An in-situ measurement and analysis method for wear characteristics of a small-diameter ball-end grinding wheel for hemispherical harmonic oscillators based on a spectral confocal sensor.

Abstract

This invention provides an in-situ measurement and analysis method for the wear characteristics of a small-diameter ball-end grinding wheel for hemispherical harmonic oscillators, based on a spectral confocal sensor. It relates to the field of ultra-precision grinding and polishing technology, addressing the problem that existing in-situ detection methods cannot eliminate system installation errors, and that sensor-acquired signal data cannot accurately characterize the true wear condition of the grinding wheel. This invention uses a spectral confocal sensor to collect relative distance data of a standard sphere, utilizing the constraint conditions of the measurement coordinate points satisfying the ideal standard spherical surface equation. Simultaneously, based on multibody theory, it establishes the kinematic chain transmission relationship of the machine tool measurement system, constructs an error transmission model of the machine tool, and solves for assembly error values. The assembly error results are then used to compensate for the grinding wheel coordinate measurement results to obtain the calibrated grinding wheel coordinates, which are further fitted to the morphology of the small-diameter ball-end grinding wheel, thus achieving in-situ measurement and analysis of the grinding wheel wear characteristics.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision grinding and polishing technology, and more specifically, to an in-situ measurement and analysis method for the wear characteristics of a small-diameter ball head grinding wheel for a hemispherical harmonic oscillator based on a spectral confocal sensor. Background Technology

[0002] The hemispherical resonator gyroscope is currently the most precise solid-state resonator gyroscope, possessing outstanding advantages such as high reliability, long lifespan, strong shock resistance, and intrinsic radiation resistance. High-quality fused silica is the best material for manufacturing hemispherical resonators, but it is also a typical difficult-to-machine, hard, and brittle material. This results in severe wear of the grinding wheel during precision and ultra-precision grinding, significantly impacting the performance of the hemispherical resonator. Therefore, accurately detecting the wear area of ​​the grinding wheel has become a key research focus.

[0003] Offline and in-situ detection are two commonly used methods. Offline detection, based on measuring equipment, can clearly observe the wear condition of the grinding wheel surface, but it negatively impacts grinding efficiency and accuracy. In-situ detection, on the other hand, relies on various sensors, such as acoustic emission sensors and vibration sensors, to collect signal features associated with the grinding wheel's wear state. A mathematical model is then used to establish the relationship between these signal features and the grinding wheel's wear state, as illustrated in "Application No.: CN202311347093.0 A Method and System for Predicting the Wear State of a Small-Diameter Ball-Head Grinding Wheel Based on Feature Dimensionality Reduction and Radial Basis Neural Network". However, collecting signal features associated with the grinding wheel's wear state using sensors cannot eliminate system installation errors, and the signal data cannot accurately represent the true wear condition of the grinding wheel. Therefore, there is an urgent need for an in-situ measurement and analysis method for the wear characteristics of small-diameter ball-head grinding wheels that can accurately solve for and eliminate assembly errors during processing. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing in-situ detection methods cannot eliminate system installation errors, and the signal data collected by sensors cannot characterize the actual wear of the grinding wheel.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides an in-situ measurement and analysis method for the wear characteristics of a small-diameter ball-end grinding wheel of a hemispherical harmonic oscillator based on a spectral confocal sensor, comprising the following steps:

[0008] S1. Before the grinding of the hemispherical resonator begins, install the standard ball on the tool spindle of the machine tool, and install the spectral confocal sensor above the fixed frame of the workpiece spindle, with the optical axis direction parallel to the rotation axis direction of the workpiece spindle; adjust the X-axis linear motion platform, Y-axis linear motion platform and Z-axis linear motion platform respectively so that the spectral confocal sensor can measure the distance of the standard ball.

[0009] The tool spindle is rotated, and the position information of the maximum rotation radius of the standard ball is collected using a spectral confocal sensor. The axial runout error of the tool spindle and the eccentricity error between the standard ball and the tool spindle are calculated. The eccentricity error is eliminated by repeated clamping.

[0010] S2. Control the rotation of the C-axis turntable, measure the relative distance between the standard ball and the zero point of the spectral confocal sensor at different angles of the C-axis turntable, calculate the centering deviation at each angle position, and eliminate the centering deviation by adjusting the U-axis micro-displacement platform so that the center of the standard ball coincides with the rotation axis of the C-axis turntable.

[0011] S3. Adjust the X, Y, and Z axes of the linear motion platform so that the distance between the spectral confocal sensor and the standard sphere remains within the measurement range during the rotation of the tool spindle and C axis. Record the XYZ axis coordinates at this time as (u, v, w).

[0012] S4. Rotate the C-axis turntable from -180° to 180° and then back to -180° at a certain angular velocity in a cyclical motion. At the same time, the tool spindle drives the standard ball to rotate at a certain angular velocity in a uniform motion. The relative distance data of the standard ball is collected by the spectral confocal sensor to obtain a series of angle data α of the C-axis turntable, angle β of the tool spindle, and relative distance t between the spectral confocal sensor and the standard ball, that is, a series of (α,β,t) coordinate data.

[0013] S5. Transform the standard spherical coordinate data measured in different coordinate systems into the same world coordinate system, utilize the constraint conditions of the measured coordinate points satisfying the ideal standard spherical equation, and at the same time, based on multibody theory, establish the kinematic chain transmission relationship of the machine tool measurement system, construct the machine tool error transmission model, and solve for the assembly error value.

[0014] S6. Replace the standard ball with a small-diameter ball-end grinding wheel. Adjust the X-axis, Y-axis, and Z-axis linear motion platforms respectively to enable the spectral confocal sensor to measure the distance to the small-diameter ball-end grinding wheel. Rotate the tool spindle and use the spectral confocal sensor to collect the position information of the maximum rotation radius of the standard ball. Calculate the eccentricity error between the small-diameter ball-end grinding wheel and the tool spindle, and eliminate the eccentricity error by repeated clamping. Control the rotation of the C-axis rotary table and use the spectral confocal sensor to measure the relative distance data between the small-diameter ball-end grinding wheel and the zero point measured by the spectral confocal sensor at different angles on the C-axis rotary table. Calculate the centering deviation value at each angle position and eliminate the centering deviation by adjusting the U-axis micro-displacement platform, so that the center of the small-diameter ball-end grinding wheel coincides with the rotation axis of the C-axis rotary table.

[0015] S7. Perform grinding of the hemispherical harmonic oscillator. During the grinding process, monitor the wear of the small-diameter ball head grinding wheel continuously. Move the X, Y, and Z axis linear motion platform to the coordinate (u, v, w) position and repeat step S4 to obtain the grinding wheel coordinate data. Use the assembly error compensation grinding wheel coordinate data calibrated by the measuring standard ball to obtain the actual measurement coordinate point of the grinding wheel. Then, transform the grinding wheel coordinate data with compensated assembly error in different coordinate systems to the same world coordinate system, fit the morphology of the small-diameter ball head grinding wheel, and perform in-situ measurement and analysis of the grinding wheel wear characteristics.

[0016] Furthermore, the standard ball mentioned in S1 is the Renishaw standard ball.

[0017] Furthermore, S2 includes the following steps:

[0018] S2-1. Establish the machine tool coordinate system O-XYZ, where the center line of the workpiece spindle coincides with the Y-axis, the direction from the workpiece spindle to the grinding wheel is the positive direction of the Y-axis, and the vertical upward direction perpendicular to the worktable is the positive direction of the Z-axis. Adjust the C-axis rotary table so that the tool spindle is in the OYZ plane, and define the position of the C-axis rotary table at this time as 0° angle.

[0019] S2-2. Focus the measurement spot of the spectral confocal sensor at the position of the maximum radius of rotation of the standard sphere, and make the measurement direction of the measurement optical axis perpendicular to the OYZ plane;

[0020] S2-3. Control the C-axis turntable to rotate to a 180° angle position, measure the relative distance data of the C-axis turntable at different angles using a spectral confocal sensor, and calculate the centering deviation value at each angle position;

[0021] S2-4. The centering deviation is eliminated by adjusting the U-axis micro-displacement platform, thereby achieving the centering adjustment of the standard ball along the radial direction of the C-axis turntable.

[0022] Furthermore, S5 includes the following process:

[0023] Transform standard spherical coordinate data measured in different coordinate systems into the same world coordinate system, and measure the standard spherical coordinate points (R). tx ,R ty ,R tz It satisfies the equation of an ideal standard sphere:

[0024] (R tx -x0) 2 +(R ty -y0) 2 +(R tz -z0) 2 =R 2

[0025] In the formula, (x0, y0, z0) are the coordinates of the center of the standard sphere in the world coordinate system, and R is the radius of the standard sphere;

[0026] The distance from a point on the sphere to the center of the sphere is:

[0027]

[0028] Where U is a parameter vector containing parameter S yx S zx S zy P ty P tz P cx P cy P wx P wz and the coordinates of the center of the standard sphere; S yx S represents the perpendicularity error between the X and Y axes. zx S represents the perpendicularity error between the Z-axis and the X-axis. zy P represents the perpendicularity error between the Z-axis and the Y-axis; ty P represents the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Y-axis. tz This indicates the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Z-axis; P cx P represents the perpendicularity error between the C-axis and the X-axis, and P represents the perpendicularity error between the C-axis and the Y-axis. wx P represents the perpendicularity error between the spectral confocal sensor and the X-axis. wz This indicates the perpendicularity error between the spectral confocal sensor and the Z-axis;

[0029] When there are k measurement points on the standard sphere, k nonlinear equations are obtained:

[0030] d i =f(α) i ,β i ,v i U i i = 1, 2, 3, ..., k

[0031] The above nonlinear equation is transformed into a nonlinear least squares problem to solve for the parameter vector U:

[0032]

[0033] Where W is the objective function;

[0034] The method for constructing the error propagation model is as follows:

[0035] Based on multibody theory, the kinematic chain transmission relationship of the machine tool measurement system is established as follows:

[0036] The grinding wheel chain includes: standard ball or small diameter ball head grinding wheel → workpiece spindle → U-axis micro-displacement platform → C-axis rotary table → Z-axis linear motion → world coordinate system; the sensor chain includes: spectral confocal sensor → Y-axis linear motion platform → X-axis linear motion platform → world coordinate system;

[0037] The homogeneous transformation matrix from the standard sphere to the world coordinate system is:

[0038]

[0039] Where, θ A θ represents the angle of tilt of the tool spindle about the X-axis, z represents the motion along the Z-axis, and θ represents the angle of tilt of the tool spindle about the X-axis. C Indicates the rotation of the C-axis rotary table, g rt (0) represents the rigid body transformation matrix of the grinding wheel connection. The motion of a rigid body is a spiral. This is the transformation matrix along the Z-axis;

[0040] The homogeneous transformation matrix of the spectral confocal sensor to the world coordinate system is:

[0041]

[0042] Where, θ w The tilt angle of the spectral confocal sensor is represented by x and y, which represent the motion commands of the X-axis and Y-axis motion platforms, respectively. rw (0) represents the rigid body transformation matrix of the sensor chain;

[0043] Therefore, the homogeneous transformation matrix from the world coordinate system to the spectral confocal sensor coordinate system is:

[0044]

[0045] In summary, the homogeneous transformation matrix from the standard spherical coordinate system to the spectral confocal sensor coordinate system is:

[0046]

[0047] Ignoring motion and installation errors, the ideal motion model is:

[0048]

[0049] The actual motion model of the machine tool is as follows:

[0050]

[0051] The actual point R on the standard sphere r Measurement point R of the spectral confocal sensor r The error matrix with positional errors is as follows:

[0052]

[0053] in:

[0054] E X E Y E Z —Components of assembly error along the X, Y, and Z axes;

[0055] R r —The actual position vector of a point on a standard sphere;

[0056] R w —The position vector of the measurement point of the spectral confocal sensor;

[0057] TT—Assembly error transformation matrix for the measurement point position of the spectral confocal sensor;

[0058] The deviation of the standard ball is expressed as:

[0059] [E x E y E z 1] T =(g wt·actual -g wt·idea )·[0 0 0 1] T

[0060] The error transformation matrix is ​​the product of the error transfer matrices among several rigid bodies:

[0061]

[0062] According to the theory of rigid body motion, the error transfer matrix between rigid bodies is expressed as:

[0063]

[0064] In the formula, j and k represent the rigid body numbers. and These are, in order, the position transformation matrix, the position error transformation matrix, the motion transformation matrix, and the motion error transformation matrix;

[0065] The error propagation model is as follows:

[0066] E x =-l·cos c·[P ty sin AP tz (1-cos A)]+d c P cx (1-cos c)+d c P cy sin c+z·S zx -d z S zx +y·S yx -y P wz -L w P wz

[0067] E y =-l·sin c·[P ty sin AP tz (1-cos A)-d c P cx sin c+d c P cy (1-cos c)-z·S zx -d c S zy +d z S zy +zP wx +x P wz

[0068] E z =-L z S zx +yP wx

[0069] Where l represents the distance between the center of the standard ball and the rotation axis of the tool spindle around the X-axis, L w L represents the measurement distance of the optical axis of the spectral confocal sensor. z The distance of the Z-axis relative to the optical axis of the spectral confocal sensor in the X direction is represented by A, which represents the angle between the workpiece spindle and the vertical axis.

[0070] Compared with the prior art, the beneficial effects of the present invention are:

[0071] 1. This invention can eliminate machine tool errors during the measurement process and reflect the true grinding wheel morphology data;

[0072] 2. This invention allows for real-time monitoring of the wear condition of small-diameter ball-end grinding wheels during the tool feed interval in ultra-precision grinding of hemispherical harmonic oscillators;

[0073] 3. This invention improves measurement efficiency and accuracy by detecting small-diameter ball-end grinding wheels in a non-contact manner;

[0074] 4. The in-situ detection of this invention can ensure the relative positional relationship between the grinding wheel and the hemispherical harmonic oscillator, avoiding errors introduced by repeated clamping. Attached Figure Description

[0075] Figure 1 This is an axonometric view of the in-situ measurement platform for standard sphericity based on a spectral confocal sensor in an embodiment of the present invention.

[0076] Figure 2 This is an in-situ measurement system for standard sphericity in an embodiment of the present invention;

[0077] Figure 3 This is a schematic diagram of the measurement points of the spectral confocal sensor in an embodiment of the present invention;

[0078] Figure 4 This is a schematic diagram of the kinematic chain of the machine tool measurement system in an embodiment of the present invention;

[0079] Explanation of reference numerals in the attached figures:

[0080] 1-Machine tool bed, 11-X-axis linear motion platform, 12-Y-axis linear motion platform, 13-Z-axis linear motion platform, 14-C-axis rotary table, 15-U-axis micro-displacement platform, 16-Workpiece spindle, 17-Tool spindle, 2-Triangular connecting frame, 3-Fixed frame, 4-Worktable, 5-Spectral confocal sensor. Detailed Implementation

[0081] In the description of this invention, it should be noted that the terms used in the various embodiments, such as "upper," "lower," "front," "rear," "left," and "right," which indicate orientation, are only used to simplify the description of the positional relationships based on the accompanying drawings and do not mean that the components and devices referred to must be operated in accordance with the specific orientations and defined operations, methods, and structures in the specification. Such directional terms do not constitute a limitation of this invention.

[0082] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0083] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0084] Specific Implementation Scheme 1: This invention provides an in-situ measurement and analysis method for the wear characteristics of a small-diameter ball-end grinding wheel using a hemispherical harmonic oscillator based on a spectral confocal sensor, such as... Figure 1 and Figure 2 As shown, the method of the present invention is based on an in-situ measurement system for a hemispherical harmonic oscillator ultra-precision grinding machine tool. The in-situ measurement system includes a machine tool and a spectral confocal sensor 5. The machine tool includes a machine bed 1, an X-axis linear motion platform 11, a Y-axis linear motion platform 12, a Z-axis linear motion platform 13, a C-axis rotary table 14, a U-axis micro-displacement platform 15, a workpiece spindle 16, a tool spindle 17, a triangular connecting frame 2, a fixed frame 3, and a worktable 4.

[0085] The machine tool bed 1 is equipped with an X-axis linear motion platform 11, a Y-axis linear motion platform 12 and a Z-axis linear motion platform 13. The X-axis linear motion platform 11 and the Y-axis linear motion platform 12 are stacked in a cross shape. The Z-axis linear motion platform 13 is installed perpendicular to the X-axis linear motion platform 11 and the Y-axis linear motion platform 12, together forming a spatial rectangular coordinate system.

[0086] The worktable 4 is mounted on the X-axis linear motion platform 11 and the Y-axis linear motion platform 12.

[0087] The workpiece spindle 16 is mounted on the worktable 4 via a fixing frame 3, and the rotation axis is parallel to the Y-axis.

[0088] The spectral confocal sensor 5 is mounted on the workpiece spindle 16, with its optical axis direction parallel to the rotation axis direction of the workpiece spindle 16.

[0089] The C-axis turntable 14 is mounted on the Z-axis linear motion platform 13 via a triangular connecting bracket 2, with the rotation axis direction parallel to the Z-axis.

[0090] The U-axis micro-displacement platform 15 is mounted on the C-axis turntable 14.

[0091] The tool spindle 17 is mounted on the U-axis micro-displacement platform 15.

[0092] The method of the present invention includes the following steps:

[0093] S1. Before the grinding of the hemispherical resonator begins, install the standard ball on the tool spindle 17 of the machine tool, and install the spectral confocal sensor 5 above the mounting bracket 3 of the workpiece spindle 16, with the optical axis parallel to the rotation axis of the workpiece spindle 16; adjust the X-axis linear motion platform 11, Y-axis linear motion platform 12, and Z-axis linear motion platform respectively so that the spectral confocal sensor 5 can measure the distance to the standard ball (the working distance of the spectral confocal sensor 5CL2-MG140 is 10.8mm, the measurement range is 400μm, and the maximum linear error is 50nm).

[0094] The tool spindle 17 is rotated, and the position information of the maximum rotation radius of the standard ball is collected by the spectral confocal sensor 5. The axial runout error of the tool spindle 17 and the eccentricity error between the standard ball and the tool spindle 17 are calculated. The eccentricity error is eliminated by repeated clamping.

[0095] S2. Control the rotation of the C-axis turntable 14, measure the relative distance between the standard ball and the zero point of the spectral confocal sensor 5 at different angles of the C-axis turntable 14, calculate the centering deviation value at each angle position, and eliminate the centering deviation by adjusting the U-axis micro-displacement platform 15 so that the center of the standard ball coincides with the rotation axis of the C-axis turntable 14.

[0096] S3. Adjust the X, Y, and Z axes of the linear motion platform 13 so that during the rotation of the tool spindle 17 and the C axis, the distance between the spectral confocal sensor 5 and the standard sphere remains within the measurement range. Record the XYZ axis coordinates at this time as (u, v, w).

[0097] S4. The C-axis rotary table 14 is rotated from -180° to 180° and then back to -180° at a certain angular velocity in a cyclical motion. At the same time, the tool spindle 17 drives the standard ball to rotate at a certain angular velocity in a uniform motion. The relative distance data of the standard ball is collected by the spectral confocal sensor 5 to obtain a series of angle data α of the C-axis rotary table 14, angle β of the tool spindle 17, and relative distance t between the spectral confocal sensor 5 and the standard ball, that is, a series of (α,β,t) coordinate data.

[0098] S5. Transform the standard spherical coordinate data measured in different coordinate systems into the same world coordinate system, utilize the constraint conditions of the measured coordinate points satisfying the ideal standard spherical equation, and at the same time, based on multibody theory, establish the kinematic chain transmission relationship of the machine tool measurement system, construct the machine tool error transmission model, and solve for the assembly error value.

[0099] S6. Replace the standard ball with a small-diameter ball-end grinding wheel. Adjust the X-axis linear motion platform 11, Y-axis linear motion platform 12, and Z-axis linear motion platform respectively to enable the spectral confocal sensor 5 to measure the distance of the small-diameter ball-end grinding wheel. Rotate the tool spindle 17 and use the spectral confocal sensor 5 to collect the position information of the maximum rotation radius of the standard ball. Calculate the eccentricity error between the small-diameter ball-end grinding wheel and the tool spindle 17, and eliminate the eccentricity error by repeated clamping. Control the rotation of the C-axis rotary table 14. Measure the relative distance data between the small-diameter ball-end grinding wheel and the zero point measured by the spectral confocal sensor 5 at different angles on the C-axis rotary table 14. Calculate the centering deviation value at each angle position. Eliminate the centering deviation by adjusting the U-axis micro-displacement platform 15, so that the center of the small-diameter ball-end grinding wheel coincides with the rotation axis of the C-axis rotary table 14.

[0100] S7. Perform grinding of the hemispherical harmonic oscillator. During the grinding process, monitor the wear of the small-diameter ball head grinding wheel continuously. Move the X, Y, and Z axis linear motion platform to the coordinate (u, v, w) position and repeat step S4 to obtain the grinding wheel coordinate data. Use the assembly error compensation grinding wheel coordinate data calibrated by the measuring standard ball to obtain the actual measurement coordinate point of the grinding wheel. Then, transform the grinding wheel coordinate data with compensated assembly error in different coordinate systems to the same world coordinate system, fit the morphology of the small-diameter ball head grinding wheel, and perform in-situ measurement and analysis of the grinding wheel wear characteristics.

[0101] Specific Implementation Scheme Two: The standard sphere mentioned in S1 is a Renishaw standard sphere, which is made of wear-resistant tungsten carbide, has a diameter of 12mm, and a roundness better than 50nm. The Renishaw standard sphere has extremely high precision and can be regarded as a standard spherical surface. All other aspects of this implementation scheme are the same as in Specific Implementation Scheme One.

[0102] Specific implementation plan three: S2 includes the following steps:

[0103] S2-1. Establish the machine tool coordinate system O-XYZ, where the center line of the workpiece spindle 16 coincides with the Y-axis, the direction from the workpiece spindle 16 to the grinding wheel is the positive Y-axis direction, and the vertical upward direction perpendicular to the worktable 4 is the positive Z-axis direction. Adjust the C-axis rotary table 14 so that the tool spindle 17 is in the OYZ plane, and define the position of the C-axis rotary table 14 at this time as 0° angle.

[0104] S2-2. Focus the measurement spot of the spectral confocal sensor 5 at the position of the maximum radius of rotation of the standard sphere, and make the measurement direction of the measurement optical axis perpendicular to the OYZ plane;

[0105] S2-3. Control the C-axis turntable 14 to rotate to a 180° angle position, measure the relative distance data of the C-axis turntable 14 at different angles through the spectral confocal sensor 5, and calculate the centering deviation value at each angle position;

[0106] S2-4. The centering deviation is eliminated by adjusting the U-axis micro-displacement platform 15, thereby achieving the radial centering adjustment of the standard ball along the C-axis turntable 14. The rest of this implementation scheme is the same as specific implementation scheme one.

[0107] Specific implementation plan four: S5 includes the following processes:

[0108] like Figure 3 As shown, standard spherical coordinate data measured in different coordinate systems are transformed into the same world coordinate system, and the standard spherical coordinate points (R) are measured. tx ,R ty ,R tz It satisfies the equation of an ideal standard sphere:

[0109] (Rtx-x0) 2 +(Rty-y0) 2 +(Rtz-z0) 2 =R 2

[0110] In the formula, (x0, y0, z0) are the coordinates of the center of the standard sphere in the world coordinate system, and R is the radius of the standard sphere;

[0111] The distance from a point on the sphere to the center of the sphere is:

[0112]

[0113] Where U is a parameter vector containing parameter S yx S zx S zy、 P ty P tz、 P cx、 P cy、 P wx、 P wz and the coordinates of the center of the standard sphere; S yx S represents the perpendicularity error between the X and Y axes. zx S represents the perpendicularity error between the Z-axis and the X-axis. zy P represents the perpendicularity error between the Z-axis and the Y-axis; ty P represents the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Y-axis. tz This indicates the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Z-axis; P cx P represents the perpendicularity error between the C-axis and the X-axis, and P represents the perpendicularity error between the C-axis and the Y-axis. wx P represents the perpendicularity error between the spectral confocal sensor 5 and the X-axis. wz This indicates the perpendicularity error between the spectral confocal sensor 5 and the Z-axis;

[0114] When there are k measurement points on the standard sphere, k nonlinear equations are obtained:

[0115] d i =f(α) i ,β i ,v i U i i = 1, 2, 3, ..., k

[0116] The Levenberg-Marquardt algorithm is used to transform the above nonlinear equations into a nonlinear least squares problem to solve for the parameter vector U:

[0117]

[0118] Where W is the objective function;

[0119] The method for constructing the error propagation model is as follows:

[0120] A spectral confocal sensor is fixed on the X-axis and Y-axis linear motion platforms, while a standard ball or small-diameter ball-end grinding wheel is fixed on the workpiece spindle, U-axis micro-displacement platform, C-axis rotary table, and Z-axis linear motion platform. The Z-axis linear motion platform and the X and Y-axis linear motion platforms are independent of each other; therefore, the measurement system is defined as consisting of a grinding wheel chain and a sensor chain.

[0121] like Figure 4 As shown, based on many-body theory, the kinematic chain transmission relationship of the machine tool measurement system is established as follows:

[0122] The grinding wheel chain includes: a standard ball or small-diameter ball-head grinding wheel → workpiece spindle 16 → U-axis micro-displacement platform 15 → C-axis rotary table 14 → Z-axis linear motion → world coordinate system; the sensor chain includes: a spectral confocal sensor 5 → Y-axis linear motion platform 12 → X-axis linear motion platform 11 → world coordinate system;

[0123] The homogeneous transformation matrix from the standard sphere to the world coordinate system is:

[0124]

[0125] Where, θ A The angle of inclination of tool spindle 17 around the X-axis is represented by z, and the motion along the Z-axis is represented by θ. C This indicates the rotation of the C-axis rotary table 14, g rt (0) represents the rigid body transformation matrix of the grinding wheel connection. The motion of a rigid body is a spiral. This is the transformation matrix along the Z-axis;

[0126] The homogeneous transformation matrix of the spectral confocal sensor 5 to the world coordinate system is:

[0127]

[0128] Where, θ w The tilt angle of the spectral confocal sensor 5 is represented by x and y, which represent the motion commands of the X-axis and Y-axis motion platforms, respectively. rw (0) represents the rigid body transformation matrix of the sensor chain;

[0129] Therefore, the homogeneous transformation matrix from the world coordinate system to the spectral confocal sensor 5 coordinate system is:

[0130]

[0131] In summary, the homogeneous transformation matrix from the standard spherical coordinate system to the coordinate system of the spectral confocal sensor 5 is:

[0132]

[0133] Ignoring motion and installation errors, the ideal motion model is:

[0134]

[0135] The actual motion model of the machine tool is as follows:

[0136]

[0137] During the measurement process, only the C-axis rotary table and the workpiece spindle rotate, while other linear motion platforms remain stationary. Furthermore, the rotational accuracy of the C-axis rotary table and the workpiece spindle is much smaller than the assembly error between the motion platforms. Therefore, the impact of the assembly error between each axis on the measurement accuracy is the primary consideration.

[0138] Ideally, the actual point Rw on the standard sphere should coincide with the measurement point Rt of the spectral confocal sensor. Therefore, the position vector relationship between the two should be expressed as:

[0139]

[0140] The actual point R on the standard sphere r Measurement point R with spectral confocal sensor 5 r The error matrix with positional errors is as follows:

[0141]

[0142] in:

[0143] E X E Y E Z —Components of assembly error along the X, Y, and Z axes;

[0144] R r —The actual position vector of a point on a standard sphere;

[0145] R w —The position vector of the measurement point of the spectral confocal sensor 5;

[0146] T T —Assembly error transformation matrix of the measurement point positions of the spectral confocal sensor 5;

[0147] The deviation of the standard ball is expressed as:

[0148] [E x E y E z 1] T =(g wt·actual -g wt·idea )·[0 0 0 1] T

[0149] The error transformation matrix is ​​the product of the error transfer matrices among several rigid bodies:

[0150]

[0151] According to the theory of rigid body motion, the error transfer matrix between rigid bodies is expressed as:

[0152]

[0153] In the formula, j and k represent the rigid body numbers. and These are, in order, the position transformation matrix, the position error transformation matrix, the motion transformation matrix, and the motion error transformation matrix;

[0154] The error propagation model is as follows:

[0155] E x =-l·cos c·[P ty sin AP tz (1-cos A)]+d c P cx (1-cos c)+d c P cy sin c+z·S zx -d z S zx +y·S yx -y P wz -L w P wz

[0156] E y =-l·sin c·[P ty sin AP tz (1-cos A)-d c Pcx sin c+d c P cy (1-cos c)-z·S zx -d c S zy +d z S zy +zP wx +x P wz

[0157] E z =-L z S zx +yP wx

[0158] Where l represents the distance between the center of the standard ball and the rotation axis of the tool spindle 17 around the X-axis, L w L represents the measurement distance along the optical axis of the 5-axis spectral confocal sensor. z The distance of the Z-axis relative to the optical axis of the spectral confocal sensor 5 in the X direction is represented by A, and A represents the angle between the workpiece spindle 16 and the vertical axis. This embodiment is otherwise identical to specific embodiment one.

[0159] The obtained error propagation model and the solution equation of the parameter vector U are then used. By combining the equations, the assembly error value can be obtained.

[0160] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for in-situ measurement and analysis of wear characteristics of a small-diameter ball-end grinding wheel based on a spectral confocal sensor, characterized in that, Includes the following steps: S1. Before the grinding of the hemispherical harmonic oscillator begins, install the standard ball on the tool spindle of the machine tool, and install the spectral confocal sensor above the fixed frame of the workpiece spindle, with the optical axis direction parallel to the rotation axis direction of the workpiece spindle; adjust the X-axis linear motion platform (11), Y-axis linear motion platform and Z-axis linear motion platform respectively so that the spectral confocal sensor can measure the distance of the standard ball. The tool spindle is rotated, and the position information of the maximum rotation radius of the standard ball is collected using a spectral confocal sensor. The axial runout error of the tool spindle and the eccentricity error between the standard ball and the tool spindle are calculated. The eccentricity error is eliminated by repeated clamping. S2. Control the rotation of the C-axis turntable, measure the relative distance between the standard ball and the zero point of the spectral confocal sensor at different angles of the C-axis turntable, calculate the centering deviation at each angle position, and eliminate the centering deviation by adjusting the U-axis micro-displacement platform so that the center of the standard ball coincides with the rotation axis of the C-axis turntable. S3. Adjust the linear motion platform of the X, Y and Z axes so that the distance between the spectral confocal sensor and the standard sphere remains within the measurement range during the rotation of the tool spindle and C axis. Record the XYZ axis coordinates at this time as (u, v, w). S4. Rotate the C-axis turntable from -180° to 180° and then back to -180° at a certain angular velocity in a cyclical motion. At the same time, the tool spindle drives the standard ball to rotate at a certain angular velocity in a uniform motion. The relative distance data of the standard ball is collected by the spectral confocal sensor to obtain a series of angle data α of the C-axis turntable, angle β of the tool spindle, and relative distance t between the spectral confocal sensor and the standard ball, that is, a series of (α, β, t) coordinate data. S5. Transform the standard spherical coordinate data measured in different coordinate systems into the same world coordinate system, utilize the constraint conditions of the measured coordinate points satisfying the ideal standard spherical equation, and at the same time, based on multibody theory, establish the kinematic chain transmission relationship of the machine tool measurement system, construct the error transmission model of the machine tool, and solve for the assembly error value. S6. Replace the standard ball with a small-diameter ball-end grinding wheel. Adjust the X-axis linear motion platform (11), Y-axis linear motion platform and Z-axis linear motion platform respectively so that the spectral confocal sensor can measure the distance of the small-diameter ball-end grinding wheel. Rotate the tool spindle and use the spectral confocal sensor to collect the position information of the maximum rotation radius of the standard ball. Calculate the eccentricity error between the small-diameter ball-end grinding wheel and the tool spindle. Eliminate the eccentricity error by repeated clamping. Control the rotation of the C-axis turntable. Measure the relative distance data between the small-diameter ball-end grinding wheel and the zero point measured by the spectral confocal sensor at different angles of the C-axis turntable. Calculate the centering deviation value at each angle position. Eliminate the centering deviation by adjusting the U-axis micro-displacement platform so that the center of the small-diameter ball-end grinding wheel coincides with the rotation axis of the C-axis turntable. S7. Perform grinding of the hemispherical harmonic oscillator. During the grinding process, monitor the wear of the small-diameter ball head grinding wheel at any time. Move the X-axis, Y-axis and Z-axis linear motion platform to the coordinate (u, v, w) position. Repeat step S4 to measure the grinding wheel coordinate data. Use the assembly error compensation grinding wheel coordinate data calibrated by the measuring standard ball to obtain the actual measurement coordinate point of the grinding wheel. Then, transform the grinding wheel coordinate data with compensated assembly error in different coordinate systems to the same world coordinate system, fit the morphology of the small-diameter ball head grinding wheel, and perform in-situ measurement and analysis of the grinding wheel wear characteristics. S5 includes the following process: The standard spherical coordinate data measured by different coordinate systems is transformed into the same world coordinate system, and the standard spherical coordinate points (R tx , R ty , R tz ) satisfy the ideal standard spherical surface equation: In the formula, (x0, y0, z0) are the coordinates of the center of the standard sphere in the world coordinate system, and R is the radius of the standard sphere; The distance from a point on the sphere to the center of the sphere is: Where U is a parameter vector containing parameter S yx S zx S zy、 P ty P tz、 P cx、 P cy、 P wx、 P wz and the coordinates of the center of the standard sphere; S yx S represents the perpendicularity error between the X and Y axes. zx S represents the perpendicularity error between the Z-axis and the X-axis. zy P represents the perpendicularity error between the Z-axis and the Y-axis; ty P represents the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Y-axis. tz This indicates the perpendicularity error between the tool spindle's rotation axis around the X-axis and the Z-axis; P cx P represents the perpendicularity error between the C-axis and the X-axis. cy Indicates the perpendicularity error between the C-axis and the Y-axis; P wx P represents the perpendicularity error between the spectral confocal sensor and the X-axis. wz This indicates the perpendicularity error between the spectral confocal sensor and the Z-axis; When there are k measurement points on the standard sphere, k nonlinear equations are obtained: The above nonlinear equation is transformed into a nonlinear least squares problem to solve for the parameter vector U: Where W is the objective function; The method for constructing the error propagation model is as follows: Based on multibody theory, the kinematic chain transmission relationship of the machine tool measurement system is established as follows: The grinding wheel chain includes: standard ball or small diameter ball head grinding wheel → workpiece spindle → U-axis micro-displacement platform → C-axis rotary table → Z-axis linear motion → world coordinate system; the sensor chain includes: spectral confocal sensor → Y-axis linear motion platform → X-axis linear motion platform (11) → world coordinate system; The homogeneous transformation matrix from the standard sphere to the world coordinate system is: Where, θ A θ represents the angle of tilt of the tool spindle about the X-axis, z represents the motion along the Z-axis, and θ represents the motion along the Z-axis. C Indicates the rotation of the C-axis rotary table, g rt (0) represents the rigid body transformation matrix of the grinding wheel chain. The motion of a rigid body is a spiral. This is the transformation matrix along the Z-axis; The homogeneous transformation matrix of the spectral confocal sensor to the world coordinate system is: Where, θ w The tilt angle of the spectral confocal sensor is represented by x and y, which represent the motion commands of the X-axis and Y-axis motion platforms, respectively. rw (0) represents the rigid body transformation matrix of the sensor chain; Therefore, the homogeneous transformation matrix for transforming from the world coordinate system to the spectral confocal sensor coordinate system is: In summary, the homogeneous transformation matrix from the standard spherical coordinate system to the spectral confocal sensor coordinate system is: Ignoring motion and installation errors, the ideal motion model is: The actual motion model of the machine tool is as follows: The actual point R on the standard sphere r Measurement point R of the spectral confocal sensor r The error matrix with positional errors is as follows: in: E X E Y E Z —Components of assembly error along the X, Y, and Z axes; R r —The actual position vector of a point on a standard sphere; R w —The position vector of the measurement point of the spectral confocal sensor; T T —Assembly error transformation matrix for the measurement point position of the spectral confocal sensor; The deviation of the standard ball is expressed as: The error transformation matrix is ​​the product of the error transfer matrices between several rigid bodies: According to the theory of rigid body motion, the error transfer matrix between rigid bodies is expressed as: In the formula, j and k represent the rigid body numbers. , , and These are, in order, the position transformation matrix, the position error transformation matrix, the motion transformation matrix, and the motion error transformation matrix; The error propagation model is as follows: Where l represents the distance between the center of the standard ball and the rotation axis of the tool spindle around the X-axis, L w L represents the measurement distance of the optical axis of the spectral confocal sensor. z The distance of the Z-axis relative to the optical axis of the spectral confocal sensor in the X direction is represented by A, which represents the angle between the workpiece spindle and the vertical axis.

2. The in-situ measurement and analysis method for wear characteristics of a small-diameter ball-end grinding wheel based on a spectral confocal sensor for a hemispherical harmonic oscillator, as described in claim 1, is characterized in that... The standard ball mentioned in S1 is the Renishaw standard ball.

3. The in-situ measurement and analysis method for wear characteristics of a small-diameter ball-end grinding wheel based on a spectral confocal sensor for a hemispherical harmonic oscillator, as described in claim 1, is characterized in that... S2 includes the following steps: S2-1. Establish the machine tool coordinate system O-XYZ, where the center line of the workpiece spindle coincides with the Y-axis, the direction from the workpiece spindle to the grinding wheel is the positive direction of the Y-axis, and the vertical upward direction perpendicular to the worktable is the positive direction of the Z-axis. Adjust the C-axis rotary table so that the tool spindle is in the OYZ plane, and define the position of the C-axis rotary table at this time as 0° angle. S2-2. Focus the measurement spot of the spectral confocal sensor at the position of the maximum radius of rotation of the standard sphere, and make the measurement direction of the measurement optical axis perpendicular to the OYZ plane; S2-3. Control the C-axis turntable to rotate to a 180° angle position, measure the relative distance data of the C-axis turntable at different angles using a spectral confocal sensor, and calculate the centering deviation value at each angle position; S2-4. The centering deviation is eliminated by adjusting the U-axis micro-displacement platform, thereby achieving the centering adjustment of the standard ball along the radial direction of the C-axis turntable.

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