Spatial pose position calibration method of spectral confocal probe based on plane and spherical joint constraints

Abstract

The present invention discloses a method for calibrating the spatial pose position of a spectral confocal probe with plane and spherical joint constraints, which belongs to the field of measurement technology, including converting point information in a contact probe coordinate system into coordinate information in a base coordinate system, converting point information in a spectral confocal probe coordinate system into coordinate information in a base coordinate system; using a spectral confocal probe to obtain at least two point information in multiple planes, establishing a linear equation group, and solving to obtain the spatial pose of the spectral confocal probe; using a spectral confocal probe to measure the coordinate information of at least three points on a spherical surface, establishing an overdetermined equation group, and solving the zero point position of the spectral confocal probe. The spatial pose position calibration method of the present invention removes the coupling between the beam direction and the zero point position by introducing the elimination of spatial equations, realizes the separate calculation of the spatial pose and the zero point position of the spectral confocal probe, and can greatly improve the accuracy and efficiency of the spectral confocal probe pose position calibration.

Description

Technical Field

[0001] The invention belongs to the field of measurement technology, and in particular relates to a method for calibrating the spatial posture position of a spectral confocal probe with joint constraints of a plane and a spherical surface. Background Art

[0002] The spectral confocal probe is a high-precision non-contact measurement sensor based on the principle of optical dispersion and confocal technology. Its light source emits a beam of complex light with a wide spectrum. After passing through the dispersion lens, spectral dispersion occurs to form monochromatic light of different wavelengths, and the focus of each wavelength corresponds to a characteristic distance value. The measuring light is directed to the surface of the object and reflected back. Only the monochromatic light that meets the confocal condition and whose focus just falls on the wavelength of the object surface can be sensed by the spectrometer through the small hole. By calculating the wavelength of the sensed focus, according to the corresponding relationship between wavelength and distance, the distance value from the physical surface to the sensor is converted. The spectral confocal probe itself has the characteristics of high precision, non-contact measurement, strong material adaptability, strong interference ability and fast measurement speed.

[0003] When the spectral confocal probe is used in industrial applications, it is usually clamped on a three-dimensional coordinate measuring machine, and the three-dimensional coordinate measuring machine is used to drive the spectral confocal probe for mobile measurement. The traditional three-dimensional offline measurement method has the disadvantages of repeated clamping of the workpiece, which easily introduces errors and reduces processing efficiency. However, the positioning reference of the spectral confocal probe is inaccurate during installation, which will inevitably cause eccentricity and inclination. These installation errors will reduce the measurement accuracy, and the unknown zero point position of the spectral confocal probe will make it impossible to solve the absolute coordinates of the workpiece in space. Therefore, it is necessary to calibrate the installation posture and zero point position of the spectral confocal probe. Summary of the invention

[0004] In response to one or more of the above defects or improvement needs in the prior art, the present invention provides a method for calibrating the spatial pose position of a spectral confocal probe with joint constraints of a plane and a spherical surface, so as to obtain the spatial pose and zero point position of the spectral confocal probe installed on a three-coordinate measuring machine.

[0005] To achieve the above-mentioned object, the present invention provides a method for calibrating the spatial position and posture of a spectral confocal probe with a plane-spherical joint constraint, which is calibrated by a three-dimensional coordinate measuring machine. The three-dimensional coordinate measuring machine is provided with a contact probe and a spectral confocal probe, and the contact probe is a standard part arranged on the three-dimensional coordinate measuring machine. The contact probe and the spectral confocal probe can be synchronously displaced in three-dimensional directions; the method for calibrating the spatial position and posture of a spectral confocal probe with a plane-spherical joint constraint comprises the following steps:

[0006] S1. Establish the base coordinate system, contact probe coordinate system, spectral confocal probe coordinate system and workpiece coordinate system respectively;

[0007] S2. Use a contact probe to obtain position information of a point on the workpiece, and convert the point information obtained in the contact probe coordinate system into coordinate information in the base coordinate system; consider the installation inclination angle of the spectral confocal probe, obtain the coordinate information of the point on the workpiece under the spectral confocal probe, and convert the point information obtained in the spectral confocal probe coordinate system into coordinate information in the base coordinate system;

[0008] S3, using a spectral confocal probe to obtain coordinate information of at least two points in a plane, moving the spectral confocal probe to measure the coordinate information of at least two points respectively, and establishing a linear equation; obtaining coordinate information of at least two points in at least three planes, establishing a linear equation group, wherein the linear equation group includes the spatial posture of the spectral confocal probe; solving the linear equation group to obtain the spatial posture of the spectral confocal probe;

[0009] S4. Use a spectral confocal probe to calculate the coordinate information of at least three points on the spherical surface, move the spectral confocal probe respectively to measure the coordinate information of at least three points, bring the at least three point information into the spherical equation, and establish an overdetermined equation group, wherein the overdetermined equation group includes the spatial posture and zero point position of the spectral confocal probe, bring the spatial posture of the spectral confocal probe in step S3 into the overdetermined equation group for solution, and obtain the zero point position of the spectral confocal probe.

[0010] As a further improvement of the present invention, in step S2, the contact probe and the spectral confocal probe are synchronously displaced, and the coordinate information of the contact probe during measurement is an accurate value;

[0011] The point information on the workpiece measured by the contact probe is brought into the workpiece point measured by the spectral confocal probe to obtain the coordinate information of the workpiece point measured by the spectral confocal probe in the base coordinate system.

[0012] As a further improvement of the present invention, the coordinate information of the workpiece point measured by the spectral confocal probe in the base coordinate system is obtained in the following manner:

[0013] The directions of the three axes XYZ in the base coordinate system, the contact probe coordinate system and the spectral confocal probe coordinate system are parallel and consistent;

[0014] Establish homogeneous transformation matrices from the base coordinate system to the X-axis coordinate system, from the X-axis coordinate system to the Y-axis coordinate system, and from the Y-axis coordinate system to the Z-axis coordinate system respectively;

[0015] Set the origin direction vector of the contact probe and base coordinate system to , obtain the homogeneous transformation matrix from the Z-axis coordinate system to the spectral confocal probe coordinate system;

[0016] Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system;

[0017] According to the homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system, the homogeneous transformation matrix from the Z-axis coordinate system to the probe coordinate system, and the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system, the homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system is obtained;

[0018] According to the principle of homogeneous transformation, the theoretical coordinates of the points on the workpiece in the base coordinate system are obtained;

[0019] The angle between the optical axis of the spectral confocal probe and the three coordinate axes is set to obtain the coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system.

[0020] As a further improvement of the present invention, the establishment of the linear equation system in step S3 includes:

[0021] S301, setting a calibration plane on a three-dimensional coordinate measuring machine, wherein the calibration plane is not parallel to any of the XYZ axes of the three coordinate axes, and establishing a plane equation; the plane equation is established based on four points in the plane;

[0022] S302, using a spectral confocal probe to calibrate a point on the plane, moving the spectral confocal probe to obtain information about another point in the calibration plane, bringing the two point information into the plane equation and subtracting them to obtain an equation after the zero point position is eliminated;

[0023] S303, select another two calibration planes, repeat step S302, and obtain equations for subtracting another two sets of two-point position information;

[0024] S304, combining the equations in S302 and S303 to establish a linear equation system, solving the equation system to obtain the spatial position and posture of the spectral confocal probe.

[0025] As a further improvement of the present invention, the theoretical coordinate calculation method of the point on the workpiece in the base coordinate system is:

[0026] The homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, and the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system are respectively:

[0027] (Formula 1)

[0028] The X m , Y m , Z m They are the coordinate readings of the contact probe, respectively;

[0029] Set the origin of the contact probe and base coordinate system to , the transformation matrix from the Z-axis coordinate system to the spectral confocal probe coordinate system is obtained as:

[0030] (Formula 2)

[0031] Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system:

[0032] (Formula 3)

[0033] The homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system is:

[0034] (Formula 4)

[0035] The coordinates of the workpiece point in the base coordinate system obtained by using the homogeneous coordinate transformation principle are:

[0036] (Formula 5).

[0037] As a further improvement of the present invention, the coordinate calculation method of the workpiece point measured by the spectral confocal probe in the base coordinate system is:

[0038] Set the angles between the optical axis of the spectral confocal probe and the three coordinate axes to The unit direction vector of the optical axis in the spectral confocal probe coordinate system is ;

[0039] The homogeneous transformation matrix that brings the unit direction vector into the base coordinate system to the workpiece coordinate system is:

[0040] (Formula 6)

[0041] The coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system are obtained using the principle of homogeneous coordinate transformation:

[0042] (Formula 7).

[0043] As a further improvement of the present invention, the establishment of the linear equation system in step S3 includes:

[0044] The plane equation is:

[0045] (Formula 8)

[0046] Among them, A, B, C, and D are the parameters of the spatial position in the plane;

[0047] The displacement value measured by the spectral confocal probe is d 1 , the displacement value of the contact probe is x 1 ,y 1 , z 1 According to formula 7, the point coordinates are ;

[0048] Substituting the point coordinates into the plane equation, we get Formula 9:

[0049] (Formula 9)

[0050] Move the spectral confocal probe to measure another point on the plane. The displacement value of the spectral confocal probe at another point is d 2 , the displacement value of the contact probe is x 2 ,y 2 、z 2 , get the coordinates of another point , substituting the point coordinates into the plane equation, we get formula 10:

[0051] (Formula 10)

[0052] Formula 9-Formula 10 gives:

[0053] (Formula 11).

[0054] As a further improvement of the present invention, in step S303, the equations obtained by calibrating the position information of two points in the other two calibration planes are:

[0055] (Formula 12)

[0056] (Formula 13)

[0057] Combining equations 11, 12, and 13, we get the linear equation system:

[0058] (Formula 14).

[0059] As a further improvement of the present invention, the establishment of the overdetermined equations in step S4 includes:

[0060] Set the coordinates of the center of the sphere in the base coordinate system to , set the angle between the optical axis of the spectral confocal probe and the three-axis coordinates of the base coordinate system to , the unit direction vector of the optical axis is calculated as: ; Set the spectral confocal probe to measure the displacement value d 7 , the reading of the contact probe is x 7 ,y7 、z 7 , the coordinates of point S on the spherical surface in the base coordinate system are :

[0061]

[0062] Point S is on the sphere, then , substitute the coordinates of point S and point O into the spherical equation:

[0063] (Formula 15)

[0064] The spectral confocal probe is used to measure the position of another point T on the spherical surface. The coordinates of point T in the base coordinate system are calculated as follows: :

[0065]

[0066] Point T is on the sphere, then , substitute the coordinates of point T and point O into the spherical equation:

[0067] (Formula 16)

[0068] The spectral confocal probe is used to measure the point information on the spherical surface multiple times. The reading of the spectral confocal probe is , the displacement information of the contact probe is , we get the overdetermined system of equations:

[0069] (Formula 17)

[0070] Among them, the constraints of formula 17 are:

[0071] (Equation 18).

[0072] As a further improvement of the present invention, the formula 17 is solved using the LM iterative solution algorithm to obtain the zero point position of the spectral confocal probe.

[0073] The above-mentioned improved technical features can be combined with each other as long as they do not conflict with each other.

[0074] In general, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

[0075] (1) The method for calibrating the spatial pose position of the spectral confocal probe with joint constraints of plane and sphere of the present invention adopts a contact probe to assist in the measurement. The standard structure of the three-coordinate measuring machine and the contact probe makes the positions of the contact probe and the three-coordinate measuring machine relatively standard. After the measurement coordinates of the contact probe and the spectral confocal probe are converted to the base coordinate system, the measurement results of the contact probe in the standard position can provide data for the spectral confocal probe. Secondly, in the calculation process, the spatial pose and zero point position of the spectral confocal probe are decoupled to realize the separate calculation of the spatial pose and zero point position, which can greatly improve the accuracy and efficiency of the calibration.

[0076] (2) The spatial pose position calibration method of the spectral confocal probe with plane-spherical joint constraints of the present invention removes the coupling between the light beam direction and the zero point position by introducing the spatial equation elimination method, and obtains a linear equation group containing only the light beam direction position parameters, thereby obtaining the spatial pose of the spectral confocal probe. This solution process can eliminate the influence of the zero point position on the spatial pose, and the method of solving the linear equation group can greatly improve the accuracy of the spatial pose; after the spatial pose is solved, the nonlinear equation group containing the zero point position is introduced for solution. At this time, an iterative algorithm is used to solve the three unknown quantities of the zero point position, which can avoid the tediousness and error problems of jointly solving the zero point position and six unknown quantities in the spatial pose in the traditional method, and greatly improve the calculation accuracy of the zero point position.

[0077] (3) The spatial pose position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface of the present invention solves the spatial pose and zero point position of the spectral confocal probe by jointly solving the plane equation and the spherical equation. During the calibration process of the spectral confocal probe, the moving position and mode of the spectral confocal probe are not restricted, and the cumbersome calibration process under multiple restriction conditions such as fixed point, fixed distance and fixed angle in the conventional calibration method can be avoided. The pose calibration process of the spectral confocal probe can be simplified and the calibration efficiency can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is a schematic structural diagram of a three-coordinate measuring machine in an embodiment of the present invention;

[0079] Figure 2 This is a schematic diagram of the plane calibration of the spectral confocal probe in an embodiment of the present invention;

[0080] Figure 3 Schematic diagram of spherical surface calibration of the spectral confocal probe in an embodiment of the present invention;

[0081] Figure 4 is a comparison diagram of simulation error results of different methods in a simulation experiment in an embodiment of the present invention;

[0082] Figure 5is a comparison diagram of the results after the simulation errors are synthesized in the simulation experiment in the embodiment of the present invention;

[0083] Figure 6 It is a flow chart of a method for calibrating the spatial posture position of a spectral confocal probe with plane-spherical joint constraints in an embodiment of the present invention. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0085] In the description of the present invention, it should be understood that, unless otherwise specified, terms such as “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “clockwise”, “counterclockwise”, “axial”, “radial”, “circumferential”, etc., indicating orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0086] In addition, unless otherwise specified, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0087] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0088] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, a first feature being "above", "above" or "above" a second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. A first feature being "below", "below" or "below" a second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is lower in level than the second feature.

[0089] Example:

[0090] See also Figures 1 to 6 The method for calibrating the spatial position and posture of the spectral confocal probe with joint constraints of plane and spherical surface in the preferred embodiment of the present invention is completed by a three-axis coordinate measuring machine, on which a spectral confocal probe and a contact probe are arranged, wherein the three-axis coordinate measuring machine includes a measuring platform, on which two sliding tracks arranged side by side are arranged along a first direction, first support columns are vertically arranged on the two sliding tracks, a connecting column is arranged between the two first support columns, the connecting column is arranged along a second direction, a telescopic column is slidably arranged on the connecting column, a spectral confocal probe and a contact probe are arranged at the lower end of the telescopic column, and the lower end of the telescopic column is telescopic, so that the spectral confocal probe and the contact probe can be synchronously moved along the third direction. The movement of the spectral confocal probe and the contact probe along the first direction, the second direction and the third direction is realized by the three-axis coordinate measuring machine to complete the measurement of the spectral confocal probe and the contact probe.

[0091] Furthermore, the contact probe in the present application is a standard structure arranged on a three-axis coordinate measuring machine, that is, the error between the contact probe and the three-axis coordinate measuring machine is controlled within a precise range, and the error is predictable or foreseeable. When the perception result of the contact probe is introduced into the posture calibration of the spectral workpiece probe, the data measured by the contact probe can be used as standard data, and the introduced error is relatively small, which is beneficial to improving the accuracy of the spectral confocal probe posture calibration.

[0092] Furthermore, the spectral confocal probe in the present application is fixed at the end of the telescopic column by a clamping structure. There will be a certain error in the relative fixation between the clamping structure and the spectral confocal probe, resulting in a deviation in the spatial posture of the spectral confocal probe, that is, the optical axis of the spectral confocal probe is deviated from the first direction, the second direction and the third direction on the three-axis coordinate measuring machine. Preferably, the first direction in the present application is the X-axis direction, the second direction is the Y-axis direction, and the third direction is the Z-axis direction.

[0093] Furthermore, the spectral confocal probe posture calibration direction in the present application is calibrated using the above-mentioned three-coordinate measuring machine, which includes the following steps:

[0094] S1. Establish the base coordinate system, contact probe coordinate system, spectral confocal probe coordinate system and workpiece coordinate system respectively;

[0095] S2. Use a contact probe to obtain position information of a point on the workpiece, and convert the point information obtained in the contact probe coordinate system into coordinate information in the base coordinate system; consider the installation inclination angle of the spectral confocal probe, obtain the coordinate information of the point on the workpiece under the spectral confocal probe, and convert the point information obtained in the spectral confocal probe coordinate system into coordinate information in the base coordinate system;

[0096] S3, using a spectral confocal probe to obtain coordinate information of at least two points in a plane, moving the spectral confocal probe to measure the coordinate information of at least two points respectively, and establishing a linear equation; obtaining coordinate information of at least two points in at least three planes, establishing a linear equation group, wherein the linear equation group includes the spatial posture of the spectral confocal probe; solving the linear equation group to obtain the spatial posture of the spectral confocal probe;

[0097] S4. Use a spectral confocal probe to calculate the coordinate information of at least three points on the spherical surface, move the spectral confocal probe respectively to measure the coordinate information of at least three points, bring the at least three point information into the spherical equation, and establish an overdetermined equation group, which includes the spatial posture and zero point position of the spectral confocal probe; bring the spatial posture of the spectral confocal probe in step S3 into the overdetermined equation group for solution to obtain the zero point position of the spectral confocal probe.

[0098] In the process of calibrating the posture of a conventional spectral confocal probe, the spatial posture and zero position of the spectral confocal probe are usually solved in the same set of equations. Since the set of equations is a nonlinear set of equations, the deviations caused by multiple unknowns will gradually accumulate during the continuous iterative calculation process, resulting in a large error between the solved spatial posture and the fixed position. Secondly, since there are errors in the installation position of the spectral confocal probe itself, in order to ensure the amount of known numbers in the set of equations, it is usually necessary to move the spectral confocal probe at a fixed point, fixed distance, fixed angle, etc., that is, to perform measurements at set points, resulting in a more complicated and cumbersome calibration process for the spectral confocal probe, as well as time-consuming and labor-intensive.

[0099] The method for calibrating the spatial pose position of a spectral confocal probe with a plane-spherical joint constraint of the present invention adopts a contact probe for assisted measurement. A three-coordinate measuring machine and the contact probe form a standard structure, so that the positions of the contact probe and the three-coordinate measuring machine are relatively standard. After the measurement coordinates of the contact probe and the spectral confocal probe are converted into a base coordinate system, the measurement result of the contact probe in the standard position can drive the displacement information of the spectral confocal probe, which can facilitate the determination of the pose of the spectral confocal probe. Secondly, the present application decouples the spatial pose and zero point position of the spectral confocal probe during the calculation process, and realizes the separate calculation of the spatial pose and zero point position of the spectral confocal probe. The fewer the unknowns in the same set of equations, the more accurate the calculation result and the higher the calculation efficiency, which can greatly improve the calibration accuracy and efficiency of the spatial pose position of the spectral confocal probe.

[0100] Specifically, the spatial pose position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in the present application refers to a calibration method for the spatial pose and zero point position of the spectral confocal probe. The base coordinate system in the present application corresponds to the machine coordinate system: OC-XYZ, which takes the absolute zero position of the grating scale of each axis in the three-axis coordinate system as the origin, and the three-axis directions and scales are parallel and consistent with the XYZ axes in the three-axis coordinate measuring machine; the contact probe coordinate system in the present application: OT-XYZ, takes the center of the stylus tip of the contact probe as the coordinate origin, and the three coordinate axes are respectively parallel to the three coordinate axes of the OC system, and the probe reading of the contact probe is the coordinate of the OT point in the OC system; the spectral confocal probe coordinate system in the present application: OS-XYZ, takes the starting point of the range of the spectral confocal probe as the coordinate origin, and the three coordinate axes are respectively parallel to the three coordinate axes of the OC coordinate system; the workpiece coordinate system in the present application: OB-XYZ, this coordinate system uses the workpiece feature to define the origin, and the XYZ axis directions and sizes are respectively parallel and consistent with the axes of the OC coordinate system.

[0101] As an optional embodiment of the present invention, in the above step S2, the contact probe and the spectral confocal probe are displaced synchronously, and the coordinate information during the measurement by the contact probe is an accurate value; the point information on the workpiece obtained by the contact probe is brought into the workpiece point calculated by the spectral confocal probe to obtain the coordinate information of the workpiece point measured by the spectral confocal probe in the base coordinate system. In conventional calibration methods, the spectral confocal probe needs to be tested at a specific point to ensure the accuracy of the position of the spectral confocal probe. The present application uses a synchronous displacement method of the spectral confocal probe and the contact probe, so that the test data of the contact probe can calibrate the displacement information of the spectral confocal probe during the test. That is, the displacement information of the spectral confocal probe moving from one point to another during the test can be obtained through the contact probe.

[0102] Further, as an optional embodiment of the present invention, the method for acquiring the coordinate information of the workpiece point measured by the spectral confocal probe in step S2 of the present application in the base coordinate system is:

[0103] Among them, the directions of the three axes XYZ in the base coordinate system, the contact probe coordinate system and the spectral confocal probe coordinate system are parallel and consistent;

[0104] Establish homogeneous transformation matrices from the base coordinate system to the X-axis coordinate system, from the X-axis coordinate system to the Y-axis coordinate system, and from the Y-axis coordinate system to the Z-axis coordinate system respectively;

[0105] Set the origin of the contact probe and base coordinate system to , get the homogeneous transformation matrix from the Z-axis coordinate system to the probe coordinate system;

[0106] Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system;

[0107] According to the homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the Z-axis coordinate system to the Y-axis coordinate system, the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system, the homogeneous transformation matrix from the Z-axis coordinate system to the probe coordinate system, and the homogeneous transformation matrix from the spectral confocal probe to the workpiece coordinate system, the homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system is obtained;

[0108] According to the principle of homogeneous transformation, the theoretical coordinates of the points on the workpiece in the base coordinate system are obtained;

[0109] The angle between the optical axis of the spectral confocal probe and the three coordinate axes is set to obtain the coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system.

[0110] Further, as an optional embodiment of the present invention, the establishment of the linear equation in step S3 of the present application includes the following steps:

[0111] S301, setting a calibration plane on a three-dimensional coordinate measuring machine, the calibration plane is not parallel to the XYZ axis of any three coordinate axes, and establishing a plane equation; the plane equation is established with four points in the plane;

[0112] S302, using a spectral confocal probe to calibrate a point on the plane, moving the spectral confocal probe to obtain information about another point in the calibration plane, bringing the two point information into the plane equation and subtracting them to obtain an equation after the zero point position is eliminated;

[0113] S303, select another two calibration planes, repeat step S302, and obtain equations for subtracting another two sets of two-point position information;

[0114] S304, combining the equations in steps S302 and S303 to establish a linear equation system, solving the equation system to obtain the spatial position and posture of the spectral confocal probe.

[0115] Further, as an optional embodiment of the present invention, the theoretical coordinate calculation method of the point on the workpiece in the base coordinate system in the present application is:

[0116] First, the homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, and the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system are:

[0117] (Formula 1)

[0118] Among them, X m , Y m , Z m They are the coordinate readings of the contact probe respectively. The contact probe is moved along the XYZ directions by a three-dimensional coordinate measuring machine to make the contact end of the contact probe contact a point on the workpiece to obtain the position information of the point on the workpiece. The coordinate reading of the contact probe is the displacement distance along the XYZ directions.

[0119] Set the origin of the contact probe and base coordinate system to , the transformation matrix from the Z-axis coordinate system to the spectral confocal probe coordinate system is obtained as:

[0120] (Formula 2)

[0121] Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system:

[0122] (Formula 3)

[0123] Combining Formula 1, Formula 2, and Formula 3, we can get the homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system:

[0124] (Formula 4)

[0125] Wherein, d is the distance between the end of the spectral confocal probe and the point on the workpiece obtained by calculation after the spectral confocal probe sends test light to the point on the workpiece;

[0126] Then, the coordinates of the workpiece point in the base coordinate system are obtained by using the principle of homogeneous coordinate transformation:

[0127] (Formula 5)

[0128] Further, as an optional embodiment of the present invention, the coordinate calculation method of the workpiece point measured by the spectral confocal probe in the base coordinate system is:

[0129] Set the angles between the optical axis of the spectral confocal probe and the three coordinate axes to The unit direction vector of the optical axis in the spectral confocal probe coordinate system is ;

[0130] The homogeneous transformation matrix that brings the unit direction vector into the base coordinate system to the workpiece coordinate system is:

[0131] (Formula 6)

[0132] The coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system are obtained using the principle of homogeneous coordinate transformation:

[0133] (Formula 7).

[0134] Further, as an optional embodiment of the present invention, the establishment of the linear equation system in step S3 of the present application includes:

[0135] First, the plane equation is:

[0136] (Formula 8)

[0137] Among them, A, B, C, and D are the parameters of the spatial positions of the four points in the plane;

[0138] In the above formula 8, a contact probe is used to measure each parameter respectively, and the SVD decomposition method (singular value decomposition method) is used to solve the plane point cloud so that the sum of the distances from the plane to all points is the shortest. In this way, the position of each point and the plane on which it is located are fitted to reduce the calculation error.

[0139] Then the spectral confocal probe is used to measure the displacement value d 1 , the displacement value of the contact probe is x 1 ,y 1 , z 1 According to formula 7, the point coordinates are ;

[0140] Substituting the point coordinates into the plane equation, we get Formula 9:

[0141] (Formula 9)

[0142] Move the spectral confocal probe to measure another point on the plane. The displacement value of the spectral confocal probe at another point is d 2 , the displacement value of the contact probe is x 2 ,y2 、z 2 , get the coordinates of another point , substituting the point coordinates into the plane equation, we get formula 10:

[0143] (Formula 10)

[0144] Formula 9-Formula 10 gives:

[0145] (Formula 11)

[0146] It can be seen from the above formula 11 that the zero point position is eliminated, and the zero point position and the spatial pose are decoupled. That is, the calculation of the spatial pose of the spectral confocal probe is not affected by the zero point position. Formula 10 only contains the spatial poses a, b, and c, so that the spatial pose of the spectral confocal probe can be obtained.

[0147] Further, as an optional embodiment of the present invention, in step S303 of the present application, the equations obtained by obtaining the position information of two points in the other two calibration planes are:

[0148] (Formula 12)

[0149] (Formula 13)

[0150] Combining equations 11, 12, and 13, we get the linear equation system:

[0151] (Formula 14)

[0152] Specifically, there are three equations and three unknowns in the above formula 14, which can be solved to obtain the three unknown quantities of the spatial posture. Optionally, the present application can also increase the number of measurement groups and establish an overdetermined linear equation system to solve the equation system The least squares solution of ;

[0153] (Formula 19)

[0154] In the formula, for The generalized inverse matrix of matrix A can be solved in this way to obtain the spatial position .

[0155] Further, as an optional embodiment of the present invention, the establishment of the overdetermined equations in step S4 in the present application includes:

[0156] Set the coordinates of the center of the sphere in the base coordinate system to , set the angle between the optical axis of the spectral confocal probe and the three-axis coordinates of the base coordinate system to , the unit direction vector of the optical axis is ; Set the spectral confocal probe to measure the displacement value d 7 , the reading of the contact probe is x 7 ,y 7 、z 7 , the coordinates of point S on the spherical surface in the base coordinate system are :

[0157]

[0158] Point S is on the sphere, then , substitute the coordinates of point S and point O into the spherical equation:

[0159] (Formula 15)

[0160] The spectral confocal probe is used to measure the position of another point T on the spherical surface. The coordinates of point T in the base coordinate system are calculated as follows: :

[0161]

[0162] Point T is on the sphere, then , substitute the coordinates of point T and point O into the spherical equation:

[0163] (Formula 16)

[0164] The spectral confocal probe is used to measure the point information on the spherical surface multiple times. The reading of the spectral confocal probe is , the displacement information of the contact probe is , we get the overdetermined system of equations:

[0165] (Formula 17)

[0166] Among them, the constraints of formula 17 are:

[0167] (Formula 18)

[0168] The present application controls the contact probe and the spectral confocal probe to measure together, uses the contact probe to measure enough points on the standard sphere to obtain the spherical equation, and then uses the spectral confocal probe to measure at least three points on the standard sphere. The above formula 14 has been used to obtain it. After substituting it into formula 17, it can be seen that the zero point position The solution process is converted into solving a decoupled nonlinear equation set. For this nonlinear equation set, the LM iterative solution algorithm can be used to solve it and obtain the zero point position.

[0169] Furthermore, for the spatial pose position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in the present application, simulation can be used to verify the error value.

[0170] Specifically, in order to correspond to the above-mentioned plane and spherical calibration methods, the simulation experiment in this application is also divided into two parts: simulation of spatial posture linear preservation algorithm and simulation of zero-point position nonlinear calibration algorithm.

[0171] In order to make the simulation experiment simulate the actual on-machine measurement process as much as possible, it is necessary to add Gaussian noise to the X, Y, and Z coordinates of the contact probe corresponding to the detection point and the measurement value d of the spectral confocal probe according to the positioning error of the three-dimensional coordinate measuring machine and the measurement error of the spectral confocal probe in the on-machine measurement system.

[0172] The production time shows that the distribution of the positioning error of the bed rail conforms to the statistical law of normal distribution. The mean of the normal distribution reflects the systematic error part of the rail positioning error; the standard deviation reflects the random error part of the rail positioning error. Among them, the rail positioning accuracy A can be expressed as:

[0173] (Formula 20)

[0174] The guide rail repeat positioning accuracy R can be expressed as:

[0175] (Formula 21)

[0176] Specifically for the three-coordinate measuring machine used in this application, the positioning accuracy of the X, Y, and Z axes reaches 0.0027mm, and the repeat positioning accuracy reaches 0.003mm. According to formulas 18 and 19, as well as the positioning accuracy and repeat positioning accuracy of the three-coordinate guide rails, the Gaussian noise mean of the XYZ three-axis coordinates is set to 0.0012mm, and the standard deviation is set to 0.0005mm. The probability of these two types of high-speed noise taking positive and negative values ​​is 50%. The spectral confocal probe used in this application has good measurement accuracy within a 10° inclination range, and the measurement error is within ±0.0003mm. Here, the Gaussian noise mean of the measurement value d of the spectral confocal probe is set to 0mm, and the standard deviation is set to 0.00015mm.

[0177] Set the light direction vector of the spectral confocal probe to α=28.44°, β=61.84°, γ=86.30°, the zero point position to (δx, δy, δz)=(12.75, 11.02, 10.77), and the diameter of the high-precision standard ball to D=25mm. Assume that the measurement value of the spectral confocal probe is a random value between 60-70mm. In actual measurement, the sensor measurement points are the surfaces of the standard plane and the sphere, so the random sampling points are placed on the surfaces of the sphere and the plane.

[0178] Then, the generated raw data are calibrated using the method proposed in this paper and the traditional spherical iteration method. The results are shown in the figure. Figure 4 Show.

[0179] Then, the calibrated three-dimensional space angle is synthesized into a vector in a direction, and the position information at the calibration point is synthesized into a distance. The synthesis result is as follows: Figure 5 Show.

[0180] Through the above Figure 4 , Figure 5 It can be seen intuitively that the error of the spectral confocal probe spatial pose position calibration method with plane spherical joint constraints in this application is much smaller than the error of the traditional spherical iterative calibration method. Here, the transmission spherical iterative calibration method refers to a method of calibrating the spatial pose and zero point position of the spectral confocal probe at the same time.

[0181] Specifically, in terms of angle synthesis error, the error of the method in this application is 0.0126°, and the error of the spherical iteration method is 0.1761°, with an accuracy improvement of 92.8%.

[0182] In terms of position synthesis error, the method error in this application is = (0.002, 0.007, 0.028), the synthesis result is ∆d=0.0075; the error of the spherical iteration method is =(0.146,0.056,0.157). The synthesis result is ∆d=0.0427, and the accuracy is improved by 82.4%.

[0183] In this simulation experiment, the calibration errors of the light-emitting direction unit vector in three dimensions are all within ±0.005mm, and the calibration errors of the zero-point position vector in three dimensions are all within ±0.03mm. In summary, the calibration errors of the above simulation experiments meet the actual measurement requirements, and the spatial position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in this application is fully feasible and effective.

[0184] Furthermore, the spatial posture position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in the present application can also be verified by experiments.

[0185] Specifically, for the spatial position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in this application, this application designs an on-machine measurement calibration experiment. In this experiment, the three-coordinate measuring machine uses Hexagon's Explorer Classic 05.07.05 bridge-type three-coordinate measuring machine, whose accuracy is 2.7±3.5L / 1000μm, and the optical sensor uses a self-developed spectral confocal probe with a measuring range of 4mm. The nominal diameter of the standard ball is 15.0830mm.

[0186] In the experiment, a standard sphere and three standard planes were used as measurement objects, and spectral confocal measurement and contact measurement were performed on them respectively. The measurement method includes the following steps:

[0187] (1) Use a fixture to clamp the spectral confocal probe and install the spectral confocal probe at the three-coordinate contact probe;

[0188] (2) Place two standard balls on the workbench of the three-dimensional coordinate measuring machine, one of which is used as the reference ball, with the center of the ball as the origin of the reference coordinate system, and the other ball as the measurement ball; place three gauge blocks on the workbench as standard planes for calibration;

[0189] (3) Use a contact probe to measure the reference ball and obtain the coordinate value of the center of the reference ball in the base coordinate system corresponding to the contact probe, so as to convert the measurement result of the contact probe into the reference coordinate system; here the contact probe is installed in the Z-axis direction of the three-dimensional coordinate measuring machine;

[0190] (4) Use a contact probe to select points on the measuring sphere, use the least squares method to fit the obtained measurement data into a spherical surface, and obtain the radius and center coordinates of the measuring sphere; use a contact probe to select points on three standard planes to obtain the plane equations of the three planes;

[0191] (5) Use a spectral confocal probe to measure at least two points on each plane, and record the coordinates of the contact probe and the measured displacement value of the spectral confocal probe; use a spectral confocal probe to measure at least 6 points on the standard sphere, and record the coordinates of the contact probe and the measured displacement value of the spectral confocal probe;

[0192] (6) Complete the collection of calibration data;

[0193] (7) Use a spectral confocal probe to measure the standard sphere and the standard plane respectively, and record the coordinates of the contact probe and the measured displacement value of the spectral confocal probe for accuracy verification.

[0194] Five groups were calibrated using the spectral confocal probe spatial posture position calibration method with plane-spherical joint constraints in this application. The results are shown in the following table:

[0195] Table 1 Multiple calibration results

[0196]

[0197] The five sets of calibrated data were used to verify the accuracy of flatness and spherical fitting error. The results are as follows:

[0198] Table 2 Calibration accuracy verification (flatness)

[0199]

[0200] Table 3 Calibration accuracy verification (spherical fitting error)

[0201]

[0202] Through the fitting errors in flatness and sphericity in Tables 2 and 3 above, it can be seen that the error of the spatial pose position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface in this application is much smaller than the calibration error of the pure spherical surface method. The calibration method in this application can greatly improve the calibration accuracy.

[0203] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calibrating the spatial position of a spectral confocal probe with joint constraints of plane and spherical surface, characterized in that: It is calibrated by a three-dimensional coordinate measuring machine, on which a contact probe and a spectral confocal probe are provided, the contact probe is a standard part arranged on the three-dimensional coordinate measuring machine, and the contact probe and the spectral confocal probe can be synchronously displaced in three-dimensional directions; the spatial position calibration method of the spectral confocal probe with joint constraints of plane and spherical surface comprises the following steps: S1. Establish the base coordinate system, contact probe coordinate system, spectral confocal probe coordinate system and workpiece coordinate system respectively; S2. Use a contact probe to obtain position information of a point on the workpiece, and convert the point information obtained in the contact probe coordinate system into coordinate information in the base coordinate system; consider the installation inclination angle of the spectral confocal probe, obtain the coordinate information of the point on the workpiece under the spectral confocal probe, and convert the point information obtained in the spectral confocal probe coordinate system into coordinate information in the base coordinate system; S3, using a spectral confocal probe to obtain coordinate information of at least two points in a plane, moving the spectral confocal probe to measure the coordinate information of at least two points respectively, and establishing a linear equation; obtaining coordinate information of at least two points in at least three planes, establishing a linear equation group, wherein the linear equation group includes the spatial posture of the spectral confocal probe; solving the linear equation group to obtain the spatial posture of the spectral confocal probe; S4. Use a spectral confocal probe to calculate the coordinate information of at least three points on the spherical surface, move the spectral confocal probe respectively to measure the coordinate information of at least three points, bring the at least three point information into the spherical equation, and establish an overdetermined equation group, wherein the overdetermined equation group includes the spatial posture and zero point position of the spectral confocal probe, bring the spatial posture of the spectral confocal probe in step S3 into the overdetermined equation group for solution, and obtain the zero point position of the spectral confocal probe.

2. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 1 is characterized in that: In the step S2, the contact probe and the spectral confocal probe are displaced synchronously, and the coordinate information of the contact probe during measurement is an accurate value; The point information on the workpiece measured by the contact probe is brought into the workpiece point measured by the spectral confocal probe to obtain the coordinate information of the workpiece point measured by the spectral confocal probe in the base coordinate system.

3. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 2 is characterized in that: The method for acquiring the coordinate information of the workpiece point measured by the spectral confocal probe in the base coordinate system in step S2 is: The directions of the three axes XYZ in the base coordinate system, the contact probe coordinate system and the spectral confocal probe coordinate system are parallel and consistent; Establish homogeneous transformation matrices from the base coordinate system to the X-axis coordinate system, from the X-axis coordinate system to the Y-axis coordinate system, and from the Y-axis coordinate system to the Z-axis coordinate system respectively; Set the origin direction vector of the contact probe and base coordinate system to , obtain the homogeneous transformation matrix from the Z-axis coordinate system to the spectral confocal probe coordinate system; Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system; According to the homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system, the homogeneous transformation matrix from the Z-axis coordinate system to the probe coordinate system, and the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system, the homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system is obtained; According to the principle of homogeneous transformation, the theoretical coordinates of the points on the workpiece in the base coordinate system are obtained; The angle between the optical axis of the spectral confocal probe and the three coordinate axes is set to obtain the coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system.

4. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 3 is characterized in that: The establishment of the linear equation system in step S3 includes: S301, setting a calibration plane on a three-dimensional coordinate measuring machine, wherein the calibration plane is not parallel to any of the XYZ axes of the three coordinate axes, and establishing a plane equation; the plane equation is established based on four points in the plane; S302, using a spectral confocal probe to calibrate a point on the plane, moving the spectral confocal probe to obtain information about another point in the calibration plane, bringing the two point information into the plane equation and subtracting them to obtain an equation after the zero point position is eliminated; S303, select another two calibration planes, repeat step S302, and obtain equations for subtracting another two sets of two-point position information; S304, combining the equations in S302 and S303 to establish a linear equation system, solving the equation system to obtain the spatial position and posture of the spectral confocal probe.

5. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 4 is characterized in that: The theoretical coordinate calculation method of the point on the workpiece in the base coordinate system is: The homogeneous transformation matrix from the base coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, and the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system are respectively: (Formula 1) The X m , Y m , Z m They are the coordinate readings of the contact probe, respectively; Set the origin of the contact probe and base coordinate system to , the transformation matrix from the Z-axis coordinate system to the spectral confocal probe coordinate system is obtained as: (Formula 2) Set the reading of the spectral confocal probe to d, and obtain the homogeneous transformation matrix from the spectral confocal probe coordinate system to the workpiece coordinate system: (Formula 3) The homogeneous transformation matrix from the base coordinate system to the workpiece coordinate system is: (Formula 4) The coordinates of the workpiece point in the base coordinate system obtained by using the homogeneous coordinate transformation principle are: (Formula 5).

6. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 5 is characterized in that: The coordinate calculation method of the workpiece point measured by the spectral confocal probe in the base coordinate system is: Set the angles between the optical axis of the spectral confocal probe and the three coordinate axes to The unit direction vector of the optical axis in the spectral confocal probe coordinate system is ; The homogeneous transformation matrix that brings the unit direction vector into the base coordinate system to the workpiece coordinate system is: (Formula 6) The coordinates of the workpiece point measured by the spectral confocal probe in the base coordinate system are obtained using the principle of homogeneous coordinate transformation: (Formula 7).

7. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 6 is characterized in that: The establishment of the linear equation system in step S3 includes: The plane equation is: (Formula 8) Among them, A, B, C, and D are the parameters of the spatial position in the plane; The displacement value measured by the spectral confocal probe is d1, and the displacement values ​​of the contact probe are x1, y1, and z1. The point coordinates are obtained according to formula 7: ; Substituting the point coordinates into the plane equation, we get Formula 9: (Formula 9) Move the spectral confocal probe to measure another point on the plane. The displacement value of the spectral confocal probe measuring the other point is d2, and the displacement values ​​of the contact probe are x2, y2, and z2. The coordinates of the other point are obtained. , substituting the point coordinates into the plane equation, we get formula 10: (Formula 10) Formula 9-Formula 10 gives: (Formula 11).

8. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 7 is characterized in that: In step S303, the equations obtained by calibrating the position information of two points in the other two calibration planes are: (Formula 12) (Formula 13) Combining equations 11, 12, and 13, we get the linear equation system: (Formula 14).

9. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 1 is characterized in that: The establishment of the overdetermined equations in step S4 includes: Set the coordinates of the center of the sphere in the base coordinate system to , set the angle between the optical axis of the spectral confocal probe and the three-axis coordinates of the base coordinate system to , the unit direction vector of the optical axis is ; Set the displacement value of the spectral confocal probe to d7, the readings of the contact probe to x7, y7, z7, and the coordinates of the point S on the spherical surface in the base coordinate system to : Point S is on the sphere, then , substitute the coordinates of point S and point O into the spherical equation: (Formula 15) The spectral confocal probe is used to measure the position of another point T on the spherical surface. The coordinates of point T in the base coordinate system are calculated as follows: : Point T is on the sphere, then , substitute the coordinates of point T and point O into the spherical equation: (Formula 16) The spectral confocal probe is used to measure the point information on the spherical surface multiple times. The reading of the spectral confocal probe is , the displacement information of the contact probe is , we get the overdetermined system of equations: (Formula 17) Among them, the constraints of formula 17 are: (Formula 18).

10. The method for calibrating the spatial position of a spectral confocal probe with plane-spherical joint constraints according to claim 9, characterized in that: Formula 17 is solved using the LM iterative solution algorithm to obtain the zero point position of the spectral confocal probe.

Images