CN116611314A - Machine tool machining process thermal error online evaluation method based on physical information neural network - Google Patents
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Abstract
The invention discloses a method for online thermal error in a machine tool machining process based on physical information neural network, which comprises the following steps: 1. the surface temperature data of the machine tool spindle are acquired by a few temperature measuring points; 2. constructing a temperature field heat transfer equation of a key part of the machine tool; 3. establishing a neural network model, and inputting temperature data and coordinates of temperature measuring points; 4. setting a loss function of the neural network as the sum of two parts, wherein the first part is the mean square difference value between the output and the actual temperature point, and the second part is the residual error value brought into the heat transfer equation by the calculation result; 5. training a neural network, and obtaining a temperature field distribution situation by using the neural network; 6. updating the neural network at regular time by using the data of actual test; 7. training a proxy model of thermal field-thermal deformation of the key component by using simulation data and measured data; 8. and establishing a machine tool topology model, and calculating a machining error by using the transfer relation of the multi-body dynamics to the thermal error of the machine tool. The invention provides a method for calculating machine tool machining process errors influenced by thermal factors in the machining process.
Description
Technical Field
The invention relates to the field of data processing of machine tools in precision machining, in particular to a machine tool machining process thermal error online evaluation method based on a physical information neural network.
Background
In the precision machining field, thermal errors caused by thermal factors account for the largest proportion of machining errors. Thus, accurate and rapid calculation of errors due to thermal influences is of great importance for precision machining. Because of the inconvenience of the real-time measurement method in the processing process, the real-time thermal error of the machine tool cannot be analyzed through measurement, and the calculation can be performed only through a simulation calculation method.
In principle, the errors caused by heat are mainly caused by the accumulation and transmission of errors caused by the thermal deformation of key parts of a machine tool and the coupling relation between the parts, so that the position of a tool deviates from a preset position during machining. Knowing the motion relationship and position transfer structure of each structural member, we can translate this critical component thermal deformation into processing errors. The method can be used for calculating by adopting a finite element analysis method by reconstructing and predicting a thermal field of a key part of the machine tool and calculating the processing position offset caused by the deformation of the key part of the machine tool based on the thermal field and the constraint condition. However, this approach has limitations, namely: the finite element method itself cannot calculate the machining error of the machine tool in real time due to huge calculation amount. The method of machine learning is another thought to analyze the machine tool machining error by using the proxy model, however, the method needs a large amount of data in the machine tool machining process as training input, and the limitation of the structure of the machine tool itself leads to the incapability of arranging a large amount of data sensors to collect data in the running process, so that the calculation and prediction of the machine tool thermal error can be completed only under the condition of a small amount of data, and the problem is a problem to be solved in the quick calculation of the machine tool machining process.
Disclosure of Invention
The invention provides a physical information-based sectional construction method for a loss function of a neural network, which aims to solve the problems that the physical information neural network is difficult to converge in training and has poor convergence effect when the physical information neural network is used for processing complex problems by carrying out sectional construction on the loss function.
The invention relates to a method for constructing a loss function of a physical information neural network, which mainly comprises the following steps:
the basic implementation idea of the physical information neural network is to embed Partial Differential Equations (PDEs) into the loss function of the neural network, so that the loss function is composed of the following two parts: a data driving part and a model driving part. Wherein the data driving part is a root mean square value of a neural network prediction result and an actual result, and the data driving part is residual data of a partial differential equation. The two parts are combined to form the loss function of the physical information neural network.
The sectional type loss function construction method is based on the principle, and comprises the following steps:
step one: abstracting the problem, finishing a differential equation set capable of solving the problem, and constructing a residual equation of the differential equation set as a part of a loss function to be added into the loss function;
step two: setting a phase loss function threshold value according to experience, wherein the phase loss function threshold value is generally about 100;
step three: setting different weight values of the model driving part and the data driving part in two stages, wherein the weight value of the model driving part is far greater than that of the data driving part (about 100 times) in the first stage, and the weight value of the data driving part is far greater than that of the model driving part (about 100 times) in the second stage;
step four: the method comprises the steps of training in stages, firstly, training in one stage, wherein the weight value of a loss function data driving and model driving part adopts a weight value in one stage, and when the loss function is reduced to a phase loss function threshold value, the weight value of the loss function data driving and model driving part adopts a weight value in two stages until the loss function is reduced to a proper value, namely, the completion is indicated.
The invention provides a method for online evaluation of thermal errors in a machining process of a computer machine tool based on a physical information neural network. The purpose and the problems solved are as follows: under the condition that parameters of key parts of the machine tool are difficult to measure, only a small amount of measuring point data is needed, real-time reconstruction and prediction are carried out on the three-dimensional temperature field of the key parts of the machine tool, and thermal deformation and processing thermal errors of the key parts are calculated.
The invention relates to a method for rapidly calculating thermal errors in a machine tool machining process by utilizing a physical information neural network, which mainly comprises the following steps:
the three-dimensional temperature field reconstruction problem of the machine tool is essentially a process of solving a classical heat transfer equation under boundary conditions and initial conditions of the machine tool operation process. Because the classical heat transfer equation is used as a Partial Differential Equation Set (PDEs) and has almost no analytic solution in the complex heat transfer condition under the three-dimensional condition, the thermal field distribution under the specific three-dimensional complex condition can be obtained only by adopting a numerical solution, but the numerical solution is more accurate, but the initial and boundary conditions of a machine tool are required to be described more accurately, and meanwhile, the numerical solution based on a finite element/finite difference method has the characteristic of long solution time, so that the numerical solution can not be used in the real-time temperature field reconstruction and prediction process of the machine tool. In practical application, although the temperature of the spindle of the machine tool can be acquired in real time by directly arranging a large number of sensor measuring points, the method firstly cannot predict the temperature change trend of the machine tool, and secondly, needs a large number of sensor measuring points, which is almost impossible to be completed in engineering practice due to the limitation of the structure and the cost of the spindle of the machine tool. Similarly, even if a machine learning method such as a neural network is used, the neural network cannot well describe the thermal field distribution and change rule of the spindle of the machine tool because massive data cannot be provided.
In order to solve the problems, a physical information neural network method is introduced, and the basic implementation thought is that PDEs are embedded into a loss function of the neural network, so that the loss function is composed of the following two parts: a data driving part and a model driving part. Wherein the data driving part is a root mean square value of a neural network prediction result and an actual result, and the data driving part is residual data of a partial differential equation. The two parts are combined to form the loss function of the physical information neural network. The method combines partial physical information and data information, so that the neural network can 'complement' the missing part of the data by utilizing the physical information and is constrained by the physical information, and the neural network can predict according with the physical rule.
Based on the above principle, the steps are as follows:
step one: the problems are abstracted, and partial differential equations capable of describing heat transfer problems of key components of the three-dimensional machine tool are arranged.
Step two: constructing a physical model of key parts of a machine tool, arranging a small number of temperature sensors, and collecting runtime data
Step three: the three-dimensional temperature field reconstruction neural network of the key part of the machine tool is constructed, and a heat transfer partial differential equation is encoded into a neural network loss function.
Step four: and carrying out normalization processing on the acquired data.
Step five: the neural network is trained using the collected data until the loss function drops to an acceptable level.
Step six: the sensor continuously collects data, and the newly collected data is used for carrying out secondary training on the neural network in time so as to achieve the effect of updating the network model, so that the model can accurately reconstruct and predict the temperature field in a long period of time.
Step seven: and constructing a physical model of the key part of the machine tool, analyzing heat source and heat transfer conditions of the key part, applying physical constraint on the structure to the key part of the machine tool, discretizing a heat transfer equation and a metal deformation equation, and solving the thermal deformation equation by adopting a finite difference or finite element method to obtain temperature-deformation data of the key part of the machine tool. These data include deformation of points at different locations in xyz three directions at different temperatures. Step eight: and (3) deriving deformation data, establishing a neural network as a temperature field-deformation proxy model, using a mean square value as a loss function of the neural network, and training the neural network by using the deformation data obtained through simulation. So that the temperature-deformation fitting capacity of the machine tool structural part can be obtained.
Step nine: the method comprises the steps of performing topological dynamics analysis on a machine tool structure, establishing a machine tool-tool processing chain and a machine tool-workpiece processing chain, carrying out joint multiplication on a motion and static homogeneous transformation matrix of each part on each chain, carrying out joint multiplication on the homogeneous transformation matrix of motion errors and static errors, calculating thermal deformation of key parts in three directions in the matrix, and finally obtaining a difference value of the two chains as a final deviation.
Drawings
FIG. 1 is a flow chart of a method for online evaluation of thermal errors in a machining process of a machine tool based on a physical information neural network
FIG. 2 is a three-dimensional block diagram of a carving machine
FIG. 3 is a comparison of the result of the prediction of the electric spindle center axis physical information neural network method and the result of the finite element method
FIG. 4 comparison of fully connected neural network predicted thermal deformation and simulation results
FIG. 5 topology block diagram of engraving machine
FIG. 6 is a graph of triaxial error over time for the engraver
Detailed Description
For a better understanding of the features and advantages of the present invention, reference is made to the following detailed description, taken in conjunction with the accompanying drawings, in which:
taking a certain carving machine as an example, the structure diagram is shown in fig. 2. By analyzing the machine tool, it was found that the main heat generating components thereof are concentrated on the electric spindle of the machine tool, specifically, the electric spindle center shaft of the machine tool is thermally deformed to cause thermal errors. Firstly, solving the real-time thermal field reconstruction and prediction problem of the central shaft under the action of a motor, wherein a heat source is arranged in a central area, and the heat exchange coefficient of the air convection coefficient of the rest surface is 10.
The relevant data for the problem are as follows:
table 1: question related data
| Length of | 0.212m |
| Maximum radius | 0.016m |
| Minimum radius | 0.0095m |
| Material | No. 45 steel |
| Air convection coefficient | 10W/(m2·K) |
| Heat source | 8.76W |
| Ambient temperature | 286.15K |
Step one: the problem is abstracted, and the system heat transfer equation is obtained by analyzing the problem as follows:
wherein k is the thermal conductivity of the material, ρ is the density of the material, C p The constant pressure specific heat capacity of the material is obtained, T is the temperature of a coordinate point, and T is time.
Because the heat transfer condition of the main shaft is complex, the initial/boundary condition is not set temporarily, and the constraint is carried out by the data.
Step two: the outside of the main shaft is provided with 35 temperature measuring points, the temperature measuring points measure the outside temperature of the main shaft, and the acquired data are used in one-stage training and two-stage model updating. Here we collect data from 0-300s, where data from 0-240s is predicted and data from 0-300s is updated.
Step three: through the equation of the first step, a corresponding model driving part can be constructed in the loss function, T is the temperature value as the output of the neural network, coordinate data and time are used as the input, the residual error of the equation is calculated by utilizing an automatic differentiation principle, the loss function is added, and the data driving part is constructed through the mean square error of the actual temperature value T and the temperature value predicted by the neural network. The loss function of the neural network thus obtained is constructed as follows:
Loss total (S) ＝w 1 Loss Data +w 2 Loss Model
Wherein w1 is a data driving part weight, and w2 is a data driving part weight. In this problem, both weights are equal, 1. Meanwhile, a fully-connected neural network model is built, the adopted structure is [4,64,128,200,200,128,64,1], and an optimizer is an Adam optimizer.
Step four: unifying the acquired coordinate points, time and temperature data, and normalizing the physical grid coordinate points to be brought in
Step five: training the neural network until the loss function is reduced to 0.08, and ending the training.
Step six: temperature field predictions were made using a neural network over a time range of 0-300s and compared to the comsol simulation results, as shown in fig. 3. And printing MSE values of the neural network prediction results. The MSE threshold, here 0.1, is set and when the MSE value rises to the threshold, the neural network is trained with data for 0-300s until the result after training should fall below the MSE value. The MSE value change curve is shown in FIG. 4. Compared with the traditional simulation method, the method predicts the three-dimensional temperature field of the central axis of the main shaft of the machine tool at the moment of 300s, the method takes 0.2898 seconds, the traditional method takes 18 seconds, and the trained temperature field results are compared, as shown in fig. 3, so that the obtained results are different.
Step seven: the method comprises the steps of importing a main shaft model into ANSYS software, constructing constraint relation, heat source and heat transfer information by adopting a simulation method, and finally determining the shape of a machine tool thermal error by the deformation of a main shaft center shaft of the machine tool according to analysis on the main shaft structure of the machine tool, wherein the main shaft center shaft of the machine tool is selected as a research object, so that the deformation data of the main shaft of an airport at different temperatures are finally obtained
Step eight: a fully-connected neural network model is built, the adopted structure is [4,64,128,200,128,64,3 ], the optimizer adopts an Adam optimizer, the input is coordinates and temperature, the output is the deformation sizes of three axes in the xyz three directions, and the data obtained by simulation are used for training until the loss function is reduced to an acceptable degree
Step nine: the engraving machine is subjected to topological structure analysis, a topological structure diagram is shown in fig. 5, and an error equation is established by using a multi-body kinematics theory, and is shown as follows.
E＝K 17p ΔK 17p K 17s ΔK 17s H w -K 12p ΔK 12p K 12s ΔK 12s K 23p ΔK 23p K 23s ΔK 23s K 34p ΔK 34p K 34s ΔK 34s K4 5p ΔK 45p K 45s ΔK 45s K 56p ΔK 56p K 56s ΔK 56s H t
Wherein: p, s are static and moving states, K ijs ，K ijp Respectively a homogeneous transformation matrix of motion and static state in an ideal state; the homogeneous transformation matrix of motion error and static error is delta K ijs ，ΔK ijp
Hw is the position of the forming point of the workpiece in the self coordinate system, and Ht is the position of the forming point of the tool in the self coordinate system
The method comprises the following steps:
D1-D7: bed to workpiece
K 17s ＝I，ΔK 17p ＝I，ΔK 17s ＝I
D1-D2 bed to y-axis
Wherein Sxy, xz, yz is perpendicularity error, Δy y For positioning error Deltax y Δz y Straightness error in x, z direction
Δαβγ y Yaw errors in roll pitch on the y-axis, respectively
D2-D3 y-axis to x-axis
K 23p ＝I，ΔK 23p ＝I，/>
Δx x For positioning error Δy x Δz x Straightness error in y, z direction
Δαβγ x Yaw errors in roll pitch on the x-axis, respectively
D3-D4 x-axis to z-axis
K 34p ＝I，ΔK 34p ＝I，/>
Δz z For positioning error Deltax z Δy z Straightness error in x and y directions
Δαβγ z Yaw errors in roll pitch in the z-axis, respectively
D4-D5z axis to spindle
K 45p ＝I，K 45s ＝I，ΔK 45p ＝I，
Thermal errors for the spindle in three axial directions
D5-D6 spindle to tool
K 56s ＝I，ΔK 56p ＝I，ΔK 56s ＝I
By the above equation, the thermal offset of the machine tool spindle obtained in the step eight is carried into the equation, and the error E is calculated, and the time-dependent changes of the errors in the three coordinate directions are 0-300s, as shown in fig. 6.
Claims (11)
1. A method for evaluating thermal errors in a machining process of a machine tool based on physical information neural network is characterized by comprising the following steps of:
carrying out rapid real-time temperature field reconstruction on key parts of the machine tool by using a physical information neural network; and then constructing a thermodynamic coupling model, and constructing a material thermal deformation data set by using a finite element or finite difference numerical method. Training a neural network for predicting thermal deformation of a key structural member of the machine tool based on the data; and analyzing the kinematic topological structure of the machine tool, and establishing a machine tool error transfer equation to finally obtain the real-time thermal error of the machine tool.
2. A real-time reconstruction and prediction method for a temperature field of a key part of a three-dimensional machine tool based on a physical information neural network is characterized by comprising the following steps of:
(1) Based on temperature measuring point data of a few key parts of the machine tool, preprocessing the obtained temperature measuring point coordinates, corresponding acquisition time and corresponding temperature data, and constructing a sample set;
(2) Constructing a heat transfer equation set of key parts of the machine tool;
(3) Constructing a neural network for the data set, wherein the neural network comprises an input layer, an output layer and a hidden layer, and a loss function of the neural network comprises data and physical information as constraint neural network training;
(4) And obtaining a reconstructed temperature field of a key component of the main shaft of the three-dimensional machine tool according to the position coordinates after the pretreatment is input into the completed neural network, and updating the neural network at fixed time by adopting a small quantity of temperature measurement points.
3. A machine tool key part temperature field deformation calculation method based on a neural network comprises the following steps: the method is characterized in that:
and constructing a physical structure model of a key part of the machine tool, and analyzing the thermal environment of the key part. Calculating a deformation equation by using a finite element method to obtain deformation data of the key component caused by thermal factors; and fitting deformation data of the simulated key parts of the machine tool caused by thermal factors by using the fully-connected neural network, so as to obtain the neural network for rapidly calculating the deformation of the key parts from the temperature field, and providing the deformation of the key parts of the machine tool by using the real-time temperature field data obtained in the last step as input.
4. A calculation method for performing topological kinematic analysis on a machine tool is characterized by comprising the following steps of: analyzing the topological structure of the machine tool, establishing a position and motion deviation transmission matrix of each part, and calculating the final error.
5. The method of claim 2, wherein the preprocessing of the measured spindle temperature data parameters comprises:
and carrying out normalization processing on the measured parameters, and unifying the measurement units of the temperature parameters and the coordinate parameters.
6. The method according to claim 2, wherein the neural network input layer is a time of the processed machine tool spindle coordinate point data corresponding to a coordinate point, the output layer is temperature data of the coordinate point in the case, and the hidden layer is a fully connected neural network.
7. The method of claim 2, wherein the set of loss functions of the neural network is divided into two parts, one part is a mean square difference value between the predicted value of the neural network and the actual temperature value, and the other part is a residual value of a heat transfer equation of a main shaft machine tool key component which is constructed according to a basic heat transfer equation and takes in the predicted data of the neural network; both parts are multiplied by a coefficient and added to be a loss function.
8. The method of claim 2, wherein after the primary training is completed, the neural network selects a small number of measuring points to continuously collect data, and the primary neural network is trained for a second time in time by using the data, so that the neural network prediction model is updated in time to meet the use requirement.
9. A method according to claim 3, characterized in that the deformation values of the critical parts of the machine tool in the case of thermal fields are obtained using simulation means, these deformation values being used as training data sets for the neural network that calculates the deformation of the critical parts.
10. A method according to claim 3, wherein a neural network is used to construct the temperature-deformation proxy model, the neural network input layer is the processed machine tool spindle coordinate point data and the temperature corresponding to the coordinate point, the output layer is the deformation data of the coordinate point under the condition, and the hidden layer is a fully connected neural network.
11. The method of claim 4, wherein the machine motion structure is analyzed to find a motion chain from the bed to the tool and the bed to the workpiece, and a difference between the motion of the two chains and the coordinate transfer matrix multiplication value is defined as a machining error of the machine structure transmitted to the workpiece.
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