A Method for Constructing a Digital Twin of the Performance of a Precision Spindle Considering Surface Topography

Abstract

The present invention discloses a method for constructing a digital twin of the performance of a precision spindle considering surface topography, including: determining surface topography parameters and relative position parameters of parts and determining their upper and lower limits, generating nested sample points, establishing high-precision and low-precision simulation models of the precision spindle with surface topography and obtaining the simulation results of the sample points, constructing a Kriging surrogate model using the simulation sample data, obtaining measured data of multiple groups of precision spindles, constructing a Kriging surrogate model using the difference between the measured data and the simulation data, constructing a Co-Kriging surrogate model and evaluating its accuracy, adding points through the point addition criterion if the accuracy requirement is not met, and updating the surrogate model until the model accuracy meets the requirement, thus completing the construction of the digital twin of the performance of the precision spindle considering surface topography. The present invention constructs a digital twin of the performance of the precision spindle through a surrogate model, taking into account both surface topography and measured data, and realizes accurate, fast, and efficient prediction of the spindle rotation accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of digital twins, and specifically relates to a method for constructing a digital twin of the performance of a precision spindle considering surface topography. Background Art

[0002] High-end CNC machine tools are an important part of modern advanced manufacturing and are known as the "mother machines of industry". As the core component of a machine tool, the rotational accuracy of a precision spindle is a key factor affecting the machining accuracy of the machine tool. Therefore, it is essential to predict the rotational accuracy of a precision spindle. Predicting the rotational accuracy of a precision spindle is to establish the relationship between the accuracy of the spindle part and its rotational accuracy. The traditional methods for predicting the rotational accuracy of a spindle mainly include geometric modeling methods and finite element modeling methods. The geometric modeling method uses the small displacement screw theory to characterize the form and position errors of parts and assumes that the parts are rigid bodies. This method does not fully consider the surface topography and deformation of the parts, resulting in low prediction accuracy for the rotational accuracy of precision spindles. When using the finite element method to simulate and analyze the rotational accuracy of a spindle, a high simulation accuracy can be obtained when the element size is small, but this is accompanied by a huge time cost. Therefore, an accurate, fast, and efficient method for predicting the rotational accuracy of a spindle is needed. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for constructing a digital twin of the performance of a precision spindle considering surface topography, aiming at the current situation that the prediction of spindle performance cannot meet the requirements of accuracy, speed, and efficiency simultaneously.

[0004] The present invention adopts the following technical solutions:

[0005] A method for constructing a digital twin of the performance of a precision spindle considering surface topography, comprising the following steps:

[0006] Step 1: Determine the surface topography parameters and the relative position parameters of the parts, and determine their upper and lower limits according to the selected parameters;

[0007] Step 2: Generate sample points of nested high-precision and low-precision models within the parameter range;

[0008] Step 3: Establish high-precision and low-precision finite element simulation models of the precision spindle with surface topography;

[0009] Step 4: Input the sample points of the nested high-precision and low-precision models described in Step 2 into the high-precision and low-precision finite element simulation models of the precision spindle described in Step 3 respectively to obtain the high-precision and low-precision simulation results of the sample points;

[0010] Step 5: Establish the connection between the high-precision and low-precision sample data by using a scaling function, convert the low-precision sample data into approximate high-precision sample data, and call the converted sample data simulation sample data;

[0011] Step 6: Construct a Kriging surrogate model using the simulation sample data;

[0012] Step 7: Obtain multiple groups of point cloud data of the precision spindle surface;

[0013] Step 8: Reconstruct the surface error of the part using the surface point cloud data described in Step 7 to obtain surface topography parameters;

[0014] Step 9: Obtain the relative position parameters of the part;

[0015] Step 10: Obtain the rotation trajectory of the precision spindle;

[0016] Step 11: Construct a Kriging surrogate model using the difference between the measurement sample data and the simulation sample data;

[0017] Step 12: Construct a Co-Kriging surrogate model using the surrogate models described in Step 6 and Step 11;

[0018] Step 13: Evaluate the accuracy of the Co-Kriging surrogate model. If the model accuracy meets the design requirements, the construction of the performance digital twin of the precision spindle considering the surface topography is completed. If the accuracy requirements are not met, perform Step 14 and Step 15;

[0019] Step 14: Generate new sample points in the space through the point addition strategy;

[0020] Step 15: Input the new sample points into the high-precision and low-precision finite element simulation models of the precision spindle described in Step 3 to obtain the high-precision and low-precision simulation results of the sample points, and add them to the sample dataset. Repeat Step 5 to Step 13 until the Co-Kriging surrogate model meets the accuracy requirements, and obtain the performance digital twin of the precision spindle considering the surface topography.

[0021] A further improvement of the present invention lies in that the method for generating the sample points of the nested high and low precision models described in Step 2 is the optimized nested Latin hypercube experimental design.

[0022] A further improvement of the present invention lies in that the method for establishing the finite element simulation model of the precision spindle with surface topography described in Step 3 is: reconstruct the surface error of the part using the surface topography parameters, and then attach the surface error of the part to the ideal finite element model.

[0023] A further improvement of the present invention lies in that the scaling function described in Step 5 is a multiplicative scaling function, and the high-precision sample point set and the scaling factor set l=(l1, l2, …, l N ) are used as inputs and outputs to construct the multiplicative scaling function The approximate model selected for constructing the scaling function is the Kriging model. Among them, the calculation formula of the scaling factor is shown in Equation (1):

[0024]

[0025] In the formula, is the scaling factor at the high-precision sample point , is the high-precision simulation result at the high-precision sample point , is the low-precision simulation result at the high-precision sample point .

[0026] A further improvement of the present invention is that the basic form of the Kriging model described in Step 6 and Step 11 is:

[0027]

[0028] In the formula, reflects the overall trend of , Z(x) is a random process with a mean of 0 and a covariance of Cov(Z(x i ), Z(x j )) = σ 2 R(x i , x j , θ), and the correlation function R(x i , x j , θ) takes θ as a parameter and characterizes the spatial correlation relationship between the sample points x i and x j .

[0029] A further improvement of the present invention is that the method for obtaining the surface point cloud data described in Step 7 is: using a high-precision three-coordinate measuring machine to obtain the point cloud data of the part surface.

[0030] A further improvement of the present invention is that the surface error reconstruction method described in Step 8 is: using basis functions to reconstruct the surface error of the part. Among them, the Zernike polynomial is used as the basis function of the toroidal surface, and the Legendre-Fourier polynomial is used as the basis function of the cylindrical surface.

[0031] A further improvement of the present invention is that the method for obtaining the precision spindle rotation trajectory described in Step 10 is: using a spindle rotation error analyzer to obtain the precision spindle rotation trajectory.

[0032] A further improvement of the present invention is that the approximate estimation of the Co-Kriging model described in Step 12 is expressed as:

[0033] Z e (x) = ρZ c (x) + Zd (x) (3)

[0034] Among them, ρ is the scaling factor, Z c (x) represents the Kriging surrogate model constructed from the simulation sample data, Z d (x) represents the Kriging surrogate model constructed from the difference between the measurement sample data and the simulation sample data.

[0035] A further improvement of the present invention lies in that the accuracy evaluation method described in step 13 is: using the mean square error index to evaluate the global accuracy of the Co-Kriging surrogate model;

[0036] The sampling strategy described in step 14 is: adopting the maximum prediction variance sampling criterion for sample sampling.

[0037] The present invention has at least the following beneficial technical effects:

[0038] A method for constructing a digital twin of the performance of a precision spindle considering surface topography provided by the present invention constructs a digital twin of the performance of a precision spindle through a surrogate model, and the surrogate model is an adaptive variable credibility surrogate model that fuses high-precision and low-precision simulation data and measurement test data; compared with the traditional spindle rotation accuracy prediction method, the present invention applies the surrogate model to the prediction of spindle rotation accuracy, and at the same time considers surface topography and measured data, thereby realizing accurate, fast, and efficient prediction of spindle rotation accuracy. Description of the Drawings

[0039] Figure 1 It is a schematic assembly diagram of a certain type of precision spindle;

[0040] Figure 2 It is a flow chart of the method for constructing a digital twin of the performance of the precision spindle of the present invention;

[0041] Figure 3 It is a flow chart of high-precision and low-precision finite element simulation modeling of a precision spindle with surface topography;

[0042] Figure 4 It is a schematic diagram of a finite element simulation model of a shaft with surface topography.

[0043] Description of the Reference Numerals:

[0044] 1. Shaft; 2. Bearing housing; 3. End cover A; 4. Bearing A1; 5. Bearing A2; 6. Outer spacer; 7. Inner spacer; 8. Bearing B; 9. End cover B. Detailed Embodiments

[0045] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and embodiments. Obviously, the accompanying drawings in the following description are only partial embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0046] The embodiment of the present invention is described by taking a certain type of precision spindle as an example. Refer to Figure 1 , Figure 1 which is an assembly schematic diagram of a certain type of precision spindle, including shaft 1, bearing housing 2, end cover A 3, bearing A1 4, bearing A2 5, outer spacer 6, inner spacer 7, bearing B 8 and end cover B 9. As Figure 2 shown, the specific steps of the method for constructing a performance digital twin of a precision spindle considering surface topography with a certain type of precision spindle as the object are as follows:

[0047] (1) Determine the surface topography parameters and the relative position parameters of the parts, and determine their upper and lower limits according to the selected parameters. The surface topography parameters are the coefficients of the basis functions selected for surface error reconstruction, and their upper and lower limits are initially given according to the part tolerances; the relative position parameters of the parts are the relative rotation angles of the spindle parts, and their upper and lower limits are expressed in radians as [0, 2π].

[0048] (2) Use the optimized nested Latin hypercube method to generate sample points of nested high-precision and low-precision models within the parameter range, use the generated sample points for surface error reconstruction, and judge whether the generated error surface meets the tolerance specifications. If it does not meet, remove this sample point, and finally obtain high-precision sample points low-precision sample points where N < n.

[0049] (3) Establish high-precision and low-precision finite element simulation models of the precision spindle with surface topography. Refer to Figure 3 , Figure 3 which is a flowchart of high-precision and low-precision finite element simulation modeling of the precision spindle with surface topography. First, establish an ideal three-dimensional model. Secondly, perform a denser division and a sparser division on the three-dimensional model of the precision spindle. The model generated when the division is denser is the high-precision finite element model of the precision spindle, and the model generated when the division is sparser is the low-precision finite element model of the precision spindle. Then, use the basis function and the surface topography parameters to reconstruct the surface error of the parts. Among them, the basis function of the toroidal surface adopts the Zernike polynomial, and the expression is as shown in Equation (1):

[0050]

[0051] where

[0052]

[0053]

[0054] wherein, is the term related to the radial direction, is the term related to the argument of the amplitude, n is the order of the polynomial, t is any positive or negative integer, and its value has the same parity as n, t ≤ n; the basis function of the cylinder uses the Legendre-Fourier polynomial, and the expression is as shown in Equation (4):

[0055]

[0056] wherein,

[0057] M = A ij P j (z)cos(iθ) + B ij P j (z)sin(iθ) (5)

[0058]

[0059] wherein, r(θ, z) represents the radius of the non-ideal cylinder at (θ, z), P j (z) is the Legendre polynomial, A ij and B ij are the coefficients in the Fourier polynomial. Finally, the surface error of the part is attached to the ideal finite element model by modifying the nodes, and high-precision and low-precision finite element simulation models of the precision spindle with surface topography are obtained, as Figure 4 shown, Figure 4 is a schematic diagram of the finite element simulation model of the shaft with surface topography, and the finite element simulation models of the other components with surface topography are similar to this.

[0060] (4) Input the high-precision sample points and the low-precision sample points into the high-precision and low-precision finite element simulation models of the precision spindle respectively, and obtain the high-precision simulation results and the low-precision simulation results The simulation result y is the offset of the center of the spindle end under the parameter conditions.

[0061] (5) Use the multiplicative scaling function to establish the connection between the high-precision and low-precision sample data. Take the high-precision sample point set and the scaling factor set l = (l1, l2,..., l N ) as the input and output to construct the multiplicative scaling function The approximate model selected for constructing the scaling function is the Kriging model. Among them, the calculation formula of the scaling factor is as shown in Equation (7):

[0062]

[0063] Wherein, is the scale factor at the high-precision sample point , is the high-precision simulation result at the high-precision sample point , is the low-precision simulation result at the high-precision sample point ;

[0064] Then, convert the low-precision sample data into approximate high-precision sample data, and call the converted sample data the simulation sample data. The calculation formula is shown in Equation (8):

[0065]

[0066] Wherein, is the low-precision simulation result at the low-precision sample point , is the scale factor at the low-precision sample point .

[0067] (6) Construct a Kriging surrogate model using the simulation sample data. First, select the correlation function and regression basis function of the Kriging model, then input the simulation sample data into the Kriging model for training, and finally obtain the Kriging model. Its basic form is:

[0068]

[0069] Wherein, reflects 's overall trend; Z(x) is a random process with a mean of 0 and a covariance of Cov(Z(x i ), Z(x j )) = σ 2 R(x i , x j , θ), and the correlation function R(x i , x j , θ) takes θ as a parameter and characterizes the spatial correlation relationship between the sample points x i and x j .

[0070] (7) Obtain multiple groups of point cloud data on the surface of the precision spindle, and use a high-precision coordinate measuring machine and a cylindricity measuring instrument to obtain the point cloud data on the surface of each part of the spindle.

[0071] (8) Obtain the surface topography parameters. First, reconstruct the surface error of the part using the acquired surface point cloud data, and then use the least squares method to minimize the sum of the squares of the errors between the reconstructed surface and the measured surface, thereby obtaining the reconstruction coefficients of the part surface, i.e., the surface topography parameters.

[0072] (9) Obtain the relative position parameters of the part. Assemble the precision spindle. During assembly, the relative rotation angle between the starting points of the part point cloud measurements is the relative position parameter of the part.

[0073] (10) Use the spindle rotation error analyzer to obtain the rotation trajectory of the precision spindle, decompose the rotation trajectory, and obtain the offset of the center of the spindle end under various parameter conditions.

[0074] (11) Construct a Kriging surrogate model using the difference between the measurement sample data and the simulation sample data.

[0075] (12) Construct a Co-Kriging surrogate model using the above two Kriging surrogate models. The approximate estimate of the constructed Co-Kriging model is expressed as:

[0076] Z e (x) = ρZ c (x) + Z d (x) (10)

[0077] where ρ is the scaling coefficient, Z c (x) represents the Kriging surrogate model constructed from the simulation sample data, and Z d (x) represents the Kriging surrogate model constructed from the difference between the measurement sample data and the simulation sample data.

[0078] (13) Evaluate the global accuracy of the Co-Kriging surrogate model using the mean square error index. If the model accuracy meets the design requirements, the construction of the performance digital twin of the precision spindle considering the surface topography is completed. If the accuracy requirements are not met, proceed to steps (14) and (15).

[0079] (14) Use the maximum prediction variance addition criterion to generate new sample points in the space and add points to the samples.

[0080] (15) Input the new sample points into the high-precision and low-precision finite element simulation models of the precision spindle to obtain the high-precision and low-precision simulation results of the sample points, add them to the sample dataset, and repeat steps (5) to (13) until the Co-Kriging surrogate model meets the accuracy requirements, and finally obtain the performance digital twin of the precision spindle considering the surface topography.

[0081] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it based on the present invention, which will be obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of the present invention claimed.

Claims

1. A method for constructing a digital twin of the performance of a precision spindle considering surface topography, characterized in that, It includes the following steps: Step 1: Determine the surface topography parameters and the relative position parameters of the part, and determine their upper and lower limits according to the selected parameters; Step 2: Generate sample points of nested high- and low-precision models within the parameter range; Step 3: Establish high-precision and low-precision finite element simulation models of the precision spindle with surface topography; Step 4: Input the sample points of the nested high- and low-precision models described in Step 2 into the high-precision and low-precision finite element simulation models of the precision spindle described in Step 3 respectively to obtain the high-precision and low-precision simulation results of the sample points; Step 5: Establish the connection between the high-precision and low-precision sample data by using the scaling function, convert the low-precision sample data into approximate high-precision sample data, and call the converted sample data the simulation sample data; Step 6: Construct a Kriging surrogate model by using the simulation sample data; Step 7: Obtain multiple groups of point cloud data of the precision spindle surface; Step 8: Reconstruct the surface error of the part by using the point cloud data described in Step 7 to obtain the surface topography parameters; Step 9: Obtain the relative position parameters of the part; Step 10: Obtain the rotation trajectory of the precision spindle; Step 11: Construct a Kriging surrogate model by using the difference between the measured sample data and the simulation sample data; Step 12: Construct a Co-Kriging surrogate model by using the surrogate models described in Step 6 and Step 11; Step 13: Evaluate the accuracy of the Co-Kriging surrogate model. If the model accuracy meets the design requirements, the construction of the performance digital twin of the precision spindle considering the surface topography is completed. If the accuracy requirements are not met, perform Step 14 and Step 15; Step 14: Generate new sample points in space by using the point addition strategy; Step 15: Input the new sample points into the high-precision and low-precision finite element simulation models of the precision spindle described in Step 3 to obtain the high-precision and low-precision simulation results of the sample points, add them to the sample data set, and repeat Step 5 to Step 13 until the Co-Kriging surrogate model meets the accuracy requirements to obtain the performance digital twin of the precision spindle considering the surface topography.

2. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The method for generating the sample points of the nested high- and low-precision models described in Step 2 is the optimized nested Latin hypercube experimental design.

3. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The method for establishing the finite element simulation model of the precision spindle with surface topography described in Step 3 is: reconstruct the surface error of the part by using the surface topography parameters, and then attach the surface error of the part to the ideal finite element model.

4. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The scaling function described in Step 5 is a multiplicative scaling function, and a set of high-precision sample points and a set of scaling factors \(l=(l_1, l_2, \ldots, l N ) are used as inputs and outputs to construct the multiplicative scaling function The approximate model selected for constructing the scaling function is the Kriging model. Among them, the calculation formula for the scaling factor is shown in Equation (1): In the formula, is the scale factor at the high-precision sample point , is the high-precision simulation result at the high-precision sample point , is the low-precision simulation result at the high-precision sample point .

5. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The basic form of the Kriging model described in Step 6 and Step 11 is: In the formula, reflects the overall trend, Z(x) is a random process with a mean of 0 and a covariance of Cov(Z(x i ), Z(x j )) = σ 2 R(x i , x j , θ), and the correlation function R(x i , x j , θ) is parameterized by θ and characterizes the spatial correlation relationship between sample points x i and x j .

6. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The method for obtaining the point cloud data of the surface described in Step 7 is: use a high-precision coordinate measuring machine to obtain the point cloud data of the part surface.

7. The method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The surface error reconstruction method described in Step 8 is: reconstruct the surface error of the part by using the basis function, where the Zernike polynomial is used as the basis function of the toroidal surface, and the Legendre-Fourier polynomial is used as the basis function of the cylindrical surface.

8. A method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The method for obtaining the rotation trajectory of the precision spindle described in Step 10 is: use a spindle rotation error analyzer to obtain the rotation trajectory of the precision spindle.

9. A method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The approximate estimation of the Co-Kriging model described in Step 12 is expressed as: Z e ψ(x) = ρZ c ψ(x) + Z d ψ(x) (3) where ρ is the scaling factor, Z c (x) represents the Kriging surrogate model constructed from the simulation sample data, Z d (x) represents the Kriging surrogate model constructed from the difference between the measurement sample data and the simulation sample data.

10. A method for constructing a digital twin of the performance of a precision spindle considering surface topography according to claim 1, characterized in that, The accuracy evaluation method described in step 13 is as follows: the global accuracy of the Co-Kriging surrogate model is evaluated using the mean square error index; The sampling point adding strategy described in step 14 is as follows: the maximum predicted variance sampling point adding criterion is used for sample point addition.

Images