R-test-based geometric error identification method for parallel head of horizontal five-axis turning plate mill

Abstract

A horizontal five-axis turning plate milling parallel head geometric error identification method based on R-test comprises the steps that firstly, analyzed parallel head geometric errors are defined, and an inverse kinematics model is solved in combination with the structure of a parallel head; then, a linkage track of a numerical control machine tool is designed, after the RTCP function is started, the 3-PRS parallel main shaft head needs to traverse all controllable freedom degrees, namely, the A axis, the B axis and the Z axis, and measurement data is the actual tool nose position error; according to a solving result of the inverse kinematics model, solving of an error coefficient matrix is completed; and finally, an actual tool nose position error and a matrix related to an error matrix coefficient matrix and a Jacobian matrix are substituted through an identification equation set, and geometric error identification of the horizontal five-axis turning plate milling parallel head is completed. According to the method, the geometric error of the horizontal five-axis turning plate milling parallel head can be quickly identified, and the method has the advantages of high efficiency, accuracy, completeness, simplicity and convenience.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical control machine tools, and particularly relates to a method for identifying geometric errors of a horizontal five-axis tilting milling parallel head based on R-test. Background Art

[0002] Numerical control machine tools, as the "machine tools of the manufacturing industry", play a crucial role in improving the manufacturing level of a country. Numerical control machine tools can machine complex curved surfaces, such as important components like engine impeller blades, and are widely used in important equipment such as airplanes and submarines, playing an important role in improving the level of major national equipment. The horizontal five-axis tilting milling parallel head machine tool, which adopts a 3-PRS parallel spindle head and an X-Y series workbench, has obvious advantages in terms of processing efficiency, processing quality, and manufacturing cost. It is widely used for machining complex curved surface parts such as molds, integral impellers, and aerospace thin-walled parts, and is the machining center with the highest efficiency in machining aerospace parts.

[0003] Currently, in the research on geometric errors of hybrid mechanisms at home and abroad, the geometric errors of the linear axes of the series workbench in the hybrid mechanism have been very mature, mainly measured by equipment such as laser interferometers. After compensating for the linear axes, the main difficulty still lies in the measurement and identification of the geometric errors of the parallel spindle head. In the literature "A DBB-Based Kinematic Calibration Method for In-Parallel Actuated Mechanisms Using a Fourier Series", Keisuke Nagao et al. in Japan used an articulated arm coordinate measuring machine to identify 31 geometric error parameters of the Exechon robot-type machine tool in 2021. However, this method cannot completely measure the geometric errors of the Exechon robot-type machine tool, and the articulated arm coordinate measuring machine is complex to operate and has low accuracy.

[0004] Zhou Hongbin et al. from Beijing Institute of Technology conducted research on the spindle error identification of parallel machine tools. In the literature "Experimental Research on Geometric Error Modeling and Compensation of 3-PRS Parallel Airbag Polishing Machine Tools", a calibration experiment was completed using a laser tracker and a coordinate measuring machine device, and a total of 35 geometric errors of the 3-PRS parallel spindle head were measured. However, there are disadvantages such as cumbersome operation, low automation level, incomplete identification of geometric error terms, and the need to further improve accuracy.

[0005] Currently, there is an urgent need for a method for identifying geometric errors of a horizontal five-axis tilting milling parallel head that is efficient, accurate, complete, and simple. Summary of the Invention

[0006] To overcome the above-mentioned disadvantages of the prior art, the object of the present invention is to provide a geometric error identification method for a horizontal five-axis tilting milling parallel head based on R-test, which can realize the rapid identification of the geometric error of the horizontal five-axis tilting milling parallel head, and has the advantages of high efficiency, accuracy, completeness and simplicity.

[0007] To achieve the above object, the present invention is realized through the following technical solutions:

[0008] A geometric error identification method for a horizontal five-axis tilting milling parallel head based on R-test, comprising the following steps:

[0009] 1) Define the geometric error terms of the horizontal five-axis tilting milling parallel head. The parallel head has 3 branch chains, and each branch chain has 14 geometric errors, for a total of 42 geometric errors, which are classified according to each structural segment on a single branch chain;

[0010] 2) Installation and data measurement of the R-test equipment: Place the R-test equipment on the workbench of the machining center and fix it with a fixture; based on the R-test equipment, after turning on the RTCP function of the machine tool, the 3-PRS parallel spindle head needs to traverse all controllable degrees of freedom - A-axis, B-axis, Z-axis, and within one stroke range, measure at a certain angular interval and record the obtained N groups of data;

[0011] 3) Establish a geometric error model according to the closed-loop vector method, as shown in Equation (1);

[0012] JδW=K a δD a +K c δD c +K b δD b +K e δD e +K l δD l +K h δD h (1)

[0013] In the formula: ——Tool spindle pose error;

[0014] ——6×6 Jacobian matrix; w i ——Link B i C i The unit vector of; e i ——Axis vector of the revolute pair; Γ i =[δT α c i δT β c i δT γ ci [, δT α , δT β , δT γ —— Differential coefficient matrix; K a , K c , K b , K e , K l , K h —— Error coefficient matrix; δD a , δD c , δD b , δD e , δD l , δD a —— Error term;

[0015] 4) Solving the error coefficient matrix: According to the inverse kinematics results of the 3-PRS parallel spindle head, solve the error coefficient matrix;

[0016] 5) Identification of geometric error terms:

[0017] Simplify and analyze Equation (1) to obtain the identification equation set, as shown in Equation (2);

[0018] δW = J -1 KδD A (2)

[0019] In the formula, J -1 —— Inverse of the Jacobian matrix; K = [K a K c K b K e K l K h —— Error coefficient matrix; —— Error identification parameter matrix;

[0020] Take the first three rows of δW as δp, and the first three rows of J -1 K as matrix A to obtain the simplified identification equation set, as shown in Equation (3);

[0021] δp = A·δD A (3)

[0022] Process Equation (3) to obtain the final identification equation set, as shown in Equation (4);

[0023] δD A =(A T A)- 1 A T δp (4)

[0024] Input the matrix A related to the error matrix coefficient matrix and the Jacobian matrix and the error data δp into Equation (4) to solve the geometric error term to be found.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] The present invention designs and runs a linkage trajectory, connects the R-test device to a computer, synchronously collects R-test displacement data, realizes the error measurement of the parallel head of the horizontal five-axis tilting milling machine, analyzes the inverse kinematic model of the 3-PRS parallel spindle head, and solves the geometric error of the parallel head of the horizontal five-axis tilting milling machine according to the measured data and the inverse kinematic model. The present invention is used for the geometric error of the parallel head of the horizontal five-axis tilting milling machine, and can directly and quickly obtain the measurement result, which has practical significance for the evaluation of the machining accuracy of the parallel head of the horizontal five-axis tilting milling machine and the future compensation direction. Description of the Drawings

[0027] Figure 1 It is a structural diagram of the 3-PRS parallel spindle head according to an embodiment of the present invention.

[0028] Figure 2 It is a trajectory planning diagram for measuring the geometric error of R-test according to an embodiment of the present invention.

[0029] Figure 3 It is a vector diagram of a single chain according to an embodiment of the present invention. Detailed Embodiments

[0030] The following describes the present invention in detail with reference to the drawings and embodiments.

[0031] A method for identifying the geometric error of the parallel head of a horizontal five-axis tilting milling machine based on R-test includes the following steps:

[0032] 1) According to the analysis of the parallel head structure, as Figure 1 shown, the parallel head is composed of 3 chains, a moving platform and a static platform. Each chain has 1 prismatic pair (P), 1 revolute pair (R) and 1 spherical pair (S), and the 3 chains are symmetrically distributed in a 120-degree circle. Define the geometric error terms of the parallel head of the horizontal five-axis tilting milling machine. The parallel head has 3 chains, and each chain has 14 geometric errors, for a total of 42 geometric errors. Classify according to each structural segment on a single chain, as shown in Table 1 specifically;

[0033] Table 1

[0034]

[0035] The total number of rotational axis geometric errors of the three chains is 42;

[0036] 2) Installation and data measurement of the R-test device: Place the R-test device on the workbench of the machining center and fix it with a fixture. After enabling the RTCP function of the machine tool based on the R-test device, the 3-PRS parallel spindle head needs to traverse all controllable degrees of freedom - the A-axis, B-axis, Z-axis, and the spindle rotates around L 1 ,L 2 in two circular arc motions, as Figure 2 shown; within the stroke range, measure at a certain angular interval and record 24 groups of data of the two circular arc motions obtained, as shown in Table 2;

[0037] Table 2

[0038]

[0039]

[0040] 3) Referring to Figure 3 the closed-loop vector diagram, according to the closed-loop vector method, establish a geometric error model. After differential simplification, the geometric error model can be obtained, as shown in Equation (1);

[0041] JδW=K a δD a +K c δD c +K b δD b +K e δD e +K l δD l +K h δD h (1)

[0042] In the formula: ——Tool spindle pose error;

[0043] ——6×6 Jacobian matrix; w i ——Unit vector of link B i C i ; e i ——Axis vector of the revolute pair; Γ i =[δT α c i δT β c i δT γ c i , δT α ,δT β ,δT γ ——Differential coefficient matrix; ——Error coefficient matrix of the lower end point of the column;

[0044] —— Coefficient matrix of ball hinge center error;

[0045] —— Coefficient matrix of column guide direction error;

[0046] —— Coefficient matrix of axis direction error of rotating pair;

[0047] —— Coefficient matrix of connecting rod length error;

[0048] —— Coefficient matrix of driving rod length error;

[0049] δD a = [δa 1 δa 2 δa 3 T —— Error at the lower end point of the column; δD c = [δc 1 δc 2 δc 3 T —— Ball hinge center error; δD b = [δb 1 δb 2 δb 3 T —— Column guide direction error; δD e = [δe 1 δe 2 δe 3 T —— Axis direction error of rotating pair; δD l = [δl 1 δl 2 δl 3 T —— Connecting rod length error; δD h = [δH 1 δH 2 δH 3 T —— Driving rod length error;

[0050] 4) Solution of error coefficient matrix: In this embodiment, the coefficient matrix of column guide direction error is taken as an example:

[0051] e in the matrix i and w i are solved from the inverse kinematics results of the 3-PRS parallel spindle head. The results at a certain measurement point are shown as follows.

[0052] ​​​​​​

[0053] 5) Identification of geometric error terms:

[0054] By simplifying and analyzing Equation (1), an identification equation set can be obtained, as shown in Equation (2);

[0055] δW = J -1 KδD A (2)

[0056] Where, J -1 —— The inverse of the Jacobian matrix; K = [K a K c K b K e K l K h —— Error coefficient matrix; —— Error identification parameter matrix;

[0057] Take the first three rows of δW as δp, and the first three rows of J -1 K as matrix A, then a simplified identification equation set can be obtained, as shown in Equation (3);

[0058] δp = A·δD A (3)

[0059] Process Equation (3) to move δD A to one side of the equation, and the final identification equation set can be obtained, as shown in Equation (4),

[0060] δD A =(A T A) -1 A T δp (4)

[0061] Input the matrix A related to the error matrix coefficient matrix and the Jacobian matrix in step (4) and the error data δp in step (2) into Equation (4), and the required geometric error terms can be solved, as shown in Table 3.

[0062] Table 3

[0063]

[0064] The advantages of this embodiment are as follows:

[0065] (1) High efficiency: By collecting data with an R-test device and combining the RTCP function of a numerically controlled machine tool, error data of multiple degrees of freedom (A-axis, B-axis, Z-axis) can be obtained simultaneously in one measurement. As shown in Table 2, only 24 sets of measurement data are required to complete the identification of 42 geometric errors, significantly reducing the time cost of multiple measurements in the traditional method.

[0066] (2) Accuracy: In this embodiment, a geometric error model is established by the closed-loop vector method, and the error coefficient matrix is solved by combining inverse kinematics, ensuring the accuracy of error identification. As shown in Table 3, the numerical distribution of each error in the identification result is reasonable and consistent with the error trend in actual machining, verifying the accuracy of the method.

[0067] (3) Completeness: This embodiment covers all 42 geometric errors of the 3-PRS parallel spindle head, including the error terms of the prismatic pair, revolute pair, and spherical pair (as shown in Table 1), avoiding the problem of missing error terms in traditional methods and achieving a comprehensive identification of the geometric errors of the parallel head.

[0068] (4) Simplicity: In this embodiment, an R-test device is used for data acquisition, which is simple to operate and highly automated. By designing the linkage trajectory (as Figure 2 shown), all measurements can be completed with only one installation, avoiding the cumbersome steps of multiple equipment adjustments in traditional methods.

Claims

1. A method for identifying geometric errors of a horizontal five-axis flap milling parallel head based on R-test, characterized in that: The following steps are involved: 1) The geometric error items of the horizontal five-axis flap milling parallel head are defined. The parallel head has three branches, each branch has 14 geometric errors, and a total of 42 geometric errors are classified according to each structural segment on a single branch; 2) Installation of R-test equipment and data measurement: Place the R-test equipment on the workbench of the machining center and fix it with a fixture; Based on the R-test equipment, after turning on the RTCP function of the machine tool, the 3-PRS parallel spindle head needs to traverse all controllable degrees of freedom - A axis, B axis, and Z axis, and measure at certain angles within a stroke range, and record the N sets of data obtained; 3) According to the closed-loop vector method, a geometric error model is established, as shown in formula (1); JδW=K a δD a +K c δD c +K b δD b +K e δD e +K l δD l +K h δD h (1) Where: ——Tool spindle position error; ——6×6 Jacobian matrix; w i ——Connecting rod B i C i The unit vector of i ——the vector of the secondary axis of rotation; Γ i =[δT α c i δT β c i δT γ c i ], δT α ,δT β ,δT γ ——differential coefficient matrix; K a ,K c ,K b ,K e ,K l ,K h ——Error coefficient matrix; δD a ,δD c ,δD b ,δD e ,δD l ,δD a ——error term; 4) Solving the error coefficient matrix: Based on the inverse kinematics results of the 3-PRS parallel spindle head, the error coefficient matrix is ​​solved; 5) Identification of geometric error terms: Simplify equation (1) and get the identification equations, as shown in equation (2); δW=J -1 KδD A (2) In the formula, J -1 ——The inverse of the Jacobian matrix; K = [K a K c K b K e K l K h ]——Error coefficient matrix; ——Error identification parameter matrix; Take the first three rows of δW as δp, J -1 The first three rows of K are the matrix A, and the simplified identification equations are as follows: δp=A·δD A (3) Processing equation (3) yields the final identification equation set, as shown in equation (4); δD A =(A T A) -1 A T δp (4) Input the matrix A related to the error matrix coefficient matrix and the Jacobian matrix and the error data δp into equation (4) to solve the required geometric error term.

Images