# Vertical Machining Center Feed Axis Thermal Error Compensation Strategy Research
## 1 Introduction
For example, artificial neural networks [11], gray theory [12], and support vector machines [13] became common methods to model thermal errors. Machine learning actually constructs a mathematical model to find the causal relationship between the input feature information and the target label value in a data set to predict the target value. This algorithmic model is commonly used in application scenarios where the correspondence between multiple variables is found. [PERSON] et al. [14] proposed the online asynchronous compensation method (OACM) to deal with static/quasi-static errors caused by thermal deformation and machine geometry, reducing more than 70% of machining errors caused by thermal deformation. [PERSON] et al. [15] established a comprehensive error model based on the MRA method for geometric and thermal errors. The experimental data showed that the error before compensation was as high as 60 \(\upmu\)m. After compensation, the error was reduced to 14 \(\upmu\)m, which achieved good compensation results. [PERSON] et al. [16] proposed a nonlinear MRA model that can accurately predict the thermal errors of CNC lathes. [PERSON] et al. [17] applied the MRA model to compensate for spatial positioning errors in machine tools. However, the technical route to realizing thermal error compensation has not yet been opened, and its compensation technique still needs to be improved in practical engineering applications. Most scholars stop at single-axis or single-scene analysis of some thermal error cases. They need help to provide a complete set of technical routes to solve such similarity problems. For most modeling approaches, thermal error models are obtained by finding the best mapping relationship between thermal errors and temperature variations at temperature-sensitive points. From the perspective of modeling theory, scholars tend to use fitting algorithms or combine various optimization algorithms to focus on outputting a single thermal error model mapping under multiple motion parameters. However, the modeling data's limitations affect the model's prediction performance, which is still only applicable to the deformation prediction under the corresponding modeling condition parameters, resulting in poor algorithmic robustness of the individual thermal error models. From the control system point of view, the traditional thermal error compensation model is more about the classification and identification of the thermal error model from the temperature-sensitive points of the machine tool. In contrast, the offline modeling model cannot guarantee an accurate adaptation of the temperature points to the thermal error model established under specific parameters. Along with the development of thermal error compensation models, data-driven thermal error compensators gradually appear in the public eye. The existing embedded compensators are primarily based on a single thermal error compensation model, which cannot flexibly embed a variety of thermal error models or rapidly iterate the development of existing thermal error models. In this paper, we propose a model classification method based on an embedded system as the control core, approximate matching of thermal error model motion parameters, and the use of dynamic loading technology to fit multiple sets of thermal error models as the technical means to achieve the classification identification and loading of compensation device models within a limited range of motion parameters, and we propose a thermal error classification model based on variable motion parameters of machine tool feed axes in an embedded environment. This embedded thermal error compensator with a dynamic loading technique can speed up the development process of the whole system, separating the underlying hardware from the application layer. It is safer and more efficient than the traditional model.