A sphericity error and smoothness integrated measuring device and measuring method thereof

Abstract

A sphericity error and smoothness integrated measuring device and its measuring method belong to the field of precision measurement technology. In order to solve the synchronous, continuous and high-precision measurement of the sphericity error and smoothness of large-sized balls, the present invention is composed of a base, an air bearing, a laser transmitter, a laser receiver, a bracket, and an air-floating ball to be measured. The air bearing is installed at the center of the base, and the air-floating ball to be measured is placed on the air bearing. The number of laser transmitters and laser receivers is 2, and the number of brackets is 4; the laser transmitter is installed on the bracket, and the bracket is installed on the base. The two laser transmitters are symmetrically placed on both sides of the air-floating ball to be measured; the laser receiver is installed on the bracket, and the bracket is installed on the base. The laser emitted by one laser transmitter is reflected by the air-floating ball to be measured and then received by a laser receiver on the same side, forming a two-way working optical path. The present invention can realize high-precision, non-contact, efficient and convenient integrated measurement of sphericity error and smoothness of large-sized spheres.

Description

Technical Field

[0001] The invention belongs to the technical field of precision measurement, and in particular relates to a sphericity error and smoothness integrated measuring device and a measuring method thereof. Background Art

[0002] In the field of precision engineering measurement technology, the accuracy of the distance between the centers of the regressive reflective spheres in the photogrammetric system will directly affect the accuracy of parameter calibration, and thus affect the accuracy of the photogrammetric system measurement. Among them, the sphericity error of the regressive reflective sphere is the main factor affecting the accuracy of the distance between the centers of the spheres.

[0003] The invention patent with the publication number CN110207615A and the invention name “A device for measuring the optical sphericity of a regressive reflective ball” discloses a technical solution including a regressive reflective ball, a rotating bracket, a light source and an imaging module. When the regressive reflective ball rotates one circle with the axis passing through its own center as the axis driven by the rotating bracket, the image formed by the imaging module will form a closed curve that can reflect the optical sphericity error of the regressive reflective ball, providing an effective, reliable and practical measuring device for the optical sphericity of the regressive reflective ball. However, although the continuous photographing and sampling of the sphere by optical imaging is intuitive, efficient and continuous, if the axis of the sphere is deviated from the central axis of the rotating bracket when the sphere is loaded, the influence caused by the eccentricity and rotation error is difficult to eliminate, and the accuracy of the sphericity error result obtained by the optical imaging method of the whole sphere is bound to be limited. Moreover, the current sphericity measurement method is difficult to achieve synchronous, continuous and high-precision measurement of the sphericity error and smoothness of large-sized balls. Summary of the invention

[0004] The problem to be solved by the present invention is to measure the sphericity error and smoothness of a large-sized ball synchronously, continuously and with high precision, and a sphericity error and smoothness integrated measuring device and a measuring method thereof are proposed.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A sphericity error and smoothness integrated measuring device, comprising a base, an air bearing, a laser transmitter, a laser receiver, a bracket, and an air-floating ball to be measured. The air bearing is installed at the center of the base, and the air-floating ball to be measured is placed on the air bearing. The number of the laser transmitter and the laser receiver is 2, and the number of the bracket is 4;

[0007] The laser transmitter is installed on a bracket, and the bracket is installed on a base. Two laser transmitters are symmetrically placed on both sides of the air floating ball to be tested;

[0008] The laser receiver is installed on the bracket, and the bracket is installed on the base. The laser emitted by a laser transmitter is reflected by the air-floating ball to be measured and then received by a laser receiver on the same side, forming two working light paths.

[0009] Furthermore, the air-floating ball to be tested is carried on the air-floating bearing without gravity and with little friction by high-pressure gas, and rotates freely on the air-floating bearing, and the center of the air-floating ball to be tested always coincides with the center of the air-floating bearing.

[0010] A sphericity error and smoothness integrated measurement method is implemented based on the sphericity error and smoothness integrated measurement device, and comprises the following steps:

[0011] S1. Start a sphericity error and smoothness integrated measuring device, then establish a three-dimensional Cartesian coordinate system based on the plane coordinate system of two sets of working optical paths, with the center of the air-floating ball to be measured as the origin, and perform working optical path jitter error processing;

[0012] S2. Under the condition that the air floating ball to be tested rotates, the laser of the laser transmitter is reflected on the air floating ball to be tested, the position coordinate data of all points on the spherical surface are collected, and the position coordinate data of specific points on the spherical surface are extracted, and then the collected data is processed for control error compensation of the attitude of the air floating ball to be tested;

[0013] S3. Interpolate the position coordinate data of the specific point on the spherical surface after processing in step S2 to obtain an interpolated coordinate data set;

[0014] S4. Calculate the spherical error based on the interpolated coordinate data set obtained in step S3;

[0015] S5. Based on the position coordinate data of all points on the spherical surface obtained in step S2, the spherical surface smoothness is evaluated;

[0016] S6. Based on the interpolated coordinate data set obtained in step S3, a spherical model of the air-floating ball to be tested is constructed.

[0017] Furthermore, the specific implementation method of step S1 includes the following steps:

[0018] S1.1. Pass high pressure gas through the air bearing;

[0019] S1.2. Install the air-floating ball to be tested on the air-floating bearing, control the center of the air-floating bearing to coincide with the center of the air-floating ball to be tested, then turn on the laser transmitter and laser receiver, adjust the height of the laser transmitter and laser receiver, so that the laser is emitted to the equatorial plane of the air-floating ball to be tested, and monitor the position of the laser on the laser receiver plane in real time;

[0020] The plane coordinate systems of the laser points on the two laser receivers are established as follows: and , the coordinates of the marked laser points are and , in the initial state, the recorded laser point position vectors are and A three-dimensional Cartesian coordinate system is established with the center of the sphere as the origin, and the coordinates of the laser point position are transformed into the coordinates of the point on the sphere where the laser is irradiated ;

[0021] S1.3. Set up two working light paths to generate laser point 1 and laser point 2 respectively. By changing the laser emission angle , to adjust the error magnification. When the position of the laser point on the air-floating ball to be measured changes to When the laser point changes distance for:

[0022] ;

[0023] By symmetrically installing two sets of laser transmitters and laser receivers for real-time synchronous sampling, differential error The elimination expression is:

[0024] ;

[0025] in, , For laser point 1 and laser point 2, The position vector at the time of sampling;

[0026] The laser point sampling step is in the nanosecond level, which is continuous and periodic in time. The laser point is expanded by Fourier series to obtain the amplitude and frequency of each level of harmonics. The expression is:

[0027] ;

[0028] in, is the function of coordinate difference value changing with time; are the amplitudes of the sine and cosine terms, respectively; denote the phase angles of the sine and cosine terms respectively; is the frequency; express Subharmonics, from which the amplitude and frequency of each level of harmonics are obtained, and the degree of system jitter is evaluated;

[0029] Then calculate the vector difference value To achieve error compensation of measurement results, the expression is:

[0030] .

[0031] Furthermore, the specific implementation method of step S2 includes the following steps:

[0032] S2.1. Control the measured air-floating ball to rotate evenly, set the specific point as the intersection point generated when the latitude increases by 15° from 0° to 90° and the longitude increases by 15° from 0° to 180° at each latitude, and collect the position coordinate data of all points on the spherical surface during the rotation of the measured air-floating ball, and extract the position coordinate data of the specific point on the spherical surface;

[0033] S2.2. When setting the axis of the air bearing, there is an eccentricity error and a rotation error. The coordinate data directly obtained at this time is a measurement result containing errors. , It is regarded as a first harmonic in time, so the Fourier transform is performed and the expression is:

[0034] ;

[0035] in, is the function of the measurement result with error at a certain angle changing with time, are the amplitudes of the fundamental, sine and cosine terms, respectively, is the angular frequency; express Subharmonics;

[0036] right Offset Processing Elimination ,think It is the mean value of the data sampled during one rotation around the axis, and the first harmonic error caused by the eccentricity is separated, and the expression is:

[0037] ;

[0038] in, , The axis of the air bearing is , Eccentricity error in direction, is the rotation error, The angle of rotation of the air-floating ball to be tested around the axis of the air-floating bearing;

[0039] S2.3. The rotation error is modeled by linear regression analysis, and the rotation error vector is expanded to be expressed as , the expression of the loss function describing the rotation error is obtained as:

[0040] ;

[0041] in, is the loss function of the rotation error, For the The coordinate vectors of the measurement points;

[0042] S2.4. Derivative the formula in step S2.3, let ,get , and then use iterative method to establish S The data evolution model iterates the angle in the gradient direction of the loss function, and the expression is:

[0043] ;

[0044] in, is the model learning rate, is the gradient of the loss function of the measurement error with respect to the rotation angle;

[0045] As the iteration proceeds Improvements are made to achieve accurate compensation of measurement results.

[0046] Furthermore, the specific implementation method of step S3 includes the following steps:

[0047] S3.1. For the position coordinate data of a specific point on the spherical surface collected and processed, first The position coordinate data of a specific point on the spherical surface is converted into the coordinates of a spherical coordinate system with the center of the ball to be measured as the origin. , the expression is:

[0048] ;

[0049] S3.2. Define an interpolation function suitable for the spherical surface characteristics, expressed as:

[0050] ;

[0051] in, is the distance between two test points on the sphere, To adjust the parameters, are two adjacent test points on the sphere; is the nominal radius of the sphere, For test point The azimuth coordinates of For test point The azimuth coordinates of For test point The elevation coordinates of For test point The elevation coordinate of

[0052] S3.3. Solve the coordinates of the spherical points under the set step size and expand all data points. The expression is:

[0053] ;

[0054] in, is the coordinate vector of the point to be interpolated, For the The weight coefficients of adjacent points, For the The distance between two test points on the sphere.

[0055] Furthermore, the specific implementation method of step S4 includes the following steps:

[0056] S4.1. Definitions The distance from the test data point to the center of the sphere The expression is:

[0057] ;

[0058] in, is the distance coordinate of the center of the ball to be measured, For the The elevation coordinates of the test data points, is the elevation coordinate of the center of the ball to be measured, For the The azimuth coordinates of the test data points, is the azimuth coordinate of the center of the ball to be measured;

[0059] S4.2. The expression for defining the spherical error function is:

[0060] ;

[0061] in, For the The distance coordinates of the test data points;

[0062] The spherical error function and the radius of the sphere to be measured Taking partial derivatives and setting them to zero with the coordinates of the center of the ball to be measured, we get the following differential equations:

[0063] ;

[0064] Then the radius of the ball to be measured is obtained by numerically solving the above formula and the coordinates of the center of the ball to be measured , and calculate the sphericity error , the expression is:

[0065] .

[0066] Furthermore, the specific implementation method of step S5 is to process the position coordinate data of all points on the spherical surface collected in step S2 to evaluate the surface finish of the air floating ball to be tested, and the expression is:

[0067] ;

[0068] in, is the surface finish of the air float ball to be tested, for N The average of the vector difference values ​​of the smoothness test points.

[0069] Furthermore, the specific implementation method of step S6 includes the following steps:

[0070] S6.1. Define a neural network for processing point cloud data, which is a three-layer neural network. The first layer is a feature extraction layer. After the obtained point data is input, the features of the point set are extracted. The expression is:

[0071] ;

[0072] in, is the activation function, are the weight matrix and bias vector of the first layer respectively, and the input data is the coordinate vector of multiple points uniformly on the sphere obtained by interpolation. , is the output of layer 1;

[0073] The second layer is the feature aggregation layer. The input data of the first layer is input into the second layer, local features are aggregated, and the output features of the second layer are obtained using the maximum pooling operation. , the expression is:

[0074] ;

[0075] The third layer is the feature connection layer. The data output from the second layer is connected and fused with the coordinate data of each point through the third layer to complete the spherical digital modeling of the air-floating ball to be tested. The expression is:

[0076] ;

[0077] in, Represents the information after the coordinate data of each point is fused with the second layer features. represents the characteristic connection function;

[0078] S6.2. Multiply the spherical digital model of the air-floating ball to be tested obtained in step S6.1 by the rotation matrix , get the rotated model, do template matching on the models before and after rotation, and take the rotation matrix with the highest confidence , The expression is:

[0079] ;

[0080] in, is the rotation axis vector, is the rotation angle;

[0081] Through rotation matrix processing, the ball can be in the same zero position during repeated measurements, which is convenient for the correction and use of the air float ball to be tested after the sphericity and smoothness evaluation.

[0082] Beneficial effects of the present invention:

[0083] The device for integrated measurement of sphericity error and finish described in the present invention adopts an air bearing to carry a large-sized sphere, provides a relative motion environment without gravity and micro-friction for the sphere, uses laser reflection to amplify the influence of the surface finish of the sphere, and realizes the differential error elimination of the rotation error of the shaft by axially symmetrically installing the laser transmitter and receiver with the axis of the air bearing as the axis, and establishes a data evolution model for the error, and improves the accuracy of error compensation by iterating the number of tests; defines an interpolation method to expand the measurement point data, improves the test accuracy and system stability; realizes the calibration of the zero position of the sphere to be measured by establishing a spherical digital model of the sphere to be measured, and gives the current sphere posture in the form of a rotation matrix; calculates the sphericity error by laser reflection, and synchronously evaluates the surface finish during the rotation of the sphere. In summary, the present invention can realize high-precision, contactless, efficient and convenient integrated measurement of sphericity error and finish for large-sized spheres. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a structural schematic diagram of a sphericity error and smoothness integrated measuring device according to the present invention;

[0085] Figure 2 A top view of a sphericity error and smoothness integrated measuring device according to the present invention;

[0086] Figure 3 The present invention provides a flow chart of a method for integrated measurement of sphericity error and smoothness. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0088] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0089] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Figure 3 The detailed instructions are as follows:

[0090] Embodiment 1:

[0091] A sphericity error and finish integrated measuring device, comprising a base 1, an air bearing 2, a laser transmitter 3, a laser receiver 4, a bracket 6, and an air-floating ball 5 to be measured. The air bearing 2 is installed at the center of the base 1, and the air-floating ball 5 to be measured is placed on the air bearing 2. The number of the laser transmitter 3 and the laser receiver 4 is 2, and the number of the bracket 6 is 4;

[0092] The laser emitter 3 is mounted on a bracket 6, and the bracket 6 is mounted on a base. Two laser emitters 3 are symmetrically placed on both sides of the air floating ball 5 to be tested;

[0093] The laser receiver 4 is mounted on a bracket 6, and the bracket 6 is mounted on a base. The laser emitted by a laser transmitter 3 is reflected by the air-floating ball 5 to be measured and then received by a laser receiver 4 on the same side, forming two working light paths.

[0094] Furthermore, the air-floating ball 5 to be tested is carried on the air-floating bearing 2 without gravity and with slight friction by high-pressure gas, and rotates freely on the air-floating bearing 2 , and the center of the air-floating ball 5 to be tested always coincides with the center of the air-floating bearing 2 .

[0095] Furthermore, the air bearing 2 has a wide measuring range and high adaptability, and can be freely expanded by replacing work surfaces of different sizes to adapt to air balls 5 to be tested of various sizes.

[0096] Embodiment 2:

[0097] A method for integrated measurement of sphericity error and smoothness is implemented based on the device for integrated measurement of sphericity error and smoothness described in Example 1, and includes the following steps:

[0098] S1. Start a sphericity error and smoothness integrated measuring device, then establish a three-dimensional Cartesian coordinate system based on the plane coordinate system of two sets of working optical paths, with the center of the air-floating ball to be measured as the origin, and perform working optical path jitter error processing;

[0099] Furthermore, the specific implementation method of step S1 includes the following steps:

[0100] S1.1. Pass high pressure gas through the air bearing;

[0101] S1.2. Install the air-floating ball to be tested on the air-floating bearing, control the center of the air-floating bearing to coincide with the center of the air-floating ball to be tested, then turn on the laser transmitter and laser receiver, adjust the height of the laser transmitter and laser receiver, so that the laser is emitted to the equatorial plane of the air-floating ball to be tested, and monitor the position of the laser on the laser receiver plane in real time;

[0102] The plane coordinate systems of the laser points on the two laser receivers are established as follows: and , the coordinates of the marked laser points are and , in the initial state, the recorded laser point position vectors are and A three-dimensional Cartesian coordinate system is established with the center of the sphere as the origin, and the coordinates of the laser point position are transformed into the coordinates of the point on the sphere where the laser is irradiated ;

[0103] S1.3. Set up two working light paths to generate laser point 1 and laser point 2 respectively. By changing the laser emission angle , to adjust the error magnification. When the position of the laser point on the air-floating ball to be measured changes to When the laser point changes distance for:

[0104] ;

[0105] By symmetrically installing two sets of laser transmitters and laser receivers for real-time synchronous sampling, differential error The elimination expression is:

[0106] ;

[0107] in, , For laser point 1 and laser point 2, The position vector at the time of sampling;

[0108] The laser point sampling step is in the nanosecond level, which is continuous and periodic in time. The laser point is expanded by Fourier series to obtain the amplitude and frequency of each level of harmonics. The expression is:

[0109] ;

[0110] in, is the function of coordinate difference value changing with time; are the amplitudes of the sine and cosine terms, respectively; denote the phase angles of the sine and cosine terms respectively; is the frequency; express Subharmonics, from which the amplitude and frequency of each level of harmonics are obtained, and the degree of system jitter is evaluated;

[0111] Then calculate the vector difference value To achieve error compensation of measurement results, the expression is:

[0112] .

[0113] S2. Under the condition that the air floating ball to be tested rotates, the laser of the laser transmitter is reflected on the air floating ball to be tested, the position coordinate data of all points on the spherical surface are collected, and the position coordinate data of specific points on the spherical surface are extracted, and then the collected data is processed for control error compensation of the attitude of the air floating ball to be tested;

[0114] Furthermore, the specific implementation method of step S2 includes the following steps:

[0115] S2.1. Control the measured air-floating ball to rotate evenly, set the specific point as the intersection point generated when the latitude increases by 15° from 0° to 90° and the longitude increases by 15° from 0° to 180° at each latitude, and collect the position coordinate data of all points on the spherical surface during the rotation of the measured air-floating ball, and extract the position coordinate data of the specific point on the spherical surface;

[0116] S2.2. When setting the axis of the air bearing, there is an eccentricity error and a rotation error. The coordinate data directly obtained at this time is a measurement result containing errors. , It is regarded as a first harmonic in time, so the Fourier transform is performed and the expression is:

[0117] ;

[0118] in, is the function of the measurement result with error at a certain angle changing with time, are the amplitudes of the fundamental, sine and cosine terms, respectively, is the angular frequency; express Subharmonics;

[0119] right Offset Processing Elimination ,think It is the mean value of the data sampled during one rotation around the axis, and the first harmonic error caused by the eccentricity is separated, and the expression is:

[0120] ;

[0121] in, , The axis of the air bearing is , Eccentricity error in direction, is the rotation error, The angle of rotation of the air-floating ball to be tested around the axis of the air-floating bearing;

[0122] S2.3. The rotation error is modeled by linear regression analysis, and the rotation error vector is expanded to be expressed as , the expression of the loss function describing the rotation error is obtained as:

[0123] ;

[0124] in, is the loss function of the rotation error, For the The coordinate vectors of the measurement points;

[0125] S2.4. Derivative the formula in step S2.3, let ,get , and then use iterative method to establish S The data evolution model iterates the angle in the gradient direction of the loss function, and the expression is:

[0126] ;

[0127] in, is the model learning rate, is the gradient of the loss function of the measurement error with respect to the rotation angle;

[0128] As the iteration proceeds Improvements are made to achieve accurate compensation of measurement results.

[0129] S3. Interpolate the position coordinate data of the specific point on the spherical surface after processing in step S2 to obtain an interpolated coordinate data set;

[0130] Furthermore, the specific implementation method of step S3 includes the following steps:

[0131] S3.1. For the position coordinate data of a specific point on the spherical surface collected and processed, first The position coordinate data of a specific point on the spherical surface is converted into the coordinates of a spherical coordinate system with the center of the ball to be measured as the origin. , the expression is:

[0132] ;

[0133] S3.2. Define an interpolation function suitable for the spherical surface characteristics, expressed as:

[0134] ;

[0135] in, is the distance between two test points on the sphere, To adjust the parameters, are two adjacent test points on the sphere; is the nominal radius of the sphere; For test point The azimuth coordinates of For test point The azimuth coordinates of For test point The elevation coordinates of For test point The elevation coordinate of

[0136] S3.3. Solve the coordinates of the spherical points under the set step size and expand all data points. The expression is:

[0137] ;

[0138] in, is the coordinate vector of the point to be interpolated, For the The weight coefficient of the adjacent points of the group, For the The distance between two test points on the sphere.

[0139] S4. Calculate the spherical error based on the interpolated coordinate data set obtained in step S3;

[0140] Furthermore, the specific implementation method of step S4 includes the following steps:

[0141] S4.1. Definitions The distance from the test data point to the center of the sphere The expression is:

[0142] ;

[0143] in, is the distance coordinate of the center of the ball to be measured, For the The elevation coordinates of the test data points, is the elevation coordinate of the center of the ball to be measured, For the The azimuth coordinates of the test data points, is the azimuth coordinate of the center of the ball to be measured;

[0144] S4.2. The expression for defining the spherical error function is:

[0145] ;

[0146] in, For the The distance coordinates of the test data points;

[0147] The spherical error function and the radius of the sphere to be measured Taking partial derivatives and setting them to zero with the coordinates of the center of the ball to be measured, we get the following differential equations:

[0148] ;

[0149] Then the radius of the ball to be measured is obtained by numerically solving the above formula and the coordinates of the center of the ball to be measured , and calculate the sphericity error , the expression is:

[0150] .

[0151] S5. Based on the position coordinate data of all points on the spherical surface obtained in step S2, the spherical surface smoothness is evaluated;

[0152] Furthermore, the specific implementation method of step S5 is to process the position coordinate data of all points on the spherical surface collected in step S2 to evaluate the surface finish of the air floating ball to be tested, and the expression is:

[0153] ;

[0154] in, is the surface finish of the air float ball to be tested, for N The average of the vector difference values ​​of the smoothness test points.

[0155] S6. Based on the interpolated coordinate data set obtained in step S3, a spherical model of the air-floating ball to be tested is constructed.

[0156] Furthermore, the specific implementation method of step S6 includes the following steps:

[0157] S6.1. Define a neural network for processing point cloud data, which is a three-layer neural network. The first layer is a feature extraction layer. After the obtained point data is input, the features of the point set are extracted. The expression is:

[0158] ;

[0159] in, is the activation function, are the weight matrix and bias vector of the first layer respectively, and the input data is the coordinate vector of multiple points uniformly on the sphere obtained by interpolation. , is the output of layer 1;

[0160] The second layer is the feature aggregation layer. The input data of the first layer is input into the second layer, local features are aggregated, and the output features of the second layer are obtained using the maximum pooling operation. , the expression is:

[0161] ;

[0162] The third layer is the feature connection layer. The data output from the second layer is connected and fused with the coordinate data of each point through the third layer to complete the spherical digital modeling of the air-floating ball to be tested. The expression is:

[0163] ;

[0164] in, Represents the information after the coordinate data of each point is fused with the second layer features. represents the characteristic connection function;

[0165] S6.2. Multiply the spherical digital model of the air-floating ball to be tested obtained in step S6.1 by the rotation matrix , get the rotated model, do template matching on the models before and after rotation, and take the rotation matrix with the highest confidence , The expression is:

[0166] ;

[0167] in, is the rotation axis vector, is the rotation angle;

[0168] Through rotation matrix processing, the ball can be in the same zero position during repeated measurements, which is convenient for the correction and use of the air float ball to be tested after the sphericity and smoothness evaluation.

[0169] The present embodiment describes an integrated sphericity error and smoothness measurement method, which uses an air-floating shaft as a loading platform for a sphere to be measured, and can provide a gravity-free, micro-friction relative motion environment for a large-sized sphere to be measured; the coordinates of each point on the surface of the sphere are collected by emitting a laser to the sphere and recording the coordinates of the reflected light spots, which can reflect the smoothness of the sphere surface; two sets of laser transmitters and receivers are symmetrically installed based on differential error elimination, and a data evolution model can be established for the system vibration error and the shaft rotation error, so that the error compensation effect can be continuously improved with the number of measurements; the measurement point data is expanded by Kriging interpolation, which improves the accuracy of the test results and the stability of the test system; while measuring the sphericity error, the surface smoothness of the sphere can be evaluated, which has the advantages of non-contact, high precision, high efficiency and convenience.

[0170] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0171] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A sphericity error and smoothness integrated measurement method, which is realized by relying on a sphericity error and smoothness integrated measurement device, wherein the sphericity error and smoothness integrated measurement device comprises a base (1), an air bearing (2), a laser transmitter (3), a laser receiver (4), a bracket (6), and an air-floating ball (5) to be measured, wherein the air bearing (2) is installed at the center position of the base (1), the air-floating ball (5) to be measured is placed on the air bearing (2), the number of the laser transmitter (3) and the laser receiver (4) is 2, and the number of the bracket (6) is 4; The laser emitter (3) is mounted on a bracket (6), and the bracket (6) is mounted on a base. The two laser emitters (3) are symmetrically placed on both sides of the air floating ball (5) to be tested; The laser receiver (4) is mounted on a bracket (6), and the bracket (6) is mounted on a base. The laser emitted by a laser transmitter (3) is reflected by the air-floating ball (5) to be measured and then received by a laser receiver (4) on the same side, thereby forming two working optical paths; The air-floating ball (5) to be tested is supported on the air-floating bearing (2) without gravity and with slight friction by high-pressure gas, and rotates freely on the air-floating bearing (2), and the center of the air-floating ball (5) to be tested always remains coincident with the center of the air-floating bearing (2); It is characterized by comprising the following steps: S1. Start a sphericity error and smoothness integrated measurement device, then establish a three-dimensional Cartesian coordinate system based on the plane coordinate system of the two sets of working optical paths, with the center of the air-floating ball to be measured as the origin, and perform jitter error processing on the working optical path; S2. Under the condition that the air floating ball to be measured is rotating, the laser of the laser transmitter is reflected on the air floating ball to be measured, the position coordinate data of all points on the spherical surface are collected, and the position coordinate data of specific points on the spherical surface are extracted, and then the collected data is subjected to the control error compensation processing of the attitude of the air floating ball to be measured; S3. Interpolate the position coordinate data of the specific point on the spherical surface processed in step S2 to obtain an interpolated coordinate data set; S4. Calculate the spherical error based on the interpolated coordinate data set obtained in step S3; S5. Based on the position coordinate data of all points on the spherical surface obtained in step S2, the spherical surface smoothness is evaluated; S6. Based on the interpolated coordinate data set obtained in step S3, a spherical model of the air-floating ball to be tested is constructed.

2. The method for integrated measurement of sphericity error and smoothness according to claim 1, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. Pass high pressure gas through the air bearing; S1.

2. Install the air-floating ball to be tested on the air-floating bearing, control the center of the air-floating bearing to coincide with the center of the air-floating ball to be tested, then turn on the laser transmitter and laser receiver, adjust the height of the laser transmitter and laser receiver, so that the laser is emitted to the equatorial plane of the air-floating ball to be tested, and monitor the position of the laser on the laser receiver plane in real time; The plane coordinate systems of the laser points on the two laser receivers are established as x1Oy1 and x2Oy2, and the coordinates of the laser points are marked as (x1, y1) and (x2, y2). In the initial state, the position vectors of the laser points are recorded as p 10 =(x 10 ,y 10 ) and p 20 =(x 20 ,y 20 ), and establish a three-dimensional Cartesian coordinate system with the center of the sphere as the origin, and transform the laser point position coordinates into the coordinates (X, Y, Z) of the point on the sphere where the laser irradiates; S1.

3. Set up two working optical paths to generate laser points 1 and 2 respectively. By changing the laser emission angle α, the error magnification can be adjusted. When the position of the laser point on the air-floating ball to be measured changes to Δl, the laser point changes by a distance Δd of: Δd=Δlcotα By symmetrically installing two sets of laser transmitters and laser receivers for real-time synchronous sampling, the differential error Δp i The elimination expression is: Δp i =p 1i -p 2i Among them, p 1i ,p 2i is the position vector of laser point 1 and laser point 2 at the i-th sampling; The laser point sampling step is in the nanosecond level, which is continuous and periodic in time. The laser point is expanded by Fourier series to obtain the amplitude and frequency of each level of harmonics. The expression is: Where P(t) is the function of the coordinate difference value changing with time; A n ,B n are the amplitudes of the sine and cosine terms respectively; η n ,ψ n They represent the phase angles of the sine and cosine terms respectively; f is the frequency; n represents the nth harmonic, from which the amplitude and frequency of each harmonic are obtained to evaluate the degree of system jitter; Then calculate the vector difference value p i To achieve error compensation of measurement results, the expression is:

3. The method for integrated measurement of sphericity error and smoothness according to claim 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. Control the measured air-floating ball to rotate evenly, set the specific point as the intersection point generated when the latitude increases by 15° from 0° to 90° in steps of 15°, and the longitude increases by 15° from 0° to 180° at each latitude. During the rotation of the measured air-floating ball, collect the position coordinate data of all points on the spherical surface, and extract the position coordinate data of specific points on the spherical surface; S2.

2. The axis of the air bearing has eccentricity error and rotation error. At this time, the coordinate data directly obtained is the measurement result r(δ, t) containing errors. r(δ, t) is regarded as a first harmonic in time, so the Fourier transform is performed to obtain the expression: Among them, r(δ, t) is the function of the measurement result with error at a certain angle over time, a0, a n ,b n are the amplitudes of the fundamental wave, sine and cosine terms respectively, ω is the angular frequency; n represents the nth harmonic; The r(δ) offset is processed to eliminate a0, and a0 is considered to be the mean value of the data sampled during one rotation around the axis. At the same time, the first harmonic error caused by the eccentricity is separated, and the expression is obtained: Among them, φ X ,φ Y is the eccentricity error of the axis of the air bearing in the X and Y directions, e is the rotation error, and δ is the angle of rotation of the air-floating ball to be measured around the axis of the air bearing; S2.

3. The rotation error is modeled by linear regression analysis, and the rotation error vector is expanded to (ε X,i ,ε Y,i ,ε Z,i ), the expression of the loss function describing the rotation error is obtained as: Among them, S(ε X,i ,ε Y,i ,ε Z,i ) is the loss function of the rotation error, (X i ,Y i ,Z i ) is the coordinate vector of the i-th measurement point; S2.

4. Derivative the formula in step S2.3, let Get ε, and then use the iterative method to establish the data evolution model of S, iterating the angle in the gradient direction of the loss function, the expression is: Among them, k is the model learning rate, is the gradient of the loss function of the measurement error with respect to the rotation angle; As the iterations proceed, S is improved to achieve accurate compensation of the measurement results.

4. The method for integrated measurement of sphericity error and smoothness according to claim 3, characterized in that: The specific implementation method of step S3 includes the following steps: S3.

1. For the position coordinate data of the specific point on the spherical surface collected after processing, first convert the position coordinate data of the specific point on the spherical surface after processing of the i-th spherical surface into the coordinates of the spherical coordinate system with the center of the ball to be measured as the origin The expression is: S3.

2. Define an interpolation function suitable for spherical characteristics, expressed as: Among them, d is the distance between two test points on the sphere, c0, c1, a are adjustment parameters, P a ,P b are two adjacent test points on the sphere; R is the nominal radius of the sphere, The test point P a The azimuth coordinates of The test point P b The azimuth coordinates of The test point P a The elevation coordinates of The test point P b The elevation coordinate of S3.

3. Solve the coordinates of the spherical points under the set step size and expand all data points. The expression is: Among them, u is the coordinate vector of the point to be interpolated, λ i is the weight coefficient of the i-th group of adjacent points, d i is the distance between two test points on the i-th group of spheres.

5. The method for integrated measurement of sphericity error and smoothness according to claim 4, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. Define the distance D from the i-th test data point to the center of the sphere i The expression is: Among them, ρ c is the distance coordinate of the center of the ball to be measured, θ i is the elevation coordinate of the i-th test data point, θ c is the elevation coordinate of the center of the ball to be measured, is the azimuth coordinate of the i-th test data point, is the azimuth coordinate of the center of the ball to be measured; S4.

2. The expression for the spherical error function is defined as: Among them, ρ i is the distance coordinate of the i-th test data point; The spherical error function, the radius R of the sphere to be measured, and the coordinates of the center of the sphere to be measured are partially derived and set to zero, and the differential equations are as follows: Then, the radius R of the ball to be measured and the coordinates of the center of the ball to be measured are obtained by numerically solving the above formula. And calculate the sphericity error E R , the expression is: E R =max(|D i -R|)-min(|D i -R|)。 6. The method for integrated measurement of sphericity error and smoothness according to claim 5, characterized in that: The specific implementation method of step S5 is to process the position coordinate data of all points on the spherical surface collected in step S2 to evaluate the surface finish of the air flotation ball to be tested, and the expression is: Wherein, Ra is the surface finish of the air flotation ball to be tested, and p0 is the average value of the vector difference values ​​of N finish test points.

7. The method for integrated measurement of sphericity error and smoothness according to claim 6, characterized in that: The specific implementation method of step S6 includes the following steps: S6.

1. Define a neural network for processing point cloud data, which is a three-layer neural network. The first layer is a feature extraction layer. After the obtained point data is input, the features of the point set are extracted. The expression is: f i =ReLU(W 1 [r i ,θ i ,φ i ]+b 1 ) Among them, ReLU is the activation function, W 1 ,b 1 are the weight matrix and bias vector of the first layer respectively, and the input data is the coordinate vector of multiple points uniformly on the sphere obtained by interpolation. f i is the output of layer 1; The second layer is the feature aggregation layer. The input data of the first layer is input into the second layer, local features are aggregated, and the output feature g of the second layer is obtained by using the maximum pooling operation. The expression is: g=MaxPooling(f i ); The third layer is the feature connection layer. The data output from the second layer is connected and fused with the coordinate data of each point through the third layer to complete the spherical digital modeling of the air-floating ball to be tested. The expression is: f i fused =concat(f i ,g) Among them, f i fused It represents the information after the coordinate data of each point is fused with the second layer features, and concat(,) represents the feature connection function; S6.

2. Multiply the spherical digital model of the air-floating ball to be tested obtained in step S6.1 by the rotation matrix R to obtain the rotated model. Perform template matching on the models before and after the rotation, and take the rotation matrix R with the highest confidence. The expression of R is: Where n is the rotation axis vector, β is the rotation angle; Through rotation matrix processing, the ball can be in the same zero position during repeated measurements, which is convenient for the correction and use of the air float ball to be tested after the sphericity and smoothness evaluation.

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