應用機器學習法於高速主軸之熱誤差預測

Abstract

工具機主軸的熱誤差是影響加工精度的主要因素之一。主軸在運轉時會因軸 承與接合處間的摩擦而導致升溫，使得主軸產生熱變形，嚴重影響工具機之加工精 度。本研究透過高速主軸的幾個特徵溫度點和主軸轉速，應用三種機器學習演算法 分別建立主軸軸向熱誤差預測模型，進一步探討不同演算法對於主軸軸向熱誤差 預測的表現。 本研究首先分析傳統前饋神經網路之建模原理與表現，考慮其簡單且適應性 高，但無法展現系統之動態時序表現，採用了門控循環單元和極限梯度提升，門控 循環單元是遞迴神經網路中的門控機制，對系統的動態時序表現能有更完整的描 述;極限梯度提升法運用集成學習，大幅度地提升樹模型的性能，有快速、準確、 可靠度高的特色。 由實驗結果得知，不論是門控循環單元模型或極限梯度提升模型對主軸之軸 向熱誤差預測表現皆優於前饋神經網路模型，特別是藉由極限梯度提升模型預測 之結果與實驗的誤差在±3內。

The thermal error of spindle is one of the primary factors that affecting the cutting accuracy of a machine tool. During operation, the temperature rising due to the friction between the bearing and joints will cause the thermal deformation of the spindle and thereby affect the cutting accuracy of the machine tool significantly. This study is to establish the estimation model of the thermal error for a high-speed spindle through its some characteristic temperature points and rotation speed by means of three machine learning algorithms. The performances of the three machine learning algorithms are discussed as well. The aforesaid three machine learning algorithms are Feedforward Neural Network (FFNN), Gate Recurrent Unit (GRU), and Extreme Gradient Boosting (XGBoost). The traditional FFNN modeling principle and performance are firstly analyzed. Then, considering the FFNN, which is simple and adaptive but it cannot show the temporal dynamic behavior of the system. In spite of the advantages of simple and adaptive, FFNN cannot show the temporal dynamic behavior of the system. Therefore, the author adopted GRU model and XGBoost model. GRU are a gating mechanism in recurrent neural networks, which have a more complete description of the temporal dynamic behavior of the system. XGBoost uses an ensemble learning algorithm to greatly improve the performance of the tree model, and has the characteristics of fast, accurate, and high reliability. The experiments show that the thermal error estimation performance of the spindle by GRU model or XGBoost model is better than that of the FFNN model, especially the error between the prediction result of the XGBoost model and the experiment is within ±3.