Suspension system and method based on natural coordinate modeling

Abstract

The invention discloses a suspension system and method based on natural coordinate modeling. The suspension system is used for identifying suspension hard point parameters and comprises a kinematic model, a suspension sensitivity analysis and calculation model and a suspension hard point parameter identification module. A kinematic model of a suspension multi-rigid-body system is established based on a natural coordinate method, the number of generalized coordinates in the model derivation process is reduced, the model derivation process is simplified, and the model solving speed is increased. An adjoint variable method is adopted to solve the sensitivity value of the suspension hard point natural coordinates to the suspension kinematics characteristic parameters, direct calculation of derivatives is avoided by introducing additional variables, and the solving complexity is reduced. And a group of design variables which have great influence on the kinematics characteristics of the suspension system are screened out according to the sensitivity analysis result, so that the calculation amount of an identification algorithm is reduced. And a BFGS variable scale optimization algorithm and a golden section method are adopted, so that the optimality of parameter identification is ensured, and a high-precision hard point coordinate identification result is output while the calculated amount is small.

Description

Technical Field

[0001] The present invention relates to the technical field of automobile chassis suspension systems, and in particular to a suspension system and method based on natural coordinate modeling. Background Art

[0002] The suspension system, a crucial component of the vehicle structure, encompasses all components involved in transmitting and connecting forces and torques between the vehicle's frame and axles. The suspension's function is to transfer ground forces and torques to the vehicle frame, cushion the impact of road surface irregularities, and reduce vibrations caused by these impacts, thereby ensuring smooth vehicle operation. Suspension hardpoints, also known as rigid connection points, are crucial structural components of the vehicle suspension system, connecting suspension components (such as shock absorbers and wheels) to the vehicle body. Proper placement of suspension hardpoints is crucial for ensuring optimal kinematic characteristics. Hardpoint location impacts performance parameters such as suspension stiffness and wheel angle, ultimately impacting vehicle ride comfort. Improper hardpoint placement can also lead to front wheel shimmy and swerve, exacerbating tire wear. Therefore, optimally selecting suspension hardpoint parameters to achieve ideal kinematic characteristics is crucial during suspension design.

[0003] Currently, numerous software programs exist for calculating vehicle performance parameters based on suspension K&C characteristics. However, these primarily rely on kinematic characteristic curve analysis and calculations, and cannot provide structural layout options such as suspension hardpoint locations. Current research on suspension hardpoint design primarily utilizes methods such as spatial analytical geometry, RSSR mechanism kinematics theory, spatial adaptive theory, and finite rotation tensors. While these methods can identify suspension hardpoint locations, they are complex modeling and computationally intensive, limiting their applicability to complex structures. Summary of the Invention

[0004] To address the shortcomings of the aforementioned existing methods and address the need for improvement, the present invention aims to provide a method for identifying suspension hardpoint parameters based on sensitivity analysis. This method establishes a kinematic model of the vehicle suspension using the natural coordinate modeling method, and derives the suspension sensitivity equations using the adjoint variable method, thereby identifying the key factors influencing the suspension's kinematic characteristics. Furthermore, the present invention employs the BFGS variable scaling optimization algorithm to identify suspension hardpoints, thereby ensuring that the suspension's kinematic characteristics closely match experimental results.

[0005] To achieve the above objectives, the present invention adopts the following technical solutions.

[0006] The present application proposes a suspension system based on natural coordinate modeling, the suspension system based on natural coordinate modeling comprising:

[0007] A kinematic model, the kinematic model including motion constraint equations and drive constraint equations, the motion constraint equations including single rigid body constraint equations and kinematic pair constraint equations; wherein the motion constraint equations and drive constraint equations are established by the following method: in a suspension system having multiple rigid bodies, analyzing the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies, and establishing the kinematic equations of the suspension system based on the natural coordinates, the kinematic equations including the motion constraint equations and the drive constraint equations;

[0008] A suspension sensitivity analysis calculation model is established by taking the natural coordinates as design variables of the suspension system and establishing the suspension sensitivity analysis calculation model based on an adjoint variable method. The suspension sensitivity analysis calculation model is used to calculate the sensitivity value of the influence of each design variable on the kinematic characteristic parameters of the suspension system, thereby providing a direction for parameter identification of suspension hard points.

[0009] A suspension hard point parameter identification module is configured to screen out a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system based on the sensitivity values, use suspension kinematic characteristic test parameters as target values, and implement parameter identification of the suspension hard points based on a BFGS variable scaling optimization algorithm and using the golden section method to optimize the search step size of the BFGS variable scaling optimization algorithm.

[0010] In some embodiments, analyzing the natural coordinates required to characterize each rigid body includes analyzing the minimum number of natural coordinates required to characterize each rigid body of the suspension system.

[0011] In some embodiments, establishing the motion constraint equation of the suspension system based on the natural coordinates includes:

[0012] Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic pair connecting two adjacent rigid bodies in the suspension system and establish the kinematic pair constraint equation;

[0013] All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system.

[0014] In some embodiments, the suspension sensitivity analysis calculation model further includes:

[0015] A general objective function of the general form of sensitivity analysis is constructed based on the calculation formula of the suspension kinematic characteristic parameters, and a first-order sensitivity calculation formula is constructed based on the motion constraint equation of the suspension system. The first-order sensitivity calculation formula contains multiple derivative terms; the suspension sensitivity analysis calculation model is used to introduce accompanying variables into the suspension hard point identification objective function, and by solving the accompanying variables, the first-order sensitivity value of the suspension hard point identification objective function with respect to the suspension hard point is solved.

[0016] In some embodiments, the multi-rigid-body suspension system includes a double wishbone suspension, which includes a lower control arm, a steering knuckle, a steering tie rod, and an upper control arm, wherein the lower control arm, steering knuckle, steering tie rod, and upper control arm are respectively the first rigid body, the second rigid body, the third rigid body, and the fourth rigid body; the upper control arm and the steering knuckle are connected respectively by ball joints, the lower control arm and the steering knuckle are connected by ball joints, the steering knuckle and the steering tie rod are connected by ball joints, the steering knuckle is fixedly connected to the wheel axle, the lower control arm is connected to the frame by two revolute pairs, the upper control arm is connected to the frame by two revolute pairs, and the steering tie rod is connected to the vehicle body by a universal joint;

[0017] The design variables of the multi-rigid body suspension system are:

[0018] b=[x c0 ,y c0 ,z c0 ,x f0 ,y f0 ,z f0 ,x p0 ,y p0 ,z p0 ,x g0 ,y g0 ,z g0 ,x n0 ,y n0 ,z n0 ,

[0019] x h0 ,y h0 ,z h0 ,x e1 ,y e1 ,z e1 ,x j ,y j ,z j ,x e4 ,y e4 ,z e4 ,x k ,y k ,z k ,x m ,y m ,z m ] T , where xc0 ,y c0 and z c0 is the natural coordinate initial value of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f0 ,y f0 and z f0 is the natural coordinate initial value of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p0 ,y p0 and z p0 is the natural coordinate initial value of the center point P where the steering knuckle is connected to the wheel axle; g0 ,y g0 and z g0 is the initial value of the natural coordinate of the wheel center G; x n0 ,y n0 and z n0 is the natural coordinate initial value of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h0 ,y h0 and z h0 is the initial value of the natural coordinate of the wheel contact point H; x e1 ,y e1 and z e1 The unit vector forming the line connecting the center points of the two revolute joints connecting the lower control arm to the frame The natural coordinate value of x j ,y j and z j The natural coordinate value of point J, the foot of the perpendicular line drawn from the center point C of the ball joint connecting the lower control arm and the steering knuckle to the connecting line of the rotation sub-center point; e4 ,y e4 and z e4 The unit vector forming the line connecting the center points of the two revolute joints connecting the upper control arm to the frame The natural coordinate value of x k ,y k and z k The natural coordinate value of point K, the foot of the perpendicular line drawn from the center point F of the ball joint connecting the upper control arm and the steering knuckle to the connecting line of the rotation sub-center point; m ,y m and z m is the natural coordinate value of the center point M of the universal joint connecting the steering tie rod and the vehicle body; vector Points K, J, and M do not change with time during the suspension movement, and their natural coordinate values ​​are constant.

[0020] The state variables are:

[0021] q=[x c ,y c ,z c ,x f,y f ,z f ,x p ,y p ,z p ,x g ,y g ,z g ,x n ,y n ,z n ,x h ,y h ,z h ] T ,

[0022] The state variable q is the natural coordinate of the design variable b that will change during the suspension movement; c ,y c and z c is the natural coordinate of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f ,y f and z f is the natural coordinate of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p ,y p and z p is the natural coordinate of the center point P where the steering knuckle is connected to the wheel axle; g ,y g and z g is the natural coordinate of the wheel center G; x n ,y n and z n is the natural coordinate of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h ,y h and z h is the natural coordinate of the wheel contact point H;

[0023] The kinematic equation of the suspension system is:

[0024] Φ(q,b,t)=(f1,f2,f3,f4,f5,f6,f7,f8,f9,f 10 ,f 11 ,f 12 ,f 13 ,f 14 ,f 15 ,f 16 ,f 17 ,f 18 ) T =0

[0025] Where t represents time, f i (i=1,2,…,17) is the motion constraint equation, f18 The driving constraint equation is:

[0026] f 18 =z g -z g0 -f(t)

[0027] z g is the vertical displacement of the wheel center G in natural coordinates, z g0 is the initial value of the natural coordinate of the vertical wheel center G, the vertical displacement of the wheel center is selected as the drive, and f(t) is the drive function;

[0028] The square of the difference between the tire alignment parameters and the target curve is used as the optimization target, and the linear weighted method is used to obtain the suspension hard point identification objective function:

[0029]

[0030] Among them, α, β, γ, Δ are the relative values ​​of the tire alignment parameters relative to the static balance position of the wheel, corresponding to the castor angle, wheel center lateral displacement, wheel camber angle and toe angle respectively; α0, β0, γ0, Δ0 are the target values ​​of each tire alignment parameter; c1, c2, c3, c4 are the corresponding weighting factors, t 1 and t 2 The start time and end time respectively;

[0031] The corresponding tire alignment parameter calculation formula is:

[0032]

[0033] β=y g -y g0

[0034]

[0035]

[0036] The general objective function is:

[0037]

[0038] in represents the first-order derivative, Represents the second-order derivative, corresponding to the constraint equations of velocity and acceleration respectively; starting time t 1 and the termination time t 2 are all related to the design variable b,

[0039] Comparing the forms of the suspension hard point identification objective function and the general objective function, the expression of the state variable function H(q,b,t) is obtained:

[0040]

[0041]

[0042] H(q,b,t) pair and Obtained by partial derivative and All are 0;

[0043] The kinematic equation Φ(q,b,t) is derived from the state variable q to obtain Φ q ;

[0044] Φ(q,b,t) takes the partial derivative of the design variable b and obtains Φ b ;

[0045] H(q,b,t) is derived from the design variable b to obtain H b ;

[0046] H(q,b,t) takes the partial derivative of the state variable q and obtains H q ;

[0047] Based on the derivation of Φ q , Φ b 、H b and H q , solve the accompanying variables in the suspension sensitivity analysis calculation model.

[0048] In some embodiments, a method for identifying suspension hard point parameters based on natural coordinate modeling is further provided, the method comprising:

[0049] Step 1: In a suspension system having multiple rigid bodies, the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies are analyzed and the kinematic equations of the suspension system are established based on the natural coordinates. The kinematic equations include motion constraint equations and drive constraint equations; wherein the motion constraint equations include single rigid body constraint equations and kinematic pair constraint equations.

[0050] Step 2: Using the natural coordinates selected in step 1 as the design variables of the suspension system, a suspension sensitivity analysis calculation model is established based on the adjoint variable method to calculate the sensitivity value of each design variable on the kinematic characteristic parameters of the suspension system, providing direction for parameter identification of the suspension hard points;

[0051] Step 3: Based on the sensitivity values ​​in step 2, a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system are screened out. Using the suspension kinematic characteristic test parameters as target values, a BFGS variable scaling optimization algorithm is used, and the search step size of the BFGS variable scaling optimization algorithm is optimized using the golden section method to achieve parameter identification of the suspension hard points.

[0052] In some embodiments, the natural coordinates required for analyzing and characterizing each rigid body in step 1 include:

[0053] The minimum number of natural coordinates required to characterize each rigid body of the suspension system is analyzed.

[0054] In some embodiments, establishing the motion constraint equation of the suspension system based on the natural coordinates includes:

[0055] Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic pair connecting two adjacent rigid bodies in the suspension system and establish the kinematic pair constraint equation;

[0056] All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system, which are solved using the Newton-Raphson iterative method.

[0057] In some embodiments, the step 2 specifically includes: constructing a general objective function of the general form of sensitivity analysis based on the suspension kinematic characteristic parameter calculation formula, constructing a first-order sensitivity calculation formula based on the motion constraint equation of the suspension system, and the first-order sensitivity calculation formula contains multiple derivative terms; introducing accompanying variables into the suspension hard point identification objective function, and solving the accompanying variables to solve the first-order sensitivity value of the suspension hard point identification objective function with respect to the suspension hard point.

[0058] Some embodiments of the present invention use the adjoint variable method to solve the sensitivity of the natural coordinates of the suspension hard point to the suspension kinematic characteristic parameters. By introducing additional variables, the direct calculation of the derivative is avoided, thereby reducing the complexity of the solution.

[0059] In some embodiments, the step 3 specifically includes: selecting a group of design variables with the largest sensitivity values ​​as parameter identification and optimization variables based on the sensitivity analysis results;

[0060] The BFGS variable scale optimization algorithm is used to optimize the selected design variables;

[0061] The search direction of the BFGS variable scale optimization algorithm is calculated by the sensitivity value, and the search step size is optimized by the golden section method.

[0062] Some embodiments of the present invention use the results of sensitivity analysis to screen out a group of design variables that have the greatest impact on the kinematic characteristics of the suspension system, thereby reducing the computational complexity of the identification algorithm.

[0063] Compared with the prior art, the present invention has at least the following significant advantages: (1) The present invention establishes a kinematic model of a suspension multi-rigid body system based on the natural coordinate method, which can reduce the number of generalized coordinates in the model derivation process, simplify the model derivation process, and improve the model solution speed; (2) The present invention adopts the adjoint variable method to solve the sensitivity value of the natural coordinate of the suspension hard point to the suspension kinematic characteristic parameters, and avoids the direct calculation of the derivative by introducing additional variables, thereby reducing the complexity of the solution; (3) The present invention uses the results of sensitivity analysis to screen out a group of design variables that have a greater impact on the kinematic characteristics of the suspension system, thereby reducing the computational complexity of the identification algorithm; and adopts the BFGS variable scale optimization algorithm and the golden section method to ensure the optimality of parameter identification, thereby achieving the output of high-precision hard point coordinate identification results with a smaller computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 FIG. 1 is a schematic diagram of a suspension system based on natural coordinate modeling according to an embodiment of the present invention.

[0065] Figure 2 The figure is a flow chart of a method for identifying suspension hard point parameters based on natural coordinate modeling according to an embodiment of the present invention.

[0066] Figure 3 This is a schematic diagram of describing a rigid body using the “two-point, two-vector” natural coordinates according to an embodiment of the present invention.

[0067] Figure 4 Schematic diagram of cylindrical natural coordinates according to an embodiment of the present invention.

[0068] Figure 5 FIG. 1 is a schematic diagram of prism secondary natural coordinates according to an embodiment of the present invention.

[0069] Figure 6 Schematic diagram of the structure of a double wishbone suspension system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0071] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0072] Figure 1 FIG1 is a schematic diagram of a suspension system based on natural coordinate modeling according to an embodiment of the present invention. Figure 1 The present application proposes a suspension system based on natural coordinate modeling, the suspension system based on natural coordinate modeling comprising:

[0073] A kinematic model, the kinematic model including motion constraint equations and drive constraint equations, the motion constraint equations including single rigid body constraint equations and kinematic pair constraint equations; wherein the motion constraint equations and drive constraint equations are established by the following method: in a suspension system having multiple rigid bodies, analyzing the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies, and establishing the kinematic equations of the suspension system based on the natural coordinates, the kinematic equations including the motion constraint equations and the drive constraint equations;

[0074] A suspension sensitivity analysis calculation model is established by taking the natural coordinates as design variables of the suspension system and establishing the suspension sensitivity analysis calculation model based on an adjoint variable method. The suspension sensitivity analysis calculation model is used to calculate the sensitivity value of the influence of each design variable on the kinematic characteristic parameters of the suspension system, thereby providing a direction for parameter identification of suspension hard points.

[0075] A parameter identification module for suspension hard points, the parameter identification module for suspension hard points is used to screen out a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system based on the sensitivity value, take the suspension kinematic characteristic test parameters as the target value, based on the BFGS variable scale optimization algorithm, and use the golden section method to optimize the search step of the BFGS variable scale optimization algorithm to achieve parameter identification of the suspension hard points. The BFGS variable scale optimization algorithm was proposed by CG Broyden, R. Fletcher, D. Goldfarb and DF Shanno in 1970, and the algorithm was named after the initials of the four people's names. The BFGS variable scale optimization algorithm is a type of algorithm commonly used in unconstrained optimization algorithms. Its iterative process only requires the first-order derivative, and there is no need to calculate the Hesse matrix. When the first-order derivative is positive, the direction of the algorithm calculation is the descending direction.

[0076] In some embodiments, analyzing the natural coordinates required to characterize each rigid body includes analyzing the minimum number of natural coordinates required to characterize each rigid body of the suspension system.

[0077] In some embodiments, establishing the motion constraint equation of the suspension system based on the natural coordinates includes:

[0078] Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic pair connecting two adjacent rigid bodies in the suspension system and establish the kinematic pair constraint equation;

[0079] All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system.

[0080] In some embodiments, the suspension sensitivity analysis calculation model further includes:

[0081] A general objective function of the general form of sensitivity analysis is constructed based on the calculation formula of the suspension kinematic characteristic parameters, and a first-order sensitivity calculation formula is constructed based on the motion constraint equation of the suspension system. The first-order sensitivity calculation formula contains multiple derivative terms; the suspension sensitivity analysis calculation model is used to introduce accompanying variables into the suspension hard point identification objective function, and by solving the accompanying variables, the first-order sensitivity value of the suspension hard point identification objective function with respect to the suspension hard point is solved.

[0082] In some embodiments, the multi-rigid-body suspension system includes a double wishbone suspension, which includes a lower control arm, a steering knuckle, a steering tie rod, and an upper control arm, wherein the lower control arm, steering knuckle, steering tie rod, and upper control arm are respectively the first rigid body, the second rigid body, the third rigid body, and the fourth rigid body; the upper control arm and the steering knuckle are connected respectively by ball joints, the lower control arm and the steering knuckle are connected by ball joints, the steering knuckle and the steering tie rod are connected by ball joints, the steering knuckle is fixedly connected to the wheel axle, the lower control arm is connected to the frame by two revolute pairs, the upper control arm is connected to the frame by two revolute pairs, and the steering tie rod is connected to the vehicle body by a universal joint;

[0083] The design variables of the multi-rigid body suspension system are:

[0084] b=[x c0 ,y c0 ,z c0 ,x f0 ,y f0 ,z f0 ,x p0 ,y p0 ,z p0 ,x g0 ,y g0 ,z g0 ,x n0 ,y n0 ,z n0 ,

[0085] x h0 ,y h0 ,z h0 ,x e1 ,y e1 ,z e1 ,x j ,y j ,z j ,x e4 ,y e4 ,z e4 ,x k ,y k ,z k ,x m ,y m ,z m ] T ,

[0086] Among them, x c0 ,y c0 and z c0 is the natural coordinate initial value of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f0 ,y f0 and z f0 is the natural coordinate initial value of the center point F of the ball joint connecting the upper control arm and the steering knuckle;p0 ,y p0 and z p0 is the natural coordinate initial value of the center point P where the steering knuckle is connected to the wheel axle; g0 ,y g0 and z g0 is the initial value of the natural coordinate of the wheel center G; x n0 ,y n0 and z n0 is the natural coordinate initial value of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h0 ,y h0 and z h0 is the initial value of the natural coordinate of the wheel contact point H; x e1 ,y e1 and z e1 The unit vector forming the line connecting the center points of the two revolute joints connecting the lower control arm to the frame The natural coordinate value of x j ,y j and z j The natural coordinate value of point J, the foot of the perpendicular line drawn from the center point C of the ball joint connecting the lower control arm and the steering knuckle to the connecting line of the rotation sub-center point; e4 ,y e4 and z e4 The unit vector forming the line connecting the center points of the two revolute joints connecting the upper control arm to the frame The natural coordinate value of x k ,y k and z k The natural coordinate value of point K, the foot of the perpendicular line drawn from the center point F of the ball joint connecting the upper control arm and the steering knuckle to the connecting line of the rotation sub-center point; m ,y m and z m is the natural coordinate value of the center point M of the universal joint connecting the steering tie rod and the vehicle body; the unit vector It is fixed to the vehicle body. J, K, and M are also points on the vehicle body and do not change during the movement of the suspension. Points K, J, and M do not change with time during the suspension movement, and their natural coordinate values ​​are constant.

[0087] The state variables are:

[0088] q=[x c ,y c ,z c ,x f ,y f ,z f ,x p ,y p ,z p ,x g ,yg ,z g ,x n ,y n ,z n ,x h ,y h ,z h ] T ,

[0089] The state variable q is the natural coordinate of the design variable b that will change during the suspension movement; c ,y c and z c is the natural coordinate of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f ,y f and z f is the natural coordinate of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p ,y p and z p is the natural coordinate of the center point P where the steering knuckle is connected to the wheel axle; g ,y g and z g is the natural coordinate of the wheel center G; x n ,y n and z n is the natural coordinate of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h ,y h and z h is the natural coordinate of the wheel contact point H;

[0090] The kinematic equation of the suspension system is:

[0091] Φ(q,b,t)=(f1,f2,f3,f4,f5,f6,f7,f8,f9,f 10 ,f 11 ,f 12 ,f 13 ,f 14 ,f 15 ,f 16 ,f 17 ,f 18 ) T

[0092] =0

[0093] Where t represents time, f i(i=1,2,…,17) represents the kinematic constraint equations of the suspension system. Seventeen kinematic constraint equations are derived from the kinematic joints of the double wishbone suspension system. Specifically, during suspension motion, the lower arm has only one degree of freedom, which allows for up-and-down movement, resulting in two constraint equations. Similarly, the upper arm also has two constraint equations. The tie rod is connected at both ends by a ball joint, resulting in one constraint equation. The six hard points distributed around the steering knuckle generate twelve constraint equations through distance constraints, resulting in a total of seventeen kinematic constraint equations for the suspension system.

[0094] f 18 Driving constraint equations for the suspension system:

[0095] f 18 =z g -z g0 -f(t)

[0096] z g is the vertical displacement of the wheel center G in natural coordinates, z g0 is the initial value of the natural coordinate of the vertical wheel center G, the vertical displacement of the wheel center is selected as the drive, and f(t) is the drive function;

[0097] The square of the difference between the tire alignment parameters and the target curve is used as the optimization target, and the linear weighted method is used to obtain the suspension hard point identification objective function:

[0098]

[0099] The objective function of suspension hard point identification is to minimize the weighted value between the tire alignment parameters calculated from the identified suspension hard points and the target values ​​of the tire alignment parameters. Among them, α, β, γ, Δ are the relative values ​​of the tire alignment parameters relative to the static equilibrium position of the wheel, corresponding to the castor angle, wheel center lateral displacement, wheel camber angle and toe angle respectively; α0, β0, γ0, Δ0 are the target values ​​of each tire alignment parameter; c1, c2, c3, c4 are the corresponding weighting factors, t 1 and t 2 are the start and end times of the study, respectively. As can be understood, the final suspension hard point identification objective function is an objective function constructed specifically for suspension hard point identification. The general objective function is a general form function used in multi-body system optimization design. The constructed suspension hard point identification objective function is a specific instance of the general objective function, specifically for suspension hard point identification.

[0100] The corresponding tire alignment parameter calculation formula is:

[0101]

[0102] β=y g -y g0

[0103]

[0104]

[0105] The general objective function is:

[0106]

[0107] in represents the first-order derivative, Represents the second-order derivative, corresponding to the constraint equations of velocity and acceleration respectively; starting time t 1 and the termination time t 2 They are all related to the design variable b, where superscript 1 represents the initial state and superscript 2 represents the final state. Denotes the general objective function and t 1 The part related to the moment state quantity, Denotes the general objective function and t 2 The part related to the moment state quantity, Represents the part of the general objective function related to the integral of the state variable function. and These two parts are related to the initial state and the final state of the system. Related to the intermediate processes of the system.

[0108] Comparing the suspension hard point identification objective function obtained by the linear weighted method in the previous article with the general objective function, the expression of the state variable function H(q, b, t) is obtained:

[0109]

[0110] H(q,b,t) pair and Obtained by partial derivative and All are 0;

[0111] The kinematic equation Φ(q,b,t) is derived from the state variable q to obtain Φ q ;

[0112] Φ(q,b,t) takes the partial derivative of the design variable b and obtains Φ b ;

[0113] H(q,b,t) is derived from the design variable b to obtain H b ;

[0114] H(q,b,t) takes the partial derivative of the state variable q and obtains H q ;

[0115] Based on the derivation of Φ q , Φ b 、H b and H q , solve the accompanying variables in the suspension sensitivity analysis calculation model.

[0116] In some embodiments, a method for identifying suspension hard point parameters based on natural coordinate modeling is also provided. The method can be performed based on the suspension system based on natural coordinate modeling in any of the above embodiments, that is, the suspension hard point parameter identification is performed using the suspension system based on natural coordinate modeling in any of the above embodiments.

[0117] refer to Figure 2 , the method comprising:

[0118] Step 1: In a suspension system having multiple rigid bodies, the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies are analyzed and the kinematic equations of the suspension system are established based on the natural coordinates. The kinematic equations include motion constraint equations and drive constraint equations; wherein the motion constraint equations include single rigid body constraint equations and kinematic pair constraint equations.

[0119] Step 2: Using the natural coordinates selected in step 1 as the design variables of the suspension system, a suspension sensitivity analysis calculation model is established based on the adjoint variable method to calculate the sensitivity value of each design variable on the kinematic characteristic parameters of the suspension system, providing direction for parameter identification of the suspension hard points;

[0120] Step 3: Based on the sensitivity values ​​in step 2, a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system are screened out. Using the suspension kinematic characteristic test parameters as target values, a BFGS variable scaling optimization algorithm is used, and the search step size of the BFGS variable scaling optimization algorithm is optimized using the golden section method to achieve parameter identification of the suspension hard points.

[0121] Some embodiments of the present invention establish a kinematic model of the suspension system based on the natural coordinate method, which can reduce the number of generalized coordinates used in the model derivation process, streamline the model derivation process, and improve the model solution speed. Furthermore, the BFGS variable scaling optimization algorithm and the golden section method are used to ensure optimal parameter identification, achieving high-precision hard point coordinate identification results while minimizing computational effort.

[0122] In some embodiments, the analyzing of the natural coordinates required to characterize each rigid body in step 1 includes: analyzing the minimum number of natural coordinates required to characterize each rigid body of the suspension system.

[0123] In some embodiments, establishing the motion constraint equation of the suspension system based on the natural coordinates includes: using a "two-point two-vector" natural coordinate method to describe each rigid body and establish a single rigid body constraint equation for each rigid body; analyzing the kinematic joint connecting two adjacent rigid bodies in the suspension system and establishing a kinematic joint constraint equation;

[0124] All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system, which are solved using the Newton-Raphson iterative method.

[0125] As a specific embodiment, based on the structure and kinematic pairs of the suspension system, the minimum number of natural coordinates required to characterize each rigid body is analyzed, and the natural coordinate modeling method is applied to establish the motion constraint equation of each rigid body in the suspension system. The motion constraint equations of all rigid bodies in the suspension system and a driving constraint equation are combined to obtain the overall kinematic model of the entire suspension system.

[0126] refer to Figure 3 In some embodiments, establishing the motion constraint equation of the suspension system based on the natural coordinates includes:

[0127] Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic pair connecting two adjacent rigid bodies in the suspension system and establish the kinematic pair constraint equation;

[0128] All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system, which are solved using the Newton-Raphson iterative method.

[0129] Specifically, obtaining the overall kinematic model of the entire suspension system includes the following steps:

[0130] Step 1.1: The natural coordinates of a rigid body are composed of the coordinate components of the point and the coordinate components of the unit vector. When using natural coordinates to describe a rigid body, determine the constraint equations of the rigid body, i.e., the single rigid body constraint equations of each rigid body and the constraint equations of the kinematic pair, i.e., the kinematic pair constraint equations. These constraint equations are all linear equations or quadratic equations.

[0131] Step 1.2: Use Figure 3 The "two points and two vectors" natural coordinates shown are used to describe a rigid body, that is, the natural coordinates of the rigid body are the coordinate components of points A and B. (i=1,2,3) and two non-coplanar vectors The coordinate components of the rigid body have 12 natural coordinates, namely the coordinate components of points A and B (i=1, 2, 3) and The coordinate components of two vectors.

[0132] Step 1.3: A single rigid body in space has only six degrees of freedom, so there are six independent rigid body constraint equations:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] in, Represents the coordinate components of points A and B (i = 1, 2, 3); Represents the coordinate components of two vectors, C1, C2, C3, C4 are constants. Formula (1) describes the condition that the distance between points A and B is constant; Formulas (2)-(4) describe The condition that the angle between two vectors is constant; Equation (5) and Equation (6) describe The above six independent rigid body constraint equations are single rigid body constraint equations for a single rigid body in space.

[0140] Step 1.4: Two adjacent rigid bodies are connected by a certain kinematic pair. During the motion process, they need to follow the motion law of the kinematic pair, which is expressed by the constraint equation of the kinematic pair.

[0141] Furthermore, among the four common types of kinematic joints—spherical, revolute, cylindrical, and prismatic—when adjacent rigid bodies are connected by a spherical joint, they share a common point; when two rigid bodies are connected by a revolute joint, they share a common unit vector. The constraint equations for spherical and revolute joints are naturally formed, eliminating the need to develop new, independent constraint equations. Instead, they can be refined based on the rigid body constraint equations, combining shared points or shared unit vectors.

[0142] Step 1.5: If Figure 4 If two adjacent rigid bodies are connected by a cylindrical pair, the two rigid bodies share the same unit vector u and the line connecting two points J and K on the two rigid bodies must be parallel to u. The vector form of the kinematic pair constraint equation of the cylindrical pair is:

[0143]

[0144] in, are the natural coordinate vectors of point K and point J respectively.

[0145] Step 1.6: If Figure 5The constraint equations for the prismatic pair described are similar to those for the cylindrical pair, with the only difference being that the rotation of the two connected rigid bodies is restricted. The kinematic pair constraint equations for the prismatic pair are based on the kinematic pair constraint equations for the cylindrical pair, and require an additional constraint equation for limiting rotation:

[0146]

[0147] in, They are the natural coordinates of point M, point N, point Q and point P in the x, y and z directions respectively.

[0148] Step 1.7: In the entire suspension system with multiple rigid bodies, the motion constraint equations and drive constraint equations derived in steps 1.2-1.6 constitute the constraint equations of the suspension system, that is, the kinematic model of the suspension system (i.e., the overall kinematic model of the suspension system) is obtained. The vector equation is expressed as:

[0149]

[0150] Among them, q represents the natural coordinate vector, t represents time, Φ K (q) is the kinematic constraint, Φ D (q,t) is the driving constraint.

[0151] Furthermore, the constraint equations of the suspension system established in step 1.7 are solved using the Newton-Raphson iterative method to obtain the natural coordinate values.

[0152] In some embodiments, step 2 specifically includes: constructing a general objective function of the general form of sensitivity analysis based on the suspension kinematic characteristic parameter calculation formula, constructing a first-order sensitivity calculation formula based on the motion constraint equation of the suspension system, and the first-order sensitivity calculation formula contains multiple derivative terms; introducing accompanying variables into the suspension hard point parameter identification objective function, and solving the accompanying variables to solve the first-order sensitivity value of the suspension hard point parameter identification objective function with respect to the suspension hard point.

[0153] In step 2, the natural coordinates selected in step 1 are used as the design state variables of the system. A suspension sensitivity analysis calculation model is established based on the method of adjoint variables, thereby calculating the sensitivity value of each design variable on the suspension kinematic characteristic parameters, providing direction for parameter identification of the suspension hard points. As a specific embodiment, the details are as follows:

[0154] Step 2-1: The kinematic equation of the suspension system is the motion constraint equation, and then the driving constraint about time is added, which is expressed as:

[0155] Φ(q,b,t)=0 (10)

[0156] where q(t)=[q1(t),q1(t),…,qn (t)] T represents the state variables of the suspension system, b=[b1,b2,b3,…,b n ] T represents the design variables of the suspension system, Φ=[Φ1,Φ2,…,Φ n ] T A function that represents the total constraint equation consisting of the kinematic and actuation constraints of the suspension system.

[0157] Step 2-2: The general objective function or kinematic equation in dynamic optimization design is expressed as:

[0158]

[0159] in represents the first-order derivative, Represents the second-order derivative, corresponding to the constraint equations of velocity and acceleration respectively; starting time t 1 and the termination time t 2 are all related to the design variable b and are generally expressed as:

[0160]

[0161] Step 2-3: For the general objective function in equation (11), take the derivative of both sides of the equation with respect to the design variable b to obtain the first-order derivative of the general objective function with respect to the design variable, that is:

[0162]

[0163] Where, and H q q b represents the chain rule, for right Find the partial derivative, for Find the partial derivative with respect to b, for q i Find the partial derivative, q i Find the partial derivative of b, and the other chain derivatives are similar; for For time t i Find the partial derivative, H i t i The H function at time, is time t i Find the partial derivative of the design variable b; H b Find the partial derivative of the H function with respect to the design variable b.

[0164] Step 2-4: According to the chain rule, take the first and second order derivatives on both sides of equation (10) to obtain the expressions for velocity and acceleration:

[0165]

[0166] Where, Φ q Find the partial derivative of the Φ(q,b,t) function with respect to the state variable q, Φ t Find the partial derivative of the Φ(q,b,t) function with respect to time t, for The overall partial derivative of the state variable q is obtained, Φ qt is Φ t Find the partial derivative of the state variable q, Φ tt Find the second derivative of the Φ(q,b,t) function with respect to time t.

[0167] Step 2-5: Derivative the design variable b on both sides of equations (10) and (14) to obtain:

[0168]

[0169] in is defined as:

[0170]

[0171] In the formula, each parameter satisfies the chain differentiation rule.

[0172] Step 2-6: After sorting out equation (15), we can get the solution matrix for the design variables:

[0173]

[0174] Step 2-7: Formula (13) is used to Related items and Integrate the relevant items by parts:

[0175]

[0176] In the formula, in the formula,

[0177] Step 2-8: Preferably, the accompanying variable method is adopted to introduce the accompanying variables v, η i (i=1,2),ζ i (i=1,2) and ξ i (i=1,2) makes the equation (18) q b , The coefficient of the corresponding term is zero, where The specific replacement process is:

[0178]

[0179] Where, v, η i (i=1,2),ζ i (i=1,2) and ξ i (i=1,2) is the introduced accompanying variable.

[0180] Step 2-9: Add the four equations in equation (19) to equation (18) without changing Ψ b The value of , so that the corresponding coefficient is equal to zero, the adjoint variable equation is obtained:

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188] Step 2-10: Based on the above steps, the derivative of the general objective function with respect to the design variables is:

[0189]

[0190] Step 2-11: From equation (20-e), we can get the accompanying variable ξ 1 :

[0191]

[0192] Step 2-12: 1 Substituting (20-a) and (20-c) together, we obtain the following system of equations:

[0193]

[0194] From formula (23), we can get ζ 1 , η 1 .

[0195] Step 2-13: From equation (20-f), we can get the accompanying variable ξ 2 :

[0196]

[0197] Step 2-14: 2 Substituting (20-b) and (20-d) together, we obtain the following system of equations:

[0198]

[0199] From equation (25), we can get ζ 2 , η 2 .

[0200] Step 2-15: Equation (20-g) can be used to solve the accompanying variables v and η 1 ,η 2 ,ζ 1 ,ζ 2 ,ξ 1 ,ξ 2 , substituting into Equation (21) we can obtain the first-order sensitivity Ψ of the general objective function Ψ(b) with respect to the design variable b b , in order to improve the efficiency of solving.

[0201] In some embodiments, step 3 specifically includes:

[0202] According to the sensitivity analysis results, a group of design variables with the largest sensitivity values ​​are selected as parameter identification and optimization variables;

[0203] The BFGS variable scale optimization algorithm is used to optimize the selected design variables;

[0204] The search direction of the BFGS variable scale optimization algorithm is calculated by the sensitivity value, and the search step size is optimized by the golden section method.

[0205] As a specific embodiment, in step 3, a set of design variables with the greatest impact on the suspension kinematic characteristic parameters is screened out. Using the suspension kinematic characteristic test parameters as target values, code based on the BFGS variable scale optimization method is written, and the golden section method is used to optimize the search step size of the BFGS algorithm to achieve parameter identification of the suspension hard points. The details are as follows:

[0206] Step 3-1: Use polynomial fitting to fit the test tire alignment parameters. Use a quadratic polynomial for the castor angle test value, and a cubic polynomial for the wheel center lateral displacement, camber, and toe angle test values.

[0207] Step 3-2: For the suspension system, design variables with greater sensitivity values ​​have a greater impact on the suspension hard-point identification objective function. Based on the combined sensitivity values ​​of each design variable to the suspension hard-point identification objective function calculated in Step 2, select the design variables with the largest sensitivity values ​​as the design variable set for suspension hard-point parameter identification. For design variables with smaller sensitivity values, their impact on the suspension system is minimal, so precise identification results are not required.

[0208] Step 3-3: Use the BFGS variable scale optimization method to identify parameters, using an imprecise set of design variables as initial values, and perform multiple optimization iterations until the difference between the kinematic characteristic parameter values ​​calculated from the optimized design variables and the test results meets the accuracy requirements. The correction formula in the BFGS method is:

[0209]

[0210] Where k is the number of iterations, i is the number of iterations in the k-th iteration process; is the inverse approximation of the second-order derivative matrix (Hesse matrix) of the general objective function in the current iteration step; s (i) is the change of the design variable, s (i) =b (i+1) -b (i) ;y (i) is the change in the gradient of the general objective function,

[0211] Step 3-4: Use the golden section method to solve the optimal step size of the BFGS variable scale optimization method in step 3-3 to improve computational efficiency.

[0212] The following is combined with Figure 6 The present invention is further described in detail with reference to the accompanying drawings and specific embodiments.

[0213] This embodiment provides a method for identifying suspension hard point parameters based on natural coordinate modeling, and is applied to the identification of suspension parameter hard points in actual suspension systems. Taking a double wishbone suspension system as an example, the structural diagram of the double wishbone suspension system is shown in FIG. Figure 6 shown. Figure 6 In the figure, rigid body (1) represents the lower control arm, rigid body (2) represents the steering knuckle, rigid body (3) represents the steering tie rod, and rigid body (4) represents the upper control arm. The upper and lower control arms are connected to the steering knuckle via ball joints at points F and C, respectively, and the steering knuckle is connected to the steering tie rod via a ball joint at point N. The steering knuckle is fixedly connected to the wheel axle, the lower control arm is connected to the frame via two revolute joints, the upper control arm is connected to the frame via two revolute joints, and the steering tie rod is connected to the vehicle body via a universal joint.

[0214] The design variables for the double wishbone suspension system are:

[0215] b=[x c0 ,y c0 ,z c0 ,x f0 ,y f0 ,z f0 ,x p0 ,y p0 ,z p0 ,x g0,y g0 ,z g0 ,x n0 ,y n0 ,z n0 ,x h0 ,y h0 ,z h0 ,x e1 ,y e1 ,z e1 ,x j ,y j ,z j ,x e4 ,y e4 ,z e4 ,x k ,y k ,z k ,x m ,y m ,z m ] T ,

[0216] Among them, the 0 subscript item is the initial value of the hard point, x c0 ,y c0 and z c0 is the natural coordinate initial value of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f0 ,y f0 and z f0 is the natural coordinate initial value of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p0 ,y p0 and z p0 is the natural coordinate initial value of the center point P where the steering knuckle is connected to the wheel axle; g0 ,y g0 and z g0 is the initial value of the natural coordinate of the wheel center G; x n0 ,y n0 and z n0 is the natural coordinate initial value of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h0 ,y h0 and z h0 is the initial value of the natural coordinate of the wheel contact point H; x e1 ,y e1 and z e1 The unit vector forming the line connecting the center points of the two revolute joints connecting the lower control arm to the frame The natural coordinate value of x j ,y j and z j The natural coordinate value of point J, the foot of the perpendicular line drawn from the center point C of the ball joint connecting the lower control arm and the steering knuckle to the connecting line of the rotation sub-center point; e4 ,ye4 and z e4 The unit vector forming the line connecting the center points of the two revolute joints connecting the upper control arm to the frame The natural coordinate value of x k ,y k and z k The natural coordinate value of point K, the foot of the perpendicular line drawn from the center point F of the ball joint connecting the upper control arm and the steering knuckle to the connecting line of the rotation sub-center point; m ,y m and z m is the natural coordinate value of the center point M of the universal joint connecting the steering tie rod and the vehicle body; vector Points K, J, and M do not change with time during the suspension movement, and their natural coordinate values ​​are constant.

[0217] The state variables are:

[0218] q=[x c ,y c ,z c ,x f ,y f ,z f ,x p ,y p ,z p ,x g ,y g ,z g ,x n ,y n ,z n ,x h ,y h ,z h ] T ,

[0219] The state variable q is the natural coordinate of the design variable b that will change during the suspension movement; c ,y c and z c is the natural coordinate of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f ,y f and z f is the natural coordinate of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p ,y p and z p is the natural coordinate of the center point P where the steering knuckle is connected to the wheel axle; g ,y g and z g is the natural coordinate of the wheel center G; x n ,y n and z nis the natural coordinate of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h ,y h and z h is the natural coordinate of the wheel contact point H.

[0220] Step S1: Based on the natural coordinate modeling method, the kinematic equation of the double wishbone suspension system is derived as follows:

[0221] Φ(q,b,t)=

[0222] (f1,f2,f3,f4,f5,f6,f7,f8,f9,f 10 ,f 11 ,f 12 ,f 13 ,f 14 ,f 15 ,f 16 ,f 17 ,f 18 ) T =0 (27)

[0223] Among them, f i (i=1,2,…,17) is the system kinematic constraint equation, the last term f 18 In the same-direction wheel hop test of the suspension system, the input of the suspension system is the vertical hop of the wheel center. g As a driver.

[0224] Step S2: Establish a suspension sensitivity analysis calculation model based on the method of accompanying variables, so as to calculate the sensitivity value of each design variable on the suspension motion characteristic parameters.

[0225] In embodiments of the present invention, the goal of suspension system parameter identification is to optimize the suspension design variables so that the curves of tire alignment parameters, including caster angle, camber angle, toe angle, and wheel center lateral displacement, during wheel bouncing, are as consistent as possible with their respective ideal curves. In some embodiments of the present invention, the square of the difference between the caster angle, camber angle, toe angle, and wheel center lateral displacement relative to the target curve is set as the optimization target, and a linear weighted method is used to obtain a comprehensive objective function, namely the suspension hard point identification objective function:

[0226] (28)

[0227] Among them, α, β, γ, Δ are the relative values ​​of the tire alignment parameters relative to the static balance position of the wheel, corresponding to the castor angle, wheel center lateral displacement, wheel camber angle and toe angle; α0, β0, γ0, Δ0 are the target values ​​of each tire alignment parameter; c1, c2, c3, c4 are the corresponding weighting factors; t 1and t 2 are the start time and end time of the research process respectively. The corresponding tire positioning parameter calculation formula is:

[0228]

[0229] β=y g -y g0 (30)

[0230]

[0231]

[0232] By comparing the suspension hard point identification objective function of formula (28) with the general objective function of formula (11), it can be found that the suspension hard point identification objective function is only related to the system process, but has nothing to do with the state of the initial moment (i.e., start time) and the end moment (i.e., end time). That is, and Is 0, only exists Combining equations (28)-(32), we can get the expression of H(q,b,t) in the suspension hard point identification objective function:

[0233]

[0234] It can be seen from formula (33) that H(q,b,t) and Obtained by partial derivative and are all 0 vectors.

[0235] The kinematic equation of the double wishbone suspension system Φ(q,b,t) is derived by partial derivative of the state variable q to obtain Φ q ; Φ(q,b,t) takes the partial derivative of the design variable b and obtains Φ b ; H(q,b,t) takes the partial derivative of the design variable b and obtains H b ; H(q,b,t) takes the partial derivative of the state variable q and obtains H q .

[0236] Based on the above derivation, Φ q , Φ b 、H b and H q , substituted into equations (22)-(25) to solve the accompanying variables in the sensitivity analysis of the double wishbone suspension system. Since the suspension hard point identification objective function of the suspension system only has the H(q,b,t) term and no G(q,b,t) term, the calculation formulas (22)-(25) are The entries are all 0 vectors.

[0237] According to the above method, this embodiment can calculate the comprehensive sensitivity value of the suspension hard point identification objective function of the natural coordinates of each hard point of the double wishbone suspension system to the suspension kinematic characteristic parameters.

[0238] Step S3: Based on the sensitivity analysis in step S2, a set of design variables with the greatest impact on the suspension kinematic characteristic parameters is selected. Taking the suspension kinematic characteristic test parameters as the target values, the BFGS variable scale optimization method is used, and the golden section method is used to optimize the search step size of the BFGS algorithm to achieve parameter identification of the suspension hard points.

[0239] The purpose of suspension system parameter identification is to curve fit the target parameter values ​​obtained from experimental suspension kinematics and a set of imprecise initial values ​​of design variables. The design variables are then optimized so that the obtained suspension kinematic parameters approach the target curve, thereby identifying the precise design variable values ​​corresponding to the target curve. In actual engineering, suspension kinematic parameters are obtained experimentally, while initial values ​​of design variables are obtained through measurement and are imprecise due to measurement errors and other factors. In an embodiment of the present invention, a set of precise design variable values ​​is given, and the suspension kinematic parameters obtained from these values ​​based on suspension kinematics serve as target values, i.e., as suspension kinematic test parameters. A disturbance is then added to the precise design variable values ​​to obtain imprecise initial values ​​of the design variables to simulate measurement errors.

[0240] The suspension kinematic characteristic test parameter values ​​are fitted. A quadratic polynomial is used for the caster angle target value, and a cubic polynomial is used for the wheel center lateral displacement, wheel camber, and toe angle target values. For the suspension system, the point with the larger sensitivity value has a greater impact on the system. In this embodiment, the sensitivity analysis result Ψ is selected. b The 15 design variables with the largest median values.

[0241] Furthermore, the BFGS variable scaling method is used to optimize the design variables. In each optimization iteration cycle, the optimized descent direction is calculated according to the sensitivity value obtained in step S2; on the other hand, the golden section method is used to calculate the optimal search step size. The design variables at the next moment are calculated according to the search direction and step size, and then the suspension hard point identification objective function value of the suspension motion characteristic parameters is calculated. If the suspension hard point identification objective function value meets the iteration termination condition, the iteration is stopped and the optimal design variables are obtained; if not, the correction formula is used to calculate And continue to the next iteration.

[0242] The results show that the identified design variables almost all return to the vicinity of the target values, and the suspension motion characteristic curve calculated from the identified design variables basically coincides with the target test curve. The trends and values ​​of the curves are very close, which shows that the hard point parameter identification of the suspension system based on sensitivity analysis is feasible and effective.

[0243] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention.

Claims

1. A suspension system based on natural coordinate modeling, characterized in that: The suspension system based on natural coordinate modeling includes: A kinematic model, the kinematic model including motion constraint equations and drive constraint equations, the motion constraint equations including single rigid body constraint equations and kinematic pair constraint equations; wherein the motion constraint equations and drive constraint equations are established by the following method: in a suspension system having multiple rigid bodies, analyzing the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies, and establishing the kinematic equations of the suspension system based on the natural coordinates, the kinematic equations including the motion constraint equations and the drive constraint equations; A suspension sensitivity analysis calculation model is established by taking the natural coordinates as design variables of the suspension system and establishing the suspension sensitivity analysis calculation model based on an adjoint variable method. The suspension sensitivity analysis calculation model is used to calculate the sensitivity value of the influence of each design variable on the kinematic characteristic parameters of the suspension system, thereby providing a direction for parameter identification of suspension hard points. A suspension hard point parameter identification module is configured to screen out a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system based on the sensitivity values, use suspension kinematic characteristic test parameters as target values, and implement parameter identification of the suspension hard points based on a BFGS variable scaling optimization algorithm and using the golden section method to optimize the search step size of the BFGS variable scaling optimization algorithm.

2. The suspension system based on natural coordinate modeling according to claim 1, characterized in that: The analyzing the natural coordinates required to characterize each rigid body includes: analyzing the minimum number of natural coordinates required to characterize each rigid body of the suspension system.

3. The suspension system based on natural coordinate modeling according to claim 2, characterized in that: The motion constraint equation of the suspension system is established based on the natural coordinates, including: Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic joints connecting two adjacent rigid bodies in the suspension system and establish the kinematic joint constraint equations; All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system.

4. The suspension system based on natural coordinate modeling according to claim 3, characterized in that: Establishing a suspension sensitivity analysis calculation model also includes: A general objective function of the general form of sensitivity analysis is constructed based on the calculation formula of the suspension kinematic characteristic parameters, and a first-order sensitivity calculation formula is constructed based on the motion constraint equation of the suspension system. The first-order sensitivity calculation formula contains multiple derivative terms; the suspension sensitivity analysis calculation model is used to introduce accompanying variables into the suspension hard point identification objective function, and by solving the accompanying variables, the first-order sensitivity value of the suspension hard point identification objective function with respect to the suspension hard point is solved.

5. The suspension system based on natural coordinate modeling according to claim 4, characterized in that: The multi-rigid-body suspension system includes a double wishbone suspension, which includes a lower control arm, a steering knuckle, a steering tie rod, and an upper control arm, wherein the lower control arm, the steering knuckle, the steering tie rod, and the upper control arm are respectively the first rigid body, the second rigid body, the third rigid body, and the fourth rigid body; the upper control arm and the steering knuckle are respectively connected by a ball joint, the lower control arm and the steering knuckle are connected by a ball joint, the steering knuckle and the steering tie rod are fixedly connected to the wheel axle, the lower control arm is connected to the frame by two revolute pairs, the upper control arm is connected to the frame by two revolute pairs, and the steering tie rod is connected to the vehicle body by a universal joint; The design variables of the multi-rigid body suspension system are: b=[x c0 ,y c0 ,z c0 ,x f0 ,y f0 ,z f0 ,x p0 ,y p0 ,z p0 ,x g0 ,y g0 ,z g0 ,x n0 ,y n0 ,z n0 ,x h0 ,y h0 ,z h0 ,x e1 ,y e1 ,z e1 ,x j ,y j ,z j ,x e4 ,y e4 ,z e4 ,x k ,y k ,z k ,x m ,y m ,z m ] T , Among them, x c0 ,y c0 and z c0 is the natural coordinate initial value of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f0 ,y f0 and z f0 is the natural coordinate initial value of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p0 ,y p0 and z p0 is the natural coordinate initial value of the center point P where the steering knuckle is connected to the wheel axle; p0 ,y g0 and z g0 is the initial value of the natural coordinate of the wheel center G; x n0 ,y n0 and z n0 is the natural coordinate initial value of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h0 ,y h0 and z h0 is the initial value of the natural coordinate of the wheel contact point H; x e1 ,y e1 and z e1 The unit vector forming the line connecting the center points of the two revolute joints connecting the lower control arm to the frame The natural coordinate value of x j ,y j and z j The natural coordinate value of point J, the foot of the perpendicular line drawn from the center point C of the ball joint connecting the lower control arm and the steering knuckle to the connecting line of the rotation sub-center point; e4 ,y e4 and z e4 The unit vector forming the line connecting the center points of the two revolute joints connecting the upper control arm to the frame The natural coordinate value of x k ,y k and z k The natural coordinate value of point K, the foot of the perpendicular line drawn from the center point F of the ball joint connecting the upper control arm and the steering knuckle to the connecting line of the rotation sub-center point; m ,y m and z m is the natural coordinate value of the center point M of the universal joint connecting the steering tie rod and the vehicle body; vector Points K, J, and M do not change with time during the suspension movement, and their natural coordinate values ​​are constant; The state variables are: q=[x c ,y c ,z c ,x f ,y f ,z f ,x p ,y p ,z p ,x g ,y g ,z g ,x n ,y n ,z n ,x h ,y h ,z h ] T , The state variable q is the natural coordinate of the design variable b that will change during the suspension movement; c ,y c and z c is the natural coordinate of the center point C of the ball joint connecting the lower control arm and the steering knuckle; f ,y f and z f is the natural coordinate of the center point F of the ball joint connecting the upper control arm and the steering knuckle; p ,y p and z p is the natural coordinate of the center point P where the steering knuckle is connected to the wheel axle; g ,y g and z g is the natural coordinate of the wheel center G; x n ,y n and z n is the natural coordinate of the center point N of the ball joint connecting the steering knuckle and the steering tie rod; h ,y h and z h is the natural coordinate of the wheel contact point H; The kinematic equation of the suspension system is: Φ(q,b,t)=(f1,f2,f3,f4,f5,f6,f7,f8,f9,f 10 ,f 11 ,f 12 ,f 13 ,f 14 ,f 15 ,f 16 ,f 17 ,f 18 ) T =0 Where t represents time, f i (i=1,2,…,17) is the motion constraint equation, f 18 The driving constraint equation is: f 18 =z g -z g0 -f(t) z g is the vertical displacement of the wheel center G in natural coordinates, z g0 is the initial value of the natural coordinate of the vertical wheel center G, the vertical displacement of the wheel center is selected as the drive, and f(t) is the drive function; The square of the difference between the tire alignment parameters and the target curve is used as the optimization target, and the linear weighted method is used to obtain the suspension hard point identification objective function: Among them, α, β, γ, Δ are the relative values ​​of the tire alignment parameters relative to the static balance position of the wheel, corresponding to the castor angle, wheel center lateral displacement, wheel camber angle and toe angle respectively; α0, β0, γ0, Δ0 are the target values ​​of each tire alignment parameter; c1, c2, c3, c4 are the corresponding weighting factors; t 1 and t 2 The start time and end time respectively; The corresponding tire alignment parameter calculation formula is: β=y g -and g0 The general objective function form of the optimization design of multi-body systems is: in represents the first-order derivative, Represents the second-order derivative, corresponding to the constraint equations of velocity and acceleration respectively; where superscript 1 represents the initial state, superscript 2 represents the final state, Denotes the general objective function and t 1 The part related to the moment state quantity, Denotes the general objective function and t 2 The part related to the moment state quantity, Represents the part of the general objective function related to the integral of the state variable function; Comparing the forms of the suspension hard point identification objective function and the general objective function, the expression of the state variable function H(q,b,t) is obtained: H(q,b,t) pair and Obtained by partial derivative and All are 0 vectors; The kinematic equation Φ(q,b,t) is derived from the state variable q to obtain Φ q ; Φ(q,b,t) takes the partial derivative of the design variable b and obtains Φ b ; H(q,b,t) is derived from the design variable b to obtain H b ; H(q,b,t) takes the partial derivative of the state variable q and obtains H q ; Based on the derivation of Φ q , Φ b 、H b and H q , solve the accompanying variables in the suspension sensitivity analysis calculation model.

6. A method for identifying suspension hard point parameters based on natural coordinate modeling, characterized in that: The method comprises: Step 1: In a suspension system having multiple rigid bodies, the natural coordinates required to characterize each rigid body and the kinematic pairs connecting adjacent rigid bodies are analyzed and the kinematic equations of the suspension system are established based on the natural coordinates. The kinematic equations include motion constraint equations and drive constraint equations; wherein the motion constraint equations include single rigid body constraint equations and kinematic pair constraint equations. Step 2: Using the natural coordinates selected in step 1 as the design variables of the suspension system, a suspension sensitivity analysis calculation model is established based on the adjoint variable method to calculate the sensitivity value of each design variable on the kinematic characteristic parameters of the suspension system, providing direction for parameter identification of the suspension hard points; Step 3: Based on the sensitivity values ​​in step 2, a set of design variables that have the greatest impact on the kinematic characteristic parameters of the suspension system are screened out. Using the suspension kinematic characteristic test parameters as target values, a BFGS variable scaling optimization algorithm is used, and the search step size of the BFGS variable scaling optimization algorithm is optimized using the golden section method to achieve parameter identification of the suspension hard points.

7. The method for identifying suspension hard point parameters based on natural coordinate modeling according to claim 6, characterized in that: The natural coordinates required to analyze and characterize each rigid body in step 1 include: The minimum number of natural coordinates required to characterize each rigid body of the suspension system is analyzed.

8. The method for identifying suspension hard point parameters based on natural coordinate modeling according to claim 7, characterized in that: The motion constraint equation of the suspension system is established based on the natural coordinates, including: Use the "two-point two-vector" natural coordinate method to describe each rigid body and establish the single rigid body constraint equation for each rigid body; analyze the kinematic joints connecting two adjacent rigid bodies in the suspension system and establish the kinematic joint constraint equations; All single rigid body constraint equations and kinematic pair constraint equations constitute the total kinematic constraint equations of the suspension system, which are solved using the Newton-Raphson iterative method.

9. The method for identifying suspension hard point parameters based on natural coordinate modeling according to claim 8, characterized in that: The step 2 specifically includes: A general objective function of the general form of sensitivity analysis is constructed based on the calculation formula of the suspension kinematic characteristic parameters, and a first-order sensitivity calculation formula is constructed based on the motion constraint equation of the suspension system. The first-order sensitivity calculation formula contains multiple derivative terms; an accompanying variable is introduced into the suspension hard point identification objective function, and by solving the accompanying variable, the first-order sensitivity value of the suspension hard point identification objective function with respect to the suspension hard point is solved.

10. The method for identifying suspension hard point parameters based on natural coordinate modeling according to claim 9, characterized in that: The step 3 specifically includes: According to the sensitivity analysis results, a group of design variables with the largest sensitivity values ​​are selected as parameter identification and optimization variables; The BFGS variable scale optimization algorithm is used to optimize the selected design variables; The search direction of the BFGS variable scale optimization algorithm is calculated by the sensitivity value, and the search step size is optimized by the golden section method.

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