1 Introduction
2 Process of Consistency Research
3 Interval Decomposition Theory of Objective Performance Tolerance
3.1 Interval Mathematics Theory—Numerical Differentiation Theory
3.2 Taylor Expansion for Asymmetric Structure
3.3 Algorithm for the Least-Squares Generalized Inverse Interval
3.3.1 Generalized Inverse Matrix
3.3.2 Generalized Inverse Matrix Theory Used to Solve Linear Equations
3.3.3 Solution of Compatible Equations
3.3.4 Solution of Incompatible Linear Equations
3.3.5 Algorithm for the Least-Squares Generalized Inverse Interval
3.4 Operation Steps for the Decomposition of the Performance Tolerance Interval
3.4.1 Coefficient Gained
3.4.2 Matrix Established
3.4.3 Matrix Solved
4 Validation of Analysis Method for Steering Characteristic Consistency
4.1 Establishment of the Vehicle Model
4.1.1 Steering System
4.1.2 Positioning Parameters of Left and Right Front Wheel Pins
4.1.3 Wheel Alignment
4.1.4 Tire Characteristics
4.1.5 Suspension System
4.2 Validation of the Vehicle Model
4.2.1 Verification of Steady-State Rotation Response
4.2.2 Verification of Transient Steering Response Performance
4.2.3 Verification of Steering Portability
4.2.4 Verification of Turn-Back Performance
4.3 Determination of Steering Target
Index | Initial value |
---|---|
Steering wheel torque | 4.5569 |
TB factor | 1.4196 |
4.4 Comprehensive Analysis of Parameter Sensitivity for Steering Performance According to the Target System
4.5 Optimization Design for Steer Target Performance
4.5.1 Optimization Objectives
Index | Target value |
---|---|
Steering wheel torque | 4.32 |
TB factor | 1.24 |
Parameter | Initial value | Optimize range |
---|---|---|
A_TOE_L | 0 | (−0.5 ,0.5) |
A_TOE_R | 0 | (−0.5, 0.5) |
CS_FY_COEFFICIENT_FL | −4.50 × 10−4 | (−4.95 × 10−4, −4.05 × 10−4) |
CS_FY_COEFFICIENT_FR | −4.50×10−4 | (−4.95×10−4, −4.05×10−4) |
CS_FY_COEFFICIENT_RL | −8.31 × 10−4 | (−9.14 × 10−5, −7.479 × 10−5) |
CS_FY_COEFFICIENT_RR | −8.31 × 10−4 | (−9.14 × 10−5, −7.479 × 10−5) |
FS_COMP_COEFFICIENT | 35 | (31.5 , 38.5) |
FY_k11 | 444.357 | (400 , 466.5) |
FY_k12 | 894.186 | (805 , 984) |
HYS_COL | 1.5 | (1.35 , 1.65) |
Mz_k12 | 17.9612 | (16 , 20) |
Mz_k13 | 38.2152 | (34 , 42) |
K102 | 40 | (32 , 48) |
K112 | 3.11 | (2.5 , 3.7) |
kToe2 | −0.501756 | (−0.55 , −0.45) |
kToe4 | 0.425353 | (0.38 , 0.47) |
4.5.2 Optimization Results
Parameter | Initial value | Optimize result |
---|---|---|
A_TOE_L | 0 | 0.0396 |
A_TOE_R | 0 | −0.2071 |
CS_FY_COEFFICIENT_FL | −4.50 × 10−4 | −4.77 × 10−4 |
CS_FY_COEFFICIENT_FR | −4.50 × 10−4 | −4.50×10−4 |
CS_FY_COEFFICIENT_RL | −8.31 × 10−5 | −8.55 × 10−5 |
CS_FY_COEFFICIENT_RR | −8.31 × 10−5 | −8.25 × 10−5 |
FS_COMP_COEFFICIENT | 35 | 32.6579 |
FY_k11 | 444.357 | 482.1273 |
FY_k12 | 894.186 | 855.736 |
HYS_COL | 1.5 | 1.5797 |
Mz_k12 | 17.9612 | 16.5643 |
Mz_k13 | 38.2152 | 41.196 |
K102 | 40 | 44.528 |
K112 | 3.11 | 3.0892 |
kToe2 | −0.501756 | −0.4831 |
kToe4 | 0.425353 | 0.3957 |
4.6 Decomposition of the Performance Tolerance Interval
4.7 Consistency
Index | Optimize result |
---|---|
Steering wheel torque | (4.32 , 4.5569) |
TB factor | (1.24 , 1.4196) |
Parameter | Optimize result |
---|---|
A_TOE_L | (0.0437, 0.0607) |
A_TOE_R | (−0.2830, −0.2090) |
CS_FY_COEFFICIENT_FL | (−5.7338 × 10−4, −4.8273 × 10−4) |
CS_FY_COEFFICIENT_FR | (−5.1340 × 10−4, −4.5370 × 10−4) |
CS_FY_COEFFICIENT_RL | (−8.6774 × 10−5, −8.6209 × 10−5) |
CS_FY_COEFFICIENT_RR | (−8.3140 × 10−5, −8.2752 × 10−5) |
FS_COMP_COEFFICIENT | (33.2196, 55.4817) |
FY_k11 | (371.7201, 535.547) |
FY_k12 | (877.1294, 922.1411) |
HYS_COL | (1.628, 1.6582) |
Mz_k12 | (16.561, 16.5643) |
Mz_k13 | (40.8417, 41.1878) |
K102 | (45.1559, 45.7792) |
K112 | (3.1133, 3.1661) |
kToe2 | (−0.5503, −0.4845) |
kToe4 | (0.3657, 0.5256) |