Multi-axis nc machine tool space geometric error fusion and decoupling method

Abstract

This invention relates to the field of CNC machine tool technology, specifically to a method for fusing and decoupling spatial geometric errors in multi-axis CNC machine tools. The method includes the following steps: Step 1. Dividing the measurement space into a spatial cube and calibrating the geometric errors of the cubic measurement space; Step 2. Using an IMU and a laser interferometer to fuse the spatial errors along each axis; Step 3. Using a nonlinear error identification curve for error estimation; Step 4. Using dual IMUs to predict the CNC machine tool errors; Step 5. Establishing a corresponding mathematical model and using dual IMUs to decouple the spatial geometric errors of the CNC machine tool. By fusing the errors measured by the laser interferometer and the IMU, the error measurement becomes more accurate, laying a solid foundation for subsequent error prediction and decoupling.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool technology, specifically to a method for fusion and decoupling spatial geometric errors in multi-axis CNC machine tools. Background Technology

[0002] CNC machine tools are important machining equipment with wide applications in industries such as aerospace and automotive. However, due to limitations in machine tool structure and manufacturing processes, spatial errors often occur during machining, leading to a decrease in machining accuracy. Spatial errors in CNC machine tools can typically be decoupled along different motion axes, and then the errors can be attributed and compensated. The first stage before error decoupling is machine tool error identification. To improve the accuracy of machine tool error decoupling, research on machine tool errors usually focuses on error identification methods. However, for the spatial geometric errors of multi-axis CNC machine tools, the accuracy control of the identification process depends solely on the accuracy of the identification tool itself; no error identification fusion model based on different tools has yet been proposed. Current solutions mostly rely on empirical adjustments and trial and error, lacking accurate error prediction and proactive control methods. Therefore, a new method is urgently needed to solve this problem. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a method for the fusion and decoupling of spatial geometric errors in multi-axis CNC machine tools.

[0004] To achieve the above objectives, the present invention is implemented through the following technical solution: a method for fusion and decoupling of spatial geometric errors in multi-axis CNC machine tools, comprising the following steps: Step 1. Dividing the measurement space into spatial cubes and calibrating the geometric errors of the cubic measurement space;

[0005] Step 2. Use an IMU and a laser interferometer to fuse the spatial errors along each axis.

[0006] Step 3. Use nonlinear error identification curves to estimate errors;

[0007] Step 4. Use dual IMUs to predict CNC machine tool errors;

[0008] Step 5. Establish the corresponding mathematical model and use dual IMUs to decouple the spatial geometric errors of the CNC machine tool.

[0009] Preferably, in step 1, the cubic measurement space has three-directional errors. The errors at the nodes of the measurement space are represented by linear vectors and conform to the triangle law of vector addition. Starting from the center of each node, the spatial error vector from that node to the top plane is assumed to be... Its spatial error vectors to the front plane and the right plane are Then the three error vectors in space can be expressed as formula (1).

[0010]

[0011] Because they are on the same spatial plane, and The geometric method is easy to obtain; the UT transformation is used to process the node error so as to quickly obtain the true spatial position of point O. The definition of the sigma point in the transformation method is shown in formula (2) to formula (4), and its corresponding weight is shown in formula (5) to formula (7).

[0012] x0=μ (2)

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] μ ′ =∑ i w i x i (8)

[0019] p ′ =∑ i w i (x i -μ ′ (x) i -μ ′ ) T (9)

[0020] We should select 2(n+1) sigma points, multiply their coordinates by their corresponding weights to form a new probability distribution, with the new mean μ. ′ With covariance matrix p ′ As shown in formulas (8) and (9),

[0021] The laser interferometer, by moving its position, can only measure points in two directions on the same plane at a time, thus forming a new two-dimensional probability distribution. Therefore, n=2, and the hyperparameters are set as k=1, α=0.3, and β=1. According to the error requirements of ISO 230-4, the error of the CNC machine tool is controlled within 0.02mm, and the motion error generated during the laser interferometer measurement process is independent. Therefore, the covariance p ′ Let's set it as follows: Data sets of different sizes are randomly generated based on this.

[0022] Preferably, in step 2, the IMU is transformed into an error sphere according to formulas (2) to (9) to obtain the mean value μ of each axis of the dual IMU. IMU and variance p′ IMU , will μ Laser Assume the actual measurement location, p′ Laser Reflecting the measurement pose state, data fusion is performed on each node along the same axis, and the true observation value at the node is obtained. These are the fused observations, which are related to Z. IMU and Z Laser The observation error Δ can be obtained by comparison. Laser and Δ IMU Based on the above two equations, by comparing the original observed values, the axial scaling coefficient α at the current node can be obtained. Laser and α IMU , denoted as formulas (14) to (15); when α Laser and α IMU When both are 1, it indicates that the measurement results of the laser interferometer and the IMU are consistent, and at this time Δ Laser With Δ IMU Both are 0, α IMU By expanding along the X, Y, and Z axes respectively, the scaling factor α in different directions can be obtained. IMU-X α IMU-Y α IMU-Z , the observed data Z IMU Divide by α along each of the three axes IMU The coordinates Z of the merged node can be obtained. Node The relationship, that is, stretching or shrinking Z along the spatial coordinate system. IMU ,

[0023] Z Node =Z Laser +k k-1 (Z IMU -Z Laser (10)

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Preferably, in step 3, the cubic measurement space is divided into 10×10×10, and the curve shown in the figure is used to identify errors in the motion state, detecting P in the grid. k Point is the theoretical point on the identification curve at time k. Each grid has n = 8 nodes for UT transformation, numbered V1 to V8. Every 4 merged nodes and point O can form a quadrangular pyramid, denoted as O-v1v2v4v3, O-v5v6v8v7, O-v1v3v5v7, O-v2v4v8v6. Starting from the i-th node, to P... k The spatial vector of a point can be expressed as The vector to point O can be represented as Point from point O to point P k The vector of a point is denoted as Then detect each node in the grid to P k All of them can be expressed as equation (16),

[0030]

[0031] In the formula After node merging, it becomes a relatively fixed value. Z can be used IMU To express, at this time The observed values ​​of each fused node can be obtained by multiplying them by the weights of each node. This can be achieved by simultaneously calculating from all 8 nodes. When the computational load is too large, performing calculations from nearby locations will effectively improve computational efficiency. k Located in O-v5v6v8v7 and relatively close to nodes v6, v8, v5, and v7, the error influence of the other four nodes can be reflected through point O. Similarly, by perpendicularly dividing point O into each plane to obtain points O1 to O6, the identification space can be further divided. Let there be two nodes v m v n O p O q Both can determine the estimation error of the identification curve within this range. They are respectively close to v m v n Point and O p O q The error at the point is expressed as in equations (17) to (18).

[0032]

[0033]

[0034] It can be represented as in different spatial vector closed loops. However, since they are based on different error estimation benchmarks, it is necessary to fuse the error estimation data from both methods. To improve the accuracy of the error estimation, the O... p O q Divide the data into equal parts multiple times, and the distance after division is d. sv With d so It can be expressed as equations (19) to (20), with the foot of the perpendicular being S. o With S v P k exist The foot of the perpendicular is S P S P Will Divide into two parts, representing S o With S v The weights of the neighboring regions are assigned as shown in equations (21) to (22), and the fused error estimates are obtained. Expressed as equation (23),

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] 5. The method for fusion and decoupling spatial geometric errors of multi-axis CNC machine tools according to claim 1, characterized in that: in step 4, the entire kinematic chain is used as the object of observation error modeling. The observation matrix can be expressed as formula (24).

[0041]

[0042] After calibration and combining with Δt, the positions of the tool TCS coordinate system and the machine tool MCS coordinate system are calculated. The IMU-2 works similarly, detecting the acceleration, velocity, and position of the table motion chain. Therefore, for x in IMU-1 and IMU-2... k Each contains p, v, and a, and its observation matrix and It can be represented as Then all are If we consider the kinematic branch as a whole, then and All views are If infinitesimals of order three and above are considered invalid observation terms and eliminated, the transfer matrix in equation (24) can be further simplified to equation (25). Equation (25) can separate all six errors in the observation matrix. The prerequisite for correct decoupling using this formula is:

[0043] a) At time k, x can be obtained in all coordinate systems. k Position, velocity, and acceleration status;

[0044] b) At time k, with 6 groups The pose data is used as a data acquisition unit for data acquisition;

[0045]

[0046] Preferably, in step 5, at least two IMUs are used to acquire measurement data for two motion chains. IMU-1 is installed on the TCS at the end of one motion chain, and IMU-2 is installed on the WCS at the end of the other motion chain. IMU-1 and IMU-2 generate theoretical and actual pose errors during spatial motion, denoted as Δr1 and Δr2. In the theoretical state, IMU-1 is perpendicular to the XY plane, and the motion relationship between the two IMUs can be represented as a right triangle. The spatial relationship of the vectors after removing the pose error of the motion branches is expressed as Equation (26).

[0047]

[0048] Because the entire kinematic chain of the machine tool is too long, resulting in excessive decoupling calculations, the kinematic branches are used as the modeling object for motion errors. The machine tool coordinate system MCS is set to a fixed value, therefore, in equation (26)... To measure the motion of the table support chain from the IMU-2 to the MCS, the WCS coordinate system where the IMU-2 is located is fixed, and the MCS is calibrated. Then the IMU-2 can measure the motion process of the table support chain in real time. Similarly, the tool support chain can also be measured in this way. The pose errors Δr1 and Δr2 of the two motion chains can be decoupled according to equations (27) and (28) respectively, so as to obtain the x of each link in the motion chain. k Actual motion state,

[0049]

[0050]

[0051] The beneficial effects of the present invention are: (1) Precise fusion: by using a laser interferometer and an IMU to fuse the errors measured by the two, the error measurement is more accurate, laying a solid foundation for subsequent error prediction and decoupling;

[0052] (2) Accurate prediction: By establishing a machine tool structure model and applying advanced mathematical algorithms, the spatial error of the machine tool under different processing conditions can be accurately predicted, providing an accurate data basis for subsequent decoupling and compensation;

[0053] (3) Significant decoupling effect: By optimizing the machine tool control strategy, the errors of each axis of the machine tool are decoupled. Decoupling reduces the mutual influence between different axes, improving machining accuracy and stability;

[0054] (4) Improve machining accuracy and efficiency: Through accurate error fusion, prediction and decoupling compensation, spatial errors in the machine tool machining process can be effectively reduced, machining accuracy and efficiency can be improved, and scrap rate and production costs can be reduced.

[0055] (5) Wide versatility and applicability: The method of the present invention can be applied to various types of multi-axis CNC machine tools, and the requirements for modification of machine tool structure and control system are relatively low, which has good versatility and applicability. Attached Figure Description

[0056] Figure 1 This is a diagram showing the measurement range of the dual-position laser interferometer of the present invention;

[0057] Figure 2 This is a spatial cubic error diagram in laser splicing according to the present invention;

[0058] Figure 3 This is a diagram showing the observation points and spatial error vectors of the measurement unit of this invention.

[0059] Figure 4 This is a sigma point plot of the error sphere transformation of the present invention;

[0060] Figure 5 This is a fusion diagram of the sensor acquisition frequencies of the present invention;

[0061] Figure 6 This is a diagram of the space measurement method of the present invention;

[0062] Figure 7 This is an observation diagram of a single measurement grid in this invention;

[0063] Figures 8(a) and 8(b) show the error vertical gradient weighting diagrams for each measurement node;

[0064] Figure 9 For the feed mechanism motion branch chain diagram;

[0065] Figure 10 The laser interferometer was used to measure the nodal error diagram of the experimental machine tool;

[0066] Figure 11An error measurement graph of the error sphere is generated using an IMU for the measurement nodes;

[0067] Figures 12(a) to 12(f) The prediction results are plotted against the gradient changes of each weight.

[0068] Figures 13(a) to 13(f) A comparison chart of residuals from two different prediction models;

[0069] Figures 14(a) to 14(e) The diagram shows the error decoupling results under four-axis linkage measurement conditions.

[0070] Figure 15(a) shows the IMU-X-axis error measurement results based on the UT method;

[0071] Figure 15(b) shows the measurement results of the IMU-Y axis error based on the UT method;

[0072] Figure 15(c) shows the measurement results of the IMU-Z axis error based on the UT method. Detailed Implementation

[0073] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0074] A method for fusing and decoupling spatial geometric errors in multi-axis CNC machine tools based on an error sphere includes the following steps:

[0075] Step 1. The geometric error of the cubic measurement space is calibrated by dividing the measurement space into spatial cubes.

[0076] (1) Three-directional error of cubic measurement space

[0077] In multiple continuous closed measurement spaces, such as Figure 1 As shown, two laser interferometers are used simultaneously to independently measure the measurement space. Viewed from the front, the measurement space is uniformly divided by four measurement planes (F1, F2, F3, F4) along the Z-axis. Viewed from the right, the measurement space is similarly uniformly divided by S1, S2, S3, S4. One of the two laser interferometers can simultaneously measure the four top planes using a vertical beam splitter, ultimately dividing a single spatial measurement cube into nine consecutive smaller measurement cubes using a total of 12 spatial planes.

[0078] According to the basic principles of spatial geometry, these nine small measuring cubes should be continuously changing in space and contained within the overall measuring space, and the sum of the volumes occupied by the nine small cubes should equal the total volume of the overall measuring space. However, due to spatial errors, the measurement data from laser interferometers in different directions are difficult to close at the intersection point. This manifests in space as the difficulty in fitting the changes in measurement values ​​in the three directions, such as... Figure 2 As shown. The points that should have been fitted in space, F1-A on the front and S4-A′ on the right plane, are separated into two points. The error vector between them in space is represented as... Extensive experimental verification has shown that this error is widely present at the spatial measurement nodes fitted by the laser interferometer.

[0079] (2) Error sphere transformation of spatial measurement grid nodes

[0080] Laser light travels in a straight line in space. Therefore, the line connecting the points in the measurement space should also be a straight line, such as... Figure 2 Points F1-A, F1-B, and F1-C should lie on a straight line. Therefore, the error at the measurement points in space can be represented by a straight-line vector, and it conforms to the triangle rule of vector addition. Figure 3 As shown, the node starts from its center, and we assume that its spatial error vector to the top plane is... Its spatial error vectors to the front plane and the right plane are The three error vectors in space can then be represented by formula (1).

[0081]

[0082] Because they are on the same spatial plane, and The spatial location of point O is easily obtained using geometric methods. However, due to positioning errors, it is difficult to determine the spatial location of point O by calculating the mean. If a laser interferometer is used to sample a large number of spatial errors of the grid nodes to construct a multivariate normal distribution, the measurement time will be too long, which is not conducive to the rapid formation of measurement data. The UT transformation is used to process the node errors so as to quickly obtain the true spatial location of point O. The definition of the sigma point in the transformation method is shown in formulas (2) to (4), and its corresponding weights are shown in formulas (5) to (7).

[0083] x0=μ (2)

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] μ′=∑ i w i x i (8)

[0090] p′=∑ i w i (x i -μ′)(x i -μ′) T (9)

[0091] Two (n+1) sigma points should be selected, and their coordinates multiplied by their corresponding weights to form a new probability distribution. The new mean μ′ and covariance matrix p′ are shown in formulas (8) and (9). The laser interferometer can only measure points in two directions on the same plane each time by moving its position, so the new probability distribution is a two-dimensional probability distribution. Therefore, n = 2, and the hyperparameters are set as k = 1, α = 0.3 and β = 1. According to the error requirements of ISO230-4, the error of the CNC machine tool should be controlled within 0.02 mm, and the motion error generated during the measurement process of the laser interferometer is independent. Therefore, the covariance p′ is temporarily set to Based on this, datasets of different sizes are randomly generated, and their distributions are shown as follows. Figure 4 .

[0092] As shown in the figure, the distributions after all UT transformations, regardless of sample size, all follow a Gaussian distribution. When the sample size is greater than 1000, the change in the mean is negligible. When the sample size is less than 1000, a small observation error will occur, denoted as v. The observation errors of the three planes can be denoted as v0 respectively. xy v yz v zx .

[0093] Step 2. Use an IMU and a laser interferometer to fuse the spatial errors along each axis.

[0094] IMUs directly measure velocity and acceleration, but indirectly measure position information. Laser interferometers, on the other hand, can only perform direct position measurements and cannot measure spatial nonlinear curves. The reliability of position errors from IMUs is lower than that from laser interferometers; therefore, laser interferometers are used as the primary measurement reference, and the decoupled position error results from the IMU are used as the interpolation basis.

[0095] By performing error sphere transformation on the IMU according to formulas (2) to (9), the mean value μ of each axis of the dual IMU can be obtained. IMU and variance p′IMU .like Figure 5 As shown, μ Laser Assume the actual measurement location, p′ Laser To reflect the measured pose state, data fusion is performed on each node along the same axis, as shown in equations (10) and (11). The actual observed values ​​at the nodes... These are the fused observations, which are related to Z. IMU and Z Laser The observation error Δ can be obtained by comparison. Laser and Δ IMU As shown in equations (12) and (13). Based on the above two equations, by comparing the original observed values, the axial scaling coefficient α at the current node can be obtained. Laser and α IMU , denoted as formulas (14) to (15). When α Laser and α IMU When both are 1, it indicates that the measurement results of the laser interferometer and the IMU are consistent, and at this time Δ Laser With Δ IMU All are 0. α IMU By expanding along the X, Y, and Z axes respectively, the scaling factor α in different directions can be obtained. IMU- α IMU-Y α IMU-Z The observed data Z IMU Divide by α along each of the three axes IMU The coordinates Z of the merged node can be obtained. Node The relationship, that is, stretching or shrinking Z along the spatial coordinate system. IMU .

[0096] Z Node =ZL aser +k k-1 (Z IMU -Z Laser (10)

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Step 3. Use nonlinear error identification curves to estimate errors.

[0103] Nonlinear error identification curves can simultaneously reflect multi-axis motion states, but they can only be measured using an IMU. For example... Figure 6As shown, the cubic measurement space is divided into 10×10×10 grids, and the curves shown are used to identify errors during motion. The redefined detection grid is as follows. Figure 7 As shown, P in the detection grid k The point is the theoretical point on the identification curve at time k. Each grid has n = 8 nodes for UT transformation, numbered V1 to V8. The detection center after fusion error is... Figure 7 As shown at midpoint 0, every 4 merged nodes and point O can form a square pyramid, denoted as O-v1v2v4v3, O-v5v6v8v7, O-v1v3v5v7, O-v2v4v8v6. Starting from the i-th node, to P... k The spatial vector of a point can be expressed as The vector to point O can be represented as Point from point O to point P k The vector of a point is denoted as Then detect each node in the grid to P k All of them can be expressed as equation (16).

[0104]

[0105] In the formula After node merging, it becomes a relatively fixed value. Z can be used IMU To express oneself. At this time... The values ​​can be calculated, and multiplying them by the weights of each node yields the observed values ​​for each fused node. This can be done by simultaneously calculating from all 8 nodes. The computational load is too large; performing calculations from a nearby location will effectively improve computational efficiency. As shown in Figures 8(a) and 8(b), P k Point O is located within the range O-v5v6v8v7 and is relatively close to nodes v6, v8, v5, and v7. The error impact of the other four nodes can be reflected through point O. Similarly, by perpendicularly dividing point O into each plane to obtain points O1 to O6, the identification space can be further subdivided. Let there be two nodes v... m v n O p O q Both can determine the estimation error of the identification curve within this range. As shown in Figure 8(a), They are respectively close to v m v n Point and O p O q The error of the point is expressed as in equations (17) to (18).

[0106]

[0107]

[0108] It can be represented as in different spatial vector closed loops. However, since they are based on different error estimation benchmarks, it is necessary to fuse the error estimation data from both methods. To improve the accuracy of the error estimation, O can be... p O q Divide the data into equal parts multiple times, and the distance after division is d. sv With d so This can be expressed as equations (19) to (20). The foot of the perpendicular is S. o With S v P k exist The foot of the perpendicular is S P S P Will Divide into two parts, representing S o With S v The weights of the neighboring regions are assigned as shown in equations (21) to (22), and the fused error estimates are obtained. It is expressed as equation (23).

[0109]

[0110]

[0111]

[0112]

[0113]

[0114] Step 4. Use dual IMUs to predict CNC machine tool errors.

[0115] In addition to motion errors, there are also observation errors in the measurement process, which are manifested as the spatial mean point offset of the IMU in the UT transformation. Since the observation process involves taking the errors in the relative motion position, velocity, and acceleration between two IMUs, the entire kinematic chain is taken as the object of observation error modeling. The observation matrix can be expressed as formula (24).

[0116]

[0117] Figure 9 The observation status of IMU-1 is given by equation (24). The matrix can simultaneously monitor acceleration and velocity. After calibration and combining with Δt, the position of the tool TCS coordinate system and the machine tool MCS coordinate system can be calculated. The IMU-2 works similarly, detecting the acceleration, velocity, and position of the table motion chain. Therefore, for x in IMU-1 and IMU-2...k Each contains p, v, and a, and its observation matrix and It can be represented as Then all are If we consider the kinematic branch as a whole, then and All views are By eliminating infinitesimals of order three and above as invalid observation terms, the transfer matrix in equation (24) can be further simplified to equation (25). Equation (25) can separate all six errors in the observation matrix. The prerequisite for correct decoupling using this formula is:

[0118] a) At time k, x can be obtained in all coordinate systems. k Position, velocity, acceleration state

[0119] b) At time k, with 6 groups The pose data is used as a data acquisition unit for data acquisition.

[0120]

[0121] Step 5. Establish the corresponding mathematical model and use dual IMUs to decouple the spatial geometric errors of the CNC machine tool.

[0122] The feed motion mechanism of a three-axis CNC milling machine is mostly like... Figure 9 As shown, the motion chains are divided into the tool chain MCS->ZCS->SCS->TCS and the table chain MCS->XCS->YCS->WCS. One IMU cannot simultaneously acquire motion data of the X, Y, and Z axes through interpolation, so at least two IMUs are needed to acquire measurement data of the two motion chains. IMUs can measure the acceleration and velocity of the inertial mass unit, and the position can be calculated according to formulas (10) to (14) based on the velocity. IMU-1 is installed on the TCS at the end of motion chain 1, and IMU-2 is installed on the WCS at the end of motion chain 2. IMU-1 and IMU-2 generate theoretical and actual pose errors in spatial motion, which are denoted as Δr1 and Δr2. In the theoretical state, IMU-1 is perpendicular to the XY plane, and the motion relationship between the two IMUs can be represented as a right triangle, such as Figure 9 In triangle ABC. The spatial relationship of the vector after removing the pose error of the motion branch can be expressed as Equation (26).

[0123]

[0124] Because the entire kinematic chain of the machine tool is too long, resulting in excessive decoupling calculations, the kinematic branches are used as the modeling object for motion errors. The machine tool coordinate system MCS is set to a fixed value, therefore, in equation (26)... The values ​​are the detection values ​​from the IMU-2 to the MCS of the table support. After fixing the WCS coordinate system where the IMU-2 is located, the MCS is calibrated, so that the IMU-2 can measure the motion process of the table support in real time. Similarly, the tool support can also be measured in this way. Then the pose errors Δr1 and Δr2 of the two motion supports can be decoupled according to equations (27) and (28) respectively, so as to obtain the x of each link in the motion support. k Actual motion state.

[0125]

[0126]

[0127] Example

[0128] The envelope cubic space edge nodes of the spatial error identification curve were measured using a Renishaw XL-80 laser interferometer. Two IMUs were fixed to the spindle end and the center of the dual rotary table clamping, respectively, with the origins of the working coordinate systems set to G54 and G55. The identification curve was simulated on three planes using a Siemens 840Dsl CNC system. The simulated trajectory of the identification curve on the G18 plane is shown below. Figure 10 As shown.

[0129] (1) Initial data acquisition of error measurement nodes

[0130] Using a spatial NURBS curve as the error identification curve, this curve is drawn through three cubic measurement spaces, denoted as measurement spaces A, B, and C, respectively. Figure 11 As shown in the figure. Each curve segment has 100 random measurement points. A laser interferometer and an IMU were used to identify errors at each measurement point. The laser interferometer recorded five reciprocating measurements along the X, Y, and Z axes, collecting the average value from each error identification point. The static measurement results of the error identification curve starting point using the IMU are shown in the figure. Figure 11 As shown, all subsequent error sphere measurements will be performed using this as the origin.

[0131] (2) Error identification results and prediction deviation

[0132] Based on formulas (10) to (15), data fusion was performed on the X, Y, and Z axes. The error identification curves passed through three cubic measurement spaces from the lower right to the upper left, named A, B, and C. 100 points were randomly selected from each error identification curve and the error sphere was measured using an IMU. Error estimation was performed according to the methods described in formulas (17) to (23). Error fusion was performed using a laser interferometer and an IMU, and error estimation was performed again using the same method. The weight information of each error estimation is shown in Figures 14(b), 14(d), and 14(e). The error predicted using only the IMU is shown by the blue lines in Figures 12(a), 12(c), and 12(e). The error after fusion of the IMU and the laser interferometer is shown by the red lines in Figures 12(a), 12(c), and 12(e). The black lines represent the direct measurement results of these points using the laser interferometer. Using the error results from direct measurement of 300 points with a laser interferometer as the measurement benchmark, residual results were obtained for error prediction using the IMU alone and error prediction after fusion. Figures 13(a)-13(f) As shown. From the perspective of residual analysis, the residual after fusion is closer to the result of direct measurement, and the residual is less than 0.02mm in most locations, which is more conducive to subsequent error decoupling work.

[0133] (3) Decoupling analysis of fusion error

[0134] like Figure 9 As shown, the top kinematic chain can be predicted independently from the IMU fusion error without further decoupling. Figure 9 The bottom motion chain shown contains four axis systems: XCS, YCS, BCS, and CCS. The error after fusing the axes in Figure 12 is decoupled according to the methods described in formulas (24) to (28), and the result is shown in Figure 14. Figures 13(a)-13(f) As can be seen, the decoupling error is relatively large at points within the 100-150 range, corresponding to the large fluctuation amplitude of the red curve of CUBE_B in Figure 12(c), and the large X and Y axis residuals of CUBE_B in Figure 13(c). The large error fluctuation within this range has a certain impact on the volatility of the decoupling results. Similarly, error fluctuations also exist in the CUBE_A0-A50 and CUBE_C0-C20 ranges in Figures 14(a) and 14(e), significantly affecting the decoupling result of XCS in Figure 14(a). Besides the aforementioned ranges, Figures 15(a)-15(c) and Figures 12(a)-12(f) As seen in other intervals, the accuracy of the fused prediction error is stronger than that of using the IMU alone for error prediction. Therefore, in most cases, the decoupling effect after fusion of error prediction is better than that of the unfused error.

[0135] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for fusing and decoupling spatial geometric errors in multi-axis CNC machine tools, characterized in that: The steps include: Step 1. Divide the measurement space into a spatial cube and calibrate the geometric error of the cubic measurement space; Step 2. Use an IMU and a laser interferometer to fuse the spatial errors along each axis; Step 3. Use nonlinear error identification curves to estimate the error; Step 4. Use dual IMUs to predict CNC machine tool errors; Step 5. Establish the corresponding mathematical model and use dual IMUs to decouple the spatial geometric errors of the CNC machine tool; In step 1, the cubic measurement space has three-directional errors. The errors at the nodes in the measurement space are represented by linear vectors and conform to the triangle law of vector addition. Each node originates from its center, and the spatial error vector from that node to the top plane is assumed to be... Its spatial error vectors to the front plane and the right plane are , Then the three error vectors in space can be expressed as formula (1). (1) Because they are on the same spatial plane, , and The results are readily obtained using geometric methods; however, the nodal errors are processed using the UT transformation method to enable rapid calculation. O The actual spatial location of the point, the definition of the sigma point in the transformation method is shown in formulas (2) to (4), and its corresponding weight is shown in formulas (5) to (7). (2) (3) (4) (5) (6) (7) (8) (9) Should be taken Given sigma points, multiply their coordinates by their corresponding weights to form a new probability distribution, and a new mean. With covariance matrix As shown in formulas (8) and (9), By moving its position, a laser interferometer can only measure points in two directions on the same plane at a time, thus forming a new probability distribution, which is a two-dimensional probability distribution. And set each hyperparameter to 1, as well as According to the error requirements of ISO 230-4, the error of CNC machine tools should be controlled within 0.02mm, and the motion error generated during the laser interferometer measurement process is independent. Therefore, the covariance... Let's set it as follows: Based on this, datasets of different sizes are randomly generated; In step 4, the entire kinematic chain is used as the object of observation error modeling, and the observation matrix can be expressed as formula (24). (24) After calibration and By combining these measurements, the positions of the tool's TCS coordinate system and the machine tool's MCS coordinate system are calculated. The IMU-2 works similarly, detecting the acceleration, velocity, and position of the table's motion chains. Therefore, for both IMU-1 and IMU-2... All contain p , v , a Its observation matrix and It can be represented as , , , , Then all are If the kinematic branch is considered as a whole, then and All views are If infinitesimals of order three and above are considered invalid observation terms and eliminated, the transfer matrix in equation (24) can be further simplified and expressed as equation (25). Equation (25) can separate all six errors in the observation matrix. The prerequisite for correct decoupling using this formula is: a) At time k, all coordinate systems can be obtained. Position, velocity, and acceleration status; b) At time k, with 6 groups The pose data is used as a data acquisition unit for data acquisition; (25) ； In step 5, at least two IMUs are used to acquire measurement data for two motion chains. IMU-1 is installed on the TCS at the end of one motion chain, and IMU-2 is installed on the WCS at the end of the other motion chain. IMU-1 and IMU-2 generate theoretical and actual pose errors during spatial motion, and the errors are denoted as . and In theory, IMU-1 is perpendicular to the XY plane, and the motion relationship between the two IMUs can be represented as a right triangle. The spatial relationship of the vectors after removing the pose error of the motion branches is expressed as Equation (26). (26) Because the entire kinematic chain of the machine tool is too long, resulting in excessive decoupling calculations, the kinematic branches are used as the modeling object for motion errors. The machine tool coordinate system MCS is set to a fixed value, therefore, in equation (26)... The detection values ​​from the IMU-2 to the MCS of the table support are used. After fixing the WCS coordinate system where the IMU-2 is located, the MCS is calibrated. Then, the IMU-2 can measure the motion process of the table support in real time. Similarly, the tool support can also be measured in this way. The positional error of the two motion supports is then used as the measurement. and Decoupling can be performed according to equations (27) and (28) respectively, so as to find the link in each link of the kinematic chain. Actual motion state, (27) (28) 。 2. The method for fusion and decoupling spatial geometric errors of multi-axis CNC machine tools according to claim 1, characterized in that: In step 2, the IMU is transformed into an error sphere according to formulas (2) to (9) to obtain the mean values ​​of each axis of the dual IMU. and variance ,Will Make the actual measurement location. Reflecting the measurement pose state, data fusion is performed on each node along the same axis, and the true observation value at the node is obtained. These are the merged observations, which are... and The observation error can be obtained by comparison. and Based on the above two equations, by comparing the original observed values, the axis scaling coefficient at the current node can be obtained. and , denoted as formulas (14)~(15); when and When both are 1, it indicates that the measurement results of the laser interferometer and the IMU are consistent. and All are 0. By expanding along the X, Y, and Z axes respectively, we can obtain the scaling factors in different directions. , , , observation data Divide by each of the three axes The coordinates of the merged node can be obtained. The relationship, that is, stretching or shrinking along the spatial coordinate system. , (10) (11) (12) (13) (14) (15)。 3. The method for fusion and decoupling spatial geometric errors of multi-axis CNC machine tools according to claim 1, characterized in that: In step 3, the cubic measurement space is divided into Error identification in motion is performed using identification curves, and the error in the mesh is detected. The point is in k The theoretical points on the identification curve at any given time, each grid has n = 8 nodes of UT transformation, for ~ Every 4 merged nodes and O Each point can form a square pyramid, denoted as . - , - , - , - From the first i Starting from each node, to The spatial vector of a point can be expressed as ,to O A point vector can be represented as Point O to The vector of a point is denoted as Then detect each node in the grid to All of them can be expressed as equation (16), (16) In the formula After node merging, it becomes a relatively fixed value. Available To express, at this time The observed values ​​of each fused node can be obtained by multiplying them by the weights of each node. This can be achieved by simultaneously calculating from all 8 nodes. If the computational load is too large, performing calculations from a nearby location will effectively improve computational efficiency. lie in - medium and distance , , , These four nodes are relatively close together, so the error impact of the other four nodes can be mitigated through... O Similarly, by dividing point O perpendicularly into each plane, we obtain... If a point is identified, the recognition space can be further divided, with two nodes. , , , Both can determine the estimation error of the identification curve within this range. , , They are close to Points and The error at the point is expressed as in equations (17) and (18). (17) (18) , It can be represented as in different spatial vector closed loops. However, since they are based on different error estimation benchmarks, it is necessary to fuse the error estimation data from both methods. To improve the accuracy of the error estimation, the data can be... , Divide the data into equal parts multiple times, and then calculate the distance after each division. and It can be expressed as equations (19)~(20), with the foot of the perpendicular being... and , exist The foot of the perpendicular is , Will Divided into two parts, description and The weights of the neighboring regions are assigned as shown in equations (21) to (22), and the fused error estimates are obtained. Expressed as equation (23), (19) (20) (21) (22) (23)。

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