AMESim Transmission Rattle Modeling

1. CAViDS Consortium AMESim Transmission Rattle Modeling A CAViDS Consortium Project Report to Eaton May 2, 2012

2. CAViDS Consortium Interim Project Objective • Understand inertia and drag effects in drive rattle on ESO-11206 • Calculate rattle threshold for each mainshaft gear • Predict independent effect of backlash, driven gear inertia, and torsional input amplitude on the mainshaft reverse gear • Predict rattle intensity for each mainshaft gear with given torsional input

3. CAViDS Consortium Step 1Rattle Threshold Calculation • Developed spreadsheet to determine threshold torsional vibration input at countershaft to cause separation at each mainshaft gear at 1500 rpm input speed in 3rd gear • Calculated drag torque on each mainshaft gear from churning bearing loss and synchro drag using formulae developed and verified for thermal project • Calculated inertia of each gear • Determined threshold angular acceleration by dividing drag torque by inertia

4. CAViDS Consortium Threshold Results • Rattle threshold torsional vibration very low compared to typical driveline vibration levels • Torsional vibration limit is 300 radians per second squared for trucks • Rattle threshold values for ES-11206 ranged from 0.4 radians per second (first gear) to 46.2 radians per second squared (OD gear) for transmission in 3rd gear at 1500 input rpm, much lower than the typical driveline torsional vibration levels.

5. CAViDS Consortium Threshold Spreadsheet

6. CAViDS Consortium Threshold Conclusions • Rattle threshold is not the controlling factor in rattle intensity in drive rattle • Other controlling factors should be evaluated for their effect

7. CAViDS Consortium Step 2AMESim Rattle Factor Study • A simple AMESim model was used to determine the effect of three basic parameters on drive rattle intensity: backlash, main shaft gear inertia, and input torsional amplitude

8. CAViDS Consortium Baseline Parameters • Input Speed – 1500 rpm • Operating Ratio – 2.52 (3rd) • Angular Acceleration – 300 rad/sec^2 • Frequency – 50 Hz • Mainshaft gear - Reverse • Mainshaft gear inertia – 0.783 kg-m^2 (ms rev) • Gear ratio - -6.75 • Backlash – 0.5 mm • Drag torque – 0.548 N-m Output Parameter • Countershaft tooth impact load (rms)

9. CAViDS Consortium Rattle Factor Study Results

10. CAViDS Consortium Parametric Effect Conclusions • Inertia, input torisonal vibration amplitude and backlash all have a significant effect on the amplitude of rattle, measured in rms terms. • Inertia seems to have the biggest effect. • The high inertia of the mainshaft reverse gear along with its higher effective backlash, because of the added backlash in the reverse idler, would seem to generate the highest amplitude of rattle compared to other mainshaft gears • A comparison of the predicted rattle levels of each mainshaft gear in an ESO-11206 transmission for a given operating condition and level of torsional vibration should be made.

11. CAViDS Consortium Step 3Prediction of Rattle Levels for Each Mainshaft Gear • Two models were used • Countershaft-mainshaft gear set • Countershaft-idler-mainshaft gear set

12. CAViDS Consortium Baseline Parameters • Input speed – 1500 rpm • Operating ratio – 2.52 (3rd) • Angular acceleration – 300 rad/sec^2 • Frequency – 50 Hz • Backlash – 0.5 mm (per mesh) • Gear ratio – calculated for each gear • Drag torque – calculated for each gear • Gear inertia – calculated for each gear Output Parameter • Countershaft tooth impact load (rms)

13. CAViDS Consortium Results

14. CAViDS Consortium Results (continued)

15. CAViDS Consortium Study Conclusions The reverse gear set has highest rms rattle tooth loads of any mainshaft gear due to high inertia, high backlash, and possible double tooth loading due to idler for a given set of operating conditions. This correlates to observations during GM testing Drag torque is not sufficient to control onset of rattle. Inertia is very important, but may not be significantly changed by design Backlash is also very important but has a minimum limit Reverse idler seems to have a significant impact on propensity to rattle but must be there Therefore, the best way to control drive idle may be to limit driveline torsional vibration. This implies need for partnership with customer to predict and control this phenomenon

16. CAViDS Consortium Next Steps Focus on driveline dynamics model improvement to include light duty drivelines. Define model users Define modeling software Determine need for further internal rattle modeling. Define modeling software