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

2 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 Reliability Evaluation of Trailer Axles

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

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

7 Figure #4: General View of Test Rig

8 Figure #5: Details of Test Set-up Table #1: Table of Test Results Sample NoHours testedLHS failedRHS failed 1200,000NN 2153,348YN 3192,595YN 4218,787NY 5179,968YN 6226,100NY

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

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

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

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 Se; Fe Su; Fu 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) Log (S;F) Log N Ne=10^6Nu=10^3N t = MTTFsm =198,076 cycles St; Ft Probability Density Distribution around S-N curve (derived from test data) 3sigma lines Calculation of MTTF of Log-Log Line for S-N Diagram S-N Mean Curve: N=(F/bN)^1/mN bN= mN= 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/Trailer System Truck Storage ContainerFrame BearingsBrakesWheelsTurning System Support Structure Trailer Running Gear axles FunctionStructure Figure #15: System Diagram

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

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

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

21 “n” Failure Limit (N) Log F Log N Fe, Se Fu, Su The integral of “n/N” over time gives an accumulated axle damage (D). nR=n/N=damage done per hour of use Mission Inputs (n) Se = endurance limit; Su=ultimate tensile strength Figure #19: Linking Mission data to Axle Characteristics 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:

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

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

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

25 List of References-Textbooks: Faires, V.M., Design of Machine Elements (4 th Ed), the MacMillan Company, Shigley, J.E., Mechanical Engineering Design, McGraw-Hill, Rausand, M and Hoyland, A., System Reliability Theory (2 nd Ed), John Wiley and Sons, 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.

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