AMESim Heat Generation Model

1. CAViDS Consortium AMESim Heat Generation Model A CAViDS Consortium Project Advisory Board Report May 10, 2011

2. CAViDS Consortium Project Objective • Develop AMESim heat generation modeling capability for gearbox systems which compares favorably with experimental results.

3. CAViDS Consortium Work Plan Phase 1: Obtain software and familiarize. (Complete) Phase 2: Model and correlate churning and gear heat generation and temperature rise. 1. Caterpillar FZG test stand model (Complete) 2. Eaton heavy duty transmssion (Underway) 3. Eaton medium duty transmission (Underway)

4. CAViDS Consortium Prior Results 1. Correlated AMESim temp rise model with Caterpillar Dynasty model of FZG test stand Correlated AMESim temp rise model with Eaton HDT test data Correlated Changenet churning loss predictions with Eaton HDT test data Developed LDP based spreadsheet for HDT sliding loss predictions Started AMESim and Changenet models for MDT churning loss predictions

5. CAViDS Consortium Goals for Last Month • Further verify and develop LDP mesh loss model • Further verify and develop AMESim heavy duty transmission churning and mesh loss models • Correlate medium duty churning loss model with Eaton data

6. CAViDS Consortium Last Month’s Accomplishments • Modified heavy transmission AMESim temp rise model for medium duty transmission and correlated with MD temp rise test data • Predicted maximum allowable losses from that model based on acceptable temperature rise • Developed spreadsheet for churning and synchronizer shear loss calculations for Eaton medium duty transmission • Correlated medium duty loss predictions with Eaton testing • Compared Changenet to AMESim churning loss predictions • Refined spreadsheet to use LDP output to calculate gear mesh losses on Eaton heavy duty transmission • Compared AMESim gear loss predictions to LDP • Developed action plan for sliding loss prediction impvovement • Evaluated AMESim churning and gear mesh prediction capability • FZG model • Developed Eaton heavy duty transmission model

7. CAViDS Consortium MD Objective Develop heat generation modeling capability for Eaton medium duty which accurately predicts no load losses and temperature rise on a spin test.

8. CAViDS Consortium Work Plan 1. Modify heavy duty AMESim thermal model • Compare temp rise measurements with predictions • Determine acceptable losses to stay below 300 degrees F • Develop model to predict thermal losses • Churning losses • Oil shear losses • Bearing losses • Seal losses

9. CAViDS Consortium AMESim Thermal Model • Used proven HD approach • Modified with MD convection/radiation areas, masses, speeds • Used test loss power as input

10. CAViDS Consortium Temp Rise Prediction Results • Need to reduce losses to from 11 LB-FT to 8 LB-FT input torque at 2500 rpm to meet 300 degrees F temperature limit

11. CAViDS Consortium Temp Rise Prediction Results

12. CAViDS Consortium Loss Prediction Approach Consider following losses 1. Churning - Use Changenet approach 2. Oil shear – Use standard shear formula 3. Bearing – Harris reference 4. Seal – Deduce from experimental results

13. CAViDS Consortium Changenet Churning Loss Equations Loss = C/2 * oil density * speed^2 * pitch radius^3 * submerged area C = 1.366 * (submerged depth/pitch diameter)^0.45 * (oil volume/pitch diameter^3)^0.1 * Froude^-0.6 * Re^-0.21 • Key assumptions: • Submerged area is defined by dynamic oil height and 1.5 times circumferential submerged area of gear (submerged arc length times gear width). • Reynolds number is peripheral gear speed times gear circumference divided by kinematic oil viscosity at temperature • Froude number is peripheral gear speed divided by gear circumference times gravity

14. CAViDS Consortium Oil Shear Loss Prediction Torque Loss = (S * R * v * A) / d S = speed differential (gear and synchronizer) – m/sec R = synchronizer gage radius - m v = dynamic viscosity of oil – kg/(m*sec) A = synchronizer area – m^2 d = gap between gear and synchronizer - m Torque on drive gear reacted through MS and CS

15. CAViDS Consortium Bearing Viscous Loss Prediction Viscous Torque = f*(v*n)^0.6667 * d^3 f = constant depending on bearing type v = viscosity in cs n = bearing speed in rpm d = mean bearing diameter in mm

16. CAViDS Consortium Seal Loss Determination

17. CAViDS Consortium Loss Prediction Spreadsheet

18. CAViDS Consortium Current Prediction Results

19. CAViDS Consortium Current Conclusions Current loss break down (by prediction) 40% churning 40% shear 20% bearing and seal Potential issues Synchro roundness Eccentricity Material

20. CAViDS Consortium AMESim Single Gear Set Churning Loss Model

21. CAViDS Consortium Churning Loss Equations Changenet Loss = C/2 * oil density * speed^2 * pitch radius^3 * submerged area C = 1.366 * (submerged depth/pitch diameter)^0.45 * (oil volume/pitch diameter^3)^0.1 * Froude^-0.6 * Reynolds^-0.21 AMESim Loss (sides) = Cs * oil density * speed^2 * tooth width * max radius^4 Cs = 0.97 * (submerged volume/oil volume)^-0.576 * (tooth width/max radius)-0.124 * (submerged depth/max radius)^0.74 * Froude^-(0.464+0.037(max radius/submerged depth)) + Re^-0.31 Loss (teeth) = Ct * oil density * speed^2 * tooth width * pitch radius^3 * tooth height Ct = 5623 * (tooth height/8 mm)^-1.5 * (tooth width/8 mm)^-0.36 * Froude^ -0.78 * Reynolds^-0.88

22. CAViDS Consortium Churning Loss Comparison

23. CAViDS Consortium HDT Gear Sliding Loss Prediction • Developed spreadsheet based on Kahraman 2007 paper using LDP predicted loads and sliding speeds • Compared to AMESim calculated sliding losses and old experimental results • Developed a set of recommended actions based on results

24. CAViDS Consortium Gear Mesh Loss PredictionLDP Approach • Use LDP to calculate gear load, sliding and rolling velocity vs. roll angle • Use empirical formulas to determine friction coefficient vs. roll angle • Calculate losses vs. roll angle • Determine average loss through mesh • Correlate with temp rise testing based on model

25. CAViDS Consortium AMESim Gear Sliding Loss Model

26. CAViDS Consortium Sliding Loss Formula Comparison LDP Coefficient of Friction = e ^C * Load Intensity ^1.03 * Slide Ratio ^1.04 * Rolling Velocity ^ -0.10 * Dynamic Viscosity ^0.75 * Effective Radius of Curvature ^-0.39 C = --8.92 – 0.35 * Sliding Ratio * Load Intensity * Log (10) (Dynamic Viscosity) +2.81 * e ^ (Sliding Ratio * Load Intensity * Log (10) (Dynamic Viscosity) + 0.62 * e ^Surface finish) AMESim Coefficient of Friction = 0.127 * Ln (0.02912 * Load Intensity) / (Oil Density * Kinematic Viscosity * Sliding Velocity * Rolling Velocity ^2) Changenet (Benedict and Kelly) Same as AMESim except Log (10) (0.2912 *………)

27. CAViDS Consortium Sliding Loss Comparison • LDP Inverse effect of temperature on losses counterintuitive • LDP model ignores asperity contact • LDP model accounts for surface finish • AMESim model closer to limited test results and shows viscosity effects consistent with intuition

28. CAViDS Consortium Recommended Further Actions • Study Kahraman’s later (2007 – present) work • Consider using OSU to further develop LDP approach and incorporate into LDP $8000. (Discuss potential funding mechanisms) • Evaluate other formulae referenced in Kahraman 2006 paper • Run dyno testing on heat rise

29. CAViDS Consortium HDT No Load Loss Model Status Made churning losses consistent with MD model Added shear losses from synchro and adjacent MS gears

30. CAViDS Consortium Next Month • Further evaluate alternative gear sliding loss models • Further verify and develop AMESim heavy duty transmission churning, synchronizer shear, bearing and seal model • Further correlate medium duty churning loss model with Eaton data • Learn to implement Changenet churning and best gear sliding equations directly into AMESim

31. CAViDS Consortium Notes • Software easy to use • LMS has great support • Capabilities will meet our needs • University license $3000 for year • Changenet churning loss calculations look promising • LDP mesh loss prediction easy to use – need development