Optimization design method for steering mechanism of digital track rubber wheel train

Abstract

The invention discloses an optimization design method for a steering mechanism of a digital track rubber wheel train, which is used in the field of track traffic and comprises the following steps of: setting boundary conditions of the steering mechanism of the digital track train in an actual operation state based on structural characteristics of the digital track train; a mathematical model containing dynamic coordination and stress balance is constructed; according to various constraint conditions of the digital track rubber wheel train, a target function used for evaluating steering performance is set, and by applying a multi-target intelligent optimization algorithm, an optimization design scheme of a steering mechanism is obtained through analysis and solving according to a mathematical model. According to the method, a dynamic coordination and stress balance mathematical model and a multi-target intelligent optimization algorithm are combined, the design of the steering mechanism is optimized, a genetic algorithm and a particle swarm optimization algorithm are integrated to adapt to different design requirements, and meanwhile, the design accuracy and efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the field of rail transportation, and in particular to a method for optimizing the design of a steering mechanism of a digital rail rubber-tyred train. Background Art

[0002] Rubber-tyred trains are different from traditional rail vehicles that are guided by steel rails. They use rubber tires to contact the ground and achieve self-steering through a steering mechanism. With the help of automatic driving technology, they can run on virtual tracks. As a rubber-tyred standard train, digital rail rubber-tyred trains have self-steering characteristics. Their steering function is achieved by the steering mechanism of the chassis. Digital rail trains consist of 2 power cars and 1 trailer. The power car is equipped with 3 axles and the trailer is equipped with 2 axles. A total of 8 axles require steering coordination.

[0003] At present, the steering mechanism design of this type of vehicle mainly refers to the design method of single-section heavy-duty vehicles. Since the traditional steering mechanism design fails to fully consider multiple factors such as train formation mode, steering control logic, wheel geometric positioning size, train suspension characteristics and driving line conditions, the traditional design concept is not suitable for the steering mechanism design of digital rail rubber-tyred trains.

[0004] Since the design does not take into account the particularities of multi-track trains, the steering mechanism designed will cause abnormal wear of train tires, inconvenience in steering operation for the driver, unbalanced force on the rod system, and in severe cases, mechanism interference will occur.

[0005] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[0006] In order to overcome the above problems, the present invention aims to propose a method for optimizing the design of a steering mechanism for a digital rail rubber-tyred train, with the aim of solving the problem that the traditional design concept is not suitable for the design of a steering mechanism for a digital rail rubber-tyred train, because the traditional steering mechanism design fails to fully consider multiple factors such as train formation mode, steering control logic, wheel geometric positioning dimensions, train suspension characteristics and running line conditions.

[0007] To this end, the specific technical solution adopted by the present invention is as follows:

[0008] A method for optimizing the design of a steering mechanism of a digital rail rubber-tyred train, the method comprising the following steps:

[0009] S1. Based on the structural characteristics of the digital rail vehicle, the boundary conditions of the digital rail train steering mechanism under actual operation are set, and a mathematical model including dynamic coordination and force balance is constructed;

[0010] S2. According to the constraints of the digital rail rubber-tyred train, an objective function for evaluating the steering performance is established, and the optimal design scheme of the steering mechanism is obtained by applying a multi-objective intelligent optimization algorithm and analyzing and solving the mathematical model;

[0011] S3. Use the optimized design scheme to predict the performance of the steering mechanism, and compare and verify it with the initial design scheme. Based on the comparison and verification results, the optimal design scheme for the steering mechanism in the digital rail rubber-wheeled train is obtained.

[0012] Optionally, based on the structural characteristics of the digital-rail vehicle, setting the boundary conditions of the digital-rail train steering mechanism under actual operation, and constructing a mathematical model including dynamic coordination and force balance includes the following steps:

[0013] S11. Collect and analyze the structural data of digital rail vehicles, obtain various states of the vehicles in actual operation based on the analysis results, and determine the key factors affecting the steering performance in various states;

[0014] S12. Based on the key factors affecting the steering performance, set the boundary conditions that the steering mechanism needs to meet under actual operating conditions;

[0015] S13. Based on the known quantities and design variables of the digital rail rubber-tyred train, a mathematical model including the dynamic coordination and force balance of the steering mechanism is established.

[0016] Optionally, the mathematical model is expressed as:

[0017]

[0018] Where, β1 represents the inner wheel angle of one axle; f represents the angle relationship equation of the longitudinally arranged steering mechanism; g1 represents the inner and outer angle relationship equation of the first axle; g2 represents the inner and outer angle relationship equation of the second axle; n1 represents the equivalent swing arm fixed to the inner steering knuckle of one axle; w 01 represents the initial angle of the rocker arm of the first axis; n2 represents the equivalent rocker arm length of the inner steering knuckle of the second axis; w 02 represents the initial angle of the two-axis rocker; m1 represents the arm length of the first axis; γ1 represents the bottom angle of the first axis; m2 represents the arm length of the second axis; γ2 represents the bottom angle of the second axis; β2 represents the inner wheel rotation angle of the second axis; X represents the design variable.

[0019] Optionally, according to various constraints of the digital rail rubber-tyred train, an objective function for evaluating the steering performance is established, and by applying a multi-objective intelligent optimization algorithm, an optimal design scheme of the steering mechanism is obtained by analyzing and solving the mathematical model, including the following steps:

[0020] S21. establishing an objective function for evaluating steering performance according to predefined constraints;

[0021] S22, optimizing the steering angle error weighting function in the steering mechanism using a genetic algorithm according to the steering mechanism kinematic equation, the optimization design objective function and the steering mechanism constraint conditions;

[0022] S23. Use the improved particle swarm algorithm to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism.

[0023] Optionally, the predefined constraints include arm length constraints, bottom angle constraints, mechanism transmission angle constraints, and interference constraints caused by road surface.

[0024] Optionally, the objective function is expressed as:

[0025]

[0026] In the formula, E dis represents the discretized expression of the objective function; w represents the weighting function; X represents the design variable; β 2max Indicates the upper limit angle of the rotation angle to be optimized; β 20 represents the lower limit of the rotation angle to be optimized; n represents the number of discrete intervals of the discretization calculation method; F represents the rotation angle error function; β2 represents the rotation angle of the inner wheel of the second axis; β 2i represents the lower limit angle of the i-th corner to be optimized; β 2n Indicates the lower limit angle of the nth corner to be optimized.

[0027] Optionally, according to the kinematic equation of the steering mechanism, the optimization design objective function and the constraints of the steering mechanism, optimizing the steering angle error weighting function in the steering mechanism by using a genetic algorithm comprises the following steps:

[0028] S221, determining a fitness function to evaluate the turning angle error, combining the difference between the actual and theoretical turning angles, and introducing a weighting factor to reflect the importance of different turning conditions;

[0029] S222. In the target search space of the steering mechanism design parameters, randomly generate parameters of each individual in the initial population, where each individual represents a set of steering mechanism design parameters;

[0030] S223. In the initial population, perform genetic operations on each individual;

[0031] S224, based on the execution results of the genetic operation, evaluate the fitness of the new generation of individuals, and select the individual with the highest fitness to continue optimization;

[0032] S225, repeating steps S223-S224 until a predetermined number of iterations or fitness threshold is reached;

[0033] S226. Extract the individual with the highest fitness as the final optimization result to obtain the optimal steering mechanism design parameters.

[0034] Optionally, using an improved particle swarm algorithm to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism includes the following steps:

[0035] S231, randomly initializing the position and velocity of particles in the defined search space, each particle representing a set of rod size parameters;

[0036] S232, establishing a fitness function to evaluate the performance of the design solution represented by each particle;

[0037] S233, combining the information of individual historical optimal position and global historical optimal position, and using the improved speed update formula to calculate the new speed of each particle;

[0038] S234, calculating the fitness value of each particle after the updated position according to the fitness function;

[0039] S235. For each particle, if the fitness value of the new position of the particle is better than its historical optimal fitness value, then update its historical optimal position; if the fitness value of the new position of any particle exceeds the current global optimal fitness value, then update the global optimal position;

[0040] S236, checking whether the maximum number of iterations or other predefined stop conditions are reached; if the maximum number of iterations or other predefined stop conditions are reached, executing step S237; if the maximum number of iterations or other predefined stop conditions are not reached, returning to step S233;

[0041] S237. Output the particle position with the highest fitness value as the optimal rod size design value of the steering mechanism.

[0042] Optionally, the expression for calculating the new velocity of each particle using the improved velocity update formula is:

[0043]

[0044] In the formula, v ij (t+1) represents the moving speed of the particle in the next iteration calculation; v ij (t) represents the moving speed of the particle in this calculation; c1, c2 and c3 represent acceleration constants; r1, r2 and r3 represent two independent random numbers with a value range of ; p bestij represents the individual's historical optimal position; x ij (t) indicates; g bestj Represents the global optimal historical position.

[0045] Optionally, the expression for calculating the fitness value according to the fitness function is:

[0046]

[0047] Where, E represents the integral expression of the angle error function; represents the integration of the error function within the range from the minimum to the maximum design angle; f t (β2) represents the theoretical angle of the longitudinal steering mechanism; f(X,β2) represents the angle of the longitudinal steering mechanism calculated based on the optimized parameters; g 1t (β1) represents the theoretical angle of the one-axis steering mechanism; g1(X,β1) represents the angle of the one-axis steering mechanism calculated based on the optimized parameters; d represents the integral sign; β2 represents the numerical value of the steering mechanism angle; g 2t (β2) represents the theoretical steering angle of the two-axis steering mechanism; g2(X, β2) represents the steering angle of the two-axis steering mechanism calculated based on the optimized parameters; F(X, β2) represents the total steering angle error function.

[0048] Compared with the prior art, the present application has the following beneficial effects: the present invention combines the mathematical model of dynamic coordination and force balance with a multi-objective intelligent optimization algorithm to optimize the steering mechanism design, integrates the genetic algorithm and the particle swarm algorithm to adapt to different design requirements, and at the same time improves the accuracy and efficiency of the design, ensuring that through comprehensive evaluation and repeated iterations, the steering mechanism design scheme with the best performance and meeting the actual application requirements is obtained, and the complex design variables and various operating conditions are effectively handled; not only the structural characteristics of the digital track vehicle and the boundary conditions under the actual operating state are considered, but also the scientificity and practicality of the design scheme are ensured by constructing a mathematical model including dynamic coordination and force balance, and the combination of the genetic algorithm and the improved particle swarm algorithm can fully explore the design space and accurately optimize the size parameters of each rod system in the steering mechanism, thereby significantly improving the steering performance; in addition, by establishing a fitness function and a weighting factor, the importance of different steering conditions can be flexibly responded to, making the design scheme more targeted. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The above characteristics, features and advantages of the present invention and their implementation methods and methods will become more clearly understood in conjunction with the following description of the embodiments, which are described in detail in conjunction with the accompanying drawings. Herein, a schematic diagram is shown:

[0050] Figure 1 is a flow chart of a method for optimizing the design of a steering mechanism for a digital rail rubber-tyred train according to an embodiment of the present invention;

[0051] Figure 2 It is a flow chart of a multi-objective intelligent optimization algorithm in a method for optimizing the design of a steering mechanism of a digital rail rubber-tyred train according to an embodiment of the present invention;

[0052] Figure 3 It is a schematic diagram of a single-axle steering mechanism in a method for optimizing the steering mechanism of a digital rail rubber-tyred train according to an embodiment of the present invention;

[0053] Figure 4 is a schematic diagram of a longitudinal link mechanism in a method for optimizing the design of a steering mechanism for a digital rail rubber-tyred train according to an embodiment of the present invention;

[0054] Figure 5 The invention discloses a simplified model of digital track train steering in a method for optimizing the steering mechanism of a digital track rubber-tyred train according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0056] According to an embodiment of the present invention, a method for optimizing the design of a steering mechanism of a digital rail rubber-tyred train is provided.

[0057] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1-Figure 2 As shown, according to the digital rail rubber-tyred train steering mechanism optimization design method of the embodiment of the present invention, the digital rail rubber-tyred train steering mechanism optimization design method comprises the following steps:

[0058] S1. Based on the structural characteristics of the digital-rail vehicle, the boundary conditions of the digital-rail train steering mechanism under actual operating conditions are set, and a mathematical model including dynamic coordination and force balance is constructed.

[0059] Preferably, based on the structural characteristics of the digital rail vehicle, setting the boundary conditions of the digital rail train steering mechanism under the actual operating state and constructing a mathematical model including dynamic coordination and force balance includes the following steps:

[0060] S11. Collect and analyze the structural data of digital rail vehicles, obtain various states of the vehicles in actual operation based on the analysis results, and determine the key factors affecting the steering performance in various states;

[0061] S12. Based on the key factors affecting the steering performance, set the boundary conditions that the steering mechanism needs to meet under actual operating conditions;

[0062] S13. Based on the known quantities and design variables of the digital rail rubber-tyred train, a mathematical model including the dynamic coordination and force balance of the steering mechanism is established.

[0063] Preferably, the mathematical model is expressed as:

[0064]

[0065] Where, β1 represents the inner wheel angle of one axle; f represents the angle relationship equation of the longitudinally arranged steering mechanism; g1 represents the inner and outer angle relationship equation of the first axle; g2 represents the inner and outer angle relationship equation of the second axle; n1 represents the equivalent swing arm fixed to the inner steering knuckle of one axle; w 01 represents the initial angle of the rocker arm of the first axis; n2 represents the equivalent rocker arm length of the inner steering knuckle of the second axis; w 02 represents the initial angle of the two-axis rocker; m1 represents the arm length of the first axis; γ1 represents the bottom angle of the first axis; m2 represents the arm length of the second axis; γ2 represents the bottom angle of the second axis; β2 represents the inner wheel rotation angle of the second axis; X represents the design variable.

[0066] It should be explained that the independent parameters selected and finally optimized in the design process are called design variables. Those that do not need to be optimized or have been determined before optimization are called known quantities. The following describes the known quantities and design variables separately:

[0067] 1) Variable definition

[0068] The known quantities in this patent are:

[0069] The main pin distances K1 and K2 in the action plane of the first and second axes;

[0070] The coordinate values ​​of O1 and O2 (x o1 ,y o1 ), (x o2 ,y o2 );

[0071] The design variables in the present invention are:

[0072] The equivalent rocker arm length n1 of the inner steering knuckle of the first axle, the initial angle w of the rocker arm of the first axle 01 , the equivalent rocker arm length n2 of the inner steering knuckle of the second axis and the initial angle w of the rocker of the second axis 02 The first-axis arm length m1, the first-axis bottom angle γ1, the second-axis arm length m2, and the second-axis bottom angle γ2 of the mechanism are expressed in vector form as follows:

[0073] X=[n1,w 01 ,n2,w 02 ,m1,γ1,m2,γ2] T ;

[0074] Combined with the previous text, the longitudinal linkage mechanism model is combined with the front and rear mechanism models to establish the overall mathematical model of the dual front axle steering system, and the following can be obtained:

[0075]

[0076] Where β=[β1,α1,α2] T ; β1 is the rotation angle of the inner wheel of one axis, α1 is the rotation angle of the outer wheel of one axis, and α2 is the rotation angle of the outer wheel of two axes.

[0077] S2. According to the constraints of the digital rail rubber-tyred train, an objective function for evaluating the steering performance is established. By applying a multi-objective intelligent optimization algorithm, the optimal design scheme of the steering mechanism is obtained based on the mathematical model analysis and solution.

[0078] Preferably, according to various constraints of the digital rail rubber-tyred train, an objective function for evaluating the steering performance is established, and by applying a multi-objective intelligent optimization algorithm, an optimal design scheme for the steering mechanism is obtained according to a mathematical model analysis and solution, including the following steps:

[0079] S21. According to predefined constraints, an objective function for evaluating steering performance is established.

[0080] Preferably, the objective function is expressed as:

[0081]

[0082] In the formula, E dis represents the discretized expression of the objective function; w represents the weighting function; X represents the design variable; β 2max Indicates the upper limit angle of the rotation angle to be optimized; β 20 represents the lower limit of the rotation angle to be optimized; n represents the number of discrete intervals of the discretization calculation method; F represents the rotation angle error function; β2 represents the rotation angle of the inner wheel of the second axis; β 2i represents the lower limit angle of the i-th corner to be optimized; β 2n Indicates the lower limit angle of the nth corner to be optimized.

[0083] The predefined constraints are as follows:

[0084] In the design of the steering mechanism, the main parameters are the arm length m and the base angle γ. Considering their value range and the transmission angle of the mechanism, three constraints can be obtained:

[0085] Arm length m∈(0.11K, 0.16K); base angle γ∈(70°, 90°); mechanism transmission angle δ≥40°;

[0086] When the wheel on one side of the steering mechanism turns to the limit position, the transmission angle on the other side reaches the minimum value, so only one side needs to be considered to have the maximum steering. The trapezoidal mechanism is a four-bar linkage. According to the mechanical principle, its transmission angle δ should not be too small, usually δ ≥ 30°. According to the geometric relationship, the expression of the minimum transmission angle constraint condition is as follows:

[0087]

[0088] Among them, m represents the length of the trapezoidal arm of the steering mechanism, K represents the kingpin distance, α max Indicates the maximum turning angle of the outer steering wheel, δ min =30°; γ represents the bottom angle of the steering mechanism trapezoid, α max Indicates the maximum turning angle of the outer steering wheel, δ min =30 indicates the minimum transmission angle.

[0089] Abnormal wear of a vehicle during driving is caused by the interference between the steering system and the suspension when the vehicle turns on a bad road surface; therefore, while optimizing the steering mechanism, the amount of interference caused by the road surface should also be taken as a design target.

[0090]

[0091] Where x i ,y i 、z i The limit values ​​of the offset of each point of the steering mechanism are obtained by dynamic simulation analysis of multi-track trains on different grades of road surfaces.

[0092] The optimization objective function is as follows:

[0093] When designing a steering system, the curve of its realization function should be as consistent as possible with the given theoretical curve; the theoretical turning angle expression can be derived:

[0094]

[0095] The equivalent rocker arm length n1 of the inner steering knuckle of the first axle, the initial angle w of the rocker arm of the first axle 01 , the equivalent rocker arm length n2 of the inner steering knuckle of the second axis and the initial angle w of the rocker of the second axis 02 The first-axis arm length m1, the first-axis bottom angle γ1, the second-axis arm length m2, and the second-axis bottom angle γ2 of the mechanism are expressed in vector form as follows:

[0096] X=[n1,w 01 ,n2,w 02 ,m1,γ1,m2,γ2] T ;

[0097] The mathematical model of the theoretical rotation angle can be expressed as:

[0098]

[0099] Among them, β 1t is the theoretical rotation angle of the inner wheel of an axle, α 1t is the theoretical rotation angle of the outer wheel of one shaft, α 2t The theoretical turning angle of the outer wheel of the second axle.

[0100] The objective function of the optimization design can be taken as the deviation E between the theoretical rotation angle and the actual rotation angle curve, and expressed as the integral of the square of the difference between the two curves:

[0101]

[0102] According to the actual driving conditions, it is usually required that the error near the small turning angle position of the steering mechanism is smaller than the error near the extreme turning angle position, so as to reduce the wear of the tire when the steering mechanism is in the common position or the common turning angle of the wheel (usually the vehicle speed is also high); this requirement can be met by the weighting function w(β2); usually β2 is in the common area [β 20 ,10°], the actual turning angle β1 given by the steering mechanism is required to be consistent with the expected value β 1t The phase difference should not be greater than 0.3°, and in the extreme region [15°, β 2max ] The internal rotation angle error shall not exceed 1°; if the angle error is allowed to be linearly related to the error E, the weighting function can be taken as:

[0103]

[0104] Then we have:

[0105]

[0106] Use the area method to find the approximate value of the integral of the above formula, and divide the integral interval into n equal small intervals, each small interval is

[0107] S22. According to the kinematic equation of the steering mechanism, the optimization design objective function and the constraints of the steering mechanism, a genetic algorithm is used to optimize the weighted function of the steering angle error in the steering mechanism.

[0108] Preferably, the predefined constraints include arm length constraints, bottom angle constraints, mechanism transmission angle constraints and interference constraints caused by road surface.

[0109] Preferably, according to the kinematic equation of the steering mechanism, the optimization design objective function and the constraints of the steering mechanism, optimizing the steering angle error weighting function in the steering mechanism by using a genetic algorithm comprises the following steps:

[0110] S221, determining a fitness function to evaluate the turning angle error, combining the difference between the actual and theoretical turning angles, and introducing a weighting factor to reflect the importance of different turning conditions;

[0111] S222. In the target search space of the steering mechanism design parameters, randomly generate parameters of each individual in the initial population, where each individual represents a set of steering mechanism design parameters;

[0112] S223. In the initial population, perform genetic operations on each individual;

[0113] S224, based on the execution results of the genetic operation, evaluate the fitness of the new generation of individuals, and select the individual with the highest fitness to continue optimization;

[0114] S225, repeating steps S223-S224 until a predetermined number of iterations or fitness threshold is reached;

[0115] S226. Extract the individual with the highest fitness as the final optimization result to obtain the optimal steering mechanism design parameters.

[0116] It should be explained that the particle swarm parameters c1 and c2 are initialized, the position boundary range and the speed boundary range are set, the particle swarm population is initialized, and the particle swarm speed is initialized; based on the optimization goal of the steering mechanism, an improved particle swarm fitness function is designed. In order to further reduce the steering mechanism angle error, β 20 and β 2max Genetic algorithm is used for optimization to obtain the optimal design dimensions of the steering mechanism under the optimal steering angle range.

[0117] S23. Use the improved particle swarm algorithm to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism.

[0118] Preferably, the improved particle swarm algorithm is used to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism, which includes the following steps:

[0119] S231, randomly initializing the position and velocity of particles in the defined search space, each particle representing a set of rod size parameters;

[0120] S232, establishing a fitness function to evaluate the performance of the design solution represented by each particle;

[0121] S233, combining the information of individual historical optimal position and global historical optimal position, and using the improved speed update formula to calculate the new speed of each particle;

[0122] S234, calculating the fitness value of each particle after the updated position according to the fitness function;

[0123] S235. For each particle, if the fitness value of the new position of the particle is better than its historical optimal fitness value, then update its historical optimal position; if the fitness value of the new position of any particle exceeds the current global optimal fitness value, then update the global optimal position;

[0124] S236, checking whether the maximum number of iterations or other predefined stop conditions are reached; if the maximum number of iterations or other predefined stop conditions are reached, executing step S237; if the maximum number of iterations or other predefined stop conditions are not reached, returning to step S233;

[0125] S237. Output the particle position with the highest fitness value as the optimal rod size design value of the steering mechanism.

[0126] Preferably, the expression for calculating the new velocity of each particle using the improved velocity update formula is:

[0127]

[0128] In the formula, v ij (t+1) represents the moving speed of the particle in the next iteration calculation; v ij (t) represents the moving speed of the particle in this calculation; c1, c2 and c3 represent acceleration constants; r1, r2 and r3 represent two independent random numbers with a value range of ; p bestij represents the individual's historical optimal position; x ij (t) indicates; g bestj Represents the global historical optimal position.

[0129] Preferably, the expression for calculating the fitness value according to the fitness function is:

[0130]

[0131] Where, E represents the integral expression of the angle error function; represents the integration of the error function within the range from the minimum to the maximum design angle; f t (β2) represents the theoretical angle of the longitudinal steering mechanism; f(X,β2) represents the angle of the longitudinal steering mechanism calculated based on the optimized parameters; g 1t (β1) represents the theoretical angle of the one-axis steering mechanism; g1(X,β1) represents the angle of the one-axis steering mechanism calculated based on the optimized parameters; d represents the integral sign; β2 represents the numerical value of the steering mechanism angle; g 2t (β2) represents the theoretical steering angle of the two-axis steering mechanism; g2(X, β2) represents the steering angle of the two-axis steering mechanism calculated based on the optimized parameters; F(X, β2) represents the total steering angle error function.

[0132] It needs to be explained that according to the kinematic equation of the steering mechanism, the optimization design objective function and the constraints of the steering mechanism, the genetic algorithm can be used to optimize the weighted function of the steering angle error in the optimization design, and then the improved particle swarm algorithm can be used to optimize the dimensions of each rod system of the steering mechanism to obtain the optimal design value of the steering mechanism.

[0133] The improved particle swarm algorithm is used to optimize the dimensions of each rod system of the steering mechanism:

[0134] 1) Particle and velocity initialization

[0135] In a D-dimensional target search space, a particle swarm is composed of N particles, where each particle is a D-dimensional vector and its spatial position is expressed as:

[0136] x i ={x i1 ,x i2 ,…,x iD}, i = 1, 2, ..., N;

[0137] The spatial position of a particle is a solution to the target optimization problem. By substituting it into the fitness function, the fitness value can be calculated, and the quality of the particle can be measured according to the size of the fitness value.

[0138] The flying speed of the i-th particle is also a D-dimensional vector, recorded as:

[0139] v i = {v i1 ,v i2 ,…,v iD}, i = 1, 2, ..., N;

[0140] The particle positions and velocities are randomly generated within a given range.

[0141] 2) Individual historical optimality and global optimality

[0142] The position with the best fitness value that the i-th particle has experienced is called the individual historical optimal position, which is recorded as:

[0143] p besti ={p besti1 ,p besti2 ,…,p bestiD}, i = 1, 2, ..., N;

[0144] The optimal position experienced by the entire particle swarm is called the global historical optimal position, which is recorded as:

[0145] g besti = {g best1 ,g best2 ,…,g bestD}, i = 1, 2, ..., N;

[0146] 3) Update the velocity and position of the particle swarm

[0147] The position update operation of a particle swarm can be represented by velocity update and position update.

[0148] Improved speed updates:

[0149] v ij (t+1)=v ij (t)+c1r1(p bestij -x ij (t))+c2r2(g bestj -x ij (t))+c3r3(g bestj -p bestij );

[0150] The location is updated to:

[0151] x ij (t+1)=xi j (t)+v ij (t+1);

[0152] Among them, subscript j represents the jth dimension of the particle, subscript i represents the ith particle, t represents the number of current iterations, c1, c2 and c3 are acceleration constants, which usually take values ​​in the interval (0,2), r1, r2 and r3 are two independent random numbers with a value range of [0,1]; c1 and c2 combine the particle's learning from individuals and learning from the group, so that the particle can learn from the individual's own search experience and the group's search experience.

[0153] Calculate the fitness value according to the fitness function and record the historical optimal value p best and the global optimal value g best ;

[0154] Use the speed update formula to update the speed of the particle group and constrain the speed that exceeds the limit;

[0155] Use the position update formula to update the position of the particle swarm and constrain the out-of-bounds position;

[0156] Calculate the fitness value according to the fitness function;

[0157] For each particle, compare its fitness value with its historical optimal fitness value. If it is better, take it as the historical optimal value p best ;

[0158] For each particle, compare its fitness value with the fitness value of the optimal position experienced by the group. If it is better, it will be taken as the global optimal value gbest ;

[0159] Determine whether the end condition is reached (the maximum number of iterations is reached). If so, output the optimal position, otherwise repeat the previous steps;

[0160] In this calculation, the number of population particles is set to 200, the dimension of each particle is 2, the speed update parameters c1 and c2 are both 2, and the number of iterative evolutions of the algorithm is 200.

[0161] S3. Use the optimized design scheme to predict the performance of the steering mechanism, and compare and verify it with the initial design scheme. Based on the comparison and verification results, the optimal design scheme for the steering mechanism in the digital rail rubber-wheeled train is obtained.

[0162] Specific examples are as follows:

[0163] The structure of the steering mechanism of a multi-track train is different according to the different trailers. It includes two types: double-axle steering and single-axle steering. The double-axle steering mechanism consists of two sets of single-axle steering mechanisms and a longitudinal coordination mechanism that interconnects them.

[0164] The single-axis steering mechanism can be regarded as a planar quadrilateral mechanism. The simplified model is as follows: Figure 3 As shown:

[0165] Among them, A and B are the rotation centers of the mechanism on the kingpin; K is the kingpin distance in the action plane of the mechanism; AE and BF are the left and right arms respectively, with arm lengths of m; EF is the steering tie rod, with a rod length of H; ∠BAE and ∠ABF are the base angles, recorded as γ; when the inner wheel rotates arbitrarily through an angle of β, the mechanism ABFE becomes ABF'E', and the corresponding outer wheel rotates through α; ​​in order to study the relationship between the inner wheel angle and the outer wheel angle, connect AF', and the length is set to d; then:

[0166] α=∠E′AF′+∠F′AB-γ;

[0167] According to the triangular relationship,

[0168]

[0169] H = K1-2mcosγ;

[0170]

[0171]

[0172] Then α=cos -1 δ1+cos -1 δ2-γ;

[0173] The longitudinal linkage mechanism between the first and second axes is a planar quadrilateral mechanism, such as Figure 4 As shown in the figure, O1C1 is the equivalent swing arm fixedly connected to the inner steering knuckle of an axle, O1 is the equivalent rotation center of the steering knuckle, the equivalent swing arm length is n1, and the initial angle is w 01 ; O2C2 is the equivalent swing arm fixed to the inner steering knuckle of the second axis, O2 is the equivalent rotation center of the steering knuckle, the equivalent swing arm length is n2, and the initial angle is w 02 ; C1C2 is a connecting rod, length is S 2 To derive the relationship between the first axis vertical arm rotation angle θ1 and the second axis vertical arm rotation angle θ2, draw lines O1C2 and O2C1, and assume And draw perpendicular lines C1C1′ and C2C2′ through C1 and C2 respectively, with C1′ and C2′ as the feet of the perpendicular.

[0174] According to the triangular relationship, we have:

[0175] In ΔC1O1C2:

[0176]

[0177] In ΔO1O2C2:

[0178]

[0179] From the above formula we get:

[0180]

[0181] The equivalent rocker arm length n1 of the inner steering knuckle of the first axle, the initial angle w of the rocker arm of the first axle 01 , the equivalent rocker arm length n2 of the inner steering knuckle of the second axis and the initial angle w of the rocker of the second axis 02 The first-axis arm length m1, the first-axis bottom angle γ1, the second-axis arm length m2, and the second-axis bottom angle γ2 of the mechanism are expressed in vector form as follows:

[0182] X=[n1,w 01 ,n2,w 02 ,m1,γ1,m2,γ2] T ;

[0183] By combining the longitudinal linkage model with the front and rear mechanism models, the overall mathematical model of the dual front axle steering system can be established, and the following can be obtained:

[0184]

[0185] Among them, β1 is a function of β2. The specific expansion equation is:

[0186]

[0187] In order to obtain the relationship between the rotation angles of each axle when the train turns, the train turning model is simplified. First, the left and right wheels of the train are simplified to an equivalent wheel at the center of the axle, and an imaginary wheel is added at the hinge point. The speed direction of the imaginary wheel is consistent with the speed direction at the hinge point. According to the basic principle of Ackerman steering, the following is obtained: Figure 5 The simplified steering model shown. In the figure, the blue thick solid line represents the three-section car body, the orange thick solid line represents the articulated device, the red line represents the imaginary wheel at the workshop articulation, the black thick solid line represents the simplified axle center equivalent wheel, O1, O2, O3 are the steering centers of the three-section car, δ1, δ3, δ4, δ5, δ6, δ8 represent the axle angles, δ11 represents the steering angle of the imaginary wheel at the first articulation point relative to the first car, δ12 represents the steering angle of the imaginary wheel at the first articulation point relative to the second car, δ 22 represents the steering angle of the imaginary wheel at the second hinge point relative to the second car, δ 23 It represents the steering angle of the imaginary wheel at the second hinge point relative to the third car, and the counterclockwise direction is the positive direction of each steering angle.

[0188] According to the simplified steering model, the basic relationship between the workshop articulation angle and the imaginary wheel steering angle at the articulation is:

[0189] θ 12 =δ 12 -δ 11 ;

[0190] θ 23 =δ 23 -δ 22 ;

[0191] where θ 12 ,θ 23 They represent the angle between the first and second carriages, and the angle between the second and third carriages respectively.

[0192] According to the simplified steering model, the basic geometric relationship of the vehicle's axle angles can be obtained through geometric deduction.

[0193] 3rd axis rotation:

[0194]

[0195] 4th axis rotation angle:

[0196]

[0197]

[0198] 5th axis rotation angle:

[0199]

[0200] 6th axis rotation angle:

[0201]

[0202] Among them, L 13 The wheelbase of the 1st and 3rd axles; L 68 The wheelbase of the 6th and 8th axles; L 1J1 L is the distance from the first axis to the first workshop hinge point; J14 L is the distance from the first workshop hinge point to the 4th axis; 5J2 L is the distance from the 5th axis to the second workshop hinge point; J28 L is the distance from the second workshop hinge point to the 8th axis; J1J2 is the distance between the two hinge points.

[0203] The digital track train has a steering longitudinal tie rod connected to the right steering knuckle of the 1st and 2nd axles. When the 1st axle is controlled to steer, the 2nd axle is driven to steer through the steering longitudinal tie rod at the same time. This is a traditional mechanical coordinated steering, so that the steering angles of the 1st and 2nd axles have a steering coordination relationship. In actual steering control, in order to make the vehicle meet the basic principle of Ackerman steering when steering, the wheels can do pure rolling and reduce wheel wear, the steering coordination relationship between the 1st and 2nd axles will be different depending on the control strategy. This patent develops two control modes of steering angle coordination relationships:

[0204] (1) The geometric center of the 1st axis and the 1st and 2nd car articulation is the reference point for tracking control

[0205] When the geometric center of the 1st axle and the 1st and 2nd car articulation is the reference point for tracking control, the instantaneous center of the speed of the first car is determined by the 1st axle angle and the imaginary wheel angle at the articulation. At this time, the 2nd axle angle can be determined according to the basic principle of Ackerman steering.

[0206] According to the simplified steering model, the coordination relationship between the 1st and 2nd axis steering can be derived:

[0207]

[0208] (2) The geometric center of axis 1 and axis 3 is the reference point for tracking control

[0209] When the geometric centers of axis 1 and axis 3 are the reference points for tracking control, the instantaneous center of speed of the first vehicle is determined by the turning angles of axis 1 and axis 3. At this time, the turning angle of axis 2 can be determined according to the basic principle of Ackermann steering.

[0210] Similarly, the steering coordination relationship between the 1st and 2nd axes can be derived based on the simplified steering model:

[0211]

[0212] In summary, with the help of the above technical scheme of the present invention, the present invention combines the mathematical model of dynamic coordination and force balance and the multi-objective intelligent optimization algorithm to optimize the steering mechanism design, integrates the genetic algorithm and the particle swarm algorithm to adapt to different design requirements, and at the same time improves the accuracy and efficiency of the design, ensuring that through comprehensive evaluation and repeated iterations, the steering mechanism design scheme with the best performance and meeting the actual application requirements is obtained, and the complex design variables and various operating conditions are effectively handled; not only the structural characteristics of the digital track vehicle and the boundary conditions under the actual operating state are considered, but also by constructing a mathematical model including dynamic coordination and force balance, the scientificity and practicality of the design scheme are ensured, and the combination of the genetic algorithm and the improved particle swarm algorithm can fully explore the design space, accurately optimize the size parameters of each rod system in the steering mechanism, thereby significantly improving the steering performance; in addition, by setting up the fitness function and the weighting factor, the importance of different steering conditions can be flexibly responded to, making the design scheme more targeted.

[0213] Although the present invention has been disclosed as above with preferred embodiments, the embodiments are merely examples for the convenience of description and are not intended to limit the present invention. Those skilled in the art may make several changes and modifications without departing from the spirit and scope of the present invention. The scope of protection claimed by the present invention shall be based on the claims.

Claims

1. A method for optimizing the steering mechanism of a digital rail rubber-tyred train, characterized in that: The optimization design method of the steering mechanism of the digital rail rubber-tyred train comprises the following steps: S1. Based on the structural characteristics of the digital rail vehicle, the boundary conditions of the digital rail train steering mechanism under actual operation are set, and a mathematical model including dynamic coordination and force balance is constructed; S2. According to the constraints of the digital rail rubber-tyred train, an objective function for evaluating the steering performance is established, and the optimal design scheme of the steering mechanism is obtained by applying a multi-objective intelligent optimization algorithm and analyzing and solving the mathematical model; S3. Use the optimized design scheme to predict the performance of the steering mechanism, and compare and verify it with the initial design scheme. Based on the comparison and verification results, the optimal design scheme for the steering mechanism in the digital rail rubber-wheeled train is obtained.

2. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 1 is characterized in that: The method of setting the boundary conditions of the steering mechanism of the digital rail train under actual operation state based on the structural characteristics of the digital rail vehicle and constructing a mathematical model including dynamic coordination and force balance includes the following steps: S11. Collect and analyze the structural data of digital rail vehicles, obtain various states of the vehicles in actual operation based on the analysis results, and determine the key factors affecting the steering performance in various states; S12. Based on the key factors affecting the steering performance, set the boundary conditions that the steering mechanism needs to meet under actual operating conditions; S13. Based on the known quantities and design variables of the digital rail rubber-tyred train, a mathematical model including the dynamic coordination and force balance of the steering mechanism is established.

3. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 2 is characterized in that: The mathematical model is expressed as: Where, β1 represents the inner wheel angle of one axle; f represents the angle relationship equation of the longitudinally arranged steering mechanism; g1 represents the inner and outer angle relationship equation of the first axle; g2 represents the inner and outer angle relationship equation of the second axle; n1 represents the equivalent swing arm fixed to the inner steering knuckle of one axle; w 01 represents the initial angle of the rocker arm of the first axis; n2 represents the equivalent rocker arm length of the inner steering knuckle of the second axis; w 02 represents the initial angle of the two-axis rocker; m1 represents the arm length of the first axis; γ1 represents the bottom angle of the first axis; m2 represents the arm length of the second axis; γ2 represents the bottom angle of the second axis; β2 represents the inner wheel rotation angle of the second axis; X represents the design variable.

4. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 1 is characterized in that: The objective function for evaluating the steering performance is established according to various constraints of the digital rail rubber-tyred train, and the optimal design scheme of the steering mechanism is obtained by applying a multi-objective intelligent optimization algorithm and analyzing and solving the mathematical model, which includes the following steps: S21. establishing an objective function for evaluating steering performance according to predefined constraints; S22, optimizing the steering angle error weighting function in the steering mechanism using a genetic algorithm according to the steering mechanism kinematic equation, the optimization design objective function and the steering mechanism constraint conditions; S23. Use the improved particle swarm algorithm to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism.

5. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 4 is characterized in that: The predefined constraint conditions include arm length constraint, bottom angle constraint, mechanism transmission angle constraint and interference constraint caused by road surface.

6. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 5 is characterized in that: The expression of the objective function is: In the formula, E dis represents the discretized expression of the objective function; w represents the weighting function; X represents the design variable; β 2max Indicates the upper limit angle of the rotation angle to be optimized; β 20 represents the lower limit angle of the rotation angle to be optimized; n represents the number of discrete intervals of the discretization calculation method; F represents the rotation angle error function; β2 represents the inner wheel rotation angle of the second axle; β 2i represents the lower limit angle of the i-th corner to be optimized; β 2n Indicates the lower limit angle of the nth corner to be optimized.

7. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 6 is characterized in that: The method of optimizing the steering angle error weighting function in the steering mechanism by using a genetic algorithm according to the steering mechanism kinematic equation, the optimization design objective function and the steering mechanism constraint conditions comprises the following steps: S221, determining a fitness function to evaluate the turning angle error, combining the difference between the actual and theoretical turning angles, and introducing a weighting factor to reflect the importance of different turning conditions; S222. In the target search space of the steering mechanism design parameters, randomly generate parameters of each individual in the initial population, where each individual represents a set of steering mechanism design parameters; S223. In the initial population, perform genetic operations on each individual; S224, based on the execution results of the genetic operation, evaluate the fitness of the new generation of individuals, and select the individual with the highest fitness to continue optimization; S225, repeating steps S223-S224 until a predetermined number of iterations or fitness threshold is reached; S226. Extract the individual with the highest fitness as the final optimization result to obtain the optimal steering mechanism design parameters.

8. The method for optimizing the steering mechanism of a digital track rubber-tyred train according to claim 7 is characterized in that: The method of using the improved particle swarm algorithm to optimize the size parameters of each rod system in the steering mechanism to obtain the optimal design value of the steering mechanism includes the following steps: S231, randomly initializing the position and velocity of particles in the defined search space, each particle representing a set of rod size parameters; S232, establishing a fitness function to evaluate the performance of the design solution represented by each particle; S233, combining the information of individual historical optimal position and global historical optimal position, and using the improved speed update formula to calculate the new speed of each particle; S234, calculating the fitness value of each particle after the updated position according to the fitness function; S235. For each particle, if the fitness value of the new position of the particle is better than its historical optimal fitness value, then update its historical optimal position; if the fitness value of the new position of any particle exceeds the current global optimal fitness value, then update the global optimal position; S236, checking whether the maximum number of iterations or other predefined stop conditions are reached; if the maximum number of iterations or other predefined stop conditions are reached, executing step S237; if the maximum number of iterations or other predefined stop conditions are not reached, returning to step S233; S237. Output the particle position with the highest fitness value as the optimal rod size design value of the steering mechanism.

9. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 8 is characterized in that: The expression for calculating the new velocity of each particle using the improved velocity update formula is: In the formula, v ij (t+1) represents the moving speed of the particle in the next iteration calculation; v ij (t) represents the moving speed of the particle in this calculation; c1, c2 and c3 represent acceleration constants; r1, r2 and r3 represent two independent random numbers with a value range of ; p bestij represents the individual's historical optimal position; x ij (t) indicates; g bestj Represents the global historical optimal position.

10. The method for optimizing the steering mechanism of a digital rail rubber-tyred train according to claim 9, characterized in that: The expression for calculating the fitness value according to the fitness function is: Where, E represents the integral expression of the angle error function; represents the integration of the error function within the range from the minimum to the maximum design angle; f t (β2) represents the theoretical angle of the longitudinal steering mechanism; f(X,β2) represents the angle of the longitudinal steering mechanism calculated based on the optimized parameters; g 1t (β1) represents the theoretical angle of the one-axis steering mechanism; g1(X,β1) represents the angle of the one-axis steering mechanism calculated based on the optimized parameters; d represents the integral sign; β2 represents the numerical value of the steering mechanism angle; g 2t (β2) represents the theoretical steering angle of the two-axis steering mechanism; g2(X, β2) represents the steering angle of the two-axis steering mechanism calculated based on the optimized parameters; F(X, β2) represents the total steering angle error function.

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