A method for collaborative control of special vehicle ride comfort parameters

Abstract

The present application belongs to the technical field of shock absorber, and particularly relates to a kind of special vehicle smoothness parameter collaborative control method, comprising: step 1: establish the theoretical model of energy feedback shock absorber, determine its shock absorbing and energy feedback characteristic representation formula;Step 2: in combination with the original design method of shock absorber, determine the parameter constraint range of energy feedback shock absorber;Step 3: according to the energy feedback shock absorber shock absorbing and energy feedback characteristic representation formula and its parameter constraint range, establish the multi-objective optimization model of energy feedback shock absorber parameter;Step 4: according to the multi-objective optimization model of energy feedback shock absorber parameter, produce optimization solution set, determine weight in combination with vehicle type and smoothness demand, obtain the multi-objective optimization solution of energy feedback shock absorber parameter, finally realize semi-active suspension energy feedback and smoothness parameter collaborative control.The method can improve the search accuracy of optimal solution, and support the processing of optimization problems with strict constraints and small feasible region.

Description

Technical Field

[0001] This invention belongs to the field of shock absorber technology, specifically relating to a method for coordinated control of ride comfort parameters for special vehicles. Background Technology

[0002] Shock absorbers are an important component of the suspension system. They suppress the oscillations when the spring absorbs vibration and the impact from the road surface, thereby improving the ride comfort of special vehicles. In addition to the vibration reduction function of traditional shock absorbers, energy-recovering shock absorbers can also recover and utilize some vibration energy, converting mechanical energy into electrical energy and providing it to the vehicle.

[0003] Currently, the parameter matching problem of energy-feeding vibration dampers is mostly reduced to a single-objective optimization problem aimed at improving energy feeding performance, which often has certain limitations.

[0004] For energy-recharged shock absorbers, their damping performance, i.e., the ride comfort of semi-active suspension, is equally important. However, it is difficult for the damping performance and energy recharge performance of energy-recharged shock absorbers to be optimized simultaneously; they are often conflicting and uncoordinated, meaning that a change in one objective will cause other objectives to change in the opposite direction. Therefore, there is an urgent need for a method for the coordinated control of ride comfort parameters for special vehicles. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The technical problem to be solved by the present invention is: how to provide a method for coordinated control of ride comfort parameters of special vehicles, which can perform coordinated matching of damper parameters, thereby taking into account both the damping performance and energy feeding performance of the energy-rechargeable damper, and thus satisfying the coordinated control of energy feeding and ride comfort of semi-active suspension, so as to maximize the ride comfort and energy feeding performance of active suspension.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention provides a method for coordinated control of ride comfort parameters for special vehicles, the method comprising the following steps:

[0009] Step 1: Establish a theoretical model of the energy-feeding vibration damper and determine its vibration reduction and energy feeding characteristics characterization formulas;

[0010] Step 2: Determine the parameter constraint range of the energy-feeding vibration damper by combining the original design method of the vibration damper;

[0011] Step 3: Based on the vibration reduction and energy feeding characteristics characterization formulas of the energy-feeding vibration damper and its parameter constraint range, establish a multi-objective optimization model for the parameters of the energy-feeding vibration damper;

[0012] Step 4: Generate an optimization solution set based on the multi-objective optimization model of the energy-rechargeable shock absorber parameters, determine the weights in combination with vehicle type and ride comfort requirements, and obtain the multi-objective optimization solution of the energy-rechargeable shock absorber parameters, ultimately realizing the coordinated control of energy recharge and ride comfort parameters of the semi-active suspension.

[0013] Step 1 includes:

[0014] The road surface excitation model is determined, and a random Gaussian white noise model for road surface excitation is adopted, the expression of which is shown below:

[0015]

[0016] In the above formula, It is the road surface excitation speed, x g (t) is the road surface excitation, f0 is the lower cutoff frequency, and S is the S0 q (n0) is the road surface roughness coefficient, u is the vehicle speed, and w(t) is uniformly distributed white noise;

[0017] A theoretical model of a vehicle's two-degree-of-freedom system is established, and the dynamic equations of the vehicle's two-degree-of-freedom suspension system are as follows:

[0018]

[0019] In the above formula, C eq This refers to the damping coefficient of the energy-rechargeable vibration damper. During vehicle operation, vertical vibrations caused by uneven road surfaces are absorbed by the energy-rechargeable vibration damper and then converted into the rotation of the generator. The generator generates damping force during rotation; the higher the rotational speed, the greater the electromagnetic damping. (m) s and m u Let x represent the sprung mass and unsprung mass of the suspension system, respectively. s x u x g These represent the sprung mass displacement, unsprung mass displacement, and road surface excitation, respectively. Indicates the velocity of the sprung mass. Indicates the acceleration of the sprung mass. This represents the acceleration of the unsprung mass, and k1 and k2 represent the suspension spring stiffness and wheel stiffness, respectively.

[0020] The excitation expression for the energy-fed vibration damper is:

[0021]

[0022] In the above formula, x0, v0, and a0 represent the excitation displacement, excitation velocity, and excitation acceleration of the energy-fed vibration damper, respectively. Indicates the velocity of the unsprung mass;

[0023] The damping force of an energy-recharged vibration damper consists of three parts: inertial force, electromagnetic force, and frictional force. The inertial force F g The expression is:

[0024]

[0025] In the above formula, J k i represents the equivalent rotational inertia of each component of the vibration damper. k It is the product of the transmission ratios of each stage between the various components of the shock absorber and the lead screw and nut;

[0026] When the motor of a regenerative vibration damper rotates, it generates electromagnetic torque, which in turn produces electromagnetic damping force F. d The expression is as follows:

[0027]

[0028]

[0029] In the above formula, T e i represents the electromagnetic torque of the motor. g i represents the product of the transmission ratios of each stage between the damper motor and the lead screw nut. s and i m These represent the reduction ratio of the shock absorber motor and the transmission ratio of the ball screw, respectively; l represents the lead of the ball screw pair; k e and k t These are the generator electromagnetic torque constant and the generator back electromotive force constant, ω. g R is the angular velocity of the motor rotor. in R and R are the equivalent resistance of the motor armature and the equivalent resistance of the external variable resistor, respectively, and η represents the transmission efficiency of the ball screw pair of the shock absorber.

[0030] During operation, energy-rechargeable vibration dampers inevitably generate mechanical damping forces due to the relative motion of different components. These mechanical damping forces reflect the internal friction losses of the energy-rechargeable vibration damper, including friction within the ball screw pair, bevel gear pair, and motor reducer, as well as the motor's wind resistance and magnetic losses. The mechanical damping force F... p It can be represented as:

[0031] F p =f c sgn(v0)+c m v0 (7)

[0032] In the above formula, f c It is Coulomb friction, c m is the viscous term of mechanical damping, and sgn is the sign function;

[0033] The total damping force of the energy-fed vibration damper is the sum of the electromagnetic damping force, inertial force, and mechanical damping force mentioned above, that is:

[0034]

[0035] In the above formula, F t It is the total damping force of the energy-fed vibration damper, C r M is the electromagnetic damping coefficient of the energy-fed vibration damper. r It is the inertial damping coefficient of the energy-fed vibration damper;

[0036] The equivalent damping coefficient of an energy-fed vibration damper reflects the damper's stiffness, and it can be adjusted by the external load resistance of the damper. Its expression is shown below:

[0037]

[0038] The root mean square (RMS) value of sprung mass acceleration is commonly used to characterize the ride comfort of special-purpose vehicles. A smaller RMS value indicates better ride comfort, while a larger RMS value indicates poorer ride comfort. The expression for the RMS value of sprung mass acceleration is shown below:

[0039]

[0040] In the above formula, T refers to duration, t refers to time, and x s (t) is x s , representing x s It is a variable that changes over time.

[0041] Based on the above, a coupled model of the energy-recharged damper and the vehicle's two-degree-of-freedom suspension system is established. The time-domain output curve of the vehicle's sprung mass acceleration based on the semi-active suspension can be obtained, and the root mean square value of the vehicle's sprung mass acceleration can be used as a characterization of the damping characteristics of the energy-recharged damper.

[0042] The energy feed power of the energy-feeding vibration damper is calculated using the following formula:

[0043]

[0044] In the above formula, E is the output voltage of the motor, I is the output current of the motor, and P is the energy feeding power of the energy-feeding vibration damper.

[0045] The energy feeding power of the energy-feeding vibration damper is used as a characterization of its energy feeding characteristics.

[0046] In step 2,

[0047] Designed for special vehicles, the relative damping coefficient ψ is used to assess the rate of vibration decay, expressed as:

[0048]

[0049] Through parameter sensitivity analysis, the parameter that has a significant impact on the damping and energy feeding characteristics of the vibration damper was determined to be the vibration damper motor reduction ratio i. s Ball screw lead l, generator electromagnetic torque constant k e Generator back electromotive force constant k t The equivalent resistance R of the external variable resistor;

[0050] By combining the specific parameters of the vehicle suspension with formulas (11) and (8), the reasonable range of values ​​for each optimized parameter of the shock absorber can be obtained.

[0051] In formula (12), the value of ψ ranges from 0.25 to 0.35.

[0052] In step 3, based on the analysis in step 2, the root mean square value of the vehicle's vertical acceleration and the reciprocal of the damper's energy feed power are selected as the optimization objectives, namely:

[0053]

[0054]

[0055] The specific range of optimized parameters for the energy-rechargeable shock absorber depends on the suspension parameters of the vehicle on which the shock absorber is to be installed.

[0056] Based on the optimization objective and optimization parameter constraints, the improved NSGA-II algorithm is used to optimize and match the important parameters of the energy-feeding damper, and solutions are selected from the obtained Pareto non-dominated solution set according to certain principles, so that the matched parameters can simultaneously optimize the energy-feeding performance and ride comfort of the semi-active suspension.

[0057] When constraints are strict and the feasible region is small, the traditional NSGA-II algorithm is prone to failure in searching for feasible solutions. Compared with the traditional NSGA-II algorithm, the improved NSGA-II algorithm introduces "gradient" information into the constraints in the optimization problem so that the program knows how to iterate in the direction of the feasible region.

[0058] In step 3, the principle of the improved NSGA-II algorithm is as follows:

[0059] For each constraint t i (x), calculate its boundary surface S in the corresponding dimension. i And the current sample x on the boundary surface S i distance d i ;

[0060] If x lies in the infeasible region, then the new function is constructed as follows:

[0061] p i (x)=k(d i )t i (x) (15)

[0062] In the above formula, k(d) i ) represents the distance d i The increasing function, in order to ensure convergence, k(d) i The calculation method for ) is as follows:

[0063] k(d i ) = m i +n i (d i (16)

[0064] In the above formula, m i Used to distinguish the fitness of feasible and infeasible solutions, n i (d i This is used to introduce gradient information into infeasible solutions.

[0065] In step 3, the improvement of the traditional NSGA-II algorithm can enhance the search accuracy for the optimal solution and support the handling of optimization problems with strict constraints and small feasible regions.

[0066] In step 4, the improved NSGA-II algorithm optimizes and matches the important parameters of the energy-feeding damper to obtain the Pareto non-dominated solution set. Then, the weights are determined according to the vehicle type and ride comfort requirements, and the optimal solution can be selected according to the specific situation.

[0067] In step 4, the weights are determined in the following manner;

[0068] First, determine the subjective weights γ of the two objective functions based on the vehicle type and ride comfort requirements. n :

[0069]

[0070] In the above formula, N an It represents the weight given by the a-th person to the n-th objective function;

[0071] The Pareto non-dominated solution set has t solutions. Using two objective functions as evaluation metrics, we obtain matrix S:

[0072] S=(s mn ) t×2 (m=1,2,···,t; n=1,2) (18)

[0073] In the above formula, s mn This represents the element in the m-th row and n-th column of matrix S;

[0074] Normalize matrix S, where the elements s in matrix S are... mn The calculation method for normalization is as follows:

[0075]

[0076] In the above formula, S max Let S be the maximum element in each column of matrix S;

[0077] Calculate the objective weights ω of the two objective functions. n :

[0078]

[0079] In the above formula, v m To calculate intermediate process variables.

[0080] Based on subjective weight γ n and objective weight ω n The comprehensive weight ψ is obtained using two linear combination coefficients. n ;

[0081] ψ n =φ1·ω n +φ2·γ n (twenty one)

[0082] In the above formula, φ1 and φ2 are the linear combination coefficients calculated by the comprehensive weight;

[0083] By assigning weights to each element of the index matrix, we obtain the weighting matrix K.

[0084]

[0085] The minimum value in each column of the weighting matrix As the optimal solution, the maximum value As the worst possible solution;

[0086]

[0087] Calculate the relationship between each solution in the weighted matrix and the optimal solution. distance Each solution and the worst solution distance

[0088]

[0089] Calculate the proximity exponent R between each solution in the Pareto nondominated solution set and the optimal level. m :

[0090]

[0091] The point closest to the maximum exponent is selected as the optimal point, thereby determining the matching of various parameters of the energy-feeding vibration damper.

[0092] The method described above can perform parameter matching of the installed energy-rechargeable shock absorbers for different vehicle types and ride comfort requirements, thereby taking into account both the damping performance and energy recharge performance of the energy-rechargeable shock absorbers, and thus meeting the coordinated control of energy recharge and ride comfort of semi-active suspensions in different vehicles, maximizing the ride comfort and energy recharge of semi-active suspensions.

[0093] (III) Beneficial Effects

[0094] Compared with existing technologies, this invention provides a method for coordinated control of ride comfort parameters for special vehicles. It can perform parameter coordination matching of the installed energy-rechargeable shock absorbers for different vehicle types and ride comfort requirements, thereby balancing the damping and energy-recharge performance of the shock absorbers. This satisfies the coordinated control of energy recharge and ride comfort of semi-active suspensions in different vehicles, maximizing both ride comfort and energy recharge performance of the semi-active suspension. The algorithm used is an improvement on the traditional NSGA-II algorithm, which can improve the accuracy of optimal solution search and support the handling of optimization problems with strict constraints and small feasible regions. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the Pareto non-dominated solution set.

[0096] Figures 2a-2c To optimize the time-domain output curves of the vehicle's vertical acceleration under different road surface grades. Among them, Figure 2a Grade A road surface Figure 2b Class B road surface Figure 2c Grade C road surface.

[0097] Figure 3 To optimize the voltage time-domain output curve of the front and rear energy-fed vibration damper. Detailed Implementation

[0098] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0099] To address the aforementioned technical problems, this invention provides a method for coordinated control of ride comfort parameters for special vehicles, the method comprising the following steps:

[0100] Step 1: Establish a theoretical model of the energy-feeding vibration damper and determine its vibration reduction and energy feeding characteristics characterization formulas;

[0101] Step 2: Determine the parameter constraint range of the energy-feeding vibration damper by combining the original design method of the vibration damper;

[0102] Step 3: Based on the vibration reduction and energy feeding characteristics characterization formulas of the energy-feeding vibration damper and its parameter constraint range, establish a multi-objective optimization model for the parameters of the energy-feeding vibration damper;

[0103] Step 4: Generate an optimization solution set based on the multi-objective optimization model of the energy-rechargeable shock absorber parameters, determine the weights in combination with vehicle type and ride comfort requirements, and obtain the multi-objective optimization solution of the energy-rechargeable shock absorber parameters, ultimately realizing the coordinated control of energy recharge and ride comfort parameters of the semi-active suspension.

[0104] Step 1 includes:

[0105] The road surface excitation model is determined, and a random Gaussian white noise model for road surface excitation is adopted, the expression of which is shown below:

[0106]

[0107] In the above formula, It is the road surface excitation speed, x g (t) is the road surface excitation, f0 is the lower cutoff frequency, and S is the S-frequency. q (n0) is the road surface roughness coefficient, u is the vehicle speed, and w(t) is uniformly distributed white noise;

[0108] A theoretical model of a vehicle's two-degree-of-freedom system is established, and the dynamic equations of the vehicle's two-degree-of-freedom suspension system are as follows:

[0109]

[0110] In the above formula, C eq This refers to the damping coefficient of the energy-rechargeable vibration damper. During vehicle operation, vertical vibrations caused by uneven road surfaces are absorbed by the energy-rechargeable vibration damper and then converted into the rotation of the generator. The generator generates damping force during rotation; the higher the rotational speed, the greater the electromagnetic damping. (m) s and m u Let x represent the sprung mass and unsprung mass of the suspension system, respectively. s x u x g These represent the sprung mass displacement, unsprung mass displacement, and road surface excitation, respectively. Indicates the velocity of the sprung mass. Indicates the acceleration of the sprung mass. This represents the acceleration of the unsprung mass, and k1 and k2 represent the suspension spring stiffness and wheel stiffness, respectively.

[0111] The excitation expression for the energy-fed vibration damper is:

[0112]

[0113] In the above formula, x0, v0, and a0 represent the excitation displacement, excitation velocity, and excitation acceleration of the energy-fed vibration damper, respectively. Indicates the velocity of the unsprung mass;

[0114] The damping force of an energy-recharged vibration damper consists of three parts: inertial force, electromagnetic force, and frictional force. The inertial force F g The expression is:

[0115]

[0116] In the above formula, J k i represents the equivalent rotational inertia of each component of the vibration damper. k It is the product of the transmission ratios of each stage between the various components of the shock absorber and the lead screw and nut;

[0117] When the motor of a regenerative vibration damper rotates, it generates electromagnetic torque, which in turn produces electromagnetic damping force F. d The expression is as follows:

[0118]

[0119]

[0120] In the above formula, T e i represents the electromagnetic torque of the motor. g i represents the product of the transmission ratios of each stage between the damper motor and the lead screw nut. s and i m These represent the reduction ratio of the shock absorber motor and the transmission ratio of the ball screw, respectively; l represents the lead of the ball screw pair; k e and k t These are the generator electromagnetic torque constant and the generator back electromotive force constant, ω. g R is the angular velocity of the motor rotor. in R and R are the equivalent resistance of the motor armature and the equivalent resistance of the external variable resistor, respectively, and η represents the transmission efficiency of the ball screw pair of the shock absorber.

[0121] During operation, energy-rechargeable vibration dampers inevitably generate mechanical damping forces due to the relative motion of different components. These mechanical damping forces reflect the internal friction losses of the energy-rechargeable vibration damper, including friction within the ball screw pair, bevel gear pair, and motor reducer, as well as the motor's wind resistance and magnetic losses. The mechanical damping force F... p It can be represented as:

[0122] F p =f csgn(v0)+c m v0 (7)

[0123] In the above formula, f c It is Coulomb friction, c m is the viscous term of mechanical damping, and sgn is the sign function;

[0124] The total damping force of the energy-fed vibration damper is the sum of the electromagnetic damping force, inertial force, and mechanical damping force mentioned above, that is:

[0125]

[0126] In the above formula, F t It is the total damping force of the energy-fed vibration damper, C r M is the electromagnetic damping coefficient of the energy-fed vibration damper. r It is the inertial damping coefficient of the energy-fed vibration damper;

[0127] The equivalent damping coefficient of an energy-fed vibration damper reflects the damper's stiffness, and it can be adjusted by the external load resistance of the damper. Its expression is shown below:

[0128]

[0129] The root mean square (RMS) value of sprung mass acceleration is commonly used to characterize the ride comfort of special-purpose vehicles. A smaller RMS value indicates better ride comfort, while a larger RMS value indicates poorer ride comfort. The expression for the RMS value of sprung mass acceleration is shown below:

[0130]

[0131] In the above formula, T refers to duration, t refers to time, and x s (t) is x s , representing x s It is a variable that changes over time.

[0132] Based on the above, a coupled model of the energy-recharged damper and the vehicle's two-degree-of-freedom suspension system is established. The time-domain output curve of the vehicle's sprung mass acceleration based on the semi-active suspension can be obtained, and the root mean square value of the vehicle's sprung mass acceleration can be used as a characterization of the damping characteristics of the energy-recharged damper.

[0133] The energy feed power of the energy-feeding vibration damper is calculated using the following formula:

[0134]

[0135] In the above formula, E is the output voltage of the motor, I is the output current of the motor, and P is the energy feeding power of the energy-feeding vibration damper.

[0136] The energy feeding power of the energy-feeding vibration damper is used as a characterization of its energy feeding characteristics.

[0137] In step 2,

[0138] Designed for special vehicles, the relative damping coefficient ψ is used to assess the rate of vibration decay, expressed as:

[0139]

[0140] Through parameter sensitivity analysis, the parameter that has a significant impact on the damping and energy feeding characteristics of the vibration damper was determined to be the vibration damper motor reduction ratio i. s Ball screw lead l, generator electromagnetic torque constant k e Generator back electromotive force constant k t The equivalent resistance R of the external variable resistor;

[0141] By combining the specific parameters of the vehicle suspension with formulas (11) and (8), the reasonable range of values ​​for each optimized parameter of the shock absorber can be obtained.

[0142] In formula (12), the value of ψ ranges from 0.25 to 0.35.

[0143] In step 3, based on the analysis in step 2, the root mean square value of the vehicle's vertical acceleration and the reciprocal of the damper's energy feed power are selected as the optimization objectives, namely:

[0144]

[0145]

[0146] The specific range of optimized parameters for the energy-rechargeable shock absorber depends on the suspension parameters of the vehicle on which the shock absorber is to be installed.

[0147] Based on the optimization objective and optimization parameter constraints, the improved NSGA-II algorithm is used to optimize and match the important parameters of the energy-feeding damper, and solutions are selected from the obtained Pareto non-dominated solution set according to certain principles, so that the matched parameters can simultaneously optimize the energy-feeding performance and ride comfort of the semi-active suspension.

[0148] When constraints are strict and the feasible region is small, the traditional NSGA-II algorithm is prone to failure in searching for feasible solutions. Compared with the traditional NSGA-II algorithm, the improved NSGA-II algorithm introduces "gradient" information into the constraints in the optimization problem so that the program knows how to iterate in the direction of the feasible region.

[0149] In step 3, the principle of the improved NSGA-II algorithm is as follows:

[0150] For each constraint t i (x), calculate its boundary surface S in the corresponding dimension. i And the current sample x on the boundary surface S i distance d i ;

[0151] If x lies in the infeasible region, then the new function is constructed as follows:

[0152] p i (x)=k(d i )t i (x) (15)

[0153] In the above formula, k(d) i ) represents the distance d i The increasing function, in order to ensure convergence, k(d) i The calculation method for ) is as follows:

[0154] k(d i ) = m i +n i (d i (16)

[0155] In the above formula, m i Used to distinguish the fitness of feasible and infeasible solutions, n i (d i This is used to introduce gradient information into infeasible solutions.

[0156] In step 3, the improvement of the traditional NSGA-II algorithm can enhance the search accuracy for the optimal solution and support the handling of optimization problems with strict constraints and small feasible regions.

[0157] In step 4, the improved NSGA-II algorithm optimizes and matches the important parameters of the energy-feeding damper to obtain the Pareto non-dominated solution set. Then, the weights are determined according to the vehicle type and ride comfort requirements, and the optimal solution can be selected according to the specific situation.

[0158] In step 4, the weights are determined in the following manner;

[0159] First, determine the subjective weights γ of the two objective functions based on the vehicle type and ride comfort requirements. n :

[0160]

[0161] In the above formula, N an It represents the weight given by the a-th person to the n-th objective function;

[0162] The Pareto non-dominated solution set has t solutions. Using two objective functions as evaluation metrics, we obtain matrix S:

[0163] S=(s mn ) t×2 (m=1,2,···,t; n=1,2) (18)

[0164] In the above formula, s mn This represents the element in the m-th row and n-th column of matrix S;

[0165] Normalize matrix S, where the elements s in matrix S are... mn The calculation method for normalization is as follows:

[0166]

[0167] In the above formula, S max Let S be the maximum element in each column of matrix S;

[0168] Calculate the objective weights ω of the two objective functions. n :

[0169]

[0170] In the above formula, v m To calculate intermediate process variables.

[0171] Based on subjective weight γ n and objective weight ω n The comprehensive weight ψ is obtained using two linear combination coefficients. n ;

[0172] ψ n =φ1·ω n +φ2·γ n (twenty one)

[0173] In the above formula, φ1 and φ2 are the linear combination coefficients calculated by the comprehensive weight;

[0174] By assigning weights to each element of the index matrix, we obtain the weighting matrix K.

[0175]

[0176] The minimum value in each column of the weighting matrix As the optimal solution, the maximum value As the worst possible solution;

[0177]

[0178] Calculate the relationship between each solution in the weighted matrix and the optimal solution. distance Each solution and the worst solution distance

[0179]

[0180] Calculate the proximity exponent R between each solution in the Pareto nondominated solution set and the optimal level. m :

[0181]

[0182] The point closest to the maximum exponent is selected as the optimal point, thereby determining the matching of various parameters of the energy-feeding vibration damper.

[0183] The method described above can perform parameter matching of the installed energy-rechargeable shock absorbers for different vehicle types and ride comfort requirements, thereby taking into account both the damping performance and energy recharge performance of the energy-rechargeable shock absorbers, and thus meeting the coordinated control of energy recharge and ride comfort of semi-active suspensions in different vehicles, maximizing the ride comfort and energy recharge of semi-active suspensions.

[0184] Example 1

[0185] This embodiment specifically includes the following steps:

[0186] 1. Establish a theoretical model for the energy-feeding vibration damper and determine its vibration reduction and energy feeding characteristics characterization formulas, including:

[0187] The road surface excitation model is determined, and a random Gaussian white noise model for road surface excitation is adopted, the expression of which is shown below:

[0188]

[0189] In the above formula, It is the road surface excitation speed, x g (t) is the road surface excitation, f0 is the lower cutoff frequency, and S is the S-frequency. q (n0) is the road surface roughness coefficient, u is the vehicle speed, and w(t) is uniformly distributed white noise;

[0190] A theoretical model of a vehicle's two-degree-of-freedom system is established, and the dynamic equations of the vehicle's two-degree-of-freedom suspension system are as follows:

[0191]

[0192] In the above formula, C eq This refers to the damping coefficient of the energy-rechargeable vibration damper. During vehicle operation, vertical vibrations caused by uneven road surfaces are absorbed by the energy-rechargeable vibration damper and then converted into the rotation of the generator. The generator generates damping force during rotation; the higher the rotational speed, the greater the electromagnetic damping. (m) s and m uLet x represent the sprung mass and unsprung mass of the suspension system, respectively. s x u x g These represent the sprung mass displacement, unsprung mass displacement, and road surface excitation, respectively. Indicates the velocity of the sprung mass. Indicates the acceleration of the sprung mass. This represents the acceleration of the unsprung mass, and k1 and k2 represent the suspension spring stiffness and wheel stiffness, respectively.

[0193] The excitation expression for the energy-fed vibration damper is:

[0194]

[0195] In the above formula, x0, v0, and a0 represent the excitation displacement, excitation velocity, and excitation acceleration of the energy-fed vibration damper, respectively. Indicates the velocity of the unsprung mass;

[0196] The damping force of an energy-recharged vibration damper consists of three parts: inertial force, electromagnetic force, and frictional force. The inertial force F g The expression is:

[0197]

[0198] In the above formula, J k i represents the equivalent rotational inertia of each component of the vibration damper. k It is the product of the transmission ratios of each stage between the various components of the shock absorber and the lead screw and nut;

[0199] When the motor of a regenerative vibration damper rotates, it generates electromagnetic torque, which in turn produces electromagnetic damping force F. d The expression is as follows:

[0200]

[0201]

[0202] In the above formula, T e i represents the electromagnetic torque of the motor. g i represents the product of the transmission ratios of each stage between the damper motor and the lead screw nut. s and i m These represent the reduction ratio of the shock absorber motor and the transmission ratio of the ball screw, respectively; l represents the lead of the ball screw pair; k e and k t These are the generator electromagnetic torque constant and the generator back electromotive force constant, ω. g R is the angular velocity of the motor rotor. inR and R are the equivalent resistance of the motor armature and the equivalent resistance of the external variable resistor, respectively, and η represents the transmission efficiency of the ball screw pair of the shock absorber.

[0203] During operation, energy-rechargeable vibration dampers inevitably generate mechanical damping forces due to the relative motion of different components. These mechanical damping forces reflect the internal friction losses of the energy-rechargeable vibration damper, including friction within the ball screw pair, bevel gear pair, and motor reducer, as well as the motor's wind resistance and magnetic losses. The mechanical damping force F... p It can be represented as:

[0204] F p =f c sgn(v0)+c m v0 (7)

[0205] In the above formula, f c It is Coulomb friction, c m is the viscous term of mechanical damping, and sgn is the sign function;

[0206] The total damping force of the energy-fed vibration damper is the sum of the electromagnetic damping force, inertial force, and mechanical damping force mentioned above, that is:

[0207]

[0208] In the above formula, F t It is the total damping force of the energy-fed vibration damper, C r M is the electromagnetic damping coefficient of the energy-fed vibration damper. r It is the inertial damping coefficient of the energy-fed vibration damper;

[0209] The equivalent damping coefficient of an energy-fed vibration damper reflects the damper's stiffness, and it can be adjusted by the external load resistance of the damper. Its expression is shown below:

[0210]

[0211] The root mean square (RMS) value of sprung mass acceleration is commonly used to characterize the ride comfort of special-purpose vehicles. A smaller RMS value indicates better ride comfort, while a larger RMS value indicates poorer ride comfort. The expression for the RMS value of sprung mass acceleration is shown below:

[0212]

[0213] In the above formula, T refers to duration, t refers to time, and x s (t) is x s , representing x s It is a variable that changes over time.

[0214] Based on the above, a coupled model of the energy-recharged damper and the vehicle's two-degree-of-freedom suspension system is established. The time-domain output curve of the vehicle's sprung mass acceleration based on the semi-active suspension can be obtained, and the root mean square value of the vehicle's sprung mass acceleration can be used as a characterization of the damping performance of the energy-recharged damper.

[0215] The energy feed power of the energy-feeding vibration damper is calculated using the following formula:

[0216]

[0217] In the above formula, E is the output voltage of the motor, I is the output current of the motor, and P is the energy feeding power of the energy-feeding vibration damper.

[0218] The power of the energy-feeding damper is used as a characterization of its energy-feeding performance.

[0219] 2. Based on the original design method of the vibration damper, determine the parameter constraint range of the energy-feeding vibration damper.

[0220] Designed for special vehicles, the relative damping coefficient ψ is used to assess the rate of vibration decay, expressed as:

[0221]

[0222] In the above formula, the value of ψ ranges from 0.25 to 0.35;

[0223] Through parameter sensitivity analysis, the parameter that has a significant impact on the damping and energy feeding characteristics of the vibration damper was determined to be the vibration damper motor reduction ratio i. s Ball screw lead l, generator electromagnetic torque constant k e Generator back electromotive force constant k t The equivalent resistance R of the external variable resistor.

[0224] By combining the specific parameters of the vehicle suspension with formulas (11) and (8), the reasonable range of values ​​for each optimized parameter of the shock absorber can be obtained.

[0225] Taking the suspension system parameters of a certain special vehicle as an example, they are shown in the table below:

[0226] Table 1 Parameters of a Special Vehicle's Suspension System

[0227]

[0228]

[0229] Calculated using equation (12), the range of values ​​for each optimized parameter of the vibration damper is as follows:

[0230]

[0231] 3. Based on the vibration reduction and energy feeding characteristics characterization formulas of the energy-feeding vibration damper and its parameter constraint range, a multi-objective optimization model for the parameters of the energy-feeding vibration damper is established.

[0232] Based on the above analysis, the root mean square value of the vehicle's vertical acceleration and the reciprocal of the damper's feed power are chosen as the optimization objectives, namely:

[0233]

[0234]

[0235] Based on the optimization objective and optimization parameter constraints, the improved NSGA-II algorithm is used to optimize and match the important parameters of the energy-feeding damper. The solution is selected from the obtained Pareto non-dominated solution set according to certain principles, so that the matched parameters can optimize the energy feeding performance and ride comfort of the semi-active suspension at the same time.

[0236] The optimization algorithm is set with a crossover probability of 0.8, a mutation probability of 0.1, a crossover exponent of 20, a mutation exponent of 20, a population size of 200, and 1000 iterations. The resulting Pareto non-dominated solution set is as follows: Figure 1 As shown:

[0237] 4. Based on the multi-objective optimization model of the energy-rechargeable shock absorber parameters, the optimization solution set is generated. The weights are determined in combination with the vehicle type and ride comfort requirements to obtain the multi-objective optimization solution of the energy-rechargeable shock absorber parameters, and finally the coordinated control of energy recharge and ride comfort parameters of the semi-active suspension is realized.

[0238] The improved NSGA-II algorithm optimizes and matches the important parameters of the energy-feeding shock absorber to obtain the Pareto non-dominated solution set. Then, the weights are determined according to the vehicle type and ride comfort requirements. The optimal solution can be selected according to the specific situation. The weights are determined in the following way.

[0239] First, determine the subjective weights γ of the two objective functions based on the vehicle type and ride comfort requirements. n :

[0240]

[0241] In the above formula, N an It represents the weight given by the a-th person to the n-th objective function.

[0242] The Pareto non-dominated solution set has t solutions. Using two objective functions as evaluation metrics, we obtain matrix S:

[0243] S=(s mn ) t×2 (m=1,2,···,t; n=1,2) (17)

[0244] In the above formula, s mn This represents the element in the m-th row and n-th column of matrix S;

[0245] Normalize matrix S, where the elements s in matrix S are... mn The calculation method for normalization is as follows:

[0246]

[0247] In the above formula, S max Let S be the maximum element in each column of matrix S;

[0248] Calculate the objective weights ω of the two objective functions. n :

[0249]

[0250] In the above formula, v m To calculate intermediate process variables.

[0251] Based on subjective weight γ n and objective weight ω n The comprehensive weight ψ is obtained using two linear combination coefficients. n ;

[0252] ψ n =φ1·ω n +φ2·γ n (20)

[0253] In the above formula, φ1 and φ2 are the linear combination coefficients calculated by the comprehensive weight;

[0254] By assigning weights to each element of the index matrix, we obtain the weighting matrix K.

[0255]

[0256] The minimum value in each column of the weighting matrix As the optimal solution, the maximum value As the worst possible solution;

[0257]

[0258] Calculate the relationship between each solution in the weighted matrix and the optimal solution. distance Each solution and the worst solution distance

[0259]

[0260] Calculate the proximity exponent R between each solution in the Pareto nondominated solution set and the optimal level. m :

[0261]

[0262] The point closest to the maximum exponent is selected as the optimal point, thereby determining the matching of various parameters of the energy-feeding vibration damper.

[0263] Since the above optimization pertains to a semi-active suspension system for a specific vehicle, experts can determine subjective weights based on the ride comfort and energy dissipation requirements of the specific vehicle. Ten experts scored the ride comfort and energy dissipation performance of the semi-active energy-dissipating suspension, resulting in the following table:

[0264] Table 2: Expert Scoring Results

[0265]

[0266] Calculated using Equation 16-24, the top ten solutions in the optimized solution set are shown in the table below:

[0267] Table 3: Top ten solutions in the optimization solution set

[0268]

[0269] Finally, the solution set with sequence number 1 was determined as the matching parameters for the energy-feeding vibration damper.

[0270] The comparison results between the optimal solution and the initial solution are shown in the table below:

[0271] Table 4: Comparison of parameters before and after optimization

[0272]

[0273] A coupled analysis of the energy-feeding damper and the vehicle's two-degree-of-freedom suspension system was performed on the parameters before and after optimization, and the time-domain output curves of the vehicle's vertical acceleration under various road conditions before and after optimization were obtained, as shown in the figure. Figures 2a-2c As shown.

[0274] An experiment was conducted on the electrical output of the energy-feeding vibration damper, and the electrical output curves of the energy-feeding vibration damper before and after optimization were measured as follows: Figure 3 As shown:

[0275] Through experimental and simulation analysis, and after parameter optimization and matching, the vibration reduction performance and energy feeding performance of the energy-feeding damper are balanced, thereby satisfying the coordinated control of energy feeding and ride comfort in semi-active suspension, as shown in Figure 2 and... Figure 3 It can be seen that the root mean square value of the vehicle body vertical acceleration of the energy-recharged shock absorber is reduced by an average of 10.3%, while the energy-recharged power of the shock absorber is increased by 300.6%, and both the damping performance and the energy-recharged performance have been improved to a certain extent.

[0276] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for coordinated control of ride comfort parameters for special vehicles, characterized in that, The method includes the following steps: Step 1: Establish a theoretical model of the energy-feeding vibration damper and determine its vibration reduction and energy feeding characteristics characterization formulas; The theoretical model of the energy-feeding vibration damper mentioned in step 1 includes the road excitation model, the vehicle two-degree-of-freedom system theoretical model, the damper damping force model, and the damper energy-feeding power model. The vibration reduction characteristics in step 1 are characterized by the root mean square value of the sprung mass acceleration of the vehicle, as shown in the following formula; (1) In the above formula, T refers to duration and t refers to time. That is ,express It is a variable that changes over time; The power feeding characteristics in step 1 are characterized by power feeding, as shown in the following formula; (2) In the above formula, It is the output voltage of the motor. It is the electromagnetic torque constant of the generator. It is the rotational angular velocity of the motor rotor. It is the equivalent resistance of the motor armature. It is the output current of the motor. It is the energy feed power of the energy-feeding vibration damper; Step 2: Determine the parameter constraint range of the energy-feeding vibration damper by combining the original design method of the vibration damper; The original design method for the shock absorber in step 2 refers to the design of special vehicles, using relative damping coefficients. The magnitude of the vibration decay rate is used to assess the rate of decay, and the expression is: (3) In the above formula, It is the damping coefficient of the energy-fed vibration damper. It refers to the suspension spring stiffness. It is the sprung mass of the suspension system; The parameter constraint range for the energy-feeding vibration damper in step 2 is determined through parameter sensitivity analysis; Step 3: Based on the vibration reduction and energy feeding characteristics characterization formulas of the energy-feeding vibration damper and its parameter constraint range, establish a multi-objective optimization model for the parameters of the energy-feeding vibration damper; The multi-objective optimization model in step 3 uses the root mean square value of the sprung mass acceleration and the feed power as dual objectives, and adopts the improved NSGA-II algorithm to solve the multi-objective optimization model, thus solving the search failure problem of traditional algorithms in small feasible regions. Step 4: Generate an optimization solution set based on the multi-objective optimization model of the energy-rechargeable shock absorber parameters, determine the weights in combination with vehicle type and ride comfort requirements, and obtain the multi-objective optimization solution of the energy-rechargeable shock absorber parameters, ultimately realizing the coordinated control of energy recharge and ride comfort parameters of the semi-active suspension. The weight determination in step 4 involves first determining the subjective weights of two objective functions—rhythm performance and energy recovery performance—based on vehicle type and ride comfort requirements. : (4) In the above formula, It is the first Personal opinion on the first The weights given by the objective function, It refers to the number of experts; Then, the objective weights of the two objective functions, namely smoothness performance and power feed performance, are calculated. : (5) In the above formula, , To calculate intermediate process variables; Based on subjective weight and objective weight The comprehensive weight is obtained using two linear combination coefficients. ; (6) In the above formula, , The linear combination coefficients are calculated using the comprehensive weights.

2. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 1, characterized in that, Step 1 includes: The road surface excitation model is determined, and a random Gaussian white noise model for road surface excitation is adopted, the expression of which is shown below: (7) In the above formula, It is the road surface excitation speed. It is road surface excitation. It is the lower cutoff frequency. It is the road surface roughness coefficient. It's the vehicle speed. It is uniformly distributed white noise; A theoretical model of a vehicle's two-degree-of-freedom system is established, and the dynamic equations of the vehicle's two-degree-of-freedom suspension system are as follows: (8) In the above formula, It is the damping coefficient of the energy-rechargeable vibration damper. During vehicle operation, the vertical vibration caused by uneven road surface is absorbed by the energy-rechargeable vibration damper and then converted into the rotation of the generator. When the generator rotates, it generates damping force. The higher the speed, the greater the electromagnetic damping. and These represent the sprung mass and unsprung mass of the suspension system, respectively. , , These represent the sprung mass displacement, unsprung mass displacement, and road surface excitation, respectively. Indicates the velocity of the sprung mass. Indicates the acceleration of the sprung mass. Indicates the acceleration of the unsprung mass. and These represent the suspension spring stiffness and wheel stiffness, respectively. The excitation expression for the energy-fed vibration damper is: (9) In the above formula, , , These represent the excitation displacement, excitation velocity, and excitation acceleration of the energy-fed vibration damper, respectively. Indicates the velocity of the unsprung mass; The damping force of an energy-rechargeable vibration damper consists of three parts: inertial force, electromagnetic force, and frictional force. The expression is: (10) In the above formula, Let be the equivalent rotational inertia of each component of the vibration damper. It is the product of the transmission ratios of each stage between the various components of the shock absorber and the lead screw and nut; When the motor of a regenerative vibration damper rotates, it generates electromagnetic torque, which in turn produces electromagnetic damping force. The expression is as follows: (11) (12) In the above formula, This represents the electromagnetic torque of the motor. This represents the product of the transmission ratios of each stage between the vibration damper motor and the lead screw nut. and These represent the reduction ratio of the shock absorber motor and the transmission ratio of the ball screw, respectively. Indicates the lead of the ball screw pair. and These are the generator electromagnetic torque constant and the generator back electromotive force constant, respectively. It is the rotational angular velocity of the motor rotor. and These are the equivalent resistances of the motor armature and the external variable resistor, respectively. This indicates the transmission efficiency of the ball screw pair in the shock absorber; During operation, energy-rechargeable vibration dampers inevitably generate mechanical damping forces due to the relative motion of different components. These mechanical damping forces reflect the internal friction losses of the energy-rechargeable vibration damper, including friction within the ball screw pair, bevel gear pair, and motor reducer, as well as wind resistance and magnetic losses from the motor. It can be represented as: (13) In the above formula, It is Coulomb friction. It is the viscous term of mechanical damping. It is a symbolic function; The total damping force of the energy-fed vibration damper is the sum of the electromagnetic damping force, inertial force, and mechanical damping force mentioned above, that is: (14) In the above formula, It is the total damping force of the energy-fed vibration damper. It is the electromagnetic damping coefficient of the energy-feeding vibration damper. It is the inertial damping coefficient of the energy-fed vibration damper; The equivalent damping coefficient of an energy-fed vibration damper reflects the damper's stiffness, and it can be adjusted by the external load resistance of the damper. Its expression is shown below: (15) The root mean square value of sprung mass acceleration is commonly used to characterize the ride comfort of special vehicles. That is, the smaller the root mean square value of sprung mass acceleration, the better the ride comfort of the special vehicle; the larger the root mean square value of sprung mass acceleration, the worse the ride comfort of the special vehicle. The expression for the root mean square value of sprung mass acceleration is shown in equation (1). Based on the above, a coupled model of the energy-recharged damper and the vehicle's two-degree-of-freedom suspension system is established. The time-domain output curve of the vehicle's sprung mass acceleration based on the semi-active suspension can be obtained, and the root mean square value of the vehicle's sprung mass acceleration can be used as a characterization of the damping characteristics of the energy-recharged damper. The power of the energy-feeding vibration damper is calculated according to formula (2); The energy feeding power of the energy-feeding vibration damper is used as a characterization of its energy feeding characteristics.

3. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 2, characterized in that, In step 2, Designed for special vehicles, using relative damping coefficient The magnitude of the vibration decay rate is used to assess the rate of vibration decay, as shown in equation (3); Through parameter sensitivity analysis, the damping and energy feeding characteristics of the vibration damper were determined to be significantly affected by the reduction ratio of the vibration damper motor. Ball screw pair lead Generator electromagnetic torque constant Generator back electromotive force constant Equivalent resistance of external variable resistor ; By combining the specific parameters of the vehicle suspension with formulas (2) and (14), the reasonable range of values ​​for each optimized parameter of the shock absorber can be obtained.

4. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 3, characterized in that, In the formula (3), The value range is 0.25 to 0.

35.

5. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 3, characterized in that, In step 3, based on the analysis in step 2, the root mean square value of the vehicle's vertical acceleration and the reciprocal of the damper's power feed are selected as the optimization objectives, namely: (16) (17) The specific range of optimized parameters for the energy-rechargeable shock absorber depends on the suspension parameters of the vehicle on which the shock absorber is to be installed. Based on the optimization objective and optimization parameter constraints, the improved NSGA-II algorithm is used to optimize and match the important parameters of the energy-feeding damper, and solutions are selected from the obtained Pareto non-dominated solution set according to certain principles, so that the matched parameters can simultaneously optimize the energy-feeding performance and ride comfort of the semi-active suspension. When constraints are strict and the feasible region is small, the traditional NSGA-II algorithm is prone to failure in searching for feasible solutions. Compared with the traditional NSGA-II algorithm, the improved NSGA-II algorithm introduces "gradient" information into the constraints in the optimization problem so that the program knows how to iterate in the direction of the feasible region.

6. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 5, characterized in that, In step 3, the principle of the improved NSGA-II algorithm is as follows: For each constraint Calculate its boundary surface in the corresponding dimension. and the current sample On the boundary surface S i distance d i ; If x lies in the infeasible region, then the new function is constructed as follows: (18) In the above formula, For distance d i For an increasing function, in order to ensure convergence... The calculation method is as follows: (19) In the above formula, Used to distinguish the fitness of feasible and infeasible solutions. Used to introduce gradient information into infeasible solutions.

7. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 6, characterized in that, In step 3, the improvement of the traditional NSGA-II algorithm can improve the search accuracy for the optimal solution and support the handling of optimization problems with strict constraints and small feasible regions.

8. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 6, characterized in that, In step 4, the improved NSGA-II algorithm optimizes and matches the important parameters of the energy-feeding damper to obtain the Pareto non-dominated solution set. Then, the weights are determined according to the vehicle type and ride comfort requirements, and the optimal solution can be selected according to the specific situation.

9. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 8, characterized in that, In step 4, the weights are determined in the following manner; First, determine the subjective weights of the two objective functions based on the vehicle type and ride comfort requirements. The calculation method is shown in equation (4); Pareto non-dominated solution set has a total of The solution involves using two objective functions as evaluation metrics to obtain a matrix. : (20) In the above formula, Representation matrix The Middle Line number Column elements; For matrix Normalization is performed, where the matrix medium elements The calculation method for normalization is as follows: (21) In the above formula, For matrix The largest element in each column; Calculate the objective weights of the two objective functions according to equation (5). : Based on subjective weight and objective weight The comprehensive weight is obtained using two linear combination coefficients. The calculation method is shown in equation (6); By assigning weights to each element of the index matrix, a weighted matrix is ​​obtained. , (22) The minimum value in each column of the weighting matrix As the optimal solution, the maximum value As the worst possible solution; (23) Calculate the relationship between each solution in the weighted matrix and the optimal solution. distance Each solution and the worst solution distance : (24) Calculate the proximity index of each solution in the Pareto nondominated solution set to the optimal level. : (25) The point closest to the maximum exponent is selected as the optimal point, thereby determining the matching of various parameters of the energy-feeding vibration damper.

10. The method for coordinated control of ride comfort parameters for special vehicles as described in claim 9, characterized in that, The method described above can perform parameter matching of the installed energy-rechargeable shock absorbers according to different vehicle types and ride comfort requirements, thereby taking into account both the damping performance and energy recharge performance of the energy-rechargeable shock absorbers, and thus meeting the coordinated control of energy recharge and ride comfort of semi-active suspensions in different vehicles, maximizing the improvement of ride comfort and energy recharge of semi-active suspensions.

Images