Hydraulic Integrated Interconnected Regenerative Suspension: Sensitivity Analysis and Parameter Optimization
Abstract
:1. Introduction
2. Modeling
2.1. Working Principle of the HIIRS
2.2. Modeling of the HIIRS System
2.3. The Half-Vehicle Models with Various Suspensions
2.3.1. The Half-Vehicle Model with the HIIRS
2.3.2. The Half-Vehicle Model with a Conventional Spring-Damper Suspension
2.3.3. The Half-Vehicle Model with an Anti-Roll Bar Suspension
3. Performance Indices
3.1. Random Road Excitation
3.2. Ride Comfort
3.3. Road Holding
3.4. Energy-Harvesting Power
4. Sensitivity Analysis
4.1. Morris Method
4.2. Sensitivity Analysis Result
5. Parameter Optimization
5.1. Single Objective Optimization
5.1.1. Optimization of Ride Comfort
5.1.2. Optimization of Road Holding
5.2. Multi-Objective Optimization
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Symbol | Description | Symbol | Description |
---|---|---|---|
HIIRS | Hydraulic integrated interconnected regenerative suspension | HIS | Hydraulic interconnected suspension |
Ts | Traditional suspension | ARB | Anti-roll bar |
Sprung mass | Pre-charge pressure of high-pressure accumulator | ||
Unsprung mass (j = l, r = left, right) | Pre-charge gas volume of high-pressure accumulator | ||
Sprung mass moment of inertia about the roll axis | Pre-charge pressure of low-pressure accumulator | ||
Distance from c.g. to suspension strut (j = l, r = left, right) | Pre-charge gas volume of low-pressure accumulator | ||
Mechanical suspension spring stiffness | Circuit external resistance | ||
Tire stiffness | Inner diameter of hydraulic cylinder | ||
Tire damping coefficient | Hydraulic motor displacement | ||
Traditional suspension damping coefficient | Inner diameter of hydraulic pipeline | ||
rms | Root-mean-square | Initial pressure of hydraulic system |
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Symbol | Value | Units | Description |
---|---|---|---|
1400 | kg | Sprung mass | |
105 | kg | Unsprung mass (j = l, r = left, right) | |
523 | Kgm2 | Sprung mass moment of inertia about the roll axis | |
0.825 | M | Distance from c.g. to suspension strut (j = l, r = left, right) | |
112 | kN/m | Mechanical suspension spring stiffness | |
1200 | kN/m | Tire stiffness | |
300 | Ns/m | Tire damping coefficient | |
3800 | Ns/m | Traditional suspension damping coefficient |
Impedance Matrix | Description | Elements |
---|---|---|
Impedance matrix of upper chamber of hydraulic cylinder | ||
Impedance matrix of hydraulic pipeline | ||
Impedance matrix of check valve | ||
Impedance matrix of high-pressure accumulator unit | , | |
Identity matrix | ||
Impedance matrix of energy harvesting unit | , | |
Identity matrix | ||
Impedance matrix of low-pressure accumulator unit | ||
Impedance matrix of check valve | ||
Impedance matrix of hydraulic pipeline | ||
Impedance matrix of upper chamber of hydraulic cylinder |
Symbol | Range | Units | Description |
---|---|---|---|
Pa | Pre-charge pressure of high-pressure accumulator | ||
m3 | Pre-charge gas volume of high-pressure accumulator | ||
Pa | Pre-charge pressure of low-pressure accumulator | ||
m3 | Pre-charge gas volume of low-pressure accumulator | ||
Circuit external resistance | |||
[10, 70] | mm | Inner diameter of hydraulic cylinder | |
[] | m3/rev | Hydraulic motor displacement | |
[10, 30] | mm | Inner diameter of hydraulic pipeline | |
Pa | Initial pressure of hydraulic system |
Parameter | |||||||||
---|---|---|---|---|---|---|---|---|---|
Sensitivity | 0.7907 | 0.0544 | 0.0444 | 0.0335 | 0.0124 | 0.0206 | 0.014 | 0.014 | 0.016 |
Sensitivity | 0.8462 | 0.0343 | 0.0293 | 0.0263 | 0.0124 | 0.0165 | 0.0107 | 0.0126 | 0.0115 |
Sensitivity | 0.1466 | 0.1405 | 0.6325 | 0.0054 | 0.0153 | 0.0146 | 0.0116 | 0.0179 | 0.0156 |
Parameters | Variation Range | Initial | Optimization Solution |
---|---|---|---|
Resistance | |||
Inner diameter of hydraulic cylinder | |||
Displacement of hydraulic motor | |||
Damping coefficient in TS | |||
Anti−roll bar stiffness in ARB | |||
Damping coefficient in ARB | 3800 | 2282.3 | |
Bounce acceleration RMS of HIIRS | 1.5155 | 0.7338 | |
Roll acceleration RMS of HIIRS | 0.5762 | 0.4807 | |
Total weighted acceleration RMS of HIIRS | 1.6628 | 0.7938 | |
Bounce acceleration RMS of TS | 1.6205 | 0.9567 | |
Roll acceleration RMS of TS | 0.5880 | 0.5855 | |
Total weighted acceleration RMS of TS | 1.6866 | 1.0254 | |
Bounce acceleration RMS of ARB | 1.6205 | 0.9541 | |
Roll acceleration RMS of ARB | 0.5060 | 0.3416 | |
Total weighted acceleration RMS of ARB | 1.6515 | 0.9781 |
Parameters | Variation Range | Initial | Optimization Solution |
---|---|---|---|
Resistance | 10 | 162 | |
Inner diameter of hydraulic cylinder | |||
Displacement of hydraulic motor | |||
Damping coefficient of Ts | 3800 | 8541 | |
Damping coefficient of ARB | 3800 | 9309.3 | |
Anti−roll bar stiffness | |||
Tire dynamic load RMS of HIIRS | 2369.1 | 2172.2 | |
Tire dynamic load RMS of TS | 3150.9 | 2696.9 | |
Tire dynamic load RMS of ARB | 3110.5 | 2646.1 |
Optimization Objectives | Ride Comfort | Road Holding |
---|---|---|
Resistance | 203 | 162 |
Inner diameter of hydraulic cylinder | ||
Displacement of hydraulic motor | ||
Ride comfort objective function | ||
Road holding objective function |
Parameter | |||
---|---|---|---|
Resistance R | 4.5208 | 3.86 | 5.1703 |
0.039 | 0.0412 | 0.0388 | |
Bounce acceleration RMS | 0.7757 | 0.9050 | 0.9050 |
0.4699 | 0.4769 | 0.4769 | |
Total acceleration RMS | 0.8294 | 0.95 | 0.9494 |
Tire dynamic load RMS | 2600 | 2353.7 | 2393.6 |
Energy-harvesting power | 83.73 | 175.8 | 255.1 |
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Guo, S.; Chen, L.; Pan, Y.; Wang, X.; Tan, G. Hydraulic Integrated Interconnected Regenerative Suspension: Sensitivity Analysis and Parameter Optimization. Electronics 2023, 12, 891. https://doi.org/10.3390/electronics12040891
Guo S, Chen L, Pan Y, Wang X, Tan G. Hydraulic Integrated Interconnected Regenerative Suspension: Sensitivity Analysis and Parameter Optimization. Electronics. 2023; 12(4):891. https://doi.org/10.3390/electronics12040891
Chicago/Turabian StyleGuo, Sijing, Liang Chen, Yu Pan, Xuxiang Wang, and Gangfeng Tan. 2023. "Hydraulic Integrated Interconnected Regenerative Suspension: Sensitivity Analysis and Parameter Optimization" Electronics 12, no. 4: 891. https://doi.org/10.3390/electronics12040891