Systematic Derivation of Objective Requirements on Vehicle Steering System

Produktbeschreibung

This thesis answers the question how to derive subsystem requirements with respect to given targets at vehicle level and how to evaluate the performance of subsystems and modules at early stages of design and prototyping. It is shown that based on identified subsystem properties the expectable performance of the vehicle is predictable much earlier than vehicle prototypes are available for test drives.

Contents
Nomenclature IX
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII
Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIV
1 Introduction 1
1.1 Target-Driven Process of Basic Vehicle Design . . . . . . . . . . . . . . . . . . 2
1.1.1 Virtual Development Methods . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Target Cascading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Vehicle Steering Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Desired Steering Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Undesired Steering Feedback . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Opportunities for Substructuring Methods . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Top-down (Decoupling) . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Bottom-up (Coupling) . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Substructuring the Vehicle Steering 13
2.1 Vehicle System and Subsystem Subdivision . . . . . . . . . . . . . . . . . . . 13
2.2 Basic Theory of Substructuring . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Subsystem Characterization with Frequency Response Functions . . . 16
2.2.2 Classification of Substructuring Methods . . . . . . . . . . . . . . . . . 17
2.3 Frequency Based Substructuring Method . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 General Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Subsystem Coupling based on Impedance (Primal Formulation) . . . . 20
2.3.3 Subsystem Coupling based on Admittance (Dual Formulation) . . . . 21
2.3.4 Subsystem Decoupling (Dual Approach) . . . . . . . . . . . . . . . . . 24
2.4 Mechanical Four-Pole Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 General Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.2 Subsystem Coupling with Mechanical Four-Poles . . . . . . . . . . . . 30
2.4.3 Subsystem Decoupling with Mechanical Four-Poles . . . . . . . . . . . 32
3 Deriving Requirements on Subsystem Level 35
3.1 Defining Vehicle Targets Regarding Steering Vibration . . . . . . . . . . . . . 35
3.1.1 Steering Vibration Limit for Steady-State Driving . . . . . . . . . . . 36
3.1.2 Steering Vibration Limit under Braking . . . . . . . . . . . . . . . . . 38
3.2 Substructuring Methods Applied to Steering Vibration . . . . . . . . . . . . 40
3.2.1 Coupling / Decoupling Front Axle and Steering with LM-FBS Method 40
3.2.2 Coupling / Decoupling Front Axle and Steering with Four-Pole Method 48
3.2.3 Capabilities and Limits of the Methods in Comparison . . . . . . . . . 51
3.3 Setting Subsystem Requirements derived from Vehicle Targets . . . . . . . . . 55
3.3.1 Expressing Vehicle Targets by Mechanical Four-Pole Coefficients . . . 5
3.3.2 Derivation of Necessary and Sufficient Limits to Subsystem Dynamics 58
3.3.3 Derivation of Exact Limits to Subsystem Dynamics . . . . . . . . . . . 59
3.3.4 Mutual Dependencies of the Four-Pole Coefficients . . . . . . . . . . . 60
4 Subsystem Analysis of the Steering 63
4.1 Simplified Steering Model based on Lumped Masses . . . . . . . . . . . . . . 64
4.1.1 Case A: Passive Behavior of the Force-less Electric Motor . . . . . . . 67
4.1.2 Case B: Passive Behavior of the Motion-less Electric Motor . . . . . . 68
4.1.3 Case C: Active Behavior of the Steering-Torque Controlled Electric Motor 68
4.1.4 Case D: Active Behavior of the Rack-Force Controlled Electric Motor 69
4.1.5 Interactions of the Four-Pole Coefficients of the Steering . . . . . . . . 70
4.1.6 Eigenmodes of the Simplified Steering Model . . . . . . . . . . . . . . 71
4.1.7 Exemplary Results of the Simplified Steering Model . . . . . . . . . . 74
4.2 Virtual Subsystem Analysis of the Steering with a Detailed Physical Model . 76
4.2.1 Basic Principle of Electric Power Steering . . . . . . . . . . . . . . . . 76
4.2.2 Detailed Physical Model of Electric Power Steering . . . . . . . . . . . 77
4.2.3 Results of Virtual Steering Subsystem Analysis . . . . . . . . . . . . . 83
4.3 Experimental Subsystem Analysis of the Steering . . . . . . . . . . . . . . . . 84
4.3.1 Experimental Testing of the Complete Steering Assembly . . . . . . . 84
4.3.2 Corrective Measures at Experimental Steering Testing . . . . . . . . . 85
4.3.3 Experimental Testing of the Steering Gear Subassembly . . . . . . . . 87
4.3.4 Experimental Testing of the Upper Steering Column Subassembly . . 88
4.3.5 Integrating Measured Dynamics of Subassemblies . . . . . . . . . . . . 89
4.3.6 Results of Experimental Steering Subsystem Analysis . . . . . . . . . 91
5 Subsystem Analysis of the Front Axle 93
5.1 Simplified Front-Axle Model based on Lumped Masses . . . . . . . . . . . . . 94
5.2 Simplified Front-Axle Model including Tire Dynamics . . . . . . . . . . . . . 102
5.3 Detailed MBS Model of the Front Axle . . . . . . . . . . . . . . . . . . . . . . 106
5.4 Roller Test-Rig for Virtual Analysis of the Front Axle . . . . . . . . . . . . . 108
5.4.1 Application-Specific Requirements on the Roller Test-Rig . . . . . . . 108
5.4.2 Generic Requirements on the Roller Test-Rig . . . . . . . . . . . . . . 109
5.4.3 Realization of the Roller Test-Rig . . . . . . . . . . . . . . . . . . . . . 110
5.5 Virtual Subsystem Analysis of the Front Axle . . . . . . . . . . . . . . . . . . 112
5.5.1 Eigenmodes of the Front-Axle Subsystem . . . . . . . . . . . . . . . . 113
5.5.2 Four-Pole Coefficients of the Front-Axle Subsystem . . . . . . . . . . . 115
5.5.3 Corrective Measures at Virtual Front-Axle Testing . . . . . . . . . . . 117
5.5.4 Results of Virtual Front-Axle Subsystem Analysis . . . . . . . . . . . 118
6 Resulting Subsystem Requirements 123
6.1 Linear Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.1.1 Predicting Vehicle Performance with Directly Assembled Subsystems . 124
6.1.2 Deriving Limits to Steering Dynamics . . . . . . . . . . . . . . . . . . 127
6.1.3 Deriving Limits to Front-Axle Dynamics . . . . . . . . . . . . . . . . . 130
6.2 Nonlinear Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2.2 Subsystem Nonlinearities Experienced in Practice . . . . . . . . . . . . 132
6.2.3 Predicting Vehicle Performance with Iteratively Assembled Subsystems 134
6.2.4 Deriving Amplitude-Dependent Limits to Steering Dynamics . . . . . 138
6.2.5 Deriving Amplitude-Dependent Limits to Front-Axle Dynamics . . . . 145
6.2.6 Comparing Linear versus Nonlinear Requirement Derivation . . . . . . 150Contents VII
7 Requirement-Based Module Design Using Solution Spaces 153
7.1 Robust Design with Solution Spaces . . . . . . . . . . . . . . . . . . . . . . . 154
7.1.1 The Basic Idea of Solution Spaces . . . . . . . . . . . . . . . . . . . . 154
7.1.2 Procedural Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.2 Robust Steering-Module Design . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.2.1 Procedural Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2.2 Design-of-Experiment Study on Steering Modules . . . . . . . . . . . . 160
7.2.3 Solution Spaces for Design Parameters of the Steering . . . . . . . . . 164
7.3 Robust Front-Axle Module Design . . . . . . . . . . . . . . . . . . . . . . . . 168
7.3.1 Procedural Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.3.2 Design-of-Experiment Study on Front-Axle Modules . . . . . . . . . . 170
7.3.3 Analysis of Correlation and Sensitivity . . . . . . . . . . . . . . . . . . 176
7.3.4 Solution Spaces for Design Parameters of the Front Axle . . . . . . . . 180
7.3.5 Solution Spaces for Bushing Dynamics . . . . . . . . . . . . . . . . . . 183
8 Conclusion 189
8.1 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.1.1 Substructuring the Vehicle Steering . . . . . . . . . . . . . . . . . . . 189
8.1.2 Deriving Requirements on Subsystem Level . . . . . . . . . . . . . . . 190
8.1.3 Subsystem Analysis of Steering and Front Axle . . . . . . . . . . . . . 190
8.1.4 Resulting Subsystem Requirements . . . . . . . . . . . . . . . . . . . . 191
8.1.5 Requirement-Based Module Design . . . . . . . . . . . . . . . . . . . 192
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Bibliography 195
A Appendix 1 205
A.1 Basic Transfer Function Representations . . . . . . . . . . . . . . . . . . . . . 205
A.2 Transfer Matrices Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 206
A.3 Parameter Sets for Simplified Models . . . . . . . . . . . . . . . . . . . . . . . 208
A.4 Exemplary Results of Simplified Models . . . . . . . . . . . . . . . . . . . . . 209
A.5 User Interface to Operate the Virtual Roller Test-Rig . . . . . . . . . . . . . . 209
A.6 Graphical Interpretation of Limiting Curves . . . . . . . . . . . . . . . . . . . 217
A.7 DoE Input Table for the Steering Design-Study . . . . . . . . . . . . . . . . . 219
A.8 DoE Input Table for the Front-Axle Design-Study . . . . . . . . . . . . . . . 220

Keywords: Substrukturierung, Anforderungsableitung, Fahrzeuglenkung, Fahrzeugauslegung, Lenkungsauslegung, Vorderachse, BMW AG, Lenkungsvibration, Robustes Design, Lösungsräume, Unsicherheiten, Substructuring, Requirement Derivation, Vehicle Steering, Vehicle Design, Steering Design, Front Axle, BMW AG, Steering Vibration, Robust Design, Solution Spaces, Uncertainties