WO2023272835A1 - 一种主轴安装误差及主轴与c轴同轴度的检测与辨识方法 - Google Patents
一种主轴安装误差及主轴与c轴同轴度的检测与辨识方法 Download PDFInfo
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- 238000001514 detection method Methods 0.000 claims abstract description 32
- 238000005259 measurement Methods 0.000 claims abstract description 32
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- 238000012360 testing method Methods 0.000 claims abstract description 8
- 238000009434 installation Methods 0.000 claims description 52
- 238000007689 inspection Methods 0.000 claims description 16
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000013480 data collection Methods 0.000 claims description 3
- 238000006073 displacement reaction Methods 0.000 claims description 3
- 238000000926 separation method Methods 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000003754 machining Methods 0.000 description 3
- 238000000691 measurement method Methods 0.000 description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
- G01B11/27—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes
Definitions
- the invention relates to the technical field of numerically controlled machine tool parameter measurement, in particular to a method for detecting and identifying the installation error of a spindle and the coaxiality of the spindle and a C-axis.
- CNC machine tools with large swing angles and large stroke ranges have been widely used.
- the biggest feature of this type of machine tool is that it has a C rotary axis, which expands the rotation range of the swing angle and the range of processed parts is also wider.
- the oscillating head composed of the spindle and the C-axis is an important functional part of the machine tool, and its rotation accuracy is a key indicator reflecting the performance of the CNC machine tool. Due to the rotation accuracy of the oscillating head, it is not only affected by its own geometric error, but also by the installation error of the spindle during the machining process. will determine the surface topography and texture distribution of the machined parts.
- the rotation error caused by the rotation of the C-axis will reduce the overall accuracy of the machine tool's swing head; when measuring the coaxiality of the spindle and the C-axis in the invention patent with the application number "CN201510779253.8", the installation of the spindle is not considered
- the influence of errors on the measurement results, the accuracy of the identification results depends on the precision of the spindle installation, but the actual situation is not optimistic.
- the errors caused by the coaxiality of the C-axis and the installation of the spindle are not effectively integrated as the research object, so that the established detection and identification model is relatively simple, which is not conducive to effectively separating the comprehensive error of the rotary motion of the machine tool , which is not conducive to elucidating the mechanism of action of each error factor.
- the present invention provides a detection and identification method for the installation error of the main shaft and the coaxiality between the main shaft and the C-axis, so as to achieve the measurement position deviation effectively while considering more error sources Value separation and identification, and the identification results are accurate and effective.
- the present invention adopts the following technical solutions:
- a method for detecting and identifying the installation error of the main shaft and the coaxiality between the main shaft and the C-axis comprising the following steps:
- Step 1 Measurement data collection: use the detection instrument to measure and record the position deviation ( ⁇ x, ⁇ y) of the ball head and the center of the baseball when the C-axis and the main shaft are at different rotational angle positions;
- Step 2 Main shaft installation tilt error identification: extract the measurement data when the C-axis rotates at least one cycle in the above step 1, use the least squares to fit the circle to obtain the center of motion radius, and combine the different rod lengths of the ball head to calculate the main shaft Installation tilt error;
- Step 3 Identification of the translation error of the main shaft installation and the coaxiality error between the main shaft and the C-axis: extract the measurement data of the C-axis and the main shaft for at least one rotation in step 1, and perform sine function fitting to obtain the translation error of the main shaft installation and the coaxiality error of the main shaft and the C-axis Shaft concentricity error;
- Step 4 Calculate the average value of multiple identifications: repeat the steps 1 to 3, perform multiple measurements, and take the average value of the identification results.
- step 1 the specific steps of said step 1 are as follows:
- Step 1-1 The measuring instrument is installed on the workbench, and the machine tool is driven to make the center of the ball-end inspection rod contact the testing instrument;
- Step 1-2 According to the stroke of the C-axis and the main shaft, divide the movement position points at a certain interval, and install different lengths of the ball head on the main shaft, and rotate it for at least one circle to measure the position deviation of the ball center of the ball head.
- the steps 1-2 specifically adopt the following experimental scheme:
- C represents the movement position angle of the C-axis
- S represents the movement position angle of the main shaft
- ⁇ c and ⁇ s represent the movement distance between the C-axis and the main shaft, respectively
- i and j represent the serial numbers of the measured angles.
- step 2 the specific steps of said step 2 are as follows:
- R 2 (xA) 2 +(yB) 2 (1)
- R is the radius of the fitting circle
- a and B represent the coordinate values of the center coordinates on the XY plane
- x and y represent the coordinate values of the points on the fitting circle curve
- Step 2-3 Calculate the distance from the position deviation point to the center of the circle as l i :
- Step 2-4 Calculate the sum of squares of the difference between the radius of the fitted circle and the distance of the deviation point:
- Step 2-5 Finally get the spindle installation tilt error:
- ⁇ represents the inclination error of the main shaft installation
- L 1 and L 2 respectively represent the lengths of two different lengths of the ball-end inspection rod
- R 1 and R 2 represent the lengths of the ball-end inspection rod with the length of L 1 and L 2 respectively Fitting circle radius.
- step 3 the specific steps of said step 3 are as follows:
- the sinusoidal curve equation formed by the deviation value is as follows:
- y represents the ordinate of the point on the fitted curve
- ⁇ represents the abscissa of the point on the fitted curve
- a, b, c, d represent the amplitude, angular frequency, initial phase and offset distance of the sinusoidal curve respectively;
- Step 3-2 Use the position deviation data measured by the rotation of the main shaft to calculate the translation error of the main shaft installation:
- a s represents the amplitude of the spindle motion data fitting
- L 1 represents the length of the ball center inspection rod
- ⁇ represents the tilt error of the tool installation
- r s represents the translation error of the spindle installation, combined with the initial phase, the X and Y coordinates projection on axis;
- Step 3-3 Substitute the position deviation data measured between the C-axis and the main shaft into the calculation, that is, the coaxiality between the main shaft and the C-axis in the X and Y directions is:
- m x , m y represent the coaxiality error between the main shaft and the C axis in the X and Y directions respectively
- c s , c c represent the phases of the sinusoidal fitting between the main shaft deviation data and the C axis deviation data
- the detection instrument is any one of an R-test measuring instrument, a laser tracker, and a laser displacement sensor.
- the basic principle of the present invention is to detect the deviation between the actual tool tip position and the theoretical tool tip position when the machine tool rotates, and then use two kinds of ball-tip inspection rods with different lengths to complete the error identification, and drive the C-axis, After the spindle rotates for at least one cycle at a certain movement interval, combined with the collected measurement data, the least squares fitting method is used to complete the solution of the spindle installation error and the coaxiality error between the spindle and the C-axis of the five-axis CNC machine tool with C-axis, so that In the follow-up detection, the ball head detection stick does not need to be pre-adjusted, and the rapid detection of the position deviation data of the center of the ball detection can be completed by subtracting the components of the error proposed by the present invention at different angles, which overcomes the need to use coaxiality adjustment in traditional methods It is easy to use the numerical control system to program the measurement cycle to realize automatic detection, which further improves the automatic detection and software processing capabilities, and has better practicability.
- the method of the present invention is efficient and accurate, and has strong practicability.
- the present invention can still effectively realize the separation and identification of measurement position deviation values in consideration of more error sources, the identification results are accurate and effective, and it is easy to realize automatic detection and identification , that is, the detection instrument is installed at a fixed position on the workbench, and the ball-tip inspection rod is placed in the tool magazine.
- automatic detection can be realized by writing a measurement cycle.
- software tools can be developed to realize automatic identification.
- Fig. 1 is a flow chart of a method for detecting and identifying the installation error of the main shaft and the coaxiality between the main shaft and the C-axis provided by the present invention
- Fig. 2 is a structural schematic diagram of a CA double-swing head type five-axis CNC machine tool with a C rotation axis;
- Fig. 3 is a schematic diagram of the installation error of the main shaft and the coaxiality of the main shaft and the C-axis in the present invention
- Fig. 4 is a principle diagram for solving the installation error of the main shaft and the coaxiality between the main shaft and the C-axis in the present invention.
- this embodiment provides a detection and identification method for the installation error of the main shaft and the coaxiality between the main shaft and the C-axis, including the following steps:
- Step 1 Measurement data collection: use the detection instrument to measure and record the position deviation ( ⁇ x, ⁇ y) of the ball head and the center of the baseball when the C-axis and the main shaft are at different rotational angle positions;
- Step 2 Main shaft installation tilt error identification: extract the measurement data when the C-axis rotates at least one cycle in the above step 1, use the least squares to fit the circle to obtain the center of motion radius, and combine the different rod lengths of the ball head to calculate the main shaft Installation tilt error;
- Step 3 Identification of the translation error of the main shaft installation and the coaxiality error between the main shaft and the C-axis: extract the measurement data of the C-axis and the main shaft for at least one rotation in step 1, and perform sine function fitting to obtain the translation error of the main shaft installation and the coaxiality error of the main shaft and the C-axis Shaft concentricity error;
- Step 4 Calculate the average value of multiple identifications: repeat the steps 1 to 3, perform multiple measurements, and take the average value of the identification results.
- the "at least one rotation” in the above steps 2 and 3 may be 1 rotation, 1.5 rotations or 2 rotations, etc.
- step 1 the specific steps of the step 1 are as follows:
- Step 1-1 The measuring instrument is installed on the workbench, and the machine tool is driven to make the center of the ball-end inspection rod contact the testing instrument;
- Step 1-2 According to the stroke of the C-axis and the main shaft, divide the movement position points at a certain interval, and install different lengths of the ball head on the main shaft, and rotate it for at least one circle to measure the position deviation of the ball center of the ball head.
- C represents the movement position angle of the C-axis
- S represents the movement position angle of the main shaft
- ⁇ c and ⁇ s represent the movement distance between the C-axis and the main shaft, respectively
- i and j represent the serial numbers of the measured angles.
- step 2 Specifically, the specific steps of the step 2 are as follows:
- R 2 (xA) 2 +(yB) 2 (1)
- R is the radius of the fitting circle
- a and B represent the coordinate values of the center coordinates on the XY plane
- x and y represent the coordinate values of the points on the fitting circle curve
- Step 2-3 Calculate the distance from the position deviation point to the center of the circle as l i :
- Step 2-4 Calculate the sum of squares of the difference between the radius of the fitted circle and the distance of the deviation point:
- Step 2-5 Finally get the spindle installation tilt error:
- ⁇ represents the inclination error of the main shaft installation
- L 1 and L 2 respectively represent the lengths of two different lengths of the ball-end inspection rod
- R 1 and R 2 represent the lengths of the ball-end inspection rod with the length of L 1 and L 2 respectively Fitting circle radius.
- step 3 the specific steps of the step 3 are as follows:
- the sinusoidal curve equation formed by the deviation value is as follows:
- y represents the ordinate of the point on the fitted curve
- ⁇ represents the abscissa of the point on the fitted curve
- a, b, c, d represent the amplitude, angular frequency, initial phase and offset distance of the sinusoidal curve respectively;
- Step 3-2 Using the position deviation data measured by the rotational movement of the main shaft, combined with Figure 4, the translation error of the main shaft installation can be calculated:
- a s represents the amplitude of the spindle motion data fitting
- L 1 represents the length of the ball center inspection rod
- ⁇ represents the tilt error of the tool installation
- r s represents the translation error of the spindle installation, combined with the initial phase, the X and Y coordinates projection on axis;
- Step 3-3 Substitute the position deviation data measured between the C-axis and the main shaft into the calculation, that is, the coaxiality between the main shaft and the C-axis in the X and Y directions is:
- m x , m y represent the coaxiality error between the main shaft and the C axis in the X and Y directions respectively
- c s , c c represent the phases of the sinusoidal fitting between the main shaft deviation data and the C axis deviation data
- the detection instrument is any one of the R-test measuring instrument, laser tracker, and laser displacement sensor, and the measurement methods are simple and diverse, and of course are not limited to the above-mentioned several detection instruments.
- the least squares fitting method is used to complete the installation error of the main shaft and the main shaft and the C-axis of the five-axis CNC machine tool with the C-axis.
- the solution of the coaxiality error makes it unnecessary to pre-adjust the ball head during the subsequent detection.
- the identification method used in the present invention can still effectively realize the separation and identification of the measurement position deviation value under the condition of considering more error sources, so as to achieve convenient and accurate acquisition of the C-axis coaxiality and spindle installation of the five-axis CNC machine tool with C-axis Error can provide data source for machine tool assembly debugging and precision compensation; it is easy to carry out automatic detection and identification in the whole implementation process, that is, the detection instrument is installed at a fixed position on the workbench, and the ball-tip inspection rod is placed in the tool magazine, and the The above-mentioned detection method realizes automatic detection by writing a measurement cycle; the above-mentioned identification algorithm is used to develop a software tool to realize automatic identification, and the applicability is stronger.
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Abstract
本发明公开了一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，涉及数控机床参数测量技术领域，包括以下步骤：步骤1：测量数据采集，利用检测仪器测量并记录C轴及主轴在不同转角位置时球头检棒球心的位置偏差；步骤2：提取步骤1中C轴旋转至少一周时的测量数据，利用最小二乘拟合圆得到球心运动半径，结合球头检棒的不同杆长计算出主轴安装倾斜误差；步骤3：提取步骤1中C轴及主轴旋转至少一周时的测量数据，进行正弦函数拟合得到主轴安装平移误差及主轴与C轴同轴度误差；步骤4：重复步骤1至步骤3，进行多次测量，取辨识结果的平均值,本发明可有效的实现测量位置偏差值的分离和辨识，为机床精度的快速评价提供数据来源。
Description
本发明涉及数控机床参数测量技术领域，具体涉及一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法。
随着数控加工对象零件的形状及曲面日趋复杂，大摆角、行程范围大的数控机床得到了广泛应用。该类型机床最大特点是带C旋转轴，从而扩大了摆角的旋转范围，加工零件的范围也更广。主轴与C轴组成的摆头作为机床重要功能部件，其回转精度是反映数控机床性能的关键指标，由于摆头的回转精度，不仅受自身几何误差的影响，在加工过程中还受主轴安装误差的影响，将决定着被加工零件的表面形貌纹理分布。
目前，对于带C旋转轴的数控机床进行主轴安装误差及同轴度检测时，有传统手工测量方法如使用检棒、百分表等仪器，其缺陷在于易引入人为操作误差、自动化程度低，结果的准确性依赖于操作人员的技术水平。为提高自动化测量水平，在申请号为“CN201810601644.4”的发明专利中利用圆光栅及自准直仪完成了主轴回转误差的测量及辨识，该方法设备测量精度高，但仍存在未考虑机床C轴旋转运动引起的回转误差，机床摆头的整体精度将有所降低；在申请号为“CN201510779253.8”的发明专利中进行主轴与C轴同轴度测量时，并未考虑到主轴安装误差对测量结果的影响，辨识结果的准确性取决于主轴安装的足够精密，但实际情况并不乐观。
总体而言，现有技术方法中没有将C轴同轴度与主轴安装引起的误差作为研究对象进行有效集成，使得建立的检测与辨识模型相对单一，既不利于有效分离机床回转运动的综合误差，也不利于阐明各误差因素的作用机理。
发明内容
针对现有技术中的缺陷，本发明提供一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，以达到在考虑更多误差源的情况下，仍能有效的实现测量位置偏差值的分离和辨识，辨识结果准确有效的作用。
为解决上述的技术问题，本发明采用以下技术方案：
一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，包括以下步骤：
步骤1：测量数据采集：利用检测仪器测量并记录C轴及主轴在不同转角位置时球头检棒球心的位置偏差(Δx,Δy)；
步骤2：主轴安装倾斜误差辨识：提取所述步骤1中C轴旋转至少一周时的测量数据，利用最小二乘拟合圆得到球心运动半径，结合球头检棒的不同杆长计算出主轴安装倾斜误差；
步骤3：主轴安装平移误差及主轴与C轴同轴度误差辨识：提取所述步骤1中C轴及主轴旋转至少一周时的测量数据，进行正弦函数拟合得到主轴安装平移误差及主轴与C轴同轴度误差；
步骤4：多次辨识求平均值：重复所述步骤1至步骤3，进行多次测量，取辨识结果的平均值。
优选地，所述步骤1的具体步骤如下：
步骤1-1：测量仪器安装在工作台上，驱动机床使球头检棒中心与检测仪器接触；
步骤1-2：根据C轴、主轴行程，按一定间隔划分运动位置点，并安装不同长度的球头检棒于主轴上，旋转至少一周测量球头检棒球心的位置偏差。
优选地，所述步骤1-2具体采用以下实验方案：
| 序号 | C轴位置 | 主轴位置 | 球头检棒长度 |
| 1 | C＝(i-1)Δc | S＝(j-1)Δs | L1 |
| 2 | C＝(i-1)Δc | 不限 | L2 |
其中，C表示C轴的运动位置角，S表示主轴的运动位置角，Δc、Δs分别表示C轴与主轴的运动间隔，i、j表示测量角度的序号。
优选地，所述步骤2的具体步骤如下：
步骤2-1：所述步骤1中的C轴旋转时产生的位置偏差为(Δx
ci,Δy
ci)，i＝1,2,…，设偏差点所构成的最小二乘拟合圆曲线方程如下：
R
2＝(x-A)
2+(y-B)
2 (1)
式中，R为拟合圆半径，A、B代表圆心坐标在XY平面的坐标值，x，y表示拟合圆曲线上的点的坐标值；
步骤2-2：令a＝-2A，b＝-2B，k＝A
2+B
2-R
2，可得最小二乘拟合圆曲线方程的另一个形式：
x
2+y
2+ax+by+k＝0 (2)
步骤2-3：计算位置偏差点到圆心的距离为l
i：
l
i
2＝(Δx
ci-A)
2+(Δy
ci-B)
2 (3)
步骤2-4：计算拟合圆半径与偏差点距离之间差的平方和：
Q
i＝∑
(l
i
2-R
2)
2＝∑(Δx
ci
2+Δy
ci
2+aΔx
ci+bΔy
ci+k)
2 (4)
代入测量数据求解该式，平方和最小时，即可得到拟合圆半径R；
步骤2-5：最后得到主轴安装倾斜误差：
式中，θ表示主轴安装倾斜误差，L
1、L
2分别表示两种不同杆长的球头检棒长度，R
1、R
2分别表示L
1、L
2杆长的球头检棒产生的拟合圆半径。
优选地，所述步骤3的具体步骤如下：
步骤3-1：提取所述步骤1中C轴旋转时产生的位置偏差的Δx
ci或Δy
ci，主轴旋转的位置偏差的Δx
sj或Δy
sj，i＝j＝1,2,…，以Y向偏差值构成的正弦曲 线方程如下：
y＝asin(bφ+c)+d (6)
式中，y表示拟合曲线上点的纵坐标，φ表示拟合曲线上点的横坐标，a、b、c、d分别表示正弦曲线的幅值、角频率、初相、偏距；
对于一系列的偏差点(φ,Δy)去拟合所述正弦曲线方程，则有：
Q＝∑(a sin(bΔx+c)+d-Δy)
2 (7)
要使得Q最小，应满足：
求解式(8)得到正弦曲线方程的各系数结果；
步骤3-2：利用主轴旋转运动测得的位置偏差数据，计算主轴安装平移误差：
r
s＝a
s-L
1sinθ (9)
式中，a
s表示主轴运动数据拟合的幅值，L
1表示球心检棒的长度，θ表示刀具安装倾斜误差，r
s表示主轴安装平移误差，结合初相计算出在X、Y坐标轴上的投影；
步骤3-3：将C轴与主轴测得的位置偏差数据代入计算，即得主轴与C轴同轴度在X、Y方向上则为：
m
x＝r
ccosc
c+r
scosc
s
m
y＝r
csinc
c+r
ssinc
s (10)
式中，m
x、m
y分别表示在X、Y方向上主轴与C轴同轴度误差，c
s、c
c分别表示主轴偏差数据与C轴偏差数据正弦拟合的相位，r
c表示C轴运动数据的拟合半 径，其中r
c＝a
c-L
1sinθ，a
c表示C轴运动数据拟合的幅值。
优选地，在步骤1中，检测仪器为R-test测量仪、激光跟踪仪、激光位移传感器中的任一种。
本发明的有益效果体现在：
1、本发明的基本原理是通过检测机床旋转运动时实际刀尖点位置与理论刀尖点位置的偏差，再利用两种不同长度的球头检棒完成误差辨识，通过在分别驱动C轴、主轴按一定运动间隔旋转至少一周后，结合采集得到的测量数据，利用最小二乘拟合方式完成对带C轴五轴数控机床的主轴安装误差及主轴与C轴同轴度误差的求解，使得在后续检测时球头检棒无需预先调整，可通过减去本发明所提误差在不同角度下的分量，从而完成检棒球心位置偏差数据的快速检测，克服了传统手段必须使用同轴度调整器的不足，易于利用数控系统编制测量循环实现自动化检测，进一步提高了自动化检测和软件处理能力，实用性更优。
2、本发明方法高效准确，实用性强，本发明在考虑更多误差源的情况下，仍能有效的实现测量位置偏差值的分离和辨识，辨识结果准确有效，且易于实现自动化检测与辨识，即把检测仪器安装在工作台固定位置，球头检棒放置于刀库中，基于本发明检测方法可通过编写测量循环实现自动化检测，基于本发明辨识方法可开发软件工具实现自动辨识。
为了更清楚地说明本发明具体实施方式或现有技术中的技术方案，下面将对具体实施方式或现有技术描述中所需要使用的附图作简单地介绍。在所有附图中，类似的元件或部分一般由类似的附图标记标识。附图中，各元件或部分并不一定按照实际的比例绘制。
图1为本发明提供的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法的流程图；
图2为带C旋转轴的CA双摆头型五轴数控机床的结构示意图；
图3为本发明中主轴安装误差及主轴与C轴同轴度的示意图；
图4为本发明中主轴安装误差及主轴与C轴同轴度求解原理图。
为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。通常在此处附图中描述和示出的本发明实施例的组件可以以各种不同的配置来布置和设计。
因此，以下对在附图中提供的本发明的实施例的详细描述并非旨在限制要求保护的本发明的范围，而是仅仅表示本发明的选定实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
应注意到：相似的标号和字母在下面的附图中表示类似项，因此，一旦某一项在一个附图中被定义，则在随后的附图中不需要对其进行进一步定义和解释。
由于机床安装制造及装配误差的影响，使得C轴轴线与主轴之间将产生同轴度误差，而且主轴锥面在长期使用的过程中不断被磨损，引起刀柄安装在主轴中会产生安装倾斜误差和安装平移误差，如附图3所示。因此需要借助球头芯棒来进行检测并校正，以保持机床良好的加工精度。
实施例
如图1-4所示，本实施例提供一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，包括以下步骤：
步骤1：测量数据采集：利用检测仪器测量并记录C轴及主轴在不同转角位置时球头检棒球心的位置偏差(Δx,Δy)；
步骤2：主轴安装倾斜误差辨识：提取所述步骤1中C轴旋转至少一周时 的测量数据，利用最小二乘拟合圆得到球心运动半径，结合球头检棒的不同杆长计算出主轴安装倾斜误差；
步骤3：主轴安装平移误差及主轴与C轴同轴度误差辨识：提取所述步骤1中C轴及主轴旋转至少一周时的测量数据，进行正弦函数拟合得到主轴安装平移误差及主轴与C轴同轴度误差；
步骤4：多次辨识求平均值：重复所述步骤1至步骤3，进行多次测量，取辨识结果的平均值。
需要说明的是，上述步骤2和步骤3中所述“旋转至少一周”可为1周、1.5周或2周等。
具体地，所述步骤1的具体步骤如下：
步骤1-1：测量仪器安装在工作台上，驱动机床使球头检棒中心与检测仪器接触；
步骤1-2：根据C轴、主轴行程，按一定间隔划分运动位置点，并安装不同长度的球头检棒于主轴上，旋转至少一周测量球头检棒球心的位置偏差。
具体地，所述步骤1-2具体采用以下实验方案：
| 序号 | C轴位置 | 主轴位置 | 球头检棒长度 |
| 1 | C＝(i-1)Δc | S＝(j-1)Δs | L1 |
| 2 | C＝(i-1)Δc | 不限 | L2 |
其中，C表示C轴的运动位置角，S表示主轴的运动位置角，Δc、Δs分别表示C轴与主轴的运动间隔，i、j表示测量角度的序号。
具体地，所述步骤2的具体步骤如下：
步骤2-1：所述步骤1中的C轴旋转时产生的位置偏差为(Δx
ci,Δy
ci)，i＝1,2,…，设偏差点所构成的最小二乘拟合圆曲线方程如下：
R
2＝(x-A)
2+(y-B)
2 (1)
式中，R为拟合圆半径，A、B代表圆心坐标在XY平面的坐标值，x，y表示拟合圆曲线上的点的坐标值；
步骤2-2：令a＝-2A，b＝-2B，k＝A
2+B
2-R
2，可得最小二乘拟合圆曲线方程的另一个形式：
x
2+y
2+ax+by+k＝0 (2)
步骤2-3：计算位置偏差点到圆心的距离为l
i：
l
i
2＝(Δx
ci-A)
2+(Δy
ci-B)
2 (3)
步骤2-4：计算拟合圆半径与偏差点距离之间差的平方和：
Q
i＝∑(l
i
2-R
2)
2＝∑(Δx
ci
2+Δy
ci
2+aΔx
ci+bΔy
ci+k)
2 (4)
代入测量数据求解该式，平方和最小时，即可得到拟合圆半径R；
步骤2-5：最后得到主轴安装倾斜误差：
式中，θ表示主轴安装倾斜误差，L
1、L
2分别表示两种不同杆长的球头检棒长度，R
1、R
2分别表示L
1、L
2杆长的球头检棒产生的拟合圆半径。
具体地，所述步骤3的具体步骤如下：
步骤3-1：提取所述步骤1中C轴旋转时产生的位置偏差的Δx
ci或Δy
ci，主轴旋转的位置偏差的Δx
sj或Δy
sj，i＝j＝1,2,…，以Y向偏差值构成的正弦曲线方程如下：
y＝asin(bφ+c)+d (6)
式中，y表示拟合曲线上点的纵坐标，φ表示拟合曲线上点的横坐标，a、b、c、d分别表示正弦曲线的幅值、角频率、初相、偏距；
对于一系列的偏差点(φ,Δy)去拟合所述正弦曲线方程，则有：
Q＝∑(a sin(bΔx+c)+d-Δy)
2 (7)
要使得Q最小，应满足：
求解式(8)得到正弦曲线方程的各系数结果；
步骤3-2：利用主轴旋转运动测得的位置偏差数据，这里结合图4，即可计算主轴安装平移误差：
r
s＝a
s-L
1sinθ (9)
式中，a
s表示主轴运动数据拟合的幅值，L
1表示球心检棒的长度，θ表示刀具安装倾斜误差，r
s表示主轴安装平移误差，结合初相计算出在X、Y坐标轴上的投影；
步骤3-3：将C轴与主轴测得的位置偏差数据代入计算，即得主轴与C轴同轴度在X、Y方向上则为：
m
x＝r
ccosc
c+r
scosc
s
m
y＝r
csinc
c+r
ssinc
s (10)
式中，m
x、m
y分别表示在X、Y方向上主轴与C轴同轴度误差，c
s、c
c分别表示主轴偏差数据与C轴偏差数据正弦拟合的相位，r
c表示C轴运动数据的拟合半径，其中r
c＝a
c-L
1sinθ，a
c表示C轴运动数据拟合的幅值。
具体地，在步骤1中，检测仪器为R-test测量仪、激光跟踪仪、激光位移传感器中的任一种，测量方式简单多样，当然也不限于上述几种检测仪器。
本发明在分别驱动C轴、主轴按一定运动间隔旋转至少一周后，结合采集得到的测量数据，利用最小二乘拟合方式完成对带C轴五轴数控机床的主轴安装误差及主轴与C轴同轴度误差的求解，使得在后续检测时球头检棒无需预先调整，可通过减去本发明所提误差在不同角度下的分量，从而完成检棒球心位置偏差数据的快速检测，克服了传统手段必须使用同轴度调整器的不足，易于 利用数控系统编制测量循环实现自动化检测，进一步提高了自动化检测和软件处理能力，实用性更优。
本发明所用辨识方法在考虑更多误差源的情况下，仍能有效的实现测量位置偏差值的分离和辨识，达到方便准确的获得带C轴五轴数控机床的C轴同轴度及主轴安装误差，可为机床装配调试及精度补偿提供数据来源；在整个实现过程中易于进行自动化检测与辨识，即把检测仪器安装在工作台固定位置，球头检棒放置于刀库中，即可将上述检测方法通过编写测量循环实现自动化检测；利用上述辨识算法开发软件工具实现自动辨识，适用性更强。
最后应说明的是：以上各实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述各实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分或者全部技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的范围，其均应涵盖在本发明的权利要求和说明书的范围当中。
Claims (6)
- 一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，包括以下步骤：步骤1：测量数据采集：利用检测仪器测量并记录C轴及主轴在不同转角位置时球头检棒球心的位置偏差(Δx,Δy)；步骤2：主轴安装倾斜误差辨识：提取所述步骤1中C轴旋转至少一周时的测量数据，利用最小二乘拟合圆得到球心运动半径，结合球头检棒的不同杆长计算出主轴安装倾斜误差；步骤3：主轴安装平移误差及主轴与C轴同轴度误差辨识：提取所述步骤1中C轴及主轴旋转至少一周时的测量数据，进行正弦函数拟合得到主轴安装平移误差及主轴与C轴同轴度误差；步骤4：多次辨识求平均值：重复所述步骤1至步骤3，进行多次测量，取辨识结果的平均值。
- 根据权利要求1所述的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，所述步骤1的具体步骤如下：步骤1-1：测量仪器安装在工作台上，驱动机床使球头检棒中心与检测仪器接触；步骤1-2：根据C轴、主轴行程，按一定间隔划分运动位置点，并安装不同长度的球头检棒于主轴上，旋转至少一周测量球头检棒球心的位置偏差。
- 根据权利要求2所述的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，所述步骤1-2具体采用以下实验方案：
序号 C轴位置 主轴位置 球头检棒长度 1 C＝(i-1)Δc S＝(j-1)Δs L1 2 C＝(i-1)Δc 不限 L2 其中，C表示C轴的运动位置角，S表示主轴的运动位置角，Δc、Δs分别表示C轴与主轴的运动间隔，i、j表示测量角度的序号。 - 根据权利要求3所述的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，所述步骤2的具体步骤如下：步骤2-1：所述步骤1中的C轴旋转时产生的位置偏差为(Δx ci,Δy ci)，i＝1,2,…，设偏差点所构成的最小二乘拟合圆曲线方程如下：R 2＝(x-A) 2+(y-B) 2 (1)式中，R为拟合圆半径，A、B代表圆心坐标在XY平面的坐标值，x，y表示拟合圆曲线上的点的坐标值；步骤2-2：令a＝-2A，b＝-2B，k＝A 2+B 2-R 2，可得最小二乘拟合圆曲线方程的另一个形式：x 2+y 2+ax+by+k＝0 (2)步骤2-3：计算位置偏差点到圆心的距离为l i：l i 2＝(Δx ci-A) 2+(Δy ci-B) 2 (3)步骤2-4：计算拟合圆半径与偏差点距离之间差的平方和：Q i＝Σ(l i 2-R 2) 2＝Σ(Δx ci 2+Δy ci 2+aΔx ci+bΔy ci+k) 2 (4)代入测量数据求解该式，平方和最小时，即可得到拟合圆半径R；步骤2-5：最后得到主轴安装倾斜误差：
式中，θ表示主轴安装倾斜误差，L 1、L 2分别表示两种不同杆长的球头检棒长度，R 1、R 2分别表示L 1、L 2杆长的球头检棒产生的拟合圆半径。 - 根据权利要求4所述的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，所述步骤3的具体步骤如下：步骤3-1：提取所述步骤1中C轴旋转时产生的位置偏差的Δx ci或Δy ci，主轴旋转的位置偏差的Δx sj或Δy sj，i＝j＝1,2,…，以Y向偏差值构成的正弦曲线方程如下：y＝a sin(bφ+c)+d (6)式中，y表示拟合曲线上点的纵坐标，φ表示拟合曲线上点的横坐标，a、b、c、d分别表示正弦曲线的幅值、角频率、初相、偏距；对于一系列的偏差点(φ,Δy)去拟合所述正弦曲线方程，则有：Q＝Σ(a sin(bΔx+c)+d-Δy) 2 (7)要使得Q最小，应满足：
求解式(8)得到正弦曲线方程的各系数结果；步骤3-2：利用主轴旋转运动测得的位置偏差数据，计算主轴安装平移误差：r s＝a s-L 1sinθ (9)式中，a s表示主轴运动数据拟合的幅值，L 1表示球心检棒的长度，θ表示刀具安装倾斜误差，r s表示主轴安装平移误差，结合初相计算出在X、Y坐标轴上的投影；步骤3-3：将C轴与主轴测得的位置偏差数据代入计算，即得主轴与C轴同轴度在X、Y方向上则为：m x＝r ccos c c+r scos c sm y＝r csin c c+r ssin c s (10)式中，m x、m y分别表示在X、Y方向上主轴与C轴同轴度误差，c s、c c分别表示主轴偏差数据与C轴偏差数据正弦拟合的相位，r c表示C轴运动数据的拟合半径，其中r c＝a c-L 1sinθ，a c表示C轴运动数据拟合的幅值。 - 根据权利要求1所述的一种主轴安装误差及主轴与C轴同轴度的检测与辨识方法，其特征在于，在步骤1中，所述检测仪器为R-test测量仪、激光跟踪仪、激光位移传感器中的任一种。
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