A Steering Parameter Optimization Design Method Based on Non - dominated Sorting Genetic Algorithm

Abstract

The present invention discloses a method for optimizing the design of steering parameters based on the non-dominated sorting genetic algorithm, which is characterized by the following steps: conducting a theoretical analysis of the steering transmission fluctuation of the steering system; establishing a double cross-axis universal joint steering gear model and applying constraints; converting the parameters into hard point position coordinate parameters for optimization; and optimizing the hard point position coordinate parameters by using the NSGA-II algorithm. The present invention uses the non-dominated sorting genetic algorithm to optimize the intermediate shaft knuckle phase angle and key point coordinates of the steering shaft, and obtains the best steering shaft layout scheme. After optimization, the amplitude fluctuation of the steering transmission ratio is significantly reduced, the understeering characteristic is improved. At the same time, the phase fluctuation of the steering transmission ratio is eliminated, and the steering symmetry is improved. In addition, through simulation, it is verified that optimizing the steering shaft layout can improve the stability of the steering system, improve the anti-roll performance, and improve the steering response speed.

Description

Technical Field

[0001] The present invention belongs to the technical field of automotive steering systems, and particularly relates to an optimization design method for steering parameters based on non-dominated sorting genetic algorithm. Background Art

[0002] When studying the steering system, many researchers rarely consider the influence of the steering ratio fluctuation on the transient and steady-state steering performance of the vehicle, and the steering ratio fluctuation during the steering process cannot be ignored. Ideally, in the steering system, if the angular difference between the steering wheel and the steering gear of the rack and pinion steering gear is zero, the steering shaft part can achieve constant-speed transmission, and the entire steering system can achieve a non-fluctuating steering ratio. Under actual working conditions, due to the non-constant transmission characteristics of the double cross-axis universal joint, as well as the layout forms of the input shaft, intermediate shaft, and output shaft, the angular difference between the steering wheel and the steering gear is not zero, resulting in a fluctuation in the steering ratio.

[0003] In order to minimize the adverse effects of the steering ratio fluctuation of the steering system on the vehicle handling stability, it is necessary to reasonably arrange the drive shaft of the steering system. However, it is very difficult to complete the arrangement process based on experience because among the structural parameters of the steering system, the angles between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft, the angles between the two planes determined by the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft, the initial phase angle of the steering wheel, and the phase angle of the intermediate shaft yoke are difficult to measure. Therefore, a feasible solution for the steering shaft arrangement is given, that is, by conducting actual measurements on a real vehicle, importing the coordinates of each connection point of the steering shaft into ADAMS, establishing a steering gear model based on the actual data, then fixing the coordinates of the input point and the output point, and converting the difficult-to-measure steering shaft angle parameters into easily measurable coordinate parameters for optimization. This solution to achieve the optimal steering shaft arrangement by adjusting the coordinates is easier to implement. Based on this, the structural parameters of the steering system of a certain passenger vehicle were actually measured, a virtual prototype model of the steering system was established using ADAMS, and the non-dominated sorting genetic algorithm was used to optimize the intersection coordinates of the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft, the initial phase angle of the steering wheel, and the phase angle of the intermediate shaft yoke, and an optimized steering system layout scheme was obtained. Its feasibility can be verified by means of simulation and other methods in the later stage.

[0004] Therefore, in order to solve the above technical problems, the present invention provides an optimization design method for steering parameters based on non-dominated sorting genetic algorithm. Summary of the Invention

[0005] In order to solve the above technical problems, the object of the present invention is to provide an optimization design method for steering parameters based on non-dominated sorting genetic algorithm, which can be used to optimize the steering shaft arrangement and improve the steering system parameters.

[0006] To achieve the above technical effects, the present invention is realized through the following technical solutions: A method for optimizing the design of steering parameters based on the non-dominated sorting genetic algorithm, characterized by including the following steps:

[0007] S1. Conduct a theoretical analysis of the steering transmission fluctuation of the steering system;

[0008] S2. Establish a double universal joint steering gear model and apply constraints;

[0009] S3. Convert the included angle parameters between the input shaft and the intermediate shaft, the intermediate shaft and the output shaft, and the included angle between the two planes determined by the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft into hard point position coordinate parameters for optimization;

[0010] S4. Use the NSGA-II algorithm to optimize the hard point position coordinate parameters.

[0011] Furthermore, in S1, the theoretical analysis of the steering transmission fluctuation of the steering system is as follows: The transmission ratio i of the entire steering system is expressed as in Equation (1):

[0012]

[0013] i c i r i l are respectively the steering shaft transmission ratio, the rack and pinion steering gear transmission ratio, and the steering tie rod transmission ratio, dδ are respectively the steering wheel angle increment and the steering wheel angle increment. In the entire steering system, the rack and pinion steering gear transmission ratio and the steering tie rod transmission ratio are constant, and the transmission ratio fluctuation of the steering shaft causes the transmission ratio fluctuation of the entire steering system;

[0014] In the steering system, if friction losses are ignored, according to the law of conservation of energy, there is a relationship as shown in Equation (2) between the torque transmission ratio and the angular transmission ratio of the steering system:

[0015]

[0016] In Equation (2), i T is the torque transmission ratio of the steering system, T RT is the steering resistance torque overcome by the steering knuckle, T h is the torque on the steering wheel, η SG is the efficiency of the steering gear under the actual load, η SL is the efficiency of the steering transmission mechanism under the actual load;

[0017] From Equation (2), it can be obtained that:

[0018]

[0019] As can be seen from Equation (3), when η SG , η SL and T Rt are constant, T h is proportional to i. The greater the fluctuation of i, the greater the fluctuation of T h ; therefore, reducing the fluctuation of the transmission ratio of the steering system can improve the torque fluctuation of the steering wheel;

[0020] According to the above theoretical analysis, further exploration shows that the goal of steering system design is to achieve zero angular difference transmission for the space double universal joint with cross shafts in the middle of the input shaft and output shaft during the transmission process of the steering shaft; achieving zero angular difference transmission between the input shaft and the output shaft requires satisfying two conditions simultaneously: (1) the angles between the two planes where the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are located are equal to the phase angles of the driving and driven forks of the intermediate shaft; (2) the angles between the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are equal.

[0021] Furthermore, S2 includes the following steps:

[0022] S2.1. Establish a steering gear model with a double universal joint with cross shafts;

[0023] S2.2. Define the initial angular displacement of the steering wheel relative to the input shaft universal joint and the initial phase angle parameter of the intermediate shaft universal joint, and verify the influence on the steering transmission ratio;

[0024] S2.3. Apply simulation constraints to the double universal joint with cross shafts.

[0025] Furthermore, in S2.1, establishing the steering gear model with a double universal joint with cross shafts is based on the steering system of a certain vehicle model, and the coordinates of its four steering hard points A, B, C, and D are measured and quantified. Among them, point A is the center coordinate of the steering wheel, point B is the intersection coordinate of the input shaft and the intermediate shaft, point C is the intersection coordinate of the intermediate shaft and the output shaft, and point D is the intersection coordinate of the output shaft and the steering tie rod; in S2.2, the initial angle only changes the phase of the steering transmission ratio and has no influence on the amplitude. The phase angle of the joint fork affects not only the phase fluctuation of the steering transmission ratio but also the amplitude fluctuation; in S2.3, the simulation constraint of the universal joint with cross shafts is a rotational pair constraint.

[0026] Furthermore, S3 includes the following steps:

[0027] S3.1. Use the space vector method to convert the angles between the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft into hard point coordinate parameters for optimization;

[0028] S3.2. Use the space vector method to convert the angle between the two planes determined by the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft into hard point coordinate position parameters for optimization.

[0029] Further, optimize the hard point coordinate position parameters to the coordinates of hard points B and C; when points A and D are fixed, the magnitudes of φ, α1, and α2 can be adjusted by changing the coordinates of points B and C; where: α1 and α2 are the angles between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft in the double Cardan joint steering system, respectively, and φ is the angle between the two planes determined by adjacent shafts.

[0030] Further, S4 includes the following steps:

[0031] S4.1. Assemble the established steering gear model and the suspension system into a front suspension model in ADAMS and perform steering simulation;

[0032] S4.2. Import the simulation file (command file) in ADAMS into Isight, use MATLAB as the solver, and run ADAMS, Isight, and MATLAB jointly;

[0033] S4.3. Write an optimization target file using MATLAB;

[0034] S4.4. Set the optimization variable range, constraint conditions, and number of iterations, and run the optimization.

[0035] Further, in S4.3, an optimization target file is written using MATLAB as follows:

[0036]

[0037] where β is the angle between the planes where the driving and driven forks of the intermediate shaft are located;

[0038] Therefore, the optimization variables, optimization target, and constraint condition expressions are as shown in Equation (27):

[0039]

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] The present invention uses the non-dominated sorting genetic algorithm to optimize the phase angle of the intermediate shaft joint fork and the key point coordinates of the steering shaft, and obtains the best steering shaft layout scheme. After optimization, the amplitude fluctuation of the steering transmission ratio is significantly reduced, which increases the steering degree of the vehicle during steering and improves the understeering characteristics. At the same time, adjusting the initial phase angle of the steering wheel eliminates the phase fluctuation of the steering transmission ratio and improves the steering symmetry. In addition, a vehicle steady-state turning simulation with a fixed radius and a steering wheel sinusoidal input sweep simulation are carried out. Through the simulation, it is verified that optimizing the steering shaft layout can appropriately reduce the transient yaw rate gain, improve the stability; appropriately reduce the body roll angle gain, improve the anti-roll performance; appropriately reduce the lateral acceleration relative to the steering wheel angle lag time, and improve the steering response speed. Brief Description of the Drawings

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0043] Figure 1 Schematic diagram of the key structural parameters of the steering shaft;

[0044] Figure 2 Schematic diagram of the initial angle and the phase angle of the joint fork;

[0045] Figure 3 Constant velocity drive constant velocity cone;

[0046] Figure 4 Virtual prototype model of the steering system;

[0047] Figure 5 Effect on the fluctuation of the transmission ratio of the steering shaft;

[0048] Figure 6 Effect on the fluctuation of the transmission ratio of the steering system;

[0049] Figure 7 Effect on the fluctuation of the transmission ratio of the steering shaft;

[0050] Figure 8 Effect on the fluctuation of the transmission ratio of the steering system;

[0051] Figure 9 Hook joint constraint;

[0052] Figure 10 Constant velocity joint constraint;

[0053] Figure 11 Revolute joint constraint;

[0054] Figure 12 Effect of the constraint type on the fluctuation of the transmission ratio of the steering shaft;

[0055] Figure 13 Effect of the constraint type on the fluctuation of the transmission ratio of the steering system;

[0056] Figure 14 Wheel angle difference between the Hook joint, revolute joint and the transmission ratio of the steering shaft without fluctuation;

[0057] Figure 15 Flow chart of the non-dominated sorting genetic algorithm;

[0058] Figure 16 Iteration diagram of the objective function f1

[0059] Figure 17 Iteration graph for the objective function f2

[0060] Figure 18 Pareto front graph for the objective functions f1 and f2

[0061] Figure 19 Steering shaft layout forms before and after optimization

[0062] Figure 20 Fluctuation curve of the steering shaft transmission ratio before and after the optimization of the hard point coordinates

[0063] Figure 21 Fluctuation curve of the steering system transmission ratio before and after the optimization of the hard point coordinates

[0064] Figure 22 Wheel angle difference on the same side (left side) without fluctuation of the steering shaft transmission ratio before and after optimization

[0065] Figure 23 Adjust the initial angle to improve the steering symmetry of the steering shaft

[0066] Figure 24 Adjust the initial angle to improve the steering symmetry of the steering system

[0067] Figure 25 Curve of the steering wheel angle change relative to the lateral acceleration obtained from the fixed - radius steady - state turning simulation

[0068] Figure 26 Gain curve of the transient yaw rate relative to the steering wheel angle obtained from the steering wheel sinusoidal sweep - input simulation

[0069] Figure 27 Gain curve of the transient yaw rate relative to the steering wheel angle obtained from the steering wheel sinusoidal sweep - input simulation

[0070] Figure 28 Gain curve of the vehicle body roll angle relative to the lateral acceleration obtained from the steering wheel sinusoidal sweep - input simulation

[0071] Figure 29 Lag time curve of the lateral acceleration relative to the steering wheel angle obtained from the steering wheel sinusoidal sweep - input simulation Detailed implementation manners

[0072] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0073] Example 1

[0074] Only by theoretically analyzing the reasons for the fluctuation of the steering ratio of the steering system can the key factors affecting the fluctuation of the steering ratio be optimized specifically.

[0075] The transmission ratio of the entire steering system is expressed as in Equation (1):

[0076]

[0077] i c 、i r 、i l are the steering shaft transmission ratio, the rack and pinion steering gear transmission ratio, and the tie rod transmission ratio respectively, dδ are the steering wheel angle increment and the steering wheel angle increment respectively.

[0078] In the entire steering system, the rack and pinion steering gear transmission ratio and the tie rod transmission ratio are constant, and the fluctuation of the steering shaft transmission ratio causes the fluctuation of the transmission ratio of the entire steering system.

[0079] In the steering system, if the frictional losses are ignored, according to the law of conservation of energy, there is a relationship as shown in Equation (2) between the torque transmission ratio and the angular transmission ratio of the steering system:

[0080]

[0081] In Equation (2), i T is the torque transmission ratio of the steering system, T Rt is the steering resistance torque overcome by the knuckle, T h is the torque on the steering wheel, η SG is the efficiency of the steering gear under the actual load, η SL is the efficiency of the steering transmission mechanism under the actual load.

[0082] From Equation (2), it can be obtained that:

[0083]

[0084] It can be seen from Equation (3) that when η SG 、η SL and T Rt are constant, T h is proportional to i, and the greater the fluctuation of i, the greater the fluctuation of T h . Therefore, optimizing the fluctuation of the transmission ratio of the steering system can improve the fluctuation of the steering wheel torque.

[0085] Such as Figure 1 and Figure 2The parameters α1 and α2 defined in [reference] are the angles between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft in the double Cardan joint steering system respectively. φ is the angle between the two planes determined by adjacent shafts, β is the angle between the planes where the driving and driven forks of the intermediate shaft are located, and γ is the initial phase angle of the steering wheel relative to the input shaft joint fork at zero steering angle.

[0086] Let be the angle difference between the input shaft and the intermediate shaft, be the angle difference between the intermediate shaft and the output shaft. Then the angle difference of the double Cardan joint steering system can be expressed as Equation (4):

[0087]

[0088] The angle transmission formula for the driving and driven shaft Cardan joints is Equation (5):

[0089]

[0090] In Equation (5): is the input shaft angle, is the output shaft angle. Let the amplitudes of the angle differences between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft be According to Equation (5), the angle difference between the input shaft and the intermediate shaft the angle difference between the intermediate shaft and the output shaft can be approximately expressed as Equations (6) and (7):

[0091]

[0092] Also:

[0093]

[0094] So Equation (7) can be replaced by:

[0095]

[0096] In Equation (9), can be neglected:

[0097]

[0098] Combined with Equation (4), the angle difference between the input shaft and the output shaft can be obtained as:

[0099]

[0100] Introduce the initial phase angle γ of the relative double Cardan joint input shaft angle Perform trigonometric identity transformation on Equation (11) as Equation (12):

[0101]

[0102] Wherein:

[0103]

[0104] In formula (12):

[0105]

[0106] Meanwhile, in order to simplify the calculation and derivation, it can be expressed as:

[0107]

[0108] Based on the above derivation, the equivalent included angle α e is introduced. Substituting formula (15) into formula (14), we get:

[0109]

[0110] So we have:

[0111]

[0112] In the design of the steering system, the design goal is to achieve zero angular displacement difference transmission between the input shaft and the output shaft by a spatial double universal joint with cross shafts, that is, to achieve In formula (17): Thus, when , we have α e = 0, and formula (18) is obtained:

[0113]

[0114] Since:

[0115]

[0116] So the necessary and sufficient condition for formula (18) to have a solution is

[0117]

[0118] Solving it gives:

[0119]

[0120] According to the above derivation, the transmission ratio i of the steering shaft cEqual to 1 (i.e., achieving zero angular displacement difference transmission between the input shaft and the output shaft) requires simultaneously satisfying two conditions: (1) The angles between the two planes where the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are located are equal to the phase angles of the driving and driven forks of the intermediate shaft, i.e., φ = β; (2) The angles between the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are equal, i.e., α1 = α2. Therefore, when φ = β and the output shaft is arranged on the rotating conical surface as shown in Figure 3 (α1 = α2), the input shaft and the output shaft will satisfy the constant speed transmission condition.

[0121] In step S2.1, the coordinates of four hard points A, B, C, and D of the steering system of a certain vehicle model were actually measured (as shown in Figure 2 , point A is the coordinate of the steering wheel center, point B is the coordinate of the intersection of the input shaft and the intermediate shaft, point C is the coordinate of the intersection of the intermediate shaft and the output shaft, and point D is the coordinate of the intersection of the output shaft and the steering tie rod), and a virtual prototype model of the steering system was established as shown in Figure 4 , and the initial angular displacement of the steering wheel relative to the universal joint of the input shaft and the initial phase angle parameter of the universal joint of the intermediate shaft were defined. The steering transmission ratio fluctuation includes amplitude fluctuation and phase fluctuation. In order to clarify whether β and γ affect the amplitude fluctuation or the phase fluctuation of the steering transmission ratio, four groups of data of 0, 45, 90, and 135 were taken for comparative analysis, and the steering shaft transmission ratio curve and the transmission ratio curve of the steering system were obtained as shown in 5- Figure 8 . From Figure 5 and Figure 6 , it can be seen that the initial angle only changes the phase of the steering transmission ratio and has no influence on the amplitude. From Figure 7 and Figure 8 , it can be seen that the phase angle of the knuckle not only affects the phase fluctuation of the steering transmission ratio but also affects the amplitude fluctuation.

[0122] In the said step S2.3: The rotational pair constraint of the cross-axis universal joint is closer to the actual steering working condition. To highlight its advantages, a Hooke joint constraint was established, and the two were compared with the ideal constant speed joint constraint type. The forms of the Hooke joint constraint, the rotational pair constraint, and the constant speed joint constraint are as shown in Figures 9 - 11 . The influence of different constraint types on the steering shaft transmission ratio fluctuation and the transmission ratio fluctuation of the entire steering system is as shown in Figures 12 - 14 , Figure 14 is the difference in the wheel rotation angles on the same side (left side) between the Hooke joint, the rotational pair, and the ideal constant speed joint. From Figure 12 and Figure 13 , it can be seen that compared with using the Hooke joint constraint, the steering transmission ratio obtained by simulation using the rotational pair constraint is closer to the constant speed transmission ratio. From Figure 14 , it can be seen that the difference in the wheel rotation angles on the same side (left side) between the rotational pair and the constant speed joint is smaller.

[0123] In the said step S3.1, when points A and D are fixed, the magnitudes of φ, α1, and α2 can be adjusted by changing the coordinates of points B and C.

[0124] The angle parameters can be obtained by using the space vector method. The coordinates of point A and point D are known. The coordinates of point B and point C are taken as optimization variables. The coordinates of point A, point B, point C and point D in space are respectively set as:

[0125]

[0126] Vector and vector Vector and vector The dot product is as shown in Equation (23):

[0127]

[0128] From Equation (23), the angle between adjacent two axes can be obtained:

[0129]

[0130] Furthermore, in the step S3.2, to determine the angle between the two planes determined by the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft, the space vector method can be used to find the two normal vectors of the plane determined by the input shaft and the intermediate shaft, and the plane determined by the intermediate shaft and the output shaft respectively. The angle between the two normal vectors is the angle between the two planes.

[0131] By the vector product operation of the space vector, the two normal vectors of the plane determined by the input shaft and the intermediate shaft, and the plane determined by the intermediate shaft and the output shaft can be obtained as:

[0132]

[0133] Therefore, from Equation (25), the plane angle φ of the dihedral angle of the plane determined by the input shaft and the intermediate shaft, and the plane determined by the intermediate shaft and the output shaft can be obtained:

[0134]

[0135] Based on the above analysis, there is a connection between the angle parameters of the steering shaft and the position coordinates of the hard points B and C as shown in Equations (22)-(26). Therefore, the position coordinates of the hard points B and C are directly used as optimization variables.

[0136] In the step S4.1, the following optimization target file is written by using MATLAB:

[0137]

[0138] By using program iterative calculation and performing operations, the optimization parameters can be obtained, and then the relevant parameters are simulated to determine the optimization effect.

[0139] Example 2

[0140] First, perform a steering simulation on the established suspension model. The simulation parameters are shown in Table 1:

[0141] Table 1. Steering simulation parameters

[0142]

[0143]

[0144] After the simulation, obtain the ADAMS command.cmd model file. Import it into Isight, and write a batch file runcar.bat and a solver file runsolver.bat.

[0145] Define the input and output variables for optimizing the steering shaft structure parameters as shown in Table 2:

[0146] Table 2. Optimization variables

[0147]

[0148] The flowchart of the non-dominated sorting genetic algorithm is as Figure 15 , and the main parameters are shown in Table 3:

[0149] Table 3. Main parameters of the adaptive genetic algorithm

[0150]

[0151] The iterative processes of the objective functions f1 and f2 are as Figure 16 , 17 , and the pareto front solutions are as Figure 18 .

[0152] After 640 iterations, obtain the optimized coordinates of point B and point C and the phase angle of the intermediate shaft knuckle as shown in Table 4 below:

[0153] Table 4. Variable values before and after optimization

[0154]

[0155] Obtain the spatial layout forms of the steering shaft before and after optimization as Figure 19 .

[0156] Obtain the steering shaft structure parameters before and after optimization as shown in Table 5:

[0157] Table 5. Steering shaft structure parameters before and after optimization

[0158]

[0159] In Table 5, α1', α2', φ', and β' are the optimized structural parameters of the steering shaft respectively.

[0160] It can be obtained from Table 5 that the angle difference between two adjacent shafts before optimization: f1 = |α1 - α2| = 3.5, the difference between the included angle between two planes and the phase angle of the intermediate shaft yoke is f2 = |β - φ| = 5.4, and the differences after optimization are: f1' = |α1' - α2'| = 2, f2' = |β' - φ'| = 1.6. Comparing the results before and after optimization, it can be known that the optimized steering shaft arrangement is closer to the constant speed operation condition.

[0161] The transmission ratio curves of the steering shaft before and after optimization are obtained as Figure 20 , and the transmission ratio curve of the entire steering system is as Figure 21 , and the curves of the front wheel steering angle and the angle difference between the same-side (left side) wheels of the constant speed drive before and after optimization are as Figure 22 .

[0162] Comparing Figure 20 and Figure 21 the transmission ratio curves of the steering shaft before and after optimization and the transmission ratio curve of the entire steering system, it can be seen that the fluctuation of the transmission ratio of the optimized steering shaft is significantly reduced. As Figure 22 can be seen, the steering angle of the optimized wheel is closer to the angle of the same-side (left side) wheel when the transmission ratio has no fluctuation. The amplitude change of the output shaft angular velocity curve is shown in Table 6:

[0163] Table 6. Output shaft angular velocity fluctuation range (deg / s)

[0164]

[0165]

[0166] It can be seen from Table 6 that the angular velocity fluctuation of the optimized steering shaft is smaller.

[0167] By adjusting the initial angle, the phase fluctuation can be reduced and the steering symmetry can be improved. Adjusting near the initial angle of 110 degrees before optimization, the obtained transmission ratio curve of the adjusted steering shaft is as Figures 23 - 24 .

[0168] From Figure 23 and Figure 24 it can be seen that after adjusting the initial angle within a certain range, when the best initial angle is 120°, the steering symmetry is the best.

[0169] Example 3

[0170] During the turning process of the vehicle on a circular path with a fixed radius, as the lateral acceleration continuously increases, the vehicle needs to adjust the steering wheel angle to ensure that the motion curvature of the vehicle remains unchanged. During steady-state turning, the change in lateral acceleration relative to the steering wheel angle characterizes the understeer degree of the vehicle, reflecting the amount of steering wheel operation during the turning process.

[0171] The established steering gear model is assembled with the suspension system and the body system into a complete vehicle for a steady-state turning simulation at a fixed radius. The parameters for the steady-state turning simulation at a fixed radius are shown in the following table:

[0172] Table 7. Parameters for the steady-state turning simulation at a fixed radius

[0173]

[0174] To study the steady-state characteristics during turning, a steady-state turning simulation at a fixed radius is carried out with a turning radius of 40 meters and a vehicle speed range of 6 km / h to 72 km / h. Figure 25 The curve of the steering wheel angle relative to the lateral acceleration obtained from the steady-state turning simulation at a fixed radius.

[0175] From Figure 25 it can be seen that the reduction in the fluctuation of the steering ratio makes the understeer degree of the vehicle increase during turning, improving the understeer characteristics.

[0176] Example 4

[0177] To study the transient characteristics during turning, the established steering gear model is assembled with the suspension system and the body system into a complete vehicle. A sine signal is used as the steering wheel input for a sweep-frequency simulation. The parameters for the sine sweep-frequency simulation of the steering wheel are shown in Table 8:

[0178] Table 8. Parameters for the sine sweep-frequency simulation of the steering wheel

[0179]

[0180] As Figure 26 is the gain curve of the yaw rate relative to the steering wheel angle obtained from the sine sweep-frequency input simulation of the steering wheel. The turning process is generally completed in the low-frequency domain, and the driver rotates the steering wheel to complete the turning process mainly in the range of 0 - 1.5 Hz. Therefore, the change in the gain curve in the 0 - 1.5 Hz frequency band is taken as the basis for evaluating the transient steering stability.

[0181] From Figure 27 it can be seen that the transient yaw rate gain fluctuates near a certain curve. To more clearly compare the changes in each transient index before and after the optimization of the steering ratio, frequency-domain curves are obtained after filtering the curves of the transient yaw rate gain, the gain of the vehicle speed roll angle relative to the lateral acceleration, and the lag time curve of the lateral acceleration relative to the steering wheel angle, as shown in Figures 27 - 29 .

[0182] Comparison Figures 27 - 29 From the steady-state evaluation indexes of the whole vehicle before and after optimization, it can be seen that the yaw rate gain and roll angle gain curves after optimization are very close to the curves of constant-speed transmission (no fluctuation in transmission ratio). After reducing the transmission ratio fluctuation of the steering system, the transient yaw rate gain decreases, improving the stability; the roll angle gain of the vehicle body decreases, improving the anti-roll performance; the lateral acceleration lag time relative to the steering wheel angle decreases, improving the steering response speed.

Claims

1. A steering parameter optimization design method based on non-dominated sorting genetic algorithm, characterized in that, It includes the following steps: S1. Conduct a theoretical analysis of the steering transmission fluctuation of the steering system; S2. Based on the results of the theoretical analysis, establish a double-cardan joint steering gear model and apply constraints, specifically as follows: S2.

1. Establish a double-cardan joint steering gear model; S2.

2. Define the initial rotation angle of the steering wheel relative to the input shaft cardan joint and the initial phase angle parameter of the intermediate shaft cardan joint, and verify the influence on the steering transmission ratio; S2.

3. Apply simulation constraints to the double-cardan joint; S3. Then optimize the hard point position coordinate parameters, specifically as follows: S3.

1. Use the space vector method to convert the included angles between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft into hard point coordinate parameters for optimization; S3.

2. Use the space vector method to convert the included angle between the two planes determined by the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft into hard point coordinate position parameters for optimization; S4. Use the NSGA-II algorithm to optimize the hard point position coordinate parameters, specifically as follows: S4.

1. Assemble the established steering gear model and the suspension system in ADAMS into a front suspension model and conduct a steering simulation; S4.

2. Import the simulation file in ADAMS into Isight, use MATLAB as the solver, and run ADAMS, Isight, and MATLAB jointly; S4.

3. Use MATLAB to write an optimization target file; S4.

4. Set the optimization variable range, constraint conditions, and number of iterations, and run the optimization; In S1, the theoretical analysis of the steering transmission fluctuation of the steering system is as follows: The transmission ratio i of the entire steering system is expressed as in Equation (1): i c 、 i r 、 i l are the steering shaft transmission ratio, the rack and pinion steering gear transmission ratio, and the tie rod transmission ratio respectively, dδ are the steering wheel angle increment and the steering wheel angle increment respectively; in the entire steering system, the rack and pinion steering gear transmission ratio and the tie rod transmission ratio are constant, and the fluctuation of the steering shaft transmission ratio causes the fluctuation of the entire steering system transmission ratio; In the steering system, ignoring the friction loss, according to the law of conservation of energy, there is a relationship as in Equation (2) between the torque transmission ratio and the angular transmission ratio of the steering system: In Equation (2), i T is the torque transmission ratio of the steering system, T RT is the steering resistance torque overcome by the steering knuckle, T h is the torque applied to the steering wheel, η SG is the efficiency of the steering gear under the actual load, η SL is the efficiency of the steering linkage under the actual load; From Equation (2), we get: It can be obtained from Equation (3) that when η SG and η SL and T Rt are constant, T h is proportional to i. The greater the fluctuation of i, the greater the fluctuation of T h . Reducing the fluctuation of the transmission ratio of the steering system can improve the steering wheel torque fluctuation; The goal of the steering system design is to achieve zero angular difference transmission of the space double-cardan joint in the intermediate transmission between the input shaft and the output shaft during the transmission process of the steering shaft; at the same time, two conditions are met: (1) The included angles between the two planes where the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are located are equal to the phase angles of the main and driven forks of the intermediate shaft; (2) The included angles between the input shaft and the intermediate shaft, and the intermediate shaft and the output shaft are equal.

2. The steering parameter optimization design method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that In S2.1, the establishment of the double-cardan joint steering gear model is based on the steering system of a certain vehicle model, and the four steering hard point coordinates A, B, C, and D are measured and quantified. Among them, point A is the steering wheel center coordinate, point B is the intersection coordinate of the input shaft and the intermediate shaft, point C is the intersection coordinate of the intermediate shaft and the output shaft, and point D is the intersection coordinate of the output shaft and the steering tie rod; in S2.2, the initial angle only changes the phase of the steering transmission ratio and has no influence on the amplitude, and the joint fork phase angle not only affects the phase fluctuation of the steering transmission ratio but also affects the amplitude fluctuation; in S2.3, the simulation constraint of the cardan joint is a revolute pair constraint.

3. A steering parameter optimization design method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that Optimize the hard point coordinate position parameters to the coordinates of hard points B and C; when points A and D are fixed, the magnitudes of φ, α1, and α2 can be adjusted by changing the coordinates of points B and C; where: α1 and α2 are the angles between the input shaft and the intermediate shaft, and between the intermediate shaft and the output shaft in the double cardan joint steering system respectively, φ is the angle between the two planes determined by adjacent shafts, A is the coordinate of the steering wheel center, B is the coordinate of the intersection point of the input shaft and the intermediate shaft, C is the coordinate of the intersection point of the intermediate shaft and the output shaft, and D is the coordinate of the intersection point of the output shaft and the steering tie rod.

4. A steering parameter optimization design method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that In S4.3, the optimization target file was written using MATLAB as follows: Where, β is the angle between the planes where the driving and driven forks of the intermediate shaft are located, A is the coordinate of the steering wheel center, B is the coordinate of the intersection point of the input shaft and the intermediate shaft, C is the coordinate of the intersection point of the intermediate shaft and the output shaft, and D is the coordinate of the intersection point of the output shaft and the steering tie rod; Therefore, the optimization variables, optimization target, and constraint condition expressions are as shown in Equation (27):

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