Reliability Evaluation of Trailer Axles -Larry McLean

1. Final Project for DESE-6070HV7 Statistical Methods for Reliability Engineering Dr. Ernesto Gutierrez-Miravete Rensselaer at Hartford 05Dec08 Reliability Evaluation of Trailer Axles -Larry McLean

2. Reliability Evaluation of Trailer Axles TABLE of CONTENTS TITLE: PG Executive Summary…………………………...………………..3 Recommendations……………...…....…………………………3 Conclusions………………………………………………………3 Introduction………………………………………………………4 Component Description………………………………………..5 Component Reliability Structure……………………………..5 Component Test Description………………………………….7 Component Test Results………………………………………9 Component Test Data Reduction……...……………………10 Component Context (System Description)………………..17 System Reliability Analysis…………………...……………..18 Appendix 1: Component FMEA……………..………………26

3. Executive Summary • A process for evaluating the in-service reliability of a trailer axle is described here. • Since the trailer axle has undergone some testing, it has been used to characterize the reliability behavior of the axle, based on some simplifying assumptions. A more complete analysis is recommended involving stress analysis of the component. • Using simplifying assumptions, a sample calculation is done to calculate the in-service reliability of the axle. Due to lack of data, the calculation, has no basis in reality, but would be useful as a model for performing a real analysis. • Maple, Minitab and ‘R’ were indispensable in manipulating and curve-fitting data and creating equations that made fundamental analysis possible. • Recommendations • On the occasion of further testing, place strain gauges at key locations on the axle. • Finite Element stress analysis of the axle. • Detailed information about the material properties of the axle would allow comparison between analysis and testing to be meaningful. • With this information and the rig test, it could be determined if the component was attaining its expected life. • It also would provide a vehicle for studying the design features with the twin aims of increasing reliability and reducing cost. • Field testing to determine the environment that the axle is subjected to in-service. • The objective of this testing would be to derive equations that could describe the service mission of the axle and allow a complete analysis of the reliability. • Strain gauges coupled with trailer load information, road conditions and trailer speed are all important. • A model of the trailer and associated suspension hardware. • This would allow a prediction of the impact of varying environmental factors on the forces the axle sees. • This would extend the usefulness of field testing and minimize the testing required. • Conclusions • The axle system reliability functions can be represented by using a single Weibull equation. • The failure mode of the axle was consistent and demonstrated two symmetrical weak points on the axle. • By generalizing Miner’s Rule, it is possible to create ‘mission’ formulas that can be used to estimate axle reliability. • Monte Carlo methods are useful in taking these general equations and predicting in-service axle reliability. • Using fitting techniques, the reliability curve can become the basis for calculating all the traditional reliability functions.

4. Figure #1: In-service Trailer axles

6. Other Failures LHS Load Point Failure RHS Load Point Failure 77.5” Bearing Span 44” Springs Axle Brakes Wheels Figure #2: The Axle Component Figure #3: Axle Failure Event Tree

7. Figure #4: General View of Test Rig

8. Figure #5: Details of Test Set-up

9. Figure #6a: Sample 3 (LHS) Crack Initiation

10. Figure #6b: Sample 3 (LHS) Failure

11. Separate(R1=R2): Shape: 6.89321 Scale: 233,763 Rss=R1*R2 MTTFss=197,593 cycles Merged: Shape: 6.83966 Scale: 212,004 MTTFsm=198,076 cycles Figure #7: Comparison of “Merged” vs “Separate” Probability Density Distributions

12. Figure 8: Probability Plots of Failure Data (Separate Modes) Figure 9: Weibull Plots of Failure Data (Separate Modes)

13. Figure 10: Probability Plots of Failure Data (Merged Modes) Figure 11: Weibull Plots of Failure Data (Separate Modes)

14. Figure 12: Normal Plots of Failure Data (Separate Modes)

15. Probability Density Distribution around S-N curve (derived from test data) Log (S;F) 3sigma lines Su; Fu S-N Mean Curve: N=(F/bN)^1/mN bN=153008 mN=-0.10034 St; Ft Se; Fe Log N Nu=10^3 N t = MTTFsm =198,076 cycles Ne=10^6 Se = Endurance Limit of Material Su = Ultimate Tensile Strength of the Material St = Peak tensile stress (somewhere on the axle) during testing Fe = Load applied to the axle when the peak stress is Se (somewhere on the axle) Fu = Load applied to the axle when the peak stress is Su (somewhere on the axle) Ft = Load applied to the axle when the peak stress is St (somewhere on the axle) Calculation of MTTF of Log-Log Line for S-N Diagram Figure 13: Calculation of axle S-N Characteristic

16. Figure #14: Weibull Probability Plots of Monte Carlo Analysis to determine bN distribution to match Test Data

17. Truck/TrailerSystem Truck Trailer Frame Running Gear Storage Container Bearings Brakes Wheels Support Structure axles Turning System Structure Function Figure #15: System Diagram

18. axle Structural Evaluation Mission Specification Static Loading Material Selection and Fabrication Process Dynamic Loading and Structural Analysis of attachments (Brakes, bearings, cams…etc) Figure #16: Structural Requirements of axle

19. Field Data Nominal Mission Definition • Variation in Cargo Load • Variation in Road Surface • Variation in vehicle speed • Driving habits Data Reduction and Analysis Road Test Results Mission Inputs: Axle Load (or stress) frequency distribution Rig Data Axle Strength Characteristics: Axle F/N Diagrams Monte Carlo Axle Reliability Calculation Axle Fatigue Performance Characteristics Output: Axle Reliability Figure #17: Reliability Analysis

20. Mission Definition: Test Results Frequency Speed 2 Dynamic Load (Variable Stress) Speed 1 Cargo Load (Mean Stress) Figure #18: Mission Data Other Variables: • Road: 1) Rural Road; 2) Secondary; Road 3) Highway

21. Log F Se = endurance limit; Su=ultimate tensile strength Fu, Su Failure Limit (N) “n” Mission Inputs (n) Fe, Se nR=n/N=damage done per hour of use Log N Miner’s Rule: If n1/N1+n2/N2+…+nr/Nr<1 then a failure will not occur. “n” and “N” are each stochastic in nature. Representing n/N approximately as a continuous function, the above formula can be generalized to: • The integral of “n/N” over time gives an accumulated axle damage (D). Figure #19: Linking Mission data to Axle Characteristics

22. Sample Solution: By assuming that n can be represented by a formula of the form: And: The ratio “n/N” can be written: A plot of the “N” and the “n” curve according with the above assumptions is plot on a Log-Log chart in Figure #19: Figure #20: Reliability Plot for Axle

23. Results of MC Analysis Figure #21: Fitted Plot of Reliability Results

24. MTTF=99064 Figure 22: Plots of Axle Reliability Functions Generated by Maple Probability Density Function Hazard Function

25. List of References-Textbooks: Faires, V.M., Design of Machine Elements (4th Ed), the MacMillan Company, 1965. Shigley, J.E., Mechanical Engineering Design, McGraw-Hill, 1977. Rausand, M and Hoyland, A., System Reliability Theory (2nd Ed), John Wiley and Sons, 2004. Verzani, John, Using R for Introductory Statistics, Chapman and Hall/CRC, 2005 Abernathy, R.E.; Breneman, J.E.; Medlin, CH; Reinman, GL; Weibull Analysis Handbook; November 1983.