A machine tool precision design method based on attitude deviation prior and error sensitivity

Abstract

The present invention discloses a method for designing machine tool precision based on posture deviation and error sensitivity. The method comprises: establishing a spatial geometric error model of a five-axis machine tool; constructing a geometric error sampling group and inputting it into the model together with the test sampling points for processing to obtain the posture deviation of the tool; performing overall scaling processing of the initial tolerance value of the geometric error term with equivalent precision to obtain the initial tolerance value that meets the precision requirements; performing cost optimization processing using a sensitivity analysis method based on variance decomposition to obtain the cost-optimized tolerance value of the geometric error term, iterating until the posture deviation reaches the target precision, and outputting the final tolerance value to realize the precision design of the five-axis machine tool. The method of the present invention does not require pre-measurement of all the geometric errors of the machine tool, and has excellent application flexibility and versatility, which makes up for the problem that most existing studies ignore the posture deviation of the five-axis machine tool. The output precision allocation scheme can simultaneously ensure that the posture deviations of the machine tool all reach the target precision.

Description

Technical Field

[0001] The present invention relates to a machine tool precision design method based on posture deviation prior and error sensitivity, relates to the field of machine tool processing precision design, and specifically relates to a machine tool precision design method. Background Art

[0002] Five-axis machine tools offer unique advantages in complex surface machining and are widely used in aviation, aerospace, shipbuilding, automotive, and defense industries. Their machining accuracy directly reflects a country's advanced manufacturing technology. Geometric error is one of the primary factors affecting machine tool machining accuracy. It is characterized by high systematicity, good repeatability, and long-term stability. Therefore, compensating for geometric error and rationally designing geometric accuracy have become viable methods for improving overall machine tool machining accuracy.

[0003] Accuracy allocation of machine tool geometric errors is a crucial step in forward machine tool precision design. However, current approaches to allocating accuracy to five-axis machine tools primarily rely on empirical data and lack theoretical guidance. Existing research on geometric error accuracy allocation for five-axis machine tools requires pre-measurement of all machine tool geometric errors and identification of key errors based on these measurements. These methods can only qualitatively identify key geometric error terms, while relatively few studies have quantitatively determined guidance or recommended values ​​for the widths of various geometric error tolerance bands. This results in limited guidance for forward machine tool design. Furthermore, most studies focus solely on positioning deviations, neglecting consideration of attitude deviations. This results in uncertainties in workpiece machining quality during operations where attitude deviations are critical, such as side milling, boring, and reaming. Summary of the Invention

[0004] To address the issues presented in the prior art, this invention provides a method for machine tool precision design based on attitude deviation prioritization and error sensitivity. This invention proposes the concept of cost sensitivity and a precision allocation method that sequentially adjusts geometric error terms that affect attitude deviation and those that do not. This method addresses the limitations of existing research on practical application, which stem from the requirement to pre-measure all geometric errors of a machine tool. Furthermore, most studies fail to consider the cost of geometric error terms and attitude deviation for five-axis machine tools.

[0005] The technical solution adopted in the present invention is:

[0006] The machine tool precision design method based on attitude deviation prior and error sensitivity of the present invention includes:

[0007] 1) Based on the kinematic chain and topological structure of the five-axis machine tool, the spatial geometric error model of the five-axis machine tool is established through the homogeneous coordinate transformation method.

[0008] 2) According to the initial tolerance values ​​of various geometric error items of the five-axis machine tool, normal distribution sampling is performed to obtain several groups of sampling values ​​of various geometric error items, thereby constructing several groups of geometric error sampling groups; each group of geometric error sampling groups and the test sampling points in the five-axis coordinates of the five-axis machine tool are input into the spatial geometric error model of the five-axis machine tool for processing, and after processing, the spatial geometric error model of the five-axis machine tool outputs a group of position deviations and posture deviations of the five-axis machine tool corresponding to each test sampling point.

[0009] 3) For the initial tolerance values ​​of each geometric error item of the five-axis machine tool and the position deviation and posture deviation of the tool of each group of five-axis machine tools obtained by each geometric error sampling group, an overall scaling processing with equivalent accuracy is performed to obtain the initial tolerance values ​​of each geometric error item that meets the accuracy requirements.

[0010] 4) Based on the initial tolerance values ​​of each geometric error term that meets the accuracy requirements, cost optimization processing is performed using a sensitivity analysis method based on variance decomposition. After processing, the cost-optimized tolerance values ​​of each geometric error term are obtained, and the cost-optimized tolerance values ​​of each geometric error term are returned to the same operation as the initial tolerance values ​​in step 2) until the posture deviation and position deviation of the tool of the five-axis machine tool reach the preset target accuracy in turn, and the final tolerance values ​​of each geometric error term that meet the accuracy requirements are output as the optimal accuracy of the five-axis machine tool, thereby realizing the accuracy design of the five-axis machine tool.

[0011] The cost can be specifically measured by the width of the allowable interval of the geometric error term.

[0012] In the step 2), the five-axis machine tool includes 41 geometric error items, and the initial tolerance value of each geometric error item is the preset allowable interval width corresponding to each geometric error item. The selected initial tolerance value of the geometric error item is roughly selected based on the conventional value or measured value of each geometric error item. The initial value will not affect the optimal accuracy distribution scheme output by the final convergence of the method; each group of geometric error sampling groups includes a sampling value of each of the 41 geometric error items.

[0013] The selection of the test sampling points of the five-axis coordinates of the five-axis machine tool is as follows:

[0014] For each of the four body diagonals in the rectangular workspace of the three linear axes of the five-axis machine tool, M test sampling points are selected symmetrically on both sides of the center of the body diagonal, and a total of 4M test sampling points are selected for the four body diagonals; for the rotating axis B axis of the five-axis machine tool, N mutually spaced test sampling points are arbitrarily selected within the travel range of the rotating axis B axis; for the rotating axis C axis of the five-axis machine tool, P mutually spaced test sampling points are arbitrarily selected within the travel range of the rotating axis C axis, and finally m test sampling points are selected, m = 4M + N + P.

[0015] A set of geometric error sampling groups and each selected test sampling point are input into the spatial geometric error model of the five-axis machine tool. After processing, the spatial geometric error model of the five-axis machine tool outputs a set of position deviations and posture deviations of the tool of the five-axis machine tool generated at each test sampling point.

[0016] The spatial geometric error model of the five-axis machine tool is as follows:

[0017]

[0018] Among them, ΔP and ΔO are the position deviation and posture deviation of the tool of the five-axis machine tool respectively; E is the error matrix of the five-axis machine tool; l is the tool length of the five-axis machine tool; ΔP x , ΔP y and ΔP z They are the components of the tool position deviation ΔP in the X, Y and Z directions of the five-axis coordinates of the five-axis machine tool, ΔO x , ΔO y and ΔO z are the components of the tool posture deviation in the X, Y and Z directions of the five-axis coordinates of the five-axis machine tool; is the actual transformation matrix from the tool coordinate system to the workpiece coordinate system in the five-axis coordinates of the five-axis machine tool, It is the ideal transformation matrix from the tool coordinate system to the workpiece coordinate system in the five-axis coordinates of the five-axis machine tool; each set of geometric error sampling groups and the test sampling points of the five-axis coordinates of the five-axis machine tool are input into the error matrix E of the five-axis machine tool.

[0019] The spatial geometric error model of the five-axis machine tool includes all 41 geometric errors of the five-axis machine tool. The input of the model is the 41 geometric error values ​​and the five-axis nominal displacement, that is, several test sampling points selected in the five-axis coordinates. The output is the position deviation and posture deviation of the tool of the five-axis machine tool under the five-axis coordinates and error level.

[0020] In step 3), before performing a sensitivity analysis on the initial value solution, the initial value solution needs to be scaled to a certain extent using the precision equivalent overall scaling algorithm proposed in the present invention so that the solution's posture deviation has the target accuracy. Only then can the sensitivity analysis and cost analysis of the solution be performed. The precision equivalent overall scaling process is specifically as follows:

[0021] After obtaining the position deviation and posture deviation of the tools of each geometric error sampling group and its corresponding five-axis machine tools according to step 2), the position deviation and posture deviation of the tools of each five-axis machine tool corresponding to each geometric error sampling group are judged by frequency thresholds. First, the first frequency f of all tools whose position deviations are less than the preset position deviation threshold is counted. PThen, the second frequency f of all tools whose posture deviation is less than the preset posture deviation threshold is counted. O , when the first frequency f P and the second frequency f O When one or two of the frequencies are not in the preset frequency interval [f0-Δf, f0+Δf], where f0 is the preset frequency and Δf is half of the preset frequency interval width, feedback scaling is performed on the current geometric error sampling group, i.e., the first frequency f that is not in the preset frequency interval is used to P Or the second frequency f O The frequency difference between the initial frequency f0 is used as feedback to scale the initial tolerance values ​​of each geometric error item of the five-axis machine tool as a whole to obtain the precision optimization tolerance value of each geometric error item, and then return to step 2) to perform the same operation as the initial tolerance value until the first frequency f P and the second frequency f O When the number of times the frequency range is within the preset frequency interval [f0-Δf, f0+Δf] reaches the preset number of simulations, the tolerance values ​​of each geometric error item that meets the accuracy requirements are output.

[0022] In step 4), the cost optimization process based on the sensitivity analysis method of variance decomposition is specifically as follows:

[0023] 4.1) Establish geometric error cost tolerance model and error cost sensitivity model.

[0024] 4.2) For each angular error term that affects the posture deviation in each geometric error term, the tolerance value of each angular error term in the tolerance value of each geometric error term that meets the precision requirements obtained in step 3) is input into the geometric error term cost tolerance model for processing. After processing by the geometric error term cost tolerance model, the part processing cost of the five-axis machine tool is output. Then, a sensitivity analysis is performed on each angular error term. The tolerance value of each angular error term is input into the error cost sensitivity model for processing. The error cost sensitivity model outputs the cost sensitivity index of each angular error term. The cost sensitivity index of each angular error term is used as feedback to perform feedback scaling processing on the tolerance value of each angular error term to obtain the cost optimized tolerance value of each angular error term. Then, return to step 2) and perform the same operation as the initial tolerance value until the obtained part processing cost of the five-axis machine tool reaches the lowest. At this time, the cost sensitivity index of the angular error term that affects the posture deviation converges, and the final tolerance value of each angular error term that meets the precision requirements is output.

[0025] 4.3) For each residual error term that affects the position deviation in each geometric error term, perform the same operation as for each angular error term in step 4.2). When the cost sensitivity of the residual error term converges, the final tolerance value of each residual error term that meets the accuracy requirements is output.

[0026] 4.4) The final tolerance values ​​of each angular error term and each residual error term that meet the accuracy requirements are together the final tolerance values ​​of each geometric error term that meet the accuracy requirements, which serves as the optimal accuracy of the five-axis machine tool, thereby realizing the precision design of the five-axis machine tool, so that the posture deviation and position deviation of the five-axis machine tool reach the target accuracy.

[0027] In the step 4.1), the geometric error term cost tolerance model specifically adopts the reciprocal square model.

[0028] The geometric error cost tolerance model is as follows:

[0029]

[0030] Where C(T) represents the part machining cost under tolerance value T; A represents a fixed cost constant that is independent of tolerance value T; and B represents the characteristic curve coefficient that is related to tolerance value T. This coefficient must be determined based on the difficulty of achieving high precision for different geometric error terms. Specifically, for difficult-to-achieve conditions, the coefficient should be larger, while for easy-to-achieve conditions, the coefficient should be smaller.

[0031] In step 4.1), the error cost sensitivity model is as follows:

[0032]

[0033] Among them, ω i represents the cost sensitivity index of the i-th geometric error term; represents the average sensitivity of the i-th geometric error term at each test sampling point in the overall workspace of the five-axis machine tool; C i represents the estimated cost of the i-th geometric error term, k i represents the cost coefficient of the i-th geometric error term, T i Indicates the tolerance value of the i-th geometric error term.

[0034] The sensitivity analysis method based on variance decomposition is used to perform sensitivity analysis on the spatial geometric error model, and the sensitivity index of 41 geometric error items at a certain five-axis coordinate point P is obtained. P S i (i=1,2,…,41). Then, by testing the sampling point P j A sensitivity analysis is performed at each of the test sampling points P. j Sensitivity index at Finally, the sensitivity indices of the 41 geometric errors at all test sampling points are averaged, and the obtained average sensitivity index is used to express the sensitivity of the geometric errors in the overall workspace of the machine tool, as shown below:

[0035]

[0036] The specific form of the cost sensitivity index finally obtained is the ratio of the average sensitivity index of the geometric error term to the estimated cost, which reflects the impact of the cost change of the geometric error term on the accuracy.

[0037] In step 4.2), the cost sensitivity index of each angle error term is used as feedback to perform feedback scaling processing on the tolerance value of each angle error term, as follows:

[0038] First, obtain the cost sensitivity index ω of each angle error term that affects the posture deviation i Then, the average cost sensitivity index of each angle error term is calculated Then, the cost sensitivity index ω of each angle error term that affects the posture deviation is i The difference between the average value and the average value is used as feedback to perform feedback scaling on the tolerance value of each angle error item, that is, the initial tolerance value is The tolerance value obtained meets the accuracy requirements Adjust the cost optimization tolerance value Where k represents the scaling factor, and the cost optimization tolerance value is obtained.

[0039] The electronic device of the present invention comprises: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method described above.

[0040] The computer-readable storage medium of the present invention stores program data thereon, and when the program data is executed by a processor, the method described above is implemented.

[0041] The beneficial effects of the present invention are:

[0042] 1) The method of the present invention does not require pre-measurement of all the geometric errors of the machine tool. It only requires the approximate distribution range of each geometric error item and a suitable cost tolerance model, which can provide a reference for precision design at the beginning of machine tool design; 2) The present invention can reasonably modify the geometric error model and cost tolerance model according to the specific machine tool configuration and enterprise data, and has better application flexibility and versatility; 3) The present invention makes up for the problem that most existing studies ignore the posture deviation of five-axis machine tools. The output precision distribution scheme can simultaneously ensure that the position deviation and posture deviation of the machine tool reach the target accuracy.

[0043] In summary, the present invention reduces the cost of the output precision allocation scheme through the error cost sensitivity index, and achieves the target precision of the posture deviation and position deviation of the machine tool by successively adjusting the geometric error terms affecting the posture deviation and the position deviation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of the method of the present invention;

[0045] Figure 2 The following is a schematic diagram of the structure and kinematic chain structure of the BC double-turntable five-axis machine tool, where: Figure 2 (a) is a schematic diagram of the structure of the BC double-turntable five-axis machine tool. Figure 2 (b) is a schematic diagram of the kinematic chain structure of the BC double-turntable five-axis machine tool;

[0046] Figure 3 : is a test sampling point distribution diagram of the linear axis and the rotation axis in an embodiment of the present invention;

[0047] Figure 4 This is a sensitivity analysis result diagram of the initial tolerance value for posture deviation optimization performed by the method of the present invention;

[0048] Figure 5 The cost reduction curve of the posture deviation optimization of the present invention and the sensitivity analysis result diagram after convergence, where: Figure 5 (a) is a schematic diagram of the cost reduction curve of the posture deviation optimization of the present invention, Figure 5 (b) is a sensitivity analysis result diagram after convergence of the posture deviation optimization of the present invention;

[0049] Figure 6 The cost reduction curve of the position deviation optimization of the present invention and the sensitivity analysis result diagram after convergence, wherein, Figure 6 (a) is a schematic diagram of the cost reduction curve of the position deviation optimization of the present invention, Figure 6 (b) is a sensitivity analysis result diagram after convergence of the position deviation optimization of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] like Figure 1 As shown, the machine tool precision design method based on posture deviation and error sensitivity of the present invention is specifically as follows:

[0052] 1) Based on the kinematic chain and topological structure of the five-axis machine tool, the spatial geometric error model of the five-axis machine tool is established through the homogeneous coordinate transformation method.

[0053] 2) According to the initial tolerance values ​​of various geometric error items of the five-axis machine tool, normal distribution sampling is performed to obtain several groups of sampling values ​​of various geometric error items, thereby constructing several groups of geometric error sampling groups; each group of geometric error sampling groups and the test sampling points in the five-axis coordinates of the five-axis machine tool are input into the spatial geometric error model of the five-axis machine tool for processing, and after processing, the spatial geometric error model of the five-axis machine tool outputs a group of position deviations and posture deviations of the five-axis machine tool corresponding to each test sampling point.

[0054] The five-axis machine tool includes 41 geometric error items. The initial tolerance value of each geometric error item is the preset allowable interval width corresponding to each geometric error item. The initial tolerance value of the selected geometric error item is roughly selected based on the conventional value or measured value of each geometric error item. The initial value will not affect the optimal accuracy distribution scheme output by the final convergence of the method; each group of geometric error sampling groups includes a sampling value of each of the 41 geometric error items.

[0055] The selection of test sampling points for the five-axis coordinates of the five-axis machine tool is as follows:

[0056] For each of the four body diagonals in the rectangular workspace of the three linear axes of the five-axis machine tool, M test sampling points are selected symmetrically on both sides of the center of the body diagonal, and a total of 4M test sampling points are selected for the four body diagonals; for the rotating axis B axis of the five-axis machine tool, N mutually spaced test sampling points are arbitrarily selected within the travel range of the rotating axis B axis; for the rotating axis C axis of the five-axis machine tool, P mutually spaced test sampling points are arbitrarily selected within the travel range of the rotating axis C axis, and finally m test sampling points are selected, m = 4M + N + P.

[0057] A set of geometric error sampling groups and each selected test sampling point are input into the spatial geometric error model of the five-axis machine tool. After processing, the spatial geometric error model of the five-axis machine tool outputs a set of position deviations and posture deviations of the tool of the five-axis machine tool generated at each test sampling point.

[0058] The spatial geometric error model of the five-axis machine tool is as follows:

[0059]

[0060] Among them, ΔP and ΔO are the position deviation and posture deviation of the tool of the five-axis machine tool respectively; E is the error matrix of the five-axis machine tool; L is the tool length of the five-axis machine tool; ΔP x , ΔP y and ΔP z They are the components of the tool position deviation ΔP in the X, Y and Z directions of the five-axis coordinates of the five-axis machine tool, ΔO x , ΔO y and ΔO zare the components of the tool posture deviation in the X, Y and Z directions of the five-axis coordinates of the five-axis machine tool; is the actual transformation matrix from the tool coordinate system to the workpiece coordinate system in the five-axis coordinates of the five-axis machine tool, It is the ideal transformation matrix from the tool coordinate system to the workpiece coordinate system in the five-axis coordinates of the five-axis machine tool; each set of geometric error sampling groups and the test sampling points of the five-axis coordinates of the five-axis machine tool are input into the error matrix E of the five-axis machine tool.

[0061] The spatial geometric error model of the five-axis machine tool includes all 41 geometric errors of the five-axis machine tool. The input of the model is the 41 geometric error values ​​and the five-axis nominal displacement, that is, several test sampling points selected in the five-axis coordinates. The output is the position deviation and posture deviation of the tool of the five-axis machine tool under the five-axis coordinates and error level.

[0062] 3) For the initial tolerance values ​​of each geometric error item of the five-axis machine tool and the position deviation and posture deviation of the tool of each group of five-axis machine tools obtained by each geometric error sampling group, an overall scaling processing with equivalent accuracy is performed to obtain the initial tolerance values ​​of each geometric error item that meets the accuracy requirements.

[0063] Before performing sensitivity analysis on the initial value solution, it is necessary to scale the initial value solution to a certain extent using the precision equivalent overall scaling algorithm proposed in this invention so that the posture deviation of the solution reaches the target accuracy. Only then can the sensitivity analysis and cost analysis of the solution be performed. The precision equivalent overall scaling process is as follows:

[0064] After obtaining the position deviation and posture deviation of the tools of each geometric error sampling group and its corresponding five-axis machine tools according to step 2), the position deviation and posture deviation of the tools of each five-axis machine tool corresponding to each geometric error sampling group are judged by frequency thresholds. First, the first frequency f of all tools whose position deviations are less than the preset position deviation threshold is counted. P Then, the second frequency f of all tools whose posture deviation is less than the preset posture deviation threshold is counted. O , when the first frequency f P and the second frequency f O When one or two of the frequencies are not in the preset frequency interval [f0-Δf, f0+Δf], where f0 is the preset frequency and Δf is half of the preset frequency interval width, feedback scaling is performed on the current geometric error sampling group, i.e., the first frequency f that is not in the preset frequency interval is used to P Or the second frequency f OThe frequency difference between the initial frequency f0 is used as feedback to scale the initial tolerance values ​​of each geometric error item of the five-axis machine tool as a whole to obtain the precision optimization tolerance value of each geometric error item, and then return to step 2) to perform the same operation as the initial tolerance value until the first frequency f P and the second frequency f O When the number of times the frequency range is within the preset frequency interval [f0-Δf, f0+Δf] reaches the preset number of simulations, the tolerance values ​​of each geometric error item that meets the accuracy requirements are output.

[0065] 4) Based on the initial tolerance values ​​of each geometric error term that meet the accuracy requirements, cost optimization processing is performed using a sensitivity analysis method based on variance decomposition. After processing, the cost-optimized tolerance values ​​of each geometric error term are obtained. The cost-optimized tolerance values ​​of each geometric error term are returned to the same operation as the initial tolerance values ​​in step 2) until the attitude deviation and position deviation of the tool of the five-axis machine tool successively reach the preset target accuracy. The final tolerance values ​​of each geometric error term that meet the accuracy requirements are output as the optimal accuracy of the five-axis machine tool, thereby achieving the accuracy design of the five-axis machine tool. The cost can be specifically measured by the width of the allowable range of the geometric error term.

[0066] The cost optimization process based on the sensitivity analysis method of variance decomposition is as follows:

[0067] 4.1) Establish geometric error cost tolerance model and error cost sensitivity model.

[0068] The geometric error term cost tolerance model specifically adopts the inverse square model.

[0069] The geometric error cost tolerance model is as follows:

[0070]

[0071] Where C(T) represents the part machining cost under tolerance value T; A represents a fixed cost constant that is independent of tolerance value T; and B represents the characteristic curve coefficient that is related to tolerance value T. This coefficient must be determined based on the difficulty of achieving high precision for different geometric error terms. Specifically, for difficult-to-achieve conditions, the coefficient should be larger, while for easy-to-achieve conditions, the coefficient should be smaller.

[0072] The error cost sensitivity model is as follows:

[0073]

[0074] Among them, ω i represents the cost sensitivity index of the i-th geometric error term; represents the average sensitivity of the i-th geometric error term at each test sampling point in the overall workspace of the five-axis machine tool; Ci represents the estimated cost of the i-th geometric error term, k i represents the cost coefficient of the i-th geometric error term, T i Indicates the tolerance value of the i-th geometric error term.

[0075] The sensitivity analysis method based on variance decomposition is used to perform sensitivity analysis on the spatial geometric error model, and the sensitivity index of 41 geometric error items at a certain five-axis coordinate point P is obtained. P S i (i=1,2,…,41). Then, by testing the sampling point P j A sensitivity analysis is performed at each of the test sampling points P and P, and 41 geometric errors are obtained. j Sensitivity index at Finally, the sensitivity indices of the 41 geometric errors at all test sampling points are averaged, and the obtained average sensitivity index is used to express the sensitivity of the geometric errors in the overall workspace of the machine tool, as shown below:

[0076]

[0077] The specific form of the cost sensitivity index finally obtained is the ratio of the average sensitivity index of the geometric error term to the estimated cost, which reflects the impact of the cost change of the geometric error term on the accuracy.

[0078] 4.2) For each angular error term that affects the posture deviation in each geometric error term, the tolerance value of each angular error term in the tolerance value of each geometric error term that meets the precision requirements obtained in step 3) is input into the geometric error term cost tolerance model for processing. After processing by the geometric error term cost tolerance model, the part processing cost of the five-axis machine tool is output. Then, a sensitivity analysis is performed on each angular error term. The tolerance value of each angular error term is input into the error cost sensitivity model for processing. The error cost sensitivity model outputs the cost sensitivity index of each angular error term. The cost sensitivity index of each angular error term is used as feedback to perform feedback scaling processing on the tolerance value of each angular error term to obtain the cost optimized tolerance value of each angular error term. Then, return to step 2) and perform the same operation as the initial tolerance value until the obtained part processing cost of the five-axis machine tool reaches the lowest. At this time, the cost sensitivity index of the angular error term that affects the posture deviation converges, and the final tolerance value of each angular error term that meets the precision requirements is output.

[0079] The cost sensitivity index of each angle error term is used as feedback to perform feedback scaling on the tolerance value of each angle error term, as follows:

[0080] First, obtain the cost sensitivity index ω of each angle error term that affects the posture deviationi Then, the average cost sensitivity index of each angle error term is calculated Then, the cost sensitivity index ω of each angle error term that affects the posture deviation is i The difference between the average value and the average value is used as feedback to perform feedback scaling on the tolerance value of each angle error item, that is, the initial tolerance value is The tolerance value obtained meets the accuracy requirements Adjust the cost optimization tolerance value Where k represents the scaling factor, and the cost optimization tolerance value is obtained.

[0081] 4.3) For each residual error term that affects the position deviation in each geometric error term, perform the same operation as for each angular error term in step 4.2). When the cost sensitivity of the residual error term converges, the final tolerance value of each residual error term that meets the accuracy requirements is output.

[0082] 4.4) The final tolerance values ​​of each angular error term and each residual error term that meet the accuracy requirements are together the final tolerance values ​​of each geometric error term that meet the accuracy requirements, which serves as the optimal accuracy of the five-axis machine tool, thereby realizing the precision design of the five-axis machine tool, so that the posture deviation and position deviation of the five-axis machine tool reach the target accuracy.

[0083] The present invention takes the BC dual-turret five-axis machine tool as an example to provide a more complete and clear description of the specific implementation of the present invention. The specific embodiments of the present invention are as follows:

[0084] 1) Based on the kinematic chain and topological structure of the BC dual-turret five-axis machine tool, the spatial geometric error model of the machine tool is established through the homogeneous coordinate transformation method, as follows:

[0085] like Figure 2 (a) and Figure 2(b) shows the simplified structure and kinematic connection of a BC dual-turret five-axis machine tool. This machine tool includes three linear axes, X, Y, and Z, and two rotary axes, B and C. The kinematic chain is of the type WCBMXYZT, where W refers to the workpiece, C to the C-axis, B to the B-axis, M to the bed, X to the X-axis, Y to the Y-axis, Z to the Z-axis, and T to the tool. The B and C axes belong to the workpiece kinematic chain, while the X, Y, and Z axes belong to the tool kinematic chain. The kinematic chain follows the sequence "WCS → CCS → BCS → MCS → XCS → YCS → ZCS → TCS." WCS represents the workpiece coordinate system, while CCS, BCS, XCS, YCS, and ZCS represent the coordinate systems of the C, B, X, Y, and Z axes, respectively. MCS represents the machine coordinate system, and TCS represents the tool coordinate system. The kinematic chain of this five-axis machine tool consists of five moving parts: the X / Y / Z / B / C axes. These five moving axes involve a total of 41 geometric errors, including 30 position-dependent geometric errors (PDGEs) and 11 position-independent geometric errors (PIGEs), as shown in Table 1.

[0086] Table 1 List of geometric error items of BC dual-rotary table five-axis machine tool

[0087]

[0088] In the expression of PDGEs, δ represents the straightness error, ε represents the angular error, the first subscript represents the direction of the straightness error or the rotation axis of the angular error, and the second subscript represents the axis where the error is located. For example, δ YX Indicates the straightness error of the X-axis in the Y direction, ε YX Represents the angular error of the X-axis rotating around the Y-axis. PIGEs includes the perpendicularity error and the positioning deviation of the vertical axis of the rotation axis. Among them, S represents the perpendicularity error, its subscript represents the two axes involved in the perpendicularity error, and o represents the positioning deviation of the vertical axis of the rotation axis. The first subscript represents the rotation axis, and the second subscript represents the direction of the positioning deviation. The ideal transformation matrix from the tool coordinate system to the workpiece coordinate system is obtained by the homogeneous coordinate transformation method. and the actual transformation matrix from the tool coordinate system to the workpiece coordinate system In this embodiment, the actual transformation matrix The form is as follows:

[0089]

[0090] Among them, X, Y, Z, B and C represent the nominal displacement of the five axes respectively, and the ideal transformation matrix is This can be obtained by setting all 41 geometric error terms in the above equation to zero. Then the error matrix E is calculated, and finally the position deviation ΔP and attitude deviation ΔO of the machine tool can be calculated.

[0091] 2) Select the geometric error cost tolerance model, the five-axis machine tool tool pose target accuracy, and the initial tolerance value of the geometric error term, specifically:

[0092] The selected cost tolerance model is based on the commonly used reciprocal square model. The target accuracy of the tool pose for a five-axis machine tool is assessed by the probability that the position and attitude deviations of randomly sampled points within the machine's workspace are less than a threshold. Specifically, the probability that the position deviation ΔP ≤ 20 μm and the attitude deviation ΔO ≤ 0.04 urad are both within 95 ± 1%. The initial tolerance values ​​for the selected geometric error terms are roughly selected based on conventional values ​​or measured values ​​for each geometric error term. These initial values ​​do not affect the final optimized value output by the method's final convergence. Specifically, the straightness error term is selected as [-0.01, 0.01] mm, and the angular error term is selected as [-0.02, 0.02] mrad.

[0093] 3) Perform sensitivity analysis on the angular error term that affects the posture deviation in the geometric error term, calculate the cost sensitivity index, and make adjustments and iterations based on the calculation results to make the machine tool posture deviation reach the target accuracy. Specifically:

[0094] First, the initial tolerance value of the geometric error term is scaled to a certain extent by the overall scaling algorithm proposed in this invention, so that the posture deviation of the scheme has the target accuracy. The scaled tolerance value that meets the accuracy requirements is used as the initial optimization value, as shown in Table 2.

[0095] Table 2 Initial values ​​of attitude deviation optimization

[0096]

[0097] The units are straightness error / mm ​​and angular error / μrad; * indicates that the geometric error term has changed.

[0098] In Table 2, ε ZX , ε ZY , ε ZZ 、S XY 、S BX The five angular error terms have not changed. This is because in the process of establishing the local coordinate system, the vectors of these angular error terms are parallel to the tool axis and will not affect the posture deviation. ZY , ε ZZ The two angular error terms coincide with the tool axis and will not affect the position deviation. Therefore, the actual number of error terms that need to be allocated is 39.

[0099] Then, a sensitivity analysis is performed on the scaled solution. The sensitivity analysis method adopts the Sobol method based on variance decomposition. The input of the established geometric error model is 41 geometric error terms and a five-axis coordinate point P. Therefore, a single Sobol sensitivity analysis can only obtain the sensitivity index of the 41 geometric errors to the deviation of the machine tool at the five-axis coordinate point P. P S i (i=1,2,…,41), the sensitivity index characterizes the importance of each geometric error on the positioning deviation of the machine tool at that point. In order to improve the versatility of sensitivity analysis, a sensitivity analysis of the overall workspace of the machine tool is proposed.

[0100] like Figure 3 As shown in the figure, 6 sampling points are selected symmetrically along the 4 diagonal lines of the machine tool linear axis workspace to form a total of 24 3-axis coordinates. Then, 5 sampling points are selected within the travel range of the machine tool B axis and 6 sampling points are selected within the travel range of the C axis. After arranging and combining the sampling points of the linear axis and the rotary axis, 720 test sampling points P are obtained. j (j=1,2,…,720).

[0101] For each sampling point P j By performing a single Sobol sensitivity analysis on the position deviation and attitude deviation, the sensitivity index of the 41 geometric errors of the machine tool at that point can be obtained. The sensitivity index of the geometric error in all sampling points is averaged to obtain the sensitivity index of the geometric error in the overall working space of the machine tool, as shown in the following formula:

[0102]

[0103] in, Indicates the i-th geometric error at the five-axis coordinate point P j The sensitivity index, The sensitivity index of the i-th geometric error in the overall working space of the machine tool (hereinafter referred to as the sensitivity index) is expressed. The sensitivity analysis of the optimization initial values ​​shown in Table 2 is performed, and the results are as follows: Figure 4 As shown in the figure, the sensitivities of the geometric error terms are inconsistent, indicating that the degree of influence of the geometric errors on the final positioning deviation is inconsistent; and the cost sensitivities of the geometric error terms are also inconsistent, indicating that the contribution of the unit cost of the geometric error terms to the final accuracy is also inconsistent.

[0104] The inverse square cost tolerance model is used to calculate the cost of each geometric error of the scaled solution, and then the total geometric error cost of the scaled solution is calculated, as shown in the following formula:

[0105]

[0106] Among them, C(T i ) represents the cost of the i-th geometric error, T i Indicates the width of the tolerance zone for the i-th geometric error, k i represents the cost coefficient of the i-th geometric error. In this embodiment, considering that the difficulty of controlling linear axis PDGEs is usually greater than that of controlling rotary axis PDGEs, and in most cases PIGEs are much larger than PDGEs, is the coefficient k of the cost tolerance model of linear axis PDGEs, rotary axis PDGEs, and PIGEs. i Assign 1, 0.5 and 4 respectively.

[0107] Calculate the cost sensitivity of each geometric error term as shown below:

[0108]

[0109] Among them, ω i represents the cost sensitivity index of the i-th geometric error, Represents the sensitivity index of the i-th geometric error, C i represents the cost of the i-th geometric error.

[0110] Then, the angular error terms that affect the attitude deviation are adjusted iteratively. First, the cost sensitivity index ω of all angular error terms that affect the attitude deviation in the tolerance configuration is calculated. i ; Then, calculate the average cost sensitivity of each geometric error term Then, the tolerance of each geometric error term is calculated as the difference Adjust for feedback to get adjusted tolerance value Then, the adjusted tolerance value Use the aforementioned overall scaling algorithm to scale the posture deviation to the target accuracy, and output the scaled accuracy allocation scheme as the tolerance configuration optimization value. Finally, repeat the first step until the cost sensitivity of all angular error terms affecting the posture deviation converges, and then output the current tolerance configuration as the final optimization value, see Table 3.

[0111] Table 3 Geometric error terms generated during attitude deviation optimization

[0112]

[0113] The unit is the angle error term / μrad.

[0114] During the iteration process, only the angle error term that affects the posture deviation is counted. The cost reduction curve and the sensitivity analysis results after convergence can be found in Figure 6 (a) and Figure 6As shown in (b), the geometric error cost is reduced by 15.2% during the optimization of the pose deviation.

[0115] 4) When the cost sensitivity of the angle error term affecting the posture error converges, sensitivity analysis is performed on the remaining error terms, the cost sensitivity index is calculated, and adjustments are made iteratively based on the calculation results to make the machine tool position deviation reach the target accuracy. Specifically:

[0116] The iterative adjustment method for the residual error term is similar to that for the angular error term, except that the iterative adjustment target shifts from the angular error term that affects the attitude deviation to the residual error term. The constraints and dependent variables in the overall scaling algorithm and sensitivity analysis shift from attitude deviation to position deviation. The overall scaling of the tolerance configuration scheme using position deviation as a constraint yields the optimized initial values ​​shown in Table 4.

[0117] Table 4 Initial value of position deviation optimization

[0118]

[0119] The units are straightness error term / mm and angular error term / μrad.

[0120] Similarly, when the cost sensitivity of the residual error term converges, the current tolerance configuration is output as the optimization final value, see Table 5.

[0121] Table 5 Position deviation optimization final value

[0122]

[0123]

[0124] The units are straightness error term / mm and angular error term / μrad.

[0125] During the iteration process, only the residual error term is counted. The cost reduction curve and the sensitivity analysis results after convergence can be found in Figure 6 (a) and Figure 6 As shown in (b), the geometric error cost is reduced by 34.4% during the optimization of position deviation.

[0126] 5) When the cost sensitivity of the residual error term converges, the accuracy allocation scheme is output to achieve the accuracy allocation with the most optimized cost, specifically:

[0127] The tolerance list of geometric error items after allocation is completed can be found in the combination of Table 3 and Table 5. If this method is not used and a uniform allocation scheme is used, when the scheme has the target accuracy, the tolerance list of geometric error items can be found in Table 6.

[0128] Table 6 Uniform distribution scheme

[0129]

[0130] The units are straightness error term / mm and angular error term / μrad.

[0131] Compared with the uniform distribution scheme, the accuracy distribution scheme output by this method reduces the overall cost by 27.8% while maintaining the target accuracy of the machine tool posture deviation and position deviation.

[0132] To verify the effectiveness of the allocation results, 10,000 sampling points were randomly selected in a uniform distribution within the machine tool workspace according to the travel of each axis. The number and frequency of points with attitude deviation ΔO ≤ 0.04urad and position deviation ΔP ≤ 20μm were counted. The results are shown in Table 7. The frequencies are all within the 95±1% range, indicating that the position deviation and attitude deviation of this allocation scheme meet the aforementioned target accuracy requirements.

[0133] Table 7 Deviation statistics of random sampling points in the workspace

[0134]

[0135] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A machine tool precision design method based on attitude deviation prior and error sensitivity, characterized in that: include: 1) Based on the kinematic chain and topological structure of the five-axis machine tool, the spatial geometric error model of the five-axis machine tool is established through the homogeneous coordinate transformation method; 2) performing normal distribution sampling based on the initial tolerance values ​​of each geometric error item of the five-axis machine tool to obtain several groups of sampled values ​​of each geometric error item, thereby constructing several groups of geometric error sampling groups; inputting each group of geometric error sampling groups and a test sampling point in the five-axis coordinates of the five-axis machine tool into a spatial geometric error model of the five-axis machine tool for processing; after processing, the spatial geometric error model of the five-axis machine tool outputs a group of position deviations and posture deviations of the five-axis machine tool corresponding to each test sampling point; 3) Performing precision equivalent overall scaling processing on the initial tolerance values ​​of each geometric error item of the five-axis machine tool and the position deviation and posture deviation of the tool of each group of five-axis machine tools obtained by each geometric error sampling group, and obtaining the initial tolerance values ​​of each geometric error item that meet the precision requirements after processing; 4) Based on the initial tolerance values ​​of each geometric error term that meets the accuracy requirements, cost optimization processing is performed using a sensitivity analysis method based on variance decomposition. After processing, the cost-optimized tolerance values ​​of each geometric error term are obtained, and the cost-optimized tolerance values ​​of each geometric error term are returned to the same operation as the initial tolerance values ​​in step 2) until the posture deviation and position deviation of the tool of the five-axis machine tool reach the preset target accuracy in turn, and the final tolerance values ​​of each geometric error term that meet the accuracy requirements are output as the optimal accuracy of the five-axis machine tool, thereby realizing the accuracy design of the five-axis machine tool.

2. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 1 is characterized in that: In step 2), the five-axis machine tool includes 41 geometric error items, and the initial tolerance value of each geometric error item is the preset allowable interval width corresponding to each geometric error item; each geometric error sampling group includes a sample value of each of the 41 geometric error items; The selection of the test sampling points of the five-axis coordinates of the five-axis machine tool is as follows: For each of the four body diagonals in the rectangular workspace of the three linear axes of the five-axis machine tool, M test sampling points are symmetrically selected on both sides of the center of the body diagonal, and a total of 4M test sampling points are selected for the four body diagonals; for the rotation axis B axis of the five-axis machine tool, N mutually spaced test sampling points are arbitrarily selected within the travel range of the rotation axis B axis; for the rotation axis C axis of the five-axis machine tool, P mutually spaced test sampling points are arbitrarily selected within the travel range of the rotation axis C axis, and finally m test sampling points are selected, where m = 4M + N + P; A set of geometric error sampling groups and each selected test sampling point are input into the spatial geometric error model of the five-axis machine tool. After processing, the spatial geometric error model of the five-axis machine tool outputs a set of position deviations and posture deviations of the tool of the five-axis machine tool generated at each test sampling point.

3. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 1 is characterized in that: In step 3), the overall scaling process with equivalent precision is specifically as follows: After obtaining the position deviation and posture deviation of the tools of each geometric error sampling group and its corresponding five-axis machine tools according to step 2), the position deviation and posture deviation of the tools of each five-axis machine tool corresponding to each geometric error sampling group are judged by frequency thresholds. First, the first frequency f of all tools whose position deviations are less than the preset position deviation threshold is counted. P Then, the second frequency f of all tools whose posture deviation is less than the preset posture deviation threshold is counted. O , when the first frequency f P and the second frequency f O When one or two of the frequencies are not in the preset frequency interval [f0-Δf, f0+Δf], where f0 is the preset frequency and Δf is half of the preset frequency interval width, feedback scaling is performed on the current geometric error sampling group, i.e., the first frequency f that is not in the preset frequency interval is used to P Or the second frequency f O The frequency difference between the initial frequency f0 is used as feedback to scale the initial tolerance values ​​of each geometric error item of the five-axis machine tool as a whole to obtain the precision optimization tolerance value of each geometric error item, and then return to step 2) to perform the same operation as the initial tolerance value until the first frequency f P and the second frequency f O When the number of times the frequency range is within the preset frequency interval [f0-Δf, f0+Δf] reaches the preset number of simulations, the tolerance values ​​of each geometric error item that meets the accuracy requirements are output.

4. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 1 is characterized in that: In step 4), the cost optimization process based on the sensitivity analysis method of variance decomposition is specifically as follows: 4.1) Establish geometric error cost tolerance model and error cost sensitivity model; 4.2) For each angular error term that affects the posture deviation in each geometric error term, the tolerance value of each angular error term in the tolerance value of each geometric error term that meets the precision requirements obtained in step 3) is input into the geometric error term cost tolerance model for processing. After processing by the geometric error term cost tolerance model, the part processing cost of the five-axis machine tool is output. Then, a sensitivity analysis is performed on each angular error term. The tolerance value of each angular error term is input into the error cost sensitivity model for processing. The error cost sensitivity model outputs a cost sensitivity index for each angular error term. The cost sensitivity index of each angular error term is used as feedback to perform feedback scaling processing on the tolerance value of each angular error term to obtain the cost optimized tolerance value of each angular error term. Then, return to step 2) and perform the same operation as the initial tolerance value until the obtained part processing cost of the five-axis machine tool reaches the lowest, and the final tolerance value of each angular error term that meets the precision requirements is output. 4.3) For each residual error term that affects the position deviation in each geometric error term, perform the same operation as for each angular error term in step 4.2), and output the final tolerance value of each residual error term that meets the accuracy requirements; 4.4) The final tolerance values ​​of each angular error term and each residual error term that meet the accuracy requirements are together the final tolerance values ​​of each geometric error term that meet the accuracy requirements, which serves as the optimal accuracy of the five-axis machine tool, thereby realizing the precision design of the five-axis machine tool, so that the posture deviation and position deviation of the five-axis machine tool reach the target accuracy.

5. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 4 is characterized in that: In the step 4.1), the geometric error term cost tolerance model specifically adopts the reciprocal square model.

6. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 4 is characterized in that: In step 4.1), the error cost sensitivity model is as follows: Among them, ω i represents the cost sensitivity index of the i-th geometric error term; represents the average sensitivity of the i-th geometric error term at each test sampling point in the overall workspace of the five-axis machine tool; C i represents the estimated cost of the i-th geometric error term, k i represents the cost coefficient of the i-th geometric error term, T i Indicates the tolerance value of the i-th geometric error term.

7. The machine tool precision design method based on posture deviation prior and error sensitivity according to claim 4 is characterized in that: In step 4.2), the cost sensitivity index of each angle error term is used as feedback to perform feedback scaling processing on the tolerance value of each angle error term, as follows: First, obtain the cost sensitivity index ω of each angle error term that affects the posture deviation i Then, the average cost sensitivity index of each angle error term is calculated Then, the cost sensitivity index ω of each angle error term that affects the posture deviation is i The difference between the average value and the average value is used as feedback to perform feedback scaling on the tolerance value of each angle error item to obtain the cost optimization tolerance value.

8. An electronic device, characterized in that: include: A memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having program data stored thereon, characterized in that: When the program data is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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