A rapid measurement method for six-dimensional pose error at the end of a dual-chain five-axis machine tool

Abstract

This invention discloses a rapid method for measuring the six-dimensional pose error of the end effector of a dual-chain five-axis machine tool. The method includes the following steps: The machine tool is moved to any two-dimensional position within the workspace via multi-axis linkage control; a laser tracker is used to measure the position information of the target balls at the end of the tool chain and the end of the workpiece chain, respectively; the measurement coordinate system and the machine tool coordinate system are aligned; according to the instructions of the machine tool CNC system, the position information of six target balls on the target ball supports at the end of the tool chain and the end of the workpiece chain in the measurement coordinate system is calculated and input into the tracker; the tracker locates the target balls according to the instructions and measures their actual positions; and then the six-dimensional error of the end effector is calculated based on the actual positions of the target balls. The method proposed in this invention can automatically measure the six-dimensional spatial error of a dual-chain five-axis machine tool with only one coordinate alignment, without changing stations. The modeling process is simple, clear, and easy to program, significantly improving the measurement cost and efficiency of spatial errors.

Description

Technical Field

[0001] This invention relates to the field of machine tool error measurement technology, and in particular to a rapid method for measuring the six-dimensional pose error at the end of a dual-chain five-axis machine tool. Background Technology

[0002] Due to their greater flexibility and machining efficiency, five-axis machine tools are playing an increasingly important role in the aerospace, automotive, medical equipment, and mold manufacturing industries as modern manufacturing develops. The spatial accuracy of a five-axis machine tool is one of the key performance indicators for evaluating its task capability and application value. Because most five-axis machine tools employ a dual-chain (tool chain and workpiece chain) structure, the methods for measuring the six-dimensional error at the end of the chain are extremely scarce and inefficient. Therefore, there is an urgent need for a method that can quickly measure the six-dimensional pose error at the end of a chain-driven five-axis machine tool.

[0003] Among numerous measuring instruments, laser trackers have advantages such as simple operation, fast measurement speed, and large measurement range. However, most existing trackers can only perform single-target ball measurements, inevitably amplifying the effects of human error and repeatability error when measuring spatial errors. Therefore, how to utilize the measurement advantages of trackers while reducing measurement errors is a key issue that needs to be addressed for the rapid measurement of six-dimensional pose errors at the end of a five-axis machine tool. Summary of the Invention

[0004] The purpose of this invention is to propose a rapid measurement method for the six-dimensional pose error of the end effector of a dual-chain five-axis machine tool. This method can quickly measure the six-dimensional pose error of the end effector of a dual-chain five-axis machine tool based on a tracker. This invention is beneficial for theoretical research on machine tool precision design and for the rapid evaluation of machine tool precision in engineering projects.

[0005] The proposed rapid measurement method for six-dimensional pose error at the end of a dual-chain five-axis machine tool includes the following steps:

[0006] Step 1: Using multi-axis linkage control, move the machine tool to any two positions in the workspace. Use a laser tracker to measure the position information of the target ball at the end of the tool chain and the end of the workpiece chain, and align the measurement coordinate system with the machine tool coordinate system. This includes the following steps:

[0007] Step 1.1 Fix the two triangular target ball supports to the worktable and the end of the tool respectively, and denote the centers of the three target balls on the worktable as W0, ... i (i = 1~3), the centers of the three target balls at the end of the cutter are respectively T i (i = 1~3), the center point of the worktable is point W, the tool execution point is point T, the machine tool coordinate system is {R0}, the tracking instrument measurement coordinate system is {R1}, the tool chain target ball support integrated coordinate system is {R3}, and the workpiece chain auxiliary support coordinate system is {R4}.

[0008] Step 1.2 Control the machine tool to move to any two positions P in the workspace j (j=1,2), hold the target ball and measure the position vectors of W1 and T1 in the measurement coordinate system {R1} under the two configurations. and remember The coordinates in coordinate system {R3} are: remember The coordinate vector in coordinate system {R4} is Let the coordinates of points W and T in the frame coordinate system be respectively and Let l be the position vector pointing from the origin of the machine tool coordinate system {R0} to the origin of the measurement coordinate system {R1}. 0 / 1 The attitude matrix of the measurement coordinate system {R1} relative to the machine tool coordinate system {R0} is: 0 R1, let the toolchain rotation matrix be R t，j The workpiece chain rotation matrix is ​​R. w，j .

[0009] Step 1.3 Establish equations based on the vector closed loop.

[0010]

[0011] Solving for the given information

[0012] Then, based on the vector closed-loop equations

[0013]

[0014] Solving for the given information This completes the coordinate alignment between the machine tool coordinate system {R0} and the measurement coordinate system {R1}.

[0015] Step 2: According to the instructions of the machine tool CNC system, calculate the position information of the six target balls on the target ball support at the end of the tool chain and the end of the workpiece chain in the measurement coordinate system, and input it into the tracker. The tracker locates the target balls according to the instructions and measures their actual positions, and then calculates the six-dimensional error of the end effector based on the actual positions of the target balls. (Includes the following steps:)

[0016] Step 2.1: The CNC system controls the machine tool to reach P in the workspace. k Point, at P k Let the position vectors of points W and T be w and w', respectively. k and t k (Given) The coordinates in coordinate system {R3} are: (Given) The coordinate vector in coordinate system {R4} is (Given) The toolchain rotation matrix is ​​Rt，k The workpiece chain rotation matrix is ​​R. w，k ;

[0017] Step 2.2: Calculate the theoretical positions of the three pairs (six) of target balls in the measurement coordinate system for the tool chain and workpiece chain. and

[0018]

[0019]

[0020] Step 2.3, The data is transmitted in real time to the tracking system, controlling the trackers to sequentially reach T. i and W i Points, measuring the actual position coordinates of each target point in the measurement coordinate system. and Based on the relationship between the measurement coordinate system {R1} and the frame coordinate system {R0}, the actual position coordinates of each target point in the frame coordinate system {R0} are calculated. and

[0021] Step 2.4: Based on the error vector closure, T i Point relative to W i Point pose error vector It can be written as

[0022]

[0023] In the formula, Δr is the end-effector position error of the machine tool, and Δθ is the end-effector position t and ΔΔ w These represent the attitude errors at the end of the toolchain and the end of the workpiece chain, respectively. The above equation can be written in matrix form.

[0024]

[0025] In the formula, This represents the vector composed of the positional errors of the three pairs of target points corresponding to the auxiliary support. The slant matrix represents the position vector; ξ is the end-effector pose error screw, and K is the vector from ξ to... The mapping matrix is ​​used to calculate the final six-dimensional error spinor using the least squares method.

[0026]

[0027] Since angles cannot be directly added or subtracted, further calculations are needed to solve for the end-effector attitude error.

[0028] ΔR=ΔR t ΔR w ;

[0029] In the formula, ΔR is the total end-point attitude error matrix. t and ΔR w These are the toolchain end-of-line attitude error matrices and the workpiece end-of-line attitude error matrices, respectively. Based on the small error assumption, the end-of-line attitude error vector Δθ can be written as follows:

[0030]

[0031] In the formula, ΔR(i,j) is the element in the i-th row and j-th column of matrix ΔR.

[0032] This invention provides a rapid method for measuring the six-dimensional pose error at the end of a dual-chain five-axis machine tool. The specific beneficial effects are:

[0033] The method proposed in this invention can automatically measure the six-dimensional spatial error of a dual-chain five-axis machine tool by means of only one coordinate alignment and without changing stations. The modeling process is simple, clear and easy to program, which can significantly improve the measurement cost and efficiency of spatial error. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of a five-axis machine tool.

[0035] Figure 2 This is the coordinate system of a certain five-axis machine tool.

[0036] Figure 3 A vector diagram for solving the end-effector pose error of a five-axis machine tool. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0038] Appendix Figure 1 The diagram shows a schematic of a dual-chain five-axis machine tool. Taking this machine tool as an example, the method of the present invention will be described.

[0039] Step 1: Using multi-axis linkage control, move the machine tool to any two positions in the workspace. Use a laser tracker to measure the position information of the target ball at the end of the tool chain and the end of the workpiece chain, and align the measurement coordinate system with the machine tool coordinate system. This includes the following steps:

[0040] Step 1.1: Fix the two triangular target ball supports to the worktable and the end of the tool respectively. Record the centers of the three target balls on the worktable as W0, ... and W0, respectively. i (i = 1~3), the centers of the three target balls at the end of the cutter are respectively T i(i = 1~3), the center point of the worktable is point W, the tool execution point is point T, the machine tool coordinate system is {R0}, the tracking instrument measurement coordinate system is {R1}, the tool chain target ball support integrated coordinate system is {R3}, and the workpiece chain auxiliary support coordinate system is {R4}.

[0041] Step 1.2 Control the machine tool to move to any two positions P in the workspace j (j=1,2), hold the target ball and measure the position vectors of W1 and T1 in the measurement coordinate system {R1} under the two configurations. and remember The coordinates in coordinate system {R3} are: remember The coordinate vector in coordinate system {R4} is Let the coordinates of points W and T in the frame coordinate system be respectively and Let l be the position vector pointing from the origin of the machine tool coordinate system {R0} to the origin of the measurement coordinate system {R1}. 0 / 1 The attitude matrix of the measurement coordinate system {R1} relative to the machine tool coordinate system {R0} is: 0 R1, let the toolchain rotation matrix be R t，j The workpiece chain rotation matrix is ​​R. w，j As attached Figure 2 As shown.

[0042] Step 1.3 Establish equations based on the vector closed loop.

[0043]

[0044] Solving for the given information

[0045] Then, based on the vector closed-loop equations

[0046]

[0047] Solving for the given information This completes the coordinate alignment between the machine tool coordinate system {R0} and the measurement coordinate system {R1}.

[0048] Step 2: According to the instructions of the machine tool CNC system, calculate the position information of the six target balls on the target ball support at the end of the tool chain and the end of the workpiece chain in the measurement coordinate system, and input it into the tracker. The tracker locates the target balls according to the instructions and measures their actual positions, and then calculates the six-dimensional error of the end effector based on the actual positions of the target balls. (Includes the following steps:)

[0049] Step 2.1: The CNC system controls the machine tool to reach P in the workspace. k Point, at P k Let the position vectors of points W and T be w and w', respectively.k and t k (Given) The coordinates in coordinate system {R3} are: (Given) The coordinate vector in coordinate system {R4} is (Given) The toolchain rotation matrix is ​​R t，k The workpiece chain rotation matrix is ​​R. w，k ;

[0050] Step 2.2: Calculate the theoretical positions of the three pairs (six) of target balls in the measurement coordinate system for the tool chain and workpiece chain. and

[0051]

[0052]

[0053] Step 2.3, The data is transmitted in real time to the tracking system, controlling the trackers to sequentially reach T. i and W i Points, measuring the actual position coordinates of each target point in the measurement coordinate system. and Based on the relationship between the measurement coordinate system {R1} and the frame coordinate system {R0}, the actual position coordinates of each target point in the frame coordinate system {R0} are calculated. and Let the position error vectors of points T and W be Δr, respectively. T and Δr W Let the actual position vectors of points T and W be respectively... True t k and True w k T i Point and W i The point position errors are respectively and

[0054] Step 2.4: Close the loop based on the error vector (as shown in the attached diagram). Figure 3 As shown), T i Point relative to W i Point pose error vector It can be written as

[0055]

[0056] In the formula, Δr is the end-effector position error of the machine tool, and Δθ is the end-effector position t and Δθ w These represent the attitude errors at the end of the toolchain and the end of the workpiece chain, respectively. The above equation can be written in matrix form.

[0057]

[0058] In the formula, This represents the vector composed of the positional errors of the three pairs of target points corresponding to the auxiliary support. The slant matrix represents the position vector; ξ is the end-effector pose error screw, and K is the vector from ξ to... The mapping matrix is ​​used to calculate the final six-dimensional error spinor using the least squares method.

[0059]

[0060] Since angles cannot be directly added or subtracted, a further calculation is needed to solve for the end-effector attitude error.

[0061] ΔR=ΔR t ΔR w ;

[0062] In the formula, ΔR is the total end-point attitude error matrix. t and ΔR w These are the toolchain end-of-line attitude error matrices and the workpiece end-of-line attitude error matrices, respectively. Based on the small error assumption, the end-of-line attitude error vector Δθ can be written as follows:

[0063]

[0064] In the formula, ΔR(i,j) is the element in the i-th row and j-th column of matrix ΔR.

[0065] The present invention ultimately yields a six-dimensional error at the end of the machine tool. The accompanying drawings are merely a preferred example. The above embodiments are only for describing the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for rapid measurement of six-dimensional pose error at the end of a dual-chain five-axis machine tool, characterized in that: The machine tool is moved to any two-dimensional position in the workspace by multi-axis linkage control. A laser tracker is used to measure the position information of the target balls at the end of the tool chain and the end of the workpiece chain, aligning the measurement coordinate system with the machine tool coordinate system. Based on the instructions from the machine tool CNC system, the position information of the six target balls on the target ball supports at the end of the tool chain and the end of the workpiece chain in the measurement coordinate system is calculated and input into the tracker. The tracker locates the target balls according to the instructions and measures their actual positions. Then, the six-dimensional error of the end effector is calculated based on the actual positions of the target balls. The process includes the following steps: Step 1: Using multi-axis linkage control, move the machine tool to any two positions in the workspace. Use a laser tracker to measure the position information of the target ball at the end of the tool chain and the end of the workpiece chain, and align the measurement coordinate system with the machine tool coordinate system. This includes the following steps: Step 1.1 Fix the two triangular target ball supports to the worktable and the end of the tool respectively, and denote the centers of the three target balls on the worktable as W0, ... i (i = 1~3), the centers of the three target balls at the end of the cutter are respectively T i (i = 1~3), the center point of the worktable is point W, the tool execution point is point T, the machine tool coordinate system is {R0}, the tracking instrument measurement coordinate system is {R1}, the tool chain target ball support integrated coordinate system is {R3}, and the workpiece chain auxiliary support coordinate system is {R4}. Step 1.2 Control the machine tool to move to any two positions P in the workspace j (j=1,2), hold the target ball and measure the position vectors of W1 and T1 in the measurement coordinate system {R1} under the two configurations. and Let the vector from point T to point T1 be... The coordinates in coordinate system {R3} are: Let the vector pointing from point W to point W1 be... The coordinate vector in coordinate system {R4} is Let the coordinates of points W and T in the machine tool coordinate system be respectively and Let l be the position vector pointing from the origin of the machine tool coordinate system {R0} to the origin of the measurement coordinate system {R1}. 0 / 1 The attitude matrix of the measurement coordinate system {R1} relative to the machine tool coordinate system {R0} is: 0 R1, let the toolchain rotation matrix be R t,j The workpiece chain rotation matrix is ​​R. w，j ; Step 1.3 Establish equations based on the vector closed loop. Solving for the given information Then, based on the vector closed-loop equations Solving for the given information This completes the coordinate alignment between the machine tool coordinate system {R0} and the measurement coordinate system {R1}. Step 2: According to the instructions of the machine tool CNC system, calculate the position information of the six target balls on the target ball support at the end of the tool chain and the end of the workpiece chain in the measurement coordinate system, and input it into the tracker. The tracker locates the target balls according to the instructions and measures their actual positions. Then, it calculates the six-dimensional error of the end of the machine tool based on the actual positions of the target balls. This includes the following steps: Step 2.1: The CNC system controls the machine tool to reach P in the workspace. k Point, at P k Let the position vectors of points W and T be w and w', respectively. k and t k , The coordinates in coordinate system {R3} are: The coordinate vector in coordinate system {R4} is The toolchain rotation matrix is ​​R t，k The workpiece chain rotation matrix is ​​R. w,k ; Step 2.2: Calculate the theoretical positions of the three pairs of target balls in the measurement coordinate system for the tool chain and workpiece chain. and Step 2.3, The data is transmitted in real time to the tracking system, controlling the trackers to sequentially reach T. i and W i Points, measuring the actual position coordinates of each target point in the measurement coordinate system. and Based on the measurement coordinate system {R1} and the machine tool coordinate system The relationship between the target points is used to calculate the actual position coordinates of each target point in the machine tool coordinate system {R0}. and Step 2.4: Based on the error vector closure, T i Point relative to W i Point pose error vector for In the formula, Δr is the end-effector position error of the machine tool, and Δθ is the end-effector position t and Δθ w These are the attitude errors at the end of the tool chain and the end of the workpiece chain, respectively; the above equation can be written in matrix form. In the formula, This represents the vector consisting of the positional errors of the three pairs of target points on the auxiliary support. The slant matrix represents the position vector; ξ is the end-effector pose error screw, and K is the vector from ξ to... The mapping matrix is ​​used to calculate the final six-dimensional error spinor using the least squares method. Since angles cannot be directly added or subtracted, further calculations are needed to solve for the end-effector attitude error. ΔR=ΔR t ΔR w ; In the formula, ΔR is the total end-point attitude error matrix. t and ΔR w These are the toolchain end-of-line attitude error matrix and the workpiece end-of-line attitude error matrix, respectively; based on the small error assumption, the end-of-line attitude error vector Δθ is... In the formula, ΔR(i,j) is the element in the i-th row and j-th column of matrix ΔR.

Images