Rotating shaft five-degree-of-freedom error synchronous measurement method and device based on multi-surface composite white light interference

Abstract

The invention discloses a rotating shaft five-degree-of-freedom error synchronous measurement method and device based on multi-surface composite white light interference. The device comprises a precise rotating shaft (1), a clamp (2), an adjusting unit and a white light interference device. One end of the precision rotating shaft (1) is connected with one end of the clamp (2), the other end of the clamp (2) is fixedly connected with one end of the adjusting unit, the other end of the adjusting unit is provided with the reference piece (5), the white light interference device is located right in front of the reference piece (5), and the reference piece (5) is provided with three prismatic surfaces; the measurement method comprises the following steps: S1, realizing synchronous measurement of five-degree-of-freedom motion of the rotating shaft based on multi-surface composite white light interference; and S2, the installation error of the measuring device is separated. According to the method, the five-degree-of-freedom error motion of the rotating shaft can be synchronously solved, and efficient and accurate technical support is provided for performance evaluation and error compensation of the precise rotating shaft.

Description

Technical Field

[0001] This invention belongs to the field of optical precision measurement technology, specifically relating to a method and device for synchronous measurement of five-degree-of-freedom error of a rotating axis using multi-faceted composite white light interference. Background Technology

[0002] Precision spindles are a crucial component of machine tools, with increasingly stringent precision requirements, progressing from the micrometer level and beyond, and moving towards the nanometer and sub-nanometer levels. During rotation, precision spindles inevitably generate five degrees of freedom motion errors, including in-plane radial motion and out-of-plane axial and tilting motion. These errors directly affect the microstructure and forming accuracy of the final product; therefore, improving the motion accuracy of precision spindles is essential for ensuring machining precision.

[0003] Some scholars have focused on measuring motion errors in a single direction, proposing several methods, such as optical measurement methods based on laser collimation, which measure the radial error of the spindle by measuring changes in the reflected or refracted laser beam; machine vision methods that identify radial motion by calculating the two-dimensional image of the test target; using circular gratings with autocollimators to detect spindle radial errors; and using industrial cameras and self-made standards to achieve high-speed dynamic radial error measurement of spindles based on trajectory tracking. While these methods have relatively simple devices, they struggle to reflect the coupling relationships between errors in multiple degrees of freedom, thus limiting their practical applications.

[0004] To comprehensively evaluate shaft performance, simultaneous multi-degree-of-freedom measurement is essential. To address this, many researchers have attempted to acquire error information in multiple directions simultaneously by combining multiple sensors. For example, the most common method involves using two standard spheres combined with five capacitive sensors to measure the synchronous radial and axial error motion of the spindle. Laser Doppler vibrometers are used to measure the radial error of precision spindles, obtaining radial and tilt error motion by identifying changes in the position of reflected or refracted laser spots. However, this method struggles to directly measure axial motion, thus requiring additional axial sensors. Some researchers employ heterodyne interferometry for axial motion measurement. Although these methods may use different devices, their underlying mechanisms often result in multi-degree-of-freedom measurements being performed through independent components. This leads to highly complex devices for simultaneously measuring five degrees of freedom motion errors, which typically rely on high-precision fixtures and require extremely precise sensor mounting positions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and apparatus for synchronous measurement of five-DOF error of a rotating shaft using multi-faceted composite white light interferometry, thereby achieving synchronous measurement of the 5DOF error motion of a precision rotating shaft.

[0006] The technical solution adopted in this invention is:

[0007] A multi-faceted composite white light interferometer with a five-degree-of-freedom rotation axis error synchronous measurement device includes a precision rotation axis, a fixture, an adjustment unit, and a white light interferometer.

[0008] One end of the precision rotating shaft is installed and connected to one end of the clamp, and the other end of the clamp is fixedly connected to one end of the adjustment unit. A reference piece is installed on the other end of the adjustment unit, and the white light interference device is located directly in front of the reference piece. The reference piece has three facets.

[0009] Furthermore, the white light interference device includes a micro-interference objective, a tube mirror, a white light source, and an industrial camera. The micro-interference objective is mounted on one end of the tube mirror, and the other end is connected to the industrial camera. The industrial camera achieves sampling control and data transmission by connecting to a computer. The white light source is installed in a side opening on one side of the tube mirror.

[0010] Furthermore, the adjustment unit includes a dual-axis leveling frame and a dual-axis displacement fine-tuning stage. One end of the dual-axis leveling frame is fixedly connected to the clamp, and the other end is fixedly connected to the dual-axis displacement fine-tuning stage. The reference piece is pressed into the dual-axis displacement fine-tuning stage. The dual-axis leveling frame can adjust the tilt angle of the two axes of the reference piece so that the end face of the reference piece is parallel to the end face of the spindle. The dual-axis displacement fine-tuning stage can adjust the displacement of the reference piece in the two axes in the direction perpendicular to the spindle axis.

[0011] Furthermore, the white light source is an LED white light source, and the bottom of the tube mirror is fixed on a two-axis rotary table that is fixed to the worktable.

[0012] Furthermore, combined Figure 2 The reference component is a triangular pyramidal microstructure with an oblique angle. The base of the pyramid is an equilateral triangle with a side length of 632 μm. The vertex of the pyramid is directly above the center of the base triangle and is set at a height of 11 μm from the base.

[0013] A measurement method for a multi-faceted composite white light interferometer with a five-degree-of-freedom rotation axis error synchronous measurement device includes the following steps:

[0014] Step S1: Synchronous measurement of five-degree-of-freedom motion of the rotating shaft is achieved based on multi-faceted composite white light interferometry;

[0015] Step S2: Separate the installation error of the measuring device.

[0016] Further, step S1 specifically includes:

[0017] Before measurement, adjust the relative positions of the reference piece and the white light interferometer so that interference fringes are present on the three facets in the image acquired by the industrial camera. The precision rotating shaft rotates at a set speed, and the industrial camera acquires images at different times.

[0018] Suppose that the three facets of the reference element pass through a virtual plane parallel to the reference mirror in the interferometer objective and with the same optical path difference. This virtual plane is called the Peak Coherence Plane (PCP), and it coincides with the focal plane of the interferometer objective, allowing the image to be projected onto this virtual plane. An image coordinate system is defined on the PCP, where... shaft and The axis is located on the PCP. The axis is along the optical axis of the interference lens, with the origin at the image center;

[0019] Sampling and calculation of white light interference fringes in a single frame image: Using image processing methods, threshold segmentation is employed to extract bright fringe regions from the image. Based on the segmentation results, fringe straight line fitting is performed to calculate the linear expression of each fringe in the image. Then, the positions of pairwise intersections and the center position are calculated. Finally, based on the intersection and center positions, the multi-faceted composite white light interference fringe image is segmented into multiple independent sub-images. Each sub-image contains complete information of a single set of interference fringes. Subsequently, each set of interference fringes is solved individually to obtain the position expression of the corresponding facet in the image coordinate system.

[0020] (Equation 1)

[0021] in Let g be the normal vector of the desired face in the image coordinate system, and g is a constant term in the expression.

[0022] For each group of interference fringes after segmentation, the direction of the zero-order bright fringe and its normal direction are obtained by threshold segmentation, edge detection, and line fitting methods in image processing. A line segment is defined by extending a certain length along the normal from a point on the zero-order bright fringe to both sides of the zero-order bright fringe. Through image processing methods, on the line segment Within the range, a grayscale profile is constructed to obtain a sequence of actual interference curves, and then the line segments are... Translate a small distance along the direction of the zero-order bright fringe to define a new line segment. Then, perform grayscale profiling to obtain a new set of actual interference curve sequences. Repeat this process multiple times to obtain several sets of actual interference curve sequences.

[0023] Using the Hilbert transform method, these sets of actual interference curve sequences are analyzed to accurately extract several zero optical path difference positions and record the corresponding pixel positions. Finally, the least squares fitting method is used to accurately fit the expression of the straight line L in the image coordinate system for the zero-order bright fringe. This straight line L is the intersection line of the desired facet and the PCP.

[0024] (Equation 2)

[0025] Due to the various points on the reference part's edge surface Different z-values ​​result in interference fringe projections on the edge surface. The white light interference intensity curve on the Z-axis is calibrated by vertical scanning, yielding the following expression for the white light interference intensity curve:

[0026] (Equation 3)

[0027] in For carrier frequency, For the initial phase, is the width of the Gaussian function, used to describe the envelope function of the white light interference fringe pattern, and z is the height value. This corresponds to the light intensity at that altitude.

[0028] The pixel scale of the image coordinate system is converted to the length scale of the actual coordinate system. Using the peak intensity point as the origin, a sequence of actual interference curves is obtained by constructing a grayscale profile along the normal to the precisely calculated straight line L. The actual distance of each point in the sequence from the peak point is... Using the x-axis as the horizontal axis, after normalization, we obtain a sequence of actual interference curves consisting of N discrete points. ;

[0029] Then, the actual interference curve sequence is obtained through peak detection and curve fitting methods. The width of the three-level bright stripes And the width of the third bright fringe of the white light interference intensity curve I(z). The slope m of the measured plane normal to the corresponding edge face is obtained:

[0030] (Equation 4)

[0031] From the expression for the position of the facet in Equation 1, it can be seen that along the direction of the normal vector of line L... The horizontal unit vector is ,in The corresponding edge position expression along the normal vector direction The slope of the plane, i.e., the slope of the theoretical plane normal, is obtained by taking the derivative of the implicit function:

[0032] (Equation 5)

[0033] Will Substituting the values, we get:

[0034] (Equation 6)

[0035] The slope of the theoretical plane normal of the prism From Equation 6, we obtain that m is the slope of the measured plane normal. Setting them equal, we can solve for the coefficient. :

[0036] (Equation 7)

[0037] The coefficients in the expression for the position of the facet are obtained accordingly. The position expressions of the three facets of the reference part in the image coordinate system are determined by three sets of white light interference fringes, and after normalization, they are in the following form:

[0038] (Equation 8)

[0039] in, It is the first The components of the normal vector of each edge face The constant term of the expression for the position of the i-th facet is obtained by fitting it in Equation 2;

[0040] By solving a system of equations consisting of the positional expressions of the three facets, the position of the cone apex in the image coordinate system at any given moment can be uniquely determined. The cone apex coordinates calculated from the first frame image Using this as a reference, determine the 3-DOF relative motion of the reference component at time k of the image frame. ;

[0041] Given that the normal vectors of the three facets in the image coordinate system at a certain moment are... Assuming Let the normal vectors of the three facets of the reference piece be the normal vectors at their corresponding positions in the first frame image. Using these as a reference, there exists a rotation matrix R that rotates the normal vector of each facet at the reference position in the image coordinate system to the normal vector of that facet at a certain moment:

[0042] (Equation 9)

[0043] Equation 9 uses the Kabsch algorithm to solve for the rotation matrix R. The sum of the normal vectors of these three facets can then describe the change in the reference part's attitude, using the sum vector from the first frame as an example. Using this as a reference, the sum vector of the reference element at time k in the image coordinate system after relative rotation is calculated through the rotation matrix R. In obtaining and Then, the five-degree-of-freedom relative motion of the rotation axis in space was uniquely determined by the reference component during the k-th frame image.

[0044] Furthermore, in step S1, the precision spindle rotates at a speed of 8.33 rpm, and the industrial camera captures images at different times at a frame rate of 50 fps.

[0045] Further, step S2 specifically includes:

[0046] Based on the five-degree-of-freedom relative motion results obtained in step S1, the systematic errors caused by the installation are separated, including in-plane motion error separation and out-of-plane motion error separation.

[0047] The in-plane motion error measurement and error separation are as follows: Taking the position of the reference part at the start of data recording as a reference, the motion trajectory of the cone vertex of the reference part calculated in the image coordinate system is a circle centered on the main axis rotation center. The relative movement at frame k is... This includes the eccentric motion component caused by installation eccentricity;

[0048] Decompose motion into image coordinates. shaft and In the axis direction, in the k-th frame image, the rotation axis along Axial and radial motion error and along Axial and radial motion error Represented as:

[0049] (Equation 10)

[0050] in, Indicates the equivalent eccentric radius. This represents the initial phase, where ω is the rotational angular frequency. This indicates the position of the spindle rotation center in the image coordinate system;

[0051] The out-of-plane motion error measurement and error separation are specifically as follows: During the rotation of the axis, due to installation errors, the vector measured in the k-th frame... The trajectory in space is a cone centered on the axis of rotation, and the axis of rotation is perpendicular to the image coordinate system. There will also be two axes, each orbiting around the image coordinate system. shaft and Static deflection of the shaft and This deflection angle reflects the installation error between the axis of rotation and the optical axis of the white light interferometer.

[0052] The sum vector of the k-th frame Seeking a way around shaft and The tilt angle of the shaft is:

[0053] (Equation 11)

[0054] in The sum vector calculated for the k-th frame image The components of each axis, To bypass The tilt angle of the axis, To bypass The inclination angle of the axis;

[0055] Decompose the tilting motion of the reference component into... shaft and The axis, in the k-th grayscale image, rotates around the axis. Tilting motion error of the shaft and around Tilting motion error of the shaft Represented as:

[0056] (Equation 12)

[0057] in, This represents the fixed deflection angle between the axis of the reference component and the axis of rotation of the rotating shaft, where ω is the angular frequency of rotation. Indicates the initial phase. and This represents the static deflection angle between the axis of rotation and the Z-axis of the image coordinate system;

[0058] The axial error motion is directly obtained as:

[0059] (Equation 13)

[0060] in The relative movement along the Z-axis at time k of the image frame.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] This invention utilizes the high sensitivity of white light interference to height changes to achieve synchronous measurement of the 5DOF motion error of a precision rotating shaft and proposes an error separation method for installation errors, etc. Compared with other multi-sensor combined measurement systems, the measurement device of this invention is simple, requiring only an industrial camera with a white light interference objective lens, which greatly simplifies the measurement system structure, reduces assembly and adjustment difficulty, and reduces reliance on high-precision standard parts. Although some existing optical measurement systems have relatively simple devices, they are difficult to reflect the coupling relationship between multi-degree-of-freedom errors. This invention can simultaneously calculate the five-degree-of-freedom error motion of the rotating shaft, providing efficient and accurate technical support for the performance evaluation and error compensation of precision rotating shafts.

[0063] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the five-degree-of-freedom error measurement device for rotating shaft based on multi-faceted composite white light interference in this invention;

[0065] Figure 2 This is a structural schematic diagram of a reference component;

[0066] Figure 3 This is a schematic diagram of the five-degree-of-freedom error measurement method for rotating shafts based on multi-faceted composite white light interference in this invention;

[0067] Figure 4 This is a schematic diagram of extracting the interference curve sequence from the grayscale profile of an image.

[0068] Figure 5 This is a schematic diagram for calculating the normal slope of the reference edge plane;

[0069] Figure 6 This is a schematic diagram of the in-plane motion error measurement and error separation of the measuring device;

[0070] Figure 7 This is a schematic diagram of the out-of-plane motion error measurement and error separation of the measuring device. Detailed Implementation

[0071] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0072] Combination Figure 1 A multi-faceted composite white light interference rotating shaft five-degree-of-freedom error synchronous measurement device, comprising a precision rotating shaft 1, a fixture 2, an adjustment unit and a white light interference device;

[0073] One end of the precision rotating shaft 1 is mounted and connected to one end of the clamp 2 (by clamping with an expansion sleeve), and the other end of the clamp 2 is fixedly connected to one end of the adjustment unit. A reference element 5 is mounted on the other end of the adjustment unit. The white light interference device is located directly in front of the reference element 5, and the reference element 5 has three facets, such as... Figure 2 As shown.

[0074] Preferably, the white light interference device includes a micro-interference objective lens 6, a tube lens 7, a white light source 8, and an industrial camera 9. The micro-interference objective lens 6 is installed at one end of the tube lens 7, and the other end is connected to the industrial camera 9. The industrial camera 9 realizes sampling control and data transmission by connecting to a computer. The white light source 8 is installed in a side opening on one side of the tube lens 7.

[0075] Preferably, the adjustment unit includes a dual-axis leveling frame 3 and a dual-axis displacement fine-tuning stage 4. One end of the dual-axis leveling frame 3 is fixedly connected to the clamp 2 by bolts, and the other end is fixedly connected to the dual-axis displacement fine-tuning stage 4 by bolts. The reference piece 5 is pressed into the dual-axis displacement fine-tuning stage 4. The dual-axis leveling frame 3 can adjust the tilt angle of the two axes of the reference piece 5 so that the end face of the reference piece 5 is parallel to the end face of the spindle. The dual-axis displacement fine-tuning stage 4 can adjust the displacement of the two axes of the reference piece 5 in the direction perpendicular to the spindle axis, thereby reducing the eccentricity of the reference piece's rotation axis from the spindle axis.

[0076] The precision rotating shaft 1 drives the dual-axis leveling frame 3, the dual-axis displacement fine-tuning stage 4, and the reference piece 5 to rotate. The white light interference device fixed in front of the reference piece 5 acquires the multi-faceted composite white light interference fringe image generated by the interference on the surface of the reference piece 5 through the interference objective lens 6 and the industrial camera 9. The image is transmitted to the computer, and the position and pose change of the reference piece 5 as it rotates with the precision rotating shaft 1 is calculated. Then, the five-degree-of-freedom error motion of the rotating shaft is analyzed.

[0077] Preferably, the white light source 8 is an LED white light source, and the bottom of the tube mirror 7 is fixed on a two-axis turntable 10 that is fixed to the worktable.

[0078] Preferably, the reference component 5 is a triangular pyramidal microstructure with an oblique angle. The base of the pyramid is an equilateral triangle with a side length of 632 μm, and the vertex of the pyramid is directly above the center of the base triangle, with a height of 11 μm from the base.

[0079] A measurement method for a multi-faceted composite white light interferometer with a five-degree-of-freedom rotation axis error synchronous measurement device includes the following steps:

[0080] Step S1: Synchronous measurement of five-degree-of-freedom motion of the rotating shaft is achieved based on multi-faceted composite white light interferometry;

[0081] Step S2: Separate the installation error of the measuring device.

[0082] Preferably, step S1 specifically comprises:

[0083] Before measurement, adjust the relative positions of reference piece 5 and white light interferometer so that interference fringes are present on the three facets in the image acquired by industrial camera 9. Precision rotating shaft 1 rotates at a set speed, and industrial camera 9 acquires images at different times.

[0084] Suppose that the three facets of reference element 5 pass through a virtual plane parallel to the reference mirror in interference lens 6 and with the same optical path difference. This virtual plane is called the Peak Coherence Plane (PCP), and it coincides with the focal plane of interference lens 6, allowing the image to be projected onto this virtual plane. An image coordinate system is defined on the PCP, where... shaft and The axis is located on the PCP. The axis is along the optical axis of the interference lens 6, with the origin at the image center;

[0085] Sampling and calculation of white light interference fringes in a single frame image: Using image processing methods, threshold segmentation is employed to extract bright fringe regions from the image. Based on the segmentation results, fringe straight line fitting is performed to calculate the linear expression of each fringe in the image. Then, the positions of pairwise intersections and the center position are calculated. Finally, based on the intersection and center positions, the multi-faceted composite white light interference fringe image is segmented into multiple independent sub-images. Each sub-image contains complete information of a single set of interference fringes. Subsequently, each set of interference fringes is solved individually to obtain the position expression of the corresponding facet in the image coordinate system.

[0086] (Equation 1)

[0087] in Let g be the normal vector of the desired face in the image coordinate system, and g is a constant term in the expression.

[0088] For each group of interference fringes after segmentation, the direction of the zero-order bright fringe and its normal direction are obtained through threshold segmentation, edge detection, and line fitting methods in image processing, such as... Figure 3 As shown, a line segment is defined as an extension of a certain length along the normal to a point on a zero-order bright fringe, pointing towards both sides of the zero-order bright fringe. Through image processing methods, on the line segment Within the range, a grayscale profile is constructed to obtain a sequence of actual interference curves, and then the line segments are... Translate a small distance along the direction of the zero-order bright fringe to define a new line segment. Then, perform grayscale profiling to obtain a new set of actual interference curve sequences. Repeat this process multiple times to obtain several sets of actual interference curve sequences.

[0089] Using the Hilbert transform method, these sets of actual interference curve sequences are analyzed to accurately extract several zero optical path difference positions and record the corresponding pixel positions. Finally, the least squares fitting method is used to accurately fit the expression of the straight line L in the image coordinate system for the zero-order bright fringe. This straight line L is the intersection line of the desired facet and the PCP.

[0090] (Equation 2)

[0091] like Figure 4 As shown, due to the points on the reference part's edge... Different z-values ​​result in interference fringe projections on the edge surface. The white light interference intensity curve on the Z-axis is calibrated by vertical scanning, yielding the following expression for the white light interference intensity curve:

[0092] (Equation 3)

[0093] in For carrier frequency, For the initial phase, The width of the Gaussian function describes the envelope function of the white light interference fringe pattern. These three parameters can be calibrated using the vertically scanned interference curve. z is the height value. This corresponds to the light intensity at that altitude.

[0094] The pixel scale of the image coordinate system is converted to the length scale of the actual coordinate system. Using the peak intensity point as the origin, a sequence of actual interference curves is obtained by constructing a grayscale profile along the normal to the precisely calculated straight line L. The actual distance of each point in the sequence from the peak point is... Using the x-axis as the horizontal axis, after normalization, we obtain a sequence of actual interference curves consisting of N discrete points. ;

[0095] Then, the actual interference curve sequence is obtained through peak detection and curve fitting methods. The width of the three-level bright stripes And the width of the third bright fringe of the white light interference intensity curve I(z). ,like Figure 5 As shown, the slope m of the measured plane normal to the corresponding edge face is obtained:

[0096] (Equation 4)

[0097] From the expression for the position of the facet in Equation 1, it can be seen that along the direction of the normal vector of line L... The horizontal unit vector is ,in The corresponding edge position expression along the normal vector direction The slope of the theoretical plane normal (i.e., the rate of change of z with respect to the horizontal displacement) is obtained by taking the derivative of the implicit function:

[0098] (Equation 5)

[0099] Will Substituting the values, we get:

[0100] (Equation 6)

[0101] The slope of the theoretical plane normal of the prism From Equation 6, we obtain that m is the slope of the measured plane normal. Setting them equal, we can solve for the coefficient. :

[0102] (Equation 7)

[0103] The coefficients in the expression for the position of the facet are obtained accordingly. The position expressions of the three facets of the reference part in the image coordinate system are determined by three sets of white light interference fringes, and after normalization, they are in the following form:

[0104] (Equation 8)

[0105] in, It is the first The components of the normal vector of each edge face The constant term of the expression for the position of the i-th facet is obtained by fitting it in Equation 2;

[0106] By solving a system of equations consisting of the positional expressions of the three facets, the position of the cone apex in the image coordinate system at any given moment can be uniquely determined. The cone apex coordinates calculated from the first frame image Using this as a reference, determine the 3-DOF relative motion of the reference component at time k of the image frame. ;

[0107] Given that the normal vectors of the three facets in the image coordinate system at a certain moment are... Assuming Let the normal vectors of the three facets of the reference piece be the normal vectors at their corresponding positions in the first frame image. Using these as a reference, there exists a rotation matrix R that rotates the normal vector of each facet at the reference position in the image coordinate system to the normal vector of that facet at a certain moment:

[0108] (Equation 9)

[0109] Equation 9 uses the Kabsch algorithm to solve for the rotation matrix R. The sum of the normal vectors of these three facets can then describe the change in the reference part's attitude, using the sum vector from the first frame as an example. Using this as a reference, the sum vector of the reference element at time k in the image coordinate system after relative rotation is calculated through the rotation matrix R. In obtaining and Then, the five-degree-of-freedom relative motion of the rotation axis in space was uniquely determined by the reference component during the k-th frame image.

[0110] Preferably, in step S1, the precision rotating shaft 1 rotates at a speed of 8.33 rpm (3000° per minute), and the industrial camera 9 captures images at different times at a frame rate of 50 fps.

[0111] Preferably, step S2 specifically comprises:

[0112] Based on the five-degree-of-freedom relative motion results obtained in step S1, the systematic errors caused by the installation are separated, including in-plane motion error separation and out-of-plane motion error separation.

[0113] In-plane motion error measurement and error separation specifically include: such as Figure 6 As shown, taking the position of the reference part at the start of data recording as a reference, the trajectory of the cone vertex of the reference part calculated in the image coordinate system is a circle centered on the main axis rotation center. The relative movement at frame k is... This includes the eccentric motion component caused by installation eccentricity;

[0114] Decompose motion into image coordinates. shaft and In the axis direction, in the k-th frame image, the rotation axis along Axial and radial motion error and along Axial and radial motion error Represented as:

[0115] (Equation 10)

[0116] in, Indicates the equivalent eccentric radius. This represents the initial phase, where ω is the rotational angular frequency. This indicates the position of the spindle rotation center in the image coordinate system;

[0117] The specific methods for measuring and separating out-of-plane motion errors are as follows: Figure 7 As shown, during the rotation of the axis, due to installation errors, the vector measured in the k-th frame is... The trajectory in space is a cone centered on the axis of rotation, and the axis of rotation is perpendicular to the image coordinate system. There will also be two axes, each orbiting around the image coordinate system. shaft and Static deflection of the shaft and This deflection angle reflects the installation error between the axis of rotation and the optical axis of the white light interferometer.

[0118] The sum vector of the k-th frame Seeking a way around shaft and The tilt angle of the shaft is:

[0119] (Equation 11)

[0120] in The sum vector calculated for the k-th frame image The components of each axis, To bypass The tilt angle of the axis, To bypass The inclination angle of the axis;

[0121] Decompose the tilting motion of the reference component into... shaft and The axis, in the k-th grayscale image, rotates around the axis. Tilting motion error of the shaft and around Tilting motion error of the shaft Represented as:

[0122] (Equation 12)

[0123] in, This represents the fixed deflection angle between the axis of the reference component and the axis of rotation of the rotating shaft, where ω is the angular frequency of rotation. Indicates the initial phase. and This represents the static deflection angle between the axis of rotation and the Z-axis of the image coordinate system;

[0124] The axial error motion is directly obtained as:

[0125] (Equation 13)

[0126] in The relative movement along the Z-axis at time k of the image frame.

[0127] The five-degree-of-freedom error motion of the rotating shaft can be calculated using the above method, including the motion along... Axial and radial motion error ,along Axial and radial motion error , around Tilting motion error of the shaft , around Tilting motion error of the shaft and axial error movement .

[0128] The steps for adjusting the relative positions of the reference component and the interference device in step S1 are as follows: Observe the approximate width of the fringes when static, and fine-tune the two-axis turntable 10 so that the imaging plane is approximately perpendicular to the rotation axis; observe the change in the width of the fringes in the image when the rotation axis rotates slowly, and move the rotation axis 1 so that the rotation center is approximately located at the center of the image; and fine-tune the tilt angle of the calibration component through the two-axis leveling frame 3, and fine-tune the eccentric distance between the center of the pyramid and the rotation center through the two-axis displacement fine-tuning stage 4 to ensure that the fringed image does not deviate from the camera's field of view during the dynamic rotation of the rotation axis.

[0129] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A device for synchronously measuring the error of a five-degree-of-freedom rotating axis using multi-faceted composite white light interferometry, characterized in that, Includes a precision rotating shaft (1), a clamp (2), an adjustment unit, and a white light interference device; One end of the precision rotating shaft (1) is installed and connected to one end of the clamp (2), and the other end of the clamp (2) is fixedly connected to one end of the adjustment unit. A reference piece (5) is installed on the other end of the adjustment unit. The white light interference device is located directly in front of the reference piece (5), and the reference piece (5) has three facets.

2. The multi-faceted composite white light interferometer with five degrees of freedom rotation axis synchronous measurement device according to claim 1, characterized in that, The white light interference device includes a micro-interference objective (6), a tube mirror (7), a white light source (8), and an industrial camera (9). The micro-interference objective (6) is installed at one end of the tube mirror (7), and the other end is connected to the industrial camera (9). The industrial camera (9) realizes sampling control and data transmission by connecting to a computer. The white light source (8) is installed in a side opening on one side of the tube mirror (7).

3. The multi-faceted composite white light interferometer with five degrees of freedom rotation axis synchronous measurement device according to claim 2, characterized in that, The adjustment unit includes a dual-axis leveling frame (3) and a dual-axis displacement fine-tuning stage (4). One end of the dual-axis leveling frame (3) is fixedly connected to the clamp (2), and the other end is fixedly connected to the dual-axis displacement fine-tuning stage (4). The reference piece (5) is pressed into the dual-axis displacement fine-tuning stage (4). The dual-axis leveling frame (3) can adjust the tilt angle of the two axes of the reference piece (5) so that the end face of the reference piece (5) is parallel to the end face of the main shaft. The dual-axis displacement fine-tuning stage (4) can adjust the two-axis displacement of the reference piece (5) in the direction perpendicular to the main shaft axis.

4. The multi-faceted composite white light interferometer with five degrees of freedom rotation axis synchronous measurement device according to claim 3, characterized in that, The white light source (8) is an LED white light source, and the bottom of the tube mirror (7) is fixed on a two-axis turntable (10) that is fixed to the worktable.

5. The multi-faceted composite white light interferometer with five degrees of freedom rotation axis synchronous measurement device according to claim 2, characterized in that, The reference component (5) is a triangular pyramidal microstructure with an oblique angle. The base of the pyramid is an equilateral triangle with a side length of 632 μm. The vertex of the pyramid is directly above the center of the base triangle and is set at a height of 11 μm from the base.

6. A measurement method for a five-degree-of-freedom error synchronous measurement device for multi-faceted composite white light interferometry according to any one of claims 2-5, characterized in that, Includes the following steps: Step S1: Synchronous measurement of five-degree-of-freedom motion of the rotating shaft is achieved based on multi-faceted composite white light interferometry; Step S2: Separate the installation error of the measuring device.

7. The measurement method according to claim 6, characterized in that, Step S1 specifically involves: Before measurement, adjust the relative positions of the reference piece (5) and the white light interferometer so that interference fringes are present on the three facets in the image acquired by the industrial camera (9). The precision rotating shaft (1) rotates at a set speed, and the industrial camera (9) acquires images at different times. Suppose that the three facets of the reference element (5) pass through a virtual plane that is parallel to the reference mirror in the interference objective (6) and has the same optical path difference. This virtual plane is called the Peak Coherence Plane (PCP), and it coincides with the focal plane of the interference objective (6), allowing the image to be projected onto this virtual plane. An image coordinate system is defined on the PCP, where... shaft and The axis is located on the PCP. The axis is along the optical axis of the interference objective (6), with the origin at the center of the image; Sampling and calculation of white light interference fringes in a single frame image: Using image processing methods, threshold segmentation is employed to extract bright fringe regions from the image. Based on the segmentation results, fringe straight line fitting is performed to calculate the linear expression of each fringe in the image. Then, the positions of pairwise intersections and the center position are calculated. Finally, based on the intersection and center positions, the multi-faceted composite white light interference fringe image is segmented into multiple independent sub-images. Each sub-image contains complete information of a single set of interference fringes. Subsequently, each set of interference fringes is solved individually to obtain the position expression of the corresponding facet in the image coordinate system. (Equation 1) in Let g be the normal vector of the desired edge in the image coordinate system, and g is a constant term in the expression. For each group of interference fringes after segmentation, the direction of the zero-order bright fringe and its normal direction are obtained by threshold segmentation, edge detection, and line fitting methods in image processing. A line segment is defined by extending a certain length along the normal from a point on the zero-order bright fringe to both sides of the zero-order bright fringe. Through image processing methods, on the line segment Within the range, a grayscale profile is constructed to obtain a sequence of actual interference curves, and then the line segments are... Translate a small distance along the direction of the zero-order bright fringe to define a new line segment. Then, perform grayscale profiling to obtain a new set of actual interference curve sequences. Repeat this process multiple times to obtain several sets of actual interference curve sequences. Using the Hilbert transform method, these sets of actual interference curve sequences are analyzed to accurately extract several zero optical path difference positions and record the corresponding pixel positions. Finally, the least squares fitting method is used to accurately fit the expression of the straight line L in the image coordinate system for the zero-order bright fringe. This straight line L is the intersection line of the desired facet and the PCP. (Equation 2) Due to the various points on the reference part's edge surface Different z-values ​​result in interference fringe projections on the edge surface. The white light interference intensity curve on the Z-axis is calibrated by vertical scanning, yielding the following expression for the white light interference intensity curve: (Equation 3) in For carrier frequency, For the initial phase, is the width of the Gaussian function, used to describe the envelope function of the white light interference fringe pattern, and z is the height value. This corresponds to the light intensity at that altitude. The pixel scale of the image coordinate system is converted to the length scale of the actual coordinate system. Using the peak intensity point as the origin, a sequence of actual interference curves is obtained by constructing a grayscale profile along the normal to the precisely calculated straight line L. The actual distance of each point in the sequence from the peak point is... Using the x-axis as the horizontal axis, after normalization, we obtain a sequence of actual interference curves consisting of N discrete points. ; Then, the actual interference curve sequence is obtained through peak detection and curve fitting methods. The width of the three-level bright stripes And the width of the third bright fringe of the white light interference intensity curve I(z). The slope m of the measured plane normal to the corresponding edge face is obtained: (Equation 4) From the expression for the position of the facet in Equation 1, it can be seen that along the direction of the normal vector of line L... The horizontal unit vector is ,in The corresponding edge position expression along the normal vector direction The slope of the plane, i.e., the slope of the theoretical plane normal, is obtained by taking the derivative of the implicit function: (Equation 5) Will Substituting the values, we get: (Equation 6) The slope of the theoretical plane normal of the prism From Equation 6, we obtain that m is the slope of the measured plane normal. Setting them equal, we can solve for the coefficient. : (Equation 7) The coefficients in the expression for the position of the facet are obtained accordingly. The position expressions of the three facets of the reference part in the image coordinate system are determined by three sets of white light interference fringes, and after normalization, they are in the following form: (Equation 8) in, It is the first The components of the normal vector of each edge face The constant term of the expression for the position of the i-th facet is obtained by fitting it into Equation 2; By solving a system of equations consisting of the positional expressions of the three facets, the position of the cone apex in the image coordinate system at any given moment can be uniquely determined. The cone apex coordinates calculated from the first frame image Using this as a reference, determine the 3-DOF relative motion of the reference component at time k of the image frame. ; Given that the normal vectors of the three facets in the image coordinate system at a certain moment are... Assuming Let the normal vectors of the three facets of the reference piece be the normal vectors at their corresponding positions in the first frame image. Using these as a reference, there exists a rotation matrix R that rotates the normal vector of each facet at the reference position in the image coordinate system to the normal vector of that facet at a certain moment: (Equation 9) Equation 9 uses the Kabsch algorithm to solve for the rotation matrix R. The sum of the normal vectors of these three facets can then describe the change in the reference part's attitude, using the sum vector from the first frame as an example. Using this as a reference, the sum vector of the reference element at time k in the image coordinate system after relative rotation is calculated through the rotation matrix R. In obtaining and Then, the five-degree-of-freedom relative motion of the rotation axis in space was uniquely determined by the reference component during the k-th frame image.

8. The measurement method according to claim 7, characterized in that, In step S1, the precision rotating shaft (1) rotates at a speed of 8.33 rpm, and the industrial camera (9) captures images at different times at a frame rate of 50 fps.

9. The measurement method according to claim 7, characterized in that, Step S2 specifically involves: Based on the five-degree-of-freedom relative motion results obtained in step S1, the systematic errors caused by the installation are separated, including in-plane motion error separation and out-of-plane motion error separation. The in-plane motion error measurement and error separation are as follows: Taking the position of the reference part at the start of data recording as a reference, the motion trajectory of the cone vertex of the reference part calculated in the image coordinate system is a circle centered on the main axis rotation center. The relative movement at frame k is... This includes the eccentric motion component caused by installation eccentricity; Decompose motion into image coordinates. shaft and In the axis direction, in the k-th frame image, the rotation axis along Axial and radial motion error and along Axial and radial motion error Represented as: (Equation 10) in, Indicates the equivalent eccentric radius. This represents the initial phase, where ω is the rotational angular frequency. This indicates the position of the spindle rotation center in the image coordinate system; The out-of-plane motion error measurement and error separation are specifically as follows: During the rotation of the axis, due to installation errors, the vector measured in the k-th frame... The trajectory in space is a cone centered on the axis of rotation, and the axis of rotation is perpendicular to the image coordinate system. There will also be two axes, each orbiting around the image coordinate system. shaft and Static deflection of the shaft and This deflection angle reflects the installation error between the axis of rotation and the optical axis of the white light interferometer. The sum vector of the k-th frame Seeking a way around shaft and The tilt angle of the shaft is: (Equation 11) in The sum vector calculated for the k-th frame image The components of each axis, To bypass The tilt angle of the axis, To bypass The inclination angle of the axis; Decompose the tilting motion of the reference component into... shaft and The axis, in the k-th grayscale image, rotates around the axis. Tilting motion error of the shaft and around Tilting motion error of the shaft Represented as: (Equation 12) in, This represents the fixed deflection angle between the axis of the reference component and the axis of rotation of the rotating shaft, where ω is the angular frequency of rotation. Indicates the initial phase. and This represents the static deflection angle between the axis of rotation and the Z-axis of the image coordinate system; The axial error motion is directly obtained as: (Equation 13) in The relative movement along the Z-axis at time k of the image frame.

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