WO2019144254A1 - 一种数控机床直线轴转角误差快速检测方法 - Google Patents

一种数控机床直线轴转角误差快速检测方法 Download PDF

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WO2019144254A1
WO2019144254A1 PCT/CN2018/073694 CN2018073694W WO2019144254A1 WO 2019144254 A1 WO2019144254 A1 WO 2019144254A1 CN 2018073694 W CN2018073694 W CN 2018073694W WO 2019144254 A1 WO2019144254 A1 WO 2019144254A1
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axis
measurement
speed
accelerometer
measured
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PCT/CN2018/073694
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English (en)
French (fr)
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王永青
刘阔
吴嘉锟
刘海波
刘志松
刘海宁
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大连理工大学
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Priority to PCT/CN2018/073694 priority Critical patent/WO2019144254A1/zh
Priority to US16/462,238 priority patent/US10900779B2/en
Publication of WO2019144254A1 publication Critical patent/WO2019144254A1/zh

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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
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
    • G01B21/24—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms

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  • the invention belongs to the technical field of numerical control machine tools, and particularly relates to a rapid detection method for linear axis rotation angle error of a numerical control machine tool.
  • the rotation angle error of the linear axis of the machine tool is a characteristic of the deflection angle of the motion pair. It is an important index to evaluate the geometric accuracy of the machine tool. Its size directly affects the machining quality of the workpiece and gradually increases during the service of the machine tool. Therefore, the acquisition of the linear axis angle error is of great significance for the evaluation of the geometric accuracy of the machine tool and the timely maintenance of the machine tool. For this reason, the detection of the linear axis rotation angle error is included in the various types of machine tool accuracy inspection standards. In actual production, machine tool manufacturers and user units use laser interferometers, ballbars and other testing instruments to periodically detect the angular error of the linear axis of the machine tool.
  • the research shows that the rapid detection of the linear axis rotation angle error of CNC machine tools should meet the basic conditions of high measurement efficiency, strong data processing capability, small device size, low price, convenient installation and debugging, and it has great engineering challenges.
  • the motion deflection angle is obtained by integral, and then the deflection angle measured by the accelerometer is used to correct, and the linear axis angle error is quickly obtained, which is a rapid detection of the linear axis rotation angle error of the numerical control machine tool.
  • the possibility is a rapid detection of the linear axis rotation angle error of the numerical control machine tool.
  • CN103234512A disclosed a high-precision attitude angle and angular velocity measuring device for a three-axis air floating platform.
  • the method uses a smart probe, a gyro, a four-sided prism, and a laser tracker.
  • the Kalman filter algorithm obtains angle and angular velocity information to achieve high-precision dynamic measurement.
  • this method has many measuring devices, complicated debugging, measurement and time consuming.
  • Beijing Sanchi Technology Development Co., Ltd. disclosed a method for accuracy compensation of inertial measurement unit in the patented CN102135431A.
  • the method uses the angular velocity information output by the fiber optic gyro, and the attitude attitude system calculates the attitude angle according to the angular velocity information. .
  • the method is extremely expensive and is subject to external disturbances such as temperature, and cannot meet the detection requirements of the linear axis rotation angle of the numerical control machine tool under complicated working conditions.
  • the object of the invention is to overcome the deficiencies of the prior methods, and to solve the problem of rapid detection of the linear axis rotation angle error of the numerical control machine tool, and to invent a rapid detection method for the linear axis rotation angle error of the machine tool.
  • the device used in the method is an accelerometer and a gyroscope, and has the advantages of strong anti-interference ability and high detection efficiency; the device has few components, small components, low cost, compact structure and simple assembly.
  • the method uses an accelerometer to detect the gravity vector component, determines the installation error, and provides a basis for the correction of the measurement angle error.
  • the accelerometer is used to measure the angle error to correct the gyroscope measurement result, thereby increasing the measurement accuracy; using the same rotation angle error
  • the noise distribution law at different speeds is preserved by filtering to preserve the high SNR component.
  • the measurement data of the high SNR bandwidth in each speed is combined to increase the measurement bandwidth.
  • the measurement system is installed on the linear axis of the machine tool. It can realize the rapid detection of the linear axis rotation angle error of the machine tool, the operation is simple, the equipment integration is high, and the automation is easy.
  • a rapid detection method for linear axis rotation angle error of numerical control machine tool adopting gyroscope and accelerometer to measure the deflection angle of linear axis uniform motion, and then calculate the pitch angle error, yaw angle error and roll angle error of linear axis; firstly, The measuring device is mounted on the linear axis, and the initial rotation angle error generated by the installation is determined by the accelerometer; then, the linear axis moves at three different speeds at a constant speed, and the data acquisition card automatically performs multi-channel acquisition and storage of the motion measurement point measurement data; The Kalman filter principle is used to fuse the accelerometer and gyroscope measurement angle information to obtain the angular error measured at three speeds. Subsequently, the same geometric error signal is decomposed into different frequency components to filter the measurement angle error at different speeds. Finally, the measurement angle errors at the three speeds after filtering are superimposed to complete the rapid measurement of the linear axis angle error of the machine tool;
  • the first step is to assemble a linear detection device for linear axis rotation angle error detection device
  • Three single-axis accelerometers 1 # single-axis accelerometer 1, 2 # single-axis accelerometer 2 and 3 # single-axis accelerometer 3 consisting of a three-way accelerometer group; three gyroscopes: 4 # single-axis gyroscope 4, 5 # single-axis gyroscope 5 and 6 # single-axis gyroscope 6 three-way gyroscope; ensure 1 # single-axis accelerometer 1 measurement direction is I direction, 2 # single-axis accelerometer 2 measurement direction is n direction , 3 # single-axis accelerometer measurement direction is t direction; ensure 4# single-axis gyroscope 4 measurement around the n-axis coordinate axis rotation angle, the angle start side is I coordinate axis, clockwise rotation is positive; 5 # single-axis gyroscope 5 Measure the rotation angle around the coordinate axis in the t direction.
  • the initial angle of the angle is the I coordinate axis, and the counterclockwise rotation is positive.
  • the 6 # single axis gyro 6 measures the rotation angle around the I axis.
  • the angle is the t coordinate axis and the clockwise rotation is positive.
  • Three single-axis accelerometers and three single-axis gyroscopes are respectively fixed in the detection box 7 by nuts; the detection box 7 is fixed on the linear axis 8 of the numerical control machine tool through the side flanges, and the linear axis of the measuring device and the numerical control machine tool is completed. Clamping
  • the second step is the measurement of the installation error of the measuring device.
  • g is the gravitational acceleration of the measurement position; adjust the flange nut of the detection box until the installation pitch angle error ⁇ c and the roll angle error ⁇ c are within 0.1°;
  • the third step is the measurement of the linear axis angle error of CNC machine tools.
  • the three measuring speeds are high speed v max , medium speed v mid or low speed v min respectively .
  • the measuring device is respectively in the I direction.
  • the high speed v max , the medium speed v mid , and the low speed v min move from either side of the linear axis to the other side, and the data acquisition system of the upper computer stores the coordinates of each measuring point and the output digital signal data; wherein the moving speed is:
  • V max is the maximum feed speed of the motion axis; the sampling frequency f max of the accelerometer under the high speed motion of the linear axis corresponding to the three speeds, the sampling frequency f mid of the accelerometer under the linear motion of the linear axis and the low speed motion of the linear axis
  • the sampling frequency f min of the accelerometer is:
  • the output signal is output at the i-th measuring point under the condition that the measuring speed is val.
  • the output signal is output at the i-th measuring point under the condition that the measuring speed is val, r is the number of measuring points in the cross-section trajectory, and k is the accelerometer label.
  • K # accelerometer is measured under a condition val speed measurement time of the i-th measuring point,
  • K # is an accelerometer to measure the time of the i-th measuring point at high speed
  • K # is an accelerometer to measure the time the i-th measuring point in the medium speed condition
  • K # is an accelerometer to measure the time of the i-th measuring point at low speed
  • the fourth step is to correct the rotation angle of the linear axis based on Kalman filter.
  • the initial value is set, and the k # accelerometer measures the deflection angle at the first measuring point under the condition that the measuring speed is val.
  • the corrected deflection angle of the i-1th measuring point under the condition that the measuring speed is val, where k 4, 5, 6;
  • the measured value covariance of the corrected deflection angle of the i-th measuring point is measured under the condition that the measuring speed is val;
  • the formulas (6) to (10) are continuously calculated repeatedly, and the measured corrected deflection angle subset of the linear axis at three measurement speeds is calculated. among them, For the measuring distance of the i measuring point in the I direction,
  • the fifth step is the filtering and data fusion based on spatial frequency continuous conditions.
  • the measurement obtains the I-direction motion axis at high speed.
  • Medium speed Low speed
  • the measured deflection angle subsets ⁇ k,max , ⁇ k,mid and ⁇ k,min are respectively filtered to measure the upper limit frequency f u,val and the lower limit frequency f d,val
  • Filtering the upper limit frequency for high speed in the I direction Filtering the lower limit frequency for high speed in the I direction; Filtering the upper limit frequency for the medium speed in the I direction, Filtering the lower limit frequency for the medium speed in the I direction; Filtering the upper limit frequency for low speed in the I direction, Filtering the lower limit frequency for the medium speed in the I direction;
  • the filter measurement corrected deflection angle subset is obtained. among them
  • the measurement direction speed is val
  • the measurement after the i-th measurement point is filtered to correct the deflection angle signal
  • l i is the measurement distance of the i measurement point
  • the measured elements in the measured displacement subset are added to complete the data fusion, that is,
  • the measurement direction speed is high speed
  • the measurement of the i-th measuring point is corrected to correct the deflection angle signal
  • the measured deflection angle signal is measured after the i-th measuring point is filtered under the condition that the measuring direction speed is medium speed
  • the measurement direction speed is low
  • the measurement of the i-th measuring point is corrected to correct the deflection angle signal
  • the collection is a total set of measured corners
  • the invention has the beneficial effects that the accelerometer and the gyroscope are used to measure the deflection angle of the linear motion pair during the uniform motion, and the deflection angle error of the linear motion axis is obtained, thereby realizing the linear motion axis rotation angle of the numerical control machine tool. The error is measured quickly.
  • Figure 1 is a block diagram of a geometric accuracy rapid detection device.
  • Figure 2 is a diagram of the geometric accuracy rapid detection device detection.
  • Figure 3 is a schematic diagram showing the distribution of measured acceleration subsets of the linear axis in the n direction at three speeds.
  • Figure 4 is a schematic diagram showing the distribution of measured acceleration subsets of the linear axis in the I direction at three speeds.
  • Figure 5 is a schematic diagram showing the distribution of angular rate subsets of the linear axis around the t direction at three speeds.
  • Figure 6 is a schematic diagram of a subset of yaw angles of the accelerometer measured in the t direction at three measurement speeds.
  • Figure 7 is a schematic diagram of a subset of measured corrected deflection angles of the linear axis about the t direction at three measurement speeds.
  • Figure 8 is a schematic diagram of a subset of modified deflection angles for filtering measurements in the t direction.
  • Figure 9 is a schematic diagram of the measurement of the total corner set around the t direction.
  • I, n, and t are the I direction, the n direction, and the t direction.
  • the first step is to assemble a linear detection device for linear axis rotation angle error detection device
  • Three single-axis accelerometers 1 # single-axis accelerometer 1, 2 # single-axis accelerometer 2, 3 # single-axis accelerometer 3 consisting of three-way accelerometer group; three gyroscopes: 4 # single-axis gyroscope 4, 5 # single-axis gyroscope 5, 6 # single-axis gyroscope 6 three-way gyroscope.
  • Guarantee 1 # single-axis accelerometer 1 measurement direction is I direction; 2 # single-axis accelerometer 2 measurement direction is n direction; 3 # single-axis accelerometer measurement direction is t direction; guarantee 4# single-axis gyroscope 4 measurement around n
  • the direction coordinate axis rotation angle, the angle starting point is the I coordinate axis, clockwise rotation is positive; 5 # single axis gyroscope 5 measuring the rotation angle around the t direction coordinate axis, the angle starting point is the I coordinate axis, the counterclockwise rotation is positive; 6 #
  • the single-axis gyroscope 6 measures the rotation angle around the coordinate axis of the I direction, the starting angle of the angle is the t coordinate axis, and the clockwise rotation is positive;
  • the three single-axis accelerometers and the three single-axis gyroscopes are respectively fixed in the detection box 7 by nuts;
  • the detection box 7 is fixed on the linear shaft by the side flanges, and the clamp
  • the second step is the measurement of the installation error of the measuring device.
  • the third step is the measurement of the linear axis angle error of CNC machine tools.
  • the data acquisition system of the upper computer simultaneously stores the coordinates of each measuring point and outputs digital signal data.
  • the maximum feed speed of the motion axis is 500mm/s.
  • the fourth step is to correct the rotation angle of the linear axis based on Kalman filter.
  • the yaw angle measured by the 1# single-axis accelerometer 1 and 2# single-axis accelerometer 2 at each measuring point measured by the 1# single-axis accelerometer 2 is calculated by the formula (5), and the 6-accelerometer is obtained in the three measurements.
  • the initial value is set, and the accelerometer is measured at a measuring speed of 500 mm/s, 100 mm/s, 20 mm/s, and the measured yaw angles at the first measuring point are 0.024°, 0.025°, and 0.024° as the 5# single-axis gyro.
  • the corrected deflection angle of the first measuring point of the instrument 5 under the conditions of measuring speeds of 500 mm/s, 100 mm/s, and 20 mm/s.
  • the measured value covariance of the corrected deflection angle of the first measuring point of the 5# single-axis gyroscope at the measurement speeds of 500 mm/s, 100 mm/s, and 20 mm/s is set to 1.
  • Set the measurement noise variance of each measuring point of the 5 # single-axis gyroscope to 0.001 at each measuring speed.
  • Set the measurement noise variance of each single-axis accelerometer to 1 at each measurement point.
  • the fifth step is the filtering and data fusion based on spatial frequency continuous conditions.
  • the measurement subset is filtered separately, and the upper limit of the measurement of the corrected deflection angle subset is obtained under the condition of high-speed measurement.
  • the lower limit is The upper limit of the filter for measuring the corrected deflection angle subset under the condition of medium speed measurement is The lower limit is The upper limit of the filter for measuring the corrected deflection angle subset under the condition of low speed measurement is The lower limit is Obtained as described above: Figure 8 - Filtering the corrected yaw angle subset around the t direction.
  • the invention relates to a rapid detection method for a linear axis rotation angle error of a numerical control machine tool, which measures an angle of deflection of a linear motion pair in a moving direction by an accelerometer and a gyroscope, and further calculates a rotation angle error of the linear motion axis. It provides the possibility for rapid detection of corner errors of CNC machine tools.

Abstract

一种数控机床直线轴转角误差快速检测方法，首先将测量装置安装于直线轴，并通过加速度计确定安装产生的初始转角误差；然后，直线轴以三种不同速度匀速运动，上层测量系统自动进行多通道采集、存储运动测点测量数据；接着，采用卡尔曼滤波原理对加速度计与陀螺仪测量转角信息进行融合得到三种速度下测量的角度误差；随后，基于相同几何误差信号可分解为不同频率分量，对不同测速下测量角度误差进行滤波；最后，对滤波后的三种测速下的测量角度误差进行叠加，完成机床直线轴角度误差快速测量。具有测量效率高、数据处理能力强，可实现机床直线运动轴转角误差的快速测量，操作简单，设备集成度高、便于实现自动化。

Description

一种数控机床直线轴转角误差快速检测方法 技术领域
本发明属于数控机床技术领域，特别涉及一种数控机床直线轴转角误差快速检测方法。
背景技术
机床直线轴的转角误差作为运动副运行偏转角度的表征，是评估机床几何精度重要指标，其大小直接影响工件的加工质量，且在机床服役过程中逐渐增大。因此，直线轴转角误差的获取对机床几何精度的评估与机床及时维护具有重要意义。为此，对直线轴转角误差的检测被列入各类机床精度检验标准中。实际生产中，机床厂家与用户单位采用激光干涉仪、球杆仪等检测仪器对机床直线轴的转角误差进行定期检测。然而，由于检测装置的大体积、高造价、调试繁琐、测量耗时长，严重制约机床精度检测效率，影响正常生产进程。尤其是对于生产线，坚决避免频繁停机。因此，寻求一种数控机床直线轴转角误差快速检测方法，迫在眉睫。
研究表明，数控机床直线轴转角误差的快速检测，应满足测量效率高、数据处理能力强、装置体积小、价格低廉、安装调试便捷的基本条件，具有极大的工程挑战性。通过对陀螺仪获取运动副在运动时的角速率，积分得到运动偏转角，再结合加速度计测量的偏转角进行修正，完成直线轴转角误差的快速获取，为数控机床直线轴转角误差的快速检测提供了可能性。
2013年哈尔滨工业大学李莉、夏红伟等在专利发明CN103234512A中公开了一种三轴气浮台高精度姿态角度及角速度测量装置，该方法采用智能测头、陀螺、四面棱镜，与激光跟踪仪通过卡尔曼滤波算法得角度与角速度信息，实现了高精度动态测量。然而，该方法测量装置多、调试复杂、测量及其耗时。 2010年，北京三驰科技发展有限公司在专利发明CN102135431A中公开了一种惯性测量单元精度补偿的方法，该方法采用光纤陀螺输出的角速度信息，并由航姿系统根据该角速度信息解算出姿态角度。然而，该方法采用装置造价极高、且易受到温度等外界干扰，无法满足复杂工况下数控机床直线轴转角的检测需求。
发明内容
本发明目的在于克服现有方法不足，针对数控机床直线轴转角误差快速检测问题，发明了一种机床直线轴转角误差快速检测方法。该方法采用的装置为加速度计与陀螺仪，具有抗干扰能力强、检测效率高等优势；装置的组件少，各组件体积小，成本低、结构紧凑简单，便于组装。该方法利用加速度计检测重力矢量分量，确定安装误差，为测量角度误差的矫正提供依据；基于卡尔曼滤波，采用加速度计测量角度误差对陀螺仪测量结果进行修正，增加测量精度；利用相同转角误差于不同测速下的噪声分布规律，通过滤波保留高信噪比成分，基于空间频率连续分布原则，融合各测速中高信噪比带宽的测量数据，增加测量带宽；将测量系统安装于机床直线轴，可实现机床直线轴转角误差的快速检测，操作简单，设备集成度高、便于实现自动化。
本发明的技术方案：
一种数控机床直线轴转角误差快速检测方法，采用陀螺仪与加速度计测量直线轴匀速运动时的偏转角度，进而计算得到直线轴的俯仰角误差、偏摆角误差与滚转角误差；首先，将测量装置安装于直线轴上，并通过加速度计确定安装产生的初始转角误差；然后，直线轴以三种不同速度匀速运动，数据采集卡自动进行多通道采集和存储运动测点测量数据；接着，采用卡尔曼滤波原理对加速度计与陀螺仪测量转角信息进行融合，得到三种速度下测量的角度误差； 随后，基于相同几何误差信号分解为不同频率分量，对不同测速下测量角度误差进行滤波；最后，对滤波后的三种速度下的测量角度误差进行叠加，完成机床直线轴角度误差快速测量；
具体步骤如下：
第一步，组装数控机床直线轴转角误差快速检测装置
采用三个单轴加速度计：1 #单轴加速度计1、2 #单轴加速度计2和3 #单轴加速度计3组成的三向加速度计组；三个陀螺仪：4 #单轴陀螺仪4、5 #单轴陀螺仪5和6 #单轴陀螺仪6组成的三向陀螺仪；保证1 #单轴加速度计1测量方向为I方向，2 #单轴加速度计2测量方向为n方向，3 #单轴加速度计测量方向为t方向；保证4#单轴陀螺仪4测量绕n方向坐标轴转角，角度始边为I坐标轴，顺时针旋转为正；5 #单轴陀螺仪5测量绕t方向坐标轴转角，角度始边为I坐标轴，逆时针旋转为正；6 #单轴陀螺仪6测量绕I方向坐标轴转角，角度始边为t坐标轴，顺时针旋转为正；三个单轴加速度计与三个单轴陀螺仪分别通过螺母固定在检测盒7中；检测盒7通过侧边法兰固定在数控机床直线轴8上，完成测量装置与数控机床直线轴8的装夹；
第二步，测量装置在机安装误差测量
首先，控制数控机床直线轴I并运动到其任意一端；然后，上位机的数据采集系统存储各1 #单轴加速度计1、2 #单轴加速度计2和3 #单轴加速度计3的测量数据分别为
Figure PCTCN2018073694-appb-000001
得到测量装置安装俯仰角误差α c与滚转角误差γ c，
Figure PCTCN2018073694-appb-000002
其中，g为测量位置的重力加速度；调整检测盒法兰螺母，直至安装俯仰角误差 α c与滚转角误差γ c在0.1°以内；
第三步，数控机床直线轴转角误差测量
首先，设定val(val＝max,mid,min)为测量装置的测量速度，三种测量速度分别为高速v max、中速v mid或低速v min；然后，将测量装置沿I方向分别以高速v max、中速v mid、低速v min从直线轴的任意一侧运动到另一侧，同时上位机的数据采集系统高频存储各测点坐标及输出数字信号数据；其中运动速度为：
Figure PCTCN2018073694-appb-000003
其中，V max为运动轴的最大进给速度；三种速度对应的直线轴高速运动下加速度计的采样频率f max，直线轴中速运动下加速度计的采样频率f mid与直线轴低速运动下加速度计的采样频率f min分别为：
Figure PCTCN2018073694-appb-000004
测量获得直线轴在三种测量速度下的测量加速度子集
Figure PCTCN2018073694-appb-000005
与角速率子集
Figure PCTCN2018073694-appb-000006
Figure PCTCN2018073694-appb-000007
为k #加速度计在测量速度为val条件下、于第i测点输出信号，
Figure PCTCN2018073694-appb-000008
为k #加速度计在测量速度为val条件下、于第i测点输出信号，r为截面轨迹内的测点数，k为加速度计标 号，
Figure PCTCN2018073694-appb-000009
为k #加速度计在测量速度为val条件下于第i测点的测量时间，
Figure PCTCN2018073694-appb-000010
其中，
Figure PCTCN2018073694-appb-000011
为k #加速度计在高速条件下于第i测点的测量时间，
Figure PCTCN2018073694-appb-000012
为k #加速度计在中速条件下于第i测点的测量时间，
Figure PCTCN2018073694-appb-000013
为k #加速度计在低速条件下于第i测点的测量时间；
第四步，基于卡尔曼滤波的直线轴测量转角修正
本方法中，设定
Figure PCTCN2018073694-appb-000014
为加速度计在测量速度为val条件下、于第i测点测得的偏转角，其中，k＝1，2，3分别代表测量得到的俯仰角
Figure PCTCN2018073694-appb-000015
偏摆角
Figure PCTCN2018073694-appb-000016
与滚转角
Figure PCTCN2018073694-appb-000017
首先计算由三向加速度计于不同测速下各测点测量偏转角，
Figure PCTCN2018073694-appb-000018
然后，设定初始值，k #加速度计在测量速度为val条件下、于第1测点测量偏转角
Figure PCTCN2018073694-appb-000019
分别作为4 #单轴陀螺仪4、5 #单轴陀螺仪5、6 #单轴陀螺仪6在测量速度为val条件下，于第1测点的修正偏转角
Figure PCTCN2018073694-appb-000020
其中k＝1，2，3；设定k #单轴陀螺仪在测量速度为val条件下，第1测点的修正偏转角的测量值协方差
Figure PCTCN2018073694-appb-000021
为非零的任意值，其中k＝4,5,6；
接着，对直线轴各测点测量偏转角进行迭代计算
Figure PCTCN2018073694-appb-000022
其中，i∈[2,r]，
Figure PCTCN2018073694-appb-000023
为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量偏转角，其中k＝4,5,6；
Figure PCTCN2018073694-appb-000024
为k #单轴陀螺仪在测量速度为val条件下，第i-1测点的修正偏转角，其中k＝4,5,6；
根据测量值求出修正偏转角的值，
Figure PCTCN2018073694-appb-000025
其中，k＝4,5,6，
Figure PCTCN2018073694-appb-000026
为k #单轴陀螺仪在测量速度为val条件下于第i测点卡尔曼滤波增益，
Figure PCTCN2018073694-appb-000027
Figure PCTCN2018073694-appb-000028
Figure PCTCN2018073694-appb-000029
其中，
Figure PCTCN2018073694-appb-000030
为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量偏转角的协方差；
Figure PCTCN2018073694-appb-000031
为k #单轴陀螺仪在测量速度为val条件下，第i测点的修正偏转角的测量值协方差；
Figure PCTCN2018073694-appb-000032
为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量噪声方差，其中k＝4,5,6；
Figure PCTCN2018073694-appb-000033
为k #单轴加速度计在测量速度为val条件下，第i测点的测量噪声方差，其中k＝1,2,3；
不断重复计算公式(6)～(10)，计算获得直线轴在三种测量速度下的测量修正偏转角子集
Figure PCTCN2018073694-appb-000034
其中，
Figure PCTCN2018073694-appb-000035
为i测点沿I方向的测量距离，
Figure PCTCN2018073694-appb-000036
其中，
Figure PCTCN2018073694-appb-000037
为沿I方向的高速，
Figure PCTCN2018073694-appb-000038
为沿I方向的高速运动下加速度计的采样频率；
第五步，基于空间频率连续条件的滤波与数据融合
首先，测量获得I方向运动轴在高速
Figure PCTCN2018073694-appb-000039
中速
Figure PCTCN2018073694-appb-000040
低速
Figure PCTCN2018073694-appb-000041
测量条件下的测量修正偏转角子集Θ k,max、Θ k,mid与Θ k,min；分别对测量子集进行滤波，滤波上限频率f u,val与下限频率f d,val为
Figure PCTCN2018073694-appb-000042
Figure PCTCN2018073694-appb-000043
Figure PCTCN2018073694-appb-000044
其中，
Figure PCTCN2018073694-appb-000045
为I方向高速下滤波上限频率，
Figure PCTCN2018073694-appb-000046
为I方向高速下滤波下限频率；
Figure PCTCN2018073694-appb-000047
为I方向中速下滤波上限频率，
Figure PCTCN2018073694-appb-000048
为I方向中速下滤波下限频率；
Figure PCTCN2018073694-appb-000049
为I方向低速下滤波上限频率，
Figure PCTCN2018073694-appb-000050
为I方向中速下滤波下限频率；
按上述操作，得到滤波测量修正偏转角子集
Figure PCTCN2018073694-appb-000051
其中
Figure PCTCN2018073694-appb-000052
为k #单轴陀螺仪在测量方向速度为val条件下，第i测点滤波后的测量修正偏转角信号；l i为i测点的测量距离；
接着，将低速、中速、高速测量条件下，测量得到的测量位移子集中各元素相加，完成数据融合，即
Figure PCTCN2018073694-appb-000053
其中，
Figure PCTCN2018073694-appb-000054
为k #单轴陀螺仪在测量方向速度为高速条件下，第i测点滤波后的测 量修正偏转角信号；
Figure PCTCN2018073694-appb-000055
为k #单轴陀螺仪在测量方向速度为中速条件下，第i测点滤波后的测量修正偏转角信号；
Figure PCTCN2018073694-appb-000056
为k #单轴陀螺仪在测量方向速度为低速条件下，第i测点滤波后的测量修正偏转角信号；元素
Figure PCTCN2018073694-appb-000057
的集合为测量转角总集，
Figure PCTCN2018073694-appb-000058
最后，计算得到直线轴俯仰角α、偏摆角β与滚转角γ为
Figure PCTCN2018073694-appb-000059
本发明的有益效果：采用了加速度计与陀螺仪测量直线运动副匀速运动过程中垂于运动方向的偏转角度，进而得到直线运动轴的偏转角度误差的方法，实现了对数控机床直线运动轴转角误差快速测量。
附图说明
图1是几何精度快速检测装置组成图。
图2是几何精度快速检测装置检测图。
图3是直线轴在三种速度下于n方向的测量加速度子集分布示意图。
图4是直线轴在三种速度下于I方向的测量加速度子集分布示意图。
图5是直线轴在三种速度下绕t方向的测量角速率子集分布示意图。
图6是加速度计在三种测量速度下绕t方向的测量的偏摆角子集示意图。
图7是直线轴在三种测量速度下绕t方向的测量修正偏转角子集示意图。
图8是绕t方向滤波测量修正偏转角子集示意图。
图9是绕t方向测量转角总集示意图。
图中：1-1#加速度计；2-2#单轴加速度计；3-3#单轴加速度计；4-4#单轴陀螺仪计；5-5#单轴陀螺仪，6-6#单轴陀螺仪；7-检测盒；8-数控机床直线轴；
I、n、t为I方向、n方向与t方向。
具体实施方式
下面将结合附图和技术方案详细说明本发明的具体实施方式。
第一步，组装数控机床直线轴转角误差快速检测装置
采用三个单轴加速度计：1 #单轴加速度计1、2 #单轴加速度计2、3 #单轴加速度计3组成的三向加速度计组；三个陀螺仪：4 #单轴陀螺仪4、5 #单轴陀螺仪5、6 #单轴陀螺仪6组成的三向陀螺仪。保证1 #单轴加速度计1测量方向为I方向；2 #单轴加速度计2测量方向为n方向；3 #单轴加速度计测量方向为t方向；保证4#单轴陀螺仪4测量绕n方向坐标轴转角，角度始边为I坐标轴，顺时针旋转为正；5 #单轴陀螺仪5测量绕t方向坐标轴转角，角度始边为I坐标轴，逆时针旋转为正；6 #单轴陀螺仪6测量绕I方向坐标轴转角，角度始边为t坐标轴，顺时针旋转为正；三个单轴加速度计与三个单轴陀螺仪分别通过螺母固定在检测盒7中；检测盒7通过侧边法兰固定在直线轴上，完成测量装置与数控机床直线轴8的装夹。
第二步，测量装置在机安装误差测量
首先，控制数控机床直线轴I并运动到其任意一端。然后，上位机的数据采集系统存储各1 #、2 #、3 #单轴加速度计1、2、3的测量数据分别为0.00045g、0.00095g、0.9999g，得到测量装置安装俯仰角误差α c＝arcsin(0.00045g/g)＝0.025°与滚转角误差β c＝arcsin(0.00095g/cos(0.025)g)＝0.054°。
第三步，数控机床直线轴转角误差测量
以测量直线轴偏转角为例，将测量装置沿I方向以高速v max＝500mm/s、中速v mid＝500/5＝100mm/s、低速v min＝500/25＝20mm/s分别运动到另一侧，同时上位机的数据采集系统高频存储各测点坐标及输出数字信号数据。其中，运动轴的最大进给速度为500mm/s。直线轴高速运动下加速度计的采样频率为 f max＝500/0.5×4＝4000Hz，直线轴中速运动下加速度计的采样频率为f mid＝4000/500×100＝1000Hz，直线轴低速运动下加速度计的采样频率为f min＝4000/500×20＝160Hz。按上述操作获得：附图3-直线轴在三种速度下于n方向的测量加速度子集分布，附图4-直线轴在三种速度下于I方向的测量加速度子集分布、附图5-直线轴在三种速度下绕t方向的测量角速率子集分布。
第四步，基于卡尔曼滤波的直线轴测量转角修正
首先通过公式(5)计算由1#单轴加速度计1、2#单轴加速度计2测量的于三种测量速度下各测点测量偏摆角，得到附图6-加速度计在三种测量速度下绕t方向的测量的偏摆角子集。
然后，设定初始值，加速度计在测量速度为500mm/s、100mm/s、20mm/s条件下于第1测点的测量偏摆角0.024°、0.025°、0.024°作为5#单轴陀螺仪5在测量速度为500mm/s、100mm/s、20mm/s条件下第1测点的修正偏转角。设定5#单轴陀螺仪在测量速度为500mm/s、100mm/s、20mm/s条件下第1测点的修正偏转角的的测量值协方差均为1。设定5 #单轴陀螺仪在各测速下各测点的测量噪声方差为0.001。设定各单轴加速度计在在各测速下各测点的测量噪声方差为1。
接着，通过计算公式(6)～(10)，计算直线轴在三种测量速度下的测量修正偏转角子集。按上述操作获得：附图7-直线轴在三种测量速度下绕t方向的测量修正偏转角子集。
第五步，基于空间频率连续条件的滤波与数据融合
首先，分别对测量子集进行滤波，测量获得高速测量条件下测量修正偏转角子集的滤波上限为
Figure PCTCN2018073694-appb-000060
下限为
Figure PCTCN2018073694-appb-000061
测量获得中速测量条件下测量修正偏转角子集的滤波上限为
Figure PCTCN2018073694-appb-000062
下限为
Figure PCTCN2018073694-appb-000063
测量获得低速测量条件下测量修正偏转角子集的滤波上限为
Figure PCTCN2018073694-appb-000064
下限为
Figure PCTCN2018073694-appb-000065
按上述操作获得：附图8-绕t方向滤波测量修正偏摆角子集。
最后，将低速、中速和高速测量条件下测量得到的测量位移子集中各元素相加，完成数据融合。按上述操作获得：附图9-绕t方向测量转角总集。最终得到偏摆角为0.039°。
本发明所述的一种数控机床直线轴转角误差快速检测方法，它通过加速度计、陀螺仪测量直线运动副匀速运动时垂于运动方向的偏转角度，通进而计算得到直线运动轴的转角误差，为数控机床转角误差的快速检测提供了可能性。
以上所述一种数控机床直线轴转角误差快速检测方法仅本发明的较佳方法，故凡依本发明专利申请范围所述的特征及原理所做的等效变化或修饰，均包括本发明专利申请范围内。

Claims (1)

  1. 一种数控机床直线轴转角误差快速检测方法，采用陀螺仪与加速度计测量直线轴匀速运动时的偏转角度，进而计算得到直线轴的俯仰角误差、偏摆角误差与滚转角误差；首先，将测量装置安装于直线轴上，并通过加速度计确定安装产生的初始转角误差；然后，直线轴以三种不同速度匀速运动，数据采集卡自动进行多通道采集和存储运动测点测量数据；接着，采用卡尔曼滤波原理对加速度计与陀螺仪测量转角信息进行融合，得到三种速度下测量的角度误差；随后，基于相同几何误差信号分解为不同频率分量，对不同测速下测量角度误差进行滤波；最后，对滤波后的三种速度下的测量角度误差进行叠加，完成机床直线轴角度误差快速测量；
    其特征在于，步骤如下：
    第一步，组装数控机床直线轴转角误差快速检测装置
    采用三个单轴加速度计：1 #单轴加速度计1、2 #单轴加速度计2和3 #单轴加速度计3组成的三向加速度计组；三个陀螺仪：4 #单轴陀螺仪4、5 #单轴陀螺仪5和6 #单轴陀螺仪6组成的三向陀螺仪；保证1 #单轴加速度计1测量方向为I方向，2 #单轴加速度计2测量方向为n方向，3 #单轴加速度计测量方向为t方向；保证4#单轴陀螺仪4测量绕n方向坐标轴转角，角度始边为I坐标轴，顺时针旋转为正；5 #单轴陀螺仪5测量绕t方向坐标轴转角，角度始边为I坐标轴，逆时针旋转为正；6 #单轴陀螺仪6测量绕I方向坐标轴转角，角度始边为t坐标轴，顺时针旋转为正；三个单轴加速度计与三个单轴陀螺仪分别通过螺母固定在检测盒7中；检测盒7通过侧边法兰固定在数控机床直线轴8上，完成测量装置与数控机床直线轴8的装夹；
    第二步，测量装置在机安装误差测量
    首先，控制数控机床直线轴I并运动到其任意一端；然后，上位机的数据采 集系统存储各1 #单轴加速度计1、2 #单轴加速度计2和3 #单轴加速度计3的测量数据分别为
    Figure PCTCN2018073694-appb-100001
    得到测量装置安装俯仰角误差α c与滚转角误差γ c，
    Figure PCTCN2018073694-appb-100002
    其中，g为测量位置的重力加速度；调整检测盒法兰螺母，直至安装俯仰角误差α c与滚转角误差γ c在0.1°以内；
    第三步，数控机床直线轴转角误差测量
    首先，设定val为测量装置的测量速度，三种测量速度分别为高速v max、中速v mid或低速v min；然后，将测量装置沿I方向分别以高速v max、中速v mid、低速v min从直线轴的任意一侧运动到另一侧，同时上位机的数据采集系统高频存储各测点坐标及输出数字信号数据；其中运动速度为：
    Figure PCTCN2018073694-appb-100003
    其中，V max为运动轴的最大进给速度；三种速度对应的直线轴高速运动下加速度计的采样频率f max，直线轴中速运动下加速度计的采样频率f mid与直线轴低速运动下加速度计的采样频率f min分别为：
    Figure PCTCN2018073694-appb-100004
    测量获得直线轴在三种测量速度下的测量加速度子集
    Figure PCTCN2018073694-appb-100005
    与角速率子集
    Figure PCTCN2018073694-appb-100006
    为k #加速度计在测量速度为val条件下、于第i测点输出信号，
    Figure PCTCN2018073694-appb-100007
    为k #加速度计在测量速度为val条件下、于第i测点输出信号，r为截面轨迹内的测点数，k为加速度计标号，
    Figure PCTCN2018073694-appb-100008
    为k #加速度计在测量速度为val条件下于第i测点的测量时间，
    Figure PCTCN2018073694-appb-100009
    其中，
    Figure PCTCN2018073694-appb-100010
    为k #加速度计在高速条件下于第i测点的测量时间，
    Figure PCTCN2018073694-appb-100011
    为k #加速度计在中速条件下于第i测点的测量时间，
    Figure PCTCN2018073694-appb-100012
    为k #加速度计在低速条件下于第i测点的测量时间；
    第四步，基于卡尔曼滤波的直线轴测量转角修正
    设定
    Figure PCTCN2018073694-appb-100013
    为加速度计在测量速度为val条件下、于第i测点测得的偏转角，其中，k＝1，2，3分别代表测量得到的俯仰角
    Figure PCTCN2018073694-appb-100014
    偏摆角
    Figure PCTCN2018073694-appb-100015
    与滚转角
    Figure PCTCN2018073694-appb-100016
    首先计算由三向加速度计于不同测速下各测点测量偏转角，
    Figure PCTCN2018073694-appb-100017
    然后，设定初始值，k #加速度计在测量速度为val条件下、于第1测点测量 偏转角
    Figure PCTCN2018073694-appb-100018
    分别作为4 #单轴陀螺仪4、5 #单轴陀螺仪5、6 #单轴陀螺仪6在测量速度为val条件下，于第1测点的修正偏转角
    Figure PCTCN2018073694-appb-100019
    其中k＝1，2，3；设定k #单轴陀螺仪在测量速度为val条件下，第1测点的修正偏转角的测量值协方差
    Figure PCTCN2018073694-appb-100020
    为非零的任意值，其中k＝4,5,6；
    接着，对直线轴各测点测量偏转角进行迭代计算
    Figure PCTCN2018073694-appb-100021
    其中，i∈[2,r]，
    Figure PCTCN2018073694-appb-100022
    为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量偏转角，其中k＝4,5,6；
    Figure PCTCN2018073694-appb-100023
    为k #单轴陀螺仪在测量速度为val条件下，第i-1测点的修正偏转角，其中k＝4,5,6；
    根据测量值求出修正偏转角的值，
    Figure PCTCN2018073694-appb-100024
    其中，k＝4,5,6，
    Figure PCTCN2018073694-appb-100025
    为k #单轴陀螺仪在测量速度为val条件下于第i测点卡尔曼滤波增益，
    Figure PCTCN2018073694-appb-100026
    Figure PCTCN2018073694-appb-100027
    Figure PCTCN2018073694-appb-100028
    其中，
    Figure PCTCN2018073694-appb-100029
    为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量偏转角的协方差；
    Figure PCTCN2018073694-appb-100030
    为k #单轴陀螺仪在测量速度为val条件下，第i测点的修正偏转角的测量值协方差；
    Figure PCTCN2018073694-appb-100031
    为k #单轴陀螺仪在测量速度为val条件下，第i测点的测量噪声方差，其中k＝4,5,6；
    Figure PCTCN2018073694-appb-100032
    为k #单轴加速度计在测量速度为val条件下，第i测点的测量噪声方差，其中k＝1,2,3；
    不断重复计算公式(6)～(10)，计算获得直线轴在三种测量速度下的测 量修正偏转角子集
    Figure PCTCN2018073694-appb-100033
    其中，
    Figure PCTCN2018073694-appb-100034
    为i测点沿I方向的测量距离，
    Figure PCTCN2018073694-appb-100035
    其中，
    Figure PCTCN2018073694-appb-100036
    为沿I方向的高速，
    Figure PCTCN2018073694-appb-100037
    为沿I方向的高速运动下加速度计的采样频率；
    第五步，基于空间频率连续条件的滤波与数据融合
    首先，测量获得I方向运动轴在高速
    Figure PCTCN2018073694-appb-100038
    中速
    Figure PCTCN2018073694-appb-100039
    低速
    Figure PCTCN2018073694-appb-100040
    测量条件下的测量修正偏转角子集Θ k,max、Θ k,mid与Θ k,min；分别对测量子集进行滤波，滤波上限频率f u,val与下限频率f d,val为
    Figure PCTCN2018073694-appb-100041
    Figure PCTCN2018073694-appb-100042
    Figure PCTCN2018073694-appb-100043
    其中，
    Figure PCTCN2018073694-appb-100044
    为I方向高速下滤波上限频率，
    Figure PCTCN2018073694-appb-100045
    为I方向高速下滤波下限频率；
    Figure PCTCN2018073694-appb-100046
    为I方向中速下滤波上限频率，
    Figure PCTCN2018073694-appb-100047
    为I方向中速下滤波下限频率；
    Figure PCTCN2018073694-appb-100048
    为I方向低速下滤波上限频率，
    Figure PCTCN2018073694-appb-100049
    为I方向中速下滤波下限频率；
    按上述操作，得到滤波测量修正偏转角子集
    Figure PCTCN2018073694-appb-100050
    其中
    Figure PCTCN2018073694-appb-100051
    为k #单轴陀螺仪在测量方向速度为val条件下，第i测点滤波后的测量修正偏转角信号；l i为 i测点的测量距离；
    接着，将低速、中速、高速测量条件下，测量得到的测量位移子集中各元素相加，完成数据融合，即
    Figure PCTCN2018073694-appb-100052
    其中，
    Figure PCTCN2018073694-appb-100053
    为k #单轴陀螺仪在测量方向速度为高速条件下，第i测点滤波后的测量修正偏转角信号；
    Figure PCTCN2018073694-appb-100054
    为k #单轴陀螺仪在测量方向速度为中速条件下，第i测点滤波后的测量修正偏转角信号；
    Figure PCTCN2018073694-appb-100055
    为k #单轴陀螺仪在测量方向速度为低速条件下，第i测点滤波后的测量修正偏转角信号；元素
    Figure PCTCN2018073694-appb-100056
    的集合为测量转角总集，
    Figure PCTCN2018073694-appb-100057
    最后，计算得到直线轴俯仰角α、偏摆角β与滚转角γ为
    Figure PCTCN2018073694-appb-100058
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