Gap distribution and motion stability control method for high-speed actuators of stamping equipment

Abstract

The present invention discloses a method for gap distribution and motion stability control of a high-speed actuator of stamping equipment, which belongs to the technical field of high-speed stamping equipment. The method establishes a kinematic pair gap distribution optimization model with the motion stability of the high-speed actuator of stamping equipment as the goal and the processing cost and total gap as the constraints; an adaptive sampling method based on local curvature is proposed to obtain samples of high-value design variables to train the proxy model, and the normalized cross-validation error is used to efficiently terminate the training process; a genetic algorithm is used to solve the gap distribution optimization model of the high-speed actuator of stamping equipment and output the result. The present invention establishes a proxy model between the kinematic pair gap and the objective function based on the adaptive sampling method of local curvature, reduces the number of dynamic simulations of the high-speed actuator of stamping equipment during the optimization process, and alleviates the computational burden of gap distribution of stamping equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed stamping equipment, and in particular relates to a method for controlling gap distribution and motion stability of a high-speed actuator of stamping equipment. Background Art

[0002] Due to the relative motion between parts and the existence of machining and assembly errors, clearances in the kinematic pairs of high-speed actuators of stamping equipment are inevitable. The existence of kinematic pair clearances will cause impact forces to be generated during the service of the equipment, resulting in a decrease in the kinematic stability of the stamping equipment. Therefore, it is necessary to reasonably characterize the kinematic stability of the high-speed actuators of stamping equipment and reasonably allocate kinematic pair clearances during the design phase. However, in engineering practice where time-consuming tools such as dynamic simulation are used as auxiliary technologies, especially when clearances are considered, the computing resources required for clearance allocation are very large.

[0003] The proxy model technology can approximate the actual physical model in the sample space, provide an approximate alternative solution for the calculation of the objective function, and greatly reduce the calculation time of the actual gap allocation optimization process. However, the gap allocation problem of high-speed actuators of stamping equipment can use indicators such as power spectrum entropy and Coriolis entropy to evaluate the uncertainty of motion performance. Its clearance of the kinematic pair often shows strong nonlinear characteristics. Therefore, using a proxy model to fit the functional relationship between the two will have a contradiction between accuracy and efficiency. If the sampling of the sample space is completed directly in a single time, the sample size is too small, and the motion performance objective function of the gap allocation problem cannot be accurately represented in the design space; if the sample size is too large, although the global approximation accuracy of the proxy model will be improved, the required computational cost will be significantly increased. Summary of the invention

[0004] In order to solve the shortcomings of the prior art and achieve the purpose of effectively controlling the gap distribution and motion stability of the high-speed actuator of the stamping equipment, the present invention adopts the following technical solutions:

[0005] The method for gap distribution and motion stability control of a high-speed actuator of a stamping equipment comprises the following steps:

[0006] Step S1: Taking the minimization of the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation as the goal, taking the manufacturing cost and the total gap as the constraints, and taking the high-speed actuator motion pair gap as the design variable, a stamping equipment high-speed actuator gap allocation optimization model is constructed;

[0007] Step S2: adopting an adaptive sampling method based on local curvature to obtain samples of high-value design variables, and then training an active learning Kriging model for predicting the motion stability of high-speed actuators to approximate the objective function value;

[0008] Step S3: Combining the genetic algorithm and the active learning Kriging model, the high-speed actuator gap allocation optimization model is solved to obtain the optimal gap allocation scheme for the motion stability of the high-speed actuator of the stamping equipment under the given manufacturing cost and total gap constraints.

[0009] Furthermore, in step S1, the expression of the gap distribution optimization model of the high-speed actuator of the stamping equipment is as follows:

[0010]

[0011] in, The power spectrum entropy representing the deviation of the stamping equipment slide velocity and acceleration from the ideal situation; Represents the design vector composed of the clearances of n kinematic pairs of the high-speed actuator; and The slider velocity functions represent the actual and ideal situations, respectively. and The slider acceleration functions represent the actual and ideal situations, respectively. and represents a given weight factor, It means the slider reciprocates for one cycle; represents the manufacturing cost associated with the kinematic clearance, represents known parameters relevant to manufacturing, represents a given cost ceiling value; Indicates the total clearance of the high-speed actuator motion pair, Indicates a given upper limit on the total gap; and They represent the lower and upper limits of the design vector x, respectively, and are given according to the processing capability and the relative motion requirements of parts.

[0012] Furthermore, the step S2 comprises the following steps:

[0013] Step S2.1: Generate using Latin hypercube sampling within the range of design variables points, used to construct the total sample pool and select Points are used to construct the initial point set as the input of the training sample;

[0014] Step S2.2: construct a dynamic simulation model of the high-speed actuator of the stamping equipment in MSC ADAMS software, and calculate the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation as the output of the training sample set;

[0015] Step S2.3: construct an active learning Kriging model using the current training samples;

[0016] Step S2.4: Calculate the normalized cross-validation prediction error of the current training sample ,judge Is it less than the convergence threshold? , if the convergence condition is not met, jump to step S2.5, if it is met, stop sampling and obtain an active learning Kriging model that meets the convergence condition;

[0017] Step S2.5: Select high-value sample points based on the learning function assisted by local curvature.

[0018] Furthermore, the normalized cross-validation prediction error in step S2.4 is The formula is as follows:

[0019]

[0020] in, represents the output predicted by the active learning Krging model after removing the i-th training sample point, Indicates the output obtained by MSC ADAMS software simulation calculation corresponding to the i-th training sampling point, represents the number of samples in the training data set, and They represent the minimum and maximum output values ​​obtained by simulation calculation respectively.

[0021] Furthermore, the step S2.5 comprises the following steps:

[0022] Step S2.5.1: Use the currently trained active learning Kriging model to predict the remaining sample pool The output of the Hessian matrix is ​​about the input ,in Represents the total sample pool Remove the remaining samples that have been used for training. After completing the Kriging model training, the output Hessian matrix of the input can be directly predicted;

[0023] Step S2.5.2: Using the predicted Heather matrix Calculate the local curvature at the sample point and obtain the curvature term;

[0024] Step S2.5.3: Calculate the remaining sample pool The minimum distance between the sample point and the training sample is obtained to obtain the distance term;

[0025] Step S2.5.4: Based on the curvature term and the distance term, construct a learning function based on local curvature. Use the learning function to find new training samples and go to step S2.2.

[0026] Furthermore, in step S2.5.1, a single-output active learning Kriging model is expressed as:

[0027]

[0028] in, represents the input vector of the active learning Kriging model, represents a given regression function vector, p represents the number of regression functions, represents the regression fitting parameter vector; represents the vector composed of Gaussian functions R, represents the input value of the training data set, represents the number of samples in the training data set, represents the residual vector.

[0029] Furthermore, in step S2.5.1, the Hesser matrix is ​​composed of the second-order derivatives of the output with respect to the input, and the Hesser matrix predicted by the active learning Kriging model is It is expressed as:

[0030]

[0031] Among them, the high-dimensional matrix and The calculation method for each element in is as follows:

[0032]

[0033]

[0034] Among them, i and j represent the index of the input vector. represents the index of the regression function, Indicates the index of the input value for the sample point in the training data set.

[0035] Furthermore, in step S2.5.2, the local curvature is normalized, and the obtained curvature term is expressed as follows:

[0036]

[0037]

[0038] in, Represents the Hesser matrix The i-th eigenvalue of ; and They represent the minimum and maximum values ​​of the local curvature in the remaining sample pool, respectively.

[0039] Furthermore, in step S2.5.3, the minimum distance is normalized, and the distance term obtained is expressed as follows:

[0040]

[0041]

[0042] in, represents the Euclidean distance function, represents the input value of the sample point in the current training set, Represents a given distance scaling factor.

[0043] Furthermore, in step S2.5.4, the learning function , new training samples , represents the curvature term, Represents the distance term.

[0044] The advantages and beneficial effects of the present invention are:

[0045] The present invention aims to minimize the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation, takes the manufacturing cost and the total gap as constraints, takes the high-speed actuator motion pair gap as the design variable, constructs a stamping equipment high-speed actuator gap allocation optimization model, uses a genetic algorithm to perform iterative optimization, and obtains the best gap allocation scheme for the stamping equipment high-speed actuator motion stability under the given manufacturing cost and total gap constraints, thereby achieving effective control of the high-speed actuator motion stability.

[0046] The present invention designs a new local curvature-assisted learning function to improve the accuracy of the Kriging model for predicting the motion stability of high-speed actuators under limited training sampling. First, the Kriging model is derived and the Hesser matrix of the output about the input is predicted. The local curvature at the sample point is calculated using the Hesser matrix, so that the nonlinear degree of the objective function with respect to the design variables in different regions can be fully reflected; secondly, the data redundancy and aggregation of the training samples are avoided with the help of the distance term; finally, the learning function is constructed by combining the local curvature and the distance term to identify high-value training samples and update the Kriging model. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a method for gap distribution and motion stability control of a high-speed actuator of stamping equipment in an embodiment of the present invention.

[0048] Figure 2 It is an ADAMS dynamic simulation model diagram of the high-speed actuator of the stamping equipment in the embodiment of the present invention. DETAILED DESCRIPTION

[0049] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0050] like Figure 1 As shown, the method for gap distribution and motion stability control of a high-speed actuator of a stamping equipment comprises the following steps:

[0051] Step S1: constructing a gap distribution optimization model for high-speed actuators of stamping equipment;

[0052] Specifically, the goal is to minimize the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation, the manufacturing cost and the total gap are taken as constraints, and the high-speed actuator motion pair gap is taken as the design variable to build a stamping equipment high-speed actuator gap allocation optimization model.

[0053]

[0054] in, The power spectrum entropy representing the deviation of the stamping equipment slide velocity and acceleration from the ideal situation; Represents the design vector composed of the clearances of the seven kinematic pairs of the high-speed actuator; and The slider velocity functions represent the actual and ideal situations, respectively. and The slider acceleration functions represent the actual and ideal situations, respectively. It means that the slider reciprocates for one cycle when the spindle speed is 300r / min; Represents the manufacturing cost associated with the kinematic clearance; Indicates the total clearance of the high-speed actuator motion vice; and Respectively represent the lower and upper limits of the design vector value;

[0055] Step S2: Generate a total sample pool using Latin hypercube sampling and select initial samples, build a high-speed actuator dynamics simulation model according to the current design variables, calculate the objective function value corresponding to the current design variables, use the training set to establish an active learning Kriging proxy model, and determine whether the convergence condition is met. If so, proceed to step S3; otherwise, use the Kriging model to predict the output of the Hesser matrix about the input, use the Hesser matrix to calculate the local curvature corresponding to the sampling point, calculate the distance term of the remaining sample pool about the current training sample, build a learning function based on the local curvature and distance term, and add training samples, return to the construction of the high-speed actuator dynamics simulation model according to the current design variables, and continue to execute until the convergence condition is met;

[0056] Specifically, an adaptive sampling method based on local curvature is used to obtain the sampling of high-value design variables, and then the Kriging model is trained to approximate the objective function value, which specifically includes the following steps:

[0057] Step S2.1: Generate using Latin hypercube sampling within the range of design variables Points are used to construct the total sample pool , 60 points are selected from them to construct the initial point set as the input of the training sample;

[0058] Step S2.2: Construct a dynamic simulation model of the high-speed actuator of stamping equipment in MSC ADAMS software, such as Figure 2 As shown, the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation is calculated as the output of the training sample set;

[0059] Step S2.3: construct an active learning Kriging model using the current training samples;

[0060] Step S2.4: Calculate the normalized cross-validation prediction error of the current training sample :

[0061]

[0062] in, is the output predicted by the Krging model after removing the i-th training sample point, is the output obtained by MSC ADAMS software simulation calculation corresponding to the i-th training sampling point, is the number of samples in the training dataset, and are the minimum and maximum output values ​​obtained by simulation calculation;

[0063] judge Is it less than the convergence threshold 0.02? If the convergence condition is not met, go to step S2.5. If it is met, stop sampling and obtain a Kriging model that meets the convergence condition.

[0064] Step S2.5: Select high-value sample points according to the learning function assisted by local curvature;

[0065] Step S2.5.1: Use the currently trained Kriging model to predict the remaining sample pool The output of the Hessian matrix is ​​about the input ,in is the total sample pool Remove the remaining samples that have been used for training;

[0066] Step S2.5.2: Using the predicted Heather matrix Calculate the local curvature at the sample point and normalize it to get

[0067]

[0068]

[0069] in, It is the Heather matrix The i-th eigenvalue of ; and are the minimum and maximum values ​​of the local curvature in the remaining sample pool, respectively;

[0070] Step S2.5.3: Calculate the remaining sample pool The minimum distance between the sample point and the training sample, and normalize it to get the distance term

[0071]

[0072]

[0073] in, is the Euclidean distance function, is the input value of the sample point in the current training set;

[0074] Step S2.5.4: Constructing a learning function based on local curvature , using the learning function to find new training samples , and go to step S2.2.

[0075] Step S3: Searching for the optimal solution by combining genetic algorithm and Kriging model;

[0076] Specifically, the optimization model of high-speed actuator gap allocation is solved by combining genetic algorithm and Kriging model, and the optimal gap allocation scheme for the motion stability of high-speed actuator of stamping equipment is obtained under given manufacturing cost and total gap constraints.

[0077] The values ​​of the kinematic clearance of the high-speed actuator before and after optimization are shown in Table 1. The weighted sum of the power spectrum entropy of the slider velocity and acceleration of the stamping equipment before optimization was 1.5322, and after optimization it was 1.2101, a decrease of 21.02%; the manufacturing cost related to the kinematic clearance of the high-speed actuator before optimization was 40.9132, and after optimization it was 39.9899, ​​a decrease of 2.26%; the total clearance before optimization was 0.28mm, and after optimization it was 0.2797mm, a decrease of 0.11%. The optimization results meet the requirements of motion stability control of high-speed actuators of stamping equipment.

[0078] Table 1 Comparison of initial value and optimization result of motion pair clearance of high-speed actuator

[0079] <![CDATA[ x 1]]> <![CDATA[ x 2]]> <![CDATA[ x 3]]> <![CDATA[ x 4]]> <![CDATA[ x 5]]> <![CDATA[ x 6]]> <![CDATA[ x 7]]> Initial value (mm) 0.03 0.03 0.03 0.05 0.05 0.05 0.04 After optimization(mm) 0.0364 0.0391 0.0399 0.0403 0.0440 0.0364 0.0436

[0080] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling the gap distribution and motion stability of a high-speed actuator of a stamping equipment, characterized in that The steps include: Step S1: Taking the minimization of the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation as the goal, taking the manufacturing cost and the total gap as the constraints, and taking the high-speed actuator motion pair gap as the design variable, a stamping equipment high-speed actuator gap allocation optimization model is constructed; Step S2: adopting an adaptive sampling method based on local curvature to obtain samples of high-value design variables, and then training an active learning model for predicting the motion stability of high-speed actuators to approximate the objective function value; comprising the following steps: Step S2.1: Generate N using Latin hypercube sampling within the range of design variables p points, used to construct the total sample pool P, and select N from it s Points are used to construct the initial point set as the input of the training sample; Step S2.2: construct a dynamic simulation model of a high-speed actuator of a stamping equipment, and calculate the power spectrum entropy of the deviation between the stamping equipment slider movement speed and acceleration and the ideal situation as the output of the training sample set; Step S2.3: construct an active learning model using the current training samples; Step S2.4: Calculate the normalized cross-validation prediction error ε of the current training sample cv , judge ε cv Is it less than the convergence threshold ε? If the convergence condition is not met, jump to step S2.

5. If it is met, stop sampling and obtain an active learning model that meets the convergence condition. Step S2.5: Select high-value sample points according to the learning function assisted by local curvature; Step S3: Combining the genetic algorithm and the active learning model, the high-speed actuator gap allocation optimization model is solved to obtain the optimal gap allocation scheme for the motion stability of the high-speed actuator of the stamping equipment under the given manufacturing cost and total gap constraints.

2. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 1, characterized in that: In step S1, the expression of the gap distribution optimization model of the high-speed actuator of the stamping equipment is as follows: x min ≤x≤x max Where F(x) represents the power spectrum entropy of the deviation of the stamping equipment slider motion speed and acceleration from the ideal situation; x = [x1,...,x n ] represents the design vector composed of the clearances of n kinematic pairs of the high-speed actuator; and Represent the actual and ideal slider velocity functions, respectively. and represents the actual and ideal slider acceleration functions, α and β represent the given weight factors, T0 represents one cycle of slider reciprocating motion; C(x) represents the manufacturing cost related to the kinematic pair clearance, a0, a1, a2, a3 represent the known parameters related to manufacturing, C0 represents the given cost upper limit; G(x) represents the total clearance of the kinematic pair of the high-speed actuator, G0 represents the given total clearance upper limit; x min and x max They represent the lower and upper limits of the design vector x, respectively, and are given according to the processing capability and the relative motion requirements of parts.

3. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 1, characterized in that: The normalized cross-validation prediction error ε in step S2.4 cv The formula is as follows: in, represents the output predicted by the active learning model after removing the i-th training sample point, y i Indicates the output obtained by software simulation calculation corresponding to the i-th training sampling point, N t represents the number of samples in the training data set, y min and max They represent the minimum and maximum output values ​​obtained by simulation calculation respectively.

4. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 1, characterized in that: The step S2.5 comprises the following steps: Step S2.5.1: Use the currently trained active learning model to predict the remaining sample pool P r The output of the Hessian matrix H with respect to the input, where P r Represents the total sample pool P minus the remaining samples that have been used for training; Step S2.5.2: Calculate the local curvature at the sample point using the predicted Heather matrix H to obtain the curvature term; Step S2.5.3: Calculate the remaining sample pool P r The minimum distance between the sample point and the training sample is obtained to obtain the distance term; Step S2.5.4: Based on the curvature term and the distance term, construct a learning function based on local curvature, use the learning function to find new training samples, and go to step S2.

2.

5. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 4, characterized in that: In step S2.5.1, a single-output active learning model is represented as: Where x=[x1,x2,...,x n ] represents the input vector of the active learning model, f(x)=[f1(x),f2(x),...,f p (x)] represents the given regression function vector, p represents the number of regression functions, β * represents the regression fitting parameter vector; represents the vector composed of Gaussian functions R, Represents the input value of the training data set, N t represents the number of samples in the training data set, γ * represents the residual vector.

6. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 5, characterized in that: In step S2.5.1, the Heather matrix is ​​composed of the second-order derivatives of the output with respect to the input. The Heather matrix H predicted by the active learning model is expressed as: H(x)=H f (x)b * +H r (x)c * Among them, the high-dimensional matrix H f (x) and H r The calculation method for each element in (x) is as follows: Where i and j represent the index of the input vector, k = 1, 2, ..., p represents the index of the regression function, and l = 1, 2, ..., N t Represents the index of the input value to the training dataset.

7. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 4, characterized in that: In step S2.5.2, the local curvature is normalized, and the obtained curvature term is expressed as follows: Among them, λ i represents the i-th eigenvalue of the Hessian matrix H; L min and L max They represent the minimum and maximum values ​​of the local curvature in the remaining sample pool, respectively.

8. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 4, characterized in that: In step S2.5.3, the minimum distance is normalized, and the distance term obtained is expressed as follows: D(x)=min(E(x,s1),...,E(x,s i ),...,E(x,s Nt )),x∈P r Where E(·) represents the Euclidean distance function, s i ,i=1,2....,N t Represents the input value of the sample point in the current training set, and τ represents a given distance scaling factor.

9. The method for gap distribution and motion stability control of a high-speed actuator of stamping equipment according to claim 4, characterized in that: In step S2.5.4, the learning function New training samples represents the curvature term, Represents the distance term.

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