CN111272088B - Measuring algorithm for profile pitch diameter of sliding block of rolling linear guide rail pair - Google Patents

Measuring algorithm for profile pitch diameter of sliding block of rolling linear guide rail pair Download PDF

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CN111272088B
CN111272088B CN202010157674.8A CN202010157674A CN111272088B CN 111272088 B CN111272088 B CN 111272088B CN 202010157674 A CN202010157674 A CN 202010157674A CN 111272088 B CN111272088 B CN 111272088B
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displacement sensor
laser displacement
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coordinate system
equation
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CN111272088A (en
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欧屹
俞福春
王凯
冯虎田
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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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
    • G01B11/08—Measuring arrangements characterised by the use of optical techniques for measuring diameters

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Abstract

本发明公开了一种滚动直线导轨副滑块型面中径的测量算法，将传感器置于滑块外侧两端，对滑块内滚道倾斜扫掠测量；对于滑块的大基准面与侧基准面，分别通过两个激光位移传感器测出其平面度，通过倾斜扫掠滑块内滚道得到半个椭圆轮廓数据点，经过最小二乘法进行椭圆拟合，求解出拟合椭圆的形心位置，改变滑块位置，扫掠出滑块不同截面的半椭圆轮廓，求解出对应的拟合椭圆形心位置，将同一滚道的拟合椭圆形心位置坐标点通过数学分析，计算出滚道中心轴线的直线方程，计算滑块左右滚道中心轴线的空间距离即为滚动直线导轨副滑块中径，进而测定滑块大基准面与侧基准面的平行度。为滚动直线导轨副的中径测量提出了一套完整的算法。

Figure 202010157674

The invention discloses a measuring algorithm for the profile diameter of a pair of sliding blocks of rolling linear guide rails. The flatness of the reference plane is measured by two laser displacement sensors, and half ellipse profile data points are obtained by tilting and sweeping the inner raceway of the slider, and ellipse fitting is performed by the least square method to solve the centroid of the fitted ellipse. position, change the position of the slider, sweep out the semi-elliptical contours of different sections of the slider, solve the corresponding fitting ellipse centroid position, and calculate the rolling Calculate the space distance between the center axis of the left and right raceways of the slider, which is the middle diameter of the pair of rolling linear guide rails, and then determine the parallelism between the large datum plane and the side datum plane of the slider. A complete set of algorithms is proposed for the pitch diameter measurement of rolling linear guides.

Figure 202010157674

Description

Measuring algorithm for profile pitch diameter of sliding block of rolling linear guide rail pair
Technical Field
The invention belongs to the field of rolling linear guide rail pair sliding block detection, and particularly relates to a measuring algorithm for a rolling linear guide rail pair sliding block profile pitch diameter.
Background
The sliding block is an important component of the rolling linear guide rail pair, the requirements on the size and the position precision of the middle diameter of the sliding block of the rolling linear guide rail pair are high, the contact angle of a steel ball and a raceway is directly influenced, the pre-tightening force of the linear guide rail pair is further influenced, and the use performance of the rolling linear guide rail pair is finally changed. Starting from improving the products of the domestic rolling linear guide rail pair, the detection of the middle diameter of the sliding block profile of the rolling linear guide rail pair is necessary.
The measurement of the intermediate diameter of the sliding block of the rolling linear guide rail pair is mainly divided into contact measurement and non-contact measurement. The contact measurement method has high precision, but the operation is complicated, the influence of the thought factors is large, and the automatic measurement cannot be realized. The non-contact measuring method is characterized in that a laser displacement sensor sweeps a roller path, and the intermediate diameter of a sliding block is fitted in a computer.
Because the span of the sliding block of the rolling linear guide rail pair is small, the size of the laser displacement sensor is large, the laser displacement sensor and the sliding block are easy to interfere, the sensor cannot be arranged in the groove of the sliding block, and the pitch diameter of the sliding block is directly measured. At present, the non-contact method is still in a blank for detecting the middle diameter of the sliding block of the rolling linear guide rail pair.
Disclosure of Invention
The invention aims to provide a measuring algorithm for the intermediate diameter of a sliding block profile of a rolling linear guide rail pair.
The technical scheme adopted by the invention is as follows:
a measurement algorithm for the pitch diameter of a sliding block profile of a rolling linear guide rail pair comprises the following steps:
step 1, constructing a coordinate system: constructing a clamp space rectangular coordinate system, a space rectangular coordinate system of a slide block to be measured, a space rectangular coordinate system composed of a laser displacement sensor system, space rectangular coordinate systems of a first laser displacement sensor and a second laser displacement sensor, and space oblique coordinate systems of the first laser displacement sensor and the second laser displacement sensor;
constructing a space rectangular coordinate system of the fixture, specifically a space rectangular coordinate system o of a calibration block fixedly connected on the fixture0-x0y0z0Wherein x is0Axis perpendicular to the table of the jig, y0The axis being along the length of the clamping table, z0Axis along the width of the clamping table, x0Axis, y0Axis, z0The axes follow the right hand rule;
space rectangular coordinate system o for constructing slide block to be measured1-x1y1z1Wherein x is1The axis being perpendicular to the side reference plane of the slide to be measured, y1Axial direction is the same as the guide direction of the slide block to be measured, z1The axis being perpendicular to the large reference plane, x, of the slide to be measured1Axis, y1Axis, z1The axes follow the right hand rule;
space rectangular coordinate system o formed by constructing laser displacement sensor system2-x2y2z2Wherein y is2Axial direction and y 1The axes are in the same direction, x2The axis being in the vertical plane with y2The axis being vertical, pointing upwards, z2Axis and x2Axis, y2The axes follow the right hand rule;
constructing a spatial rectangular coordinate system o of the first laser displacement sensor3-x3y3z3Wherein z is3The axis is the moving direction of the first laser displacement sensor, x3Axis perpendicular to z3Axis and located at z3In-plane, y, formed by axis and laser radiation line3Axis and z3Axis, x3The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the first laser displacement sensor4-x4y4z4In the actual data acquisition process, the data point is in the spatial oblique coordinate system o of the first laser displacement sensor4-x4y4z4Middle collection, wherein z4Axis z3Axis, y4Axis y3Axis, x4The axis represents the direction of light exiting the sensor, which is x3The included angle between the axes is the mounting inclination angle beta1；
Constructing a spatial rectangular coordinate system o of the second laser displacement sensor5-x5y5z5Wherein z is5The axis is the moving direction, x, of the second laser displacement sensor5Axis perpendicular to z5Axis and located at z5In-plane, y, formed by axis and laser radiation line5Axis and z5Axis, x5The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the second laser displacement sensor6-x6y6z6In the actual data acquisition process, the data point is in the spatial inclined coordinate system o of the second laser displacement sensor6-x6y6z6Middle Collection, z 6Axis z5Axis, y6Axis y5Axis, x6Representing the direction of light emission from the sensor, which is in conjunction with x5The included angle between the axes is the mounting inclination angle beta2；
A first laser displacement sensor and a second laser displacement sensor in the laser displacement sensor system are arranged along z2Two raceways of the slide block to be measured are measured in the axial direction, a calibration cylinder, a slide block to be measured and a calibration block are fixedly connected to a slide block bracket, and the slide block bracket drives the calibration cylinder, the slide block to be measured and the calibration block to be measured along y2The third laser displacement sensor, the fourth laser displacement sensor, the fifth laser displacement sensor and the sixth laser displacement sensor are fixedly connected on the experiment table, wherein the third laser displacement sensor and the fourth laser displacement sensor are used forCollecting data of side reference surfaces of the slide block to be detected and the calibration block, wherein a fifth laser displacement sensor and a sixth laser displacement sensor are used for collecting data of the slide block to be detected and the large reference surface of the calibration block;
step 2, obtaining a system error curve under the rectangular coordinate system of the clamp space by using the calibration block: measuring two surfaces of the calibration block, which are matched with the clamp, by a third laser displacement sensor and a fourth laser displacement sensor of the side reference surface, a fifth laser displacement sensor and a sixth laser displacement sensor of the large reference surface to obtain two linear data of the large reference surface and the side reference surface, wherein the two linear data are used as error curves of a clamp system and are used for subsequent compensation;
Step 3, determining the planeness of the large reference surface and the side reference surface of the slide block to be detected: measuring the large reference surface and the side reference surface of the slide block to be measured by a third laser displacement sensor, a fourth laser displacement sensor, a fifth laser displacement sensor and a sixth laser displacement sensor to obtain two linear data of the large reference surface and the side reference surface of the slide block to be measured, taking the error curve of the clamp system obtained in the step 2 as a compensation curve to obtain coordinate values of the large reference surface and the side reference surface of the slide block to be measured under a clamp space rectangular coordinate system, and calculating the planeness of the large reference surface and the side reference surface of the slide block to be measured by utilizing a planar least square fitting equation;
step 4, the first laser displacement sensor and the second laser displacement sensor sweep a calibration cylinder, fitting by using a least square method of an ellipse, and solving a general equation of the calibration ellipse;
step 5, constructing the general equation of the ellipse obtained in the step 4 and the installation inclination angle beta of the first laser displacement sensor and the second laser displacement sensor1、β2And solving for the mounting tilt angle beta1、β2: the mounting inclination angle beta1The included angle between the vertical line of the movement direction of the first laser displacement sensor and the light ray emitted by the first laser displacement sensor in the plane formed by the light ray emitted by the first laser displacement sensor and the movement direction of the first laser displacement sensor; mounting angle of inclination beta 2Is a plane formed by the light emitted by the second laser displacement sensor and the movement direction of the second laser displacement sensorThe included angle between the vertical line of the movement direction of the inner second laser displacement sensor and the light emitted by the second laser displacement sensor;
step 6, determining the installation deflection angle alpha of the first laser displacement sensor and the second laser displacement sensor rotating around the self movement direction axis1、α2And solving the installation deflection angle alpha1、α2(ii) a The installation deflection angle α1Is x3Axial direction and direction of movement y of the carriage2The included angle between the axes; mounting deflection angle alpha2Is x5Axial direction and direction of movement y of the carriage2The included angle between the axes;
step 7, calculating the coordinates of the center point of the inner raceway of the slide block to be tested: the first laser displacement sensor and the second laser displacement sensor sweep the inner raceway of the slide block to be detected, the data points of the raceway of the slide block to be detected under a spatial oblique coordinate system of the first laser displacement sensor and the second laser displacement sensor are collected, and the coordinates (x) of the raceway central points of the raceway of the slide block to be detected Roll1 and the raceway Roll2 under the spatial oblique coordinate system are calculated by adopting elliptical least square fitting4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) Coordinates (x) of center points of the rolling paths Roll1 and Roll2 in the space oblique coordinate system 4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) The coordinates (x) of the center points of the roller paths Roll1 and Roll2 under a space rectangular coordinate system formed by a displacement sensor system are converted into coordinates2Roll1,y2Roll1,z2Roll1)、(x2Roll2,y2Roll2,z2Roll2)；
Step 8, measuring different sections of the slide block to be measured, solving coordinates of center points of the roller paths Roll1 and Roll2 with different sections under a space rectangular coordinate system formed by a displacement sensor system, and fitting direction vectors of central axes of the roller paths Roll1 and Roll 2;
and 9, solving the distance between the central axis of the rolling way room 1 and the central axis of the rolling way room 2 according to the direction vectors of the central axes of the rolling ways room 1 and the rolling way room 2 fitted in the step 8, wherein the distance is the pitch diameter of the rolling way of the sliding block of the rolling linear guide pair.
The invention has the beneficial effects that:
(1) according to the invention, the laser displacement sensors are arranged at two ends of the outer side of the sliding block and are obliquely arranged for measurement, so that the problem of interference between the laser displacement sensors and the sliding block during detection is avoided;
(2) the principle that the interface shape of the cylinder is an ellipse is ingeniously utilized, the point on the central axis of the cylinder is the circle center of the ellipse with the corresponding section, the position information of the circular hole of the roller way in the sliding block is effectively extracted, and the viewpoint is novel;
(3) the invention skillfully utilizes the calibration cylinder as a detection reference to reversely calculate the installation inclination angle of the laser displacement sensor, and the cylinder used for calibration is easy to process to high precision so as to meet the use requirement;
(4) The invention skillfully converts the problem of measuring the intermediate diameter of the sliding block into the distance between the sliding blocks in different planes, converts the data acquired under different coordinate systems into the same coordinate system through the geometric relationship and coordinate transformation, and solves the intermediate diameter of the sliding block by solving the distance between the sliding blocks in different planes, thus being visual and convenient for calculation.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
FIG. 1 is a layout view of a sensor of the present invention.
Fig. 2 is a spatial rectangular coordinate system diagram of the fixture, the slider to be measured, the displacement sensor system, the first laser displacement sensor and the second laser displacement sensor, and the first laser displacement sensor and the second laser displacement sensor.
FIG. 3 is a coordinate system o3-x3y3z3And a coordinate system o4-x4y4z4The relationship between them.
FIG. 4 is a coordinate system o5-x5y5z5And a coordinate system o5-x5y5z5The relationship between them.
FIG. 5 is a profile view of a half ellipse obtained by sweeping a calibration cylinder block according to the present invention.
FIG. 6 is a full ellipse profile fitted from a half ellipse swept through the calibration cylinder block according to the present invention.
Fig. 7 is a profile view of two semi-ellipses resulting from the sweeping of the inner raceway of the slider of the present invention.
FIG. 8 is a diagram of two elliptical profiles fitted from two semi-ellipses resulting from sweeping the inner track of the slider according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a measuring algorithm for the profile pitch diameter of a sliding block of a rolling linear guide rail pair, which comprises the following steps:
step 1, constructing a coordinate system, specifically constructing a clamp space rectangular coordinate system, a slide block 3 to be measured space rectangular coordinate system, a space rectangular coordinate system composed of a displacement sensor system, space rectangular coordinate systems of a first laser displacement sensor 2 and a second laser displacement sensor 4, and space oblique coordinate systems of the first laser displacement sensor 2 and the second laser displacement sensor 4;
constructing a space rectangular coordinate system of the fixture, specifically a space rectangular coordinate system o of a calibration block 10 fixedly connected on the fixture0-x0y0z0Wherein x is0Axis perpendicular to the table of the jig, y0The axis being along the length of the clamping table, z0Axis along the width of the clamping table, x0Axis, y0Axis, z0The axes follow the right hand rule;
space rectangular coordinate system o for constructing slide block 3 to be measured1-x1y1z1Wherein x is1The axis is perpendicular to the side reference plane of the slide 3 to be measured, y 1The axial direction is the same as the guiding direction of the slide block 3 to be measured, z1The axis being perpendicular to the large reference plane, x, of the slide 3 to be measured1Axis, y1Axis, z1The axes follow the right hand rule;
space rectangular coordinate system o formed by constructing laser displacement sensor system2-x2y2z2Wherein y is2Axial direction and y1The axes are in the same direction, x2The axis being in the vertical plane with y2The axis being vertical, pointing upwards, z2Axis and x2Axis, y2The axes follow the right hand rule;
constructing a spatial rectangular coordinate system o of the first laser displacement sensor 23-x3y3z3Wherein z is3The axis is the moving direction, x, of the first laser displacement sensor 23Axis perpendicular to z3Axis and located at z3In-plane, y, formed by axis and laser radiation line3Axis and z3Axis, x3The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the first laser displacement sensor 24-x4y4z4In the actual data acquisition process, the data point is in the spatial oblique coordinate system o of the first laser displacement sensor 24-x4y4z4Middle collection, wherein z4Axis z3Axis, y4Axis y3Axis, x4Representing the direction of light emission from the sensor, which is in conjunction with x3The angle between the axes being the mounting deflection angle beta1；
Constructing a spatial rectangular coordinate system o of the second laser displacement sensor 45-x5y5z5Wherein z is5The axis is the moving direction, x, of the second laser displacement sensor 45Axis perpendicular to z5Axis and located at z5In-plane, y, formed by axis and laser radiation line 5Axis and z5Axis, x5The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the second laser displacement sensor 46-x6y6z6In the actual data acquisition process, the data point is in the spatial oblique coordinate system o of the second laser displacement sensor 46-x6y6z6Middle Collection, z6Axis z5Axis, y6Axis y5Axis, x6Representing sensor lightDirection of emission, which is in conjunction with x5The angle between the axes being the mounting deflection angle beta2；
The first laser displacement sensor 2 and the second laser displacement sensor 4 in the laser displacement sensor system are arranged along the z direction2Two raceways of the slide block 3 to be measured are measured in the axial direction, the slide block bracket 9 is fixedly connected with the calibration cylinder 1, the slide block 3 to be measured and the calibration block 10, and in the measuring process, the slide block bracket 9 drives the calibration cylinder 1, the slide block 3 to be measured and the calibration block 10 to be measured along y2The device comprises a third laser displacement sensor 5, a fourth laser displacement sensor 6, a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8 which are axially moved and fixedly connected to a laboratory bench, wherein the third laser displacement sensor 5 and the fourth laser displacement sensor 6 are used for collecting data of side reference surfaces of a slide block 3 to be measured and a calibration block 10, and the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 are used for collecting data of a large reference surface of the slide block 3 to be measured and the calibration block 10;
And seven space coordinate systems are constructed, so that subsequent explanation and calculation are facilitated.
Step 2, obtaining a system error curve under the clamp space rectangular coordinate system by using the calibration block 10: the third laser displacement sensor 5 and the fourth laser displacement sensor 6 collect data of a side datum plane of the calibration block 10, the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 collect data of a large datum plane of the calibration block 10, and the slider bracket 9 collects data of a large datum plane of the calibration block 10 along the y direction2The distance of the shaft movement is collected by the grating. Respectively taking data acquired by the grating as a horizontal axis and data acquired by the third laser displacement sensor 5 and the fourth laser displacement sensor 6 as a vertical axis to obtain two curve data of the reference surface on the side of the calibration block 10; respectively taking data collected by the grating as a horizontal axis and data collected by the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 as a vertical axis to obtain two curve data of the large reference surface of the calibration block 10, and taking the obtained four curves as error curves of the fixture system for subsequent compensation;
the carriage bracket 9 follows y2In the axial direction movement process, the third laser displacement sensor 5, the fourth laser displacement sensor 6, the fifth laser displacement sensor 7, the sixth laser displacement sensor 8 and the grating measure a series of seats Value of (0x2,0y2,0z2) For the fifth laser displacement sensor 7, the sixth laser displacement sensor 8,0x2the value is measured by a distance meter, and a fifth laser displacement sensor 7, a sixth laser displacement sensor 8 and a calibration block 10 are positioned at x in the experimental process2No numerical value change in the axial direction, the numerical value is constant,0y2the value is read by a grating scale,0z2the values are collected in real time by a laser displacement sensor. For the third laser displacement sensor 5 and the fourth laser displacement sensor 6,0z2the value is measured by a distance meter, and the third laser displacement sensor 5, the fourth laser displacement sensor 6 and the calibration block 10 are in z during the experiment process2No numerical value change in the axial direction, the numerical value is constant,0y2the value is read by a grating scale,0x2the values are collected in real time by a laser displacement sensor. The system error curve under the rectangular coordinate system of the clamp space is obtained by measuring two surfaces of the calibration block 10 matched with the clamp and reflecting the principle of corresponding plane characteristics by measuring representative data on the two surfaces of the calibration block for subsequent compensation.
Step 3, determining the planeness of the large reference surface and the side reference surface of the slide block 3 to be tested: the third laser displacement sensor 5 and the fourth laser displacement sensor 6 collect data of a side datum plane of the slide block 3 to be detected, the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 collect data of a large datum plane of the slide block 3 to be detected, and the slide block bracket 9 collects data of a large datum plane of the slide block 3 to be detected along y 2The distance of the shaft movement is collected by the grating. Respectively taking data collected by the grating as a horizontal axis and data collected by the third laser displacement sensor 5 and the fourth laser displacement sensor 6 as a vertical axis to obtain two curve data of the side reference surface of the sliding block 3 to be detected; respectively taking data collected by the grating as a horizontal axis and data collected by the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 as a vertical axis to obtain two curve data of the large reference surface of the slide block 3 to be detected, taking the error curve of the clamp system obtained in the step 2 as a compensation curve to obtain coordinate values of the large reference surface and the side reference surface of the slide block 3 to be detected under a clamp space rectangular coordinate system, and solving the coordinate values of the large reference surface and the side reference surface of the slide block to be detected under the clamp space rectangular coordinate system by utilizing a planar least square fitting equationMeasuring the planeness of the large reference surface and the side reference surface of the sliding block 3;
in the same step 2, a third laser displacement sensor 5, a fourth laser displacement sensor 6, a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8 are arranged along the y direction2In the axial direction movement process, the large reference surface and the side reference surface of the slide block 3 to be measured are measured to obtain a series of coordinate values (1x2,1y2,1z2) For the third laser displacement sensor 5, the fourth laser displacement sensor 6,1z2the value of which is determined in step 2 0z2The values are equal, are constant values,1y2the optical grating is used for reading the image,1x2the values are collected by a third laser displacement sensor 5 and a fourth laser displacement sensor 6 in real time; for the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8,1x2the value of which is determined in step 20x2The values are equal, are constant values,1y2the optical grating is used for reading the image,1z2the values are acquired by the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 in real time. And (3) using the system error curve under the rectangular coordinate system of the fixture space obtained in the step (2) for compensation to obtain the coordinates of the large reference surface and the side reference surface of the slide block 3 to be measured relative to the rectangular coordinate system of the fixture space:
(1x0,1y0,1z0)＝((1x2-0x2),(1y2-0y2),(1z2-0z2)) (1)
data measured for the laser displacement sensors 7, 8. Establishing a least square fitting equation of the large reference surface as follows:
Figure GDA0003211546310000081
in the formula (A), (B)1x0,1y0,1z0) Is composed of a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8Measuring i-1, 2.. n, wherein n is the number of collected points;
for coefficient A of equation (2)1、B1、C1The partial derivatives are solved to obtain an equation set as:
Figure GDA0003211546310000082
solving the system of equations in equation (3) results in:
Figure GDA0003211546310000091
the equation coefficient A is obtained from equation (4)1,B1,C1Obtaining the least square method evaluation result t of the planeness of the large reference surface1Comprises the following steps:
Figure GDA0003211546310000092
the surfaces measured by the third laser displacement sensor 5 and the fourth laser displacement sensor 6 establish a least square fitting equation of the side reference surface as follows:
Figure GDA0003211546310000093
In the formula (A), (B)1x0,1y0,1z0) Measured by a third laser displacement sensor 5 and a fourth laser displacement sensor 6, i is 1,2.. n, n is the number of collected points;
similarly, the least square method evaluation result t of the flatness of the side datum plane is obtained through the formula (3), the formula (4) and the formula (5)2Comprises the following steps:
Figure GDA0003211546310000094
and 4, sweeping the calibration cylinder 1 through the first laser displacement sensor 2 and the second laser displacement sensor 4, and solving the coefficient of the general equation of the ellipse by using least square fitting of the ellipse.
When the first laser displacement sensor 2 measures the calibration cylinder 1, a series of profile data can be obtained (3x4,3y4,3z4) The least squares fit equation for the ellipse is constructed as:
Figure GDA0003211546310000095
wherein (A) and (B)3x4,3y4,3z4) Measuring profile data of a calibration cylinder 1 by a first laser displacement sensor 2 and a grating, wherein i is 1,2.. n, and n is the number of collected points; wherein3x4iThe values are collected by the first laser displacement sensor 2,3z4ithe values are collected by a grating which is,3y4the value is measured by a distance measuring instrument, and the first laser displacement sensor 2 and the calibration cylinder 1 are arranged at y in the measuring process4No number value is changed in the direction, and the direction is a fixed value.
Equation coefficient A in equation (8)0,B0,C0,D0,E0The partial derivative is calculated as:
Figure GDA0003211546310000101
unfolding to obtain:
Figure GDA0003211546310000102
solving the equation set in the formula (10) to obtain the elliptic equation coefficient A fitted by the calibration cylinder 10,B0,C0,D0,E0；
Step 5, constructing the elliptic equation obtained in the step 4 and the installation inclination angle beta of the first laser displacement sensor 2 and the second laser displacement sensor 4 1、β2. Mounting angle of inclination beta1In a plane formed by light rays emitted by the first laser displacement sensor 2 and the moving direction of the first laser displacement sensor 2, an included angle between a vertical line of the moving direction of the first laser displacement sensor 2 and the light rays emitted by the first laser displacement sensor 2 is formed; mounting angle of inclination beta2The included angle between the vertical line of the moving direction of the second laser displacement sensor 4 and the light emitted by the second laser displacement sensor 4 is in the plane formed by the light emitted by the second laser displacement sensor 4 and the moving direction of the second laser displacement sensor 4. The actual mounting inclination angle beta of the first laser displacement sensor 2 and the second laser displacement sensor 4 which are mounted in an inclined way is solved1、β2；
For the first laser displacement sensor 2, a spatial oblique coordinate system (x)4,y4,z4) The lower actual coordinate point and the theoretical coordinate point (x) in the space rectangular coordinate system3,y3,z3) The following relationships exist:
Figure GDA0003211546310000103
for an ellipse in any position, it can be described according to 5 independent parameters: center point (x)0,z0) Major semi-axis a, minor semi-axis b (assuming a)>b) Angle of inclination theta in a rectangular spatial coordinate system o4-x4y4z4The ellipse equation at any arbitrary position is expressed as:
Figure GDA0003211546310000111
due to the presence of beta1Deviation of angle generation, oblique coordinate system o3-x3y3z3From a rectangular coordinate system o4-x4y4z4The coordinate transformation relationship is substituted to obtain an actual ellipse equation:
Figure GDA0003211546310000112
The expansion of the formula (13) is a quintuple quartic nonlinear equation, and the complicated nonlinear equation is transformed and multiplied by a linear equation by using a variable substitution method, namely A1x4 2+B1x4z4+C1z4 2+D1x4+E1y4+F 10, wherein
A1＝cos2θ/a2+sin2θ/b2
B1＝2cosθ(cosβ1sinθ-cosθsinβ1)/a2-2sinθ(sinβ1sinθ+cosβ1cosθ)/b2
C1＝(cosβ1sinθ-cosθsinβ1)2/a2+(sinβ1sinθ+cosβ1cosθ)2/b2
D1＝(2sinθ(y0cosθ-x0sinθ)/b2-2cosθ(x0cosθ+y0sinθ)/a2
E1＝-2(cosβ1sinθ-cosθsinβ1)(x0cosθ+y0sinθ)/a2-2(sinβ1sinθ+cosβ1cosθ)(y0cosθ-x0sinθ)/b2
F1＝(x0cosθ+y0sinθ)2/a2+(y0cosθ-x0sinθ)2/b2-1
(14)
Figure GDA0003211546310000113
Then the elliptic equation under the oblique coordinate system is converted into:
A4x4 2+B4x4z4+C4z4 2+D4x4+E4y4+1＝0 (16)
and (3) making the least square fitting equation coefficient of the ellipse constructed by the formula (8) equal to the ellipse equation coefficient under the oblique coordinate system of the formula (16) to form an equation set:
Figure GDA0003211546310000121
in the equation set (17), the major axis 2a of the ellipse and the center point (x)0,z0) Inclination angle theta and installation inclination angle beta1For unknown parameters, the diameter of the calibration cylinder 1 with the short shaft 2b as the calibration cylinder is known, five unknowns are combined to form five equation sets, and the installation inclination angle beta of the first laser displacement sensor 2 is calculated and calculated1A value of (d);
similarly, the mounting inclination angle β of the second laser displacement sensor 4 can be obtained from equations (11) to (17) for the second laser displacement sensor 42The value of (c).
Step 6, determining the installation deflection angle alpha of the first laser displacement sensor 2 and the second laser displacement sensor 4 rotating around the self movement direction axis1、α2. Mounting deflection angle alpha1Is x3Axial direction and direction y of movement of the carriage 92The included angle between the axes; mounting deflection angle alpha2Is x5Axial direction and direction y of movement of the carriage 92The angle between the axes. The actual installation deflection angle alpha of the first laser displacement sensor 2 and the second laser displacement sensor 4 is solved 1、α2；
The slider bracket 9 follows y2The direction is moved by delta L, and the distance is read by the grating ruler. The front and back numerical value variation of the first laser displacement sensor 2 is delta d1The front and rear numerical variation of the second laser displacement sensor 4 is Δ d2. The actual installation deflection angles of the first laser displacement sensor 2 and the second laser displacement sensor 4 are
Figure GDA0003211546310000122
Step 7, calculating the coordinates of the center point of the roller way in the slide block 3 to be measured through a first excitationThe optical displacement sensor 2 and the second laser displacement sensor 4 sweep the inner raceway of the slider 3 to be detected, data points of the raceway of the slider 3 to be detected under a spatial oblique coordinate system of the first laser displacement sensor 2 and the second laser displacement sensor 4 are collected, and the coordinates of the central points of the raceways Roll1 and Roll2 (x is the coordinate of the central point of the raceway Roll1 and the central point of the raceway Roll2 of the slider 3 to be detected and the raceway Roll2 under the spatial oblique coordinate system are calculated by adopting elliptical least square fitting4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) The coordinates of the center point of the raceway Roll1 and the coordinates (x) of the center point of the raceway Roll2 in a spatial oblique coordinate system4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) Converting the coordinate (x) of the elliptic central point under a space rectangular coordinate system formed by a displacement sensor system2Roll1,y2Roll1,z2Roll1)、(x2Roll2,y2Roll2,z2Roll2)；
When the first laser displacement sensor 2 is along z4When the inner contour of the roller path of the slide block 3 to be measured is measured in the axial direction, the inner roller path contour obtained by sweeping in the measuring direction is a semiellipse, and a series of inner roller path data can be obtained ( 1x4,1y4,1z4)。
The least squares fit equation for the ellipse is constructed as:
Figure GDA0003211546310000131
wherein (A) and (B)1x4i,1y4i,1z4i) For the profile data of the first laser displacement sensor 2 and the track Roll1 measured by the grating, i is 1,2.. n, n is the number of points acquired.
The partial derivatives of coefficients A, B, C, D, E in equation (19) are:
Figure GDA0003211546310000132
equation (20) expands to:
Figure GDA0003211546310000133
solving the formula (21) to obtain A, B, C, D and E;
for a general ellipse equation:
x4Roll1 2+Ax4Roll1z4Roll1+Bz4Roll1 2+Cx4Roll1+Dz4Roll1+E＝0 (22)
the coordinate of the central point of the ellipse represented by the general elliptic equation of formula (22) is the coordinate of the central point of the rolling way Roll1 in the spatial inclined coordinate system of the first laser displacement sensor 2, and is represented as:
Figure GDA0003211546310000134
coordinates (x) of the center point of the roller path Roll1 under the space oblique coordinate system of the first laser displacement sensor 24Roll1,y4Roll1,z4Roll1) Converted into the coordinate (x) of the center point of the roller path Roll1 under the space rectangular coordinate system of the first laser displacement sensor 23Roll1,y3Roll1,z3Roll1) The following relationship exists between the two:
Figure GDA0003211546310000141
coordinates (x) of the center point of the roller path Roll1 under the space rectangular coordinate system of the first laser displacement sensor 23Roll1,y3Roll1,z3Roll1) Converted into the coordinate (x) of the center point of the roller path Roll1 under a space rectangular coordinate system formed by a displacement sensor system2Roll1,y2Roll1,z2Roll1) The following relationship exists between the two:
Figure GDA0003211546310000142
wherein (x)20Roll1,y20Roll1,z20Roll1) And the coordinate value of the origin of the rectangular coordinate system of the first laser displacement sensor 2 under the rectangular coordinate system of the displacement sensor system composition space. x is the number of 20Roll1Read by a motor encoder, y20Roll1、z20Roll1Read by a grating ruler.
At this point, the coordinates of the center point of the ellipse of the roller path Roll1 which are fitted are obtained from the spatial oblique coordinate system (x) of the first laser displacement sensor 24Roll1,y4Roll1,z4Roll1) To the laser displacement sensor system to form a space rectangular coordinate system (x)2Roll1,y2Roll1,z2Roll1) The conversion of (1).
For the second laser displacement sensor 4, similarly, by applying the equations (19) to (25), the coordinate point (x) of the center point of a certain section of another raceway Roll2 of the slider 3 to be measured at the center of the raceway Roll2 in the rectangular coordinate system of the displacement sensor system composition space can be obtained2Roll2,y2Roll2,z2Roll2)。
And 8, measuring different sections of the slide block 3 to be measured according to the step 7, and solving the coordinates of the roller ways Roll1 with different sections and the center point of Roll2 in a space rectangular coordinate system formed by the displacement sensor system. A linear equation for the central axis of the raceways Roll1, Roll2 is fitted.
For the rolling path Roll1, the slide block 3 to be measured is fixed on the slide block bracket 9, the slide block bracket 9 is moved, when the first laser displacement sensor 2 just can collect the data of the rolling path in the slide block 3 to be measured, the data is recorded as the position 1, and the rolling path in the slide block is swept by the obliquely installed laser displacement sensor 2. Fitting the swept data points of the roller track in the slide block 3 to be measured to obtain the coordinates of the central point, and selecting the coordinates of the central point from the spatial oblique coordinate system o of the first laser displacement sensor 2 4-x4y4z4Space rectangular coordinate system o formed by transforming to displacement sensor system2-x2y2z2And obtaining a space rectangular coordinate system o formed by the central point of a fitting ellipse of the cross section of the raceway Roll1 in the displacement sensor system at the position 12-x2y2z2Coordinates of (A), (B) and (C)1x2Roll1,1y2Roll1,1z2Roll1)；
And (4) moving the sliding block brackets to enable the sliding block brackets to be located at the position k, and in connection with the step 8-1, when the sliding block brackets are located at different positions, the distance between the positions of the sliding block brackets is 1cm, and the distance is controlled by a servo motor. When the movable sliding block bracket 9 is measured to be in different positions, the fitting ellipse central point of the cross section of the roller path Roll1 forms a space rectangular coordinate system o in a displacement sensor system2-x2y2z2Coordinates of (A), (B) and (C)kx2Roll1,ky2Roll1,kz2Roll1)，k＝1,2...10。
Coordinate points obtained when the slider bracket 9 is in different positions fit a straight line equation of the central axis of the raceway Roll 1. Since the central axis of the roller path Roll1 passes through x2o2z2And (3) surface, the space linear equation can be simplified as follows:
Figure GDA0003211546310000151
wherein (x)01,y01,z01) At any point on the central axis of the roller path Roll1, (m)Roll1,1,nRoll1) The normal vector of the central axis of the raceway Roll1 is that the radial section of the raceway Roll1 is in an elliptic arc shape, the central axis of the raceway Roll1 represents a straight line consisting of the centers of the elliptic arcs of different radial sections of the raceway Roll1, and y is01＝0x01,z01,mRoll1,nRoll1Are required parameters.
The linear equation can be simplified as:
Figure GDA0003211546310000152
In matrix form:
Figure GDA0003211546310000153
the kth point equation is:
Figure GDA0003211546310000154
the equation for the parallel 10 points is:
Figure GDA0003211546310000161
least square fitting:
Figure GDA0003211546310000162
simplifying into the following steps:
Figure GDA0003211546310000163
m can be obtained by solving the matrixRoll1,nRoll1,x01,y01The parameters of the linear equation. The direction vector of the central axis of the roller path Roll1 is obtained
Figure GDA0003211546310000164
For the central axis of the roller path 2, the direction vector of the central axis of the roller path 2 can be obtained by the same motions from the equation (26) to the equation (32)
Figure GDA0003211546310000165
And 9, solving the distance between the central axis of the roller path Roll1 and the central axis of the roller path Roll2 according to the direction vector of the central axis of the roller path Roll1 and the central axis of the roller path 2 which are fitted in the step 8, namely the pitch diameter of the roller path of the sliding block of the rolling linear guide rail pair.
According to the direction vectors of the central axes of the ball paths Roll1 and Roll2 fitted in the step 8, the distance between the central axes of the ball paths Roll1 and Roll2 is solved, namely the pitch diameter of the slide block ball path, and the distance between the two central axes is as follows:
Figure GDA0003211546310000166
wherein
Figure GDA0003211546310000167
Is the direction vector of the central axis of the roller way 1 and the roller way 2,
Figure GDA0003211546310000168
Figure GDA0003211546310000169
is the direction of the connecting line of any point on the two straight lines,
Figure GDA00032115463100001610
according to the invention, high-precision laser displacement sensors are arranged on two sides of the end part of the sliding block, the sliding block roller path is obliquely swept, the data point of the sweeping result is a half ellipse, and the acquired data is fitted by adopting a least square method. And solving the centroid coordinate of the fitting ellipse, wherein the centroid coordinate of the fitting ellipse is the centroid of the inner raceway of the detection sliding block. The actual installation inclination angle of the laser displacement sensor can be calibrated by measuring a calibration cylinder with known size and installation position coordinates; the actual installation deflection angle of the laser displacement sensor can be calibrated by measuring a calibration block with a known installation position; on the basis of considering the inclination angle and the deflection angle of the laser displacement sensor, fitting a series of centroidal point coordinates of the same raceway to form a linear equation of a central shaft by detecting the centroidal coordinates of inner raceways fitting different sections of the slider, and solving the non-coplanar linear distance of the linear equation of the centers of the inner raceways which are symmetrical at two sides of the slider, namely the pitch diameter of the slider; the large reference surface and the side reference surface of the slide block are detected by the other two pairs of laser displacement sensors, and an algorithm for detecting the middle diameter of the profile surface of the slide block of the rolling linear guide rail pair is provided.
The present invention will be described in further detail with reference to examples.
Example 1:
the detection of the profile pitch diameter of the rolling linear guide pair slider is described with reference to fig. 1, 2, 3, and 4 in the drawings of the specification. The calibration block 10 and the calibration cylinder block 1 are fixedly connected on the slide block bracket 9, the standard size of the used calibration cylinder is 9.996mm, the roundness is 0.003mm, and the straightness is 0.003 mm. A slider reference surface measuring system consisting of a third laser displacement sensor 5, a fourth laser displacement sensor 6, a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8 is fixed on a test bed, a slider bracket 9, a calibration block 10 fixedly connected on the slider bracket 9, a calibration cylinder 1 and a slider 3 to be measured are fixed on the test bed along y2The shaft moves, and a slide block inner track measuring system consisting of the first laser displacement sensor 2 and the second laser displacement sensor 4 can move along the z direction2Axis and x2The axis movement is that the slide block inner track measuring system composed of the first laser displacement sensor 2 and the second laser displacement sensor 4 can be opposite to the slide block reference surface measuring system composed of the third laser displacement sensor 5, the fourth laser displacement sensor 6, the fifth laser displacement sensor 7 and the sixth laser displacement sensor 8 along the z direction 2The shaft moves.
Firstly, the carriage 9 carries the fixed calibration block 10 along y2And the surface of the matching surface of the calibration block 10 and the sliding block bracket 9 is measured as a compensation curve by a sliding block reference surface measuring system consisting of a third laser displacement sensor 5, a fourth laser displacement sensor 6, a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8 through shaft movement. Then a slider reference surface measuring system consisting of a third laser displacement sensor 5, a fourth laser displacement sensor 6, a fifth laser displacement sensor 7 and a sixth laser displacement sensor 8 measures the surface of the slider 3 to be measured, which is matched with the slider bracket 9, the error curve acquired in the previous step is used for data compensation of the large slider reference surface and the side reference surface, and the large slider reference surface and the side reference surface in the fixture coordinate system o can be obtained0-x0y0z0And (4) the following coordinate points. The parallelism between the large reference surface and the side reference surface of the slide block to be measured can be obtained by using the formulas (1) to (7).
First laser displacement sensor2. Second laser displacement sensor 4 combined in-slider track measurement system along z2The axis moves, and the outer contour data point coordinates of the calibration cylinder 1 are collected, as shown in fig. 5; fitting the collected calibration cylinder 1 data points to an ellipse as shown in fig. 6; the actual diameter of the calibration cylinder 1 is 9.996mm, and the installation inclination angles of the first laser displacement sensor 2 and the second laser displacement sensor 4 can be solved by connecting the formulas (8) to (11):
β1＝0.1321°,β2＝0.1569°
The slider bracket 9 follows z2The axis direction moves, the distance between the calibration blocks 10 is collected by the first laser displacement sensor 2 and the second laser displacement sensor 4, and the installation deflection angle of the first laser displacement sensor 2 and the installation deflection angle of the second laser displacement sensor 4 can be solved by adopting the formula (18):
α1＝119.561°,α2＝60.964°
the track measuring system in the slide block formed by the first laser displacement sensor 2 and the second laser displacement sensor 4 is along z2The shaft moves to acquire the coordinate top of the inner raceway of the slide block 3 to be detected, as shown in fig. 7; and fitting the centroid of the truncated inclined plane profile under the space inclined coordinate system of the laser displacement sensors 2 and 4 by using the formulas (19) to (23) as follows:
(x4Roll1,y4Roll1,z4Roll1)＝(5.135,0,5.896),(x6Roll2,y6Roll2,z6Roll2) (5.231,0,5.896) where Roll1 and Roll2 denote raceways Roll1 and Roll 2. Fig. 8 is an inner raceway fit full ellipse graph.
Changing the position of the slider bracket 9 to enable the first laser displacement sensor 2 and the second laser displacement sensor 4 to move along the z direction2And sweeping the inner roller path of the sliding block in the axial direction, and fitting the obtained data to form a centroid coordinate point of the inner roller path. Repeating the above steps for 10 times, and then converting the centroid coordinate points obtained under the oblique spatial coordinate system of the first laser displacement sensor 2 and the second laser displacement sensor 4 into the central point coordinate (x) under the rectangular spatial coordinate system composed of the displacement sensor systems by using the equations (24) and (25) 2Roll1,y2Roll1,z2Roll1),(x2Roll2,y2Roll2,z2Roll2)。
And fitting central axis equations of the inner roller way Roll1 and the inner roller way Roll2 by using the equations (26) to (32). The pitch diameter of the sliding block is solved by using a formula (33): d is 45.324 mm.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. The algorithm for measuring the pitch diameter of the profile surface of the sliding block of the rolling linear guide rail pair is characterized by comprising the following steps of:
step 1, constructing a coordinate system: constructing a clamp space rectangular coordinate system, a space rectangular coordinate system of a slide block (3) to be measured, a space rectangular coordinate system composed of a laser displacement sensor system, space rectangular coordinate systems of a first laser displacement sensor (2) and a second laser displacement sensor (4), and space oblique coordinate systems of the first laser displacement sensor (2) and the second laser displacement sensor (4);
constructing a space rectangular coordinate system of the clamp, in particular to a space rectangular coordinate system o of a calibration block (10) fixedly connected on the clamp0-x0y0z0Wherein x is0Axis perpendicular to the table of the jig, y 0The axis being along the length of the clamping table, z0Axis along the width of the clamping table, x0Axis, y0Axis, z0The axes follow the right hand rule;
constructing a space rectangular coordinate system o of the slide block (3) to be measured1-x1y1z1Wherein x is1The axis is perpendicular to the lateral reference surface of the slide (3) to be measured, y1The axial direction is the same as the guide direction of the slide block (3) to be measured, z1The axis is perpendicular to the large reference plane, x, of the slide (3) to be measured1Axis, y1Axis, z1The axes follow the right hand rule;
space rectangular coordinate system o formed by constructing laser displacement sensor system2-x2y2z2Wherein y is2Axial direction and y1The axes are in the same direction, x2The axis being in the vertical plane with y2The axis being vertical, pointing upwards, z2Axis and x2Axis, y2The axes follow the right hand rule;
constructing a spatial rectangular coordinate system o of the first laser displacement sensor (2)3-x3y3z3Wherein z is3The axis is the moving direction x of the first laser displacement sensor (2)3Axis perpendicular to z3Axis and located at z3In-plane, y, formed by axis and laser radiation line3Axis and z3Axis, x3The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the first laser displacement sensor (2)4-x4y4z4In the actual data acquisition process, a data point is in a spatial inclined coordinate system o of the first laser displacement sensor (2)4-x4y4z4Middle collection, wherein z4Axis z3Axis, y4Axis y3Axis, x4The axis represents the direction of light exiting the sensor, which is x 3The included angle between the axes is the mounting inclination angle beta1；
Constructing a spatial rectangular coordinate system o of the second laser displacement sensor (4)5-x5y5z5Wherein z is5The axis is the moving direction, x, of the second laser displacement sensor (4)5Axis perpendicular to z5Axis and located at z5In-plane, y, formed by axis and laser radiation line5Axis and z5Axis, x5The axes follow the right hand rule;
constructing a spatial oblique coordinate system o of the second laser displacement sensor (4)6-x6y6z6In the actual data acquisition process, a data point is in a spatial inclined coordinate system o of the second laser displacement sensor (4)6-x6y6z6Middle Collection, z6Axis z5Axis, y6Axis y5Axis, x6Representing the direction of light emission from the sensor, which is in conjunction with x5The included angle between the shafts being mounting inclinationBevel angle beta2；
A first laser displacement sensor (2) and a second laser displacement sensor (4) in the laser displacement sensor system are arranged along the z direction2Two raceways of the slide block (3) to be measured are measured in the axial direction, a calibration cylinder (1), the slide block (3) to be measured and a calibration block (10) are fixedly connected to a slide block bracket (9), and in the measuring process, the slide block bracket (9) drives the calibration cylinder (1), the slide block (3) to be measured and the calibration block (10) to be measured along y2The device comprises a third laser displacement sensor (5), a fourth laser displacement sensor (6), a fifth laser displacement sensor (7) and a sixth laser displacement sensor (8), wherein the third laser displacement sensor (5) and the fourth laser displacement sensor (6) are fixedly connected to an experiment table, the third laser displacement sensor and the sixth laser displacement sensor are used for acquiring data of side reference surfaces of a slide block (3) to be detected and a calibration block (10), and the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8) are used for acquiring data of a large reference surface of the slide block (3) to be detected and the calibration block (10);
Step 2, obtaining a system error curve under the rectangular coordinate system of the clamp space by using the calibration block (10): a third laser displacement sensor (5) and a fourth laser displacement sensor (6) on the side reference surface, a fifth laser displacement sensor (7) and a sixth laser displacement sensor (8) on the large reference surface measure two surfaces of the calibration block (10) matched with the clamp to obtain two linear data of the large reference surface and the side reference surface respectively, and the two linear data are used as an error curve of the clamp system for subsequent compensation;
step 3, determining the planeness of the large reference surface and the side reference surface of the slide block (3) to be tested: measuring a large reference surface and a side reference surface of the slide block (3) to be measured by a third laser displacement sensor (5), a fourth laser displacement sensor (6), a fifth laser displacement sensor (7) and a sixth laser displacement sensor (8) to obtain two linear data of the large reference surface and the side reference surface of the slide block (3) to be measured, taking the clamp system error curve obtained in the step (2) as a compensation curve to obtain coordinate values of the large reference surface and the side reference surface of the slide block (3) to be measured under a clamp space rectangular coordinate system, and calculating the planeness of the large reference surface and the side reference surface of the slide block (3) to be measured by using a planar least square fitting equation;
step 4, the first laser displacement sensor (2) and the second laser displacement sensor (4) sweep the calibration cylinder (1), and a general calibration ellipse equation is solved by fitting with a least square method of an ellipse;
Step 5, constructing the general equation of the ellipse obtained in the step 4 and the installation inclination angle beta of the first laser displacement sensor (2) and the second laser displacement sensor (4)1、β2And solving for the mounting tilt angle beta1、β2: the mounting inclination angle beta1The included angle between the vertical line of the movement direction of the first laser displacement sensor (2) and the light emitted by the first laser displacement sensor (2) in the plane formed by the light emitted by the first laser displacement sensor (2) and the movement direction of the first laser displacement sensor (2); mounting angle of inclination beta2The included angle between the vertical line of the moving direction of the second laser displacement sensor (4) and the light emitted by the second laser displacement sensor (4) in the plane formed by the light emitted by the second laser displacement sensor (4) and the moving direction of the second laser displacement sensor (4);
step 6, determining the installation deflection angle alpha of the first laser displacement sensor (2) and the second laser displacement sensor (4) rotating around the self movement direction axis1、α2And solving the installation deflection angle alpha1、α2(ii) a The installation deflection angle α1Is x3The axial direction and the movement direction y of the sliding block bracket (9)2The included angle between the axes; mounting deflection angle alpha2Is x5The axial direction and the movement direction y of the sliding block bracket (9)2The included angle between the axes;
step 7, calculating the coordinates of the center point of the roller way in the slide block (3) to be measured: the first laser displacement sensor (2) and the second laser displacement sensor (4) sweep the inner raceway of the slider (3) to be detected, raceway data points of the slider (3) to be detected under a spatial oblique coordinate system of the first laser displacement sensor (2) and the second laser displacement sensor (4) are collected, and coordinates (x) of the raceway center points of the slider (3) to be detected and the raceway ROLL1 and the raceway ROLL2 under the spatial oblique coordinate system are calculated by adopting elliptical least square fitting 4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) Coordinates (x) of center points of the rolling paths ROLL1 and ROLL2 in the space oblique coordinate system4Roll1,y4Roll1,z4Roll1)、(x6Roll2,y6Roll2,z6Roll2) The coordinates (x) of the center points of the rolling paths ROLL1 and ROLL2 under a space rectangular coordinate system formed by a displacement sensor system are converted into coordinates2Roll1,y2Roll1,z2Roll1)、(x2Roll2,y2Roll2,z2Roll2)；
Step 8, measuring different sections of the slide block (3) to be measured, solving the coordinates of the central points of the rolling paths ROLL1 and ROLL2 with different sections under a space rectangular coordinate system formed by a displacement sensor system, and fitting the direction vectors of the central axes of the rolling paths ROLL1 and ROLL 2;
and 9, solving the distance between the central axis of the rolling way ROLL1 and the central axis of the rolling way ROLL2 according to the direction vectors of the central axes of the rolling ways ROLL1 and ROLL2 which are fitted in the step 8, namely the pitch diameter of the rolling way of the sliding block of the rolling linear guide rail pair.
2. The algorithm for measuring the pitch diameter of the sliding block profile of the rolling linear guide rail pair according to claim 1, wherein the step 2 of obtaining the system error curve of the rectangular fixture space coordinate system specifically comprises: in the process that the sliding block tray (9) moves along the y2 axis direction, a series of coordinate values are measured by the third laser displacement sensor (5), the fourth laser displacement sensor (6), the fifth laser displacement sensor (7), the sixth laser displacement sensor (8) and the grating (coordinate value:) 0x2,0y2,0z2) For the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8),0x2the values were measured by a range finder before the experiment, were fixed values,0y2the value is read by a grating scale,0z2the values are collected by a fifth laser displacement sensor (7) and a sixth laser displacement sensor (8) in real time, for the third laser displacement sensor (5) and the fourth laser displacement sensor (6),0z2the value is measured by a distance meter, is a fixed value,0y2the value is read by a grating scale,0x2the values are acquired by a third laser displacement sensor (5) and a fourth laser displacement sensor (6) in real time, and the data acquired by the grating is taken as the horizontal axis and the third laser is taken as the horizontal axisThe data collected by the displacement sensor (5) and the fourth laser displacement sensor (6) are used as vertical axes to obtain two curve data of a reference surface on the side of the calibration block (10), the data collected by the grating is used as a horizontal axis, the data collected by the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8) is used as a vertical axis to obtain two curve data of a large reference surface of the calibration block (10), and the obtained four curves are used as error curves of the fixture system for subsequent compensation.
3. The rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 2, wherein the step 3 of determining the flatness of the large reference surface and the side reference surface of the slider (3) to be measured specifically comprises:
Step 3-1: the slider tray (9) is arranged along the y direction2In the axial direction movement process, a third laser displacement sensor (5), a fourth laser displacement sensor (6), a fifth laser displacement sensor (7), a sixth laser displacement sensor (8) and a grating measure the large reference surface and the side reference surface of the slide block (3) to be measured to obtain a series of coordinate values (A and B)1x2,1y2,1z2) For the third laser displacement sensor (5) and the fourth laser displacement sensor (6),1z2value and0z2the values are equal, are constant values,1y2the value is read by a grating scale,1x2the values are collected by a third laser displacement sensor (5) and a fourth laser displacement sensor (6) in real time; for the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8),1x2value and0x2the values are equal, are constant values,1y2the optical grating is used for reading the image,1z2the values are acquired by a fifth laser displacement sensor (7) and a sixth laser displacement sensor (8) in real time, the data acquired by the grating are respectively taken as a transverse axis, the data acquired by the third laser displacement sensor (5) and the fourth laser displacement sensor (6) are taken as a longitudinal axis, two curve data of the side reference surface of the sliding block (3) to be detected are obtained, the data acquired by the grating are respectively taken as the transverse axis, the data acquired by the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8) are taken as the longitudinal axis, and the size of the sliding block (3) to be detected is obtained And (3) using the two curve data of the reference surface to compensate the system error curve under the rectangular coordinate system of the fixture space obtained in the step (2) to obtain the coordinates of the large reference surface and the side reference surface of the slide block (3) to be measured relative to the rectangular coordinate system of the fixture space:
(1x0, 1y0,1z0)＝((1x2-0x2),(1y2-0y2),(1z2-0z2)) (1)；
step 3-2: for data measured by the fifth laser displacement sensor (7) and the sixth laser displacement sensor (8), a least square fitting equation of a large reference surface is established as follows:
Figure FDA0003252026630000041
in the above formula (1x0,1y0,1z0) The data points after error compensation in the step 3-1 are set as i 1,2.. N, and N is the number of collected points;
step 3-3, relating the equation in step 3-2 to equation coefficient A1、B1、C1The partial derivatives are solved to obtain an equation set as:
Figure FDA0003252026630000042
step 3-4: solving the equation set in the step 3-3, and obtaining the result:
Figure FDA0003252026630000043
step 3-5: the equation coefficient A is obtained from the step 3-41,B1,C1Obtaining the least square method evaluation result t of the planeness of the large reference surface1Comprises the following steps:
Figure FDA0003252026630000051
step 3-6: the surfaces measured by the third laser displacement sensor (5) and the fourth laser displacement sensor (6) establish a least square fitting equation of the side reference surface as follows:
Figure FDA0003252026630000052
similarly, the least square method evaluation result t of the flatness of the side datum plane is obtained through the steps 3-3 and 3-42Comprises the following steps:
Figure FDA0003252026630000053
4. the rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 3, wherein the step 4 specifically comprises:
Step 4-1: when the first laser displacement sensor (2) measures the calibration cylinder (1), a series of profile data (1) is obtained3x4,3y4,3z4)；
Step 4-2: the least square fitting equation of the calibration ellipse is constructed as follows:
Figure FDA0003252026630000054
wherein (A) and (B)3x4,3y4,3z4) Is a first laser displacement sensor (2) and a grating at o4-x4y4z4Profile data of a calibration cylinder (1) measured in a coordinate system, i being 1,2.. N, N being the number of points acquired, wherein3x4iThe values are acquired by a first laser displacement sensor (2),3z4ithe values are collected by a grating which is,3y4the value is measured by a distance meter and is a fixed value;
step 4-3: the partial derivative of the equation in step 4-2 is calculated as:
Figure FDA0003252026630000055
unfolding to obtain:
Figure FDA0003252026630000061
step 4-4: solving the equation set in the step 4-3 to obtain an elliptic equation coefficient A fitted by the calibration cylinder (1)0,B0,C0,D0,E0。
5. The rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 4, wherein the step 5 specifically comprises:
step 5-1: for the first laser displacement sensor (2), a spatial oblique coordinate system (x)4,y4,z4) The lower actual coordinate point and the theoretical coordinate point (x) in the space rectangular coordinate system3,y3,z3) The following relationships exist:
x3＝x4-z4sinβ1
y3＝y4
z3＝z4cosβ1 (11)
step 5-2: for an ellipse at any position, according to 5 independent parameters: center point (x)0,z0) A long semi-axis A, a short semi-axis B, an inclination angle theta, and a rectangular space coordinate system o 4-x4y4z4The ellipse equation at any arbitrary position is expressed as:
Figure FDA0003252026630000062
due to the presence of beta1Deviation of angle generation, and spatial oblique coordinate system o3-x3y3z3With a spatial rectangular coordinate system o4-x4y4z4The coordinate transformation relationship is substituted to obtain an actual ellipse equation:
Figure FDA0003252026630000063
the expansion of the above formula (13) is a quinary quartic nonlinear equation, and the complicated nonlinear equation is transformed and multiplied by a linear equation by using the following variable substitution method, namely A1x4 2+B1x4z4+C1z4 2+D1x4+E1y4+F10, wherein
A1＝cos2θ/a2+sin2θ/b2
B1＝2cosθ(cosβ1sinθ-cosθsinβ1)/a2-2sinθ(sinβ1sinθ+cosβ1cosθ)/b2
C1＝(cosβ1sinθ-cosθsinβ1)2/a2+(sinβ1sinθ+cosβ1cosθ)2/b2
D1＝(2sinθ(y0cosθ-x0sinθ)/b2-2cosθ(x0cosθ+y0sinθ)/a2
E1＝-2(cosβ1sinθ-cosθsinβ1)(x0cosθ+y0sinθ)/a2-2(sinβ1sinθ+cosβ1cosθ)(y0cosθ-x0sinθ)/b2
F1＝(x0cosθ+y0sinθ)2/a2+(y0cosθ-x0sinθ)2/b2-1 (14)
A4＝A1/F1
B4＝B1/F1
C4＝C1/F1
D4＝D1/F1
E4＝E1/F1 (15)
Then the elliptic equation under the spatial oblique coordinate system is converted into:
A4x4 2+B4x4z4+C4z4 2+D4x4+E4y4+1＝0 (16)；
step 5-3: and (3) making the least square fitting equation coefficient of the constructed ellipse equal to the ellipse equation coefficient under the spatial oblique coordinate system to form an equation set:
A4＝A0
B4＝B0
C4＝C0
D4＝D0
E4＝E0 (17)
in the equation set (17), the major axis 2a of the ellipse and the center point (x)0,z0) Inclination angle theta and installation inclination angle beta1For unknown parameters, the diameter of the calibration cylinder (1) with the short shaft 2b as the known diameter, five unknowns are combined to form five equation sets, and the installation inclination angle beta of the first laser displacement sensor (2) is calculated and calculated1A value of (d);
step 5-4: for the second laser displacement sensor (4), the installation inclination angle beta of the second laser displacement sensor (4) is obtained by adopting the steps 5-1, 5-2 and 5-32The value of (c).
6. The rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 5, wherein the step 6 specifically comprises:
Step 6-1: the slider bracket (9) is arranged along the y direction2The direction movement is delta L, the distance is read by the grating ruler, and the front and back numerical value variation of the first laser displacement sensor (2) is deltad1The front and back numerical variation of the second laser displacement sensor (4) is delta d2；
Step 6-2: the actual installation deflection angles of the first laser displacement sensor (2) and the second laser displacement sensor (4) are as follows:
Figure FDA0003252026630000081
Figure FDA0003252026630000082
7. the rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 6, wherein the step 7 specifically comprises:
step 7-1: when the first laser displacement sensor (2) is along z4When the inner contour of the roller path of the slide block (3) to be measured is measured in the axial direction, the inner roller path contour obtained by sweeping in the measuring direction is a semiellipse, and a series of inner roller path data are obtained (1x4,1y4,1z4)；
Step 7-2: the least squares fit equation for the ellipse is constructed as:
Figure FDA0003252026630000083
wherein (A) and (B)1x4i,1y4i,1z4i) Profile data of a roller path ROLL1 measured by a first laser displacement sensor (2) and a grating, wherein i is 1,2.. N, and N is the number of collected points;
and 7-3: the partial derivatives are calculated for coefficients A, B, C, D, E in equation (19) as:
Figure FDA0003252026630000084
equation (20) expands to:
Figure FDA0003252026630000085
and 7-4: solving the formula (21) to obtain A, B, C, D and E;
and 7-5: for a general ellipse equation: x is the number of4Roll1 2+Ax4Roll1z4Roll1+Bz4Roll1 2+Cx4Roll1+Dz4Roll1+E＝0(22)，
The coordinate of the central point of the ellipse represented by the formula (22) is the coordinate of the central point of the rolling way ROLL1 in the spatial oblique coordinate system of the first laser displacement sensor (2), and is represented as:
Figure FDA0003252026630000091
And 7-6: the center point coordinate (x) of the roller path ROLL1 under the spatial oblique coordinate system of the first laser displacement sensor (2)4Roll1,y4Roll1,z4Roll1) Converted into the coordinate (x) of the center point of the raceway ROLL2 under the space rectangular coordinate system of the first laser displacement sensor (2)3Roll1,y3Roll1,z3Roll1) The following relationship exists between the two:
x3Roll1＝x4Roll1-z4Roll1sinβ1
y3Roll1＝y4Roll1＝0
z3Roll1＝z4Roll1cosβ1 (24)
and 7-7: the central point coordinate (x) of the roller path ROLL1 under the space rectangular coordinate system of the first laser displacement sensor (2)3Roll1,y3Roll1,z3Roll1) The central point coordinate (x) of the roller path ROLL1 under a space rectangular coordinate system formed by a displacement sensor system is converted into2Roll1,y2Roll1,z2Roll1) The following relationship exists between the two:
x2Roll1＝x20Roll1+x3Roll1sinα1
y2Roll1＝y20Roll1+y3Roll1cosα1
z2Roll1＝z20Roll1+z3Roll1 (25)
wherein (x)20Roll1,y20Roll1,z20Roll1) The coordinate value, x, of the origin of the space rectangular coordinate system of the first laser displacement sensor (2) under the displacement sensor system forming space rectangular coordinate system20Roll1Read by a motor encoder, y20Roll1、z20Roll1Reading by a grating ruler; at this point, the coordinate of the center point of the roller path ROLL1 is fitted from the spatial oblique coordinate system (x) of the first laser displacement sensor (2)4Roll1,y4Roll1,z4Roll1) To a displacement sensor system to form a space rectangular coordinate system (x)2Roll1,y2Roll1,z2Roll1) The conversion of (1);
and 7-8: for the second laser displacement sensor (4), the steps from 7-1 to 7-7 are also adopted to obtain the raceway center point coordinate (x) of the raceway ROLL2 of the other raceway ROLL2 of the slide block (3) to be detected under the rectangular coordinate system of the displacement sensor system composition space 2Roll2,y2Roll2,z2Roll2)。
8. The rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 7, wherein the step 8 specifically comprises:
step 8-1: for the rolling way ROLL1, a sliding block (3) to be detected is fixed on a sliding block bracket (9), the sliding block bracket (9) is moved, when the first laser displacement sensor (2) just can collect the rolling way data in the sliding block (3) to be detected, the position is marked as position 1, the first laser displacement sensor (2) sweeps the rolling way in the sliding block, the swept rolling way ROLL1 data point of the sliding block (3) to be detected is fitted with the rolling way central point coordinate, and the rolling way central point coordinate is matched from a spatial oblique coordinate system o of the first laser displacement sensor (2)4-x4y4z4Space rectangular coordinate system o formed by transforming to displacement sensor system2-x2y2z2Obtaining the rolling path ROLL at the position 11 section of fitting raceway center point in displacement sensor system to form a space rectangular coordinate system o2-x2y2z2Coordinates of (A), (B) and (C)1x2Roll1,1y2Roll1,1z2Roll1)；
Step 8-2: moving the slider bracket (9) to different positions K, wherein the distance between adjacent positions is 1CM, according to the step 8-1, the rolling path ROLL1 is at different positions, and the fitting rolling path central point of the section forms a space rectangular coordinate system o in the displacement sensor system2-x2y2z2Coordinates of (A), (B) and (C)kx2Roll1,ky2Roll1,kz2Roll1)，k＝1,2...10；
Step 8-3: fitting a straight line equation of the central axis of the rolling way ROLL1 according to the data points obtained in the step 8-2, wherein the central axis of the rolling way ROLL1 passes through x 2o2z2And (3) surface, the space linear equation can be simplified as follows:
Figure FDA0003252026630000101
wherein (x)01,y01,z01) At any point along the central axis of the raceway rol 1,
Figure FDA0003252026630000102
the normal vector of the central axis of the rolling path ROLL1 is that the radial section of the rolling path ROLL1 is in an elliptic arc shape, the central axis of the rolling path ROLL1 represents a straight line consisting of the elliptic arc centers of different radial sections of the rolling path ROLL1, y01＝0，x01,z01,mRoll1,nRoll1Is a required parameter;
the linear equation is simplified into:
Figure FDA0003252026630000103
in matrix form:
Figure FDA0003252026630000104
the Kth point equation is:
Figure FDA0003252026630000105
the equation for the parallel 10 points is:
Figure FDA0003252026630000106
least square fitting:
Figure FDA0003252026630000107
simplifying into the following steps:
Figure FDA0003252026630000111
m can be obtained by solving the matrixRoll1,nRoll1,x01,y01The direction vector of the central axis of the rolling way ROLL1 is obtained as the parameters of a linear equation
Figure FDA0003252026630000112
Step 8-4: for the central axis of the rolling way ROLL2, the step 8-1 to the step 8-3 are also applied to obtain the direction vector of the central axis of the rolling way ROLL2 as
Figure FDA0003252026630000113
9. The rolling linear guide pair slider profile pitch diameter measurement algorithm according to claim 8, characterized in that step 9: according to the direction vectors of the central axes of the rolling paths ROLL1 and ROLL2 fitted in the step 8, the distance between the rolling path ROLL1 and the central axis of the rolling path ROLL2 is solved, namely the pitch diameter of the sliding block rolling path, and the distance between the two central axes is as follows:
Figure FDA0003252026630000114
wherein
Figure FDA0003252026630000115
Are respectively the direction vectors of the central axes of the rolling way ROLL1 and the rolling way ROLL2,
Figure FDA0003252026630000116
Figure FDA0003252026630000117
Is the direction of the connecting line of any point on the two straight lines,
Figure FDA0003252026630000118
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