CN104374317A

CN104374317A - Machine tool error calibration method based on multi-point measurement technology of laser tracker

Info

Publication number: CN104374317A
Application number: CN201410638347.9A
Authority: CN
Inventors: 陈洪芳; 石照耀; 闫昊; 谭志
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2014-11-06
Filing date: 2014-11-06
Publication date: 2015-02-25
Anticipated expiration: 2034-11-06
Also published as: CN104374317B

Abstract

The invention relates to a machine tool error calibration method based on laser tracker multi-point measurement technology, which belongs to the technical field of precision testing. Based on this measurement method, the points to be measured are first arranged and numbered on the machine tool. When measuring, move the standard spherical target mirror to each point to be measured, and the laser tracker will measure outside the area of the point to be measured, and move the laser tracker in turn to obtain the three-dimensional coordinates of the points to be measured at different stations and the interference between adjacent points to be measured For the length measurement value, use the error equation for the interference length measurement value, and use the least square principle to solve the initial coordinate value of each station and the initial distance value under the corresponding station. Using the initial value of each station point, the measured value of the point to be measured and the distance value from the station to the initial point to be measured, the correction value of each point to be measured can be solved by the linear expansion of the error equation of the interferometric length measurement value. Therefore, the positioning accuracy of the space measurement point on the machine tool is improved.

Description

A machine tool error calibration method based on laser tracker multi-point measurement technology

技术领域 technical field

本发明涉及一种测量方法，特别是基于激光跟踪仪多点测量技术的机床误差标定方法。属于精密测试技术领域。 The invention relates to a measurement method, in particular to a machine tool error calibration method based on laser tracker multi-point measurement technology. It belongs to the technical field of precision testing. the

背景技术 Background technique

随着现代工业的不断发展，对机床的精度提出了越来越高的要求。机床的精度和精度稳定性是机床的重要技术指标。因为在工业测量、制造的过程中，由于受到磨损以及变形、安装等不同的因素影响，使得机床存在误差。 With the continuous development of modern industry, higher and higher requirements are put forward for the precision of machine tools. The accuracy and precision stability of machine tools are important technical indicators of machine tools. Because in the process of industrial measurement and manufacturing, due to the influence of different factors such as wear, deformation and installation, there are errors in the machine tool. the

提高机床精度已经受到很多研究者的重视。一般提高机床精度有两种基本方法，一种是误差预防，另一种是误差补偿法，其中误差补偿方法常见的有：实物基准测量法、激光球杆仪、正交光栅测量法、激光干涉测量法等，以激光干涉仪最为常用，激光干涉仪虽具有较高的测量精度，但对不同误差测量时需要搭建不同的测量光路，检测周期较长，不能满足高精度、快速检测要求。 Improving the accuracy of machine tools has attracted the attention of many researchers. Generally, there are two basic methods to improve the accuracy of machine tools, one is error prevention, and the other is error compensation method. Among them, the common error compensation methods are: physical reference measurement method, laser ballbar, orthogonal grating measurement method, laser interference Laser interferometer is the most commonly used measurement method. Although laser interferometer has high measurement accuracy, it needs to build different measurement optical paths when measuring different errors, and the detection cycle is long, which cannot meet the high-precision and rapid detection requirements. the

为此有必要发明一种适合于机床，能快速标定其误差的方法，以提高机床空间测量点的定位精度。 Therefore, it is necessary to invent a method that is suitable for machine tools and can quickly calibrate its errors, so as to improve the positioning accuracy of machine tool space measurement points. the

发明内容 Contents of the invention

技术的机床误差标定方法，具有高精度、快速实时跟踪测量和操作简单等特点。 The advanced machine tool error calibration method has the characteristics of high precision, fast real-time tracking measurement and simple operation. the

为达到以上目的，本发明是采取如下技术方案予以实现的： To achieve the above object, the present invention is achieved by taking the following technical solutions:

一种基于激光跟踪仪多点测量技术的机床误差标定方法，包括下述测量步骤： A method for calibrating machine tool errors based on laser tracker multi-point measurement technology, comprising the following measurement steps:

测量时，首先确定机床各轴的移动范围，然后在机床各个轴系移动范围内规划待测点，待测点的选取需要分布在整个机床的测量空间内，并按顺序编号：第1待测点，第2待测点…第n待测点，通常按待测点的排放顺序编号，编号顺序没有强制要求，但是要记住各个待测点对应的编号和总共待测点的个数n。然后用目标靶镜替换下机床的探针，将激光跟踪仪放置到机床测量空间的边缘，设该站位为激光跟踪仪的初始站位，站位摆放要满足不妨碍机床的移动路径，并保证各个站位下激光跟踪仪到靶镜具有直线视距，确保激光跟踪头能够跟随预先设置的待测点路径。 When measuring, first determine the movement range of each axis of the machine tool, and then plan the points to be measured within the movement range of each axis of the machine tool. The selection of the points to be measured needs to be distributed in the measurement space of the entire machine tool, and numbered in sequence: 1st to be measured Point, the second point to be measured...the nth point to be measured, usually numbered according to the sequence of the points to be measured, the numbering sequence is not mandatory, but remember the number corresponding to each point to be measured and the total number of points to be measured n . Then replace the probe of the machine tool with the target target mirror, place the laser tracker on the edge of the machine tool measurement space, and set this position as the initial position of the laser tracker. And ensure that the laser tracker at each station has a straight line of sight to the target mirror, and ensure that the laser tracking head can follow the pre-set path of the point to be measured. the

通常将跟踪仪放置在机床测量台的周边，这样可以最大限度满足待测点的移动范围并确保激光跟踪仪的站位不影响机床的移动。 Usually, the tracker is placed around the measuring platform of the machine tool, which can satisfy the movement range of the point to be measured to the greatest extent and ensure that the position of the laser tracker does not affect the movement of the machine tool. the

控制机床移动到每个待测量点，并测量此时的干涉测长值并记录待测点在机床坐标系下的坐标值，下述所有坐标系的坐标值都是机床坐标系下的坐标值，依次移动激光跟踪仪到其余站位，假设站位个数为m，每个站位的坐标为(X_k,Y_k,Z_k),其中k＝1,2,…,m。在机床上布置了n个待测点，待测点的坐标为(x_i,y_i,z_i)，其中i＝1,2,…,n。站位个数需要满足等式m×n≥3n+4m。。依次移动激光跟踪仪到各个站位，并按待测点顺序测量完所有待测点直到完成所有站位的测量。 Control the machine tool to move to each point to be measured, measure the interferometric length measurement value at this time and record the coordinate value of the point to be measured in the machine tool coordinate system. The coordinate values of all the following coordinate systems are the coordinate values in the machine tool coordinate system , moving the laser tracker to other stations in turn, assuming that the number of stations is m, and the coordinates of each station are (X _k , Y _k , Z _k ), where k=1,2,...,m. n points to be measured are arranged on the machine tool, and the coordinates of the points to be measured are (xi _, y _i , zi ₎ , where i=1, 2, . . . , n. The number of stations needs to satisfy the equation m×n≥3n+4m. . Move the laser tracker to each station in turn, and measure all the points to be measured in order until the measurement of all stations is completed.

设激光跟踪仪到机床的初始待测点的距离为，测量过程中激光跟踪仪获取待测点间相对干涉测量增量为l_i，在机床坐标下，选取编号为1的待测点为初始测量点，各个站位下的初始测量点均为此待测点，当目标反射镜从初始测量点T₀(x,y,z),移动到任意待测点T_i(x,y,z)，激光跟踪仪干涉测长增量为l，则按空间两点直线方程可以建立如下关系式： Assuming that the distance from the laser tracker to the initial point to be measured on the machine tool is , the relative interferometric increment between the points to be measured obtained by the laser tracker during the measurement is l _i , and under the coordinates of the machine tool, the point to be measured with number 1 is selected as the initial point The measurement point, the initial measurement point under each station is the point to be measured, when the target mirror moves from the initial measurement point T ₀ (x,y,z) to any point to be measured T _i (x,y,z ), and the interferometric length measurement increment of the laser tracker is l, then the following relationship can be established according to the space two-point straight line equation:

$\sqrt{{(({x x}_{i i} - - {X x}_{j j}))}^{22} + + {(({y the y}_{i i} - - {Y Y}_{j j}))}^{22} + + {(({z z}_{i i} - - {Z Z}_{j j}))}^{22}} = = {d d}_{j j} + + {l l}_{i i} - - - - - - ((11))$

上式中i和j分别是机床待测点数和激光跟踪仪站位数。假设激光跟踪仪在m个站位下测量待测点，在机床坐标系下，每个站位的坐标为(X_j,Y_j,Z_j)，其中j＝1,2,…,m。机床上有n个待测点，待测点的坐标为(x_i,y_i,z_i)，其中i＝1,2,…,n。 In the above formula, i and j are respectively the number of machine tool points to be measured and the number of laser tracker stations. Assuming that the laser tracker measures the points to be measured at m stations, in the machine tool coordinate system, the coordinates of each station are (X _j , Y _j , Z _j ), where j=1,2,...,m. There are n points to be measured on the machine tool, and the coordinates of the points to be measured are (x _i , y _i , z _i ), where i=1, 2,...,n.

实际测量时，l_i的真值可以利用高精度的干涉相对测距代替，则第j个站位下的第i个待测点的误差方程为: In actual measurement, the true value of _l can be replaced by high-precision interferometric relative ranging, then the error equation of the i-th point to be measured under the j-th station is:

${v v}_{ij ij} = = ((\sqrt{{(({x x}_{i i} - - {X x}_{j j}))}^{22} + + {(({y the y}_{i i} - - {Y Y}_{j j}))}^{22} + + {(({z z}_{i i} - - {Z Z}_{j j}))}^{22}} - - {d d}_{i i})) - - {l l}_{i i} - - - - - - ((22))$

设待测点(x_i,y_i,z_i)集合为T，站位坐标(X_j,Y_j,Z_j)集合为P，激光仪干涉测长l_i集合为L，每个站位下到初始待测点的距离d_j集合为D；利用最小二乘方法处理等式(2)使得误差平方和E(T,P,D)最小： Let the set of points to be measured (xi _, y _i , _zi ) be T, the set of station coordinates (X _j , Y _j , Z _j ) be P, and the set of laser interferometric length measurement l _i be L, each station The set of distances d _j down to the initial point to be measured is D; use the least squares method to process equation (2) to minimize the sum of squared errors E(T,P,D):

$E E. ((T T,, P P,, D D.)) = = \underset{i i = = 11}{Σ Σ} \underset{j j = = 11}{Σ Σ} {v v}_{ij ij}^{22} ((L L,, P P,, T T,, D D.)) ((i i = = 1,2,3 1,2,3,, . . . . . . n no,, j j = = 1,2,3 1,2,3,, . . . . . . m m)) - - - - - - ((33))$

由于等式(2)是一个非线性方程组，直接用等式(2)求解异常繁锁，采用下述方式给予解决： Since equation (2) is a nonlinear equation system, it is extremely complicated to solve it directly with equation (2), and it is solved in the following way:

已假设有n个机床待测点，有m个激光跟踪仪站位数；在机床坐标系下，未知参数为3n个待测点坐标T_i(x_i,y_i,z_i)和3m个激光跟踪站位坐标P_j(X_j,Y_j,Z_j)以及m个每个站位下到初始待测点的距离d_j。 It has been assumed that there are n machine tool points to be measured and m laser tracker stations; in the machine tool coordinate system, the unknown parameters are 3n points to be measured coordinates T _i (xi _, y _i , zi ₎ and 3m Laser tracking station coordinates P _j (X _j , Y _j , Z _j ) and the distance d _j from each station to the initial point to be measured.

所以未知数一共为3n+4m，而每个站位可以提供n个干涉测长值，总共m×n个方程，为使等式有解，需要满足m×n≥3n+4m，对等式(2)进行线性展开可得： Therefore, the total number of unknowns is 3n+4m, and each station can provide n interferometric length measurement values, a total of m×n equations, in order to make the equation have a solution, it is necessary to satisfy m×n≥3n+4m, for the equation ( 2) Perform linear expansion to get:

$\begin{matrix} {v v}_{ij ij} = = {L L}_{ij ij}^{o o} - - {d d}_{j j}^{00} - - {l l}_{i i} + + \frac{(({x x}_{i i}^{00} - - {X x}_{j j}^{00}))}{{L L}_{ij ij}^{00}} (({Δx Δx}_{i i} - - {ΔX ΔX}_{j j})) + + \frac{(({y the y}_{i i}^{00} - - {Y Y}_{j j}^{00}))}{{L L}_{ij ij}^{o o}} ((Δ Δ {y the y}_{i i} - - {ΔY ΔY}_{j j})) \\ + + \frac{(({z z}_{i i}^{00} - - {Z Z}_{j j}^{00}))}{{L L}_{ij ij}^{o o}} (({Δz Δz}_{i i} - - {ΔZ ΔZ}_{j j})) - - Δ Δ {d d}_{j j} \end{matrix} - - - - - - ((44))$

其中： in:

等式(4)即为优化解算模型，式中上标为零的变量为解算时需要给定的迭代初值，其中Δx_i，Δy_i，Δz_i，，，分别为参考坐标系待测点的坐标改正值与激光跟踪仪站位坐标质点的改正值，为每个站位质点到初始待测点的距离的改正值。实际测量中初值可以直接读取参考坐标系下需要优化待测点的三维坐标值。而激光跟踪仪各个站位质点的坐标初值，，和每个站位质点到初始待测点的距离初值需要用如下方法来求取： Equation (4) is the optimized solution model, where the variable with superscript zero is the iterative initial value that needs to be given during the solution, where Δx _i , Δy _i , Δz _i , , are the reference coordinate system to be The coordinate correction value of the measuring point and the correction value of the laser tracker station coordinate particle are the correction value of the distance from each station particle to the initial point to be measured. actual measurement The initial value can directly read the three-dimensional coordinate value of the point to be measured that needs to be optimized in the reference coordinate system. The initial value of the coordinates of each station mass point of the laser tracker, and the initial value of the distance from each station mass point to the initial point to be measured need to be obtained by the following method:

设激光跟踪仪站位坐标的近似值作为迭代初值，所以不妨设需要求取改正值的待测点坐标暂时为真值，则等式(1)中待测点坐标T_i(x,y,z)和干涉测长增量为已知变量，利用每个站位下的待测点坐标值和干涉测长增量，分别标定激光跟踪仪质点在各个站位下的坐标值和对应站位下质点到的初始待测点距离值，当j＝1时，则等式(1)变为： Let the approximate value of the station coordinates of the laser tracker be used as the initial value of the iteration, so it is advisable to assume that the coordinates of the points to be measured that need to be corrected are temporarily true values, then the coordinates of the points to be measured T _i (x, y, z) and the interferometric length measurement increment are known variables, use the coordinate value of the point to be measured and the interferometric length measurement increment under each station to calibrate the coordinate value of the particle of the laser tracker at each station and the corresponding station Lower mass point to the initial measured point distance value, when j=1, then equation (1) becomes:

$\sqrt{{(({x x}_{i i} - - {X x}_{11}))}^{22} + + {(({y the y}_{i i} - - {Y Y}_{11}))}^{22} + + {(({z z}_{i i} - - {Z Z}_{11}))}^{22}} = = {d d}_{11} + + {l l}_{i i} - - - - - - ((55))$

将等式(5)写成误差方程： Write equation (5) as an error equation:

${v v}_{i i} = = \sqrt{{(({x x}_{i i} - - {X x}_{11}))}^{22} + + {(({y the y}_{i i} - - {Y Y}_{11}))}^{22} + + {(({z z}_{i i} - - {Z Z}_{11}))}^{22}} - - (({d d}_{11} + + {l l}_{i i})) - - - - - - ((66))$

其中，,,为激光跟踪仪在机床坐标系下第一个站位的坐标值，(x_i,y_i,z_i)为对应站位下测量的待测点坐标值，为第1站位下各个待测点对应的误差值。 Among them, ,, is the coordinate value of the first station of the laser tracker in the machine tool coordinate system, (x _i , y _i , z _i ) is the coordinate value of the point to be measured measured at the corresponding station, and is the first station Below is the error value corresponding to each point to be measured.

设对上式进行最小二乘求解可得： set up The least squares solution to the above formula can be obtained:

$\begin{matrix} \frac{{&PartialD; &PartialD; v v}_{i i}^{22}}{&PartialD; &PartialD; {X x}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} (({x x}_{i i}^{22} + + {y the y}_{i i}^{22} + + {z z}_{i i}^{22} - - {l l}_{i i}^{22})) - - 22 {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i}^{22} {X x}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {y the y}_{i i} {x x}_{i i} {Y Y}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {z z}_{i i} {x x}_{i i} {Z Z}_{11} \\ - - 22 {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} {x x}_{i i} {d d}_{11} + + {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} k k = = 00 \end{matrix} - - - - - - ((77))$

$\begin{matrix} \frac{{&PartialD; &PartialD; v v}_{i i}^{22}}{&PartialD; &PartialD; {Y Y}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} (({x x}_{i i}^{22} + + {y the y}_{i i}^{22} + + {z z}_{i i}^{22} - - {l l}_{i i}^{22})) - - 22 {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} {y the y}_{i i} {X x}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {y the y}_{i i}^{22} {Y Y}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {z z}_{i i} {y the y}_{i i} {Z Z}_{11} \\ - - 22 {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} {y the y}_{i i} {d d}_{11} + + {Σ Σ}_{i i = = 11}^{n no} {y the y}_{i i} k k = = 00 \end{matrix} - - - - - - ((88))$

$\begin{matrix} \frac{{&PartialD; &PartialD; v v}_{i i}^{22}}{&PartialD; &PartialD; {Z Z}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} (({x x}_{i i}^{22} + + {y the y}_{i i}^{22} + + {z z}_{i i}^{22} - - {l l}_{i i}^{22})) - - 22 {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} {z z}_{i i} {X x}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {{y the y}_{i i} {z z}_{i i} Y Y}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {{z z}_{i i}^{22} Z Z}_{11} \\ - - 22 {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} {z z}_{i i} {d d}_{11} + + {Σ Σ}_{i i = = 11}^{n no} {z z}_{i i} k k = = 00 \end{matrix} - - - - - - ((99))$

$\begin{matrix} \frac{{&PartialD; &PartialD; v v}_{i i}^{22}}{&PartialD; &PartialD; {d d}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} (({x x}_{i i}^{22} + + {y the y}_{i i}^{22} + + {z z}_{i i}^{22} - - {l l}_{i i}^{22})) - - 22 {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} {l l}_{i i} {X x}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {y the y}_{i i} {{l l}_{i i} Y Y}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {z z}_{i i} {l l}_{i i} {Z Z}_{11} \\ - - 22 {Σ Σ}_{i i = = 11}^{n no} {{l l}_{i i}^{22} d d}_{11} + + {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} k k = = 00 \end{matrix} - - - - - - ((1010))$

$\begin{matrix} \frac{{&PartialD; &PartialD; v v}_{i i}^{22}}{{&PartialD; &PartialD; k k}_{11}} = = {Σ Σ}_{i i = = 11}^{n no} (({x x}_{i i}^{22} + + {y the y}_{i i}^{22} + + {z z}_{i i}^{22} - - {l l}_{i i}^{22})) - - 22 {Σ Σ}_{i i = = 11}^{n no} {x x}_{i i} {X x}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {y the y}_{i i} {Y Y}_{11} - - 22 {Σ Σ}_{i i = = 11}^{n no} {z z}_{i i} {Z Z}_{11} \\ - - 22 {Σ Σ}_{i i = = 11}^{n no} {l l}_{i i} {d d}_{11} + + {Σ Σ}_{i i = = 11}^{n no} k k = = 00 \end{matrix} - - - - - - ((1111))$

联立等式(7)和(11)可求得机床坐标系下第1站位的坐标值和对应站位下的初始距离值d，同理当。时，可以求得其余站位在机床坐标系的坐标值和对应站位下的初始距离值d。利用各个站位点的初始值和待测点测量值以及对应站位到初始待测点的距离值，即可以通过等式(4)求解出各个待测点的改正值。 Simultaneously combining equations (7) and (11), the coordinate value of the first station in the machine tool coordinate system and the initial distance value d in the corresponding station can be obtained, and the same is true. , the coordinate values of other stations in the machine tool coordinate system and the initial distance value d under the corresponding stations can be obtained. Using the initial value of each station point, the measured value of the point to be measured and the distance value from the corresponding station to the initial point to be measured, the correction value of each point to be measured can be obtained through equation (4). the

将改正值加上原测量点的三维值即为最终优化后的高精度三维坐标值。 Adding the correction value to the three-dimensional value of the original measurement point is the final optimized high-precision three-dimensional coordinate value. the

综上，本发明方法基于激光跟踪仪多点定位测量技术，利用激光跟踪仪高精度测长值作为约束，能有效提高机床空间测量点三维坐标值的精度。 In summary, the method of the present invention is based on the multi-point positioning measurement technology of the laser tracker, and uses the high-precision length measurement value of the laser tracker as a constraint, which can effectively improve the accuracy of the three-dimensional coordinate value of the machine tool space measurement point. the

附图说明 Description of drawings

图1为激光跟踪多点测量模型示意图。 Figure 1 is a schematic diagram of the laser tracking multi-point measurement model. the

图2是基于激光跟踪仪多点测量技术的机床误差标定方法的示意图。 Fig. 2 is a schematic diagram of a machine tool error calibration method based on laser tracker multi-point measurement technology. the

图3为利用激光多点测量优化模型求取的各个坐标改正值曲线图 Figure 3 is a curve diagram of each coordinate correction value obtained by using the laser multi-point measurement optimization model

具体实施方式 Detailed ways

下面结合附图对本发明作进一步说明： The present invention will be further described below in conjunction with accompanying drawing:

1)如图2所示，通过机床布置若干待测点，规划好待测点的移动路径并编号。然后把主轴上的探针换成激光跟踪仪的标准球靶镜，按待测点编号移动目标靶镜测量待测点。依次移动激光跟踪仪到不同的站位下，再次按相同编号顺序重复测量待测点。 1) As shown in Figure 2, arrange several points to be measured through the machine tool, plan the moving path of the points to be measured and number them. Then replace the probe on the spindle with the standard spherical target mirror of the laser tracker, and move the target mirror to measure the point to be measured according to the number of the point to be measured. Move the laser tracker to different stations in turn, and repeat the measurement of the points to be measured in the same numbered order. the

2)假设有96个待测点，即n＝96。测量时一共移动了5次站位，即m＝5。在机床坐标系下，待测点的坐标值为Ti(x_i,y_i,z_i)，测出相邻待测点间的干涉测长值l_i，然后利用每个站位下的待测点坐标值T _i(x_i,y_i,z_i)和干涉测长值l_i，通过等式(7)(11)的联立求解可求得激光跟踪仪站位坐标近似值和和对应站位下激光跟踪仪到初始待测点距离的近似值，同理可求得激光跟踪仪在其余站位下的站位坐标近似值值，进而作为等式(4)迭代求解的变量初值。将激光跟踪仪各个站位近似值和待测点测量值以及站位到初始待测点距离的近似值代入等式(4)，即可求解出各个待测点的改正值。利用求取的待测点改正值加上参考坐标系下直接测量得到的待测点初值，即为修正后的高精度待测点坐标值。 2) Suppose there are 96 points to be measured, ie n=96. A total of 5 stations were moved during the measurement, that is, m=5. In the machine tool coordinate system, the coordinate value of the point to be measured is Ti(x _i , y _i , z _i ), and the interferometric length measurement value l _i between adjacent points to be measured is measured, and then using the point to be measured at each station The measurement point coordinate value T _i (xi _, y _i , _zi ) and the interferometric length measurement value l _i can be obtained by the simultaneous solution of equation (7) (11) and the approximate value and corresponding The approximate value of the distance from the laser tracker to the initial point to be measured under the station can be obtained similarly to the approximate value of the station coordinates of the laser tracker under other stations, and then used as the initial value of the variable for the iterative solution of equation (4). Substituting the approximate value of each station of the laser tracker, the measured value of the point to be measured, and the approximate value of the distance from the station to the initial point to be measured into equation (4), the correction value of each point to be measured can be solved. The corrected value of the point to be measured is calculated and the initial value of the point to be measured obtained by direct measurement in the reference coordinate system is the corrected coordinate value of the point to be measured with high precision.

3)用2)中的方法依次求出5个站位的初始值和以及对应站位到初始待测点的距离值，加上待测点的坐标测量值，即可通过等式(4)求解出各个待测点的改正值。将改正值加上待测量点的三维值即为最终优化后的高精度三维坐标值。 3) Use the method in 2) to successively calculate the initial values of the five stations and the distance values from the corresponding stations to the initial point to be measured, and add the measured coordinates of the points to be measured, then the equation (4) Solve the correction value of each point to be measured. Adding the correction value to the three-dimensional value of the point to be measured is the final optimized high-precision three-dimensional coordinate value. the

实施例2： Example 2:

为了验证激光跟踪多点测量优化解算模型的有效性和正确性，进行如下实验，激光跟踪仪在5个站位下测量由三坐标测量机提供的36个空间待测点，其坐标值如表1所示。 In order to verify the effectiveness and correctness of the optimal solution model for laser tracking multi-point measurement, the following experiments were carried out. The laser tracker measured 36 points to be measured in space provided by the three-coordinate measuring machine at 5 stations. The coordinate values are as follows: Table 1 shows. the

表1 三坐标测量机提供的36测量点(单位：mm) Table 1 36 measurement points provided by three-coordinate measuring machine (unit: mm)

总共测量机床三个平面，每个平面测量12个待测点，三平面的Z轴坐标分别为-550.738mm、-400.738mm、-250.738mm，以Z＝-550.738mm的平面为起始测量平面，顺时针在该平面移动余下12测量点并编号，编号1的首层起始点空间坐标值为(600.498mm，550.831mm，-550.738mm)，编号13的第二层起始点坐标值为(600.498mm，550.831mm，-400.738mm)，编号25的第三层起始点坐标值为(600.498mm，550.831mm，-250.738mm)。对激光多点测量优化模型求取的各个坐标改正值绘制如图3所示的曲线图。从图中可以看出，机床的三轴测量误差在0.01mm到-0.008mm之间。 A total of three planes of the machine tool are measured, and each plane measures 12 points to be measured. The Z-axis coordinates of the three planes are -550.738mm, -400.738mm, -250.738mm respectively, and the plane of Z=-550.738mm is the starting measurement plane , move the remaining 12 measurement points clockwise on the plane and number them. The space coordinate value of the starting point of the first layer of No. 1 is (600.498mm, 550.831mm, -550.738mm), and the coordinate value of the starting point of the second layer of No. 13 is (600.498 mm, 550.831mm, -400.738mm), the coordinate value of the starting point of the third layer No. 25 is (600.498mm, 550.831mm, -250.738mm). The curves shown in Figure 3 are drawn for each coordinate correction value calculated by the laser multi-point measurement optimization model. It can be seen from the figure that the three-axis measurement error of the machine tool is between 0.01mm and -0.008mm. the

Claims

1., based on a machine tool error scaling method for laser tracker multimetering technology, comprise following measuring process:

During measurement, first the moving range of each axle of lathe is determined, then in each axle system moving range of lathe, tested point is planned, in the measurement space that the choosing of tested point needs to be distributed in whole lathe, and number in order: the 1st tested point, the 2nd tested point ... n-th tested point, presses the discharge serial number of tested point usually, number order does not have mandatory requirement, but will remember the number n of the numbering that each tested point is corresponding and tested point altogether; Then the probe of lathe is displaced with target mirror, laser tracker is placed into the edge in machine tool measuring space, if this erect-position is the initial erect-position of laser tracker, erect-position puts the mobile route that will meet and not hinder lathe, and laser tracker has straight line sighting distance to target mirror under ensureing each erect-position, guarantee that laser tracking head can follow the tested point path pre-set;

Usually tracker is placed on the periphery of machine tool measuring platform, the moving range of tested point can be met so to greatest extent and guarantee that the erect-position of laser tracker does not affect the movement of lathe;

Control lathe and move to each point to be measured, and measure interference length-measuring value now and record the coordinate figure of tested point under lathe coordinate system, the coordinate figure of following all coordinate systems is all the coordinate figure under lathe coordinate system, move laser tracker successively to all the other erect-positions, suppose that erect-position number is m, the coordinate of each erect-position is (X _k, Y _k, Z _k), wherein k=1,2 ..., m; Lathe arranges n tested point, and the coordinate of tested point is (x _i, y _i, z _i), wherein i=1,2 ..., n; Erect-position number demand fulfillment equation m × n>=3n+4m; ; Move laser tracker successively to each erect-position, and by the complete all tested points of tested point proceeding measurement until complete the measurement of all erect-positions;

If laser tracker is d to the distance of the initial tested point of lathe _j, in measuring process, laser tracker obtains relative interference measurement increment between tested point is l _i, under machine coordinates, choosing the tested point being numbered 1 is initial measurement point, and the initial measurement point tested point all for this reason under each erect-position, when target mirror is from initial measurement point T ₀(x, y, z), moves to any tested point T _i(x, y, z), laser tracker interference length-measuring increment is l, then spatially two-point defined line equation can set up following relational expression:

\sqrt{{(x_{i} - X_{j})}^{2} + {(y_{i} - Y_{j})}^{2} + {(z_{i} - Z_{j})}^{2}} = d_{j} + l_{i} - - - (1)

In above formula, to be that lathe is to be measured respectively count and laser tracker standing capacity i and j; Suppose that laser tracker measures tested point under m erect-position, under lathe coordinate system, the coordinate of each erect-position is (X _j, Y _j, Z _j), wherein j=1,2 ..., m; Lathe has n tested point, the coordinate of tested point is (x _i, y _i, z _i), wherein i=1,2 ..., n;

During actual measurement, l _itrue value high-precision interference can be utilized relatively to find range replacement, then the error equation of i-th tested point under a jth erect-position is:

v_{ij} = (\sqrt{{(x_{i} - X_{j})}^{2} + {(y_{i} - Y_{j})}^{2} + {(z_{i} - Z_{j})}^{2}} - d_{i}) - l_{i} - - - (2)

If tested point (x _i, y _i, z _i) gather for T, erect-position coordinate (X _j, Y _j, Z _j) gather for P, laser interference length-measuring l _iset is L, to the distance d of initial tested point under each erect-position _jset is D; Least square method process equation (2) is utilized to make error sum of squares E (T, P, D) minimum:

E (T, P, D) = \underset{i = 1}{Σ} \underset{j = 1}{Σ} v_{ij}^{2} (L, P, T, D) (i = 1,2,3, . . . n, j = 1,2,3, . . . m) - - - (3)

Because equation (2) is a Nonlinear System of Equations, directly use equation (2) to solve abnormal cumbersome, adopt following manner to solve:

Suppose there be n lathe tested point, had m laser tracker standing capacity; Under lathe coordinate system, unknown parameter is 3n tested point coordinate Ti (x _i, y _i, z _i) and 3m laser tracking erect-position coordinate P _j(X _j, Y _j, Z _j) and m each erect-position under to the distance d of initial tested point _j; So unknown number is 3n+4m altogether, and each erect-position can provide n interference length-measuring value, m × n equation altogether, for making equation have solution, and demand fulfillment m × n>=3n+4m, peer-to-peer (2) is carried out linear expansion and can be obtained:

\begin{matrix} v_{ij} = L_{ij}^{o} - d_{j}^{0} - l_{i} + \frac{(x_{i}^{0} - X_{j}^{0})}{L_{ij}^{0}} ({Δx}_{i} - {ΔX}_{j}) + \frac{(y_{i}^{0} - Y_{j}^{0})}{L_{ij}^{o}} ({Δy}_{i} - {ΔY}_{j}) \\ + \frac{(z_{i}^{0} - Z_{j}^{0})}{L_{ij}^{o}} ({Δz}_{i} - {ΔZ}_{j}) - {Δd}_{j} \end{matrix} - - - (4)

Wherein:

L_{ij}^{0} = {({(x_{i}^{0} - X_{j}^{0})}^{2} + {(y_{i}^{0} - Y_{j}^{0})}^{2} + {(z_{i}^{0} - Z_{j}^{0})}^{2})}^{1 / 2}

Equation (4) is optimization and resolves model, needs given iterative initial value, wherein Δ x when the variable being designated as zero is and resolves in formula _i, Δ y _i, Δ z _i, Δ X _j, Δ Y _j, Δ Z _jbe respectively the coordinate correction value of reference frame tested point and the corrected value of laser tracker erect-position coordinate particle, Δ d _jfor each erect-position particle is to the corrected value of the distance of initial tested point; In actual measurement initial value needs the D coordinates value optimizing tested point under can directly reading reference frame; And the coordinate initial value of each erect-position particle of laser tracker with the distance initial value of each erect-position particle to initial tested point need to ask for the following method:

If the approximate value of laser tracker erect-position coordinate is as iterative initial value, so the tested point coordinate needing to ask for corrected value might as well be set temporarily as true value, then tested point coordinate T in equation (1) _i(x, y, z) and interference length-measuring increment l _ifor known variables, utilize the tested point coordinate figure under each erect-position and interference length-measuring increment, respectively the coordinate figure P of Calibration of Laser tracker particle under each erect-position _jthe initial tested point distance value d that under (x, y, z) and corresponding erect-position, particle arrives _j, as j=1, then equation (1) becomes:

\sqrt{{(x_{i} - X_{1})}^{2} + {(y_{i} - Y_{1})}^{2} + {(z_{i} - Z_{1})}^{2}} = d_{1} + l_{i} - - - (5)

Write equation (5) as error equation:

v_{i} = \sqrt{{(x_{i} - X_{1})}^{2} + {(y_{i} - Y_{1})}^{2} + {(z_{i} - Z_{1})}^{2}} - (d_{1} + l_{i}) - - - (6)

Wherein, X ₁, Y ₁, Z ₁for the coordinate figure of laser tracker first erect-position under lathe coordinate system, (x _i, y _i, z _i) tested point coordinate figure i=1 for measuring under corresponding erect-position, 2 ..., n, v _iit is the error amount that under the 1st erect-position, each tested point is corresponding;

If

k = X_{1}^{2} + {Y_{1}}^{2} + Z_{1}^{2} - d_{1}^{2},

Carry out least square to above formula to solve and can obtain:

\begin{matrix} \frac{{&PartialD; v}_{i}^{2}}{{&PartialD; X}_{1}} = Σ_{i = 1}^{n} x_{i} (x_{i}^{2} + y_{i}^{2} + z_{i}^{2} - l_{i}^{2}) - 2 Σ_{i = 1}^{n} x_{i}^{2} X_{1} - 2 Σ_{i = 1}^{n} y_{i} x_{i} Y_{1} - 2 Σ_{i = 1}^{n} z_{i} x_{i} Z_{1} \\ - 2 Σ_{i = 1}^{n} l_{i} x_{i} d_{1} + Σ_{i = 1}^{n} x_{i} k = 0 \end{matrix} - - - (7)

\begin{matrix} \frac{{&PartialD; v}_{i}^{2}}{{&PartialD; Y}_{1}} = Σ_{i = 1}^{n} x_{i} (x_{i}^{2} + y_{i}^{2} + z_{i}^{2} - l_{i}^{2}) - 2 Σ_{i = 1}^{n} x_{i} y_{i} X_{1} - 2 Σ_{i = 1}^{n} y_{i}^{2} Y_{1} - 2 Σ_{i = 1}^{n} z_{i} y_{i} Z_{1} \\ - 2 Σ_{i = 1}^{n} l_{i} y_{i} d_{1} + Σ_{i = 1}^{n} y_{i} k = 0 \end{matrix} - - - (8)

\begin{matrix} \frac{{&PartialD; v}_{i}^{2}}{{&PartialD; Z}_{1}} = Σ_{i = 1}^{n} x_{i} (x_{i}^{2} + y_{i}^{2} + z_{i}^{2} - l_{i}^{2}) - 2 Σ_{i = 1}^{n} x_{i} z_{i} X_{1} - 2 Σ_{i = 1}^{n} y_{i} z_{i} Y_{1} - 2 Σ_{i = 1}^{n} z_{i}^{2} Z_{1} \\ - 2 Σ_{i = 1}^{n} l_{i} z_{i} d_{1} + Σ_{i = 1}^{n} z_{i} k = 0 \end{matrix} - - - (9)

\begin{matrix} \frac{{&PartialD; v}_{i}^{2}}{{&PartialD; d}_{1}} = Σ_{i = 1}^{n} l_{i} (x_{i}^{2} + y_{i}^{2} + z_{i}^{2} - l_{i}^{2}) - 2 Σ_{i = 1}^{n} x_{i} l_{i} X_{1} - 2 Σ_{i = 1}^{n} y_{i} l_{i} Y_{1} - 2 Σ_{i = 1}^{n} z_{i} l_{i} Z_{1} \\ - 2 Σ_{i = 1}^{n} l_{i}^{2} d_{1} + Σ_{i = 1}^{n} l_{i} k = 0 \end{matrix} - - - (10)

\begin{matrix} \frac{{&PartialD; v}_{i}^{2}}{{&PartialD; k}_{1}} = Σ_{i = 1}^{n} (x_{i}^{2} + y_{i}^{2} + z_{i}^{2} - l_{i}^{2}) - 2 Σ_{i = 1}^{n} x_{i} X_{1} - 2 Σ_{i = 1}^{n} y_{i} Y_{1} - 2 Σ_{i = 1}^{n} z_{i} Z_{1} \\ - 2 Σ_{i = 1}^{n} l_{i} d_{1} + Σ_{i = 1}^{n} k = 0 \end{matrix} - - - (11)

The initial distance value d under the coordinate figure of the 1st erect-position under lathe coordinate system and corresponding erect-position can be tried to achieve in simultaneous equation (7) and (11), with should j=2,3 ... during m, can in the hope of the initial distance value d of all the other erect-positions under the coordinate figure and corresponding erect-position of lathe coordinate system; Utilize the initial value of each erect-position point and tested point measured value and corresponding erect-position to the distance value of initial tested point, namely can pass through the corrected value that equation (4) solves each tested point;

Corrected value is added the three-dimensional value of former measurement point is the high-precision three-dimensional coordinate figure after final optimization pass.