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USER`S MANUAL - Halpin Engineering, LLC

1. As users begin to create and save various analyses the saved files depend upon database entries being available upon next use For example suppose a user creates a material definition titled 440C and then defines a bearing named XYZ Bearing that uses the 440C material for the inner outer rings and balls Every time the user wants to run an analysis with XYZ Bearings ORBIS will search the material database for a valid definition named 440C If this name is not found ORBIS will generate an error message telling the user the material could not be found This same situation occurs for all database entries and any user saved analysis setup files Beanng Propertes a Lubricant Properties Gear Al Entes Bewring Name Bangle Berro Rolling Elements Outer Ring Material Name 440C Stainless Pitch Diameter ri 2305 ni 5 Outer Diameter r 235 Young s Modulus ps 2 567 Bement Diameter n 2500 LR Width Or 5 OR Width On 5 Poisson s Ratio 25 Number of Elements 23 iy Curvature 3 Raceway Curvature 53 Free Contact Ange deg 25 eu TEE 9 Land Heght Oi 20 Sere A E NOTE Atmospheric viscosity and the pressure coefficient of viscosity Free Radai Play n u Land Diameter r Coefficient of Thermal Expansion injin F 5 5706 A ite inion pr RMS Roughness Microinch 5 v t Oni 2 Dam Height nid Dem Diameter in A e Gear Entries Add To Database Gear Entries _ Add To Database Lubricant Na
2. Cese Description Lubricant Name Specify a name for the lubricant Atmospheric Viscosity Ibf sec in2 Specifies the viscosity of the lubricant Pressure Coefficient of Viscosity in Ibf Specifies the pressure coefficient of viscosity of the lubricant Clear Entries Button Clears all input entries does NOT clear the database entries Add To Database Button Adds new entry to the Lubricant Database Lubricant Database Window Shows the current entries in the Lubricant Database View Parameters Button Displays the parameters of a selected lubricant database entry Delete From Database Button Deletes the selected database entry from the database Close Button Closes the Lubricant Database Editor Figure 14 Lubricant Database Inputs 2 3 Analysis Results Window Professionally formatted analysis output is provided in a standalone window as shown in the following figure Refer to section 4 0 for a detailed description of all available output Results are organized to provide quick access and easy interpretation All results windows float which enables the user to keep the results from an analysis run active then return to the main window and modify their setup and submit an altered analysis The user can then compare both analysis results side by side Typically Result Window is not saved within ORBIS However options do exist to save the results to a text file or print them Since O
3. F Stiffness Kzz ff of Friction Contact R Clamp Load Ibf R Clamp Load lbf Export raw data to file Plot Results Select Input Variable Description Drop down menu to select independent variable see parameter options in the figure to the right Note each input parameter associated with a bearing row is applied to all bearings in the system For example if Free Contact Angle is selected as the input parameter all bearing rows will be analyzed with the range of free contact angles defined in entry fields 2 and 3 below Vary From To Specifies the minimum and maximum values inclusive to vary the independent variable between of Increments Specifies the number of points to plot Orbis will use the specified variable limits and number of increments to determine equally spaced data points Default value is 5 increments Nominal Value Row 1 This is a non editable field that provides the nominal value of the selected independent parameter This is provided for user reference Select Output Row Specifies which output row to be used to plot output dependent variable Output Variable Selections Checkbox selection of all possible output variables User may select any number of output variables to analyze Orbis will provide a separate plot window for each output variable Export raw data to file Selecting this checkbox will allow the user to save the raw plot data to a deli
4. Us EMS AAA 13 Fig re 10 Database Ed ii e a A dia 14 Figure 11 Bearing Database Inputs 00 eccecccecseesseesceesceesecaecnseceseceseceseeeeeeeeseceseeeseeeseecsaecaeeeseenseeeaeee 15 Figure 12 Shoulder Height Definitions for h d Values 00 ecccceescessceeeeseeeceeeeseeeceaeeaeeeeeesecaeeeeeeaeenaeenees 16 Figure 13 Material Database Inputs 2 0 0 0 ececeeseeseeeeceseeseeseceaecaeeeceeaecaeeeneeseceaeeaeseeceaeeaeeeceaecaeeeeeeaeenaeenees 17 Figure 14 Lubricant Database Inputs cccocccssccessescssaeessoeaes sete saneestensaveenseshasseennosnsesgavadencesssvdcontondaveacoavenses 18 Figure 15 Results WOW dit aaa ARS EEE AEE dicta 19 Figure 16 Flexible Shaft Window ccesceccssscssesseeeceseeseeeeceaecaeeeceeaecaaeeseeseceaeeaeseecsaecaeeeeeeaecaeeeneeaeenaeentes 21 Figure 17 Sensitivity Studies Dialog cccccecccccsseesseesseessecssecesecesecnseensecseeseeeseeeeeseeeseecaeecssecnseenseenseseaeen 23 Figure 18 Plot Windows ii A ti iaa E 24 Figure 19 Tolerance Studies Dialog ccescssessseeeceseeseeeceaecsesencesecaeceeceseceaeeaeseeceaeeaeeeeeeaecaaeeneeseeaeenees 25 Figure 20 Dahl Torque Hysteresis Utility cc eceeceseeseeescesecseeeeeesecseeeeeeseceaeeaeeseceaecaeeeceaecaeeeneeseeaeenees 26 Figure 21 System Preferences Dialog c c ccccsssesesessonecnsetecunsestenacuhesntectssecnsensdesesuacenteneesdedntvessoncntedaces 27 Figure 22 System Model Illustrating Analytic Process For Compliant Ring Considerat
5. as the final results can be quite sensitive to these parameters Additional initial parameters needed in the model include bearing row placement material definition of assembly components and preload definition including the condition at which preload force applies and whether it is applied by rigid clamping or constant force springs The next step calculates any bearing ring distortions due to interference fitting on the mating diameters All bearing interference fits cause internal clearance loss thereby changing both the initial contact angle and endplay of the bearing This new mounted contact angle establishes the initial condition for any subsequent preloading Additionally for rigid type preloading where a precision ground preload gap is determined with the bearing rings radially unrestrained the change in endplay due to press fits will alter the gap to be clamped At this point the model applies preloading As shown in the figure the preload condition and type must be considered The defined preload will either apply in the mounted radially restrained or unmounted radially free condition For mounted preload conditions the preload forces are directly applied to the bearing with previously established initial conditions due to fitup effects For the case where preload is specified at unmounted conditions which is common for duplex pairs with precision ground rings or spacers the model must first determine the axial preload displacemen
6. occur if the specified bearing name already exists within the database Database Entry This are provides access to all current bearing names stored within the database View Edit Properties Button Once a database entry is selected within the database window selecting this button will populate the bearing parameters into the input fields Delete Entry Button With a database entry selected this button will permanently delete the entry from the database Close Button Copyright 2009 2013 Halpin Engineering LLC All rights reserved Closes the Bearing Database Editor Figure 11 Bearing Database Inputs 15 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com aie Web http www HalpinEngineeringLLC com 2 2 1 1 Shoulder Height Definitions Land and dam heights as discussed in the preceding section can be defined as h d ratios or diameters The figure below illustrates an outer ring with the heights for the land h and the dam ha identified The term dam refers to the non contacting shoulder GHA AT Figure 12 Shoulder Height Definitions for h d Values 2 2 2 Material Database Editor The material database editor allows the user to define their own unique materials Since material definitions are needed for both bearing definitions and shaft housing definitions it is recommended that the user initially take the time to define
7. 0 0000E00 6 4095E 16 7 8383E00 3 3847E 01 3 1263E 01 0 0000E00 0 0000E00 6 2152E 16 6 4095E 16 7 3072E00 3 3847E 01 3 1263E 01 0 0000 00 0 0000E00 6 2152 16 6 4095E 16 7 8383E00 3 3847E 01 3 1263E 01 0 0000E00 0 0000E00 6 2152E 16 6 4095E 16 9 3341E00 3 3846 01 3 1263E 01 0 0000E00 0 0000E00 6 2153E 16 6 4096E 16 1 1537E01 3 3844E 01 3 1262 01 0 0000E00 0 0000E00 6 2155E 16 6 4097E 16 1 4116E01 3 3842E 01 3 1261E 01 0 0000E00 0 0000E00 6 2156E 16 6 4098E 16 1 6757E01 3 3840E 01 3 1259E 01 0 0000E00 0 0000E00 6 2158E 16 6 4099E 16 1 9226 01 3 3838 01 3 1258E 01 0 0000E00 0 0000E00 1 1603E02 1 1604E02 2 3379E01 1 9339 05 1 7680 05 0 0000 00 0 0000E00 5 2220E02 5 2220E02 2 5146E01 3 1926 05 2 9189E05 0 0000E00 0 0000E00 1 0088 03 1 0088E03 2 6507E01 l 0 0000E00 1 4528 03 1 4528 03 2 7466E01 0 0000E00 1 7602 03 1 7602 03 2 803401 1 8698E03 1 8698 03 2 8222 01 1 7602 03 1 7602 03 2 8034E01 1 4528 03 1 4528 03 2 7466E01 y 0 0000E00 1 0088E03 1 0088E03 2 6507E01 l 0 0000E00 5 2220E02 2 5146E01 2 9189E05 l 0 0000E00 Description Key result parameters are tabulated for each bearing row This area provides quick access to available key parameters 1 Result Summary A scrollable selectable text window containing the complete analysis output See section 4 0 2 Detailed Results for a comprehensive listing of available output contained in the detailed results section of the results windo
8. 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com LLC Web http www HalpinEngineeringLLC com Free Contact Angle deg Inner Raceway Curvature Outer Raceway Curvature Preload bf Options Vary sign convention on load components load 1 only 6 Y Apply tolerances to all bearing rows Notes 1 This utility evaluates all permutations of min max tolerances and reports the resulting maximum contact stress condition If truncation is found the routine will stop iterating and report the truncated results 2 WARNING Due to the large number of possible permutations this routine may take several minutes to complete i e A two bearing row system with varied sign convention on load components and tolerances applied to all rows has 4 096 possible permutations Analyze Description Free Contact Angle deg Specify min and max free contact angles in degrees Inner Raceway Curvature Specify min and max inner raceway curvatures ratio of raceway radius to ball diameter Outer Raceway Curvature Specify min and max outer raceway curvatures ratio of raceway radius to ball diameter Preload Specify min and max preload always as a positive value Orbis will correct sign based on contact angle orientation and the assumption that the preload should load through the contact angle Vary Sign Convention Checkbox to specify if sign convention should be varied on all
9. 9 Rigd Spring O R Fitup in 2 1 4 Life Factor 1 0 Shaft I D in Dynamic Viscous Torque Factor 1 7 Le Comp toad 2 Housing 0 0 n Analysis peee R Row Preload bf Spring Rate Ibf in Inputs ShaftRotates 9 Load fixed to shaft Coeff of Friction Ball Contact 2 1 2 Housing Rotates Load fixed to housing Enter external load applied in x direction axial Ibf Input Field Description 2 1 5 Figure 2 Main Graphical Interface 2 1 1 System Inputs The System Inputs area is where external loading and housing shaft material definitions are defined See the following figure for descriptions of each input field CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 7 of 37 Halpin LLC Engineering Phone Email 310 650 8982 info HalpinEngineeringLLC com Web http www HalpinEngineeringLLC com Fx Ibf Fx bf Fy bf Fz bf Fyy in4bf Fzz in bf Location in Enable additional load points F nO Temperature Units 9 DegF DegC 8 Shaft Temp 68 Housing Temp Allowable Mean Hertzian Stress psi Shaft Material Housing Material 2 Lubricant a3 Description External axial load components for up to three load points positive is toward the right Fy Ibf External radial load components for up to three load points positive is upwards Fz Ibf External ra
10. E Dahl Torque Hysteresis Ctrl D System Preferences Ctrl P f Ctrl 0 Ctrl S Description The file menu provides standard file options such as Open Save Save As and Exit ORBIS maintains a unique file type that allows the user to save their bearing analysis setup Tools Menu The tools menu provides advanced analysis utilities shown below Selecting this utility allows the user to load a pre configured comma delimited file with an Batch Process Load Cases unlimited number of load cases Each load case is applied to the current defined bearing system and the results are saved to separate results files Selecting this menu option launches the Shaft Flexibility Analysis dialog See section 2 4 for a detailed explanation of this dialog window Selecting this utility launches the Sensitivity Studies window See section 2 5 for a detailed explanation of this dialog window Selecting this utility launches the Tolerance Analysis window See section 2 6 for a detailed explanation of this dialog window Selecting this menu launches the Dhal Torque Hysteresis window See section 2 7 for a detailed explanation of this dialog window Selecting this utility launches the System Preferences window See section 2 8 for a detailed explanation of this dialog window This menu provides an About window to show key parameters regarding the current software version and lease expiration date File Menu Shaft Flexibility Sensitivity S
11. Solution Attempts 75 Ti 6Al 4V 5 4 3 3 0 5 0 5 2 7515 6 L _2 37 6Al 4V Output Options 4 Show Rigid Analysis Results CO Analyze Flexible Shaft 11 V Plot Shaft Deflections Description 1 Shaft Sketch An engineering sketch is provided for the user defined setup 2 Load Points All user defined load points are labeled L1 L2 etc with their x axis coordinate 3 Element Dimensions Each user defined shaft element is sketched and dimensioned along the length x axis 4 Bearings All user defined bearings are sketched and x axis coordinates are shown All shaft elements are defined here All shaft elements are cylindrical and each successive 5 Shaft Element Definition element must start where the previous element ended Additionally shaft elements must Table exist for the entire span of the defined system consisting of the left most bearing row or load location to the right most bearing or load location Element Material Unique element properties are assigned in the material column This column is directly linked 6 to the Material database and materials are easily assigned by selecting from a drop down Properties menu as shown on right 7 Solver Convergence You can modify the maximum allowable step error and the maximum number of solution attempts The solver has an adaptive method that continuously reduces the load increment step
12. all of their most widely used materials before proceeding with analysis setups If need be all separate windows within ORBIS where material assignments are needed for setup will contain a material editor button that provides direct access to the database editor See the following figure for a detailed description of the material editor Copyright 2009 2013 Halpin Engineering LLC All rights reserved 16 of 37 FE Halpin LLC Engineering Phone Email 310 650 8982 Material Name Material Properties Material Name Young s Modulus psi Poisson s Ratio Specific Density Ibm in 3 Coefficient of Thermal Expansion infin F _ Add To Database Kl Clear Entries Material Database 1440C Stainles 8 9 l View Parameters Delete From Database Description Specify a name for the material Young s Modulus psi Specifies Young s Modulus for the material Poisson s Ratio Specifies Poisson s ratio for the material Specific Density lbm in Specifies the specific density of the material Coefficient of Thermal Expansion in in F Specifies the coefficient of thermal expansion for the material Clear Entries Button Clears all input entries does NOT clear the database entries Add To Database Button Adds new entire to the Material Database Material Database Window Shows the current entries in the Material Datab
13. as if performing a standard analysis run Once the system is completely defined the user selects the Dahl Torque Hysteresis option from the Tools menu A new dialog will appear as shown in the figure below with various configuration options Copyright 2009 2013 Halpin Engineering LLC All rights reserved 25 of 37 Phone Email 310 650 8982 info HalpinEngineeringLLC com Halpin Engineering LLC Web http www HalpinEngineeringLLC com Step 1 Generate Dahl Parameters Select Torque Units in ozf w Select Angle Units Degrees w Dahl Torque Hysteresis Edit Contact Coefficient of Friction Row 1 Row 2 Row 3 Row 4 Row 5 0 085 Generate Dahl Parameters Torque Stiffness 1 7253E02 Steady State Coulomb Torque 9 1026 00 Torque in ozf Step 2 Setup Torque Loop Plotting No of Points Per Loop Reversal Angles gt 0 0 02 0 04 0 08 5 0 16 0 321 ES 0 5 Angle di Clear Table ngle deg Description Drop down menu allows selection from units of in ozf in Ibf ft Ibf gm cm N cm or N m All subsequent results will be in selected units Drop down menu allows selection from units of degrees or radians All subsequent results will Torque Units Angle Units be in selected units Coefficient of Friction Tabular input of contact coefficient of friction for each bearing row Modifications of this parameter wi
14. as the difference between the bearing 1 0E 5 lbf Error reaction forces and the applied preload force The ring expansion error is defined as the difference between APp input Ring into the Jones model a fixed ring model and the resulting APp due to Expansion 1 0E 7 in ring deflections Ring deflections are determined by using the resulting Error ball normal forces and associated contact angle to determine an equivalent radial pressure on the bearing ring 4 0 Output Descriptions The following sections describe the analysis output generated by ORBIS 4 1 Input Parameters This section provides a list of the user inputs used to generate the analysis results These are provided to the user as reference 4 2 External Applied Loads This section displays the user defined system load components and the application point at which they are applied location is along the x axis Loading information for up to three separate load points will be displayed 4 3 Ball Crossing Angles Ball Crossing Angles are displayed for each row and are defined as the angular rotation required by a given ring inner or outer to cause a ball to travel to an adjacent ball station These results are based on the mounted bearing contact angle and do not apply at under any external loading conditions 4 4 Internal Clearances This section provides bearing diametral or radial and axial free play Results are given for both initial free and final condi
15. cya tek id ici i 35 4 13 19 Element Roll Velocity 20 ccccccccsseessecneeceteceeceseceseceeeeseeeseeeeeaeceseeeseeessecsaecsaecnaeceseenaeees 35 4 13 20 Pitch Orbit Velocity na an r a aa a r A a a be eta Aa 35 4 1321 Minimum Film Heignts ocsccsve cvees sibs menen aid ai 35 4 13 22 Minimum Lambda Vali oniiir a raria as EE EE E EEan Esas 36 4 1323 Centritugal FOTCE oseere ienai tese oe ETE EEE EET aii EEE E E riada 36 4 13 24 Gyroscopic Moment ceeccecsseeseeseesseeseecesecesecesecesecsseeseeeseaeeeseeeseeeseecssecsaecaecnaeeneeeaeees 36 DO DRETCPENCES wisccceeecsescescccseccoeccedesssicedicesccesnsoostacenscesdensssesdaceseecicessdcescensssederessceseceosceeseedecceceosseatacossceas 37 Figure t Coordinate sti a A o oi ds 6 Figure 2 Main Graphical Interface cceecesccsseeceeseceeeseeseceaessesseceaecaeeeceeaecaeeeceeseceaeeaeeeeceaesaesenceaecaeeeneeaes 7 Figure 3s Systemi INpuls edo ad e 0 8 Figure 4 Dynamic Analysis IMputS ooonnconnnnnnnnnononincnnconononnnonncnnononnnnc nono conc c nano conan ron rnn anna arena nina 9 Figure 5 Syste Display ici dia i a a titi 10 Figure 6 Bearing Row Inputs oooooonnoonnoonnoononononononon cono nonn nooo nonn nono nono nono nn cnn ran r rn r anar rn nn rrnnrnanrron neon nena necinnss 11 Figure 7 Convergent and Divergent Contact Angles oocococonncnccnoninccococononncnnnnononncnncco nono nonncnnc nn connannc canon 12 Fipure 8 Input Field Description ses cia iii catas 12 Froure 9
16. ellipse that is closest to the land diameter This value is represented as a ratio of its height from the center of the raceway to the ball diameter 4 13 12 Lower Edge Location The Lower Edge Location represents the edge of the contact ellipse that is closest to the dam diameter This value is represented as a ratio of its height from the center of the raceway to the ball diameter Copyright 2009 2013 Halpin Engineering LLC All rights reserved 34 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com LLC Web http www HalpinEngineeringLLC com 4 13 13 Contact Normal Approach Contact Normal Approach represents the total combined deflection of the contacting bodies rolling element and raceway This deflection is along the normal direction to the contact area 4 13 14 Contact Normal Stiffness Contact Normal Stiffness represents the stiffness of the rolling element to raceway contact area stiffness in the normal direction 4 13 15 Spinning Velocity Spinning Velocity is the angular velocity of the rolling element about the axis of rotation that is normal to the contact on the un controlling race Per Jones 1964 race control theory spin can only occur on one raceway while pure rolling occurs on the other Based on the spinning velocity output one can deduce race control i e if there is zero spinning velocity on a given raceway than that raceway is in control 4 13 16 Rolling
17. load components Selecting this checkbox will run all permutations of positive and negative load components Apply Tolerances to all rows Checkbox to specify how tolerances are applied to the system Selecting this checkbox causes all bearing rows to have specified tolerances analyzed Un selecting this checkbox activates item 7 below and tolerances are only applied to selected bearing row Row Selection Drop down When active the drop down menu is used to specify which bearing row to apply the specified tolerances Analyze Button Button to begin analysis of tolerances Close Button Closes the Tolerance Analysis dialog window Figure 19 Tolerance Studies Dialog 2 7 Dahl Torque Hysteresis The Dahl Torque utility is used to analyze the torsional stiffness torque versus angle of the bearing system during startup or direction reversal This phenomenon occurs through small finite angles of rotation often most apparent when direction of rotation is reversed at speeds sufficiently slow such that viscous drag is negligible The utility provides quick inspection of the reversing torque slope and steady state torque Additionally the utility can quickly generate small angle hysteresis loops for both graphical plot inspection and data export The analysis procedures of this utility follow those set forth by Todd and Johnson 1986 To perform a Dahl torque analysis the user configures their system within the main window
18. of the user s system e g if the user system contained two rows placed at 0 5 and 0 5 along the x axis the system Jacobian would be computed at x 0 0 4 9 3 Stiffness at Load Point When performing a flexible shaft analysis the output contains additional complete stiffness matrices for each load point specified in the system This matrix represents the full 5 x 5 stiffness matrix of the system at the specified load point Stiffness results include effects of shaft compliance and bearing stiffness s in their final loaded equilibrium state 4 9 4 Row Stiffness Matrix This section provides complete 5x5 stiffness derivatives for each bearing row Stiffness results correspond to the quasi static equilibrium state of the system in its final loaded state 4 10 Fatigue Life This section provides individual ring and total system fatigue cycles for various conditions Note Fatigue results are only generated for dynamic analysis runs Outputs include L10 life adjusted L10 life and adjusted life with consideration for film thickness L10 Fatigue life calculations are based on the Lundberg Palmgren theories as shown in Jones 1964 The adjusted life output is based on the life factor theory adopted in AFBMA 1990 standards This result includes the user defined life factor input along with a computed factor based on the user reliability input The life factor input allows the user to enter a combined factor to account for items su
19. options dialog appears by selecting the right mouse button anywhere within the plot window Options exist to modify plot properties copy to clipboard save plot as an image print and zoom scale axes Independent Parameter All plots have the independent parameter along the abscissa Appropriate units will be specified Dependent Parameter All plots have the dependent parameter along the ordinate Appropriate units will be specified Mouse Zoom Start Mouse zooming rectangular is achieved by selecting the upper left corner of a rectangle with the left mouse button and dragging the mouse to the lower right hand corner Mouse Zoom End To complete zoom release the left mouse button with the mouse pointer at the desired lower right corner of the zoom rectangle Figure 18 Plot Windows 2 6 Tolerance Analysis ORBIS can perform tolerance studies of key bearing parameters with the Tolerance Analysis dialog This utility iteratively solves all permutations of user specified tolerances min and max conditions and provides the combination causing worst case Hertzian contact stress in a results window Additionally truncation is checked for all iterations and if truncation is found the utility stops and displays a result window with the truncated conditions Reference the following figure for a description of the Tolerance Studies utility Copyright 2009 2013 Halpin Engineering LLC All rights reserved 24 of
20. size until either the step error is satisfied or the maximum number of solution attempts has been exceeded 8 Output Options Output options exist for showing the rigid shaft analysis results same results one would get with a normal Orbis analysis from the main window and whether shaft deflections should be plotted 9 Edit Materials Button Launches the Material Database editor 10 Sketch Button Once the user has input the shaft element definitions selecting the Sketch button updates the sketch window Analyze Flexible Shaft Button Runs the flexible shaft analysis and produces a results window Figure 16 Flexible Shaft Window Copyright 2009 2013 Halpin Engineering LLC All rights reserved 21 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com as Web http www HalpinEngineeringLLC com 2 5 Sensitivity Studies ORBIS enables rapid bearing design and quick solutions to common what if scenarios via the Sensitivity Studies utility This utility allows the user to vary almost any input parameter independent parameter and plot them against any output parameter dependent parameter The Sensitivity Study dialog is accessed from the Tools menu see section 2 1 6 on the main window This utility requires a complete analysis definition within the main window and also requires the dynamic analysis mode be selected The following subsection discusses in
21. RBIS generally produces analysis results within a fraction of a second the primary means of saving an analysis is to save the analysis setup from the file menu on the main window The saved file can then be reopened and all original analysis setup parameters will be restored To produce the results window the user simply selects the Analyze button to recreate the results window Copyright 2009 2013 Halpin Engineering LLC All rights reserved 18 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com a Web http www HalpinEngineeringLLC com Result Summary Row 1 Row 2 Row 3 x Mean Stress psi 4 8837E05 4 0163E05 Max Truncation 3 7078E00 1 8751E01 Mounted Preload bf 1 0000 02 1 0000 02 Friction Torque in ozf 7 1629E02 4 1013E02 2 detailed Results Ball Excursions Description Row 2 Row 3 Row 4 Maximum Excursion in 1 7173E 02 Row 1 Output Element Normal Ball Normal Ball Contact Mean Hertz Mean Hertz Truncated Truncated Load O R Angle O R Stress IR Stress O R Length LR Length O R bf dea dea psi psi 6 4099E 16 1 9226 01 3 3838E 01 3 1258E 01 0 0000E00 0 0000E00 6 4098E 16 1 6757E01 3 3840E 01 3 1259E 01 0 0000E00 0 0000E00 6 4097E 16 1 4116E01 3 3842 01 3 1261 01 0 0000E00 0 0000E00 6 4096E 16 11537801 3 3844E 01 3 1262E 01 0 0000E00 0 0000E00 6 4095E 16 9 3341E00 3 3846E 01 3 1263E 01 0 0000E00
22. Velocity Rolling Velocity is the relative angular velocity of the rolling element about its own axis of rotation parallel to the contact on the controlling race 4 13 17 Spinning Torque Spinning Torque is the component of torque generated by interfacial slip within the contact area due to rolling element spin 4 13 18 Rolling Torque Rolling Torque is the component of torque generated by interfacial slip within the contact area due to pure rolling 4 13 19 Element Roll Velocity The Element Roll Velocity represents the rotational velocity of the rolling elements as seen relative to the pitch orbit velocity 4 13 20 Pitch Orbit Velocity The Pitch Orbit Velocity is the rotational velocity of the bearing pitch diameter about its spin axis This is essentially the angular velocity of rolling element cage or retainer 4 13 21 Minimum Film Height The Minimum Film Height represents the thinnest point of the lubricant along the center line of the contact ellipse This calculation is based on the Hard EHL theory by Hamrock and Dowson 1981 for fully flooded conditions Copyright 2009 2013 Halpin Engineering LLC All rights reserved 35 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com es Web http www HalpinEngineeringLLC com 4 13 22 Minimum Lambda Value Lambda is a dimensionless parameter that is often used to describe the lubricant regime of the bearing Its value is determine
23. YRBIS aent Bearing Analysis Software USER S MANUAL Updated for Version 2 3 Copyright 2009 2013 Halpin Engineering LLC All rights reserved Table of Contents 1 0 Getting Started A OO 5 LE System Requirements esr eien i RE da e a dat aaa ie 5 L2 Installation IMStTUCIONS sida tidad attend 5 1 3 Java Runtime Environment raar a aaa eaa a a a A aa a Ea RS 5 LA Coordinate Systems o a AE E h 5 1 5 Numerical Input Formatting oooccoocconnnonnnonnnnononononnnnnnn nono nonn nono nono nono nono nac n nr n nro r rra r anar rnnrrnn rra 6 2 0 User Interfaces ooooomoomossmosoosionsonocscconcccncoccconc cono nono nono ccoo aconnconnccon conc ccoo n conc Snas nsee vs oeoo neri nas 6 21 Main Graphical Interface mito auto id tdo a ada al Ea dadas 6 2 1 1 A E 7 2 1 2 Dynamic Analysis Inputs cc ccccccccssecsneceneceseceeceececeeeeseeeseeeseecseecssecsaecseceaeenseeseesereenneesgs 8 23 System Display a A days AT 9 ALA Beating ROW puts sii a a O N 10 21 5 Input Fi ld Descriptions Jesieni een iis ea dia Sauteed EREE a a bez 12 21 67 User Menus nai oee ie ae AA A A di 13 2 2 Database Editos ieena arer a e a iaa do 13 2 2 1 Bearing Database Editor hiisi lebre aapi a E a e ei TA O a eT r 14 2 2 2 Material Database Edito iii a a a R a ii 16 2 2 3 Eubricant Database Edition adds 17 2 3 Analysis Results Window 020 cceccccsivesncetvees atada EE EENE EEN E KE css 18 24 Flexible Shaft A nal Ze
24. aring Row Inputs located in the lower right is where all pertinent parameters for defining configuration of each bearing row in the system such as row location housing shaft fits preload contact angle orientation etc e Input Field Description located bottom center provides key details and helpful information for each input field Upon placing the cursor within a given input field applicable infomation is displayed in the Input Field Description area See subsequent sections for details about each input field in the main graphical interface To submit an analysis the user simply selects the Analyze button at the bottom of the window Analysis results will appear in a new window See section 2 3 for a description on the Results window and section 4 0 for a detailed description of each output parameter File Tools Help Fx bf Fy bf Fz bf Da System System eee Display GRA Enable additional load points Y 2 1 3 Temperature Units 9 DegF DegC Shaft Temp 68 Housing Temp Allowable Mean Hertzian Stress psi Shaft Material 15 5PH Row 1 Rowena Jeonan Housing Material 15 5PH Contact Angle Preload Condition Row Parameters ca ne 20014 lt Divergent Un Mounted Bearing SSRI 6632 15 gt Cor 13 Mounted i Y Perform Dynamic Analysis EIN et Row Location in Bearing Row Velocity rpm 750 Preload Type LR Fitup in Inputs Reliability 0
25. ase H 1 2 3 4 5 6 7 8 9 View Parameters Button Displays the parameters of a selected material database entry p o Delete From Database Button Deletes the selected database entry from the database m en Close Button Closes the Bearing Database Editor Figure 13 Material Database Inputs 2 2 3 Lubricant Database Editor info HalpinEngineeringLLC com Web http www HalpinEngineeringLLC com The lubricant database editor allows the user to define their own unique lubricants ORBIS currently requires lubricant properties independent of temperature This means the user must define and subsequently select appropriate lubricant definitions that are pertinent to the temperature used in their analysis See the following figure for a detailed description of the lubricant editor Copyright 2009 2013 Halpin Engineering LLC All rights reserved 17 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com as Web http www HalpinEngineeringLLC com Lubricant Properties Lubricant Name Atmospheric Viscosity Ibf secfin 2 Pressure Coefficient of Viscosity in 2 1bf NOTE Atmospheric viscosity and the pressure coefficient of viscosity values must pertain to the lubricant temperature 4 J Gear entries _ Add To Database Lubricant Database Zz Lubricant 6 Th View Parameters Delete From Database
26. ch as materials cleanliness and misalignments Bamberger 1971 provides a useful reference for computing various life factors The adjusted life with film includes an additional lubricant factor which is also provided for reference The film parameter is from Bamberger 1971 and follows the AFMBA recommended average curve and uses the minimum film parameter as discussed below All fatigue calculations use the individual rolling element results and do not require determination of an equivalent radial load on the bearing row Copyright 2009 2013 Halpin Engineering LLC All rights reserved 32 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com aie Web http www HalpinEngineeringLLC com 4 11 Bearing Torque Bearing torque results are only generated for dynamic analysis runs Two types of torque are considered friction torque and viscous torque Friction torque output represents the torque associated with rolling and spinning within the contact area when the balls start rotating Precisely this is the torque due to interfacial slip aka Heathcoate Slip at the contact ellipse ORBIS uses the Race Control theory from Jones 1964 and therefore only allows spin to occur on one raceway The computed torque output can be scaled with the coefficient of friction input parameter Reference Jones 1964 for the friction torque calculations used by ORBIS Viscous torque output is based on the Palmgren
27. cutive entry for non consecutive entry selection select each entry while holding the control key Import button Selecting this button imports the selected remote database entries into the default database The database does not allow duplicate entries and will check each import entry for existing names within the default database If duplicates are found the user will be asked to confirm overwriting or skip the duplicate import Default Database Entries Displays the entries from the user s default database System Force Balance Error This entry specifies the allowable system force balance error for solver convergence Norm of the residuals Acceptable values are between zero and one exclusive O lt value lt 1 The system force balance convergence criteria will be determined by multiplying this value by the RSS of the applied external loading In the case where the RSS of the external loading is less than one this value will be used directly For example if the RSS of the external loading is 1 000 Ibf and the system force balance error is 1 0E 5 default value then the system will converge to equilibrium within 0 01 Ibf Max Solver Iterations Specifies the maximum number of numerical solver iterations before aborting Max Preload Error This entry specifies the maximum allowable force error for determining the preloaded state Acceptable values are greater than zero 0 lt value Max Preload Iterations Spec
28. d by taking the ratio of the minimum film height to the root sum squares RSS of the contacting surface roughness Mathematically lambda is defined as follows hm in Rraceway Roa 4 13 23 Centrifugal Force The Centrifugal Force output represents the radial body force of the rolling element due to its orbital velocity and mass This force tends to create differing contact angles between the inner and outer race contacts and is treated in the analysis per Jones 1964 qian 4 13 24 Gyroscopic Moment The Gyroscopic Moment output represents the spinning body moment of the rolling element due to its angular velocity and inertia The influences of this force are treated in the analysis per Jones 1964 Copyright 2009 2013 Halpin Engineering LLC All rights reserved 36 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com ie Web http www HalpinEngineeringLLC com 5 0 References Anon 1990 Load Ratings and Fatigue Life for Ball Bearings ANSI AFBMA 9 1990 The Anti Friction Bearing Manufacturers Associations Washington DC Bamberger E N 1971 Life Adjustment Factors for Ball and Roller Bearings An Engineering Design Guide American Society for Mechanical Engineers New York Hamrock B J and Dowson D 1981 Ball Bearing Lubrication The Elastohydrodynamics of Elliptical Contacts Wiley New York N Y Jones A B 1964 The Mathematical Theory of Roll
29. des the resulting bearing reaction force components on the shaft at each bearing row These forces include all mounting preloading and external loading conditions and apply at the center of their respective bearing row locations Copyright 2009 2013 Halpin Engineering LLC All rights reserved 31 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com ae Web http www HalpinEngineeringLLC com 4 8 Inner Ring Displacements This section provides the components of the displaced inner rings due to mounting preloading and external loading All non axial results are based on fixed outer ring theory developed by Jones 1964 4 9 Stiffness Output Orbis provides three different types of stiffness calculations axial stiffness with ring compliance considerations system Jacobian diagonal terms and complete 5x5 stiffness derivatives for each bearing row Refer to subsequent sections for a description of each type of stiffness result 4 9 1 Axial Stiffness with Ring Compliance This result provides the system axial stiffness at mounted and preloaded state with compliant ring considerations Effects from external loading are not included in this result 4 9 2 System Jacobian This result provides the system Jacobian diagonal terms These results apply in the fully loaded condition Additionally the system Jacobian assumes a rigid system during external load application Results apply at the center point
30. dial load components for up to three load points positive is out of the page Fyy in Ibf External moments about the Y Axis for up to three load points Fzz in Ibf External moments about the Z Axis for up to three load points Load Location in Location of external load points along X Axis Enable additional load points Checkboxes for second and third load points Select checkboxes to enable load component inputs Temperature Units Radio button toggles between Fahrenheit and Celsius units 1 2 3 4 5 6 7 8 9 Shaft Housing Temp F Bulk temperatures of the shaft and housing Allowable Mean Hertzian Stress psi Allows user to specify an allowable contact stress All elements with contact stress above the specified allowable will be highlighted in the output file Shaft Material Allows user to assign shaft material from the material database Housing Material Allows user to assign housing material from the material database Lubricant Allows user to assign lubricant to all bearing rows from the lubricant database Figure 3 System Inputs 2 1 2 Dynamic Analysis Inputs ORBIS offers both static and dynamic analysis modes Static mode is useful for simple slow speed applications where dynamic effects are negligible The static solver is also quicker due to the reduction in parameters required to converge Dynamic analysis mode provides full analysis outpu
31. en truncated elements are found additional output is provided directly after the first table of the affected row This output computes peak center stresses and peak edge stresses for all elements exhibiting truncation The method used follows the publication by Frantz and Leveille 2001 This output reports peak not mean stresses and all edge stresses include a nominal 1 8X edge concentration factor Since this factor is applied directly to the stress the user may manually modify edge stresses based on alternate edges stress factors as they see fit 4 13 6 Truncated Length The Truncated Length represents the percent of the total length of the contact ellipse along the major axis that is truncated due to shoulder or dam override ORBIS will automatically highlight all elements that have any truncation 4 13 7 Ellipse Semi Major The Ellipse Semi Major output represents one half of the major dimension of the contact ellipse 4 13 8 Ellipse Semi Minor The Ellipse Semi Minor output represents one half of the minor dimension of the contact ellipse 4 13 9 Max Sub Surface Shear The Max Sub Surface Shear is the peak shear stress developed below the raceway surface due to contact stress 4 13 10 Max Shear Depth The Max Shear Depth is the distance along the normal to the contact area below the raceway surface at which maximum shear stress is developed 4 13 11 Upper Edge Location The Upper Edge Location represents the edge of the contact
32. er Specifies the maximum number of preload solver iterations before aborting Max Internal Clearance Error 0 lt Value Specifies the maximum allowable internal dearance error During mounting and preloading the solver will converge on each bearing s change in internal dearance within this value OES cose _ _ Close Description Each system preference category is accessed by selecting the appropriate tab Database Location This area contains the folder location to the default database files The browse button brings up a folder selection dialog that allows the user to specify their preferred directory for storing their databases Select Database Type To perform a database import or simply view contents of a database the user must select which type of database to be displayed Once the type is specified the two scroll panes see 6 amp 7 populate with the appropriate entry names Load Remote Database Select this button to bring up a folder selection dialog Within the folder selection dialog the user will navigate to a desired database Note this button is only active once a database type is specified Remote Database Entries Displays entries from remote database Single entry selection is achieved by mouse selection left click on desired entry Multiple entry selection is achieved by two methods for consecutive entry selection select the first desired entry and shift click the last conse
33. er has 32 4 94 Row S finess Mati cia A aii EA code 32 4 10 Fatigue Mt A A de A AS ATA Ra 32 4 11 Bearing Torque titan dedicada 33 4 12 AID E NO 33 4 13 Row Outputs Element Wise results ccccccssccsssceseceseceseceeeceeeeseceeeseceseeeseecseeesaecsaecsaeenseeeaeees 33 4 131 Element Number ii ada 33 4 13 2 Normal Ball Gad ii aa 33 413 3 Contact Al ui ii aa Seuss E td at ins 33 4 13 4 Mean Hertz MESS dedo a 34 Copyright 2009 2013 Halpin Engineering LLC All rights reserved ALI Truncation Asi dais 34 4 13 6 Truncated Length aiii tana ana ileso barto 34 4 13 7 Ellipse Semi Major cccccssscssrcscrsessscsetssesscesecesscesscssnesscesenesnassncssnsesuaesnsesuesaneceeeteasseaeees 34 4 138 Ellipse Semi MINO ii ld iii dida 34 4 13 9 Max Sub Surface Shatain a iee E E E 34 41310 Max Shear Depths e m en A A a aies 34 4 1311 Upper Edge Location se mirisne a A A EARN 34 4 13 12 Lower Edge Location men aeeoeia Keek da REEE ee edad nea EEE RE 34 4 13 13 Contact Normal Approach ccccccccccsseesseceneceseceseceseceecseeeseeeeeseeeseeeseeeseecaaecsaecnseceaeenaeees 35 4 13 14 Contact Normal Stiffness ccccccccssecesecsteceseceseceseceeecseeeseeeeeseeeseeeseeeseecsaecsaecnaeenaeenaeens 35 4 1315 Spinning Velo tists bivalents Bec eae GAs 35 4 13 16 Rolling Velocity aiii ai add a 35 ALIMTA Spinning Torgu ve li tad e dod de sk aad deed dt id Laa Ed a ieS 35 AAS AS Rowling LOrQue initial ali ol cache
34. ibes the overall solution model Rotating mechanical systems modeled within ORBIS are described by three primary components the housing shaft and bearings The compliance model developed makes a key assumption that in the local vicinity of the bearing these components can be expressed with a series of nested concentric cylinders The representative cylinders must have uniform constant wall thickness and all deflections remain within the linear elastic region of the material Due to various sudden changes in the boundary conditions of these cylinders such as when the fit between mating cylinders transitions from clearance to interference the system model is technically nonlinear However the solution is deterministic and with use of conditional logic can be solved with a systematic approach The system model as outlined in Figure 22 essentially follows the same logical process necessary to assemble a rotational mechanical system initial conditions are defined the bearings are fit into the assembly preload is applied to the bearings and external loading is finally applied to the mounted and preloaded system The parameters describing relative axial ring displacements and internal clearance changes are tracked at each step of the process ultimately leading to the final state of the bearings The first step in the model is to define all initial conditions Users should take care to accurately describe initial bearing geometry and assembly fits
35. ifies the maximum number of numerical solver iterations on preload convergence before aborting Max Internal Clearance Error Specifies the maximum allowable internal clearance error for convergence in inches Acceptable values are greater than zero 0 lt value During mounting and preloading routines the solver will converge on each bearing row s change in internal clearance within this value Reset Defaults Select this button to restore all solver options to their default values Close Button Copyright 2009 2013 Halpin Engineering LLC All rights reserved Closes the system preference dialog window Figure 21 System Preferences Dialog 27 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com es Web http www HalpinEngineeringLLC com 3 0 Brief Technical Background ORBIS uses numerical techniques to solve the user defined system of one or more bearing rows simultaneously A solution to the system is achieved when the sum of all bearing row reaction forces is sufficiently close to the external applied forces system equilibrium ORBIS does not use pre generated lookup tables within the computations and the primary solution methods follow the mathematical theories developed and published by A B Jones 1964 However since Jones only developed theories for fixed ring analysis ORBIS has incorporated a model to account for bearing ring compliance The following briefly descr
36. iled outputs for each element of each row are provided in tabular form Output tables are repeated for each bearing row in the user s system These tables differ depending on whether the analysis is static or dynamic All outputs correspond to the system equilibrium state after application of all external loading 4 13 1 Element Number The Element Number is simply an indexing scheme to identify each of the rolling elements uniquely 4 13 2 Normal Ball Load The Normal Ball Load is the load applied by each ball into each raceway contact This load is directly normal to the contact ellipse 4 13 3 Contact Angle The Contact Angle output describes the angle of the normal ball load vector to the plane extending through the centers of all ball centers Copyright 2009 2013 Halpin Engineering LLC All rights reserved 33 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com aie Web http www HalpinEngineeringLLC com 4 13 4 Mean Hertz Stress The Mean Hertz Stress output represents the average Hertzian contact stress over the elliptical contact area Peak stress for an elliptical contact can be computed by multiplying the mean stress by 3 2 ORBIS will automatically highlight in red all values that exceed the user defined allowable mean Hertzian stress from the main user interface All stress results assume the contact ellipse if fully contained within the raceway 4 13 5 Truncation Analysis Wh
37. ing Element Bearings in Mechanical Design and Systems Handbook H A Rothbart ed McGraw Hill New York N Y article 13 Todd M J and Johnson K L 1986 A Model For Coulomb Torque Hysteresis in Ball Bearings in International Journal Mechanical Science Vol 29 No 5 pp 339 354 Great Britain Frantz P P and Leveille A R 2001 An Approach to Predicting the Threshold of Damage to an Angular Contact Bearing During Truncation Aerospace Report No TR 2001 8565 4 El Segundo CA Harris T A 2001 Rolling Bearing Analysis 4 Edition John Wiley amp Sons New York NY Copyright 2009 2013 Halpin Engineering LLC All rights reserved 37 of 37
38. ingLLC com To perform an analysis that considers shaft flexibility the user completes their system setup within the main window as if performing a standard rigid analysis Once the system is setup the user selects the Shaft Flexibility option from the Tools menu to open the Flexible Shaft Analyzer window as shown in the figure below Here the user defines their shaft elements reviews their final setup and submits the final analysis If the initially defined rigid system has constant section dimensions determined by validating all defined bearing I D s and shaft 1 D s are constant ORBIS will prepopulate one shaft element within the Flexible Shaft Analyzer window that extends through the complete system The user may override this assumption by editing the table of shaft elements For cases where the bearing I D s or shaft I D s are not constant throughout the system no prepopulated elements are provided and the user will need to define shaft elements that extend through all bearing and load locations CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 20 of 37 Halpin Engineering LLC Phone 310 650 8982 Email info HalpinEngineeringLLC com Web http www HalpinEngineeringLLC com D 4 X Start n X End in LD in O D in Material Solver Convergence Material 1 5 Ti 6Al 4v SNAN O Max Step Error lbf x 5 Ti 6Al 4V 0 5 2 25 T1 6AI 4V Max No of
39. ions 29 Figure 23 Bearing Nomenclature ecceeeccesccssesseeeceseeseeseceaecaeseceeaecaaseceeseceaeeaeeeeceaecaeeeeceaeceeeeeeaeeaeenees 31 Copyright 2009 2013 Halpin Engineering LLC All rights reserved Table of Tables Table 1 Numeric Formatting Examples cccccccsccssscsssceseceeceseceecseecseceeeseeeseeeseecaaecsaecaeceaecsaeseueeseeeeeeeeags 6 Table 2 Solver Convergence Criteria erisir oiiae n uE i i E TEEVEE EEEE GETE 30 Copyright 2009 2013 Halpin Engineering LLC All rights reserved Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com es Web http www HalpinEngineeringLLC com 1 0 Getting Started 1 1 System Requirements The following minimum system requirements are needed to run ORBIS e Windows 7 Vista Windows XP Windows 2000 Windows 2003 Windows 2008 Server e Display monitor with minimum resolution of 1024 by 768 pixels e 128 MB of free disk space e 256MBRAM e Available USB port e Java 6 0 or greater see below for more details 1 2 Installation Instructions Run the automated installer steps below to complete installation Administrator rights are needed to complete the installation properly Note ORBIS will install to All Users on a given machine 1 Insert the installation CD and navigate to your CD directory 2 Double click the Setup exe 3 Follow installer instructions to complete installation 1 3 Java Runtime Environme
40. is Utility 2 8 System Preferences The system preferences dialog is available from the tools menu reference 2 1 6 These preferences are persistent meaning they remain in effect each time the user launches and runs ORBIS until changed from this dialog Options available are shown in the figure below Copyright 2009 2013 Halpin Engineering LLC All rights reserved 26 of 37 Phone Email 310 650 8982 info HalpinEngineeringLLC com Halpin Engineering ace Web _ http www HalpinEngineeringLLC com Database Location Specify default location for databases C Program Files x86 Orbis System Force Balance Error lbf 0 lt Value lt 1 Specifies the maximum allowable system force balance error Convergence criteria will be determined by multiplying this value by the root sum squares RSS of the applied external loading IF RSS of external loads is less than one entered value is used directly Max No of System Solver Iterations 1 lt Integer Specifies the maximum number of system force balance solver iterations before aborting Number of required iterations will increase as the system force balance error is reduced Database Importing Default Database Entries Sample Bearing Remote Database Entries Tabbed Pane Selection Max Preload Force Balance Error Ibf 0 lt Value Specifies the maximum allowable preload force balance error Max No of Preload Solver Iterations 1 lt Integ
41. is as you traverse in the positive direction along the x axis Preload Type Specification for type of preloading Options are rigid or spring Rigid preloading activates input fields for inner and outer ring clamping forces Spring preloading activates inputs for the spring rate Preload Condition Specifies the condition at which the specified preload is defined Un mounted conditions means the rings are radially free at the specified preload Mounted conditions apply the preload force based on the mounted fit up conditions which include changes to internal clearance from interference fitting and ring clamping I R Clamp Load lbf Input field for the inner ring clamp load Only active for rigid preload type O R Clamp Load Ibf Input field for the outer ring clamp load Only active for rigid preload type Spring Rate Ibf in Input field for the preload spring stiffness Only active for spring preload type Bearing Drop down selection to assign the bearing for the active row The drop down menu will contain all bearings defined in the user defined bearing database Row Location in Input field for the axial location along x axis of the active bearing row LR Fitup in Input field for the inner ring fitup to the shaft Fitup is defined as the difference in the shaft O D to the free bearing I D A positive value indicates interference fits O R Fitup in Input field for the oute
42. ll proportionally alter the resulting stead state hysteresis torque Generate Dahl Parameters Button Selecting button generates torque stiffness and stead state torque results See 55 8 6 below Torque Stiffness Result has units of torque divided by angle where units are as specified above Steady State Coulomb Torque Steady State friction torque value with units as specified above This can be adjusted by altering the contact coefficients of friction No of Points Per Loop Specifies the number of solution points per hysteresis loop Points are always equally spaced from reversal angles specified Reversal Angles Table allows multiple reversal angles to be generated in the plot output Units are as specified above Angles must be entered as positive values greater than zero A separate loop is generated for each defined table entry Export Plot Data Checkbox Selecting this checkbox creates a save dialog once the Plot Torque Loops button is pressed The user will then be able to save the data from the plot to a delimited text file for post processing Clear Table Button Button simply clears all reversal angle data within the table Plot Torque Loops Button Clicking this button generates the torque loop plot based on all above user settings Generated plot window has all standard zoom and right click context menu options as discussed in Figure 18 Figure 20 Dahl Torque Hysteres
43. me Sample Lubricant Atmospheric Viscosity bf secin 2 133286 Pressure Coefficient of Viscosity n 2 bf 1 8204 Material 440C Stainless Lubricant Database Add To Database Events Properties al _ Delete From Database _ Delete From Database dose Close Figure 10 Database Editors 2 2 1 Bearing Database Editor The Bearing Database Editor allows the user to add edit view or delete bearings to the database See the following figure for a detailed description of the editor Note that certain parameters may be defined in more than one way For example the free contact angle can be derived from the radial play ball diameter and curvature ratios or input directly Thus ORBIS allows the user to enter either set of information To edit existing database entries simply select the existing database entry and click the View Parameters button All entry fields are populated and the user can then make their changes To shave the changes use the Add To Database button ORBIS will then ask to verify you want to overwrite the old entry with the new one If you want to keep the old entries you must rename the new one with a unique name Copyright 2009 2013 Halpin Engineering LLC All rights reserved 14 of 37 Halpin Phone Engineering Email LLC Web 310 650 8982 info HalpinEngineeringLLC com http www HalpinEngineeringLLC com Bearing P
44. mited text file Plot Results Button Button to perform analysis and plot final results If user selected Export raw data to file checkbox the user will be presented with File Save dialog to specify a file name and directory for the data file prior to plotting the data Close Button Closes the Sensitivity Studies dialog Figure 17 Sensitivity Studies Dialog 2 5 1 Sensitivity Studies Plot Windows The plot windows generated from a sensitivity study are interactive Separate plot windows are generated for each dependent variable selected in the sensitivity dialog See the following figure for a description of user options within the plot windows Copyright 2009 2013 Halpin Engineering LLC All rights reserved 23 of 37 Halpin Engineering LLC Phone 310 650 8982 Email info HalpinEngineeringLLC com Web http www HalpinEngineeringLLC com Max Mean Hertzian Stress Max Mean Hertzian Stress Copy Zoom In Save as Zoom Out gt Auto Range gt 150 000 m 125 000 Stress psi E 75 000 gt 100 125 150 175 209 225 250 27 5 30 0 32 35 0 37 100 125 150 175 200 225 250 275 30 0 32 Row Preload Ibf Row Preload Ibf Curve Description Data is plotted with a smooth curve fit where actual solution points are indicated with circles Note the smooth curve fit may not always follow data accurately Plot Options Dialog The plot
45. model which was republished by Harris 2001 This model accounts for lubricant viscosity and requires use of a viscous torque factor Hence the viscous torque output can be scaled by direct modification of the viscous torque factor To achieve optimal torque predictions the user will need to tune both the coefficient of friction at the ball contact and the lubricant viscous torque factor This is most accurately done by use of existing test data of a known configuration The coefficient of friction should be tuned first based on breakaway or slow speed test data The viscous torque factor is then tuned based on test data for two different operational speeds Note that viscosity is highly sensitive to temperature 4 12 Ball Excursions Dynamic runs include output showing the maximum ball excursion for each bearing row This output represents the maximum circumferential excursion in units of inches a ball travels relative to the average ball path Another way to view this is the maximum amplitude a ball travels within the retainer pocket This result is achieved by taking the orbital velocities of each ball determining the average velocity of all balls integrating the orbital velocities through one full revolution and finally computing the difference between actual integrated ball positions and the average ball positions Final reported excursion represents the maximum ball departure from the average 4 13 Row Outputs Element Wise results Deta
46. nt In order for the software to run properly the host computer must have Java Runtime Environment JRE version 6 0 or greater installed The JRE is an industry standard and will generally already be installed on most modern computers If your computer does not have JRE 6 0 or greater already installed you may install the version included from the installation directory or download the latest version from the Sun Oracle website www oracle com To install the version included from the ORBIS CD follow these steps 1 Open the Java folder on the CD ORBIS Java 2 Double click jre 6uXX windows i586 s exe to install on Windows platforms Windows 7 Vista Windows XP Windows 2000 Windows 2003 and Windows 2008 Server Note the XX in the filename denotes the particular update to the JRE Version 6 1 4 Coordinate Systems ORBIS uses a standard right handed coordinate system for all loads and deflections As shown in the figure below the x axis is aligned with the shaft spin axis with positive pointing rightward on the page and the positive y axis is defined as pointing upward on the page Positive moments rotations follow right hand rule along respective axes Copyright 2009 2013 Halpin Engineering LLC All rights reserved 5 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com a Web http www HalpinEngineeringLLC com Y creas X spin axis Z Figure 1 Coordinate Sys
47. oordinate system is shown in upper right corner of sketch window Button Sketch Selecting the Sketch button refreshes the sketch window with current user defined inputs Button Bearings Button opens the Bearing Database dialog window see section 2 2 1 Button Materials Button opens the Material Database dialog window see section 2 2 2 WlOINID UN AJIN e Button Lubricants Button opens the Lubricant Database dialog window see section 2 2 3 Figure 5 System Display 2 1 4 Bearing Row Inputs The Bearing Row Input area is where the user defines necessary inputs for each bearing row in the system See the following figure for a detailed description of each input type A common mistake for new users is improper sign convention on the Row Preload field The user must consider the orientation of the contact angle and specify an appropriate sign on the row preload input Contact angles are defined using convergent and divergent terminology see section 2 1 4 1 for details These terms relate to whether the contact angle line of action converges or diverges toward the spin axis as you traverse along the positive x axis rightward along the spin axis For example the leftmost bearing in a duplex pair of bearings configured in a back to back or DB orientation has a divergent contact angle Ifthis bearing was preloaded normally there would be a residual force acting on the inner ring toward the right which i
48. ory while thermal loading accounts for both radial and axial expansions System Parameters initial conditions AP w mounted rings System Loading Final Results Figure 22 System Model Illustrating Analytic Process For Compliant Ring Considerations 3 1 Convergence Criteria ORBIS uses the IEEE 754 technical standards for all floating point arithmetic All calculations use at least 64 bit precision Key calculations pertaining to matrix inversion and the overall system Jacobian are extended to 128 bit precision to improve accuracy of the solver The default criteria for convergence are show below Refer to section 2 8 for instructions on how to change these settings CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 29 0f 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com ae Web http www HalpinEngineeringLLC com Table 2 Solver Convergence Criteria Default Parameter Error Comments The allowable system equilibrium error is defined as a percentage of the System applied external loading Euclidean norm of force components Error is Equilibrium 0 001 defined as the difference between the norm of all bearing row reaction Error forces and the norm of the external applied forces In the case where there is zero external loading the error defaults to 1 0E 5 lbf Preload Force Preload force error is defined
49. r load is fixed relative to the shaft or housing Viscous Torque Factor Figure 4 Dynamic Analysis Inputs 2 1 3 System Display The system display area provides a proportional engineering sketch of the user defined system Many key details about the user setup are identified within the sketch To avoid setup mistakes perhaps due to mistyped inputs it is recommended to review this sketch prior to submitting an analysis The system sketch is also copied and included in the results window as a figure See the following figure for a detailed description of the information provided in the system display panel Copyright 2009 2013 Halpin Engineering LLC All rights reserved 9 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com cas Web http www HalpinEngineeringLLC com oT G SSRI 6632 15 SSRI 6632 15 z x NS O Row 1 Row 2 Description Name of each bearing in the system is shown above the bearing row sketch Bearing Sketchi Bearing Name sketches contain user defined contact angle orientation and any preload spring definitions Sketch Bearing Row No Each row is labeled to match the corresponding Bearing Row Input tab Sketch Row location Center location x axis coordinate of each bearing row is shown below the bearing Sketch Load Location Axial location x axis coordinate of each load point is shown Sketch Coordinate System C
50. r ring fitup to the housing Fitup is defined as the difference in the free bearing O D and the housing 1 D A positive value indicates interference fits Shaft I D in Specifies the I D of a hollow shaft For non constant shaft wall thicknesses use the appropriate shaft I D at the bearing row location For a solid shaft input a zero value Housing O D in Specifies the O D of the housing For non constant housing wall thicknesses use the appropriate housing O D at the bearing row location Row Preload Ibf Specifies the preload force applied to the active bearing row Preload forces are directional and must include the appropriate sign convention To preload a bearing through its contact angle standard preloading specify a positive preload for divergent contact angles and a negative preload for convergent contact angles Coeff of Friction Ball Contact CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved Specifies the rolling contact friction coefficient for the active bearing row Figure 6 Bearing Row Inputs 11 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com aie Web _ http www HalpinEngineeringLLC com 2 1 4 1 Contact Angle Orientation Contact angle orientation is assigned within the bearing row input region as discussed in the preceding section Terminology for convergent and divergent is further illustrated in the figure below Dive
51. rgent Contact Convergent Contact Angle Orientation Angle Orientation N Figure 7 Convergent and Divergent Contact Angles 2 1 5 Input Field Description The input field description area provides helpful information to the user for all input fields When the user places their cursor in one of the input fields done by clicking the mouse in a field or pressing the tab button to advance to the next input field a description about that field appears in the Input Field description area The following figure illustrates the description displayed when the user clicks within the Fx lbf input field penaas LR Clamp Load bf 0 da ous Ti SE Housing O D in OR Ch Load B 0 a Row Preload bf Rate Ibf in Load t Sito edt Coeff of Friction Ball Contact 075 Enter external load applied in x direction axial Ibf Analyze Exit Figure 8 Input Field Description CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 12 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com ae Web http www HalpinEngineeringLLC com 2 1 6 User Menus User menus are available within the main graphical interface See the following figure for a detailed description of the available menu options Help Help Batch Process Load Cases Ctrl B Shaft Flexibility Ctrl F 5 Sensitivity Studies Ctrl S Tolerance Studies Ctrl T Ctrl
52. ro tada ai ATA A taa caca sabes 19 ZO SCNSIPVItY Studies iii IA ES 22 2 5 1 Sensitivity Studies Plot Windows cccccssccsseceseceseceseceeecseeeeeneeeseeeseeeseecseecsaecsaecaeenseenaeees 23 2 6 Tolerance Analysis A A a E 24 2 7 Dahl Torque Hytrin A aida E A desa 25 28r System Preferentes o eee oE ERE E E a eesk ances EEEE E AEE E R NSE 26 3 0 Brief Technical Background e sseossesssesssesssosssesssesssesssessseossecssosssoossoossoossoossoossoossoossoossoossoossoosess 28 3 1 Convergence ClritellA ooooocnonococononncoonnonnnnononnnonnn a E aa aat aTa aAA E aaa aaie 29 4 0 Output DEScripGons s 005 ccccssecccsvesnocersseonsosveracscncdonscesdansdecasessnadeodnoacencseccseedunesoonssocesaseeascdncsooewasese 30 A Input Parameters aena EE E TE A EA A A AO 30 42 External Apphed Load ii E REE AA E A EE 30 4 3 Ball Crossi Angles rr A A E EEEE at E a 30 AA Internal CaranteS ieoi tne reier aa e a Lacowseelandidee uncdbedbonaedadesonentgelanstueeseeeees 30 4 5 Bearing Ring Properties cintia osito 31 4 6 Preload Data is IA LA Ts ai 31 Ac Reaction Forces OO adi A A a 31 4 8 Inner Ring Displacements ainia ita vested EENE EEE KE 32 4 95 Stiffness Ouuu aida said lo A A AA ATA A than cheat date ea td dsd 32 4 9 1 Axial Stiffness with Ring Compliance cecccesccessceseceeeceeeeeeeeeeseeeseeeseeeseeesaecaecnseenseenaeees 32 49 27 System Jacobi tica o rl nr ti E 32 4 9 3 Stiiness at Eoad Pont ie ennie A A act denne seed
53. roperties Bearing Name Rolling Elements Pitch Diameter in Element Diameter in 3 Number of emer Y Free Contact Angle deg 5 Free Radial Play in RMS Roughness Microinch Inner Ring Inner Diameter in LR Width in Land Height h d Dam Height h d Dam Diameter in 7 RMS Roughness Microinch Raceway Curvature f ETA E Outer Ring Outer Diameter in O R Width in Raceway Curvature Land Height h d Land Diameter in Dam Height n d Dam Diameter in RMS Roughness Mircoinch Bearing Name Material Material View Edit Properties Description Specify a name for the bearing Pitch Diameter in Diameter that describes the rolling element centers often the average between the bearing I D and O D Element Diameter in Diameter of the ball Number of Elements Number of balls in a single bearing row Free Contact Angle deg Contact angle of bearing with no external loading Must be a positive value Only active when radio button is selected Free Radial Play in Radial free play is synonymous with diametral play and represents the total linear travel along a radial direction the inner ring can move relative to the outer ring when axially unrestrained and negligible force is applied Only active when radio button is selected RMS Roughness micro inch Surface roughne
54. s positive X in ORBIS coordinates Subsequently the rightmost bearing in this hypothetical DB pair has a convergent contact angle and requires a preload force acting to the left or negative in ORBIS coordinates on the inner ring Note positive values entered within ORBIS do not require the prefix plus sign CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 10 of 37 Phone 310 650 8982 Email info HalpinEngineeringLLC com Halpin Engineering LLC Web http www HalpinEngineeringLLC com Define Total of Bearing Rows 1 X G Row 1 Contact Angle Preload Condition Row Parameters 3 9 lt Divergent Un Mounted Bearing 9 gt Convergent Mounted Flas tacoiion LR Fitup in O R Fitup in Shaft I D in Housing O D in Preload Type 4 Rigid Spring LR Clamp Load bf 6 O R Clamp Load bf 7 Bearing Rows Row Preload lbf Coeff of Friction Ball Contact Spring Rate lbffin 8 Description Drop down selection allows up to 5 bearing rows to be specified Row tabs see 2 will be activated based on number of bearing rows selected here Row Tabs Row tabs are activated based on the number of bearing rows selected Selecting an active tab allows the user to define parameters for that row Contact Angle Contact angle definition for active row A divergent contact angle extends away from or diverges from the spin ax
55. ss RMS of the ball Material Assign materials from Material Database to the rolling elements inner ring and outer ring Inner Outer Diameter in Bearing s inner or outer diameter LR O R Width in Width along the bearing axis of the inner or outer ring Raceway Curvature Raceway curvature of inner and outer rings expressed as the ratio of the raceway radius to the ball diameter Land Height h d Height of the land diameter expressed as the ratio of the radial height to the ball diameter The land is specified as the shoulder that contains the loaded contact zone Only active when radio button is selected Land Diameter in Diameter of inner or outer ring land Only active when radio button is selected Dam Height h d Height of the dam diameter expressed as the ratio of the radial height to the ball diameter The dam is specified as the shoulder that is unloaded or opposite the contact angle Dam Diameter in Diameter of inner or outer ring dam Only active when radio button is selected RMS Roughness Microinch Surface roughness RMS of the inner or outer raceway Edit Materials Button Opens the Material Database Editor Clear All Entries Button Clears all current input field entries This does NOT clear the database entries Add To Database Button Commits the specified input entries into the database under the bearing name specified A warning will
56. t AXp q with rings radially unrestrained This displacement sometimes called a preload gap will be used for rigid type preloading as an enforced ring displacement Spring type preloading essentially bypasses unmounted preload specifications since typical spring rates prohibit noticeable force increase for small deflections this assumption will be valid for spring rates much lower than the axial stiffness of the bearing which is often the case Axial preloading creates radial forces on the bearing rings that increase the bearing s internal Copyright 2009 2013 Halpin Engineering LLC All rights reserved 28 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com es Web http www HalpinEngineeringLLC com clearance the rings stretch and change the race curvature center To find the preloaded state with account for ring stretch the Jones model can be iteratively solved until the change in internal clearance equals the resultant ring deflection due to preload pressure on the raceways This algorithm must account for nonlinear behavior of axial load versus deflection and potential nonlinear radial ring stiffness due to fitup gap closure The final step is to apply external loading to the mounted and preloaded state of the bearing system External loading can occur from either applied forces moments or temperatures All external force moment loads are analyzed per Jones methods i e fixed ring the
57. t parameters such as torque fatigue life film parameters centrifugal and gyroscopic forces etcetera See the following figure for detailed descriptions of each input field Copyright 2009 2013 Halpin Engineering LLC All rights reserved 8 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com aie Web http www HalpinEngineeringLLC com Velocity rpm Reliability Life Factor Viscous Torque Factor Shaft Rotates gt Load fixed to shaft gt Housing Rotates Load fixed to housing Description a Selection of this checkbox activates the dynamic analysis inputs below Default is un checked Velocity rpm Defines the rotational velocity in RPM of the rotational member Reliability Defines the reliability for fatigue life Valid inputs are between 0 and 1 exclusive Default is 0 9 L10 equivalent Allows user to specify an overall combined life adjustment factor ORBIS will compute Life Factor reliability and lubricant regime adjustment factors however other factors such as material and operating environment must be included here Compensation factor for type of lubrication Default is 1 7 which represents a reasonable initial guess for an oil lubricated ball bearing no oil bath or jet conditions Rotational Member Radio buttons allow user to specify either shaft rotates or housing rotates Loaded Member Radio buttons allow user to specify whethe
58. tem 1 5 Numerical Input Formatting Most inputs required to perform an analysis will be numeric ORBIS accepts multiple different methods of numerical inputs but there are a few that are not allowed The table below shows examples of valid and invalid numeric input formatting Table 1 Numeric Formatting Examples Valid Inputs Invalid Inputs Description Comma notation is not allowed Spaces anywhere within the input string are not allowed 2 0 User Interfaces 2 1 Main Graphical Interface The main graphical interface is the primary window within ORBIS This window allows the user to define their bearing system and perform a majority of common analysis runs As shown in the figure below this window is organized into five regions Copyright 2009 2013 Halpin Engineering LLC All rights reserved 6 of 37 Phone 310 650 8982 Halpin Engineering LLC Email info HalpinEngineeringLLC com Web http www HalpinEngineeringLLC com e System Inputs located in the upper left region is where external loading temperatures shaft housing materials and lubricants are defined e Dynamic Analysis located in the lower left is where parameters such as velocities fatigue life reliability and life factor viscous torque factor rotational member and load fixity are defined e System Display located in the upper right provides an engineering sketch based on the user defined system e Be
59. teraction options for the plot windows generated from all sensitivity study runs In addition to the generated plots from ORBIS the user can export the raw data used to generate the plots for post processing The data is saved in a delimited text file that can be easily imported into programs such as Microsoft Excel Copyright 2009 2013 Halpin Engineering LLC All rights reserved 22 of 37 Phone 310 650 8982 Halpin Engineering Email info HalpinEngineeringLLC com e Web http www HalpinEngineeringLLC com Input Parameter Independent Variable Select Input Variable Vary From of Increments Nominal Value Row 1 Output Parameters Dependent Variables Select OutputRow 1 5 Select Output Variables to Plot System Outputs Mounted Preload E Preload Deflection Torque E Fatigue Life L10 E Diametral Free Play Mnt d Axial Free Play Mntd E LD Expansion Mntd O D Expansion Mnt d Row Forces amp Deflections E Deflection dx Deflection dy Reaction Fx T Reaction Fy E Reaction Fz Deflection dz E Reaction Fyy Deflection dyy E Reaction Fzz M Deflection dzz on Element Outputs 7 Max Mean Hertzian Stress F Max Ball Load Max Contact Angle F Max Upper Edge Location F Max Sub Surface Shear Max Shear Depth 7 Max Ball Spin Velocity Film Parameter Lambda System Stiffness Stiffness Kx E Stiffness Ky E Stiffness Kz Stiffness Kyy
60. tions Final internal clearances include changes due to mounting preloading and temperature effects Additionally clearance changes from each influence are provided separately Copyright 2009 2013 Halpin Engineering LLC All rights reserved 30 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com g Web http www HalpinEngineeringLLC com Diametral play is defined as the total linear radial distance the inner ring can move relative to the outer ring with negligible applied force Axial play is defined as the total axial displacement the inner ring can move relative to the outer ring 4 5 Bearing Ring Properties This section provides the equivalent raceway diameters used for the mounting preloading algorithm These diameters are defined as function of the bearing geometry as shown in the following figure The bearing inner and outer diameter expansion from fitup and preloading at both unmounted and mounted condition is also included 2h Dir QR ace 0 68 M ha hy ha IRrace 2h Dor GOR race 0 68 h ha d hy ha race WOR ace Figure 23 Bearing Nomenclature 4 6 Preload Data This section provides the applied preload resulting mounted preload and corresponding axial deflections for each bearing row The axial deflection shown is purely due to the mounted preload condition 4 7 Reaction Forces on Shaft This section provi
61. tudies Tolerance Studies Dahl Torque Hysteresis System Preferences Help Menu Figure 9 User Menu s 2 2 Database Editors ORBIS uses bearing material and lubricant databases to define the majority of input parameters required in a standard bearing analysis Once the user has defined their database entries they simply assign them to their analysis setup via drop down menus within the main window Database editors allow the user to view modify add and delete bearing material and lubricant database definitions The database editors are accessed from the buttons within the System Display area see section 2 1 3 Database definitions are stored in three specific files Bearings dat Materials dat and Lubricants dat These files are typically located within the ORBIS installation directory However database files can be placed anywhere such as a shared network drive In the case where multiple users have access to a Copyright 2009 2013 Halpin Engineering LLC All rights reserved 13 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com g Web http www HalpinEngineeringLLC com common network drive it is recommended that a common set of database files be used for all users See section 2 8 System Preferences for details on how to import entries from external databases or change the default location of the database files It is important to maintain databases within ORBIS
62. w Result highlighting makes important result parameters impossible to overlook Each element 3 Result Highlighting Hertzian contact stress exceeding the user specified allowable is highlighted Additionally all elements with truncation are automatically highlighted 4 Adjust Font Size Font slider adjusts font size in 1pt increments for all the detailed results text 5 Print Button Brings up a standard print dialog Only the detailed results are printed Save copies the contents of the results window to a delimited text file The delimited text file 6 Save Button provides the user with unlimited post processing options and easy importing to various software platforms such as Microsoft Excel 7 Close Button Closes the results window Figure 15 Results Window 2 4 Flexible Shaft Analyzer Orbis version 2 3 provides a new utility to account for elastic compliance of the bearing shaft Elasticity model uses Timoshenko beam element formulations that account for both bending and shear deflections in the shaft The interface allows shaft definition with up to 25 unique circular beam elements each of which may be defined with unique section dimensions and or materials See figure below for descriptions of the flexible shaft window CopyrightO 2009 2013 Halpin Engineering LLC All rights reserved 19 of 37 Halpin Phone 310 650 8982 Engineering Email info HalpinEngineeringLLC com o Web http www HalpinEngineer

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