Comprehensive error modeling and adaptive compensation method for multi-axis turning-milling machine tools considering all working conditions

Abstract

A comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning-milling compound machine tool taking into account all working conditions belongs to the field of machine tool precision improvement. The present invention first analyzes the topological structure of the nine-axis machine tool, and based on the homogeneous coordinate transformation method of the multi-body system theory, establishes a comprehensive error model taking into account all working conditions; 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 present invention improves the accuracy of modeling by establishing a comprehensive error model taking into account all working conditions and establishing different comprehensive error models for different working conditions; an adaptive compensation method is introduced to perform comprehensive error compensation on the processing chain under different working conditions, so that the compensation result is more accurate and more efficient. The method pointed out by 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.

Description

Technical Field

[0001] The present 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-milling compound machine tool taking into account all working conditions. Background Art

[0002] Machine tools play a vital role in improving my country's industrial competitiveness. To date, research on the impact of comprehensive errors on machine tool machining accuracy has primarily focused on three-axis 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 dual-turret five-axis machine tool; and Chinese patent CN202011304180.4 utilizes a five-axis AC gantry machine tool for geometric error modeling and error separation. These three-axis and five-axis machine tools have simple structures, but each utilizes only a single workpiece chain and a single tool chain to complete machining. Multi-axis turning-milling machine tools, such as the nine-axis five-axis turning-milling machine tool (hereinafter referred to as the nine-axis machine tool), can complete multiple processes in a single clamping. They are high-end manufacturing equipment urgently needed in core industries such as aviation, aerospace, military, energy, and transportation. Their functions and technical performance, to a certain extent, reflect the overall level of the machine tool industry. However, the nine-axis machine tool has multiple workpiece chains and tool chains, which complicates the process of comprehensive error modeling and compensation. Summary of the Invention

[0003] To address these issues, this paper proposes a comprehensive error modeling and adaptive compensation method for multi-axis turning-milling machine tools, taking into account all operating conditions. By analyzing the topological structure of a nine-axis machine tool and using the homogeneous coordinate transformation method of multi-body system theory to establish a comprehensive error model that takes into account all operating conditions, the comprehensive error compensation is calculated, and an adaptive compensation method is proposed. This provides a theoretical basis for comprehensive error modeling and compensation for multi-axis machine tools with multiple workpiece chains and 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-milling machine tool, taking into account all operating conditions, is proposed. The present invention first analyzes the topological structure of the nine-axis machine tool and, based on the homogeneous coordinate transformation method of multi-body system theory, establishes a comprehensive error model that takes into account all operating conditions. Secondly, the Jacobian matrix is ​​used to calculate the comprehensive error compensation for 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] Comprehensive errors include spatial errors and thermal errors. The nine-axis machine tool's motion axis system includes six linear axes and three rotary axes. The linear axes are the X1, Y, Z1, X2, Z2, and W axes, and the rotary axes are the C1, C2, and B axes. A nine-axis machine tool topology is established. Based on the relative positional relationships between the axis systems, the nine-axis machine tool is simplified into four independent and mutually independent motion chains. These chains consist of two workpiece chains and two tool chains: workpiece chain L1 and workpiece chain L2, and 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, and can 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, and can complete the processing of two working conditions: turning and milling. Theoretically, a workpiece chain and a tool chain can form a processing chain. Therefore, the processing chain combination ML under the 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 holding a tool. x represents the working condition, where 1, 2, and 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 various axis systems based on multi-body system theory and establish a comprehensive error model that takes into account all working conditions;

[0013] 2.1) First, based on the multi-body system theory, the nine-axis machine tool is simplified into a multi-body system with multiple internal bodies in relative motion. A coordinate system is fixed to 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 the two coordinate systems is expressed as . A 4×4 homogeneous matrix is ​​used to describe the relative motion of the two coordinate systems.

[0014] 2.2) Secondly, the geometric error terms of the nine-axis machine tool are analyzed based on its structure and axis system type. According to the ISO 230-1:2012 standard, there are six position-related geometric errors between the axes of a nine-axis machine tool. For linear axes, these errors are horizontal straightness error, vertical straightness error, yaw error, pitch error, roll error, and positioning error. For rotary axes, these errors are axial runout, radial runout in two directions, angular error, and yaw error along two axes. Nine-axis machine tools have a total of 54 position-related geometric errors. Furthermore, there are position-independent geometric errors between axis systems, such as perpendicularity error, parallelism error, and position deviation. Based on the relative positional relationships between axis systems, a 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 in multi-body system theory, a reference coordinate system, a tool coordinate system, a workpiece coordinate system, and the fixed coordinate systems of each axis are established. For a machine tool, the comprehensive machine error is the deviation between the ideal and actual position and posture of the tool tip relative to the workpiece point due to geometric errors when the machine tool moves to a certain position in the workspace. The ideal situation is when the machine tool has no errors, while the actual situation is when the machine tool has errors. In the actual calculation process, the coordinate values ​​of the tool tip in the tool coordinate system must be converted to the coordinate values ​​in the workpiece coordinate system under both the ideal and actual conditions. The comprehensive error is the difference between the two. To simplify calculations, the present invention uses the bed coordinate system as a reference. For a processing chain, the coordinate values ​​of the tool tip in the tool coordinate system are first converted to the bed coordinate system, and then from the bed coordinate system to the workpiece coordinate system of the workpiece chain. Based on this conversion path, the 4×4 transformation matrix of the tool coordinate system relative to the workpiece coordinate system under the ideal and actual conditions 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 between the tool coordinate system T and the bed coordinate system M 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 between the workpiece coordinate system W and the bed coordinate system M is WM T e , and the transformation matrix from the tool coordinate system T to the bed coordinate system M Expressed as:

[0020]

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

[0022] Therefore, based on the above-mentioned combined representation of the machining chain and the homogeneous coordinate transformation method based on 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 represents the workpiece chain, and the other represents 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 workpiece coordinate system relative to the bed coordinate system into the bed coordinate system relative to the workpiece coordinate system. 刀 This also has two meanings: the first represents the tool chain, and the second represents the transformation matrix of the tool coordinate system relative to the bed coordinate system. x represents the working condition, with 1, 2, and 3 representing turning, milling, and boring (drilling), respectively. For tool chain L3, x = 1, 2, 3; for tool chain L4, x = 1, 2.

[0025] 2.4) Finally, the transformation matrices between the ideal and actual workpiece (tool) chain elements are substituted into a comprehensive error model Q that accounts for all operating conditions. By inputting specific parameters into the comprehensive error model Q, the comprehensive error matrix R for a particular machining chain under a specific operating condition is output. R is a 4×4 matrix. The comprehensive error consists of position error vectors and attitude error vectors. The comprehensive error ΔE of the machining chain under this specific operating condition is composed of the first three rows and fourth column of matrix R (representing the position errors in the x, y, and z directions, respectively) and the first three rows and third column of matrix R (representing the attitude errors in the x, y, and z directions, respectively).

[0026] For a single machining chain, the aforementioned comprehensive error modeling method—that is, the method of determining the position and attitude errors of the tool relative to the workpiece from the motion of each axis—is called the forward kinematics method, and the resulting matrix is ​​called the forward kinematics matrix. To calculate the comprehensive error compensation, the inverse kinematics method is used to inversely determine the motion of each axis. This comprehensive error model, Q, encompasses the comprehensive errors of each machining chain under all operating conditions. Therefore, different parameters are input to determine the comprehensive error corresponding to a specific machining chain, and then inverse kinematics is used to determine the compensation.

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

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

[0029] 3.1) First, based on the ideal forward kinematic matrix of the machining chain, six expressions for position and attitude errors in the x, y, and z directions 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, find 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 amount of each motion axis in the processing chain.

[0033] The fourth step is the adaptive compensation method for comprehensive errors of the nine-axis machine tool under all working conditions;

[0034] As can be seen from the above, different machining chains corresponding to different working conditions lead to different comprehensive error models, which in turn leads to different compensation amounts for each axis during error compensation. Therefore, to address this issue, the present invention proposes an adaptive comprehensive error compensation method for all working conditions. This method combines the second step of considering the comprehensive error model under all working conditions with the third step of solving the compensation amount for 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 value of γ of the two tool chains respectively;

[0037] 4.2) Secondly, determine the types of tools clamped 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 status 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. The tool chain is close to the workpiece chain, and the tool chain cooperates with the workpiece chain for processing, 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, thereby performing comprehensive error compensation for the processing chain.

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

[0042] This invention establishes a comprehensive error model that accounts for all operating conditions, comprehensively considering the various complex operating conditions that multi-axis turning and milling machines may face during actual operation. Establishing different comprehensive error models for different operating conditions simplifies the comprehensive error modeling process and improves modeling accuracy. The introduction of an adaptive compensation method allows for comprehensive error compensation across the machining chain under different operating conditions, resulting in more accurate and efficient compensation results.

[0043] In summary, the method proposed 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) processing of chains L1 and chain L3, (b) is the turning processing of chains L2 and chain L4, (c) is the milling processing of chains L2 and chain L3, and the turning processing of chains L1 and chain L4, (d) is the turning processing of chains L1 and chain L3, and the milling processing of chains L2 and chain 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 with reference to specific implementation cases.

[0051] This embodiment takes a nine-axis machine tool as an example to illustrate the proposed 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, and the Y axis is connected to the B axis. 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 that can be processed simultaneously without affecting each other. λ, β indicate whether the tool is clamped, with a value of 0 or 1. When the value is 0, the tool is not clamped, and when the value is 1, 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 For workpiece chain L1, L n For workpiece chain L2, or m = 2, n = 1, indicating that L m For 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) processing 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 processing, and the workpiece chain L1 and the tool chain L4 perform turning processing, 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 various axis systems based on 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, a nine-axis machine tool has a total of 79 geometric error items, including 54 position-dependent 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}、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} coincide. Define {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 in the ideal and actual situations of the nine-axis machine tool is analyzed.

[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 conversion matrix results of the tool coordinate system 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 machining chain and the homogeneous coordinate transformation method based on 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, one of which represents the workpiece chain L1 or L2, and the other 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. pThis has two meanings: the first represents the tool chain, and the second represents the transformation matrix of the tool coordinate system relative to the bed coordinate system. x represents the working condition, with 1, 2, and 3 representing turning, milling, and boring (drilling), respectively. When x = 1, 2, or 3, p = 3, indicating a tool chain of L3; when x = 1 or 2, p = 4, indicating a tool chain of L4.

[0077] 2.4) Finally, by substituting equations (7) and (8) into equation (9), we can obtain 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 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 third column elements of matrix R, D 3×1 Contains the first three rows and fourth column of 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 formula (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 is input into the model with λ=1, β=0, x=1, p=3 and m=1. The model can be first expressed as That is, it means that the workpiece chain L1 and the tool chain L3 cooperate in the turning working condition. Then, based on the singular function, the transformation matrix between the workpiece (tool) coordinate system and the bed coordinate system under the ideal and actual conditions of the corresponding workpiece (tool) chain 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 kinematic matrix F(U) at this time gives us six expressions for the motion quantities x, y, z, α, and β of each axis. These expressions include the position error vector P(U) and the attitude error vector V(U) in the x, y, and z directions.

[0086] 3.2) Next, perform partial differential calculations on the motion of each axis based on the six expressions to obtain the Jacobian matrix J. J is a 6×5 matrix, where the first row contains the partial differential results of the position error in the x-direction with respect to the motion of each axis, the second row contains the partial differential results of the position error in the y-direction with respect to the motion of each axis, the third row contains the partial differential results of the position error in the z-direction with respect to the motion of each axis, the fourth row contains the partial differential results of the attitude error in the x-direction with respect to the motion of each axis, the fifth row contains the partial differential results of the attitude error in the y-direction with respect to the motion of each axis, and the sixth row contains the partial differential results of the attitude error in the z-direction with respect to the motion of each axis.

[0087] 3.3) Then, find 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 equation (11):

[0090] ΔU=J1ΔE(13)

[0091] The fourth step is the adaptive compensation method for comprehensive errors of the nine-axis machine tool under all working conditions;

[0092] The flowchart of the proposed adaptive compensation method is as follows: Figure 5 As shown in the figure, the analysis is combined with the comprehensive error model considering all working conditions in the second step and the compensation of each motion axis in the third step. This solution only considers the processing of one workpiece chain and one tool chain, and does not consider the case where one workpiece chain is processed with 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, i.e., λ and β = 0, no comprehensive error compensation is performed.

[0094] 4.2) Next, if a tool is clamped (i.e., λ and β = 1), determine whether the tool type clamped by the two tool chains is a turning tool, a milling cutter, or a boring (drilling) tool, i.e., determine whether x = 1, 2, or 3. Simultaneously, 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, i.e., 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 determined which tool chain is performing which working condition at this time.

[0096] 4.4) Then, determine the position 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 workpiece chain L1, m=1, then it cooperates with workpiece chain L1 for processing; if it is close to workpiece chain L2, m=2, then it cooperates with workpiece chain L2 for processing.

[0097] 4.5) Finally, depending on the different processing chains, the values ​​of the identified parameters λ, β, x, p, and m are substituted into the comprehensive error model considering 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 for a nine-axis, five-axis turning-milling machine tool was established, taking into account all operating conditions. An adaptive compensation method was proposed. This method can determine different comprehensive errors based on different operating conditions, thereby obtaining corresponding comprehensive compensation amounts and performing comprehensive error compensation. This makes the compensation method more targeted and the compensation results more accurate.

[0099] The above-described embodiments merely express the implementation methods of the present invention, but should not 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 variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A comprehensive error modeling and adaptive compensation method for a multi-axis linkage turning-milling machine tool taking into account all working conditions, characterized in that: The comprehensive error modeling and adaptive compensation method includes 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 various axis systems based on 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 workpiece coordinate system relative to the bed coordinate system into 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. In the fourth step, the comprehensive error model under all working conditions considered in the second step and the compensation amount of each motion axis solved in the third step are analyzed to realize the adaptive compensation of the comprehensive error 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-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 rotary axes; the linear axes are X1, Y, Z1, X2, Z2 and W axes, and the rotary axes are C1, C2 and B axes; a topological structure of the nine-axis machine tool is established, and 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 and workpiece chain L2, and tool chain L3 and tool chain L4; The workpiece chain L1 consists of the bed-C1 axis-workpiece; the workpiece chain L2 consists of the bed-W axis-C2 axis-workpiece; the tool chain L3 consists of the 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 or drilling tools to complete the three working conditions of turning, milling, and boring or drilling. The tool chain L4 consists of the bed-Z2 axis-X2 axis-tool. The tool-holding components in the chain can hold turning tools and milling cutters to complete the two working conditions of turning and milling. A workpiece chain and a tool chain can form a processing chain when they are processed together. 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 is clamping the tool; x represents the working condition, 1, 2, 3 represent turning, milling and boring or drilling three working conditions 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-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 relative motion 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 based on its structure and axis system type; 2.3) Based on the comprehensive error modeling method of homogeneous coordinate transformation in 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 point in the tool coordinate system is converted to the coordinate value in the workpiece coordinate system under ideal and actual conditions respectively. The comprehensive error is the difference between the two. The bed coordinate system is selected as the reference. For a processing chain, the coordinate value of the tool tip point 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. Based on this transformation path, the 4×4 transformation matrix of the tool coordinate system relative to the workpiece coordinate system under ideal and actual conditions is calculated to obtain the comprehensive error. A comprehensive error model Q that takes into account all working conditions is established using the combined representation of the machining chain and the homogeneous coordinate transformation method based on 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. By inputting specific parameters into the comprehensive error model Q, the 4×4-order comprehensive error matrix R of a certain processing chain under specific working conditions is output; 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 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 above 2.4) is specifically: Ideally, the transformation matrix from the workpiece coordinate system W to the bed coordinate system M is And the transformation matrix between the tool coordinate system T and the bed coordinate system M 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 between the workpiece coordinate system W and the bed coordinate system M is , and the transformation matrix from the tool coordinate system T to the bed coordinate system M 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 ideal forward kinematic matrix of the machining chain, six expressions for position and attitude errors in the x, y, and z directions are obtained; 3.2) Perform partial differentiation 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) 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, i.e., determine the value 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 motion status of the two tool chains; 4.3) Determine the combination of two tool chains and clamping tools; 4.4) Determine the position of the two tool chains relative to the two workpiece chains. The tool chain is close to the workpiece chain, and then cooperates with the workpiece chain to process, and 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, and solve the comprehensive error compensation amount of each motion axis in the processing chain through the third step to perform comprehensive error compensation on the processing chain.

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