A method for constructing a digital twin model for end milling with variable parameters

Abstract

The present invention belongs to the technical field of end milling, and in particular, relates to a method for constructing a digital twin model for end milling with variable parameters, characterized in that the number of temperature measurement points in the actual end milling process is determined based on the digital twin model, and the actual temperature monitoring time series data in the end milling process is combined to predict the thermal deformation of the contact position between the tool and the workpiece surface during the end milling process, and to guide the optimization of the end milling process parameters in real time during the end milling process, and to predict the temperature and thermal deformation of the contact area between the tool and the workpiece. The beneficial effect of the present invention is that it can accurately predict the temperature and thermal deformation changes caused by the changes in the heat source and the convection heat transfer coefficient caused by the changes in the process parameters and environmental factors, thereby effectively guiding the optimization design of the end milling process parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of end milling, and in particular relates to a method for constructing a digital twin model of end milling with variable parameters. Background Art

[0002] The quality of workpieces in conventional end milling is almost entirely determined by surface finish and dimensional accuracy. In dry end milling, thermal deformation is the main factor affecting the surface finish and dimensional accuracy of the workpiece being processed. Therefore, accurately predicting the thermal deformation at the contact point between the tool and the workpiece, thereby guiding the optimization design of end milling process parameters, is of great practical significance for improving the quality of end milling workpieces.

[0003] The finite element method is used to numerically simulate the end milling process, and the thermal deformation of the contact position between the tool and the workpiece surface and the temperature distribution and change law of the workpiece as a whole can be predicted during the end milling process. The Chinese invention with application number 201711461516.6 discloses a coupled numerical simulation prediction method for the milling machining error of a complex workpiece surface, including the following steps: establishing a single-step analysis standard finite element model and extracting analysis files, establishing a cutting theory model, preprocessing finite element mesh nodes, determining the instantaneous cutting force at the cutting position at time k, initializing the finite element analysis model file at time k, finite element analysis, machining error calculation, judging whether all the nodes on the surface to be cut have completed the calculation, converting the machining residual error set at each cutting position obtained after all cycles are completed into a workpiece surface machining error point cloud, and obtaining a surface machining error cloud. This method can realize the simulation analysis of the surface residual machining error after machining of the complex workpiece surface, obtain the surface error point cloud after the final machining, obtain the machining surface quality evaluation parameters by processing the surface point cloud data, and effectively obtain the fluctuation and distribution law of the machining surface error.

[0004] However, the calculation time of the finite element method is long and the efficiency is low. The finite element method is also limited to the calculation of the process parameters determined in the early stage of end milling, and cannot consider the fluctuation of thermal deformation caused by temperature fluctuation caused by some interference factors in the end milling process. Therefore, it is impossible to monitor and predict the thermal deformation of the contact area between the tool and the workpiece surface during the end milling process in real time. Summary of the invention

[0005] The purpose of the present invention is to provide a method for constructing a digital twin model for end milling processing with variable parameters, to overcome the shortcomings of the prior art, and to solve the problem of disturbance interference in the thermal deformation prediction of the contact area between the tool and the workpiece caused by changes in the tool speed or the external environment during the end milling process, which leads to changes in the heat generation in the contact area between the tool and the workpiece or changes in the convective heat transfer of the workpiece.

[0006] In order to achieve the above technical objectives, the present invention is implemented by adopting the following technical solutions:

[0007] A method for constructing a digital twin model for end milling with variable parameters, characterized in that the number of temperature measurement points in the actual end milling process is determined based on the digital twin model, and the temperature and thermal deformation of the contact position between the tool and the workpiece surface during the end milling process are predicted in combination with the actual temperature monitoring time series data during the end milling process, so as to guide the optimization of the end milling process parameters in real time during the end milling process.

[0008] Compared with the prior art, the beneficial effects of the present invention are: 1) It solves the problem that the finite element calculation efficiency of the thermal deformation of the contact position between the tool and the workpiece during the end milling process is too low, and it cannot consider the temperature and thermal deformation fluctuations caused by the disturbance of process parameters and environmental factors during the end milling process. 2) It can accurately predict the temperature and thermal deformation changes caused by the changes in heat source and convection heat transfer coefficient caused by the changes in process parameters and environmental factors, thereby effectively guiding the optimization design of end milling process parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 1 is a schematic diagram of the positions of the 10 monitoring points at the lower end, and (b) is a schematic diagram of the positions of the 10 monitoring points at the upper end;

[0010] Figure 2 It is the temperature time series data of the temperature monitoring point positions during the end milling process in the embodiment of the present invention, wherein (a) is the temperature time series data of the 10 monitoring points at the lower end, and (b) is the temperature time series data of the 10 monitoring points at the upper end;

[0011] Figure 3 is the thermal deformation time series data of the contact position between the tool and the workpiece surface during the end milling process in the embodiment of the present invention;

[0012] Figure 4 It is the optimization process of the constructed basic model by the MLR, AIC and p-value judgment criteria in the embodiment of the present invention, wherein (a) the coefficients of each item of the basic model, (b) the AIC values ​​of the remaining items when the independent variable items are deleted separately, (c) the coefficient results of the remaining items after deleting the independent variable items with smaller AIC, and (d) the coefficient results of each item of the final digital twin model;

[0013] Figure 5 are the fitting results of the change in heat source value, the change in convective heat transfer coefficient and the relative average error rate in the embodiment of the present invention, wherein (a) is the fitting result of the change in heat source value and the average error rate, and (b) is the fitting result of the change in convective heat transfer coefficient and the average error rate;

[0014] Figure 6 is a comparison of the calculation results of different models with different heat source value changes in the embodiments of the present invention, as expressed in percentage relative to the heat source value in Table 1, (a) 50%, (b) 75%, (c) 105%, (d) 110%, (e) 115%, (f) 125%, (g) 150%;

[0015] Figure 7 1 is a comparison of the calculation results of different models in which the heat source value and the convective heat transfer coefficient vary simultaneously in the embodiment of the present invention, as expressed in percentage relative to the heat source and convective heat transfer coefficient in Table 1, (a) 50%, (b) 75%, (c) 125%, and (d) 150%. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0017] The present invention provides a method for constructing a digital twin model for end milling with variable parameters, characterized in that the number of temperature measurement points in the actual end milling process is determined based on the digital twin model, and the temperature and thermal deformation of the contact position between the tool and the workpiece surface in the end milling process are predicted in combination with the actual temperature monitoring time series data in the end milling process, and the optimization of the end milling process parameters is guided in real time during the end milling process. The specific steps are as follows:

[0018] 1) Determine a simple workpiece geometry model and end milling process, see Figure 1 The end mill diameter is 16 mm, the feed rate is 0.00125 m / s, and the tool path spacing is 10 mm;

[0019] 2) The finite element (FEM) calculation method is used to establish a finite element model of the workpiece to be processed, and its physical parameters are shown in Table 1. Since this method focuses on fine processing, the volume reduction of the workpiece during the processing is ignored, and the processing process is modeled as a heat conduction problem with a moving heat source;

[0020] Set boundary conditions according to the processing parameters. For the numerical simulation of the thermal analysis finite element model, the top surface of the workpiece is the loading area, and the others are the thermal convection boundaries. For the numerical simulation of the structural finite element model, the bottom surface is the constraint area;

[0021] 3) According to Figure 1 The positions of the temperature monitoring points are shown in Figure 1, and the finite element model of these points is used to calculate the temperature time series data results. Figure 2. Extract the thermal deformation time series finite element model calculation data results of the contact area between the tool and the workpiece, see Figure 3 ;

[0022] The multiple linear regression (MLR) method was used to consider the time series temperature data of 20 monitoring points (all monitoring points) as the input variable (T ch1 (t), T ch2 (t),…,T chn (t) is the independent variable), and the thermal deformation time series data of the contact area between the tool and the workpiece surface (i.e., the heat source area) is regarded as the output variable (D HS (t) is the dependent variable). In addition, the goodness of fit (R 2 ) is used to determine the degree of fit of the regression equation curve to the observed value; the equation of the basic model is as follows:

[0023] D HS (t) = β0 + ∑β i T CHi (t) Formula (1)

[0024] Where D HS (t) is the thermal deformation of the contact area between the tool and the workpiece at different times; β0 is a real constant; β i is the coefficient of the i-th term of the regression equation; T CHi is the temperature time series data of the CHi-th monitoring point. After the basic model is established, the Akaike Information Criterion (AIC) and p-value judgment are used to optimize the various variables of the basic model and eliminate the variables with lower contribution, that is, to delete the variables corresponding to the larger AIC value and p-value (variables with lower contribution). Figure 4 ; After fitting, the coefficients in the initial formula can be determined as Figure 4 As shown in (a), the R 2 The value is 0.7381; when the changing trends of the independent variables are similar, collinearity problems will occur, which is the main reason for the low efficiency of the basic model. AIC is usually used to solve the collinearity problem. In order to eliminate the collinearity problem of the initial model, the variable items of the monitoring points are deleted one by one, and the AIC value is calculated using the variable items of other monitoring points. The AIC value is as follows Figure 4 (b) as shown.

[0025] By comparing the AIC values, the AIC value of the model with the temperature variable of the monitoring point deleted alone is greater than the AIC value of the model without deletion, indicating that the process of deleting the temperature variable of the monitoring point alone is conducive to improving the efficiency of the model. Therefore, the monitoring point 19 was reasonably deleted in the basic model.

[0026] The temperature variable model of the monitoring point optimized by MLR fitting has a p value corresponding to the independent variable term greater than 1×10 -4, which shows that the model is still inefficient. Therefore, we delete the large p values ​​(greater than 1×10 -4 ) and refit the equation using the MLR method, such as Figure 4 (c) and Figure 4 (d).

[0027] The optimization process was carried out twelve times, and the R of the basic model after each optimization was 2 The values ​​are 0.7663, 0.762, 0.7527, 0.7508, 0.743, 0.7394, 0.7233, 0.7114, 0.7001, 0.6849, 0.666 and 0.6382 respectively. The optimized basic model consists of six independent variable terms. At this time, the R 2 The value is 0.6382, which is greater than the expected value. The standard value is 0.6. The basic model expression of the optimization process is as follows:

[0028] D HS (t)=7.8149-1.3920T CH1 (t)-0.7622T CH3 (t)+1.2526T CH8 (t)+0.3531T CH10 (t)+0.3179T CH11 (t)+0.1742T CH17 (t) Formula (2)

[0029] 4) The basic model combined with the finite element model is used to calculate the temperature time series result data of the workpiece during the end milling process under different working conditions (parameter changes are shown in Table 2), and the time series result calculation of the thermal deformation of the contact area between the tool and the workpiece is completed. In this example, the variable parameters are selected as the heat source value and the convection heat transfer coefficient. The main reason is that the change of these two parameters has a crucial influence on the generation and transfer of heat during the end milling process, and they are the two parameters that are most likely to fluctuate during the end milling process.

[0030] Table 2 Parameter changes

[0031]

[0032] 5) Formula (3) is used to calculate the relative average error rate between the finite element model calculation results of the thermal deformation in the contact area between the tool and the workpiece and the basic model calculation results.

[0033]

[0034] In the formula, is the relative average error rate of different finite element model results compared with the basic model. FEMis the thermal deformation result of finite element calculation at different times, d MC Optimization results of thermal deformation are calculated for the basic model at different times.

[0035] 6) The relative average error rate corresponding to the change rate of the single heat source and the change rate of the single convection heat transfer coefficient is the x-axis As the y-axis, draw a curve (see Figure 5 ) and perform equation fitting to obtain the equations between the heat source change rate, the convection coefficient change rate and the relative average error rate, such as equations (4) and (5):

[0036]

[0037]

[0038] In the formula, and are the relative average error rates corresponding to the heat source change rate and the convective heat transfer coefficient change rate, μHS is the heat source change rate, μHTC is the rate of change of convective heat transfer coefficient.

[0039] 7) Using the MLR method, combined with the change rate of the heat source and the convective heat transfer coefficient at the same time and the corresponding relative average error rate data, a new heat source, convective heat transfer coefficient change rate and relative average error rate are established The relationship is as follows:

[0040]

[0041] 8) Combining equations (2) and (6), the digital twin model that can be applied to the prediction of workpiece thermal deformation in variable parameter end milling is finally obtained as follows:

[0042]

[0043] The calculation results of different ways of changing the heat source parameters and the convective heat transfer coefficient parameters are shown in the example. Figure 6 and Figure 7 The final calculation results of the digital twin model are closer to the calculation results of the finite element model than those of the basic model, and can more accurately calculate the thermal deformation of the contact area between the tool and the workpiece during the variable parameter end milling process.

[0044] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing a digital twin model for end milling with variable parameters, characterized in that: Based on the digital twin model, the number of temperature measurement points in the actual end milling process is determined, and combined with the actual temperature monitoring time series data in the end milling process, the temperature and thermal deformation of the contact position between the tool and the workpiece surface during the end milling process are predicted, and the optimization of the end milling process parameters is guided in real time during the end milling process. The specific steps include: 1) Using the finite element (FEM) calculation method, a finite element model of the workpiece to be processed is established, boundary conditions are set according to the processing parameters, the simulation calculation of the entire end milling process is completed, and the temperature time series data of each temperature monitoring point during the processing and the thermal deformation time series data of the contact position between the tool and the workpiece are output; 2) Using the multivariate linear regression (MLR), Akaike information criterion (AIC) and p-value judgment method, combined with the calculation data of the finite element model, a basic model was constructed as follows: D HS (t) = β0 + ∑β i T CHi (t) Formula (1) Where D HS (t) is the thermal deformation of the contact area between the tool and the workpiece at different times; β0 is a real constant; β i is the coefficient of the i-th term of the regression equation; T CHi is the temperature time series data of the CHi-th monitoring point; 3) The heat source value of the contact area between the tool and the workpiece and the convection heat transfer coefficient between the workpiece and the environment are changed to different degrees, and the finite element calculation of the workpiece end milling process under these working conditions is completed and the corresponding time series result data of temperature and thermal deformation are output; 4) The basic model is combined with the finite element model to calculate the temperature time series result data of the workpiece during the end milling process under different working conditions, and the time series result calculation of the thermal deformation in the contact area between the tool and the workpiece is completed; 5) Formula (2) is used to calculate the relative average error rate between the finite element model calculation results of the thermal deformation of the contact area between the tool and the workpiece and the basic model calculation results, and the basic model is optimized; In the formula, is the relative average error rate of different finite element model results compared with the basic model; d FEM Calculate the thermal deformation results of the finite element model at different times, d MC Calculate the optimization results of thermal deformation for the basic model at different times; 6) The relative average error rate corresponding to the change rate of the single heat source and the change rate of the single convection heat transfer coefficient is the x-axis As the y-axis, the curve is drawn and the equation is fitted to obtain the equations between the heat source change rate, the convection coefficient change rate and the relative average error rate, such as equations (3) and (4): In the formula, and are the relative average error rates corresponding to the heat source change rate and the convective heat transfer coefficient change rate, μHS is the heat source change rate, μHTC is the rate of change of convective heat transfer coefficient, a, b, c, d, e, f are constants; 7) Using the MLR method, combined with the change rate of the heat source and the convective heat transfer coefficient at the same time and the corresponding relative average error rate data, a new heat source, convective heat transfer coefficient change rate and relative average error rate are established The relationship is as follows: 8) Combining equations (1) and (5), we finally get a digital twin model that can be used to predict workpiece temperature and thermal deformation in variable parameter end milling, as follows:

2. The method for constructing a digital twin model for end milling with variable parameters according to claim 1, characterized in that: The variable parameter refers to any one or any combination of two or more of density, heat source, thermal conductivity, convection heat transfer coefficient, initial temperature, ambient temperature, elastic modulus, Poisson's ratio, and linear expansion coefficient.

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