阅读说明：本技术 一种用于六方轴直线度检测系统的误差补偿方法 (Error compensation method for hexagonal axis straightness detection system ) 是由 周娟 黄宇杭 于 2020-05-27 设计创作，主要内容包括：本发明公开了一种用于六方轴直线度检测系统的气动三爪卡盘偏心误差补偿方法。针对六方轴直线度检测系统中气动三爪卡盘偏心所产生的回转误差,分为测量和补偿两个阶段；采用六方轴相对面相减原理获取在三组相对面方向上的偏移量；在测量回转误差过程中系统考虑轴自身弯曲所产生的挠度误差,并据此作为回转误差补偿方程中的测量量进行修正,从而构建误差补偿模型。(The invention discloses a pneumatic three-jaw chuck eccentricity error compensation method for a hexagonal axis straightness detection system. Aiming at the rotation error generated by the eccentricity of a pneumatic three-jaw chuck in a hexagonal axis straightness detection system, the method comprises two stages of measurement and compensation; acquiring offsets in the directions of the three groups of opposite surfaces by adopting a hexagonal axis opposite surface subtraction principle; in the process of measuring the rotation error, the deflection error generated by the bending of the shaft per se is taken into consideration by the system, and is used as the measurement quantity in the rotation error compensation equation for correction, so that an error compensation model is constructed.)

1. An error compensation method for a hexagonal straightness detection system is characterized by comprising the following steps:

(1) selecting a calibration hexagonal shaft with the length of S, and loading the calibration hexagonal shaft to the hexagonal shaft straightness detection system;

(2) measuring at an actual measuring point C which is on the calibrated hexagonal shaft and has a distance of m with the left pneumatic three-jaw chuck to obtain the offset (C) in the direction of three groups of opposite surfaces of the calibrated hexagonal shaft_α，C_β，C_γ) And converting it into the axis vector coordinate (x) of point C_c,y_c) (ii) a Defining the ideal measuring point of the calibrated hexagonal axis when the deflection error of the point C is 0 as C ', and setting the axis vector coordinate of the ideal measuring point C ' as (x '_c,y'_c) The deflection error of point C relative to point C' is (Δ x)_c,Δy_c) Then there is (x)_c,y_c)＝(x'_c+Δx_c,y'_c+Δy_c)；

Measuring an actual measurement point D with the distance of m from the pneumatic three-jaw chuck on the right side on the calibrated hexagonal shaft to obtain an axis vector coordinate (x) of the point D_d,y_d) (ii) a Setting the calibration hexagonal axis at DAn ideal measurement point D 'is defined as D' when the point deflection error is 0, and the axis vector coordinate of the ideal measurement point D 'is (x'_d,y'_d) The deflection error of point D relative to point D' is (Δ x)_d,Δy_d) Then there is (x)_d,y_d)＝(x'_d+Δx_d,y'_d+Δy_d)；

(3) Detaching the calibrated hexagonal shaft from the hexagonal shaft straightness detection system, rotating the calibrated hexagonal shaft by 180 degrees, and reloading the calibrated hexagonal shaft straightness detection system;

(4) measuring the point C rotated by 180 degrees to obtain the axis vector coordinate (x) of the actual measurement point C'_c,y”_c) Then there is (x) "_c,y”_c)＝(x'_c-Δx_c,y'_c-Δy_c)；

Measuring the D point rotated by 180 degrees to obtain the axis vector coordinate (x) of the actual measurement point D'_d,y”_d) Then there is (x) "_d,y”_d)＝(x'_d-Δx_d,y'_d-Δy_d)；

(5) Obtaining coordinates of ideal measuring points C ' and D ' from (2), (3) and (4), wherein the coordinates of the point C ' are:

and the coordinates of point D' are:

(6) according to the coordinates of the ideal measuring points C 'and D', determining a space straight line equation connecting C 'and D' as follows:

the ideal clamping point a ' of the left pneumatic three-jaw chuck on the calibrated hexagonal axis when the deflection error is 0 and the ideal clamping point B ' of the right pneumatic three-jaw chuck on the calibrated hexagonal axis are also on the spatial straight line, wherein the coordinates of the point a ' are as follows:

and the coordinates of point B' are:

(7) substituting the Z-axis coordinate of any point N to be measured between the point A 'and the point B' into the space linear equation to obtain the coordinate (X) of the point N_n,Y_n) And converting it into a rotation error offset (N) in the direction of each opposite surface of the calibrated hexagonal axis_α，N_β，N_γ)；

(8) The calibrated hexagonal shaft is detached, the hexagonal shaft to be measured is loaded to the hexagonal shaft linearity detection system, and the offset (P ') of the detected point P in the direction of each opposite surface of the hexagonal shaft to be measured is determined for any point P to be measured on the hexagonal shaft to be measured'_α，P'_β，P'_γ) Subtracting the amount of slewing error offset (P) calculated from (7)_α，P_β，P_γ) The result is the measurement result after error compensation;

(9) a plurality of points are taken on the hexagonal axis to be detected for detection, and the coordinates (x) of the plurality of points are obtained after error compensation and conversion are carried out according to the step (8)_j,y_j) N, · j ═ 1, 2; and calculating corresponding straightness errors by obtaining a reference axis and shaft curve fitting, thereby determining the maximum deflection position required by the straightening work of the shaft and the axial position corresponding to the measuring point.

2. The error compensation method for the hexagonal-axis straightness detection system according to claim 1, wherein a hexagonal axis with the best available straightness is selected as a calibration axis, six outer surfaces of the calibration axis are sequentially marked according to the sequence of the labels 1-6, a capacitive grating micrometer is arranged at a position m away from the two ends of the pneumatic three-jaw chuck, the left micrometer is marked as L, the right micrometer is marked as R, and the rest capacitive grating micrometers are equidistantly distributed in the middle of L, R; controlling the pneumatic three-jaw chucks at the two ends to clamp the calibration hexagonal shaft, marking the upward surface of the calibration hexagonal shaft as U before the computer starts to test, and marking the upward surface of the pneumatic three-jaw chucks at the two ends as U; the pneumatic three-jaw chuck clamps the calibration hexagonal shaft to rotate for a circle for measurement; when the pneumatic three-jaw chuck clamps the calibration hexagonal shaft to rotate for one circle for carrying out deflection measurement, the surface of the pneumatic three-jaw chuck structure marked as U and facing upwards is required to be kept consistent in the front and back rotating directions.

3. The error compensation method for the straightness detection system according to claim 2, wherein the calculation method for converting the offset in the direction of each opposite face of the calibrated hexagonal axis into the axis vector coordinate is as follows:

wherein i is the reference number of six outer surfaces of the hexagonal shaft, i is 1,2,3,_i,i+3a set of offsets for the hexagonal axis relative to the outer surfaces i and i +3,_a,_b,_cis an offset as claimed in claim 1, i.e._i,i+3Offset on three groups of opposite surfaces corresponding to the three groups of opposite surfaces on the abc three-axis coordinate system, phi is an axis vector under a rectangular coordinate system, and the included angle between the theta axis vector and the x axis.

4. The error compensation method for a hexagonal straightness detection system of claim 3, wherein the reference axis is calculated by:

wherein N is the number of the measuring points, (x)_j,y_j) (j ═ 1,2,. N) are the coordinates of the N measurement points.

5. The error compensation method for a hexagonal-axis straightness detection system of claim 4, wherein the axis curve fitting calculation is:

y(x)＝β₀+β₁x+β₂x²…+β_nxⁿ

where y (x) is an axis curve fitting function, and β k (k ═ 1,2.., n) is an undetermined coefficient of the axis curve expression.

6. The utility model provides a hexagonal axle straightness accuracy detecting system, is including the pneumatic three-jaw chuck that is used for the centre gripping hexagonal axle, drives through synchronous pulley pneumatic three-jaw chuck pivoted motor, and with the capacitive grid micrometer of hexagonal axle indirect contact still includes chuck and proximity switch that has six draw-in grooves, its characterized in that, whenever the draw-in groove is close during the proximity switch, the capacitive grid micrometer accepts detection signal and reads and transmit data, thereby realizes right the rotation detection of hexagonal axle straightness accuracy.

Technical Field

The invention relates to the technical field of straightness measurement, in particular to an error compensation method for a hexagonal axis straightness detection system.

Background

The pneumatic three-jaw chuck is a mechanical device for positioning and clamping a workpiece by utilizing radial movement of movable clamping jaws uniformly distributed on a chuck body, and comprises a chuck, the movable clamping jaws, an air pressure gyrator, an electric control part and other connecting components. The workpiece is clamped by the pneumatic three-jaw chuck, the mounting process is simple, convenient and labor-saving, automatic centering can be realized, and the clamping force is stable and adjustable. With the changing market demand, the automatic centering precision requirement of some high-precision equipment on the pneumatic three-jaw chuck is relatively increased. However, in actual measurement, factors such as the surface structure of the clamped workpiece, the rotating speed of the driving motor and the like cause the intersection point of the action lines of the three movable clamping jaws to deviate, namely, the clamping center point deviates from the ideal center point, so that a rotation error is generated. Therefore, the compensation of the rotation error of the pneumatic three-grab chuck is an important factor for improving the measurement accuracy of the straightness of the hexagonal axis.

Error compensation is an important part of instrument design and machining. For the rotation error of the shaft, a common error compensation method is to analyze error sources and analyze the influence form of each error on a measurement result; secondly, error correction is obtained in a certain mode, a corresponding mathematical model is established, error difference is eliminated from the measured data, and the purpose of improving the measurement precision is achieved. The method is mainly applied to the field of error measurement such as roundness, cylindricity and rotation error of a circular shaft, a sensor is placed at different positions by adopting a reverse method, repeated measurement is carried out on the same to-be-measured value simultaneously or sequentially, error correction quantity is solved according to a built mathematical model by utilizing a determined position relation and the same or known measurement conditions according to multiple measurement results, and error compensation is carried out on measurement data. However, as the position of the sensor changes, multiple or multiple measurements are required, which increases computational and measurement complexity and is not suitable for real-time compensation in dynamic models. Most of the traditional methods are based on a round axis to obtain error correction, and the prior researches lack the measurement and error compensation of rotation errors of an axis with irregular surface. Therefore, how to provide a method for compensating the eccentricity error of the pneumatic three-jaw chuck for a six-axis linearity detection system becomes a problem to be solved by those skilled in the art.

Disclosure of Invention

In view of the above problems, the present invention provides a pneumatic three-jaw chuck eccentricity error compensation method for a hexagonal axis straightness detection system, which compensates a gyration error caused by eccentricity of the pneumatic three-jaw chuck in a process of measuring the hexagonal axis straightness, and can detect and compensate offset errors of each measurement point in three sets of opposite surface directions in real time by using a hexagonal axis opposite surface subtraction method, and can eliminate the influence of a deflection error by using a reversal method of rotating the hexagonal axis, improve the compensation accuracy of an error compensation model, and improve the measurement accuracy of the hexagonal axis straightness.

The invention provides an error compensation method for a hexagonal axis straightness detection system in a first aspect, which comprises the following steps:

(1) selecting a calibration hexagonal shaft with the length of S, and loading the calibration hexagonal shaft to the hexagonal shaft straightness detection system;

(2) measuring at an actual measuring point C which is on the calibrated hexagonal shaft and has a distance of m with the left pneumatic three-jaw chuck to obtain the offset (C) in the direction of three groups of opposite surfaces of the calibrated hexagonal shaft_α，C_β，C_γ) And converted into the axis vector coordinate (x) of the point C_c,y_c) (ii) a Defining an ideal measuring point of the calibrated hexagonal axis when the deflection error of the point C is 0 as C ', and setting the axis vector coordinate of the ideal measuring point C ' as (x '_c,y'_c) The deflection error of point C relative to point C' is (Δ x)_c,Δy_c) Then there is (x)_c,y_c)＝(x'_c+Δx_c,y'_c+Δy_c)；

Measuring an actual measurement point D with the distance of m from the pneumatic three-jaw chuck on the right side on the calibration hexagonal shaft to obtain an axis vector coordinate (x) of the point D_d,y_d) (ii) a Defining the ideal measuring point of the calibrated hexagonal axis when the deflection error of the point D is 0 as D ', and setting the axis vector coordinate of the ideal measuring point D ' as (x '_d,y'_d) The deflection error of point D relative to point D' is (Δ x)_d,Δy_d) Then there is (x)_d,y_d)＝(x'_d+Δx_d,y'_d+Δy_d)；

(3) Detaching the calibrated hexagonal shaft from the hexagonal shaft straightness detection system, rotating the calibrated hexagonal shaft by 180 degrees, and reloading the calibrated hexagonal shaft straightness detection system;

(4) measuring the point C rotated by 180 degrees to obtain the axis vector coordinate (x) of the actual measurement point C'_c,y"_c) Then there is (x) "_c,y"_c)＝(x'_c-Δx_c,y'_c-Δy_c)；

Measuring the D point rotated by 180 degrees to obtain the axis vector coordinate (x) of the actual measurement point D'_d,y"_d) Then there is (x) "_d,y"_d)＝(x'_d-Δx_d,y'_d-Δy_d)；

(5) Obtaining coordinates of ideal measuring points C ' and D ' from (2), (3) and (4), wherein the coordinates of the point C ' are:

and the coordinates of point D' are:

(6) according to the coordinates of the ideal measuring points C 'and D', determining a space straight line equation connecting C 'and D' as follows:

the ideal clamping point a ' of the left pneumatic three-jaw chuck on the calibrated hexagonal axis when the deflection error is 0 and the ideal clamping point B ' of the right pneumatic three-jaw chuck on the calibrated hexagonal axis are also on the spatial straight line, wherein the coordinates of the point a ' are as follows:

and the coordinates of point B' are:

(7) substituting the Z-axis coordinate of any point N to be measured between the point A 'and the point B' into the space straight line equation to obtain the coordinate (X) of the point N_n,Y_n) And converting it into a rotation error offset (N) in the direction of each opposite surface of the calibrated hexagonal axis_α，N_β，N_γ)；

(8) Unloading the calibrated hexagonal shaft, loading the hexagonal shaft to be tested to the hexagonal shaft straightness detection system, and for any point P to be tested on the hexagonal shaft straightness detection system,the offset (P ') of the detected point P in the direction of each opposite surface of the to-be-measured six-direction shaft'_α，P′_β，P′_γ) Subtracting the amount of slewing error offset (P) calculated from (7)_α，P_β， P_γ) The result is the measurement result after error compensation;

(9) a plurality of points are taken on the hexagonal axis to be detected for detection, and the coordinates (x) of the plurality of points are obtained after error compensation and conversion are carried out according to the step (8)_j,y_j) N, · j ═ 1, 2; and calculating corresponding straightness errors by obtaining the fitting of a reference axis and a shaft curve, thereby determining the maximum deflection position required by the straightening work of the shaft and the axial position corresponding to the measuring point of the maximum deflection position.

Furthermore, selecting an available hexagonal shaft with the best straightness as a calibration shaft, sequentially marking six outer surfaces of the calibration shaft according to the sequence of the labels 1-6, respectively arranging a capacitive grating micrometer at a position m away from the pneumatic three-jaw chucks at two ends, marking a left-side micrometer as L, marking a right-side micrometer as R, and equidistantly distributing the rest capacitive grating micrometers in the middle of L, R; controlling the pneumatic three-jaw chucks at the two ends to clamp and calibrate the hexagonal shaft, marking the upward surface of the calibrated hexagonal shaft as U before the computer starts to test, and marking the upward surface of the pneumatic three-jaw chuck at the two ends as U; the pneumatic three-jaw chuck clamps the calibration hexagonal shaft to rotate for a circle for measurement; when the pneumatic three-jaw chuck clamps the calibrated hexagonal shaft to rotate for one circle for measuring deflection, the surface of the pneumatic three-jaw chuck structure marked as U and facing upwards is required to be kept consistent in the front and back rotating directions.

Furthermore, the calculation method for converting the offset in the direction of each opposite surface of the calibrated hexagonal axis into the axis vector coordinate is as follows:

wherein i is the index of six outer surfaces of the hexagonal axis, i is 1,2,3, i, i +3 is the offset of a group of hexagonal axes relative to the outer surfaces i and i +3, a, b, c are the offsets described in claim 1, i, i +3 corresponds to the offsets of three groups of opposite surfaces on the three-axis abc coordinate system, Φ is the axial vector of the rectangular coordinate system, and the included angle between the theta axial vector and the x axis.

Further, the reference axis is calculated by:

wherein N is the number of the measuring points, (x)_j,y_j) (j ═ 1,2,. N) are the coordinates of the N measurement points.

Further, the axis curve fitting is calculated by:

y(x)＝β₀+β₁x+β₂x²·+β_nxⁿ

the invention provides a hexagonal axis straightness detection system which comprises a pneumatic three-jaw chuck for clamping a hexagonal axis, a motor for driving the pneumatic three-jaw chuck to rotate through a synchronous pulley, a capacitive micrometer indirectly contacted with the hexagonal axis, a chuck with six clamping grooves and a proximity switch, wherein when the clamping grooves are close to the proximity switch, the capacitive micrometer receives a detection signal to read and is also close to the proximity switch

And transmitting data so as to realize rotation detection of the straightness of the hexagonal axis.

The technical scheme provided by the invention has the beneficial effects that:

(1) aiming at the process of detecting the straightness of the hexagonal axis, the error influence generated by indirect contact between the capacitive grating micrometer and the hexagonal axis can be eliminated by adopting the opposite surface subtraction method, the offset of each measuring point of the hexagonal axis in the directions of the three groups of opposite surfaces can be detected in real time, and the offset is subjected to real-time error compensation.

(2) Aiming at the problem of eccentricity of the pneumatic three-jaw chuck, the traditional error compensation method only compensates the rotation error at the position of the movable clamping jaw, and the method utilizes a reverse method to eliminate the influence of deflection error generated by self bending of the shaft, thereby improving the compensation precision of an error compensation model and improving the measurement precision of the straightness of the hexagonal shaft.

(3) The traditional reversal method eliminates the deflection error influence of the circular shaft by changing the position of the sensor, and the reversal method provided by the invention adopts the position of the manual rotating shaft to perform rotation detection on the hexagonal shaft with an irregular surface, so that the operation is simple, the realization is easy, and the deflection error influence can be eliminated.

(4) The invention utilizes the existing hexagonal axis straightening machine equipment to carry out rotation error compensation on the non-full-circle pneumatic three-jaw chuck, is beneficial to subsequent evaluation of the straightness error of the hexagonal axis and the straightening work of the axis, and is convenient for practical engineering application.

The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.

Drawings

FIG. 1 is a schematic diagram of a pneumatic three-jaw chuck clamping hexagonal shaft mechanical structure in a process of measuring straightness according to the invention;

FIG. 2 is a schematic diagram illustrating the principle of detecting the straightness of the hexagonal axis according to the present invention;

FIG. 3 is a schematic illustration of a hexagonal axis cross-sectional offset provided by the present invention;

FIG. 4 is a schematic view of a rotation error analysis provided by the present invention;

FIG. 5 is a schematic diagram of the reverse method for eliminating deflection error analysis provided by the present invention;

FIG. 6 is a schematic diagram of the measurement and evaluation process analysis of the hexagonal straightness error provided by the present invention.

In the figure: 1. the device comprises a hexagonal shaft, 2 a movable clamping jaw, 3 a pneumatic three-jaw chuck, 4 a rotary driving motor, 5 a rotary chuck, 6 a capacitive grid micrometer measuring head, 7 and a capacitive grid micrometer.

Detailed Description

The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.

The invention provides a pneumatic three-jaw chuck eccentricity error compensation method for a hexagonal axis straightness detection system. Aiming at the rotation error generated by the eccentricity of a pneumatic three-jaw chuck in a hexagonal axis straightness detection system, the method comprises two stages of measurement and compensation; acquiring offsets in the directions of the three groups of opposite surfaces by adopting a hexagonal axis opposite surface subtraction principle; in the process of measuring the rotation error, the deflection error generated by the bending of the shaft per se is taken into consideration by the system, and is used as the measurement quantity in the rotation error compensation equation for correction, so that an error compensation model is constructed.

Firstly, the scheme adopts the opposite face subtraction method, so that the error influence caused by the indirect contact between the capacitance-grid micrometer and the hexagonal shaft can be eliminated, the offset of each measuring point of the hexagonal shaft in the directions of three groups of opposite faces can be detected in real time, and real-time error compensation is carried out. And secondly, the influence of deflection errors can be eliminated by utilizing an inverse method for rotating the hexagonal shaft, the compensation precision of an error compensation model is improved, and the straightness measurement precision of the hexagonal shaft is improved. In addition, the existing hexagonal axis straightener equipment is applied to compensate the rotation error of the non-full-circle pneumatic three-jaw chuck, and the practical engineering application is facilitated.

The following describes the specific implementation process of the present invention in detail, including the following steps:

step 1, designing a linearity detection experiment aiming at a calibrated hexagonal shaft, collecting offsets of actual measurement points close to the positions of pneumatic three-jaw chucks at two ends on three groups of opposite surfaces of the hexagonal shaft, and synthesizing an axis vector (x, y) under a rectangular coordinate system through coordinate conversion for calculating a space coordinate of a subsequent measurement point.

According to one embodiment of the invention, before a hexagonal-axis straightness detection experiment is designed, a plurality of hexagonal axes are obtained from a production site and compared, one hexagonal axis with better straightness is selected as a calibration axis, and if the total length is S, six outer surfaces are sequentially marked according to the sequence of the labels 1-6; and (3) respectively arranging a capacitive grid micrometer at a position 50mm away from the pneumatic three-jaw chucks at the two ends, marking the left-side micrometer as L, marking the right-side micrometer as R, equidistantly distributing the rest capacitive grid micrometers in the middle of L, R, marking the upward surface of the hexagonal shaft as U, and marking the upward surface of the pneumatic three-jaw chuck at the two ends as U. When the pneumatic three-jaw chuck clamps the hexagonal shaft to rotate for one circle for deflection measurement, the surface of the pneumatic three-jaw chuck structure marked as U and facing upwards is required to be kept consistent in the front and back directions of rotation.

As shown in fig. 1, in actual measurement, the pneumatic three-jaw chuck 3 is controlled to enable the movable clamping jaw 2 to clamp the hexagonal shaft 1, after the movable clamping jaw is stabilized, the rotary driving motor 4 is controlled to drive the pneumatic three-jaw chuck 3 to rotate through a synchronous belt pulley fixed with the main shaft, and the capacitive micrometer 7 is indirectly contacted with the hexagonal shaft 1; the chuck 5 is provided with 6 clamping grooves, and when the clamping grooves pass through the proximity switch, the capacitive grating micrometer 7 receives detection signals to read and transmit data, so that the rotation detection of the straightness of the hexagonal axis is realized.

The mutual positional relationship before and after the hexagonal axis is rotated by 180 ° is shown in fig. 2, and a zy coordinate system is established with the axial direction and the deflection direction as references. The measured six external surface capacitance grating micrometering values are { V1, V2, V3, V4, V5, V6}, and analysis is carried out by taking a group of opposite surface data { V1, V4} as an example, and the calculation mode is as follows:

where M is the distance from the zero point of the capacitance-gate micrometer to the z-axis,_1,4the offset of a certain measuring point of the hexagonal axis on the opposite surfaces 1 and 4 is shown, and r is half of the distance between the two opposite surfaces.

The process of synthesizing the axis vector by the offset in the present invention is described in detail with reference to fig. 3.

The offset and the axis vector can be mutually converted, and when x and y of the axis vector P at the section of the measuring point are obtained, the offset can be converted into an offset from an abc three-axis coordinate system according to a geometric relationship_a、_b、_cAs shown in FIG. 3 (a); when three phases are obtainedOffset on opposite face_a、_b、_cAlternatively, the x and y coordinates may be converted to an xy rectangular coordinate system, as shown in fig. 3 (b).

And converting the coordinates of the three output groups of offset into an axis vector. The point O represents the origin of coordinates, which represents the ideal axial center point, and the point P represents the actual center of the curved cross-section, two coordinate systems are established, one is an xy rectangular coordinate system, the other is an abc three-axis coordinate system established with reference to three sets of opposite surfaces of the ideal hexagonal axial cross-section, and the y-axis and the a-axis of the two coordinate systems coincide, as shown in fig. 3 (b). According to the geometrical relationship, the following are included in the rectangular coordinate system:

transformed by a generalized inverse matrix:

wherein, the axis P can be (x, y) and (b)_a,_b,_c) Two sets of coordinates represent the distance from the axis P to the ideal axis point OThe angle of the vector with the positive x-axis direction is represented by θ, as shown in fig. 3 (b).

Step 2, analyzing the cross section where the measuring point is located, when the deflection error does not exist in the hexagonal axis, defining a space vector (x ', y') and a deflection error vector (delta x, delta y) of the ideal measuring point, and calculating a space vector (x '+ delta x, y' + delta y) of the actual measuring point; and eliminating the influence of the self-deflection error of the shaft by utilizing a reverse method and a geometric relation, and calculating the coordinate value of the space vector of the ideal measuring point.

The process for eliminating the influence of the deflection error by using the reverse method provided by the invention is described in detail by combining fig. 4 and fig. 5.

According to the hexagonal straightness detection experiment designed in the step 1, the actual measurement point at the left micrometer L is assumed to be C, the ideal measurement point is assumed to be C ', the actual measurement point at the right micrometer R is assumed to be D, and the ideal measurement points are D', A, A ', B and B' and are distributed at the movable clamping jaws; the dotted line AB is the rotation center line when the movable clamping jaws at the two ends clamp the hexagonal shaft and is parallel to the z-axis, the spatial straight line a 'B' is the clamping center line of the movable clamping jaws at the two ends, and the curve a 'B' is the actual shape center line of the hexagonal shaft, i.e., the deflection error caused by the bending of the shaft itself exists, as shown in fig. 4. In order to show the intuitiveness of eliminating deflection errors by a reverse method, a rotation center line AB is placed above a z axis; in order to facilitate the subsequent geometric analysis of the measuring points, the rotation center line AB is coincided with the z axis, the coordinates of each measuring point on the x axis and the y axis of the space coordinate system are 0, and the coordinate on the z axis is defined as the position of the set capacitance grid micrometer.

In this embodiment, for the inverse method provided by the present invention, taking the analysis of the cross section of the actual measurement point C as an example, and because the analysis is that the cross section of the measurement point C is located, the coordinate on the z axis is equal, so the x axis coordinate and the y axis coordinate are discussed first, the z axis coordinate is discussed during the subsequent space straight line fitting, and the right actual measurement point D can be obtained similarly, including the following steps:

(1) analyzing the section of the actual measurement point C, wherein the end point A is coincident with the origin of coordinates O, and when the deflection error is generated due to the bending of the shaft, the actual measurement result is

A vector; when the shaft has no bending, the deflection error is zero, and the measuring point is an ideal measuring point CAs a deflection vector for the left side measurement point, assume C '(x'_C, y′_C)，

The actual measurement point C coordinate is ((x'_C+Δx_C,y′_C+Δy_C) As shown in fig. 5 (a);

(2) after completing the first rotation detection of the straightness accuracy according to the experiment designed in the step 1 and recording the axial vector data of the measuring points at two sides, stopping the detection, keeping the pneumatic three-jaw chucks at two ends still, controlling the movable clamping jaws to dismount the hexagonal shaft, manually rotating 180 degrees, and paying attention to that the outer surface of the hexagonal shaft marked as U faces downwards at the moment;

(3) the actual measurement point C is changed into C' after being rotated by 180 DEG, and the deflection vector is changed at the momentBecome into

Performing a second rotation detection experiment of straightness, recording data, and recording

Then the C "coordinate is (x'_c'-Δx_c，y'_c'-Δy_c) As shown in fig. 5 (b);

(4) the coordinates of the ideal measuring point C' can be obtained according to the geometric relationship

(5) The coordinates of the ideal right measuring point D' obtained by the same method are

The steps are used for analyzing the cross section where the actual measuring point is located to obtain the space coordinate of the ideal measuring point, and the purpose is to describe the process of eliminating the influence of the self-deflection error of the shaft by a reverse method in detail. According to the hexagonal axis straightness detection experiment designed in the step 1, the offset of C, C 'and D, D' points on three opposite surfaces can be directly obtained, and the space coordinates of ideal measuring points C 'and D' can be obtained by synthesizing axis vectors through coordinate conversion.

And 3, determining a space straight line according to the space vector of the ideal measuring point, and collecting the space vector and the rotation error vector which are positioned at the positions of the pneumatic three-jaw chucks at the two ends on the space straight line.

Determining a space straight line according to the space coordinates of the ideal measuring points C 'and D' obtained in the step 2, wherein the calculation mode is as follows:

wherein, A ' and B ' are also on the space straight line, and the coordinate of the point A ' is known as:

the coordinates of the B' point are:

the rotation error vector at the movable clamping jaw can be obtained according to the space coordinates of A' and B

And 4, collecting the positions z of the capacitance grid micrometer at other actual measurement points, substituting the positions z into a space linear equation, calculating the (x, y) of each actual measurement point, converting the coordinates into the offset of each measurement point on three groups of opposite surfaces under a three-axis coordinate system, and taking the offset as the offset generated by the rotation error at the measurement point.

In the step, six capacitance grid micrometers are equidistantly arranged between the capacitance grid micrometers L and R, and the position of the jth capacitance grid micrometer is marked as z_j(j ═ 1,2.. 6), namely the z-axis coordinate of the measuring point in the space coordinate system, and the z-axis coordinate is substituted into the space linear equation to obtain the j-th measuring point in z ═ z_j(j ═ 1,2,. 6) coordinates x at the section plane_j、y_jThen x is added_j、y_jThree groups are obtained according to the coordinate conversion direction abc three-axis coordinate system conversion described in the step 1Amount of offset on opposite sides_a′_j、_b′_j、_c′_jAnd accordingly, the offset is used as the rotary error offset generated at the jth measuring point due to the rotary error of the pneumatic three-jaw chuck.

And 5, designing a straightness detection experiment aiming at the common hexagonal axis, collecting the offset of each actual measurement point on three groups of opposite surfaces, subtracting the offset generated due to the rotation error, and carrying out coordinate conversion to synthesize an axis vector (delta x ', delta y') under a rectangular coordinate system, namely the space vector of each measurement point after the rotation error is compensated.

After the rotation error is measured and data is recorded according to the step 4, stopping detection, dismounting the calibration shaft, selecting other common hexagonal shafts to perform a linearity detection experiment, and obtaining the offset of the jth measuring point on the three groups of opposite surfaces_aj、_bj、_cjIn this case, j is 1,2.. and 8, and the rotation error offset obtained in step 4 is subtracted, and the calculation method is as follows:

wherein, Delta_aj、Δ_bj、Δ_cjThe offset of the jth measuring point on the three opposite surfaces after the rotation error is compensated for can be converted into z-z of the jth measuring point_j(j ═ 1,2,. 8) axis vector coordinates (Δ x 'in cross section'_j, Δy′_j)。

And 6, during actual measurement, subtracting the value of the rotation error offset as the output of the error compensation model, namely the output of the error-compensated capacitance grid micrometer.

Obtaining eight measurement point space coordinates (delta x ') after compensation of rotation errors according to the step 5'_j,Δy′_j,z_j) And (j ═ 1,2.., 8), and the output is used as the output of the error-compensated capacitance grid micrometer, so that the linearity of the common hexagonal axis can be reflected by performing space curve fitting subsequently.

And 7, acquiring output data of the plurality of capacitive grating micrometers, and calculating corresponding straightness errors by obtaining a reference axis and axis curve fitting for facilitating subsequent evaluation of the straightness errors of the hexagonal axis and alignment of the axis, so as to determine the maximum deflection position required by the alignment work of the axis and the axial position corresponding to the measuring point of the maximum deflection position.

The measurement and evaluation process of the straightness error of the hexagonal axis in the invention is described in detail with reference to fig. 6. Acquiring output data of a plurality of capacitance grid micrometers according to the step 6, and acquiring coordinates (x) of a plurality of measurement points after error compensation_j,y_j) N, where N is 8, j is 1,2. And setting the linear equation of the reference axis to be estimated as y-rx + s, and estimating r and sAn objective function of

The partial derivatives of r and s are separately calculated and made equal to zero,

and

the calculation method is as follows:

collecting coordinates (x) of a plurality of measurement points according to step 6_j,y_j) J is 1,2, 8, and the undetermined coefficient is set as β_k(k ═ 1,2,. n), fitting a function

y(x)＝β₀+β₁x+β₂x²…+β_nxⁿ

Setting the objective function in the same way

For beta is_k(k ═ 1,2.. times, n) the partial derivative is calculated and made equal to zero, and the undetermined coefficient is calculated as:

so far, the implementation process steps of the invention are finished.

The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.