Thermal Error Modeling of Ball Screw Based on Neural Network System

Tech 2023-05-24 13:18:21 Source: Network

Wen|Zhang ShirenEdit|Zhang ShirenIn the pursuit of high-precision modern CNC systems, thermal error, also known as thermal deformation error, is increasingly receiving attention. According to research,Thermal deformation error has become the main source of error for CNC machine tools, accounting for 40% to 70% of the total error

Wen|Zhang Shiren

Edit|Zhang Shiren

In the pursuit of high-precision modern CNC systems, thermal error, also known as thermal deformation error, is increasingly receiving attention. According to research,Thermal deformation error has become the main source of error for CNC machine tools, accounting for 40% to 70% of the total error.

Due to the large number of heat sources inside the machine tool, which affect each other during heat transfer and dissipation, and other factors, modeling thermal errors becomes difficult,In order to minimize the impact of these errors on machining accuracy, a large number of error compensation based methods have been fully studied and developed.

The basic assumptions of these methods are:Machine tool error is a function determined by temperature distribution, position and axis movement direction.

After obtaining this information, a model of temperature and its corresponding error can be constructed,Then the Error term of this model can be predicted, and then real-time compensation can be made to the machining process, so as to improve the machining accuracy of the workpiece.

At present, the commonly used modeling method for thermal errors both domestically and internationally is to use data fitting to construct the empirical relationship between discrete temperature points and thermal errors,Among them, modeling methods based on neural networks have been widely studied.

Most of these methods have conducted thermal error modeling on the spindle of machine tools, and their application in modeling the thermal error of the ball screw in the linear feed system of machine tools is mainly discussed in the research,A data preprocessing method was introduced based on the characteristics of the training dataset, and the final experimental results showed that,The neural network system reduces the maximum error in thermal error modeling accuracy from 10pm to 2um.

Thermal error analysis of screw

The ball screw is composed of a screw, nut, and ball, and is the most commonly used transmission component in tool machines and precision machinery,Its main function is to convert rotational motion into linear motion, or to convert torque into axial repetitive forceAt the same time, it has the characteristics of high accuracy, traceability, and efficiency.

When the ball screw in the machine tool linear feed system operates at high speed, the temperature of the ball screw increases due to the influence of running time and speed, resulting in thermal deformation of the ball screw and a decrease in machining accuracy.

In addition to frictional heat,Environmental temperature changes also have a certain impact on the thermal deformation of the screw.

artificial neural network

artificial neural networkartificial neural network

In practice, a three-layer neural network is commonly used, which includes an input layer hidden layer and an output layer,In the input layer, each neuron receives a large amount of non-linear input information, which is transmitted, analyzed, calculated in the neuron link, and finally forms an output result, which is output in the output layer.

The hidden layer is composed of numerous neurons and links between the input and output layers, and the number of neurons in the hidden layer varies,However, the more the number is, the more significant the nonlinearity of the neural network is, which makes the robustness of the neural network more significant. As shown in Figure 1, it is a typical three-layer feedforward neural network.

In Figure 1,The number of neurons in the input layer of this network is 4, the number of neurons in the output layer is 1, and the number of neurons in the hidden layer is 9.

The process of establishing a model by correcting the weights of each layer through training samples is called the learning process. The specific learning method varies depending on the network structure and model, and the commonly used one is the backpropagation algorithm (BP algorithm).

The BP algorithm can be used to train multi-layer networks,It adopts the steepest descent method that minimizes mean square error, and a major drawback of the basic BP algorithm is its long training timeUsing the basic BP algorithm to solve practical problems is not feasible.

Levenberg MarquardBP algorithm (LMBP) to improve algorithm performance

The LMBP algorithm smoothes and harmonizes between the steepest descent method and the Gaussian Newton method, gradually switching to the Gaussian Newton method as it moves away from the minimum value,

Because LMBP algorithm uses approximate second derivative information, it is much faster than the steepest descent method, LMBP BP

Modeling of thermal error of screw

There are several steps to consider when building an ANN model,Firstly, what kind of network structure to choose 1 S

Secondly, choose a learning method

Thirdly, choose a learning algorithm,We chose the LMBP algorithm, which improves the basic BP algorithm. The input of the constructed neural network model is a quaternion (ambient temperature, ball screw temperature, front bearing temperature, position),

The composition of the training dataset is as follows:E where E=(TPQ), T=(T, T, T) represents the temperature input,

P represents a certain position, Q represents the corresponding thermal deformation, and E represents an element in the dataset, T P

In fact, the overall dataset can be viewed as a three-dimensional matrix of temperature, location, and thermal deformation,

An important feature of training data is the presence of a large amount of repetitive data, which cannot be directly used for model training. For example, under a certain temperature condition, thermal deformation needs to be detected at different positions of the lead screw,

In the experiment,

In the process of preprocessing data, temperature data and positional thermal deformation data are stored separately in two matrices to reduce the complexity of the operation. This can result in two two-dimensional data matrices:Position thermal deformation matrix (P) and temperature matrix (C), P C

Cyclically taking diagonal elements from the positional thermal deformation matrix ensures full use of the original data 2

This experiment focuses on the thermal deformation error of the Y-axis linear feed system of the VMCO850B three-axis vertical machining center. The Y-axis feed system:ML10 Y

Experimental process

The experiment is mainly divided into two stages,The first stage is data preprocessing and model training of neural networks, while the second stage is model generalization,

Experimental process4

In the process of modeling experiments, the selection of the number of hidden layer nodes is a very complex problem, with too few hidden layer nodes, poor fault tolerance, and low ability to identify unlearned samples. On the contrary

The following is an empirical formula for determining the number of hidden layer nodes: l=/n+m+a

Among them, l is the number of hidden layer nodes, m is the number of input nodes, n is the number of output nodes, and a is the adjustment constant between 1 and 10,5a9

The data detection system will collect all data used for model training, mainly including: D temperature collection, 5 @ML10Y

Through preliminary statistics on the collected data, the range of environmental temperature values is 6.9~9.5 3.8~11.8 6.2200~-73um()

Model training and its results

After preprocessing the training data, the LMBP algorithm is used to train the neural network model,

Figure 6 shows the training results under temperature conditions (7.8, 9.5, 19.6),

Figure 7 shows the predicted and actual error values of the thermal error of the Y-axis using the neural network model and the least squares fitting method under the actual collected temperature conditions (7.8, 9.15, 19.1),

In addition, the least squares model is an existing achievement of this project. Figure 8 shows the comparison effect of the output results of the two models at the Y-axis 190mm. For the convenience of drawing, only the temperature value at the front bearing is selected to represent the corresponding temperature environment. Figure 7 shows the two-dimensional result diagram of position thermal deformation, and Figure 8 shows the two-dimensional result diagram of temperature thermal deformation,10um2um

epilogue

Modeling of thermal error of screw

The experimental results indicate that,2um

In the above two calculation examples, the optimization results of the variable density method are the topology optimization results after de meshing. It can be seen from the above that, KNN

This indicates that the KNN method we adopted is feasible

The KNN algorithm is widely used in various pattern recognition,On the basis of establishing the mathematical model of continuum structure, we introduced KNN algorithm into the field of structural topology optimization design

This indicates that the optimization results are correct, KNNKNN

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