A method for optimizing and analyzing the deformation sensitivity of screw based on Sobol method

Abstract

The invention discloses a method for optimizing and analyzing the deformation sensitivity of a screw based on the Sobol method. The parameter value range of the Sobol sampling is established according to the transmission structure of the ball screw and the load condition of the screw in motion. The mathematical model of the axial stiffness and torsional stiffness of the screw transmission is established on the premise that the screw transmission operates normally under all operating conditions of the machine tool; the Sobol method is input, and the sensitivity is graded by the contribution ratio of the parameters to the output variance, and the sensitivity of the axial stiffness and torsional stiffness of different node ranges of the screw is sorted. The data output by the Sobol method is used as the result of the sensitivity analysis, and the comprehensive contribution of the axial and torsional stiffness at different nodes is analyzed. The invention can reduce the failure rate of the screw transmission to a certain extent, improve the reliability of the screw transmission, and simplify the maintenance and fault detection work of the maintenance personnel on the screw. The method is suitable for screw transmissions with different structures.

Description

Technical Field

[0001] The invention belongs to the field of ball screw wear analysis, and in particular relates to an analysis method for analyzing the contribution of different parameters when the Monte Carlo analysis is applied to the screw wear. Background Art

[0002] Screw drive is an indispensable part of machine tools. The accuracy of screw drive determines the machining accuracy and stability of machine tools to a large extent. However, due to the complex selection process and different application positions of screw drive, it is cumbersome to study the accuracy of screw. When the wear of the screw occurs in different installation positions, the failure forms are different and may be caused by many factors. Therefore, it is impossible to determine the specific contribution of the parameters that cause the failure. Therefore, it is of great significance to the maintenance of the screw and the maintenance of the accuracy of the transmission system to analyze the different parameters that cause screw wear and the contribution index of the parameters that cause wear. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of the contribution of different parameters to the wear of the screw during the screw transmission process, and propose an analysis method based on Sobol. The specific technical solution is as follows:

[0004] A method for optimizing and analyzing the axial and torsional deformation sensitivity of a screw based on the Sobol method comprises the following steps:

[0005] S1. Establish the parameter value range of the Sobol method sampling according to the transmission structure of the ball screw and the load condition of the screw in motion. In this method, starting from the screw transmission, the deformation of the load point is taken as the analysis research object, and the global sensitivity value of the axial stiffness and torsional stiffness of each load point of the screw transmission is analyzed. The load points are divided into different value ranges, and a three-dimensional model of the screw transmission is built. The grid and nodes are divided according to the structure of the transmission system, and a model is established according to the stiffness change of the load point analyzed, the sample parameters are selected, and the parameter range is analyzed.

[0006] S2. Based on the premise that the screw drive operates normally in all operating states of the machine tool, a mathematical model of the axial stiffness and torsional stiffness of the screw drive is established as the main basis for parameter analysis. The comprehensive contribution is calculated based on the influence of each node parameter on the stiffness, and the degree of deformation of the screw under load in different node ranges is obtained. The degree of wear and weakness of the screw can be analyzed, providing an important basis for the optimization of screw selection.

[0007] S3. Input the Sobol method, use the parameter to grade the sensitivity of the contribution ratio of the output variance, and rank the sensitivity of the axial stiffness and torsional stiffness of different node ranges of the screw.

[0008] S4. Use the data output by the Sobol method as the result of sensitivity analysis, and analyze the comprehensive contribution of axial and torsional stiffness at different nodes.

[0009] Furthermore, the step S1 includes: dividing the nodes and the network through structural analysis of the ball screw, establishing a stiffness model in combination with the load conditions, and selecting sampling sample parameters.

[0010] Furthermore, step S2 includes: establishing a stiffness model based on the node parameters divided in step 1, and establishing a mathematical model of axial stiffness and torsional stiffness to obtain the axial deformation of the screw.

[0011]

[0012] The loading force is F, in N, let L be the total length of the screw, l is the distance from the load point to the axial fixed point of the screw, in mm, and E is the elastic modulus of the screw material. For steel: E = 2.07 × 10 5 MPa, d is the diameter of the ball screw at the load point, unit is mm.

[0013] In the torsional direction, T is an expression formed by the concentrated inertia of the motor, the coupling and the bearing, and the inertia of the ball screw. S represents the free length between the bearing and the ball screw nut in the ball screw. G represents the shear rigidity modulus of the ball screw. B represents the moment of inertia of the polar coordinate section. R represents the angular torsional stiffness of the ball screw.

[0014]

[0015] By analyzing the mathematical model of axial and torsional strain, it can be found that the magnitude of axial deformation is related to the distance between the load point and the axial fixed point of the screw, the screw diameter at the load point, the material elastic modulus, the load force and the total length of the screw. The deformation in the torsional direction is related to the total inertia of the screw transmission system and the stiffness in the torsional direction. By analyzing the seven parameters that affect the deformation of the screw, when the other parameters remain unchanged, the axial deformation is the largest at the center of the screw and the smallest at the fixed positions at both ends. For torsional deformation, when the other parameters remain unchanged, the farther away from the fixed end, the greater the deformation.

[0016] Furthermore, the step S3 includes: using the Sobol method to perform random sampling analysis on seven parameters of n nodes.

[0017] Divide the lead screw into n segments of equal length, generating each node with a length of L n , a distribution curve of the load-comprehensive deformation of the screw is formed by randomly selecting n nodes, and the comprehensive deformation curve is related to the deformation of the screw under the load F.

[0018] Let the probability distribution type be yi ~P(a i ,b i ), where i = 1, 2, 3, 4, 5, 6, 7, corresponding to the seven parameters of the influence function y = (l, L, F, E, d, T, R), a i is the corresponding y i The mean of the uncertain variable in b i Corresponding to y i The variance of , the probability distribution is the random variable distribution.

[0019] Furthermore, the step S4 includes: using the data output by the Sobol method as the result of sensitivity analysis, and analyzing the comprehensive contribution of the axial and torsional stiffnesses at different nodes.

[0020] The torsion and axial deformation are analyzed. In the Sobol method, it can be found that the contribution of torsion deformation to wear is lower than that of axial strain. Through analysis, it can be found that the contribution of torsion deformation to screw wear is higher when the screw parameter L / d>>1. At this time, the torsion deformation and axial deformation caused by the load have a great impact on the wear of the machine tool at the same time. When analyzing and repairing machine tool precision problems, the parameters affecting torsion and axial deformation should be considered at the same time. When L / d≤1, the torsion deformation has little effect on the precision wear of the screw. When analyzing screw problems, the parameters affecting axial deformation can be given priority. Therefore, this invention proposes a reference idea and method for the wear precision analysis of the screw.

[0021] The present invention will be further described below in conjunction with the accompanying drawings BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flow chart of the analysis of this method

[0023] Figure 2 Lead screw differential model

[0024] Figure 3 is the deformation fitting curve under the loading force

[0025] Figure 4 is the comprehensive contribution of the parameter to axial and torsional DETAILED DESCRIPTION

[0026] The embodiments of the present invention are described in detail below with reference to the accompanying drawings:

[0027] like Figure 1 As shown in FIG. 1 , a method for optimizing the sensitivity of the axial and torsional deformation of a screw based on the Sobol method is shown in FIG. 1 . The specific steps are as follows:

[0028] S1. Establish the parameter value range of the Sobol method sampling according to the transmission structure of the ball screw and the load condition of the screw in motion. In this method, starting from the screw transmission, the deformation of the load point is taken as the analysis research object, and the global sensitivity value of the axial stiffness and torsional stiffness of each load point of the screw transmission is analyzed. The load points are divided into different value ranges, and a three-dimensional model of the screw transmission is built. The grid and nodes are divided according to the structure of the transmission system, and a model is established according to the stiffness change of the load point analyzed, the sample parameters are selected, and the parameter range is analyzed.

[0029] S2. Based on the premise that the screw drive operates normally in all operating states of the machine tool, a mathematical model of the axial stiffness and torsional stiffness of the screw drive is established as the main basis for parameter analysis. The comprehensive contribution is calculated based on the influence of each node parameter on the stiffness, and the degree of deformation of the screw under load in different node ranges is obtained. The degree of wear and weakness of the screw can be analyzed, providing an important basis for the optimization of screw selection.

[0030] S3. Input the Sobol method, use the parameter to grade the sensitivity of the contribution ratio of the output variance, and rank the sensitivity of the axial stiffness and torsional stiffness of different node ranges of the screw.

[0031] S4. Use the data output by the Sobol method as the result of sensitivity analysis, and analyze the comprehensive contribution of axial and torsional stiffness at different nodes.

[0032] The step S1 specifically includes:

[0033] like Figure 1 As shown in the figure, from the analysis of parameters to the contribution evaluation, the screw structure is analyzed, the screw transmission model is established, and the screw nodes are marked. The model is established according to the stiffness change of the load point. Figure 2 As shown in the figure, the screw is divided into n sections, and the length of each section is differentiated, that is, the load force on the screw as a whole is simplified to the force on each section, and n groups of different processing parameters can be obtained. By setting up the selection of sample parameters and analyzing the range of parameters. Starting from the deformation of the load point, the global sensitivity value of the axial stiffness and torsional stiffness of each load point of the screw transmission is analyzed. The sampling mechanism of the Sobol method is established through the above method, and the range is divided in the analysis node for sampling to perform quantitative evaluation of sensitivity.

[0034] The step S2 specifically includes: establishing a mathematical model of axial and torsional deformation,

[0035]

[0036]

[0037] F is the load force in N, L is the total length of the screw, l is the distance from the load point to the axial fixed point of the screw in mm, and E is the elastic modulus of the screw material. For steel: E = 2.07 × 10 5 MPa, d is the diameter of the ball screw at the load point in m, T is the expression formed by the concentrated inertia of the motor, coupling and bearing, and the inertia of the ball screw, S is the free length between the bearing and the ball screw nut in the ball screw, G is the shear rigidity modulus of the ball screw, B is the moment of inertia of the polar coordinate section, and R is the angular torsional stiffness of the ball screw.

[0038] The step S3 specifically includes: Figure 2 Each lead screw segment shown is analyzed

[0039] Divide the lead screw into n segments of equal length, and generate nodes with length L n , a distribution curve of the load-comprehensive deformation of the screw is randomly selected from n nodes, and the comprehensive deformation curve is related to the deformation of the screw under load F. Figure 3 As shown in the figure, the relationship between the loading load and deformation of each node, the relationship between the loading load F and the comprehensive deformation is F=f(x), where F is the load, x is the corresponding deformation, and the relationship is the load-deformation relationship curve.

[0040] The probability distribution type is y i ~P(a i ,b i ), where i = 1, 2, 3, 4, 5, 6, 7, corresponding to the seven parameters of the influence function y = (l, L, F, E, d, T, R), a i is the corresponding y i The mean of the uncertain variable in b i Corresponding to y i The variance of , the probability distribution is the random variable distribution.

[0041] By analyzing the n randomly generated nodes, we can get n different parameter value variables, and the kth variable is For each distribution parameter a i For example, it obeys the normal uncertainty distribution, and the Monte Carlo method is used to solve each group of probability and draw the load deformation curve.

[0042] Sample n segments of screws, assuming that the random variable n is i ~φ(0,L) obeys a uniform distribution, and the probability of selecting each variable on the screw from 0 to L is equal.

[0043] Input the Sobol method, and use the sampled parameters to grade the sensitivity of the contribution ratio of the output variance. The sensitivity of the screw length and screw diameter to the comprehensive deformation is as follows.

[0044] When the screw length L is much larger than the screw diameter d, the torsional deformation and axial deformation caused by the load will have a great impact on the wear of the machine tool. When analyzing and repairing machine tool accuracy problems, the parameters that affect torsional and axial deformation should be considered simultaneously.

[0045] When the screw length L is close to the screw diameter d, the torsional deformation has little effect on the precision wear of the screw, and the parameters affecting the axial deformation can be given priority when analyzing the screw problem. Therefore, the invention provides a reference idea and method for the wear precision analysis of the screw.

[0046] The axial stiffness and torsional stiffness of different node ranges of the screw are ranked by sensitivity.

[0047] The step S4 should also include that the wear of the screw is related to the axial strain and the torsional strain, and different parameter analysis methods of the wear in the two situations are considered through step 3.

[0048] like Figure 4 As shown in the figure, when the influence of torsional deformation is small, the wear is more severe when the parameter l is near 1 / 2 of the screw length L, and its main influencing parameters are the load and the screw diameter.

[0049] When the influence of torsional deformation is greater, the screw length L is usually shorter and the lead is smaller. The wear caused by the comprehensive deformation is mainly affected by the stiffness of the screw and the comprehensive rotational inertia composed of the concentrated inertia of the motor, coupling and bearing, and the inertia of the ball screw in the screw transmission.

Claims

1. A screw deformation sensitivity optimization analysis method based on the Sobol method, characterized in that: The following steps are involved: S1. Establish the parameter value range of sobol sampling according to the transmission structure of the ball screw and the load condition of the screw in motion; starting from the screw transmission, take the deformation of the load point as the analysis research object, analyze the global sensitivity value of the axial stiffness and torsional stiffness of each load point of the screw transmission; and divide the load point into different value ranges, build a three-dimensional model of the screw transmission, divide the grid and nodes according to the structure of the transmission system, and establish a model according to the stiffness change of the load point analyzed, build the selection of sample parameters, and analyze the range of parameters; S2. Based on the premise that the screw drive operates normally under all operating conditions of the machine tool, a mathematical model of the axial stiffness and torsional stiffness of the screw drive is established as the basis for parameter analysis; the comprehensive contribution is calculated based on the influence of each node parameter on the stiffness, the degree of deformation of the screw under load in different node ranges is obtained, and the degree of wear and weakness of the screw is analyzed to provide a basis for screw selection optimization; S3. Input the Sobol method, perform sensitivity grading on the contribution ratio of the parameters to the output variance, and perform sensitivity ranking on the axial stiffness and torsional stiffness of different node ranges of the screw; S4, using the data output by the Sobol method as the result of sensitivity analysis, and analyzing the comprehensive contribution of axial and torsional stiffness at different nodes; The step S2 comprises: Under normal operating conditions, the accuracy and processing stability of the screw transmission reach the expected lifespan; the mathematical model of the axial stiffness and torsional stiffness of the screw is theoretically established, the global contribution of each node parameter is analyzed, and the deformation of the load point is taken as the main parameter of the screw wear to analyze the weak link of the screw; the mathematical model of axial stiffness is: the axial deformation of the screw in the loading direction of the screw load point is specified as ΔL, and the loaded force is F, in N; the total length of the screw is L; l is the distance from the load point to the axial fixed point of the screw, in mm; E is the elastic modulus of the screw material; d is the diameter of the ball screw load point, in mm; get The mathematical model of torsional stiffness is: T is the expression formed by the concentrated inertia of the motor, the coupling and the bearing, and the inertia of the ball screw, S represents the free length between the bearing and the ball screw nut in the ball screw, G represents the shear rigidity modulus of the ball screw, B represents the moment of inertia of the polar coordinate section, and R represents the angular torsional stiffness of the ball screw; The relationship between the loading load F and the comprehensive deformation is F=f(x), where F is the load and x is the corresponding deformation; the relationship is the load-deformation relationship curve.

2. A screw deformation sensitivity optimization analysis method based on the Sobol method as claimed in claim 1, characterized in that: The step S1 comprises: A three-dimensional model of the screw drive is established, the screw is divided into networks and nodes, and a model is established based on the stiffness changes of the load points. The sample parameters are selected and the parameter range is analyzed. Starting from the deformation of the load points, the global sensitivity values ​​of the axial stiffness and torsional stiffness of each load point of the screw drive are analyzed. The sampling mechanism of the Sobol method is established through the above method, and the range is divided in the analysis node for sampling to perform a quantitative evaluation of the sensitivity.

3. The method for optimizing and analyzing the deformation sensitivity of a lead screw based on the Sobol method according to claim 1, characterized in that: The step S3 comprises: The Sobol method is used to rank and grade the output values ​​of the screw parameters according to their sensitivity, and to analyze the impact on the screw torsion and axial stiffness; The core of the sobol method is to decompose the lead screw model into a mathematical model of the combination of individual parameters, using the total variance to represent the degree of influence of all parameters on the result, and using the partial variance to represent the influence of a single parameter on the result; the lead screw is divided into n segments of equal length, generating a node length L for each node. n And the comprehensive deformation curve is related to the deformation of the screw under load F, and the probability distribution type is y i ~P(a i ,b i ), where i = 1, 2, 3, 4, 5, 6, 7, corresponding to the seven parameters of the influence function y = (l, L, F, E, d, T, R), a i is the corresponding y i The mean of the uncertain variable in b i Corresponding to y i The variance of , the probability distribution is the random variable distribution; By analyzing the randomly generated n nodes, we can get n different parameter value variables, among which the kth variable is For each distribution parameter a i For example, it obeys the normal uncertainty distribution, and the Monte Carlo method is used to solve each group of probability and draw the load deformation curve.

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