed the Calc button 11 for that row will become enabled Clicking on this button will cause that segment s 5 VA J data to be calculated and stored After the Calc button has been clicked for any segment s row the Plot and Print buttons for that segment will become available 11 Clicking on these buttons will bring up a plot or a printed table of data for S V A J data for that segment only More detailed plots and printouts can be obtained later from the appropriate but ton on the Home screen The plots a
32. hose programs will do a complete kinematic and dynamic anal ysis of the linkage using the SVA cam functions from Dynacam to drive it Fourbar Linkage Follower Train Figure A 16 shows the input screen for a fourbar linkage The Fourbar Mode defines the kinematic circuit of the linkage which can be either open or crossed as desired For a definition of these terms see reference 2 The Angle to Roller parameter defines the included angle between the kinematic link 2 and the arm radius to the roller This is of ten zero but can be nonzero if desired as shown in the figure The link lengths are al ways defined as the pin to pin distances of each link Link numbering is standardized with link 1 always the ground link link 2 the link directly driven by the cam and pivoted to ground link 3 a floating coupler or connecting rod and link 4 the output link in this case pivoted to ground Ground pivots are labeled O with n link number The coor dinates of pivot must be supplied in the global coordinate system Note that is possible to input a set of linkage data that is impossible to solve as the links may not be able to connect if their lengths are not compatible An error message will appear when the calculation is done if this is the case Once calculated the linkage can be animated by using the Step button to advance it one cam increment at a time or by dragging the slider bar at the bottom of the screen to left or right A motion simula tio
33. ics as well as some other Windows applications NOTE In some cases the plotted functions may not print properly from the PrintScreen button If so copy the screen to the clipboard paste it into Word and print from Word This is the recommended approach in any case Printing to Screen Printer and Disk Files Print Button Selecting the Print button from the Home screen will open the Print Select screen see Figure A 1 containing lists of variables that may be printed Buttons on the left of this screen can be clicked to direct the printed output to one of Screen Printer or Disk This choice defaults to Screen and so must be clicked each time the screen is opened to obtain either of the other options The output is different with each of these selections Selecting Screen will result in a scrollable screen window full of the requested data Scrolling will allow you to view all data requested serially This data screen can be cop 6 6 12 06 1 25 PM ROBERT L NORTON 7 Chooses up Sect hon Fere Fores Local coord p Er 1 HW Pes Fars end Match ML A bae na ee el or ea Double click system only e ma iia on any item 1 1 p F T rer 15 available cf iiit Cenim 2 21 Mas Ang Condes his li for some of Cordon 348 H i perd n In this list variables FF Global c Tum Of Sends data ram THES x P to screen assi scs
34. ix and Match allows you to pick any four of the available variables for printing You must print four variables at a time in either mode You can also select other ancil lary parameters such as the number of decimal places and the frequency of data to be printed Plotting Data Plot Button The Plot button on the Home screen brings up the PlotType screen see Figure A 2 which is the same in all programs Variables in these programs can be plotted in one of Dynacam Manual PM7 7 6 12 06 1 25 PM 8 DYNACAM USER MANUAL k PO UA BAR lo ED JS L Horton Coppiight 1958 Sole Piat Double click here to get four cartesian plots in four aligned windows Double click here to get two cartesian plots in two aligned windows Double click here to get from Double click one to four here to get one polar plot in one window superposed cartesian plots in one window FIGURE A 2 Click here to select variables for plots The PlotType screen is common to all programs that allow plotting several formats three Cartesian see below and one polar see below This screen al lows a choice among these four flavors of plots shown as plot style icons The first icon upper left provides four functions plotted on Cartesian axes in four separate win dows The second icon upper right plots two functions on Cartesian axes in separate windows The third icon lower left allows one to four functions to be plotted on c
35. lected for transformation from the upper dropdown menu The middle drop down menu allows any calculated follower function to be chosen for transformation The lower dropdown menu chooses the number of harmonics desired in the Fourier spectrum The rms sum and the spectral power are displayed in the right side bar Once a Fourier calculation is done the spectral information for the chosen follower function will be available for plotting printing and export from the Home screen buttons This FFT data a DIRACAM for Wirehows by R L Merton 2001 Sum of harmonics Yos eet al Spectral power Low Haremos Weder x ave utet vart Gpe Loss 7 Fourier transform screen in program Dynacam Dynacam_Manual PM7 24 6 12 06 1 26 PM ROBERT L NORTON 25 can be used to recreate the functions from the Fourier series harmonics as continuous functions of time in an equation solver for example LINKAGES Dynacam allows four types of linkage follower trains to be created Fourbar linkage Sixbar linkage Fourbar slider and sixbar slider as shown in Figure A 15 There are examples of each on the Examples menu Homescreen and these can be used to seed your model and give you a set of compatible links to start with The cam s SVAJ func tions can be applied either to the input link of the linkage the arm carrying the roller or to the output end of the linkage the end effector
36. linkage can be animated by using the Step button to advance it one cam increment at a time or by dragging the slider bar at the bottom of the screen to left or right A motion simula tion can be obtained by holding down the arrows at the ends of the slider bar The Plot Func button takes you to the Linkage Plot screen described below The Mass Prop button goes to the Mass Properties screen also described below Linkage Plot Screen Figure A 20 shows the Linkage Plot screen This can be switched between to and four windows with the option buttons at the top The background can be switched from white to dark The former is better for printing and the latter may look better on the screen The Select Function and Select Link boxes for each plot allow you to mix and match plots of any combination of functions available For pure linkages all the kinematic properties are angular in units of radian per time For the slider linkages everything is angular except for the parameters of the slider itself which are linear When the data are imported to one of the companion linkage programs many more parameters will be available for plotting and printing The max min and peak to peak values are displayed in boxes to the right of each plot a INM AM Phos resol Edition by RL Kortos Copyright 2006 fielease 9 0 C two Pets Por Pets fe Nite C Cert Zum Angle deg arce C DuoRyo Vale Fato Zum Angle deg Linka
37. me and disk location to save your current model data to disk The data are saved in a cus tom format and with a three character suffix unique to the particular program You should use the recommended suffix on these files as that will allow the program to see them on the disk when you want to open them later If you forget to add the suffix when saving a file you can still recover the file as described below Selecting Open from the File menu prompts you to pick a file from those available in the disk directory that you choose If you do not see any files with the program s suf fix use the pulldown menu within the Open File dialog box to choose Show All Files and you will then see them They will be read into the program properly with or without the suffix in their name as long as they were saved from the same program Copying Screens to Clipboard or Printer Copy Any screen can be copied as a graphic to the clipboard by using the standard Windows keyboard combo of Alt PrintScrn It will then be available for pasting into any compat ible Windows program such as Word or Powerpoint that is running concurrently in Win dows Most screens also provide a button to dump the screen image to an attached laser printer However the quality of that printed image may be less than could be obtained by copying and pasting the image into a program such as Word or Powerpoint and then printing it from that program It seems that Visual Basic does not print graph
38. n assumed value FIGURE A 10 Click here to see the plots Cam Dynamics screen in DYNACAM Dynamic Analysis True dynamic vibration analysis as described in Chapter 10 is available from the Vibra tion button on the Home screen once the kinetostatic calculation has been done This brings up the Select Dynamic Model screen shown in Figure A 11 Four dynamic mod els of the types described in Chapter 10 are available from this screen A fifth model for the case of a form closed follower train is also provided but is directly invoked without passing through this screen when form closure has been selected on the Dynamics screen Each model diagram has an nfo button that will display a message describing its purpose and application Either selecting the model s radio button and hitting Next or double clicking on the image of the desired model will take you to the next screen Figure A 12 shows the Dynamic Modeling screen for the 2 DOF model of an indus trial cam follower system Text boxes are provided for the input of the relevant effec tive mass and effective spring data along with assumed levels of damping The box at lower left provides control over the parameters for the 4th order adap tive step Runge Kutta ODE solver It is suggested that these be left at their default val ues The end time s value defaults to and cannot be set to less than two cycles of the camshaft but can be set longer Thus the calculation solves for at least
39. n can be obtained by holding down the arrows at the ends of the slider bar Cars Theta p ves Current angle If this plot window is blank click the Calculate button Drag the slider to move the linkage FIGURE A 16 Click the arrow to move the linkage continuously Input Data screen for a Fourbar Linkage cam follower train Dynacam Manual PM7 26 6 12 06 1 26 PM ROBERT L NORTON 27 The Plot Func button takes you to the Linkage Plot screen described below The Mass Prop button goes to the Mass Properties screen also described below Fourbar Slider Follower Train Figure A 17 shows the input screen for a fourbar slider linkage The Linkage Mode de fines the kinematic circuit of the linkage which can be either open or crossed as desired For a definition of these terms see reference 2 The Angle to Roller parameter defines the included angle between the kinematic link 2 and the arm radius to the roller The link lengths are always defined as the pin to pin distances of each link Link numbering is standardized with link always the ground link link 2 the link directly driven by the cam and pivoted to ground link 3 a floating coupler or connecting rod and link 4 the output slider in this case running against ground The Offset is the perpendicular distance be tween the axis of sliding and the pivot The Slider Angle is the angle between the global X axis and the axis of sliding Note that is possible to input a set
40. n type or mouse click to input the desired data in that field Remember that a yellow background means typed input data is expected Boxes with a cyan background feed information back to you but will not accept input Other information required from you is selected from dropdown menus or lists These have a white background Some lists allow you to type in a value different than any provided in the available list of selections If you type an inappropriate response it will simply ignore you or choose the closest value to your request Typing the first few letters of a listed selection will sometimes cause it to be selected Double clicking on a selectable item in a list will often provide a shortcut and sometimes a help screen Units The Units menu defines several units systems to choose from It is your responsibility to ensure that the data as input are in some consistent units system Units conversion is done within the program The Units menu selection that you make will convert any data that may already be present from the current unit system to the selected one Five unit systems are supported ips fps SI and two mixed unit versions of SI cm kg N s and mm kg N s These last two are really SI for dynamic calculation purposes but the length units are displayed in cm or mm and converted to m before calculating any parameters that involve dynamic equations Help All Programs The Help menus on some screens provide online access to this ma
41. nd prints are enabled at this location to allow you to lor Worstows by ML Norton 2001 7 bmw f fa Within interval conditions o l Displacement Velocity Acceleration Jerk Ping Start of interval End of interval Boundary Condition Input screen for polynomial functions in program DYNACAM 3 4 5 6 single dwell function shown Dynacam_Manual PM7 14 6 12 06 1 26 PM ROBERT L NORTON 15 determine the values of boundary conditions as you work your way through a piecewise function Polynomial Functions If any of your segments specified a Poly motion clicking the Calc button will bring up the Boundary Condition screen shown in Figure A 6 The cursor will be in the box for Number of Conditions Requested Type the number of boundary conditions BCs de sired which must be between 2 and 40 inclusive When you hit Enter or Tab or mouse click away from this box the rest of the screen will activate allowing you to type in the desired values of BCs Note that the start and end values of position that you typed on the Input screen are already entered in their respective 5 boundary condition boxes at the beginning and end of the segment Type your additional end of interval conditions on V A J and P as desired If you also need some BCs within the interval click or tab to one of the boxes in the row labeled Local Theta at the top of the screen and type in the
42. nedyne cam of the current design Checking it brings up a dialog box with some instructional information Proceeding causes the follower dynamics to be recomputed as a polydyne or splinedyne function The dynamic plots are updated and should show marked improvement in their dynamic behavior Clicking the Next button at this point brings up the Size Cam screen in order to re calculate the cam contour coordinates with the polydyne or splinedyne modifications Retain the existing values on this and the next screen and click on Next until you are back at the Home screen The cam contour data now awaiting export is that of the polydyne or splinedyne cam though the original nonpolydyne contour has been saved in another location so that comparison plots and printouts can be made from the Plot and Print menus if desired Stress Analysis The Stress button on the Home screen becomes available only if either a kinetostatic or dynamic analysis has been done If only the former was done then the kinetostatic forc es will be used to calculate the stresses If the Vibration button has been exercised then its more accurate dynamic forces are used for the stress calculation instead The Stress screen is shown in Figure A 13 The material parameters for both cam and follower must Material parameters C pte ite Yos have chosen a Kole Pars spectp Follower geometry C Drei Lena Chasey Fori u External
43. nt velocity and acceleration func tions Figure A 22 shows the Import screen When it opens detailed instructions are displayed on the screen In brief the measured data must be in R theta coordinates and can be at any uniform angular increments The data must be placed in a text file one pair of tab separated R theta numbers per line Dynacam will determine how many pairs are in the set when reading the data There should not be any header information in the file just data Dynacam_Manual PM7 31 6 12 06 1 26 PM 32 DYNACAM USER MANUAL Pars Protessional Edito by RA Morten Copyright 2006 Release 30 few EE 2 0 Interpolation REED methods uc Dts Com Oreesgs bred m Imported Mir Theta Meg Na of Data contour s Ports Les ec bd Irakin C coca Sho we Interpolated function Norton amp ssocates Design hio 1 00 11 2006 194740 EECIEN FIGURE A 22 Import Data screen in Dynacam Dynacam Manual PM7 Two interpolation methods are provided cubic spline and Fourier series The former is preferable if dwells are present because the Fourier series will add ripple to dwells But the Fourier method may do a better job of smoothing noisy data The desired angular increment at which the interpolation is to be done should be se lected from the dropdown at the left before importing data The units system should also be preselected The Import Data button
44. nual as well as specif ic instructions for various functions within the programs A number of instructional vid eos are also accessible from the help menus These download from a website and run automatically in Windows Media player or any similar program These videos provide tutorial instruction in program use You must be connected to the internet to access the online help and videos Examples The Examples pulldown menu on the Home screen provides a number of example cams that will demonstrate the program s capability Selecting an example from this menu will cause calculation of the cam and open a screen to allow viewing the results In some Dynacam_Manual PM7 5 6 12 06 1 25 PM Dynacam_Manual PM7 DYNACAM USER MANUAL cases you may need to hit a button marked Calculate or Run on the presented screen to see the results Examples can also be accessed from a dropdown menu from the input SVAJ screen Creating New Saving and Opening Files File The standard Windows functions for creating new files saving your work to disk and opening a previously saved file are all accessible in licensed installations from the pull down menu labeled File on each program s Home screen Selecting New from this menu will zero any data you may have already created within the program but before doing so will give warning and prompt you to save the data to disk The Save and Save As selections on the File menu prompt you to provide a file na
45. ny com puter that runs Windows 95 98 2000 NT XP Demonstration Versions The demonstration version of this programs is downloadable from http www designofmachinery com and allow up to 10 runs over a period of 30 days from first installation Certain features are disabled in the demonstration version such as the abil ity to open or save files and to output cam profile or linkage coordinate data If you wish Dynacam Manual PM7 3 6 12 06 1 25 PM Dynacam_Manual PM7 DYNACAM USER MANUAL to have the fully functional program you must register it and pay the license fee defined on the Registration screen Installing the Software The CD ROM contains the executable program files plus all necessary Dynamic Link Library DLL and other ancillary files needed to run the programs Run the Setup exe file from the individual program s folder on the CD ROM to automatically decompress and install all of its files on your hard drive Accept all defaults as presented When installed the program name will appear in the list under the Start button s Program menu after installation and can be run from there See the Readme file included with the in stallation package for information on licensing the program How to Use This Manual This manual is intended to be used while running the programs To see a screen referred to bring it up within the program to follow its discussion PROGRAM OPERATION All programs in the set have similar featur
46. om mon Cartesian axes in a single window This choice is of value to show a single func tion full screen or to overlay multiple functions Be advised however that multiple functions will scale to the largest function of the set so if there are large differences in magnitude between the members of the set it may be difficult to see and interpret the smaller ones The fourth icon lower right provides a polar plot of one selected func tion You may select any of these four plot styles by clicking on its icon or on the Select button above it and then clicking Next Double clicking on a plot icon will bring up the next screen immediately CARTESIAN PLOTS depict a dependent variable versus an independent variable on Cartesian x y axes In these programs the independent variable shown on the x axis may be either time or angle depending on the calculation choice made in a the program The variable for the y axis is selected from the plot menu Angular velocities and torques are vectors but are directed along the z axis in a two dimensional system So their mag nitudes can be plotted on Cartesian axes and compared because their directions are con stant known and the same Dynacam_Manual PM7 8 6 12 06 1 25 PM ROBERT L NORTON 9 POLAR PLOTS Plots of linear velocities linear accelerations and forces require a different treatment than the Cartesian plots used for the angular vector parameters Their directions are not the same and va
47. rmn Choose any F men Ci Parte C Fils four i rinter or a our items pants disk file for and their import to a 4 Fowener tara components spreadsheet iad ti ol zb from these h dropdown ips over i r i lists data to E En Peed These boxes ld de MEF show what gt x Y ws will be bmc rr MM printed FIGURE A 1 Click here to see the plots Click here to select a variable for plot The Print Select screen is common to all programs not all programs allow component selection ied to the clipboard or dumped to a printer as described above but this clip or dump will typically show only a portion of the available data i e one screen full Selecting Printer as the output device will cause the entire selection of data to print to an available printer Only some of the side bar information shown on the screen dis play will be included in this printout Selecting Disk as the output device will cause your selections to be sent to the file of your choice in an ASCII text format tab delimited that can be opened in a spread sheet program such as Excel You can then do further calculations or plotting of data within the spreadsheet program The Print Select screen has two modes for data selection Preset Formats and Mix and Match The former provides preselected sets of four variables for printing Select ing M
48. ry with time or input angle One way to represent these linear vectors is to make two Cartesian plots one for magnitude and one for angle of the vector at each time or angle step Alternatively the x and y components of the vector at each time or angle step can be presented as a pair of Cartesian plots Either of these ap proaches requires two plots per vector and has the disadvantage of being difficult to inter pret A better method for vectors that act on a moving point such as a force on a moving pin can be to make a polar plot with respect to a local nonrotating axis coordinate sys tem LNCS attached at the moving point This local nonrotating x y axis system trans lates with the point as it moves but remains always parallel to the global axis system X Y By plotting the vectors on this moving axis system we can see both their magnitude and direction at each time or angle step since we are attaching the roots of all the vectors to the moving point at which they act In some of the programs polar plots can be paused between the plotting of each vec tor Without a pause the plot can occur too quickly for the eye to detect the order in which they are drawn When a mouse click is required between the drawing of each vector their order is easily seen With each pause the current value of the independent variable time or angle as well as the magnitude and angle of the vector are displayed The programs also allow alternate presentations
49. t be accounted for in calculating the effective mass Likewise the effective spring in the sys tem must be reflected back to the follower The damping is defined by the damping ra tio C as defined for second order vibrating systems See Chapters 8 and 9 of reference 1 for further information The journal diameter and the coefficients of friction are used for calculating the fric tion torque on the shaft The Start New or Accumulate switch allows you to either make a fresh torque calculation or accumulate the torques for several cams running on a com mon shaft The energy information in the window can be used to calculate a flywheel needed for any coefficient of fluctuation chosen as described in Chapter 9 of reference 1 The program calculates a smoothed torque function by multiplying the raw camshaft torque by the coefficient of fluctuation specified in the box at lower right of the screen 20 6 12 06 1 26 PM Dynacam_Manual PM7 21 ROBERT L NORTON Undamped natural frequency 2nd row max min force amp max torque Damping coeff a CY RAGA lor Wires by A L Masten VE rep m Mass reflected to follower Puligs in Onde eei 1 eycke Spring reflected i Hinr to follower E in Hadirna Dede Por dra AGA 447 2 457 dH 0 4 21 Damped natural frequency For friction torque calculation From a piecewise T fmm Usually an pi an b
50. the cam 17 smoothed torque 20 splinedyne 23 Start New or Accumulate 20 Starting Angle 13 Stress button 23 screen 24 support 11 T Tab key using 12 Title screen 4 Torque Compensation Cam 33 U units 5 user actions possible 5 V vibration analysis 21 button 21 6 12 06 1 26 PM 36 DYNACAM USER MANUAL Dynacam_Manual PM7 36 6 12 06 1 26 PM
51. ting followers with offsets For compatibility with 3 D CAD CAM systems three coordinates are provided x y and z with z set to zero The z column is easily deleted in a spreadsheet if not needed The exported data for barrel cams is in 3 D cylindrical coordinates A lt with R set to a constant value equal to the prime cylinder radius A is the cam angle for each data point and will not be equispaced for oscillating arm followers or for surface data of any cam and lt is the axial follower displacement at A If you insist on being ornery and want to have your cam cutter data in some other form choose the Spreadsheet option and you will get every piece of data that DYNACAM has calculated for this cam But don t complain when you pick the wrong columns of data to give to the shop and your cam doesn t work ANALYSIS Kinetostatic Analysis When the cam has been sized the Dynamics button on the Home screen will become available This button brings up the Dynamics screen shown in Figure A 10 Text boxes are provided for typing in values of the effective mass of the follower system the effec tive spring constant and spring preload for a force closed follower and a damping fac tor By effective mass is meant the mass of the entire follower system as reflected back to the cam follower roller centerline or cam contact point as defined in Chapter 8 of ref erence 1 Any link ratios between the cam follower and any physical masses mus
52. value of the angle at which you wish to provide a BC That column will activate and you may type whatever additional BCs you need The box labeled Number of Conditions Selected monitors the BC count and when it matches the Number of Conditions Requested the Next button becomes available Note that what you type in any yellow text box is not accepted until you hit Enter or move off that box with the Tab key or the mouse allowing you to retype or erase with no effect until you leave the text box This is generally true throughout the program a D YWACAM lor DAR L Merten 2001 _ Even knots Autocalc Knot locations Select Select knot spline order e er d dd FIGURE A 7 Spline function screen with adjustable interior knot locations Dynacam Manual PM7 15 6 12 06 1 26 PM 16 Dynacam_Manual PM7 DYNACAM USER MANUAL Selecting the Next button from the BC screen calculates the coefficients of the poly nomial by a Gauss Jordan reduction method with partial pivoting All computations are done in double precision for accuracy If an inconsistent set of conditions is sent to the solver an error message will appear If the solution succeeds it calculates s v aj for the segment When finished it brings up a summary screen that shows the BCs you select ed and also the coefficients of the polynomial equation that resulted You may at this point want to print this screen to the printer or
53. will open a browser to find the file import it and display the raw contour as an S diagram in the upper window The Fit Functions button will do the interpolation First the selected function is fitted to the imported data then it is differentiated analytically not numerically to get velocity and acceleration These functions are then resampled at the chosen delta theta increment for display and export The Show Data button will display the original imported data and the displacement function fitted The Show Derivs button will show the velocity and acceleration func tions from the interpolated curve Save Functions stores the interpolated functions in the normal locations for Dynacam data making them available for plotting printing and further calculation Exiting this screen return you to the Home Screen where the SVAJ button will be grayed out so as to prevent inadvertent overwriting of the imported data All other pro gram functions can be applied to the interpolated cam functions Probably the best way to utilize this feature in Dynacam is to use the interpolated derivatives to determine what functions may have been used in the original cam design and where the dwells start and stop With this information a new cam can be designed 32 6 12 06 1 26 PM ROBERT L NORTON 33 using Dynacam s built in functions This approach will result in a more accurate and dynamically superior cam than will using the interpolated functions as is
54. xbar Linkage Follower Train Figure A 18 shows the input screen for a sixbar linkage The Linkage Modes define the kinematic circuits of each stage of the linkage which can independently be either open or crossed as desired For a definition of these terms see reference 2 The Angle to Roll er parameter defines the included angle between the kinematic link 2 and the arm radius to the roller The link lengths are always defined as the pin to pin distances of each link Link numbering is standardized with link 1 always the ground link link 2 the link di rectly driven by the cam and pivoted to ground link 3 a floating coupler or connecting rod link 4 a rocker pivoted to ground at O4 that connects the two couplers link 5 the second coupler and link 6 the output rocker pivoted to ground at The global coor dinates of both O4 and Og must be defined Link 4 has two branches the one labeled 4 and shown in black that connects link 3 to O4 and the one labeled 4a in color that con nects O4 to link 5 at 45 The angle between branches 4 and 4a which are part of the same link must be defined also Note that is possible to input a set of linkage data that is impossible to solve as the links may not be able to connect if their lengths are not compatible An error message will appear when the calculation is done if this is the case Once calculated the linkage can be animated by using the Step button to advance it one cam increment at a time or D
55. you to the Home Screen where a dialog box appears with instructions on exporting the cam contour data for manufacturing Exporting Cam Contour Data There is more than one way to get the cam contour data out of Dynacam for manufactur ing but only one of these is set up specifically for that purpose and it is strongly recom mended that you use it in order to avoid errors in manufacturing On the Home screen Dynacam_Manual PM7 19 6 12 06 1 26 PM 19 20 Dynacam_Manual PM7 DYNACAM USER MANUAL the File pulldown menu has an Export selection within which are selections for Spread sheet and Profile Profile is the recommended choice Depending on the type of cam designed radial or barrel and the type of follower roller or flat the selections under Profile will vary They typically will provide one or several choices that may include surface coordinates cutter centerline and roller follower centerline coordinates as appropriate In all cases these data are referenced to cam zero not to machine zero on the premise that if these two angles differ it is probably because machine zero is within a motion segment of the cam In that case one should NOT begin cutting the cam contour at machine zero The data exported for radial cams is only provided in Cartesian coordinates in order to avoid confusion and possible error by the manufacturer if they were given polar coor dinates especially for oscillating followers or for transla
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