Self-calibration method and system for laser tracking interferometer measurement field in machine tool coordinate system

Abstract

The present invention provides a method and system for self-calibrating a laser tracking interferometer measurement field in a machine tool coordinate system. The method comprises: utilizing four laser interferometer trackers to form a network and establish a measurement field and a measurement coordinate system, wherein the laser interferometer trackers collect motion data of the machine tool tool tip in real time; planning the position of calibration points within the machine tool tool tip motion range and the laser interferometer tracker's measurement range; simulating the positions of the calibration points and the laser tracking interferometers and calculating the simulation error; determining whether the simulation error is less than a threshold; if so, calculating the coordinates of the four laser interferometer trackers in the machine tool coordinate system and establishing a conversion model between the measurement field coordinate system and the machine tool's mechanical coordinate system; if not, replanning the positions of the laser interferometer trackers. The present invention can rapidly calibrate the measurement field in the machine tool's mechanical coordinate system without the need for third-party measuring instruments or standard components. After the measurement field calibration is completed, the present invention can quickly estimate the uncertainty of the measurement field.

Description

Technical Field

[0001] The present invention relates to the technical field of machine tool calibration, and in particular to a method and system for self-calibration of a laser tracking interferometer measurement field in a machine tool coordinate system. Background Art

[0002] Three-dimensional coordinate measurement systems based on the principles of multilateral methods and laser tracking interferometry have broad application prospects in the field of industrial measurement due to their numerous advantages, including system self-calibration, high precision, wide range, flexibility, dynamic operation, and on-site measurement. The system's measurement principle is quite simple: the coordinates of the measured point are determined by measuring the distance from one point in space to three known points, consistent with the positioning principle of the GPS (Global Positioning System). The system only measures length, not angle. The fact that length measurement is based on the principle of laser interferometry ensures high theoretical measurement accuracy.

[0003] When a measurement system is composed of four laser tracking interferometers, the system has redundancy, enabling self-calibration without the need for other physical benchmarks. This greatly facilitates the system's application in field measurements. Generally speaking, in practical applications, measurement systems must first be calibrated to determine system parameters and measurement uncertainty before actual measurements can be performed. Obviously, the accuracy of system calibration directly affects the system's final measurement accuracy. Therefore, improving the accuracy of system self-calibration is crucial for ensuring the system's final measurement accuracy. Since system self-calibration accuracy is related to the layout of the system's base points, moving points, and initial moving points, and the number of moving points selected during actual calibration is very large (at least nine), and the self-calibration mathematical model is nonlinear, these factors make system self-calibration a very complex issue. Summary of the Invention

[0004] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for self-calibration of the measurement field of a laser tracking interferometer in a machine tool coordinate system.

[0005] According to the present invention, a method for self-calibration of a laser tracking interferometer measurement field in a machine tool coordinate system includes the following steps:

[0006] The measurement field is constructed by connecting four laser interferometer trackers to form a network, and the laser interferometer trackers collect the motion data of the tool tip of the machine tool in real time.

[0007] Calibration point planning steps: Plan the calibration point coordinates within the machine tool tool tip motion range and the laser interferometer tracker measurement range;

[0008] Position simulation steps: Monte Carlo simulation is performed on the positions of the calibration points and the laser tracking interferometer to calculate the simulation error;

[0009] Measurement field verification steps: Determine whether the simulation error is less than the threshold. If so, calculate the positions of the four laser interferometer trackers to complete the self-calibration of the measurement field; if not, replan the positions of the laser interferometer trackers.

[0010] Preferably, the laser interferometer trackers are evenly distributed, and the four laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

[0011] Preferably, the number of the calibration points is not less than 13, and all the calibration points are in non-coplanar positions.

[0012] Preferably, the position simulation step includes:

[0013] Step S1: Based on the physical characteristics of the laser interferometer tracker and the measurement field network planning, a measurement field measurement and calibration mathematical model is established; the measurement field measurement and calibration mathematical model includes the laser interferometer tracker base station position, the measurement target mirror coordinates, the laser interferometer tracker measurement origin coordinates, and the measurement dead path length. The established model is as follows:

[0014] Assume that the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j ,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement, and the length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With P j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is:

[0015]

[0016] In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector:

[0017] ∈ ij =|Mi -P j |-L 0j -ΔL ij

[0018] Step S2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field, and use the sum of squares of the actual measurement fitting errors of multiple spatial points as the optimization target. The optimization problem is established as follows:

[0019] ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem:

[0020]

[0021] In the formula

[0022]

[0023] Step S3: Based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field, the equality constraints and solution parameters of the optimization problem are determined, and the optimization model is solved using the LM algorithm. The solution process includes:

[0024] is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station positions. A measurement coordinate system is established with the tracker base station positions [P1, P2, P3] as reference points. Six parameters are constrained by the coordinate system, reducing the total number of unknown quantities to 3m+4n-6. There are a total of m·n measurement point equations. The optimization problem has a solution:

[0025] (n-3)m>4n-6

[0026] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0027]

[0028] In the formula

[0029] F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn)

[0030]

[0031] The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is:

[0032]

[0033] Where J is the Jacobian matrix of F)x):

[0034]

[0035] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0036]

[0037] u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0038]

[0039] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0040]

[0041] When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible, and the update rule is as follows:

[0042]

[0043] Step S4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field and calculate the measurement accuracy of the measurement field:

[0044] Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance:

[0045] Erorr=0.2+0.3*L ij

[0046] After adding the error, the original measurement equation becomes:

[0047]

[0048] After simulation, solve the optimization problem:

[0049]

[0050] Calculate the expectation of each laser interferometer tracking position and variance

[0051]

[0052]

[0053] According to the present invention, a laser tracking interferometer measurement field self-calibration system in a machine tool coordinate system includes the following modules:

[0054] Measurement field building module: four laser interferometer trackers are connected and networked to form a measurement field. The laser interferometer trackers collect the motion data of the tool tip of the machine tool in real time.

[0055] Calibration point planning steps: Plan the calibration point coordinates within the machine tool tool tip motion range and the laser interferometer tracker measurement range;

[0056] Position simulation module: performs Monte Carlo simulation on the positions of calibration points and laser tracking interferometer, and calculates simulation errors;

[0057] Measurement field calibration module: determines whether the simulation error is less than the threshold. If so, calculates the positions of the four laser interferometer trackers to complete the self-calibration of the measurement field; if not, replans the positions of the laser interferometer trackers.

[0058] Preferably, the laser interferometer trackers are evenly distributed, and the four laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

[0059] Preferably, the number of the calibration points is not less than 13, and all the calibration points are in non-coplanar positions.

[0060] Preferably, the position simulation module includes:

[0061] Module M1: Based on the physical characteristics of the laser interferometer tracker and the measurement field network planning, a measurement field measurement and calibration mathematical model is established. The measurement field measurement and calibration mathematical model includes the laser interferometer tracker base station position, the measurement target mirror coordinates, the laser interferometer tracker measurement origin coordinates, and the measurement dead path length. The established model is as follows:

[0062] Assume that the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j ,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement, and the length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With P j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is:

[0063]

[0064] In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector:

[0065] ∈ ij =|M i -P j |-L 0j -ΔL ij

[0066] Module M2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field. The sum of the squares of the actual measurement fitting errors of multiple spatial points is used as the optimization target. The optimization problem is established as follows:

[0067] ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem:

[0068]

[0069] In the formula

[0070]

[0071] x=[{M i} i＝1,…,m ,{P j} j＝1,…,n ,{L 0j} j＝1,…,n ]

[0072] Module M3: Determine the equality constraints and solution parameters of the optimization problem based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field. Solve the optimization model using the LM algorithm. The solution process includes:

[0073] is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station positions. A measurement coordinate system is established with the tracker base station positions [P1, P2, P3] as reference points. Six parameters are constrained by the coordinate system, reducing the total number of unknown quantities to 3m+4n-6. There are a total of m·n measurement point equations. The optimization problem has a solution:

[0074] (n-3)m>4n-6

[0075] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0076]

[0077] In the formula

[0078] F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn)

[0079]

[0080] The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is:

[0081]

[0082] Where J is the Jacobian matrix of F(x):

[0083]

[0084] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0085]

[0086] u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0087]

[0088] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0089]

[0090] When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible, and the update rule is as follows:

[0091]

[0092] Module M4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field and calculate the measurement accuracy of the measurement field:

[0093] Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance:

[0094] Erorr=0.2+0.3*L ij

[0095] After adding the error, the original measurement equation becomes:

[0096]

[0097] After simulation, solve the optimization problem:

[0098]

[0099] Calculate the expectation of each laser interferometer tracking position and variance

[0100]

[0101]

[0102] According to a computer-readable storage medium provided by the present invention, a computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, the above-mentioned step of self-calibrating the measurement field of the laser tracking interferometer in the machine tool coordinate system is implemented.

[0103] According to the present invention, a device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, the steps of the above-mentioned method for self-calibration of the measurement field of the laser tracking interferometer in the machine tool coordinate system are implemented.

[0104] Compared with the prior art, the present invention has the following beneficial effects:

[0105] 1. The present invention can quickly calibrate the measurement field and establish a measurement coordinate system without the need for third-party measuring instruments or standard parts.

[0106] 2. After the measurement field calibration is completed, the uncertainty of the measurement field can be quickly estimated, and the calibration can be completed with at least 9 calibration points.

[0107] 3. The measurement field calibration method introduced in the present invention has no clear regulations on the selection of measurement points. It only needs to meet the two conditions of non-coplanarity and uniform distribution. There is no need to know the exact position of the measurement points. The calibration work can be completed by using a handheld target ball method. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0109] Figure 1 Schematic diagram of the multilateral method model of the present invention;

[0110] Figure 2 Schematic diagram of the measurement coordinate system of the present invention;

[0111] Figure 3 Schematic diagram of the damping coefficient μ update strategy of the present invention;

[0112] Figure 4 This is a flow chart of the uncertainty Monte Carlo simulation algorithm of the present invention. DETAILED DESCRIPTION

[0113] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0114] The present invention proposes a method for self-calibration of a laser tracking interferometer measurement field in a machine tool coordinate system, comprising the following steps:

[0115] The measurement field is constructed using a network of four laser interferometer trackers. These trackers collect real-time motion data of the tool tip. The four trackers are evenly spaced and non-coplanar, with any three trackers being non-colinear.

[0116] Calibration point planning steps: planning the coordinates of the calibration points within the range of motion of the machine tool tool tip and the measurement range of the laser interferometer tracker; the number of the calibration points is not less than 13, and all calibration points are in non-coplanar positions.

[0117] Position simulation steps: Perform Monte Carlo simulation on the positions of the calibration points and the laser tracking interferometer, and calculate the simulation error.

[0118] In a specific embodiment, the position simulation step includes:

[0119] Step S1: Based on the physical characteristics of the laser interferometer tracker and the measurement field network planning, a measurement field measurement and calibration mathematical model is established; the measurement field measurement and calibration mathematical model includes the laser interferometer tracker base station position, the measurement target mirror coordinates, the laser interferometer tracker measurement origin coordinates, and the measurement dead path length. The established model is as follows:

[0120] like Figure 1 As shown, the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j ,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement. That is, within this length range, the interferometer cannot measure the distance, and the measured object must be farther than this distance range. Length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With Pj The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is:

[0121]

[0122] In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector:

[0123] ∈ ij =|M i -P j |-L 0j -ΔL ij .

[0124] Step S2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field, and use the sum of squares of the actual measurement fitting errors of multiple spatial points as the optimization target. The optimization problem is established as follows:

[0125] ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem:

[0126]

[0127] In the formula

[0128]

[0129] x=[{M i} i＝1,…,m ,{P j} j＝1,…,n ,{L 0j} j＝1,…,n ].

[0130] Step S3: Based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field, the equality constraints and solution parameters of the optimization problem are determined, and the optimization model is solved using the LM algorithm. The solution process includes:

[0131] is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station locations. By solving this optimization problem, the actual coordinates of the measurement points can be evaluated. i With P j The relative coordinate relationship of the tracker base station is not known, so the system is underdefined and has no unique solution. Therefore, it is necessary to constrain the coordinate system. A common method is to establish a measurement coordinate system with the tracker base station position [P1, P2, P3] as the reference point, such as Figure 2 As shown, the measurement coordinate system takes the first base station coordinate P1 as the origin, the direction from P1 to P2 as the positive direction of the X-axis, and P3 is located in the XY plane to determine the Y-axis. The coordinate system constrains 6 parameters, reducing the total number of unknowns to 3m+4n-6. The system of measurement point equations has a total of m·n. The optimization problem has a solution:

[0132] (n-3)m>4n-6

[0133] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0134]

[0135] In the formula

[0136] F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn)

[0137]

[0138] The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is:

[0139]

[0140] Where J is the Jacobian matrix of F(x):

[0141]

[0142] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0143]

[0144] u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor kTend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0145]

[0146] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0147]

[0148] When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible. The update rule is as follows: k The rate of change is Figure 3 As shown:

[0149]

[0150] Step S4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field. The simulation process is as follows: Figure 4 As shown, calculate the measurement accuracy of the measurement field:

[0151] Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance:

[0152] Erorr=0.2+0.3*L ij

[0153] After adding the error, the original measurement equation becomes:

[0154]

[0155] After simulation, solve the optimization problem:

[0156]

[0157] Calculate the expectation of each laser interferometer tracking position and variance

[0158]

[0159]

[0160] If the calculated variance of the laser interferometer tracker position after Monte Carlo simulation is greater than the threshold, the positions of the four laser interferometer trackers need to be replanned.

[0161] Measurement field calibration steps: Determine whether the simulation error is less than the threshold. If so, calculate the positions of the four laser interferometer trackers to complete the self-calibration of the measurement field. If not, replan the positions of the laser interferometer trackers and repeat the above steps until the self-calibration of the measurement field is completed.

[0162] The present invention also provides a self-calibration system for a laser tracking interferometer measurement field in a machine tool coordinate system. The self-calibration system for a laser tracking interferometer measurement field in a machine tool coordinate system can be implemented by executing the process steps of the self-calibration method for a laser tracking interferometer measurement field in a machine tool coordinate system. That is, those skilled in the art can understand the self-calibration method for a laser tracking interferometer measurement field in a machine tool coordinate system as a preferred implementation of the self-calibration system for a laser tracking interferometer measurement field in a machine tool coordinate system.

[0163] A self-calibration system for a laser tracking interferometer measurement field in a machine tool coordinate system includes the following modules:

[0164] Measurement field construction module: A measurement field is formed by connecting and networking four laser interferometer trackers, which collect motion data of the tool tip of a machine tool in real time. The laser interferometer trackers are evenly distributed, and the four laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

[0165] Calibration point planning steps: planning the coordinates of the calibration points within the range of motion of the machine tool tool tip and the measurement range of the laser interferometer tracker; the number of the calibration points is not less than 13, and all calibration points are in non-coplanar positions.

[0166] Position simulation module: Perform Monte Carlo simulation on the positions of calibration points and laser tracking interferometer, and calculate the simulation error.

[0167] In a specific embodiment, the position simulation module includes:

[0168] Module M1: Based on the physical characteristics of the laser interferometer tracker and the measurement field network planning, a measurement field measurement and calibration mathematical model is established. The measurement field measurement and calibration mathematical model includes the laser interferometer tracker base station position, the measurement target mirror coordinates, the laser interferometer tracker measurement origin coordinates, and the measurement dead path length. The established model is as follows:

[0169] Assume that the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement, and the length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With P j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is:

[0170]

[0171] In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector:

[0172] ∈ ij =|M i -P j |-L 0j -ΔL ij

[0173] Module M2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field. The sum of the squares of the actual measurement fitting errors of multiple spatial points is used as the optimization target. The optimization problem is established as follows:

[0174] ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem:

[0175]

[0176] In the formula

[0177]

[0178] x=[{Mi} i＝1,…,m ,{P j} j＝1,…,n ,{L 0j} j＝1,…,n ]

[0179] Module M3: Determine the equality constraints and solution parameters of the optimization problem based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field. Solve the optimization model using the LM algorithm. The solution process includes:

[0180] x∈R 3m+4n is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station positions. A measurement coordinate system is established with the tracker base station positions [P1, P2, P3] as reference points. Six parameters are constrained by the coordinate system, reducing the total number of unknown quantities to 3m+4n-6. There are a total of m·n measurement point equations. The optimization problem has a solution:

[0181] (n-3)m>4n-6

[0182] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0183]

[0184] In the formula

[0185] F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn)

[0186]

[0187] The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is:

[0188]

[0189] Where J is the Jacobian matrix of F(x):

[0190]

[0191] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0192]

[0193] u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0194]

[0195] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0196]

[0197] When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible, and the update rule is as follows:

[0198]

[0199] Module M4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field and calculate the measurement accuracy of the measurement field:

[0200] Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance:

[0201] Erorr=0.2+0.3*L ij

[0202] After adding the error, the original measurement equation becomes:

[0203]

[0204] After simulation, solve the optimization problem:

[0205]

[0206] Calculate the expectation of each laser interferometer tracking position and variance

[0207]

[0208]

[0209] If the calculated variance of the laser interferometer tracker position after Monte Carlo simulation is greater than the threshold, the positions of the four laser interferometer trackers need to be replanned.

[0210] Measurement field calibration module: Determines whether the simulation error is less than the threshold. If so, calculates the positions of the four laser interferometer trackers and completes the self-calibration of the measurement field. If not, replans the positions of the laser interferometer trackers and re-executes the above module until the self-calibration of the measurement field is completed.

[0211] The present invention provides a computer-readable storage medium, which may be a hard disk, a USB flash drive, etc. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for self-calibrating the measurement field of a laser tracking interferometer in a machine tool coordinate system.

[0212] The present invention provides a device comprising a memory, a processor and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, the steps of the above-mentioned method for self-calibration of the measurement field of a laser tracking interferometer in a machine tool coordinate system are implemented.

[0213] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for self-calibration of a laser tracking interferometer measurement field in a machine tool coordinate system, characterized in that: The following steps are involved: The measurement field is constructed by connecting four laser interferometer trackers to form a network, and the laser interferometer trackers collect the motion data of the tool tip of the machine tool in real time. Calibration point planning steps: Plan the calibration point coordinates within the machine tool tool tip motion range and the laser interferometer tracker measurement range; Position simulation steps: Monte Carlo simulation is performed on the positions of the calibration points and the laser tracking interferometer to calculate the simulation error; Measurement field verification steps: Determine whether the simulation error is less than the threshold. If so, calculate the coordinates of the four laser interferometer trackers in the machine tool coordinate system and establish a conversion model between the measurement field measurement coordinate system and the machine tool mechanical coordinate system. If not, replan the positions of the laser interferometer trackers. The laser interferometer trackers are evenly distributed, and the four laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

2. The method for self-calibration of the laser tracking interferometer measurement field in a machine tool coordinate system according to claim 1, characterized in that: The number of the calibration points is no less than 13, and all the calibration points are in non-coplanar positions.

3. The method for self-calibration of the laser tracking interferometer measurement field in a machine tool coordinate system according to claim 1, characterized in that: The position simulation step comprises: Step S1: Establishing a mathematical model for transforming the measurement field coordinate system and the machine tool coordinate system; the transformation mathematical model includes the position of the laser interferometer tracker base station, the coordinates of the measurement target mirror, the coordinates of the laser interferometer tracker measurement origin, and the measured dead diameter length. The established model is as follows: Assume that the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j ,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement, and the length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With P j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is: In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector: ∈ ij =|M i -P j |-L 0j -ΔL ij Step S2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field, and use the sum of squares of the actual measurement fitting errors of multiple spatial points as the optimization target. The optimization problem is established as follows: ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem: In the formula x=[{M i } i＝1,…,m ,{P j } j＝1,…,n ,{L 0j } j＝1,…,n ] Step S3: Based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field, the equality constraints and solution parameters of the optimization problem are determined, and the optimization model is solved using the LM algorithm. The solution process includes: is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station positions. A measurement coordinate system is established with the tracker base station positions [P1, P2, P3] as reference points. Six parameters are constrained by the coordinate system, reducing the total number of unknown quantities to 3m+4n-6. There are a total of m·n measurement point equations. The optimization problem has a solution: (n-3)m>4n-6 The algorithm process of using LM algorithm to solve the constructed measurement model is as follows: In the formula F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn) The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is: Where J is the Jacobian matrix of F(x): According to the LM algorithm, at the iteration point x k There is a descending direction: u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point: Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible, and the update rule is as follows: Step S4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field and calculate the measurement accuracy of the measurement field: Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance: Erorr=0.2+0.3*L ij After adding the error, the original measurement equation becomes: After simulation, solve the optimization problem: Calculate the expectation of each laser interferometer tracking position and variance 4. A laser tracking interferometer measurement field self-calibration system in a machine tool coordinate system, characterized in that: Includes the following modules: Measurement field building module: four laser interferometer trackers are connected and networked to form a measurement field. The laser interferometer trackers collect the motion data of the tool tip of the machine tool in real time. Calibration point planning steps: Plan the calibration point coordinates within the machine tool tool tip motion range and the laser interferometer tracker measurement range; Position simulation module: performs Monte Carlo simulation on the positions of calibration points and laser tracking interferometer, and calculates simulation errors; Measurement field calibration module: determines whether the simulation error is less than the threshold. If so, calculates the positions of the four laser interferometer trackers to complete the self-calibration of the measurement field; if not, replans the positions of the laser interferometer trackers; The laser interferometer trackers are evenly distributed, and the four laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

5. The laser tracking interferometer measurement field self-calibration system in the machine tool coordinate system according to claim 4, characterized in that: The number of the calibration points is no less than 13, and all the calibration points are in non-coplanar positions.

6. The laser tracking interferometer measurement field self-calibration system in a machine tool coordinate system according to claim 4, characterized in that: The position simulation module includes: Module M1: Based on the physical characteristics of the laser interferometer tracker and the measurement field network planning, a measurement field measurement and calibration mathematical model is established. The measurement field measurement and calibration mathematical model includes the laser interferometer tracker base station position, the measurement target mirror coordinates, the laser interferometer tracker measurement origin coordinates, and the measurement dead path length. The established model is as follows: Assume that the laser interferometer tracker is located at the jth base station, which is represented as P in the machine tool coordinate system. j (X 0j ,Y 0j ,Z 0j ), the target mirror on the machine tool spindle is located at point M0, and the tracker sets the interference origin. The distance at this position is called the dead diameter length of the interference measurement, and the length L 0j Expressed as M0 and P j The absolute distance between the two points, when the target moves to the measuring point M i (x i ,y i ,z i ) when M i With p j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is: In the formula [x i ,y i ,z i ,X 0j ,Y 0j ,Z 0j ,L 0j ] is an unknown constant, ΔL ij To measure a known quantity, write the above equation in the form of error using a vector: ∈ ij =|M i -P j |-L 0j -ΔL ij Module M2: Establish an optimization problem based on the measurement data and the measurement calibration mathematical model of the measurement field. The sum of the squares of the actual measurement fitting errors of multiple spatial points is used as the optimization target. The optimization problem is established as follows: ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij The fitting error between the two points is minimized by minimizing the fitting error ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i To accurately estimate , we can establish the following optimization problem: In the formula x=[{M i } i＝1,…,m ,{P j } j＝1,…,n ,{L 0j } j＝1,…,n ] Module M3: Determine the equality constraints and solution parameters of the optimization problem based on the measurement coordinate system, the machine tool coordinate system, and the laser interferometer tracker station planning in the measurement field. Solve the optimization model using the LM algorithm. The solution process includes: is the unknown quantity to be identified, m is the total number of measurement points, and n is the total number of base station positions. A measurement coordinate system is established with the tracker base station positions [P1, P2, P3] as reference points. Six parameters are constrained by the coordinate system, reducing the total number of unknown quantities to 3m+4n-6. There are a total of m·n measurement point equations. The optimization problem has a solution: (n-3)m>4n-6 The algorithm process of using LM algorithm to solve the constructed measurement model is as follows: In the formula F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mn) The subscript satisfies r = (j-1)m + i, that is, the error equations of different measuring points are combined into a 1×mn-dimensional vector according to the subscript r; the gradient of the objective function h(x) is: Where J is the Jacobian matrix of F(x): According to the LM algorithm, at the iteration point x k There is a descending direction: u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point: Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under When η k When it is close to 1, it means that the quadratic function q(d) is at the iteration point x k The position fits the objective function well, and the iteration is close to the Gauss-Newton direction, and the damping coefficient μ k Take the smaller value, otherwise μ k Take a larger value; to avoid step size oscillation during iteration and obtain faster convergence speed, μ k The rate of change of should be as smooth as possible, and the update rule is as follows: Module M4: Based on the calculated measurement field calibration parameters, simulate the measurement uncertainty of the measurement field and calculate the measurement accuracy of the measurement field: Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m), and Gaussian random error is added to each measurement point according to the measured distance: Erorr=0.2+0.3*L ij After adding the error, the original measurement equation becomes: After simulation, solve the optimization problem: Calculate the expectation of each laser interferometer tracking position and variance 7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the self-calibration method of the laser tracking interferometer measurement field in the machine tool coordinate system according to any one of claims 1 to 3.

8. A device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is executed by a processor, the steps of the method for self-calibration of a laser tracking interferometer measurement field in a machine tool coordinate system according to any one of claims 1 to 3 are implemented.

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