Tuesday 7 th June

1. THE DEVELOPMENT OF A COMPUTATIONAL METHOD FOR OBTAINING THE SPECIFICATION OF A RACE CAR DAMPER UNIT Tom Brimble – A042077 MEng Automotive Engineering 7th June 2005 THE DEVELOPMENT OF A COMPUTATIONAL METHOD FOR OBTAINING THE SPECIFICATION OF A RACE CAR DAMPER UNIT Tom Brimble – MEng Automotive Eng. Tuesday 7th June

2. CONTENTS • Introduction • Brief • Damper Theory • Dynamometer Testing • Shim Stack F.E.A • Damper Simulation • Simulation Validation • Conclusions • Summary • Questions & Answers Reiger Damper Piston

3. INTRODUCTION Principle of Damper Operation • Control transmission of wheel forces to the body • Control vertical wheel motion over terrain Motorsport Application • Different requirements for different conditions • Desired performance is known • Obtaining desired performance is a black art • Usually many iterations with considerable time in between re-assembling dampers • In commercial racing environment time “off-road” is expensive in cost and potential performance gain Dampers have optimal settings for different conditions. Seen particularly with rallying Introduction

4. BRIEF & OBJECTIVES Brief • Need to reduce time taken in build process through the use of a computational model • Need to create a physically realistic model such that parameters may be used directly Literature Review • Research found two physically based damper models with good test data correlation • No models used physical representation of shim stack behaviour • Complex shim stack behaviour • Decision to modify simulation to suit damper and investigate FEA for shim stack Piston assembly on Reiger damper Shim stack assembly onto piston Brief

5. DAMPER THEORY Valve Theory • Several valve types in the damper • Model flow using orifice flow equation, derived from Bernoulli’s equation • Area vs. pressure characteristics different for each valve type Orifice Mass Flow Equation Orifice Flow Relationship Pressure Release or “Blow-Off” Valve Shim Stack Valve Orifice Flow Characteristics Blow-Off Valve Characteristics Shim Stack Valve Characteristics Effective Bulk Modulus • Represents the compressibility within the damper • Accounts for cylinder wall, damper fluid and trapped gas in system Effective Bulk Modulus Equation Damper Theory

6. DYNO TESTING Test Setup • 2 different stacks tested for bump and rebound in 3 different builds • Test used damper dynamometer and modified damper • Datalogger used to record at 1000Hz pressures and displacement Damper in operation on dynamometer Damper test schematic layout Modified damper casing Dyno Testing

7. DYNO TESTING Test Results • Datalogged data very clean with no perceivable noise • Pressures traces as expected with high peaks in rebound chamber • Consistent damper behaviour with different frequencies Comparison of different builds and freqencies Logged pressures at 1000Hz Dyno Testing

8. SHIM STACK F.E.A FEA Modelling • FEA using Scenario for Structures within Unigraphics • Problems achieving consistent and feasible results • Different load application techniques tried Displaced shim stack with pressure applied at four locations Model Limitations • Linear solver • More than 4 moving shims caused displacement “spikes” • Error factor of 10000 in results: source not identified Example failed simulation runs with odd displacements Shim Stack F.E.A

9. SHIM STACK F.E.A FEA Post-Processing • FEA results extracted via MS Excel (lower surface of lowest shim) into Matlab • Randomly located nodes translated into regular Cartesian array • Matlab routines generated to calculate orifice area Flow Area Calculation • Two methods used: • Trapezoidal area calculation using individual coordinates • Spot centre height multiplied by circumference • Method 2 proved to be an insufficiently accurate approximation Randomly located nodes Method 1 Calculation Method 2 Calculation Circle generated in Cartesian coordinates Deflected nodes around orifice perimeter Shim Stack F.E.A

10. DAMPER SIMULATION Simulation Fundamentals • Matlab initialisation file • Mass flow between chambers • Effective gas piston representing Nitrogen bladder Differential mass flow equations Damper Force Calculation Schematic damper layout Damper Simulation

11. DAMPER SIMULATION SIMULINK Model Damper Simulation

12. Cost Parameter Estimated value Cost Simulation output vs. test data SIMULATION VALIDATION Cost Function • Attempt to match test data using fminsearch • Input variable parameters • Define cost of parameter values • Define cost of simulation vs. test data • 500 Iterations with cost vs. 3 test data sets Parameter Optimisation routine Simulation Validation

13. SIMULATION VALIDATION Cost Function Results • Results show simulation attempted to soften damper performance • FEA insufficiently accurate to allow complete matching of parameters Before cost function Dynamometer output After cost function Peak Rebound Force 6000N Peak Rebound Force 4915N Peak Rebound Force 5650N • Increased hysteresis in model • All parameters moved to the limit values set by user Simulation Validation

14. SIMULATION VALIDATION Validation without FE results • Optimisation using engineering principles • Changed mass flow coefficients for • shim stack valves • Results show simulation is a good • representation of damper behaviour Simulation Validation

15. CONCLUSIONS Conclusions • The finite element analysis process used was insufficiently accurate • The complete SIMULINK model could be tuned to match test data accurately • Created complete analysis process for finite element data • Recorded several sets of data for future usage in simulation matching Recommendations • Further finite element analysis carried out using a non-linear solver • Investigate use of a purely analytical method for determining the stiffness of the shim stack Conclusions

16. CONCLUSIONS Final Computational Process Conclusions

17. SUMMARY Summary • Explained Damper Theory • Given Detailed Overview of Damper Dynamometer Testing • Explained the Finite Element Analysis Procedure used • Explained the Damper Simulation • Explained the methods used to validate the simulation • Given the conclusions of the work Summary

18. QUESTIONS QUESTIONS Q&A