Multi-axis linkage turn-milling composite machine tool comprehensive error modeling and self-adaptive compensation method considering full working conditions

Abstract

The invention discloses a multi-axis linkage turn-milling composite machine tool comprehensive error modeling and self-adaptive compensation method considering full working conditions, and belongs to the field of machine tool precision improvement. The method comprises the following steps: firstly, analyzing a topological structure of a nine-axis machine tool, and establishing a comprehensive error model considering all working conditions based on a homogeneous coordinate transformation method of a multi-body system theory; secondly, solving a comprehensive error compensation amount of each motion axis by using a Jacobian matrix; and finally, proposing a self-adaptive compensation method based on the numerical control system cutter and shaft motion information. According to the method, the comprehensive error model considering all working conditions is established, and different comprehensive error models are established for different working conditions, so that the modeling precision is improved; and a self-adaptive compensation method is introduced to carry out comprehensive error compensation on the machining chains under different working conditions, so that the compensation result is more accurate, and the efficiency is higher. The method provided by the invention provides a theoretical basis and a research idea for the aspects of structural analysis, error modeling and error compensation of the complex machine tool with a plurality of workpiece chains and a plurality of cutter chains.

Description

Technical Field

[0001] The invention belongs to the field of machine tool precision improvement, and relates to a comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling compound machine tool taking into account all working conditions. Background Art

[0002] Machine tools play an important role in improving my country's industrial competitiveness. So far, the research on the influence of comprehensive errors on machine tool processing accuracy has mostly focused on three-axis machine tools and five-axis machine tools. For example, Chinese patent CN202211159538.8 proposes a comprehensive error modeling method for three-axis CNC machine tools based on time axis compensation; Chinese patent CN202110685808.8 proposes a position-independent geometric error modeling method based on an AC double-turntable five-axis machine tool; Chinese patent CN202011304180.4 uses a five-axis AC swing head gantry machine tool for geometric error modeling and error separation. The above three-axis machine tools and five-axis machine tools have simple structures, but they only have one workpiece chain and one tool chain that cooperate with each other to complete the processing. Multi-axis linkage turning and milling machine tools, such as the nine-axis five-link turning and milling machine tools (hereinafter referred to as nine-axis machine tools), can complete multiple processes through one clamping. They are high-end manufacturing equipment urgently needed in core fields such as aviation, aerospace, military industry, energy, and transportation. Their functions and technical performances reflect the comprehensive level of the machine tool industry to a certain extent. However, the nine-axis machine tools have multiple workpiece chains and multiple tool chains, which makes their comprehensive error modeling and compensation process complicated. Summary of the invention

[0003] In view of the above problems, the present invention proposes a comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling compound machine tool taking into account all working conditions. By analyzing the topological structure of the nine-axis machine tool, a comprehensive error model taking into account all working conditions is established based on the homogeneous coordinate transformation method of multi-body system theory, and the comprehensive error compensation amount is solved, and finally an adaptive compensation method is proposed. This provides a theoretical basis for the comprehensive error modeling and compensation of a multi-axis linkage compound machine tool with multiple workpiece chains and multiple tool chains.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling compound machine tool taking into account all working conditions. The present invention first analyzes the topological structure of the nine-axis machine tool, and establishes a comprehensive error model taking into account all working conditions based on the homogeneous coordinate transformation method of multi-body system theory; secondly, the Jacobian matrix is ​​used to solve the comprehensive error compensation amount of each motion axis; finally, an adaptive compensation method based on the tool and axis motion information of the CNC system is proposed. The specific steps are as follows:

[0006] The first step is to analyze the topological structure of the nine-axis machine tool and establish a combined representation method for the machining chain under all working conditions;

[0007] The comprehensive error includes spatial error and thermal error. The motion axis system of the nine-axis machine tool includes 6 linear axes and 3 rotation axes. The linear axes are X1 axis, Y axis, Z1 axis, X2 axis, Z2 axis and W axis, and the rotation axes are C1 axis, C2 axis and B axis. The topological structure of the nine-axis machine tool is established. According to the relative position relationship between the axis systems, the nine-axis machine tool is simplified into four independent and non-interfering motion chains, which include two workpiece chains and two tool chains, namely workpiece chain L1, workpiece chain L2, tool chain L3, and tool chain L4.

[0008] The workpiece chain L1 is composed of bed-C1 axis-workpiece. The workpiece chain L2 is composed of bed-W axis-C2 axis-workpiece. The tool chain L3 is composed of bed-Z1 axis-X1 axis-Y axis-B axis-tool. The tool-holding components in the chain can hold turning tools, milling cutters and boring (drilling) cutters, so as to complete the processing of three working conditions: turning, milling and boring (drilling). The tool chain L4 is composed of bed-Z2 axis-X2 axis-tool. The tool-holding components in the chain can hold turning tools and milling cutters, so as to complete the processing of two working conditions: turning and milling. Theoretically, a workpiece chain and a tool chain can form a processing chain when they are processed together. Therefore, the processing chain combination ML under full working conditions of the nine-axis machine tool is expressed as:

[0009] ML=[A,B]=[(L 工 +γL 刀 x ),(L 工 +γL 刀 x )](1)

[0010] Among them, A and B represent two independent processing chains, which can be processed simultaneously without affecting each other. 工 Represents the workpiece chain, L 刀 represents the tool chain. γ indicates whether the tool chain is clamping a tool. x represents the working condition, 1, 2, 3 represent turning, milling and boring (drilling) respectively. For tool chain L3, x = 1, 2, 3, for tool chain L4, x = 1, 2.

[0011] From the above, we can see that different working conditions correspond to different processing chains and different comprehensive error models. Therefore, it is necessary to take the working conditions into consideration when establishing the comprehensive error model.

[0012] The second step is to analyze the geometric error transmission mechanism between the shaft systems based on the multi-body system theory and establish a comprehensive error model that takes into account all working conditions;

[0013] 2.1) First, according to the multi-body system theory, the nine-axis machine tool is simplified into a multi-body system with multiple relative motion bodies. A coordinate system is fixed on each body, and the spatial position and posture changes of two adjacent bodies i and j are calculated using the fixed coordinate system O.i -X i Y i Z i and O j -X j Y j Z j The relative transformation between them is expressed as . A 4×4 homogeneous matrix is ​​used to describe the relative motion of the two coordinate systems.

[0014] 2.2) Secondly, according to the structure and axis type of the nine-axis machine tool, its geometric error items are analyzed. According to the ISO 230-1:2012 standard, there are 6 position-related geometric errors between the axes of the nine-axis machine tool. The linear axis is the horizontal straightness error, vertical straightness error, yaw angle error, pitch angle error, roll angle error and positioning error. The rotary axis is the axial runout, radial runout in two directions, angular error and yaw angle error along two axes. The nine-axis machine tool has a total of 54 position-related geometric errors. At the same time, there are position-independent geometric errors between the axis systems, such as verticality error, parallelism error and position deviation between the axis systems. According to the relative position relationship between the axis systems, the nine-axis machine tool has a total of 25 position-independent geometric errors.

[0015] 2.3) Then, based on the comprehensive error modeling method of homogeneous coordinate transformation of multi-body system theory, a reference coordinate system, a tool coordinate system, a workpiece coordinate system and a fixed coordinate system of each axis are established. For a machine tool, the comprehensive error of the machine tool is the deviation between the ideal and actual situation in position and posture of the tool tip point relative to the workpiece point caused by the geometric error when the machine tool moves to a certain position in the workspace. The ideal situation is the situation where there is no error in the machine tool, and the actual situation is the situation where there is an error in the machine tool. In the actual calculation process, the coordinate value of the tool tip point in the tool coordinate system needs to be converted to the coordinate value in the workpiece coordinate system in the ideal situation and the actual situation, and the comprehensive error is the difference between the two. In order to simplify the calculation, the present invention selects the bed coordinate system as a reference. For a processing chain, the coordinate value of the tool tip point in the tool coordinate system in the tool chain is first converted to the bed coordinate system, and then converted from the bed coordinate system to the workpiece coordinate system of the workpiece chain. According to the conversion path, the 4×4-order conversion matrix of the tool coordinate system relative to the workpiece coordinate system in the ideal situation and the actual situation is calculated to obtain the comprehensive error.

[0016] Ideally, the transformation matrix from the workpiece coordinate system W to the bed coordinate system M is And the transformation matrix from tool coordinate system T to bed coordinate system M It is expressed as:

[0017]

[0018] in, represents the ideal initial position transformation matrix of coordinate systems W and M, Represents the ideal motion matrix between two coordinate systems. Represents the ideal initial position transformation matrix of coordinate systems T and M.

[0019] In actual situations, the transformation matrix from the workpiece coordinate system W to the bed coordinate system M is WM T e , and the transformation matrix from tool coordinate system T to bed coordinate system M It is expressed as:

[0020]

[0021] in, represents the position-independent error matrix, M T PD Represents the position-dependent error matrix. represents the position-independent error matrix.

[0022] Therefore, based on the above-mentioned combined representation of the processing chain and the homogeneous coordinate transformation method based on the multi-body system theory, a comprehensive error model Q considering all working conditions is established, which is expressed as:

[0023]

[0024] in,() _error Indicates the actual situation, () _ideal represents the ideal situation. γ represents whether the tool chain holds the tool. L 工 There are two meanings, one of which refers to the workpiece chain, and the other refers to the transformation matrix of the workpiece coordinate system relative to the bed coordinate system. Indicates L 工 The inverse operation is to transform the original transformation matrix of the workpiece coordinate system relative to the bed coordinate system into the transformation matrix of the bed coordinate system relative to the workpiece coordinate system. 刀 There are also two meanings, where the first meaning represents the tool chain, and the second meaning represents the transformation matrix of the tool coordinate system relative to the bed coordinate system. x represents the working condition, 1, 2, and 3 represent the three working conditions of turning, milling, and boring (drilling) respectively. For tool chain L3, x = 1, 2, 3, and for tool chain L4, x = 1, 2.

[0025] 2.4) Finally, the transformation matrix between the workpiece (tool) chain in the ideal and actual conditions is substituted into the comprehensive error model Q that takes into account all working conditions. By inputting specific parameters into the comprehensive error model Q, the comprehensive error matrix R of a certain processing chain under specific working conditions can be output. R is a 4×4 matrix. The comprehensive error includes the position error vector and the attitude error vector. Under this specific working condition, the comprehensive error ΔE of the processing chain consists of the first three rows and the fourth column elements of the matrix R (representing the position errors in the x, y and z directions respectively) and the first three rows and the third column elements of the matrix R (representing the attitude errors in the x, y and z directions respectively).

[0026] For only one processing chain, the above-mentioned comprehensive error modeling method, that is, the method of solving the position and posture errors of the tool relative to the workpiece from the motion of each axis is called the forward kinematics method, and the solved matrix is ​​called the forward kinematics matrix. When calculating the comprehensive error compensation, it is necessary to use the inverse kinematics method to inversely solve the motion of each axis. The comprehensive error model Q contains the comprehensive errors of each processing chain under all working conditions. Therefore, it is necessary to input different parameters to obtain the comprehensive error corresponding to a specific processing chain, and then perform inverse kinematics to solve the compensation amount based on the result.

[0027] The third step is to solve the comprehensive error compensation of each motion axis;

[0028] Inverse kinematics is to calculate the motion of each axis based on the position and posture errors of the tool relative to the workpiece. Jacobian matrix is ​​often used in inverse kinematics to solve the comprehensive error compensation. Based on the comprehensive error ΔE of a specific processing chain obtained in step 2.4), a method of using Jacobian matrix to solve the comprehensive error compensation of each motion axis of the processing chain is proposed. The steps are as follows:

[0029] 3.1) First, according to the positive kinematics matrix of the ideal machining chain, six expressions of position error and attitude error in the three directions of x, y and z are obtained;

[0030] 3.2) Secondly, perform partial differential calculations on the six expressions obtained in step 3.1) to obtain the Jacobian matrix.

[0031] 3.3) Then, solve the pseudo-inverse matrix of the Jacobian matrix;

[0032] 3.4) Finally, the pseudo-inverse matrix obtained in step 3.3) is multiplied by the comprehensive error ΔE of the specific processing chain in step 2.4) to obtain the comprehensive error compensation of each motion axis in the processing chain.

[0033] Step 4: Adaptive compensation method for comprehensive errors of nine-axis machine tools under all working conditions;

[0034] From the above, it can be seen that different machining chains corresponding to different working conditions will lead to different comprehensive error models, which will result in different compensation amounts of each axis during error compensation. Therefore, in view of the above problem, the present invention proposes a comprehensive error adaptive compensation method under all working conditions, which combines the second step of considering the comprehensive error model under all working conditions and the third step of solving the compensation amount of each motion axis for analysis.

[0035] The steps of the adaptive compensation method are as follows:

[0036] 4.1) First, determine whether the two tool chains are holding the tool, that is, determine the values ​​of γ of the two tool chains respectively;

[0037] 4.2) Secondly, determine the types of tools held by the two tool chains and whether the tool chains are moving, that is, determine the values ​​of x of the two tool chains and the movement states of the two tool chains;

[0038] 4.3) Again, determine the combination of the two tool chains and the clamping tools;

[0039] 4.4) Then, the positions of the two tool chains relative to the two workpiece chains are determined. If a tool chain is close to a workpiece chain, the tool chain will be processed in coordination with the workpiece chain, i.e., the type of the workpiece chain is determined;

[0040] 4.5) Finally, the input parameters obtained by judgment are substituted into the comprehensive error model considering all working conditions established in the second step, and the comprehensive error model of the specific processing chain is output. The comprehensive error compensation amount of each motion axis in the processing chain is solved through the third step, so as to perform comprehensive error compensation on the processing chain.

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

[0042] The present invention establishes a comprehensive error model that takes into account all working conditions, and comprehensively considers various complex working conditions that a multi-axis linkage turning and milling compound machine tool may face during actual operation. Different comprehensive error models are established for different working conditions, which simplifies the process of comprehensive error modeling and improves the accuracy of modeling; the introduction of an adaptive compensation method can perform comprehensive error compensation on the processing chain under different working conditions, making the compensation result more accurate and more efficient.

[0043] In summary, the method pointed out in the present invention provides a theoretical basis and research ideas for the structural analysis, error modeling and error compensation of complex machine tools with multiple workpiece chains and multiple tool chains. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the nine-axis machine tool structure;

[0045] Figure 2 Schematic diagram of the topological structure of a multi-body system;

[0046] Figure 3The types of machining chains under some working conditions of the nine-axis machine tool; (a) is the boring (drilling) machining of chains L1 and L3, (b) is the turning machining of chains L2 and L4, (c) is the milling machining of chains L2 and L3, and the turning machining of chains L1 and L4, (d) is the turning machining of chains L1 and L3, and the milling machining of chains L2 and L4;

[0047] Figure 4 Schematic diagram of the coordinate system position of the nine-axis machine tool;

[0048] Figure 5 Adaptive compensation flow chart under all working conditions;

[0049] In the figure: 1 bed, 2 linear axis Z2 axis, 3 linear axis X2 axis, 4 rotary axis C1 axis, 5 linear axis W axis, 6 rotary axis C2 axis, 7 linear axis X1 axis, 8 linear axis Y axis, 9 linear axis Z1 axis, 10 B axis. DETAILED DESCRIPTION

[0050] The present invention is further described below in conjunction with specific implementation cases.

[0051] This embodiment takes a nine-axis machine tool as an example to illustrate a comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling machine tool taking into account all working conditions. Figure 1 As shown, it includes a bed 1, a linear axis Z2 axis 2, a linear axis X2 axis 3, a rotary axis C1 axis 4, a linear axis W axis 5, a rotary axis C2 axis 6, a linear axis X1 axis 7, a linear axis Y axis 8, a linear axis Z1 axis 9, and a B axis 10. The connection relationship of the machine tool is briefly introduced in four motion chains. The workpiece chain L1 is connected by the bed to the C1 axis, and the C1 axis clamps the workpiece. The workpiece chain L2 is connected by the bed to the W axis, the W axis is connected to the C2 axis, and the C2 axis clamps the workpiece. The tool chain L3 is connected by the bed to the Z1 axis, the Z1 axis is connected to the X1 axis, the X1 axis is connected to the Y axis, the Y axis is connected to the B axis, and the milling head part of the B axis clamps the tool, which can clamp turning tools, milling cutters and boring (drilling) tools. The tool chain L4 is connected by the bed to the Z2 axis, the Z2 axis is connected to the X2 axis, and the X2 axis is equipped with a lower turret. The lower turret clamps the tool, which can clamp turning tools and milling cutters. The specific steps of the method described are:

[0052] The first step is to analyze the topological structure of the nine-axis machine tool and establish a combined representation method for the machining chain under all working conditions;

[0053] According to the structure of the nine-axis machine tool, draw its topological structure diagram and number it, such as Figure 2 As shown in the above topological structure diagram, the machining chain combination ML of the nine-axis machine tool under full working conditions can be expressed as:

[0054] ML=[A,B]=[(L m +λL p x ),(Ln +βL p x )](5)

[0055] Among them, A and B represent two independent processing chains, which can be processed simultaneously without affecting each other. λ, β indicate whether the tool is clamped, and the value is 0 or 1. When the value is 0, it means that the tool is not clamped, and when the value is 1, it means that the tool is clamped. L m and L n Represents a workpiece chain, satisfying m×n=2, m=1, then n=2, indicating that L m is the workpiece chain L1, L n is the workpiece chain L2, or m = 2, n = 1, indicating that L m is the workpiece chain L2, L n is the workpiece chain L1. p represents the tool chain, x represents the working condition, 1, 2, and 3 represent the three working conditions of turning, milling, and boring (drilling) respectively. When x=1, 2, and 3, p=3, indicating that the tool chain is L3; when x=1, 2, p=4, indicating that the tool chain is L4.

[0056] The machining chain types of the nine-axis machine tool under different working conditions can be obtained from the machining chain combination ML of the nine-axis machine tool under all working conditions. Figure 3 It is the processing chain type under some working conditions of the nine-axis machine tool, such as Figure 3 (a) Boring (drilling) machining of workpiece chain L1 and tool chain L3. Figure 3 (b) Turning process for workpiece chain L2 and tool chain L4, Figure 3 (c) The workpiece chain L2 and the tool chain L3 perform milling, and the workpiece chain L1 and the tool chain L4 perform turning, Figure 3 (d) The workpiece chain L1 and the tool chain L3 perform turning processing, and the workpiece chain L2 and the tool chain L4 perform milling processing.

[0057] The second step is to analyze the geometric error transmission mechanism between the shaft systems based on the multi-body system theory and establish a comprehensive error model that takes into account all working conditions;

[0058] 2.1) First, according to the geometric error definition method given in ISO 230-1:2012, the nine-axis machine tool has a total of 79 geometric error items, including 54 position-related geometric errors and 25 position-independent geometric errors, as shown in Tables 1 and 2.

[0059] Table 1 Geometric errors related to position of nine-axis machine tools

[0060]

[0061]

[0062] Table 2 Nine-axis machine tool and position-independent geometric errors

[0063]

[0064]

[0065] 2.2) Secondly, establish the machine tool origin coordinate system as follows Figure 4 As shown, the bed coordinate system is {O M}, the tool coordinate system is {O T}, the workpiece coordinate system is {O W}, B-axis fixed coordinate system is {O B}. Figure 4 When each axis is at zero point {O T} is on the rotation axis of the rotation axis, define {O M} and {O T} and define the fixed coordinate system of each linear axis and rotation axis with {O T} overlap. Definition {O W}At the intersection of the rotation axis and the end face of the rotation shaft, {O B} and {O T}There is a certain distance in the z direction, which is the length of the tool.

[0066] 2.3) Then, based on different kinematic chains, the pose transformation process of the tool coordinate system relative to the workpiece coordinate system of the nine-axis machine tool is analyzed under ideal and actual conditions.

[0067] In order to indicate that the transformation matrices corresponding to different types of tool (workpiece) chains are different, a singular function is introduced before analyzing the posture transformation process, which is expressed as:

[0068] in Among them, (j,n) is a singular function, which is an operation rule with a value of 0 or 1.

[0069] Ideally, the workpiece chain L of the nine-axis machine tool W and tool chain L T , the transformation matrix of the workpiece (tool) coordinate system relative to the bed coordinate system is expressed as:

[0070]

[0071] Among them, (1, a) is a singular function, a represents an intermediate variable, and the values ​​of m and n in formula (5) can be substituted into a. At this time, the values ​​of m and n have two meanings, where the first meaning represents the category of the workpiece chain, and the second meaning represents m(n) = a. For different workpiece chains, the output workpiece coordinate system relative to the bed coordinate system has different transformation matrix results. For example, if m = 1, the first meaning represents the workpiece chain L1, and the second meaning represents the workpiece chain at this time. The p value also has two meanings. The first meaning indicates the category of the tool chain. p=3 indicates tool chain L3, and p=4 indicates tool chain L4. The second meaning indicates that the transformation matrix results of the tool coordinate systems output by different tool chains relative to the bed coordinate system are different.

[0072] In actual situation, the workpiece chain L of the nine-axis machine tool W and tool chain L T , the transformation matrix of the workpiece (tool) coordinate system relative to the bed coordinate system is expressed as:

[0073]

[0074] Therefore, based on the above-mentioned combined representation of the processing chain and the homogeneous coordinate transformation method based on the multi-body system theory, a comprehensive error model Q considering all working conditions is established, which is expressed as:

[0075]

[0076] in,() _error Indicates the actual situation, () _ideal Indicates the ideal situation. λ, β = 0 or 1, indicating whether the tool is clamped. L m and L n There are two meanings, where the first meaning represents the workpiece chain L1 or L2, and the second meaning represents the transformation matrix of the workpiece coordinate system relative to the bed coordinate system. Indicated as L m The inverse operation is to change the transformation matrix of the original workpiece coordinate system relative to the bed coordinate system into the transformation matrix of the bed coordinate system relative to the workpiece coordinate system. Similarly, m×n=2, there are two cases: m=1, n=2, which means L m and L n For workpiece chains L1 and L2, or m = 2, n = 1, indicating that L m and L n For workpiece chains L2 and L1. pThere are two meanings, one of which is the tool chain, and the other is the conversion matrix of the tool coordinate system relative to the bed coordinate system. x represents the working condition, 1, 2, and 3 represent turning, milling, and boring (drilling) respectively. When x=1, 2, and 3, p=3, indicating that the tool chain is L3, and when x=1, 2, p=4, indicating that the tool chain is L4.

[0077] 2.4) Finally, by substituting equations (7) and (8) into equation (9), we can get the comprehensive error model Q that takes into account all working conditions. By inputting specific parameters into the comprehensive error model Q, we can output the comprehensive error matrix R under the corresponding situation, which is a 4×4-order matrix and can be expressed as:

[0078]

[0079] Among them, A 3×1 , B 3×1 , C 3×1 and D 3×1 Both are 3×1 matrices, A 3×1 Contains the first three rows and first column elements of matrix R, B 3×1 Contains the first three rows and second column elements of matrix R, C 3×1 Contains the first three rows and the third column of the matrix R, D 3×1 Contains the first three rows and fourth column of the matrix R.

[0080] The combined error ΔE for this particular processing chain is expressed as:

[0081] ΔE=[P 3×1 V 3×1 ] T (11)

[0082] Among them, P 3×1 is the 3×1 matrix D in equation (10) 3×1 , respectively represent the position errors in the x, y and z directions. V 3×1 is the 3×1 matrix C in formula (10) 3×1 , which represent the attitude errors in the x, y and z directions respectively.

[0083] In this implementation case: the comprehensive error model considering all working conditions, input λ = 1, β = 0, x = 1, p = 3 and m = 1 in the model, the model can first be expressed as That is, it means that the workpiece chain L1 and the tool chain L3 cooperate in the turning condition. Then, based on the singular function, the transformation matrix between the workpiece (tool) coordinate system and the bed coordinate system of the corresponding workpiece (tool) chain in the ideal and actual conditions is calculated. Finally, the output result can be substituted into the model as follows: Thus, the comprehensive error of the processing chain under this working condition can be obtained.

[0084] The third step is to solve the comprehensive error compensation of each motion axis;

[0085] 3.1) First, based on the ideal motion of each axis of the specific processing chain in step 2.4), U = [xy zαβ] T The forward kinematics matrix F(U) at the time of , we get 6 expressions about the motion of each axis x, y, z, α and β. It contains the position error vector P(U) and attitude error vector V(U) in the three directions of x, y and z.

[0086] 3.2) Secondly, the partial differentials of the motion of each axis are calculated for the six expressions to obtain the Jacobian matrix J. J is a 6×5 matrix, the first row of the matrix is ​​the partial differential results of the position error in the x direction with respect to the motion of each axis, the second row is the partial differential results of the position error in the y direction with respect to the motion of each axis, the third row is the partial differential results of the position error in the z direction with respect to the motion of each axis, the fourth row is the partial differential results of the attitude error in the x direction with respect to the motion of each axis, the fifth row is the partial differential results of the attitude error in the y direction with respect to the motion of each axis, and the sixth row is the partial differential results of the attitude error in the z direction with respect to the motion of each axis.

[0087] 3.3) Then, solve the pseudo-inverse matrix J1 of the Jacobian matrix:

[0088] J1=(J T J) -1 J T (12)

[0089] 3.4) Finally, the comprehensive error compensation ΔU of each motion axis in the machining chain is obtained by combining the pseudo-inverse matrix J1 and formula (11):

[0090] ΔU=J1ΔE(13)

[0091] Step 4: Adaptive compensation method for comprehensive errors of nine-axis machine tools under all working conditions;

[0092] The flowchart of the proposed adaptive compensation method is as follows: Figure 5 As shown, the comprehensive error model considering all working conditions in the second step and the compensation of each motion axis in the third step are combined for analysis. This scheme only considers the processing of one workpiece chain and one tool chain, and does not consider the processing of one workpiece chain and multiple tool chains.

[0093] 4.1) First, determine whether the tool-holding components in the two tool chains are holding the tool. If the tool is not held, that is, λ and β = 0, no comprehensive error compensation is performed.

[0094] 4.2) Secondly, if the tool is clamped, that is, λ and β = 1, then determine whether the tool type clamped by the two tool chains is a turning tool, a milling cutter or a boring (drilling) tool, that is, determine whether x = 1, 2 or 3. At the same time, determine whether the two tool chains are in motion. If the two tool chains are not in motion, no comprehensive error compensation is performed. If the two tool chains are in motion, determine whether the tool chain in motion is tool chain L3 or tool chain L4, that is, determine whether p = 3 or 4.

[0095] 4.3) Again, by combining the types of tools clamped by the two tool chains and the tool chains in motion, it can be concluded which tool chain is performing which working condition processing at this time.

[0096] 4.4) Then, determine the positions of the two tool chains relative to the two workpiece chains, that is, determine the value of m. If the tool chain is close to the workpiece chain L1, m=1, then it cooperates with the workpiece chain L1 for processing; if it is close to the workpiece chain L2, m=2, then it cooperates with the workpiece chain L2 for processing.

[0097] 4.5) Finally, according to the different processing chains, the values ​​of the identified parameters λ, β, x, p and m are substituted into the comprehensive error model taking into account all working conditions in the second step to obtain the comprehensive error corresponding to the specific processing chain. Then, according to the third step, the compensation amount of each motion axis of the processing chain is solved to perform comprehensive error compensation.

[0098] In the implementation case, a comprehensive error model considering all working conditions of the nine-axis five-link turning and milling machine tool was established, and an adaptive compensation method was proposed, which can obtain different comprehensive errors according to different working conditions, thereby obtaining the corresponding comprehensive compensation amount and performing comprehensive error compensation, making the compensation method more targeted and the compensation result more accurate.

[0099] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling machine tool taking into account all working conditions, characterized in that: The comprehensive error modeling and adaptive compensation method comprises the following steps: The first step is to analyze the topological structure of the nine-axis machine tool and establish a combined representation method for the machining chain under all working conditions; The second step is to analyze the geometric error transmission mechanism between the shaft systems based on the multi-body system theory and establish a comprehensive error model that takes into account all working conditions; The comprehensive error model Q is expressed as: in,() _error Indicates the actual situation, () _ideal represents the ideal situation; γ represents whether the tool chain holds the tool; L 工 There are two meanings, one of which is the workpiece chain, and the other is the transformation matrix of the workpiece coordinate system relative to the bed coordinate system. Indicates L 工 The inverse operation is to transform the original transformation matrix of the workpiece coordinate system relative to the bed coordinate system into the transformation matrix of the bed coordinate system relative to the workpiece coordinate system; L 刀 There are also two meanings, where the first meaning represents the tool chain, and the second meaning represents the transformation matrix of the tool coordinate system relative to the bed coordinate system; x represents the working condition, 1, 2, and 3 represent the three working conditions of turning, milling, boring, or drilling, respectively. For tool chain L3, x = 1, 2, 3, and for tool chain L4, x = 1, 2; By inputting specific parameters into the comprehensive error model Q, the comprehensive error matrix R of a certain processing chain under specific working conditions is output, and then the comprehensive error ΔE of the specific processing chain is obtained; In the third step, based on the comprehensive error ΔE of the specific processing chain obtained in the second step, the comprehensive error compensation of each motion axis of the processing chain is solved by using the Jacobian matrix. The fourth step is to combine the comprehensive error model under all working conditions in the second step with the compensation amount of each motion axis solved in the third step to perform analysis and realize adaptive compensation of comprehensive errors under all working conditions of the nine-axis machine tool.

2. The comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling machine tool taking into account all working conditions according to claim 1 is characterized in that: The first step is specifically: The motion axis system of the nine-axis machine tool includes 6 linear axes and 3 rotation axes; the linear axes are X1 axis, Y axis, Z1 axis, X2 axis, Z2 axis and W axis, and the rotation axes are C1 axis, C2 axis and B axis; a topological structure of the nine-axis machine tool is established, and the nine-axis machine tool is simplified into four independent and mutually independent motion chains, which include two workpiece chains and two tool chains, namely, workpiece chain L1, workpiece chain L2, tool chain L3, and tool chain L4; The workpiece chain L1 is composed of bed-C1 axis-workpiece; the workpiece chain L2 is composed of bed-W axis-C2 axis-workpiece; the tool chain L3 is composed of bed-Z1 axis-X1 axis-Y axis-B axis-tool, and the tool-holding parts in the chain can hold turning tools, milling cutters and boring cutters or drilling cutters to complete the processing of three working conditions: turning, milling and boring or drilling; the tool chain L4 is composed of bed-Z2 axis-X2 axis-tool, and the tool-holding parts in the chain can hold turning tools and milling cutters to complete the processing of two working conditions: turning and milling; a workpiece chain and a tool chain can form a processing chain in cooperation; then the processing chain combination ML under the full working condition of the nine-axis machine tool is expressed as: ML=[A,B]=[(L 工 +γL 刀 x ),(L 工 +γL 刀 x )](1) Among them, A and B represent two independent processing chains, which can be processed simultaneously without affecting each other; L 工 Represents the workpiece chain, L 刀 represents the tool chain; γ indicates whether the tool chain holds the tool; x represents the working condition, 1, 2, 3 represent turning, milling and boring (drilling) respectively. For tool chain L3, x=1, 2, 3; for tool chain L4, x=1, 2.

3. The comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning and milling machine tool taking into account all working conditions according to claim 2 is characterized in that: The second step is specifically as follows: 2.1) The nine-axis machine tool is simplified into a multi-body system with multiple relatively moving bodies inside; a coordinate system is fixed on each body, and the spatial position and posture changes of two adjacent bodies i and j are calculated using the fixed coordinate system O i -X i Y i Z i and O j -X j Y j Z j It is expressed as the relative transformation between Use a 4×4 homogeneous matrix to describe the relative motion of the two coordinate systems; 2.2) Analyze the geometric error terms of the nine-axis machine tool according to its structure and axis system type; 2.3) Based on the comprehensive error modeling method of homogeneous coordinate transformation of multi-body system theory, the reference coordinate system, tool coordinate system, workpiece coordinate system and the fixed coordinate system of each axis are established; In the actual calculation process, the coordinate value of the tool tip in the tool coordinate system is converted to the coordinate value in the workpiece coordinate system under ideal and actual conditions, and the comprehensive error is the difference between the two. The bed coordinate system is selected as a reference. For a processing chain, the coordinate value of the tool tip in the tool chain in the tool coordinate system is first converted to the bed coordinate system, and then converted from the bed coordinate system to the workpiece coordinate system of the workpiece chain. According to the transformation path, the 4×4-order transformation matrix of the tool coordinate system relative to the workpiece coordinate system in the ideal and actual conditions is calculated to obtain the comprehensive error; the comprehensive error model Q considering all working conditions is established by the combined representation of the machining chain and the homogeneous coordinate transformation method based on the multi-body system theory; 2.4) Substitute the transformation matrix between each body of the tool chain under ideal and actual conditions into the comprehensive error model Q taking into account all working conditions, and output a 4×4-order comprehensive error matrix R of a certain processing chain under specific working conditions by inputting specific parameters into the comprehensive error model Q; the comprehensive error includes a position error vector and an attitude error vector; under this specific working condition, the comprehensive error ΔE of the processing chain is composed of the first three rows and the fourth column elements of the matrix R and the first three rows and the third column elements of the matrix R, which represent the position errors in the x, y and z directions, and the attitude errors in the x, y and z directions, respectively.

4. The comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning-milling machine tool taking into account all working conditions according to claim 3 is characterized in that: The 2.4) mentioned above is specifically: Ideally, the transformation matrix from the workpiece coordinate system W to the bed coordinate system M is And the transformation matrix from tool coordinate system T to bed coordinate system M It is expressed as: in, represents the ideal initial position transformation matrix of coordinate systems W and M, represents the ideal motion matrix between two coordinate systems; represents the ideal initial position transformation matrix of coordinate systems T and M; In actual situations, the transformation matrix from the workpiece coordinate system W to the bed coordinate system M is WM T e , and the transformation matrix from tool coordinate system T to bed coordinate system M It is expressed as: in, represents the position-independent error matrix, M T PD represents the position-related error matrix; represents the position-independent error matrix.

5. The comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning-milling machine tool taking into account all working conditions according to claim 3 is characterized in that: The specific steps of the third step are as follows: 3.1) Based on the positive kinematics matrix of the ideal machining chain, six expressions of position error and attitude error in the x, y and z directions are obtained; 3.2) Perform partial differential calculations on the six expressions obtained in step 3.1) to obtain the Jacobian matrix; 3.3) Solve the pseudo-inverse matrix of the Jacobian matrix; 3.4) Multiply the pseudo-inverse matrix obtained in step 3.3) above by the comprehensive error ΔE of the specific processing chain in step 2.4) to obtain the comprehensive error compensation amount of each motion axis in the processing chain.

6. The comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning-milling machine tool taking into account all working conditions according to claim 5 is characterized in that: The fourth step is as follows: 4.1) Determine whether the two tool chains are holding the tool, that is, determine the values ​​of γ of the two tool chains respectively; 4.2) Determine the types of tools held by the two tool chains and whether the tool chains are moving, that is, determine the values ​​of x of the two tool chains and the movement states of the two tool chains; 4.3) Determine the combination of two tool chains and clamping tools; 4.4) Determine the positions of the two tool chains relative to the two workpiece chains, determine which workpiece chain the tool chain is close to, and then cooperate with that workpiece chain to determine the type of workpiece chain; 4.5) Substitute the input parameters obtained by judgment into the comprehensive error model considering all working conditions established in the second step, output the comprehensive error model of the specific processing chain, solve the comprehensive error compensation amount of each motion axis in the processing chain through the third step, and perform comprehensive error compensation on the processing chain.

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