Compensation method for spatial volume error of multi-axis machine tools based on feed-dependent support deformation

Abstract

The present invention discloses a method for compensating spatial volume errors of multi-axis machine tools based on feed-variable support deformation. Different feed analysis methods are proposed for different numbers of feed axes on the same support component, and the feed axes are divided into three specific working conditions. Through the deformation of the support component under specific working conditions, the deformation variable of the feed support joint surface is integrally derived, and the geometric method is further used to establish a mapping relationship between the deformation variable of the feed support joint surface and the motion error. Through the interpolation method based on n differences, a continuous motion error based on feed-variable support deformation is generated. Then, through the spatial matrix transformation method, a machine tool volume error model of feed-variable support deformation is generated. The support deformation, a system error source that changes with the feed position, is constructed into the same volume error model, which improves the accuracy of support deformation prediction, provides a more accurate numerical basis for dynamic compensation of support deformation, and provides a more accurate and intuitive evaluation basis for the structural optimization of the support component.

Description

Technical Field

[0001] The present invention relates to a multi-axis machine tool error compensation method in the machine tool field, and in particular to a multi-axis machine tool spatial volume error compensation method based on feed-dependent support deformation. Background Art

[0002] Machining accuracy is a key performance indicator for machine tools. Numerous factors influence machining accuracy, including geometric error, thermal error, vibration error, and deformation error. Deformation error refers to the error caused by deformation of machine tool components or workpieces due to stress. Machine tool supports support machine tool components, the weight of the workpiece, and cutting forces. Their deformation due to stress has a significant impact on machining accuracy.

[0003] In order to solve the problem of deformation of supporting parts affecting processing accuracy, traditional solutions include improving the rigidity of supporting parts by improving the structural layout or material properties, and adjusting the supporting points of the machine tool base to reduce the impact of the deformation of the machine tool base on processing accuracy. These methods require a lot of effort and cost, and cannot completely eliminate the elastic deformation of the supporting parts; some high-end machine tools dynamically compensate for deformation errors by adding detection and feedback devices to detect the deformation of the moving axis on the supporting parts in real time. This method can compensate for the deformation of the supporting components very well, but the cost is high and there is a problem of low reliability in the harsh processing environment of the machine tool.

[0004] With advancements in simulation and testing technology, the deformation of support systems under different operating conditions can be accurately predicted. The machine tool feed component will exert varying deformation effects on the support structure at different machining positions. Previously, researchers often ignored or simplified this effect, typically using only the deformation under a single, commonly used operating condition to represent the global deformation. This resulted in low reliability in predicting machining accuracy. Summary of the Invention

[0005] In order to solve the problems existing in the background technology, the present invention provides a multi-axis machine tool spatial volume error compensation method based on feed-variable support deformation. The purpose is to obtain a continuous error distribution in the processing space by constructing a spatial variable volume error model of continuous deformation of the feed support, thereby improving the accuracy of deformation error prediction, compensating for the error according to the error distribution, thereby improving the support structure and improving the processing accuracy.

[0006] The technical solutions of the present invention are as follows:

[0007] Step 1: Based on the deformation of each supporting component in the multi-axis machine tool under all working conditions, analyze and determine the deformation curves of the guide rails corresponding to all feed axes in each supporting component under different working conditions;

[0008] Step 2: Based on the motion positions of all feed axes in each supporting component under different working conditions, the deformation curves of the guide rails corresponding to all feed axes under different working conditions are integrated and averaged to obtain the deformation set of the feed support joint surface of all feed axes in each supporting component under different working conditions;

[0009] Step 3: processing the motion error set of all feed axes in each supporting component under different working conditions according to the feed support joint surface deformation set of all feed axes in each supporting component under different working conditions;

[0010] Step 4: Based on the motion error set of all feed axes in each support component under different working conditions, generate the feed space-varying motion error of each support component according to the number of feed axes in each support component;

[0011] Step 5: After using the spatial matrix error transfer method to transfer and integrate the feed space-varying motion errors of each supporting component, the spatial-varying volume error and spatial error model of the multi-axis machine tool are generated. The spatial-varying volume error of the multi-axis machine tool is compensated according to the spatial error model to realize error compensation of the multi-axis machine tool.

[0012] In step 1, for each feed axis of each supporting member, under each working condition, the discrete deformation data of the current feed axis at each guide rail corresponding to the current working condition is determined according to the static deformation amount of the current supporting member in the three translation directions. After linear interpolation of the deformation data of the current feed axis at each guide rail corresponding to the current working condition is performed using the cubic spline interpolation method with non-kinked boundary conditions, the deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are obtained respectively.

[0013] In step 2, for each feed axis of each supporting component, under each working condition, the deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are integrated and averaged respectively according to the motion position under the current working condition, and the feed support joint surface deformation sets of the current feed axis in the three translation directions under the current working condition are obtained respectively. The feed support joint surface deformation set is composed of the feed support joint surface deformations of the four sliding feed members in the current feed axis.

[0014] For the deformation curve of the guide rail in each translation direction under each working condition of each feed axis, the deformation of the feed support joint surface of each sliding feed member in each feed axis is obtained by the following processing formula:

[0015]

[0016] Where E represents the deformation of the feed support interface of the current sliding feed member in the current translation direction of each feed axis under the current working condition, a is the distance between the front end face of the current sliding feed member and the origin end face of the corresponding guide rail, b is the distance between the rear end face of the current sliding feed member and the origin end face of the corresponding guide rail, h1 is the first sampling step, f(x k ) represents the discrete sequence after discrete sampling of the current deformation curve, x k represents the kth sampling point, N1 represents the number of the first sampling points, f(a) represents the deformation of the front end surface of the sliding feed member at the current position, f(b) represents the deformation of the rear end surface of the sliding feed member at the current position, L slide Indicates the length of the feed support joint surface in the feed motion direction.

[0017] In step 3, for each feed axis in each supporting member under each working condition, the feed support interface deformation set in the three translation directions of the current feed axis under the current working condition is decomposed into error directions and the error mean is processed respectively, and the motion error sets in the three translation directions and three rotation directions of the current feed axis under the current working condition are respectively obtained. The motion error set includes translational motion error and rotational motion error. The translational motion error is composed of translation errors in the U-axis direction, the V-axis direction, and the W-axis direction. The rotational motion error is composed of rotation angle error around the U axis, the rotation angle error around the V axis, and the rotation angle error around the W axis. The specific processing formula is as follows:

[0018] D u =[D u11 +D u21 +D u12 +D u22 ] / 4

[0019] D v =[D v11 +D v21 +D v12 +D u22 ] / 4

[0020] D w =[D w11 +D w21 +D w12 +D w22 ] / 4

[0021]

[0022]

[0023]

[0024] Among them, the U axis direction is parallel to the plane formed by the four sliding feed parts and perpendicular to the feed axis movement direction, the V axis direction is the same as the feed axis movement direction, the W axis direction is perpendicular to the plane formed by the four sliding feed parts, and the D u Indicates the translation error in the U-axis direction, D u11 、D u21 、D u12 and D u22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the U axis direction, D v11 、D v21 、D v12 and D v22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the V axis direction, D w11 、D w21 、D w12 and D w22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the W axis direction, w h is the span between two sliding feed members on the same guide rail, w d D is the span between the two guide rails in the current feed axis. v Indicates the translation error in the V-axis direction, D w Indicates the translation error in the W-axis direction, R u Indicates the rotation angle error around the U axis, R v Indicates the rotation angle error around the V axis, h d Indicates the height difference between the two guide rails of the current feed axis when they are not on the same horizontal plane. R w Indicates the rotation angle error around the W axis.

[0025] In step 4, the method for processing the feed space-varying motion error of each supporting member includes the following steps:

[0026] S1: When the number of feed axes in each supporting member is 1, execute S2; when the number of feed axes in each supporting member is 2, execute S3; when the number of feed axes in each supporting member is 3, execute S4, thereby obtaining the feed space-varying motion error of the current supporting member;

[0027] S2: interpolating the errors in the same motion error direction in the motion error sets of the current feed axis in the three translation directions and the three rotation directions under different working conditions to obtain the motion error curves of the current feed axis in different motion error directions;

[0028] S3: First, when the first feed axis is operating in the first working condition, S2 is executed according to the motion error set of the second feed axis under different working conditions to obtain the motion error curve of the second feed axis in different motion error directions under the first working condition of the first feed axis; then, the working condition of the first feed axis is traversed and S2 is repeatedly executed to finally obtain the motion error curve of the second feed axis in different motion error directions under all working conditions of the first feed axis; finally, the motion error curves of the second feed axis in different motion error directions under all working conditions of the first feed axis are interpolated according to the same motion error direction to obtain the motion error surface of the current feed axis in different motion error directions;

[0029] S4: First, when the third feed axis works in one working condition, S3 is executed according to the motion error sets of the first feed axis and the second feed axis under different working conditions to obtain the motion error surface of the current feed axis in different motion error directions under the first working condition of the third feed axis; then the working condition of the third feed axis is traversed and changed, and S3 is repeatedly executed to finally obtain the motion error surface of the current feed axis in different motion error directions under all working conditions of the third feed axis; finally, the motion error surfaces of the current feed axis in different motion error directions under all working conditions of the third feed axis are interpolated according to the same motion error direction to obtain the motion error space of the current feed axis in different motion error directions.

[0030] In step 5, the spatial matrix error transfer method is used to transfer and integrate the feed space-variant motion errors of each supporting component in different motion error directions, and then the spatially variable volume error and spatial error models of the multi-axis machine tool in different motion error directions are generated. Specifically,

[0031] Firstly, the feed space-varying motion errors of each supporting component are transferred into the offset between the tool processing point and the workpiece to be processed point through the homogeneous transformation theory or coordinate transformation transfer method, so as to obtain the space-varying volume error of the multi-axis machine tool in different motion error directions; then, the feed space-varying motion error and error transfer method are used to integrate the space-varying volume error of the multi-axis machine tool in different motion error directions to obtain the spatial error model.

[0032] The principle of the present invention is as follows:

[0033] By dividing the working conditions and considering the influence of the feed axis's motion position on support deformation, the decisive role of the feed support interface deformation on the motion error is derived. A mapping relationship between the interface and the motion error is then established, resulting in the feed axis's variable systematic error. Single and multiple interpolation methods are proposed for different numbers of feed axes on the same support component to improve the accuracy and continuity of deformation error prediction. By constructing a volumetric error model, the motion error based on the deformation of the machine tool support component can be mapped to a spatially variable volumetric error, intuitively demonstrating the continuous distribution of machining errors within the machining space and providing a more accurate numerical basis for error compensation and layout optimization.

[0034] The present invention has the following beneficial effects:

[0035] 1. This invention uses a geometric method to construct a mapping relationship between the feed support interface and motion error. By obtaining the deformation of the support component, a method for generating the feed axis motion error is established, laying the foundation for predicting the impact of support component deformation on machining error.

[0036] 2. The present invention introduces a numerical continuous prediction method into the deformation prediction and motion error analysis process of machine tool support components, and proposes different continuous prediction methods according to the different numbers of feed axes on the same support component, thereby solving the problem of low accuracy of existing methods in predicting the static discrete deformation of machine tool support components.

[0037] 3. The present invention establishes a spatially variable volume error map of a multi-axis machine tool, representing the ideal processing area and the actual processing area in the same space, and can more clearly and intuitively obtain the error size and change trend in space. It can not only provide an evaluation index for the design of machine tool support components, but also provide a numerical basis for error compensation, thereby improving the processing accuracy of the machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a general flow chart of the method of the present invention.

[0039] Figure 2 It is a horizontal machining center which is an example of a specific implementation target of the present invention.

[0040] Figure 3 This is a spatially variable volume error diagram of an example horizontal machining center obtained by the method of the present invention. DETAILED DESCRIPTION

[0041] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0042] like Figure 1 As shown, the present invention includes the following steps:

[0043] Step 1: Based on the deformation of each supporting component in the multi-axis machine tool under all working conditions, analyze and determine the deformation curves of the guide rails corresponding to all feed axes in each supporting component under different working conditions;

[0044] Each supporting component is divided into single-axis, double-axis and three-axis feed supporting components according to the number of feed axes n in itself. Each feed axis has three working conditions, namely working in the middle position and two extreme positions of its own feed axis. Each supporting component has three working conditions. n Each feed axis consists of two parallel and spaced guide rails and four sliding feed members sliding on the two guide rails, with two sliding feed members arranged on each guide rail.

[0045] like Figure 2 In the comparative horizontal machining center shown, the primary support for the Y feed axis is the column, which has only one feed axis, Y. Its structural deformation varies with the feed of the Y axis (single axis). For the X and Z feed axes, the primary support is the bed, which has two feed axes. Its structural deformation varies with the feed of the X and Z axes (double axes). Each feed axis is divided into three operating conditions: an intermediate position and two extreme positions. For n = 1, there are three operating conditions, and for n = 2, there are nine operating conditions.

[0046] In step 1, for each feed axis of each supporting member, under each working condition, the discrete deformation data of the current feed axis at each guide rail corresponding to the current working condition is determined according to the static deformation amount of the current supporting member in the three translation directions (i.e., the xyz axis directions in the spatial coordinate system of the multi-axis machine tool). After the linear difference of the deformation data of the current feed axis at each guide rail corresponding to the current working condition is performed using the cubic spline interpolation method with non-kinked boundary conditions, the continuous deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are obtained. For a supporting member with n feed axes, each feed axis has a linear difference in the three translation directions. n Under these working conditions, the deformation curves of three translation directions are obtained for each of the two guide rails, so each feed axis has a total of 2×3 n+1 The bar becomes a curve.

[0047] In the embodiment, there is a single y feed axis (n=1) on the column. Under three working conditions, the two guide rails of the y feed axis each obtain deformation curves in three directions, with a total of 18 deformation curves; there are double x and z feed axes (n=2) on the bed. Under nine working conditions, the two guide rails of the x and z feed axes can each obtain deformation curves in three directions, with 54 deformation curves each.

[0048] Step 2: According to the motion positions of all feed axes in each supporting component under different working conditions, the deformation curves of the corresponding guide rails of all feed axes under different working conditions are integrated and averaged to obtain the deformation set of the feed support interface of all feed axes in each supporting component under different working conditions; wherein, the feed support interface is the connection surface between the four sliding feed parts and the corresponding guide rails, and the deformation amount of the feed support interface in the motion position under different working conditions determines the motion error of the feed axis. For a supporting component with n feed axes, each feed axis has a 3 n Under the working condition, the deformation variables of the feed support joint surfaces of the four sliding feed parts corresponding to the current feed axis in three directions are recorded as the four feed support joint surface deformations. The four feed support joint surface deformations constitute the feed support joint surface deformation set, so each feed axis has a total of 8×3 n+1 The feed support joint surface is deformed.

[0049] In step 2, for each feed axis of each supporting component, under each working condition, the continuous deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are integrated and averaged respectively according to the motion position under the current working condition, and the feed support joint surface deformation sets in the three translation directions of the current feed axis under the current working condition are obtained respectively. The feed support joint surface deformation set is composed of the feed support joint surface deformations of the four sliding feed parts in the current feed axis.

[0050] For each feed axis and each working condition, the continuous deformation curve of the guide rail in each translation direction is obtained by the following processing formula to obtain the feed support joint surface deformation of each sliding feed member in each feed axis:

[0051]

[0052] Where E represents the deformation of the feed support interface of the current sliding feed member in the current translation direction of each feed axis under the current working condition, a is the distance between the front end face of the current sliding feed member and the origin end face of the corresponding guide rail, v is the distance between the rear end face of the current sliding feed member and the origin end face of the corresponding guide rail, and h1 is the first sampling step. When the first sampling step is small enough, reliable accuracy can be achieved. f(x k ) represents the discrete sequence after discrete sampling of the current deformation curve, x k represents the kth sampling point, N represents the number of sampling points, and x k =a+kh(k=1,2,…,N-1), f(a) represents the deformation of the front end surface of the sliding feed member at the current position, f(b) represents the deformation of the rear end surface of the sliding feed member at the current position, L slide Indicates the length of the feed support joint surface in the feed motion direction.

[0053] Step 3: processing the motion error set of all feed axes in each supporting component under different working conditions according to the feed support joint surface deformation set of all feed axes in each supporting component under different working conditions;

[0054] The purpose of step 3 is to convert the deformation variables of each feed support joint surface obtained in step 2 into the motion error of the feed axis in 6 directions. According to the error analysis theory, the motion error can be decomposed into errors in 6 directions, namely the translation error D in the U, V, and W directions. u ,D v ,D w , and the angular error R around the U, V, and W axes u ,R v ,R w .

[0055] In step 3, for each feed axis in each supporting component under each working condition, the feed support joint surface deformation set of the current feed axis in the three translation directions under the current working condition is decomposed into error directions and the error mean is processed respectively, and the motion error sets of the current feed axis in the three translation directions and three rotation directions under the current working condition are obtained respectively. The motion error set includes translational motion error and rotational motion error. The translational motion error is composed of translation errors in the U-axis direction, the V-axis direction, and the W-axis direction. The rotational motion error is composed of rotation angle error around the U-axis, the V-axis, and the W-axis. The specific processing formula is as follows:

[0056] D u =[D u11 +D u21 +D u12 +D u22 ] / 4

[0057] D v =[D v11 +D v21 +D v12 +D v22 ] / 4

[0058] D w =[D w11 +D w21 +D w12 +D w22 ] / 4

[0059]

[0060]

[0061]

[0062] Among them, the U axis direction is parallel to the plane formed by the four sliding feed parts and perpendicular to the feed axis movement direction, the V axis direction is the same as the feed axis movement direction, the W axis direction is perpendicular to the plane formed by the four sliding feed parts, and the D u Indicates the translation error in the U-axis direction, D u11 、D u21 、D u12 and D u22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the U axis direction, D v11 、D v21 、D v12 and D v22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the V-axis direction, D w11 、D w21 、D w12 and D w22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the W axis direction, w h is the span between two sliding feed members on the same guide rail. Among the four sliding feed members, the span between two adjacent sliding feed members is the same. d D is the span between the two guide rails in the current feed axis. v Indicates the translation error in the V-axis direction, D w Indicates the translation error in the W-axis direction, R u Indicates the rotation angle error around the U axis, R v Indicates the first rotation angle error around the V axis, R′ v Indicates the second rotation angle error around the V axis, h d Indicates the height difference between the two guide rails of the current feed axis when they are not on the same horizontal plane. R w Indicates the rotation angle error around the W axis. In the specific implementation process, the UVW axis is replaced by the XYZ axis according to the machine tool configuration.

[0063] Step 4: Based on the motion error set of all feed axes in each support component under different working conditions, generate the feed space-varying motion error of each support component according to the number of feed axes in each support component;

[0064] In step 4, the method for processing the feed space-variable motion error of each supporting member includes the following steps:

[0065] S1: When the number of feed axes in each supporting member is 1, execute S2; when the number of feed axes in each supporting member is 2, execute S3; when the number of feed axes in each supporting member is 3, execute S4, thereby obtaining the feed space-varying motion error of the current supporting member, that is, when the number of feed axes is 1, the motion error curve of one feed axis in different motion error directions is the feed space-varying motion error of the supporting member; when the number of feed axes is 2, the motion error surfaces of two feed axes in different motion error directions are the feed space-varying motion error of the supporting member; when the number of feed axes is 3, the motion error space of the three feed axes in different motion error directions is the feed space-varying motion error of the supporting member;

[0066] S2: Interpolate the errors in the same motion error direction in the motion error set of the current feed axis in the three translation directions and the three rotation directions under different working conditions to obtain the motion error curves of the current feed axis in different motion error directions (6). The specific processing formula is as follows:

[0067]

[0068] Wherein, L(x) represents the error prediction value of the current feed axis when it moves to position x in each motion error direction, x0 represents the current feed axis motion position corresponding to the lower limit working condition, x1 represents the current feed axis motion position corresponding to the intermediate working condition, and x2 represents the current feed axis motion position corresponding to the upper limit working condition. According to the working condition classification method of this embodiment, x0=0, x2=T, T is the motion stroke of the feed axis; y0 is the motion error value corresponding to the motion error direction under the lower limit working condition, y1 is the motion error value corresponding to the motion error direction under the intermediate working condition, and y2 is the motion error value corresponding to the motion error direction under the upper limit working condition.

[0069] For the Y feed axis on the column in the specific implementation plan, the corresponding 6-direction motion errors DY can be obtained x (y),DY y (y),DY z (y),RY x (y),RY y (y),RY z (y), its size is related to the motion position of the Y feed axis.

[0070] S3: First, when the first feed axis is operating in the first working condition, S2 is executed according to the motion error set of the second feed axis under different working conditions to obtain the motion error curve of the second feed axis in different motion error directions under the first working condition of the first feed axis; then, the working condition of the first feed axis is traversed and S2 is repeatedly executed to finally obtain the motion error curve of the second feed axis in different motion error directions under all working conditions of the first feed axis; finally, the motion error curves of the second feed axis in different motion error directions under all working conditions of the first feed axis are interpolated according to the same motion error direction to obtain the motion error surface of the current feed axis in different motion error directions;

[0071] In specific implementation, if there are two feed axes U and V on the supporting member, first keep the U feed axis fixed in the three working conditions, and use the interpolation formula when n=1 three times to obtain the motion error curve of the V feed axis in each motion error direction when the U feed axis is in the three working conditions (that is, the relationship between the motion error and the change of the V feed axis) L Umin (v), L Umid (v), L Umax (v).

[0072]

[0073] Among them, v0 represents the V feed axis motion position corresponding to the lower limit working condition, v1 represents the V feed axis motion position corresponding to the intermediate working condition, and v2 represents the V feed axis motion position corresponding to the upper limit working condition. According to the working condition division method of this embodiment, v0=0, v2=T V , T V is the V feed axis motion range, y UminVmax Indicates the motion error value in the corresponding direction when the U feed axis is at the upper limit working condition and the V feed axis is at the lower limit working condition.

[0074] According to L Umin (v),L Umid (v),L Umax (v) The motion error surface of the UV feed axis in the corresponding motion error direction is obtained by the following formula:

[0075]

[0076] Wherein, L(u,v) represents the error prediction value of the current feed axis moving to the position (u,v) in each motion error direction, u0 represents the V feed axis motion position corresponding to the lower limit working condition, u1 represents the V feed axis motion position corresponding to the intermediate working condition, and u2 represents the V feed axis motion position corresponding to the upper limit working condition. According to the working condition division method of this embodiment, u0=0, u2=T U , TU It is the motion stroke of U feed axis.

[0077] For the X-axis and Z-axis on the bed in the specific implementation scheme, the motion errors DX in six directions can be obtained respectively. x (x,z),DX y (x,z),DX z (x,z), RX x (x,z), RX y (x,z), RX z (x,z) and DZ x (x,z),DZ y (x,z),DZ z (x,z), RZ x (x,z), RZ y (x,z), RZ z (x,z), its size is related to the motion position of the X-axis and Z-axis feed axes.

[0078] S4: First, when the third feed axis works in one working condition, S3 is executed according to the motion error sets of the first feed axis and the second feed axis under different working conditions to obtain the motion error surface of the current feed axis in different motion error directions under the first working condition of the third feed axis; then the working condition of the third feed axis is traversed and changed, and S3 is repeatedly executed to finally obtain the motion error surface of the current feed axis in different motion error directions under all working conditions of the third feed axis; finally, the motion error surfaces of the current feed axis in different motion error directions under all working conditions of the third feed axis are interpolated according to the same motion error direction to obtain the motion error space of the current feed axis in different motion error directions.

[0079] In the specific implementation, for the three feed axes UVW, first keep the U feed axis fixed in the three working conditions, and use the interpolation formula when n=2 three times to obtain the motion error surface of the VW feed axis in the corresponding motion error direction in the three working conditions (that is, the relationship between the motion error and the V and W axes) L Umin (v,w),L Umid (v,w),L Umax (v,w), and then use the following formula to process the motion error space of the three feed axes UVW in the corresponding motion error direction:

[0080]

[0081] Wherein, L(u, v, w) represents the error prediction value of the current feed axis in each motion error direction when the UVW feed axis moves to the position (u, v, w).

[0082] Step 5: After using the spatial matrix error transfer method to transfer and integrate the feed space-varying motion errors of each supporting component, the spatial-varying volume error and spatial error model of the multi-axis machine tool are generated. The spatial-varying volume error of the multi-axis machine tool is compensated according to the spatial error model to realize error compensation of the multi-axis machine tool.

[0083] In step 5, the spatial matrix error transfer method is used to transfer and integrate the feed space-variant motion errors of each supporting component in different motion error directions, and the spatially variable volume error and spatial error models of the multi-axis machine tool in different motion error directions are generated. Specifically,

[0084] First, the feed space-varying motion errors of each supporting component are transferred into the offset between the tool processing point and the workpiece to be processed point through homogeneous transformation theory or other coordinate transformation transfer methods, and the space-varying volume error of the multi-axis machine tool in different motion error directions is obtained;

[0085] Taking homogeneous transformation theory as an example, the offset between the tool processing point and the workpiece to be processed point is the error matrix of the multi-axis machine tool with different supporting components in their own processing positions. The formula is as follows:

[0086]

[0087] Where ΔW x ,ΔW y ,ΔW z are the translation errors in the x, y, and z directions respectively; Δθ x ,Δθ y ,Δθ z are the rotational errors around the x, y, and z axes respectively.

[0088] In specific implementation, the combined error matrix is:

[0089]

[0090] Where ΔW x ,ΔW y ,ΔW z are the translation errors in the x, y, and z directions respectively; Δθ x ,Δθ y ,Δθ z These are the angular errors around the x, y, and z axes. The six error values ​​are related to the motion position (x, y, z) of the machine tool feed axis.

[0091] The feed-dependent motion error and error transfer method are used to integrate the spatially varying volumetric errors of multi-axis machine tools in different motion error directions to obtain a spatial error model. This is used to take corresponding reverse compensation for different processing points in a targeted manner to weaken the influence of support deformation on processing accuracy.

[0092] Specifically, after sampling the machinable space of the multi-axis machine tool, the ideal machining space matrix N is determined, which is recorded as The formula is as follows:

[0093]

[0094] Then, the machining error matrix E is generated based on the spatially varying volume error of the multi-axis machine tool in different motion error directions, which is recorded as The formula is as follows:

[0095]

[0096] Among them, T x , T y and T z They are the x-feed axis motion range, y-feed axis motion range and z-feed axis motion range of the multi-axis machine tool, h2 is the second sampling step length, and the sampling is obtained The error value of each position is substituted into ΔE(0,0,0) when the processing position is (0,0,0) The error value in different directions, namely ΔW x ,ΔW y ,ΔW z ,Δθ x ,Δθ y ,Δθ z , forming a spatial error matrix in 6 different directions. The vector sum of the three translation errors As matrix elements, the resultant displacement space error matrix is ​​formed. The resultant displacement space error matrix is ​​used to simulate the volume error in the machining space of the machine tool and describe the difference between the actual cutting edge motion area and the ideal cutting edge.

[0097] Extract the matrices of the three translation directions from the processing error matrix E as the error matrix W set , recorded as It is also a three-dimensional matrix. The elements in the matrix are the error sets in the three translation directions under the corresponding coordinates. The formula is as follows:

[0098]

[0099] Usually, the error is very small relative to the machine tool's travel range, and the error needs to be magnified by a certain multiple m to obtain a relatively visual spatial volume error diagram. The ideal machining space matrix N plus the error matrix W times m set Then we get the spatial volume error matrix V, which is recorded as The spatial volume error matrix V is used as the spatial error model, and the N matrix and the V matrix are represented in the same three-dimensional spatial coordinate diagram to describe the difference between the ideal processing area and the processing domain containing errors, as shown in Figure 3 As shown in the figure, they represent the machine tool processing space under error-free condition and the machine tool processing space under error condition, respectively. This figure compares the processing space containing continuous variable volume error with the standard error-free processing space, and can clearly and intuitively obtain the error size and change trend in the feed space. It can not only provide a reference basis for the design of machine tool support components, but also provide a basis for the optimization of processing space layout.

[0100] Among them, the formula of the spatial volume error matrix V is as follows:

[0101]

Claims

1. A method for compensating spatial volume errors of multi-axis machine tools based on feed-dependent support deformation, characterized in that: The following steps are involved: Step 1: Based on the deformation of each supporting component in the multi-axis machine tool under all working conditions, analyze and determine the deformation curves of the guide rails corresponding to all feed axes in each supporting component under different working conditions; Step 2: Based on the motion positions of all feed axes in each supporting component under different working conditions, the deformation curves of the guide rails corresponding to all feed axes under different working conditions are integrated and averaged to obtain the deformation set of the feed support joint surface of all feed axes in each supporting component under different working conditions; Step 3: processing the motion error set of all feed axes in each supporting component under different working conditions according to the feed support joint surface deformation set of all feed axes in each supporting component under different working conditions; Step 4: Based on the motion error set of all feed axes in each support component under different working conditions, generate the feed space-varying motion error of each support component according to the number of feed axes in each support component; Step 5: After transferring and integrating the feed space-varying motion errors of each supporting component using the spatial matrix error transfer method, the space-varying volume error and spatial error model of the multi-axis machine tool are generated. The space-varying volume error of the multi-axis machine tool is compensated according to the spatial error model to achieve error compensation of the multi-axis machine tool. In step 1, for each feed axis of each supporting member, under each working condition, the discrete deformation data of the current feed axis at each guide rail corresponding to the current working condition is determined according to the static deformation amount of the current supporting member in the three translation directions. After linear interpolation of the deformation data of the current feed axis at each guide rail corresponding to the current working condition is performed using the cubic spline interpolation method with non-kinked boundary conditions, the deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are obtained respectively.

2. The method for compensating spatial volume error of a multi-axis machine tool based on feed-dependent support deformation according to claim 1, characterized in that: In step 2, for each feed axis of each supporting component, under each working condition, the deformation curves of the current feed axis in the three translation directions corresponding to each guide rail under the current working condition are integrated and averaged respectively according to the motion position under the current working condition, and the feed support joint surface deformation sets of the current feed axis in the three translation directions under the current working condition are obtained respectively. The feed support joint surface deformation set is composed of the feed support joint surface deformations of the four sliding feed members in the current feed axis.

3. The method for compensating spatial volume error of a multi-axis machine tool based on feed-dependent support deformation according to claim 2, characterized in that: For the deformation curve of the guide rail in each translation direction under each working condition of each feed axis, the deformation of the feed support joint surface of each sliding feed member in each feed axis is obtained by the following processing formula: Where E represents the deformation of the feed support interface of the current sliding feed member in the current translation direction of each feed axis under the current working condition, a is the distance between the front end face of the current sliding feed member and the origin end face of the corresponding guide rail, b is the distance between the rear end face of the current sliding feed member and the origin end face of the corresponding guide rail, h1 is the first sampling step, f(x k ) represents the discrete sequence after discrete sampling of the current deformation curve, x k represents the kth sampling point, N1 represents the number of the first sampling points, f(a) represents the deformation of the front end surface of the sliding feed member at the current position, f(b) represents the deformation of the rear end surface of the sliding feed member at the current position, L slide Indicates the length of the feed support joint surface in the feed motion direction.

4. The method for compensating spatial volume error of a multi-axis machine tool based on feed-dependent support deformation according to claim 1, characterized in that: In step 3, for each feed axis in each supporting member under each working condition, the feed support interface deformation set in the three translation directions of the current feed axis under the current working condition is decomposed into error directions and the error mean is processed respectively, and the motion error sets in the three translation directions and three rotation directions of the current feed axis under the current working condition are respectively obtained. The motion error set includes translational motion error and rotational motion error. The translational motion error is composed of translation errors in the U-axis direction, the V-axis direction, and the W-axis direction. The rotational motion error is composed of rotation angle error around the U axis, the rotation angle error around the V axis, and the rotation angle error around the W axis. The specific processing formula is as follows: D u =[D u11 +D u21 +D u12 +D u22 ] / 4 D v =[D v11 +D v21 +D v12 +D v22 ] / 4 D w =[D w11 +D w21 +D w12 +D w22 ] / 4 Among them, the U axis direction is parallel to the plane formed by the four sliding feed parts and perpendicular to the feed axis movement direction, the V axis direction is the same as the feed axis movement direction, the W axis direction is perpendicular to the plane formed by the four sliding feed parts, and the D u Indicates the translation error in the U-axis direction, D u11 、D u21 、D u12 and D u22 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the U axis direction, D v1 、D v2 、D v12 and D v2 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the V-axis direction, D w11 、D w21 、D w1 and D w2 They represent the components of the deformation of the feed support joint surface of the four sliding feed parts in the current feed axis in the W axis direction, w h is the span between two sliding feed members on the same guide rail, w d D is the span between the two guide rails in the current feed axis. v Indicates the translation error in the V-axis direction, D w Indicates the translation error in the W-axis direction, R u Indicates the rotation angle error around the U axis, R v Indicates the rotation angle error around the V axis, h d Indicates the height difference between the two guide rails of the current feed axis when they are not on the same horizontal plane. R w Indicates the rotation angle error around the W axis.

5. The method for compensating spatial volume error of a multi-axis machine tool based on feed-dependent support deformation according to claim 1, characterized in that: In step 4, the method for processing the feed space-varying motion error of each supporting member includes the following steps: S1: When the number of feed axes in each supporting member is 1, execute S2; when the number of feed axes in each supporting member is 2, execute S3; when the number of feed axes in each supporting member is 3, execute S4, thereby obtaining the feed space-varying motion error of the current supporting member; S2: interpolating the errors in the same motion error direction in the motion error sets of the current feed axis in the three translation directions and the three rotation directions under different working conditions to obtain the motion error curves of the current feed axis in different motion error directions; S3: First, when the first feed axis is operating in the first working condition, S2 is executed according to the motion error set of the second feed axis under different working conditions to obtain the motion error curve of the second feed axis in different motion error directions under the first working condition of the first feed axis; then, the working condition of the first feed axis is traversed and S2 is repeatedly executed to finally obtain the motion error curve of the second feed axis in different motion error directions under all working conditions of the first feed axis; finally, the motion error curves of the second feed axis in different motion error directions under all working conditions of the first feed axis are interpolated according to the same motion error direction to obtain the motion error surface of the current feed axis in different motion error directions; S4: First, when the third feed axis works in one working condition, S3 is executed according to the motion error sets of the first feed axis and the second feed axis under different working conditions to obtain the motion error surface of the current feed axis in different motion error directions under the first working condition of the third feed axis; then the working condition of the third feed axis is traversed and changed, and S3 is repeatedly executed to finally obtain the motion error surface of the current feed axis in different motion error directions under all working conditions of the third feed axis; finally, the motion error surfaces of the current feed axis in different motion error directions under all working conditions of the third feed axis are interpolated according to the same motion error direction to obtain the motion error space of the current feed axis in different motion error directions.

6. The method for compensating spatial volume error of a multi-axis machine tool based on feed-dependent support deformation according to claim 1, characterized in that: In step 5, the spatial matrix error transfer method is used to transfer and integrate the feed space-variant motion errors of each supporting component in different motion error directions, and then the spatially variable volume error and spatial error models of the multi-axis machine tool in different motion error directions are generated. Specifically, Firstly, the feed space-varying motion errors of each supporting component are transferred into the offset between the tool processing point and the workpiece to be processed point through the homogeneous transformation theory or coordinate transformation transfer method, so as to obtain the space-varying volume error of the multi-axis machine tool in different motion error directions; then, the feed space-varying motion error and error transfer method are used to integrate the space-varying volume error of the multi-axis machine tool in different motion error directions to obtain the spatial error model.

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