Numerical control machine tool geometric error identification method and device based on improved nine-line method

Abstract

The present invention relates to a numerical control machine tool geometric error identification method based on an improved nine-line method, comprising the following: superposing motion errors among rigid bodies on the basis of a multi-body system kinematics theory in combination with a machine tool topological structure so as to construct a comprehensive error model, and performing optimization prediction on the basis of the comprehensive error model to obtain optimal measurement positions; establishing an identification equation set at each optimal measurement position; and performing numerical control machine tool geometric error simulation identification on the basis of the equation sets. According to the present invention, the objective of optimizing a measurement strategy is achieved by changing the combination mode of identification equation sets, i.e., performing densification processing on a measurement trajectory without increasing the number of measurements, so as to collect more error information in a space; and a comprehensive error field established on the basis of an object machine tool topological structure is simulated, traversal search is carried out in the error field by using an adaptive genetic algorithm, the identification result of each point is predicted, and finally, the measurement position with the minimum influence on the identification result is obtained.

Description

A method and device for identifying geometric errors of CNC machine tools based on an improved nine-line method

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to the Chinese patent application with application number 202311651145.3 filed with the China Patent Office on December 5, 2023, entitled “A method and device for identifying geometric errors of CNC machine tools based on an improved nine-line method”, the entire contents of which are incorporated by reference into this application. Technical Field

[0003] The present invention relates to the field of measurement technology, and in particular to a method and device for identifying geometric errors of CNC machine tools based on an improved nine-line method. Background Art

[0004] The nine-line method is an indirect identification method for obtaining the geometric errors of CNC machine tools. It is widely used in the industry due to its advantages such as simple measurement process and intuitive and easy-to-understand identification model.

[0005] The following is the general process of nine-line identification:

[0006] Measure the positioning / straightness errors on the three track lines shown in Figure 1 below Substitute into formula (1) and replace the corresponding coordinate value (x i ,y i ,z i ) is also substituted into the formula and rewritten into matrix formula (2), the six error values ​​on the right side of the equal sign can be solved.

[0007] Rewrite it into matrix form

[0008] However, the application of the traditional nine-line method has the following problems:

[0009] As shown in Figure 1, the nine-line method requires six measurements along three measurement paths in a single axis. Measuring all three axis errors requires "eighteen measurements along nine lines." This process repeatedly measures multiple errors along a single path. This results in a constricted measurement path, limited error information, and limited generalization of errors across spatial points. Therefore, the measurement path needs to be densified without increasing the number of measurements.

[0010] 2. In a large number of measurement tests conducted at different coordinate points, it was found that the identification results were greatly affected by the coordinates of the measurement points. Therefore, the identification results at different measurement points also had great differences.

[0011] 3. The machine tool coordinate system is used instead of the measurement coordinate system, ignoring the error transmission of each rigid body between the motion chains shown in Figure 2. According to the kinematic theory of multi-body systems, the identification result of the nine-line method only reflects the error characteristics between the workpiece coordinate system and the tool coordinate system. In fact, this result is the result of the superposition of errors between the X, Y and Z axis worktables and many rigid bodies such as the spindle and bed between these two coordinate systems, and cannot accurately describe the required error value.

[0012] Summary of the Invention

[0013] The purpose of the present invention is to solve at least one of the deficiencies of the prior art and to provide a method and device for identifying geometric errors of CNC machine tools based on an improved nine-line method.

[0014] In order to achieve the above object, the present invention adopts the following technical solutions:

[0015] Specifically, a CNC machine tool geometric error identification method based on the improved nine-line method is proposed, which includes the following:

[0016] Step 110: Based on the kinematic theory of multi-body systems and the topology of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model. Based on the comprehensive error model and a preset fitness function, six optimal measurement positions are predicted;

[0017] Step 120: At each optimal measurement position, a linear measurement trajectory parallel to any single motion axis among the X, Y, and Z axes is established, resulting in a total of six linear measurement trajectories. A specific error term is measured for each linear trajectory, resulting in a system of six equations.

[0018] Step 130: Perform simulation identification of geometric errors of the CNC machine tool based on the equation group.

[0019] Furthermore, specifically, based on the kinematics theory of multi-body systems and the topological structure of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model, including:

[0020] Assume that the machine tool is in the initial state, create a reference coordinate system R on the machine tool, and create local coordinate systems X, Y, Z, S, T, and W on the X, Y, and Z worktables, spindle S1, tool T1, and workpiece W1, respectively. The directions are consistent with the reference coordinate system R.

[0021] Since the Z axis is directly connected to the spindle and tool, there is no relative motion. is the homogeneous transformation matrix from coordinate system Z to spindle coordinate system S; the spindle is directly connected to the tool, so is the homogeneous transformation matrix from the spindle coordinate system S to the tool coordinate system T; the workpiece is directly connected to the machine tool, so is the homogeneous transformation matrix from the workpiece coordinate system W to the reference coordinate system R;

[0022] In the error-free state, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T is:

[0023] In the error state, based on the small error assumption and the principle of homogeneous coordinate transformation, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix from the workpiece coordinate system W to the tool coordinate system T is:

[0024] At this time, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be regarded as an error motion transformation matrix superimposed on the error state. So we have:

[0025] Based on the small error assumption, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T is for:

[0026] Among them, Δ x , Δ y , Δ z is the position error of the actual cutting point of the tool relative to the ideal cutting point; Δε x , Δε y , Δε z It is the directional error of the actual cutting point of the tool relative to the ideal cutting point;

[0027] Substituting equations (8), (12), and (14) into equation (13), based on the small error assumption and ignoring the second-order and above small quantities, while eliminating the distance caused by the three-way translation, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be obtained:

[0028] Δ x , Δ y , Δ z Corresponding to the matrix on the right side of the equal sign of formula (15), the corresponding terms are extracted to obtain the comprehensive error model as shown in (16).

[0029] Furthermore, specifically, based on the comprehensive error model combined with a preset fitness function, six optimal measurement positions are predicted, including:

[0030] The coordinate values ​​of any six measurement points are taken as a measurement combination, and each combination is taken as an individual. A preset fitness function is introduced to evaluate each individual. The individual with the smallest fitness is taken as the optimal individual, and the six measurement points corresponding to the optimal individual are taken as the six best measurement positions.

[0031] Further, specifically, the process of finding the optimal individual includes:

[0032] Step 210: Encode the individuals and initialize the population;

[0033] Step 220: Evaluate the fitness of each individual in the population using a fitness function;

[0034] Step 230: Determine whether the individual has a full rank of 6. If the rank is not 6, randomly assign the current individual a preset maximum fitness and return it to the original population as an unqualified individual. If the rank is full rank of 6, determine whether the preset number of iterations, i.e., the termination condition, is met.

[0035] Step 250: If the termination condition is met, the optimization is completed. If the termination condition is not met, selection, crossover, and mutation operations are performed to generate a new generation population and the process returns to step 220 to continue.

[0036] Furthermore, specifically, the process of establishing the fitness function includes:

[0037] Expand each variable in the measurement space to a matrix of the same size using the meshgrid matrix in MATLAB;

[0038] The matrix expanded by each variable is operated by the comprehensive error model to obtain the comprehensive error matrix of the same size corresponding to each variable, and the mathematical model for describing the entire measurement space based on the comprehensive error model is obtained;

[0039] The standard deviation of the mean of the individual error differences and the coefficient of variation are calculated based on the mathematical model as the identification results.

[0040] The present invention also proposes a CNC machine tool geometric error identification device based on an improved nine-line method, comprising the following:

[0041] A comprehensive error model building module is used to superimpose the motion errors between the rigid bodies based on the kinematic theory of multi-body systems and the machine tool topology to construct a comprehensive error model. Based on the comprehensive error model and a preset fitness function, six optimal measurement positions are predicted;

[0042] a measurement equation group establishment module for establishing, at each of the optimal measurement positions, a linear measurement trajectory parallel to the direction of any single motion axis among the X, Y, and Z axes, to obtain a total of six linear measurement trajectories, and measuring a specific error term for each linear trajectory to obtain an equation group having six equations;

[0043] A simulation identification module is used to perform simulation identification of geometric errors of CNC machine tools based on the equation group.

[0044] The beneficial effects of the present invention are:

[0045] The present invention provides a method for identifying geometric errors of CNC machine tools based on an improved nine-line method.

[0046] On the one hand, the identification process of the nine-line method shows that the identification equations determine the measurement strategy during actual operation. The present invention optimizes the measurement strategy by changing the combination of the identification equations. That is, the measurement trajectory is densely processed without increasing the number of measurements to collect more error information in the space.

[0047] On the other hand, the present invention simulates a comprehensive error field based on the topological structure of the object machine tool through computer, and uses an adaptive genetic algorithm to traverse and search in the error field and predict the identification results at each point, and finally obtains the measurement position with the least impact on the identification results. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The above and other features of the present disclosure will become more apparent through a detailed description of the embodiments shown in conjunction with the accompanying drawings. The same reference numerals in the drawings of the present disclosure represent the same or similar output voltages. Obviously, the drawings described below are only some embodiments of the present disclosure. It is possible for a person skilled in the art to derive other drawings based on these drawings without inventive effort. In the drawings:

[0049] Figure 1 shows a schematic diagram of the traditional nine-line method measurement trajectory;

[0050] FIG2 is a schematic diagram of a machine tool kinematic chain involved in the background art;

[0051] FIG3 is a schematic diagram showing a measurement trajectory of a method for geometric error identification of a CNC machine tool based on an improved nine-line method according to the present invention;

[0052] FIG4 is a flow chart of a method for identifying geometric errors of CNC machine tools based on the improved nine-line method according to the present invention;

[0053] FIG5 is a schematic diagram of a kinematic chain simplified according to research requirements in a method for geometric error identification of CNC machine tools based on an improved nine-line method according to the present invention;

[0054] FIG6 is a schematic diagram showing the motion structure of the translation axis of an RRTTT five-axis CNC machine tool, which is an application example of a method for identifying geometric errors of CNC machine tools based on the improved nine-line method of the present invention;

[0055] FIG7 shows a schematic diagram of compensation identification using the traditional nine-line method;

[0056] FIG8 is a schematic diagram showing the distribution of measurement points in an error field established by a method for geometric error identification of CNC machine tools based on an improved nine-line method according to the present invention;

[0057] FIG9 is a diagram showing an algorithm optimization principle of a method for identifying geometric errors of CNC machine tools based on an improved nine-line method according to the present invention;

[0058] FIG10 is a schematic diagram showing the measurement of the straightness error in the X-axis direction when the geometric error identification method of a CNC machine tool based on the improved nine-line method of the present invention is applied;

[0059] FIG11 is a schematic diagram showing an identification error value of a CNC machine tool geometric error identification method based on an improved nine-line method according to the present invention when applied;

[0060] FIG12 is a schematic diagram showing the identification error value when the traditional nine-line method is applied;

[0061] FIG13 is a comparison diagram of three groups of errors when a CNC machine tool geometric error identification method based on the improved nine-line method of the present invention is applied and a traditional nine-line method is applied. DETAILED DESCRIPTION

[0062] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other unless there is a conflict. The same reference numerals used throughout the drawings indicate the same or similar parts.

[0063] 1 and 2 , in Example 1, the present invention proposes a method for identifying geometric errors of CNC machine tools based on an improved nine-line method, comprising the following steps:

[0064] Step 110: Based on the kinematic theory of multi-body systems and the topology of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model. Based on the comprehensive error model and a preset fitness function, six optimal measurement positions are predicted;

[0065] Step 120: At each of the optimal measurement positions, a linear measurement trajectory parallel to the direction of any single motion axis among the X, Y, and Z axes is established, resulting in a total of six linear measurement trajectories. A specific error term is measured for each linear trajectory, resulting in a system of six equations; wherein the specific error term is measured according to the matrix given by formula (5), the six errors to be measured are on the left side of the equal sign of the formula, and the small mark i (i = 1, 2, ..., 6) in the upper right corner of the six errors is the error that needs to be measured on the i-th measurement trajectory.

[0066] Step 130: Perform simulation identification of geometric errors of the CNC machine tool based on the equation group.

[0067] In step 120, the identification equation group is improved. First, the original measurement trajectory is densified. Taking the X-axis direction as an example, when six geometric errors are used as the objects to be solved, it is necessary to establish an equation group containing six equations. It is not difficult to see from formula (2) that as long as the coordinate matrix is ​​full rank, there is a unique solution.

[0068] Following the above process, each point in the measurement space can correspond to a set of error vectors shown in Equation (3). If six points on six parallel lines are obtained, then a total of six equations are obtained. The following Equation (3) is the equation group corresponding to the i-th point.

[0069] Extract one equation from each of the six equation groups shown in equation (3) and reassemble it into a new equation group. As long as the equation group contains the six errors to be solved and satisfies the full rank of the coordinate matrix, the equation group can have a unique solution.

[0070] MATLAB-assisted calculations show that there are 120 possible permutations and combinations of the six equations in the above formula, totaling 18 equations, so there are 120 equations that meet the analytical conditions. Since the coefficient matrix directly affects the results of the analysis, two groups are selected for use to enrich the optimization results of the subsequent algorithm.

[0071] The first combination is shown in Figure 3. Taking the measurement of the X-axis direction as an example, the positioning error on line 1 in Figure 3 is measured respectively. 2. Linearity error of X axis in Y direction Positioning error on line 3 Straightness error of 4 lines in Z direction Positioning error on line 5 6. Linearity error of X axis in Z direction A total of six measurements resulted in a system of six equations.

[0072] Corresponding to the following formula (4)

[0073] Rewrite it into matrix form (5), substitute the measured value into the left side of the equation, substitute the corresponding coordinate value into the right side of the equation, and solve for the six error values.

[0074] At the same time, the second combination method shown in formula (6) is given for cross search. The measurement process is the same as the above method and will not be described in detail:

[0075] Rewrite it into matrix form

[0076] This method acquires six linear measurement tracks parallel to a single axis of motion. Each track measures a specific error, for a total of six measurements. To measure all three directions, eighteen tracks and eighteen measurements are required. Compared to the nine-line method, which also requires eighteen measurements, the new method increases the density of the measurement tracks without increasing the number of measurements.

[0077] As a preferred embodiment of the present invention, specifically, based on the kinematics theory of multi-body system combined with the topological structure of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model, including:

[0078] To accurately predict the optimal measurement position, it is necessary to use a computer to simulate an error field that is identical to the processing space of the CNC machine tool. The comprehensive error model is based on the kinematic theory of multi-body systems combined with the topological structure of the machine tool and is obtained by superimposing the motion errors between the rigid bodies. Therefore, a comprehensive error mathematical model is used to establish the error field.

[0079] Combined with Figure 5, the kinematic chain is simplified according to the research needs. Assuming that the machine tool is in the initial state, a reference coordinate system R is created on the machine tool, and local coordinate systems X, Y, Z, S, T, and W are created on the X, Y, and Z worktables, spindle S1, tool T1, and workpiece W1, respectively. The directions are consistent with the reference coordinate system R.

[0080] Since the Z axis is directly connected to the spindle and tool, there is no relative motion. is the homogeneous transformation matrix from coordinate system Z to spindle coordinate system S; the spindle is directly connected to the tool, so is the homogeneous transformation matrix from the spindle coordinate system S to the tool coordinate system T; the workpiece is directly connected to the machine tool, so is the homogeneous transformation matrix from the workpiece coordinate system W to the reference coordinate system R; that is Represents the homogeneous transformation matrix from the q coordinate system to the p coordinate system, where p and q are any of R, X, Y, Z, S, T, and W;

[0081] In the error-free state, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T is: Represents the homogeneous transformation matrix from the q coordinate system to the p coordinate system in the error-free state, where p and q are any of R, X, Y, Z, S, T, and W:

[0082] In the actual state (with error), the transformation matrix of each motion axis has a small movement in each direction. For example, the Y axis of the workbench has three translation errors δ yy , δ xy , δ zy , three rotation angle errors ε yy , ε xy , ε zy , when the worktable Y moves a distance y, based on the small error assumption and the principle of homogeneous coordinate transformation, the homogeneous transformation matrix from the reference coordinate system R to the worktable Y is, where, Represents the homogeneous transformation matrix from the q coordinate system to the p coordinate system in the error state, where p and q are any of R, X, Y, Z, S, T, and W, and:

[0083] When the worktable X moves a distance x, there are three translation errors δ xx , δ yx , δ zx , three rotation angle errors ε xx , ε yx , ε zx and a perpendicularity error S xy Based on the small error assumption and the principle of homogeneous coordinate transformation, the transformation matrix from Y to X of the worktable is, where δuv represents the translation error of the v-axis in the u-axis direction. Positioning error and straightness error belong to translation error. εuv represents the angular error of the v-axis in the u-axis direction. Suv represents the verticality error of the v-axis in the u-axis direction. u and v are any of the X, Y, and Z axes, and:

[0084] When the worktable Z moves a distance z, there are three translation errors δ xz , δ yz , δ zz , three rotation angle errors ε xz , ε yz , ε zz , two perpendicularity errors S xz 、S yz , based on the small error assumption and the principle of homogeneous coordinate transformation, the transformation matrix from the workbench X to Z is:

[0085] In the error state, based on the small error assumption and the principle of homogeneous coordinate transformation, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix from the workpiece coordinate system W to the tool coordinate system T is:

[0086] At this time, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be regarded as an error motion transformation matrix superimposed on the error state. So we have:

[0087] Based on the small error assumption, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T is for:

[0088] Among them, Δ x , Δ y , Δ z is the position error of the actual cutting point of the tool relative to the ideal cutting point; Δε x , Δε y , Δε z It is the directional error of the actual cutting point of the tool relative to the ideal cutting point;

[0089] Substituting equations (8), (12), and (14) into equation (13), based on the small error assumption and ignoring the second-order and above small quantities, while eliminating the distance caused by the three-way translation, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be obtained:

[0090] Δ x , Δ y , Δ z Corresponding to the matrix on the right side of the equal sign of formula (15), the corresponding terms are extracted to obtain the comprehensive error model as shown in (16).

[0091] In this preferred embodiment, based on the actual size and structure of the machine tool and the installation range of the Renishaw XL-80 laser interferometer, the measurement point layout space of the X-axis of this CNC machine tool is shown in Table 1:

[0092] Table 1 Measurement range of three translation axes

[0093] Measurements were taken along the X, Y, and Z axes within the space, yielding 18 geometric errors and three perpendicularity errors in 20mm intervals across the three directions. To simplify the model, the standard error was determined by taking the mean of the 18 errors measured multiple times along different trajectories along a single axis. Each of the X, Y, and Z axes has six sets of errors. The coordinates of the corresponding measurement points disperse these six single-axis errors within the space, resulting in 21 geometric errors at each point within the space.

[0094] As shown in Figure 7, this is the general process from nine-line method identification to compensation. The ideal error value is used as a reference. MATLAB is used to establish a space equal to the measurement space and divide it into grids with the same distance intervals. As shown in Figure 8, each grid node is a measurement point.

[0095] Each node contains 21 standard error values. At the same time, each node introduces the comprehensive error model formula (16), so that the measured value of each point is substituted into the right side of the equation group as a simulated measurement value. Then, three comprehensive errors Δ x , Δ y , Δ z In this way, an error model that takes the topological structure into account is established. At this time, the standard error value used previously is used as a reference. Taking the X-axis as an example, the Δ x , Δ y , Δ z As the left side of the improved equations (11) and (13) The corresponding situations are shown in Table 2 below:

[0096] Table 2 Error measurement values ​​and their corresponding items

[0097] For the large number of variables in the comprehensive error model, all variables are expanded into a matrix of the same size as the coordinate space matrix (26×34×21), and then each matrix is ​​calculated according to formula (23) to obtain the comprehensive error matrix of the same size Δ μ (i.e. Δ x , Δ y and Δ z At this time, each coordinate point uniquely corresponds to a set of Δ μ .

[0098] As a preferred embodiment of the present invention, specifically, based on the comprehensive error model combined with a preset fitness function, six optimal measurement positions are predicted, including:

[0099] The coordinate values ​​of any six measurement points are taken as a measurement combination, and each combination is taken as an individual. A preset fitness function is introduced to evaluate each individual. The individual with the smallest fitness is taken as the optimal individual, and the six measurement points corresponding to the optimal individual are taken as the six best measurement positions.

[0100] Specifically, the process of finding the optimal individual includes:

[0101] Step 210: Encode the individuals and initialize the population;

[0102] Step 220: Evaluate the fitness of each individual in the population using a fitness function;

[0103] Step 230: Determine whether the individual has a full rank of 6. If the rank is not 6, randomly assign the current individual a preset maximum fitness and return it to the original population as an unqualified individual. If the rank is full rank of 6, determine whether the preset number of iterations, i.e., the termination condition, is met.

[0104] Step 250: If the termination condition is met, the optimization is completed. If the termination condition is not met, selection, crossover, and mutation operations are performed to generate a new generation population and the process returns to step 220 to continue.

[0105] Specifically, the process of establishing the fitness function includes:

[0106] Expand each variable in the measurement space to a matrix of the same size using the meshgrid matrix in MATLAB;

[0107] The matrix expanded by each variable is operated by the comprehensive error model to obtain the comprehensive error matrix of the same size corresponding to each variable, and the mathematical model for describing the entire measurement space based on the comprehensive error model is obtained;

[0108] The standard deviation of the mean of the individual error differences and the coefficient of variation are calculated based on the mathematical model as the identification results.

[0109] In this preferred embodiment, referring to FIG9 , the optimization process specifically includes the following:

[0110] In order to facilitate the algorithm optimization, it is necessary to have the function of encoding and decoding the individual (the real number encoding of (1-714) is used in this paper); secondly, the function inputs the corresponding code of the individual, and the corresponding comprehensive error is obtained through calculation. (column vector on the left side of the equal sign of Equations (12) and (14)) and the coordinate matrix (6×6 coefficient matrix on the right side of the equal sign of Equations (12) and (14)), determine whether the two coordinate matrices have a full rank of 6. If they meet the requirements, proceed to the next step of operation. If not, assign a maximum fitness value to this individual as an inferior individual and eliminate it in the subsequent process.

[0111] Taking the X-axis direction as an example, the two sets of identification errors of each of the 26 points in the single-axis direction are obtained by calculating the starting point coordinates, the comprehensive error and the two sets of coordinate matrices (the column vectors on the right side of the equal sign in Equations (12) and (14)). The first three positioning / straightness errors are obtained (the angular error is extremely small, the identification result is difficult to control and has little effect on the overall identification and subsequent compensation process, so it is not considered here). The absolute value is subtracted from the standard error value according to the corresponding coordinates to obtain the scalar value of the three sets of error differences. and

[0112] in

[0113] The first letter μ in the subscript represents the direction of error deviation, which is x, y, or z; the second letter x represents the X-axis; and the subscript i represents the i-th measurement point on the measurement path. μxi Represents the error value obtained by identification at the i-th measurement point, δ′ μxi Represents the measured error value of the i-th measurement point. Find the mean of the difference at a single point

[0114] In the above formula, L sa As a standard for evaluating the mean size of individual error differences, its size reflects the difference between the predicted value and the standard error value in terms of the mean size.

[0115] In order to avoid excessive discreteness of the coordinates of the 26 points on the path, it is also necessary to control L sa The coefficient of variation c v , first obtain the standard deviation S a :

[0116] Then take the coefficient of variation c v :

[0117] At this time c v The size of S a and L sa The influence of the two values ​​reflects the degree of variation of the observed values. In order to avoid a large degree of dispersion of the predicted values, the mean L of the error difference is continuously reduced. sa When c v value to make the predicted value closer to the standard error value.

[0118] The adaptive genetic algorithm searches the above space cyclically and continuously converges to c v At the same time, find L under a fixed number of iterations sa The minimum value of , output the individual code corresponding to the result.

[0119] After setting the parameters, the population is initialized, and then the main loop of the iteration is entered to select, cross, and mutate the population to generate a new population to be put into the next round of iteration until the preset number of iterations is reached and the loop stops.

[0120] The geometric error identification method of CNC machine tools based on the improved nine-line method proposed in this invention is compared with the original nine-line method in application as follows:

[0121] The 30 individuals were iterated 10,000 times, and the optimal fitness was 1.42. The corresponding individual code was [692 168 492 444 63 379]. The corresponding coordinate matrix after decoding was

[0122] The corresponding measurement position is X = -640 on the X axis as the starting point and X = -140 as the end point, and the measurement starting point of the point combination shown in Table 3 is obtained.

[0123] Table 3 Coordinates of the starting point of the six-point combination measurement

[0124] To verify the reliability of the data obtained by the six-point combination, the Renishaw XC-80 laser interferometer shown in Figure 10 was used to perform fixed-point measurement on the CNC machine tool. First, the sensor components were configured to monitor the measurement environment in real time. The environmental parameters are shown in Table 4.

[0125] Table 4 Test environment parameter values

[0126] The coordinates in Table 3 are measured in sequence, and the starting point is set to X = -640 mm and the end point is set to X = 140 mm. The measurement is repeated five times. At the same time, in order to reduce the influence of the backlash error, the overtravel is set to 0.05 mm. The interval between each measuring point on the path is 20 mm. The corresponding error data of the six points are measured in sequence and the coefficient matrix (19) corresponding to the measurement value of each point and its point combination is substituted into the analytical equation group given by formula (5) to obtain formula (20). The six error values ​​of each measuring point on the measurement path are obtained by analysis, as shown in Figure 10.

[0127] Substitute the measured values ​​into the left side of the above formula, and solve the six geometric errors. Solve the corresponding values ​​in turn and write them into Table 4 and draw a line graph 11

[0128] The traditional nine-line measurement method is set as a control test. The traditional nine-line method is to take any three-point combination as the measurement point for measurement, and then identify it through the corresponding coefficient matrix. The coordinates in Table 5 are taken as the measurement starting point.

[0129] Table 5 Coordinates of the starting point measured by the nine-line method

[0130] The corresponding error data of each point is measured in turn and the coefficient matrix of the measurement data and its coordinate values ​​of the measurement points is substituted into Equation (2) to obtain Equation (21). The six error values ​​of each measurement point on the measurement path are obtained by analysis, as shown in Figure 12.

[0131] Substituting the measured data into the left side of the above formula, we can get the six geometric errors shown in the figure below:

[0132] The accuracy of the two sets of identification results is determined by comparing the identification results of the two methods with the standard error values ​​of the actual measured errors through multiple indicators, as shown in Table 6 below.

[0133] Table 6 Comparison table of measured value error data

[0134] Table 7 Evaluation of various indicators of the identification values ​​obtained by the two methods

[0135] Table 8 Root mean square error (RMSE) based on actual values

[0136] By comparing the improved and traditional methods with various indicators of actual measurements, Figure 13 and Table 7 show that the mean, standard deviation, and range of the error values ​​identified by the improved method are closer to the indicators of the actual measurement errors than those obtained by the traditional method. Table 8 shows that the improved method has a smaller root mean square error than the traditional method, indicating that the improved identification results have a higher degree of confidence in reflecting the actual measured values. The geometric significance of angular error in actual measurement differs from that described by the nine-line method identification model. It is extremely small, making the identification results difficult to control and having little impact on subsequent compensation. Here, only the three linear errors that have a significant impact on actual compensation are considered.

[0137] Summarize:

[0138] 1. In order to improve the situation where the nine-line method's "nine-line eighteen-times measurement" has a thin trajectory that is difficult to describe the overall spatial error, the new method performs "eighteen-line eighteen-times measurement" based on the analytical principle of the nine-line method, so that multiple error measurements on a single point are dispersed to multiple points. This not only extracts error information over a wider range, making the identification results more generalizable to the measurement space, but also reduces the impact of repeated positioning errors.

[0139] 2. Based on the multi-body system theory, a comprehensive error model of the topological structure of the translation axis of the dual-turntable five-axis CNC machine tool was established through the homogeneous coordinate transformation method. Based on this model, the error field within the measurement range was constructed with the help of a computer. In this space, an adaptive genetic algorithm was used to search for various coordinate point combinations and predict the identification results. To a certain extent, this can improve the problems of the traditional nine-line method ignoring the machine tool topological structure problem and the deviation in the identification results caused by the influence of the measurement point coordinate values. In addition, this process can automatically filter out unsolvable singular matrices.

[0140] 3. Comparing the identification results of the new and old methods with the actual measurement results, it can be seen that the improved method has stronger follow-up performance in linear error than the traditional method, and is more reliable when used to describe linear error in geometric error.

[0141] The present invention also proposes a CNC machine tool geometric error identification device based on an improved nine-line method, comprising the following:

[0142] A comprehensive error model building module is used to superimpose the motion errors between the rigid bodies based on the kinematic theory of multi-body systems and the machine tool topology to construct a comprehensive error model. Based on the comprehensive error model and a preset fitness function, six optimal measurement positions are predicted;

[0143] a measurement equation group establishment module for establishing, at each of the optimal measurement positions, a linear measurement trajectory parallel to the direction of any single motion axis among the X, Y, and Z axes, to obtain a total of six linear measurement trajectories, and measuring a specific error term for each linear trajectory to obtain an equation group having six equations;

[0144] A simulation identification module is used to perform simulation identification of geometric errors of CNC machine tools based on the equation group.

[0145] Although the present invention has been described in considerable detail and with particularity with respect to several described embodiments, it is not intended to be limited to any of these details or embodiments or any particular embodiment, but rather should be construed as providing a broad possible interpretation of these claims in view of the prior art by reference to the appended claims, thereby effectively encompassing the intended scope of the invention. In addition, the invention has been described above in terms of embodiments foreseen by the inventors for the purpose of providing a useful description, and those insubstantial modifications of the invention that are not currently foreseen may still represent equivalent modifications of the invention.

[0146] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. As long as the technical effects of the present invention are achieved by the same means, they shall fall within the scope of protection of the present invention. Within the scope of protection of the present invention, various modifications and variations of the technical solutions and / or implementation methods may be made.

Claims

1. A method for geometric error identification of CNC machine tools based on an improved nine-line method, characterized in that: Includes the following: Step 110: Based on the kinematic theory of multi-body system and the topological structure of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model, and six optimal measurement positions are predicted based on the comprehensive error model and a preset fitness function; Step 120, at each of the optimal measurement positions, a linear measurement trajectory parallel to any single motion axis of the X, Y, and Z axes is established to obtain a total of six linear measurement trajectories, and a specific error term is measured for each linear trajectory to obtain an equation system with six equations; Step 130, performing a simulation identification of a CNC machine tool geometric error based on the equation group; Specifically, in step 120, the original measurement trajectory is first densified. Each point in the measurement space can correspond to a set of error vectors shown in formula (3). If six points on six parallel lines are obtained, then a total of six equations are obtained. The following formula (3) is the equation group corresponding to the i-th point, Wherein, i=1, 2, ..., 6, and one equation is extracted from each of the six equation groups shown in equation (3) to be reassembled into a new equation group. As long as the equation group contains the six errors to be solved and satisfies the full rank of the coordinate matrix, the equation group can have a unique solution; From the MATLAB-assisted calculation, we know that there are 120 permutations and combinations of the above six equations with a total of 18 equations that can meet the requirements. Therefore, there are 120 equations that meet the analytical conditions. Since the coefficient matrix directly affects the analytical results, two groups are selected for use to enrich the optimization results of the subsequent algorithm. The first combination, when measuring the X-axis direction, measures the positioning error on line 1 respectively 2 Line X axis straightness error in Y direction Positioning error on line 3 Straightness error of the X-axis in the Z direction on 4 lines Positioning error on line 5 6 Line X axis straightness error in Z direction A total of six measurements resulted in a system of six equations, Corresponding to the following formula (4) Rewrite it into matrix form (5), substitute the measured value into the left side of the equation, substitute the corresponding coordinate value into the right side of the equation, and solve for the six error values: At the same time, the second combination method shown in formula (6) is given to perform cross search. The measurement process is the same as the above method and will not be described in detail: Rewrite it into matrix form This method is to obtain six linear measurement tracks parallel to a single motion axis. Each measurement track measures only a specific error, and a total of six measurements are made. Among them, δuv represents the translation error of the v-axis in the u-axis direction. The positioning error and straightness error belong to the same translation error. εuv represents the angular error of the v-axis in the u-axis direction, where u and v are any of the X, Y, and Z axes.

2. The method for geometric error identification of CNC machine tools based on the improved nine-line method according to claim 1 is characterized in that: Specifically, based on the kinematics theory of multi-body systems and the topological structure of the machine tool, the motion errors between the rigid bodies are superimposed to construct a comprehensive error model, including: Assuming that the machine tool is in the initial state, a reference coordinate system R is created on the machine tool, and local coordinate systems X, Y, Z, S, T, and W are created on the X, Y, and Z worktables, spindle S1, tool T1, and workpiece W1, respectively, with the directions consistent with the reference coordinate system R; Since the Z axis is directly connected to the spindle and the tool, there is no relative motion. is the homogeneous transformation matrix from coordinate system Z to spindle coordinate system S; the spindle is directly connected to the tool, so is the homogeneous transformation matrix from the spindle coordinate system S to the tool coordinate system T; the workpiece is directly connected to the machine tool, so is the homogeneous transformation matrix from the workpiece coordinate system W to the reference coordinate system R; In the error-free state, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T is: Among them, the upper right corner of the matrix i represents the corresponding matrix in the error-free state, represents the homogeneous transformation matrix from the q coordinate system to the p coordinate system in the error-free state, where p and q are any of R, X, Y, Z, S, T, and W; In the error state, based on the small error assumption and the principle of homogeneous coordinate transformation, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix from the workpiece coordinate system W to the tool coordinate system T is: Among them, the upper right corner subscript e of the matrix represents the corresponding matrix in the error state, It represents the homogeneous transformation matrix from the q coordinate system to the p coordinate system in the error state, where p and q are any of R, X, Y, Z, S, T, and W; At this time, the homogeneous transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be regarded as an error motion transformation matrix superimposed on the error state. So we have: Based on the small error assumption, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T is for: Among them, Δ x , Δ y , Δ z is the position error of the actual cutting point of the tool relative to the ideal cutting point; Δε x , Δε y , Δε z It is the directional error of the actual cutting point of the tool relative to the ideal cutting point; Substituting equations (8), (12), and (14) into equation (13), based on the small error assumption and ignoring the second-order and above small quantities, and eliminating the distance caused by the three-dimensional translation, the error motion transformation matrix from the workpiece coordinate system W to the tool coordinate system T can be obtained: Δ x , Δ y , Δ z Corresponding to the matrix on the right side of the equal sign of equation (15), the corresponding terms are extracted to obtain the comprehensive error model as shown in (16). Among them, δuv represents the translation error of the v-axis in the u-axis direction, the positioning error and the straightness error belong to the same translation error, εuv represents the angular error of the v-axis in the u-axis direction, and Suv represents the verticality error of the v-axis in the u-axis direction, where u and v are any of the X, Y, and Z axes.

3. The method for geometric error identification of CNC machine tools based on the improved nine-line method according to claim 1, characterized in that: Specifically, based on the comprehensive error model combined with a preset fitness function, six optimal measurement positions are predicted, including: The coordinate values ​​of any six measurement points are taken as a measurement combination, and each combination is taken as an individual. A preset fitness function is introduced to evaluate each individual. The individual with the smallest fitness is taken as the optimal individual, and the six measurement points corresponding to the optimal individual are taken as the six best measurement positions.

4. The method for geometric error identification of CNC machine tools based on the improved nine-line method according to claim 3 is characterized in that: Specifically, the process of finding the optimal individual includes: Step 210: Encode the individuals and initialize the population; Step 220, evaluating the fitness of each individual in the population through a fitness function; Step 230, determine whether the individual has a full rank of 6. If the individual does not have a full rank of 6, randomly assign a preset maximum fitness to the current individual and return it to the original population as an unqualified individual. If the individual has a full rank of 6, determine whether the preset number of iterations, i.e., the termination condition, is met. Step 250: If the termination condition is met, the optimization is completed; if the termination condition is not met, selection, crossover, and mutation operations are performed to generate a new generation population and return to step 220 to continue running.

5. The method for geometric error identification of CNC machine tools based on the improved nine-line method according to claim 4 is characterized in that: Specifically, the process of establishing the fitness function includes: Each variable in the measurement space is expanded to a matrix of the same size using the meshgrid matrix in MATLAB; The matrix expanded by each variable is operated by the comprehensive error model to obtain the comprehensive error matrix of the same size corresponding to each variable, and the mathematical model for describing the entire measurement space based on the comprehensive error model is obtained; Based on the mathematical model, the standard deviation of the mean of the individual error differences and the coefficient of variation are calculated as the identification result.

6. A CNC machine tool geometric error identification device based on the improved nine-line method, characterized in that: Includes the following: A comprehensive error model building module is used to superimpose the motion errors between the rigid bodies based on the kinematic theory of multi-body systems combined with the machine tool topology to build a comprehensive error model, and to optimize and predict six optimal measurement positions based on the comprehensive error model combined with a preset fitness function; A measurement equation group establishment module is used to establish a linear measurement track parallel to any single motion axis direction of the X, Y, and Z axes at each of the optimal measurement positions, to obtain a total of six linear measurement tracks, and to measure a specific error term for each linear track to obtain an equation group with six equations; A simulation identification module, used for performing simulation identification of geometric errors of CNC machine tools based on the equation group; Specifically, when the measurement equation building module is running, the original measurement trajectory is firstly processed in a dense manner. Each point in the measurement space can correspond to a set of error vectors shown in formula (3). If six points on six parallel lines are obtained, then a total of six equations are obtained. The following formula (3) is the equation corresponding to the i-th point, Wherein, i=1, 2, ..., 6, and one equation is extracted from each of the six equation groups shown in equation (3) to be reassembled into a new equation group. As long as the equation group contains the six errors to be solved and satisfies the full rank of the coordinate matrix, the equation group can have a unique solution; From the MATLAB-assisted calculation, we know that there are 120 permutations and combinations of the above six equations with a total of 18 equations that can meet the requirements. Therefore, there are 120 equations that meet the analytical conditions. Since the coefficient matrix directly affects the analytical results, two groups are selected for use to enrich the optimization results of the subsequent algorithm. The first combination, when measuring the X-axis direction, measures the positioning error on line 1 respectively 2 Line X axis straightness error in Y direction Positioning error on line 3 Straightness error of the X-axis in the Z direction on 4 lines Positioning error on line 5 6 Line X axis straightness error in Z direction A total of six measurements resulted in a system of six equations, Corresponding to the following formula (4) Rewrite it into matrix form (5), substitute the measured value into the left side of the equation, substitute the corresponding coordinate value into the right side of the equation, and solve for the six error values: At the same time, the second combination method shown in formula (6) is given to perform cross search. The measurement process is the same as the above method and will not be described in detail: Rewrite it into matrix form This method is to obtain six linear measurement tracks parallel to a single motion axis. Each measurement track measures only a specific error, and a total of six measurements are made. Among them, δuv represents the translation error of the v-axis in the u-axis direction. The positioning error and straightness error belong to the same translation error. εuv represents the angular error of the v-axis in the u-axis direction, where u and v are any of the X, Y, and Z axes.

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