Machine tool error control method and system based on laser interferometer tracker measurement field

Abstract

The present invention provides a machine tool error compensation method based on a laser interferometer tracker measurement field, comprising: networking multiple laser interferometer trackers to form a measurement field; synchronously triggering the multiple laser interferometer trackers to collect real-time motion data of the machine tool's tool tip; calculating the spatial position error of the machine tool's tool tip using a fast redundant iterative algorithm; transmitting the calculated error to the machine tool's numerical control system to calculate corresponding compensation parameters; and compensating the machine tool's tool tip position coordinates in real time based on the calculated compensation parameters. The present invention converts the displacement deviation measurement data from four laser interferometer trackers into the spatial position deviation coordinates of the tool tip using a fast redundant iterative algorithm, achieving high-precision measurement of the tool tip's spatial position. The real-time compensation system integrates the measurement field with the numerical control system, solving the closed-loop control problem between the machine tool and the measurement field and enabling real-time compensation control of the machine tool's tool tip spatial coordinates.

Description

Technical Field

[0001] The present invention relates to the technical field of machine tool compensation, and in particular to a machine tool error compensation method and system based on a laser interferometer tracker measurement field. Background Art

[0002] A CNC machine tool is an automated machine tool equipped with a program-controlled system that allows it to move and process parts according to a pre-programmed program. Modern CNC machines are equipped with high-precision scales, resulting in extremely precise motion. However, despite their high-precision transmission systems, machining accuracy is not necessarily high. This is because there is a mechanical structure between the transmission system and the end tool. Errors in any part of the machine tool ultimately reduce the precision of the end tool's cutting motion. During the actual cutting process, the tool tip comes into direct contact with the workpiece. Thermal deformation of the spindle and feed system during machine operation, as well as wear on the tool during machining, can cause the position of the tool tip to shift, resulting in machining errors and affecting part accuracy. Therefore, quickly and reliably calculating the position of the tool tip and compensating for these errors in real time are key to ensuring machining accuracy.

[0003] In the Chinese patent document with authorization announcement number CN109345500B, a method for calculating the tip point position of a machine tool tool based on machine vision is disclosed, including step 1, setting an industrial camera and a backlight light source; step 2, setting the corresponding sampling frequency of the industrial camera to collect multiple images at different times during the rotation of the tool; processing the obtained images to obtain a binary image of the tool edge and superimposing them, thereby obtaining a binary image of the overall contour of the tool during the rotation process; step 3, obtaining the pixel values ​​of the image matrix and calculating the tool edge coordinates to obtain the outermost edge of the tool and the coordinates of the lowest point position of the tool, thus completing the entire tool tip point position calculation process. Summary of the Invention

[0004] In view of the defects in the prior art, the object of the present invention is to provide a machine tool error compensation method and system based on the measurement field of a laser interferometer tracker.

[0005] According to the present invention, a machine tool error compensation method based on a laser interferometer tracker measurement field comprises the following steps:

[0006] Step S1: using multiple laser interferometer trackers to form a network and connect to form a measurement field;

[0007] Step S2: synchronously triggering multiple laser interferometer trackers to collect the tool tip motion data of the machine tool in real time;

[0008] Step S3: Separate the machine tool error into offline geometric error and online random error based on the measured data;

[0009] Step S4: Detecting and compensating for the machine tool's offline geometric errors;

[0010] Step S5: Real-time acquisition of the machine tool tool tip motion data is triggered by synchronous measurement field, and the spatial position coordinates of the machine tool tool tip are controlled in a closed loop in real time.

[0011] Preferably, in step S1, it is assumed that the laser interferometer tracker is located at the jth base station position P j (X 0j ,Y 0j ,Z 0j ), when the target mirror on the machine tool spindle is at point M0, the tracker sets the interference origin, that is, the dead diameter length L of the interference measurement 0j 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:

[0012]

[0013] 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:

[0014] ∈ ij =|M i -P j |l 0j -Δl ij

[0015] ∈ ij For [M i ,P j ,L 0j ] and the measured value ΔL ij By minimizing the fitting error at a large number of spatial measurement points ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i The following optimization problem is established based on the precise calculation of

[0016]

[0017] In the formula

[0018]

[0019] x=[{M i} i＝1,…,m ,{P j} j＝1,…,n ,{L 0j} j＝1,…,n ]

[0020] 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:

[0021] (n-3)m>4n-6

[0022] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0023]

[0024] In the formula

[0025] F(x)=[F1(x),…,F r (x),…,F mn (x)] T (r=1,…,mm)

[0026]

[0027] 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:

[0028]

[0029] Where J is the Jacobian matrix of F(x):

[0030]

[0031] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0032]

[0033] u K is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poork Tend to the direction of steepest descent; make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0034]

[0035] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0036]

[0037] 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 shown in formula (4-27):

[0038]

[0039] 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:

[0040] Erorr=0.2+0.3*L ij

[0041] After adding the error, the original measurement equation becomes:

[0042]

[0043] After simulation, solve the optimization problem:

[0044]

[0045] Calculate the expectation of each laser interferometer tracking position and variance

[0046]

[0047]

[0048] 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.

[0049] Preferably, the number of the laser interferometer trackers is not less than four and they are evenly distributed, multiple laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

[0050] Preferably, the offline geometric error refers to the error caused by stable changes in machine tool structural parts and foundation components. The offline geometric error does not change with time, or only changes slightly over a long period of time; the online random error refers to the error caused by factors such as the machine tool ambient temperature and random errors. The online random error changes with time.

[0051] Preferably, the step S4 includes:

[0052] Step S4.1: Establish a relationship model between the position of the tool tip in the workpiece coordinate system and each motion axis in the machine tool coordinate system;

[0053] Step S4.2: Analyze the influence of the machine tool motion axis disturbance error on the machine tool tool tip position, and establish a transformation model between the tool tip point in the workpiece coordinate system and the positions of each motion axis in the machine tool coordinate system under the influence of the error.

[0054] Step S4.3: planning the machine tool offline geometric error measurement trajectory according to the relational model;

[0055] Step S4.4: The laser interferometer tracker measurement field collects the machine tool tool tip point motion error data;

[0056] Step S4.5: Separate the tool tip motion error of the machine tool into each motion axis of the machine tool through calculation using an error separation algorithm;

[0057] Step S4.6: Generate a geometric error compensation file corresponding to the CNC system based on the calculation results;

[0058] Step S4.7: Import the compensation file into the CNC system through TCP communication and make it effective.

[0059] Preferably, the step S4.1 includes:

[0060] Create a rigid body that rotates around the X, Y, and Z axes by angles α, β, and γ, and translates along the X, Y, and Z axes by displacements d. x d y and d z The second coordinate transformation matrix is:

[0061] According to the position of the rigid body in space, it can be expressed as a composite motion of translation and rotation changes, namely:

[0062] D=T(Z,d x )T(Y,d y )T(X,dz )R(Z,γ)R(Y,β)R(X,α)

[0063] Simplifying the above formula, we get:

[0064]

[0065] Preferably, the step S3.2 includes:

[0066] Establish the relationship matrix between the tool tip position in the workpiece coordinate system and the positions of each motion axis in the machine tool coordinate system:

[0067] W P=F TW (X,Y,Z) T P

[0068] in, W P represents the coordinates of the tool tip in the workpiece coordinate system. T P represents the coordinates of the tool tip in the machine tool coordinate system. Transforming the relationship matrix into an algebraic form, we get:

[0069]

[0070] That is, Ψ=f Ψ (X, Y, Z), where Ψ represents x, y, z, indicating the coordinates of the tool tip;

[0071] Differentiate the above formula:

[0072]

[0073] Convert the differential equation into matrix form:

[0074]

[0075] Among them, J(X,Y,Z) is the Jacobian matrix, which is the linear transformation matrix from the vector formed by the machine tool motion axis to the position coordinates of the tool tip point. The specific expression is:

[0076]

[0077] Establish the transformation relationship between the tool coordinate system and the workpiece coordinate system when considering the machine tool geometric error:

[0078]

[0079] The coordinate position (x, y, z) of the tool tip in the workpiece coordinate system is expressed by the NC command (X, Y, Z) as follows:

[0080]

[0081] Preferably, step S5 includes the following sub-steps:

[0082] Step S5.1: Check the data and exclude abnormal data and noise data;

[0083] Step S5.2: Calculate the spatial coordinates of the tool tip point using a fast redundant iterative algorithm;

[0084] Step S5.3: Import the spatial coordinates of the tool tip into the machine tool CNC system and calculate the compensation parameters;

[0085] Step S5.4: The CNC system performs real-time compensation on the tool tip position of the machine tool according to the compensation parameters.

[0086] Preferably, the compensation parameters are used to compensate the numerical control system using a PID controller, and the control quantity of the position PID algorithm is calculated as follows:

[0087]

[0088] Where K P , K I and K D That is, they are proportional coefficient, integral coefficient and differential coefficient respectively. Using incremental PID control algorithm, the control quantity is:

[0089] Δu(k)=u(k)-u(k-1)

[0090] =K P [e(k)-e(k-1)]+K I e(k)+K D [e(k)-2e(k-1)+e(k-2)]

[0091] Where e(k), e(k-1), and e(k-2) correspond to the current error and the previous two error values, respectively. The output Δμ = [Δx, Δy, Δz] is the increment of the previous control variable. This increment is used to compensate the motion control variable after interpolation in the machine tool NC program in real time through the TCP communication of the CNC system. The specific formula is as follows:

[0092]

[0093] Where, P k =[x k ,y k ,z k ,X 0j ,Y 0j ,Z 0j ,L 0j ], the above is the control target of the controller. Through the PID control algorithm, the control quantity is calculated as follows:

[0094]

[0095] According to the present invention, a machine tool error compensation system based on a laser interferometer tracker measurement field includes the following modules:

[0096] Module M1: Use multiple laser interferometer trackers to form a measurement field;

[0097] Module M2: Synchronously trigger multiple laser interferometer trackers to collect real-time motion data of the machine tool tip;

[0098] Module M3: Separate the machine tool error into offline geometric error and online random error based on the measured data;

[0099] Module M4: Detection and compensation of machine tool offline geometric errors;

[0100] Module M5: Real-time acquisition of tool tip motion data of machine tools is triggered by measuring field synchronization, and real-time closed-loop control of the spatial position coordinates of the tool tip of machine tools is achieved.

[0101] Compared with the prior art, the present invention has the following beneficial effects:

[0102] 1. The present invention converts the displacement measurement data deviations of four laser interferometer trackers into the spatial position coordinate deviations of the tool tip through a fast redundant iterative algorithm, achieving a high-precision measurement effect of the spatial position of the tool tip point;

[0103] 2. The present invention integrates the measurement field and the numerical control system through a real-time compensation system, solves the closed-loop control problem of the machine tool and the measurement field, and realizes real-time compensation control of the spatial coordinates of the tool tip point of the machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] 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:

[0105] Figure 1 Schematic diagram of the mathematical model of the measurement field of the present invention;

[0106] Figure 2 Schematic diagram of the measurement coordinate system of the present invention;

[0107] Figure 3 Schematic diagram of the damping coefficient μ update strategy of the present invention;

[0108] Figure 4 This is the uncertainty Monte Carlo simulation algorithm process of the present invention;

[0109] Figure 5 This is a flow chart of automatic detection, calibration and compensation of spatial errors of machine tools according to the present invention;

[0110] Figure 6This is a flow chart of the error calibration method for the laser interferometer tracker measurement field of the present invention;

[0111] Figure 7 A flow chart for rapid detection and calibration of machine tool spatial accuracy;

[0112] Figure 8 An example diagram of the instrument station and CNC system wiring for measuring the spatial error of machine tools in the measurement field;

[0113] Figure 9 Diagram of the real-time closed-loop control system of the machine tool end based on the measurement field of the laser interferometer tracker;

[0114] Figure 10 This is a schematic diagram of the filter operation logic of the present invention;

[0115] Figure 11 This is a block diagram of the PID control principle of the present invention. DETAILED DESCRIPTION

[0116] 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.

[0117] This invention discloses a machine tool error compensation method based on a laser interferometer tracker measurement field. The overall design concept of this error compensation method is as follows: A measurement field is constructed using four high-precision laser interferometer trackers. This measurement field measures the motion error of the machine tool tool tip in real time and compensates it via closed-loop feedback to the numerical control system. This achieves real-time compensation for the spatial motion error of the machine tool tool tip, capable of achieving a tool tip spatial positioning error of 0.02 mm within a range of 20 meters. The machine tool error compensation method includes the following five steps:

[0118] Step S1: Using four laser interferometer trackers to form a network and connect to form a measurement field. The number of laser interferometer trackers is not less than four and is evenly distributed. Multiple laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

[0119] Step S2: synchronously triggering multiple laser interferometer trackers to collect the tool tip motion data of the machine tool in real time;

[0120] Step S3: dividing the machine tool error into offline geometric error and online random error according to the measured data;

[0121] Step S4: Detecting and compensating for the machine tool's offline geometric errors;

[0122] Step S5: The measurement field is synchronously triggered to collect the motion data of the tool tip of the machine tool in real time, and the spatial position coordinates of the tool tip of the machine tool are controlled in a closed loop in real time.

[0123] The specific operations of step S1 are as follows.

[0124] To calculate the spatial position of the tool tip, refer to Figure 1 As shown in the figure, by minimizing the sum of squares of fitting errors at a large number of spatial measurement points, the actual coordinates of the measurement points are accurately calculated, and the LM algorithm is used to solve the constructed measurement model algorithm. The details are as follows:

[0125] In traditional multilateral measurement, the target mirror M is mounted on the spindle end of the machine tool, and the laser interferometer tracker is fixedly installed at different positions on the machine tool workbench (called base station positions), distributed around the workspace to be measured, and the base station positions are required to be non-coplanar. During the measurement process, the machine tool spindle drives the target mirror to move along a set trajectory in the measurement space and stop at a series of measuring points. The laser interferometer tracker keeps observing the target mirror and records the interference distance value at the measuring point position. For traditional laser interferometer trackers, since its two tracking and orientation rotating axes are kept orthogonal through precise assembly, and the measuring laser is emitted through the intersection of the two axes, this intersection can be abstracted as a reference point P. The position of point P remains unchanged during the tracking measurement process, and the distance measured by the tracker is the distance between the reference point P and the center point M of the target mirror.

[0126] Assume that the laser interferometer tracker is located at the jth base station position P 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 object to be measured 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 P j The absolute distance is L 0j , ΔL ij The relative displacement measured by the interferometer at this time is:

[0127]

[0128] 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:

[0129] ∈ ij =|M i -P j |L 0j -ΔL ij

[0130] ∈ 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:

[0131]

[0132] In the formula

[0133]

[0134] x=[{M i} i＝1,...,m ,{P j} j＝1,...,n ,{L 0j} j＝1,…,n ].

[0135] is a series of unknown quantities 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 set the 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. Model (4-3) is transformed to the measurement coordinate system for solution. The coordinate system constrains 6 parameters, reducing the total number of unknowns to 3m+4n-6. There are m·n measurement point equations in total. Therefore, when the number of measurement point equations is greater than the number of unknowns, the optimization problem has a solution, namely:

[0136] (n-3)m>4n-6

[0137] The algorithm process of using LM algorithm to solve the constructed measurement model is as follows:

[0138]

[0139] In the formula

[0140] F(x)=[F1(x),…,F r (x),…F mn (x)] T (r=1,…,mn)

[0141]

[0142] 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:

[0143]

[0144] Where J is the Jacobi matrix of F(x):

[0145]

[0146] According to the LM algorithm, at the iteration point x k There is a descending direction:

[0147]

[0148] μ k is the damping coefficient, used in the quasi-Hessen matrix Adjust d when the approximation is poor k Tends to the direction of steepest descent; its specific adjustment method can be similar to the trust region radius adjustment: make a quadratic Taylor expansion approximation for g(x) at the current iteration point:

[0149]

[0150] Calculate the quadratic approximation function q(d) and the original objective function at d k The ratio of the increment under

[0151]

[0152] 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 it can be taken to be close to the Gauss-Newton direction iteration, and the damping coefficient μ k Should take a smaller value, otherwise μ kShould take a larger value; in order 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: k The rate of change is Figure 3 As shown:

[0153] ifη k >0

[0154]

[0155] else

[0156] μ k+1 =μ k ·v k ;v k+1 =2v k ;

[0157] Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker (0.2+0.3μm / m). The simulation process is as follows: Figure 4 As shown, a Gaussian random error is added to each measurement point according to the measured distance:

[0158] Erorr=0.2+0.3*L ij

[0159] After adding the error, the original measurement equation becomes:

[0160]

[0161] After simulation, the solution method is the same as the original method, that is, solving the optimization problem:

[0162]

[0163] Calculate the expectation of each laser interferometer tracking position and variance

[0164]

[0165]

[0166] If the variance of the laser interferometer position calculation after Monte Carlo simulation is greater than a certain threshold The positions of the four laser interferometer trackers need to be replanned.

[0167] The solution algorithm steps can be summarized as follows:

[0168] 1. Set the convergence gradient judgment threshold ε1, step size judgment threshold ε2 and the upper limit of the number of iterations k max, initialize the initial value x0, k=0, v0=2, calculate the gradient g0, and go to step 1;

[0169] 2. If g k <ε1ork>k max , the iteration ends. Otherwise, go to step 3;

[0170] 3. Calculate the iteration step d k , if ||d k ||≤ε2(||x||+ε2), the iteration ends. Otherwise, go to step 4;

[0171] 4. Calculate the increment ratio η k If η k ≤0, the iteration direction is not the descending direction, and the damping coefficient μ is increased k And update v k , go to step 3 to recalculate the iteration step. Otherwise, go to step 5;

[0172] 5. Iteration step reception, let x k+1 =x k +d k , calculate the gradient g k+1 , update the damping coefficient μ k and v k , k=k+1, go to step 2 for the next round of iteration.

[0173] Reference Figure 5 and Figure 6 As shown, step S3 specifically includes the following sub-steps:

[0174] Step S3.1: Establish a kinematic transformation model of the machine tool tool tip motion in the workpiece coordinate system.

[0175] Create a rigid body that rotates around the X, Y, and Z axes by angles α, β, and γ, and translates along the X, Y, and Z axes by displacements d. x d y and d z The second coordinate transformation matrix, such as the rigid body rotation angle α around the X axis and translation displacement d along the X axis x The second coordinate transformation matrix is:

[0176]

[0177]

[0178] When the above rotation angle α is very small, cosα≈1, sinα≈α, so R(X,α) can be simplified as:

[0179]

[0180] According to the position of the rigid body in space, it can be expressed as a composite motion of translation and rotation changes, namely:

[0181] D=T(Z,d x )T(Y,d y )T(X,d z )R(Z,γ)R(Y,β)R(X,α)

[0182] When the values ​​of the rotation angle and translation displacement are both small, the position of the matrices on the right side of the above equation will not affect the calculation result. However, when the values ​​are large, the composite matrix must be calculated based on the order of rotation and translation. When the values ​​of the rotation angle and translation displacement are both small, the second-order and higher-order traces can be ignored, and the above equation can be simplified to:

[0183]

[0184] Step S4.2: Establish a relationship model between the tool tip position and tool axis direction in the workpiece coordinate system using the various motion axes in the machine tool coordinate system.

[0185] In order to analyze the relationship between the motion errors of each axis of the machine tool and the change of the tool posture, it is necessary to calculate the differentials and derivatives of the kinematic transformation equations, and study the impact of small movements of the machine tool motion axis in the machine tool coordinate system on the tool posture in the workpiece coordinate system, that is, to study the impact of disturbance factors on the tool path.

[0186] According to the kinematic transformation law of CNC machine tools, for any CNC machine tool composed of three translation axes, the relationship between the tool tip position in the workpiece coordinate system and the tool axis direction expressed by the positions of each motion axis in the machine tool coordinate system can be obtained as follows:

[0187] W P=F TW (X,Y,Z) T P

[0188] in, W P represents the coordinates of the tool tip in the workpiece coordinate system. T P represents the coordinates of the tool tip in the machine tool coordinate system. Transforming the relationship matrix into an algebraic form, we get:

[0189]

[0190] That is, Ψ=f Ψ (X, Y, Z), where Ψ represents x, y, z, indicating the coordinates of the tool tip;

[0191] Differentiate the above formula:

[0192]

[0193] Convert the differential equation into matrix form:

[0194]

[0195] Among them, J(X,Y,Z) is the Jacobian matrix, which is the linear transformation matrix from the vector formed by the machine tool motion axis to the position coordinates of the tool tip point. The specific expression is:

[0196]

[0197] Establish the transformation relationship between the tool coordinate system and the workpiece coordinate system when considering the machine tool geometric error:

[0198]

[0199] The coordinate position (x, y, z) of the tool tip in the workpiece coordinate system is expressed by the NC command (X, Y, Z) as follows:

[0200]

[0201] Its physical meaning represents the actual spatial coordinates of the tool tip in the workpiece coordinate system, obtained after the machine tool runs according to the instructions (X, Y, Z), taking into account machine tool geometric errors. This formula has important practical applications, for example, in correcting the online measurement results of contact probes. During online measurement, a contact probe reads the position of each axis of the machine tool when the probe is triggered by a collision. The measurement results are usually evaluated in the workpiece coordinate system. Furthermore, accuracy depends on the accuracy of the machine tool. The higher the machine tool accuracy, the more accurate the measurement results. Since machine tool geometric errors are inevitable, this formula can eliminate the measurement uncertainty caused by geometric errors.

[0202] Use the measurement field to automatically calibrate the machine tool's spatial accuracy process, refer to Figure 7 The process is shown in the following table.

[0203]

[0204]

[0205] exist Figure 7 In this system, a controller integrates a separate calculation algorithm for spatial errors. Based on the geometric error terms of each machine tool's motion axes, a dedicated compensation file for the CNC system is generated. This compensation file is transferred to the CNC system and activated to achieve automated offline spatial error compensation and calibration.

[0206] Reference Figure 9 and Figure 10 As shown, step S5 includes the following sub-steps:

[0207] Step S5.1: Check the data and exclude abnormal data and noise data;

[0208] Step S5.2: Calculate the spatial coordinates of the tool tip point using a fast redundant iterative algorithm;

[0209] Step S5.3: Import the spatial coordinates of the tool tip into the machine tool CNC system and calculate the compensation parameters;

[0210] Step S5.4: The CNC system performs real-time compensation on the tool tip position of the machine tool according to the compensation parameters.

[0211] In step S5.1, the error real-time compensation system model disclosed in the present invention is as follows: Figure 10 As shown in Figure 1, a filter is set between the coordinate transformation model and the compensation parameter calculation model to filter and denoise the calculated high-precision tool tip position information:

[0212] y p =H 2r (s)u r +H 2d (s)d+H 2ξ (s)

[0213] in:

[0214]

[0215]

[0216]

[0217]

[0218] Q(s) is Q 31 filter, τ f is the time constant of the filter, which determines the cutoff frequency of the filter. The disturbance observer can effectively suppress external disturbances and reduce the impact of the high-frequency component of the measurement estimation error on the output. Reasonable selection of the time constant τ f The disturbance rejection capability and robustness of the observer can be balanced. The robust stability condition is given by the inequality proposed by KEMPF:

[0219]

[0220] in Is a multiplicative perturbation. Here we take K p The uncertainty is 10%, τ p1 The uncertainty is 20%, τ p2 The uncertainty is -20%, τ p The uncertainty is 15% to determine l m(jω). The cutoff frequencies of the designed filters are 10Hz (Q1), 3Hz (Q2), and 1Hz (Q3), and the corresponding time constants are τ f =0.026,0.087,0.260.

[0221] The compensation value uses PID controller to compensate the numerical control system. PID controller is a feedback closed-loop control algorithm widely used in the industrial field. It has the advantages of simple principle, simple parameter setting method and easy implementation. Its basic control principle is as follows: Figure 11 As shown in the figure, r is the system's expected input control quantity, y is the system's actual output, e is the deviation between input and output, P, I, and D are the corresponding proportional, integral, and differential control quantities calculated based on the deviation, and u is the output control quantity of the PID controller. The control quantity calculation of the position PID algorithm is as follows:

[0222]

[0223] Where K P , K I and K D That is, they are proportional coefficient, integral coefficient and differential coefficient respectively. Using incremental PID control algorithm, the control quantity is:

[0224] Δu(k)=u(k)-u(k-1)

[0225] =K P [e(k)-e(k-1)]+K I e(k)+K D [e(k)-2e(k-1)+e(k-2)]

[0226] Where e(k), e(k-1), and e(k-2) correspond to the current error and the previous two error values, respectively. The output Δμ = [Δx, Δy, Δz] is the increment of the previous control variable. This increment is used to compensate the motion control variable after interpolation in the machine tool NC program in real time through the TCP communication of the CNC system. The specific formula is as follows:

[0227]

[0228] Where, P k =[x k ,y k ,z k ,X 0j ,Y 0j ,Z 0j ,L 0j The above is the control target of the controller. Through the PID control algorithm, the control quantity is calculated as follows:

[0229]

[0230] The present invention also provides a machine tool error compensation system based on a laser interferometer tracker measurement field. The machine tool error compensation system based on a laser interferometer tracker measurement field can be implemented by executing the process steps of the machine tool error compensation method based on a laser interferometer tracker measurement field. That is, those skilled in the art can understand the machine tool error compensation method based on a laser interferometer tracker measurement field as a preferred embodiment of the machine tool error compensation system based on a laser interferometer tracker measurement field.

[0231] The present invention provides a machine tool error compensation system based on the measurement field of a laser interferometer tracker, comprising the following modules:

[0232] Module M1: Use multiple laser interferometer trackers to form a measurement field;

[0233] Module M2: Synchronously trigger multiple laser interferometer trackers to collect real-time motion data of the machine tool tip;

[0234] Module M3: Separate the machine tool error into offline geometric error and online random error based on the measured data;

[0235] Module M4: Detection and compensation of machine tool offline geometric errors;

[0236] Module M5: Real-time acquisition of tool tip motion data of machine tools is triggered by measuring field synchronization, and real-time closed-loop control of the spatial position coordinates of the tool tip of machine tools is achieved.

[0237] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0238] In the description of this application, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0239] 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 machine tool error compensation method based on the measurement field of a laser interferometer tracker, characterized in that: The following steps are involved: Step S1: using multiple laser interferometer trackers to form a network and connect to form a measurement field; Step S2: synchronously triggering multiple laser interferometer trackers to collect the tool tip motion data of the machine tool in real time; Step S3: Separate the machine tool error into offline geometric error and online random error based on the measured data; Step S4: Detecting and compensating for the machine tool's offline geometric errors; Step S5: Real-time acquisition of the machine tool tool tip motion data is triggered by synchronous measurement field, and the spatial position coordinates of the machine tool tool tip are controlled in a real-time closed-loop manner; The step S4 comprises: Step S4.1: Establish a relationship model between the position of the tool tip in the workpiece coordinate system and each motion axis in the machine tool coordinate system; Step S4.2: Analyze the influence of the machine tool motion axis disturbance error on the machine tool tool tip position, and establish a transformation model between the tool tip point in the workpiece coordinate system and the positions of each motion axis in the machine tool coordinate system under the influence of the error; Step S4.3: planning the machine tool offline geometric error measurement trajectory according to the relational model; Step S4.4: The laser interferometer tracker measurement field collects the machine tool tool tip point motion error data; Step S4.5: Separate the tool tip motion error of the machine tool into each motion axis of the machine tool through calculation using an error separation algorithm; Step S4.6: Generate a geometric error compensation file corresponding to the CNC system based on the calculation results; Step S4.7: Import the compensation file into the CNC system through TCP communication and make it effective; The step S4.1 includes: Create a rigid body that rotates around the X, Y, and Z axes by angles α, β, and γ, and translates along the X, Y, and Z axes by displacements d. x d y and d z The second coordinate transformation matrix is: According to the position of the rigid body in space, it can be expressed as a composite motion of translation and rotation changes, namely: D=T(Z,d x )T(Y,d y )T(X,d z )R(Z,γ)R(Y,β)R(X,α) Simplifying the above formula, we get: The step S5 includes the following sub-steps: Step S5.1: Check the data and exclude abnormal data and noise data; Step S5.2: Calculate the spatial coordinates of the tool tip point using a fast redundant iterative algorithm; Step S5.3: Import the spatial coordinates of the tool tip into the machine tool CNC system and calculate the compensation parameters; Step S5.4: The CNC system performs real-time compensation on the tool tip position of the machine tool according to the compensation parameters.

2. The machine tool error compensation method based on the laser interferometer tracker measurement field according to claim 1, characterized in that: In step S1, it is assumed that the laser interferometer tracker is located at the jth base station position P j (X 0j ,Y 0j ,Z 0j ), when the target mirror on the machine tool spindle is at point M0, the tracker sets the interference origin, that is, the dead diameter length L of the interference measurement 0j 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 ∈ ij For [M i ,P j ,L pj ] and the measured value ΔL ij By minimizing the fitting error at a large number of spatial measurement points ∈ ij The square sum is used to realize the actual coordinates M of the measuring point i The following optimization problem is established based on the precise calculation of In the formula x=[{M i } i＝1,…,m ,{P j } j＝1,…,n ,{L 0j } j＝1,…,n ] 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: Monte Carlo simulation is performed based on the measurement error of the laser interferometer tracker of 0.2+0.3μm / m, and Gaussian random error is added to each measurement point according to the measured distance: Eroor=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 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.

3. The machine tool error compensation method based on the laser interferometer tracker measurement field according to claim 2, characterized in that: The number of the laser interferometer trackers is no less than four and they are evenly distributed. Multiple laser interferometer trackers are in non-coplanar positions, and any three laser interferometer trackers are in non-colinear positions.

4. The machine tool error compensation method based on the laser interferometer tracker measurement field according to claim 1, characterized in that: The offline geometric error refers to the error caused by stable changes in the machine tool structural parts and foundation components. The offline geometric error does not change with time, or only changes slightly over a long period of time. The online random error refers to the error caused by factors such as the machine tool ambient temperature and random errors. The online random error changes with time.

5. The machine tool error compensation method based on the laser interferometer tracker measurement field according to claim 1, characterized in that: The step S4.2 includes: Establish the relationship matrix between the tool tip position in the workpiece coordinate system and the positions of each motion axis in the machine tool coordinate system: W P=F TW (X,Y,Z) T P in, W P represents the coordinates of the tool tip in the workpiece coordinate system. T P represents the coordinates of the tool tip in the machine tool coordinate system. Transforming the relationship matrix into an algebraic form, we get: That is, Ψ=f Ψ (X, Y, Z), where ψ represents x, y, and z, indicating the coordinates of the tool tip; Differentiate the above formula: Convert the differential equation into matrix form: Among them, J(X,Y,Z) is the Jacobian matrix, which is the linear transformation matrix from the vector formed by the machine tool motion axis to the position coordinates of the tool tip point. The specific expression is: Establish the transformation relationship between the tool coordinate system and the workpiece coordinate system when considering the machine tool geometric error: The coordinate position (x, y, z) of the tool tip in the workpiece coordinate system is expressed by the NC command (X, Y, Z) as follows: 。 6. The machine tool error compensation method based on the laser interferometer tracker measurement field according to claim 1, characterized in that: The compensation parameters are used to compensate the numerical control system using a PID controller. The control quantity of the position PID algorithm is calculated as follows: Where K P , K I and K D That is, they are proportional coefficient, integral coefficient and differential coefficient respectively. Using incremental PID control algorithm, the control quantity is: Δu(k)=u(k)-u(k-1) =K P [e(k)-e(k-1)]+K I e(k)+K D [e(k)-2e(k-1)+e(k-2)] Where e(k), e(k-1), and e(k-2) correspond to the current error and the previous two error values, respectively. The output Δμ = [Δx, Δy, Δz] is the increment of the previous control variable. This increment is used to compensate the motion control variable after interpolation in the machine tool NC program in real time through the TCP communication of the CNC system. The specific formula is as follows: Where, P k =[x k ,y k ,z k ,X 0j ,Y 0j ,Z 0j ,L 0j ], the above is the control target of the controller. Through the PID control algorithm, the control quantity is calculated as follows:

7. A machine tool error compensation system based on a laser interferometer tracker measurement field, based on the machine tool error compensation method based on a laser interferometer tracker measurement field according to claim 1, comprising the following modules: Module M1: Use multiple laser interferometer trackers to form a measurement field; Module M2: Synchronously trigger multiple laser interferometer trackers to collect real-time motion data of the machine tool tip; Module M3: Separate the machine tool error into offline geometric error and online random error based on the measured data; Module M4: Detection and compensation of machine tool offline geometric errors; Module M5: Real-time acquisition of tool tip motion data of machine tools is triggered by measuring field synchronization, and real-time closed-loop control of the spatial position coordinates of the tool tip of machine tools is achieved.

Images