**Figure 1.**
Research framework.

**Figure 1.**
Research framework.

**Figure 2.**
Hardpoint positions in the front and rear suspension systems. (**a**) Hardpoint positions in the SLA strut suspension; (**b**) hardpoint positions in the multi-link suspension.

**Figure 2.**
Hardpoint positions in the front and rear suspension systems. (**a**) Hardpoint positions in the SLA strut suspension; (**b**) hardpoint positions in the multi-link suspension.

**Figure 3.**
Body-centered axis model.

**Figure 3.**
Body-centered axis model.

**Figure 4.**
Experimental platform for full vehicle dynamics.

**Figure 4.**
Experimental platform for full vehicle dynamics.

**Figure 5.**
Schematic illustration of impulse steering test.

**Figure 5.**
Schematic illustration of impulse steering test.

**Figure 6.**
Impulse steering test measurement and analysis process. (FFT: Fast Fourier Transform).

**Figure 6.**
Impulse steering test measurement and analysis process. (FFT: Fast Fourier Transform).

**Figure 7.**
Relationship between yaw rate gain and cornering speed for target vehicle.

**Figure 7.**
Relationship between yaw rate gain and cornering speed for target vehicle.

**Figure 8.**
Experimental and simulated four-parameter radar charts for the impulse steering tests.

**Figure 8.**
Experimental and simulated four-parameter radar charts for the impulse steering tests.

**Figure 9.**
Simulated four-parameter radar charts for impulse steering tests performed at different speeds.

**Figure 9.**
Simulated four-parameter radar charts for impulse steering tests performed at different speeds.

**Figure 10.**
Variation of lateral force with tire slip angle for three different cornering stiffness values.

**Figure 10.**
Variation of lateral force with tire slip angle for three different cornering stiffness values.

**Figure 11.**
Variation of understeer coefficient with vehicle speed for three different cornering stiffness values.

**Figure 11.**
Variation of understeer coefficient with vehicle speed for three different cornering stiffness values.

**Figure 12.**
Variation of yaw rate gain with vehicle speed for three different cornering stiffness values.

**Figure 12.**
Variation of yaw rate gain with vehicle speed for three different cornering stiffness values.

**Figure 13.**
Simulated four-parameter radar charts for impulse steering tests performed using different cornering stiffness values.

**Figure 13.**
Simulated four-parameter radar charts for impulse steering tests performed using different cornering stiffness values.

**Figure 14.**
Variation of yaw rate gain with vehicle speed for different initial toe-in angles.

**Figure 14.**
Variation of yaw rate gain with vehicle speed for different initial toe-in angles.

**Figure 15.**
Schematic illustration showing the relationship between toe-in angle and lateral force.

**Figure 15.**
Schematic illustration showing the relationship between toe-in angle and lateral force.

**Figure 16.**
Simulated four-parameter radar charts for impulse steering tests performed using different toe-in angle values.

**Figure 16.**
Simulated four-parameter radar charts for impulse steering tests performed using different toe-in angle values.

**Figure 17.**
Variation of yaw rate gain with vehicle speed for different initial camber angles.

**Figure 17.**
Variation of yaw rate gain with vehicle speed for different initial camber angles.

**Figure 18.**
Simulated four-parameter radar charts for impulse steering tests performed using different camber angles.

**Figure 18.**
Simulated four-parameter radar charts for impulse steering tests performed using different camber angles.

**Table 1.**
Experimental and simulation results for K_{us} in constant radius cornering tests.

**Table 1.**
Experimental and simulation results for K_{us} in constant radius cornering tests.

**Experimental Data** |

Speed (km/h) | Tire steering angle (degree) | Lateral acceleration (G) | K_{us} (rad/g) |

10 | 12.9 | 0.048 | 4.68 |

**CAE model Data** |

Speed (km/h) | Tire steering angle (degree) | Lateral acceleration (G) | K_{us} (rad/g) |

10 | 9.47 | 0.032 | 5.15 |

**Table 2.**
Simulation results for roll gradient at different speeds.

**Table 2.**
Simulation results for roll gradient at different speeds.

Velocity (km/h) | Lateral Acceleration (G) | Roll Angle (°) | Roll Gradient (°/g) |
---|

10 | 0.018 | 0.046 | 2.56 |

20 | 0.064 | 0.17 | 2.65 |

30 | 0.165 | 0.45 | 2.72 |

40 | 0.252 | 0.7 | 2.78 |

50 | 0.393 | 1.13 | 2.87 |

**Table 3.**
Full-vehicle parameters.

**Table 3.**
Full-vehicle parameters.

Designation | Symbol | Unit | Value |
---|

Front axle weight | W_{f} | N | 8829 |

Rear axle weight | W_{r} | N | 5886 |

Front wheel cornering stiffness | C_{αf} | N/rad | 78,855.7 |

Rear wheel cornering stiffness | C_{αr} | N/rad | 71,687 |

Pneumatic trail | P | m | 0.018754 |

Wheelbase | L | m | 2.8 |

Steering angle per unit lateral force | q | °/N | 1.194 × 10^{−4}(f)/1.0498 × 10^{−4}(r) |

Roll steer coefficient | ε | °/° | −0.117213(f)/0.02272(r) |

Roll angle | ∅ | ° | 0.7047 |

Lateral acceleration | A_{y} | G | 0.2521 |

Camber stiffness | C_{γ} | N/rad | 7885.57(f)/7168.7(r) |

**Table 4.**
Experimental and simulation results for the impulse steering tests.

**Table 4.**
Experimental and simulation results for the impulse steering tests.

**Experimental Data** |

Speed (km/h) | Phase lag (ϕ) (deg) | Natural frequency (fn) (Hz) | Yaw rate gain (a1) (1/s) | Damping ratio (ζ) |

70 | −36.81 | 1.9567 | 0.24618 | 0.5581 |

**CAE model Data** |

Speed (km/h) | Phase lag (ϕ) (deg) | Natural frequency (fn) (Hz) | Yaw rate gain (a1) (1/s) | Damping ratio (ζ) |

70 | −26 | 1.8825 | 0.18099 | 0.94961 |

**Table 5.**
Simulation results for impulse steering tests performed at different speeds.

**Table 5.**
Simulation results for impulse steering tests performed at different speeds.

Speed (km/h) | Phase Lag (ϕ) (deg) | Natural Frequency (fn) (Hz) | Yaw Rate Gain (a1) (1/s) | Damping Ratio (ζ) |
---|

40 | −1.849 | 2.3739 | 0.134 | 1.62 |

70 | −26 | 1.8825 | 0.18099 | 0.94961 |

80 | −26.9 | 1.8624 | 0.18402 | 0.91857 |

90 | −29.49 | 1.8544 | 0.18454 | 0.84993 |

100 | −31.98 | 1.7871 | 0.1854 | 0.7842 |

120 | −34.96 | 1.6747 | 0.18278 | 0.69063 |

**Table 6.**
Cornering stiffness values.

**Table 6.**
Cornering stiffness values.

Item | Cornering Stiffness (N/rad) |
---|

Type 1 (original) | 71,687 |

Type 2 (increased by 30%) | 93,193.1 |

Type 3 (decreased by 30%) | 50,180.9 |

**Table 7.**
Understeer coefficients computed at different vehicle speeds using different cornering stiffness values.

**Table 7.**
Understeer coefficients computed at different vehicle speeds using different cornering stiffness values.

Velocity (km/h) | K_{us} (Type 1) (rad/g) | K_{us} (Type 2) (rad/g) | K_{us} (Type 3) (rad/g) |
---|

20 | 1.560 | 1.534 | 1.598 |

30 | 0.734 | 0.705 | 0.776 |

40 | 0.443 | 0.414 | 0.486 |

50 | 0.306 | 0.275 | 0.348 |

60 | 0.232 | 0.201 | 0.272 |

70 | 0.190 | 0.158 | 0.230 |

77 | 0.194 | 0.151 | 0.235 |

80 | 0.204 | 0.168 | 0.255 |

**Table 8.**
Yaw rate gain computed at different vehicle speeds using three different cornering stiffness values.

**Table 8.**
Yaw rate gain computed at different vehicle speeds using three different cornering stiffness values.

Velocity (km/h) | Yaw Rate Gain (Type 1) (1/s) | Yaw Rate Gain (Type 2) (1/s) | Yaw Rate Gain (Type 3) (1/s) |
---|

10 | 0.57 | 0.57 | 0.57 |

20 | 1.11 | 1.13 | 1.08 |

30 | 1.57 | 1.65 | 1.50 |

40 | 1.99 | 2.14 | 1.82 |

50 | 2.32 | 2.57 | 2.04 |

60 | 2.55 | 2.93 | 2.17 |

70 | 2.68 | 3.22 | 2.21 |

77 | 2.43 | 3.12 | 2.00 |

80 | 2.23 | 2.69 | 1.78 |

**Table 9.**
Simulation results for impulse steering tests performed using different cornering stiffness values.

**Table 9.**
Simulation results for impulse steering tests performed using different cornering stiffness values.

Item | Phase Lag (ϕ) (deg) | Natural Frequency (fn) (Hz) | Yaw Rate Gain (a1) (1/s) | Damping Ratio (ζ) |
---|

Type 1 | −26 | 1.8825 | 0.18099 | 0.94961 |

Type 2 | −27.1621 | 0.89756 | 0.19171 | 1.7917 |

Type 3 | −23.08 | 2.0994 | 0.14356 | 0.86539 |

**Table 10.**
Toe-in angle design variables.

**Table 10.**
Toe-in angle design variables.

Item | Type 4 | Type 5 | Type 6 |
---|

Toe angle (°) | −1 | 0 | 1 |

**Table 11.**
Yaw rate gain computed at various vehicle speeds using three different toe-in angles.

**Table 11.**
Yaw rate gain computed at various vehicle speeds using three different toe-in angles.

Velocity (km/h) | Yaw Rate Gain (Type 4) (1/s) | Yaw Rate Gain (Type 5) (1/s) | Yaw Rate Gain (Type 6) (1/s) |
---|

30 | 1.43 | 1.57 | 1.67 |

40 | 1.73 | 1.99 | 2.18 |

50 | 1.98 | 2.32 | 2.6 |

60 | 2.19 | 2.55 | 2.94 |

70 | 2.35 | 2.68 | 3.07 |

77 | 2.18 | 2.43 | 2.67 |

80 | 2.04 | 2.23 | 2.40 |

**Table 12.**
Simulation results for impulse steering tests performed using different toe-in angles.

**Table 12.**
Simulation results for impulse steering tests performed using different toe-in angles.

Item | Phase Lag (ϕ) (°) | Natural Frequency (fn) (Hz) | Steady-State Gain (a1) (1/s) | Damping Ratio (ζ) |
---|

Type 4 | −24.88 | 1.9432 | 0.15898 | 0.9656 |

Type 5 | −26 | 1.8825 | 0.18099 | 0.94961 |

Type 6 | −25.5408 | 1.8106 | 0.1871 | 0.96911 |

**Table 13.**
Camber angle design variables.

**Table 13.**
Camber angle design variables.

Item | Type 7 | Type 8 | Type 9 |
---|

Camber angle (°) | −1 | 0 | 1 |

**Table 14.**
Simulation results for yaw rate gain given different vehicle speeds and camber angles.

**Table 14.**
Simulation results for yaw rate gain given different vehicle speeds and camber angles.

Velocity (km/h) | Yaw Rate Gain (Type 7) (1/s) | Yaw Rate Gain (Type 8) (1/s) | Yaw Rate Gain (Type 9) (1/s) |
---|

30 | 1.59 | 1.57 | 1.58 |

40 | 2.00 | 1.99 | 1.98 |

50 | 2.33 | 2.32 | 2.31 |

60 | 2.57 | 2.55 | 2.53 |

70 | 2.72 | 2.68 | 2.65 |

77 | 2.60 | 2.50 | 2.51 |

80 | 2.35 | 2.23 | 2.11 |

**Table 15.**
Simulation results for impulse steering tests performed using different camber angles.

**Table 15.**
Simulation results for impulse steering tests performed using different camber angles.

Item | Phase Lag (ϕ) (°) | Natural Frequency (fn) (Hz) | Steady-State Gain (a1) (1/s) | Damping Ratio (ζ) |
---|

Type 7 | −25.2334 | 1.686 | 0.18309 | 1.0531 |

Type 8 | −26 | 1.8825 | 0.18099 | 0.9496 |

Type 9 | −24.7735 | 1.9505 | 0.17871 | 1.0775 |

**Table 16.**
Effects of changes in steady-state design variables on vehicle handling performance.

**Table 16.**
Effects of changes in steady-state design variables on vehicle handling performance.

Item | Design Variable | Yaw Rate Gain (Steady State) | Percentage (Steady State) |
---|

Type 1 (original) | Cornering stiffness (original value) | 2.68 | 0% |

Type 2 | Cornering stiffness (increased by 30%) | 3.22 | 20% |

Type 3 | Cornering stiffness (decreased by 30%) | 2.21 | −17% |

Type 4 | Initial toe-in angle (−1°) | 2.35 | −12.3% |

Type 5 (original) | Initial toe-in angle (0°) | 2.68 | 0% |

Type 6 | Initial toe-in angle (1°) | 3.07 | 9.7% |

Type 7 | Initial camber angle (−1°) | 2.72 | 1.47% |

Type 8 (original) | Initial camber angle (0°) | 2.68 | 0% |

Type 9 | Initial camber angle (1°) | 2.65 | −1.11% |

**Table 17.**
Effects of changes in transient-state design variables on vehicle handling performance.

**Table 17.**
Effects of changes in transient-state design variables on vehicle handling performance.

Item | Design Variable | Yaw Rate Gain (Transient) | Percentage (Transient) |
---|

Type 1 (original) | Cornering stiffness (original value) | 0.18099 | 0% |

Type 2 | Cornering stiffness (increased by 30%) | 0.19171 | 5.92% |

Type 3 | Cornering stiffness (decreased by 30%) | 0.14356 | −20.7% |

Type 4 | Initial toe-in angle (−1°) | 0.15898 | −12.2% |

Type 5 (original) | Initial toe-in angle (0°) | 0.18099 | 0% |

Type 6 | Initial toe-in angle (1°) | 0.1871 | 3.38% |

Type 7 | Initial camber angle (−1°) | 0.18309 | 1.16% |

Type 8 (original) | Initial camber angle (0°) | 0.18099 | 0% |

Type 9 | Initial camber angle (1°) | 0.17871 | −1.26% |