以機器學習建立工具機進給軸的熱變位誤差模型

Machine Learning on the Thermal Positioning Error Model of Machine-Tool Feed Axis

王禹傑(Yu-Jie Wang)

指導教授 ： 張培仁

國立臺灣大學/工學院/應用力學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203043

摘要

工具機進給軸的熱變位誤差是影響製造業高速加工精度的重點要素之一，其中線性進給系統是工具機的核心部件，在高進給速率的加工下，軸承、滾珠螺桿與接合處摩擦導致溫度快速上升，機臺結構將因溫升膨脹而產生熱變位誤差影響定位精度，將改變刀尖對工件的相對位置，進而影響加工精度，因此本研究使用進給速率及溫度點變化為輸入特徵建立熱變位誤差的機器學習模型，其中熱變位誤差當中包含了幾何誤差和熱誤差的表現，於是本研究有別於以往就時序熱變位誤差直接建立預測模型，透過觀察實驗數據的不同面向並進行假設，依位置面向的觀察將熱變位誤差轉換成標準誤差與熱誤差所造成的斜率與偏差值的組合，其中標準誤差即是不隨溫度改變斜率為零的幾何誤差，且透過多項式迴歸進行擬合，以此假設轉換與就時間序熱變位誤差分別建立預測模型，並搭配有無使用皮爾森相關係數結合多元線性迴歸的向後特徵淘汰法(PCLRBE)進行特徵選擇共四種組合，對工具機X、Y及Z軸進給軸的熱變位誤差建立反向傳遞神經網路(BPNN)，並進行驗證與比較，經由皮爾森相關係數進行驗證，發現轉換後預測目標與特徵的相關性得到提升，可見此轉換透過移除非線性的標準誤差可以更好的觀察到溫度變化與熱變位誤差之間的關係，接著將時間、進給速率及19個溫度點總計21個特徵，透過特徵選擇PCLRBE篩選至進給速率及8個溫度點，共9個特徵，依測試集預測結果表明，經由轉換的PCLRBE_Converted_BPNN為最佳的熱變位誤差預測模型，透過觀察所得的關係進行轉換，使得模型能更好的收斂，並透過特徵選擇PCLRBE，將相關性低的特徵消除，減少無關特徵影響預測的準確度，因此本研究成功以PCLRBE_Converted_BPNN運用轉換預測工具機X、Y及Z軸進給軸的熱變位誤差，並將溫度感測器數由19個降至8個，降低感測器成本亦提升了預測準確度，最大絕對誤差從138.9 (μm)限縮至10.78 (μm)以內，且均方根誤差小於2.51 (μm)。

關鍵字

熱變位誤差 ； 工具機進給軸 ； 機器學習

並列摘要

The thermal positioning error of the machine-tool feed axis is one of the key elements that affect the high-speed machining accuracy of the manufacturing industry. Under high feed rate cutting, the friction between the bearing, the ball screw and the nut will cause the temperature to rise rapidly. The structure of the machine-tool will generate thermal positioning errors due to temperature rise and thermal expansion, which will affect the positioning accuracy, and will change the relative position of the tool to the workpiece, thereby affecting the machining accuracy. Therefore, this study uses the feed rate and temperature changes as input features to train a machine learning model of thermal positioning error. The thermal positioning error includes the performance of geometric error and thermal error. Therefore, this study is different from the previous training a machine learning model of time series thermal positioning error. By analyzing the experimental data and making a hypothesis, the thermal positioning error is converted into a combination of the standard error and the slope and bias caused by the thermal error. The standard error is the geometric error that removes the influence of thermal error, that is, the initial thermal positioning error zeroing the slope, and is fitted through polynomial regression. The thermal positioning error are converted based on a hypothesis and the time-series thermal positioning error, and combined with or without the use of Pearson correlation coefficient and multiple linear regression backward feature elimination (PCLRBE) for feature selection, a total of four combinations. With these four combinations, the back-propagation neural network (BPNN) of the X-axis, Y-axis and Z-axis thermal positioning error of the machine-tool is trained. It is verified by the Pearson correlation coefficient that the correlation between the predicted target and the feature is improved after converted. It can be seen that the conversion can better observe the relationship between temperature change and thermal positioning error by removing the nonlinear standard error. Then, the time, feed rate and 19 temperature points totaled 21 features, and were filtered through PCLRBE to feed rate and 8 temperature points, a total of 9 features. According to the prediction of the test set, the PCLRBE_Converted_BPNN is the best thermal positioning error prediction model, and the model can be better converged by the conversion through the observed relationship. And through PCLRBE, the features with low correlation are eliminated to reduce the influence of irrelevant features on the accuracy of prediction. Therefore, this study successfully used PCLRBE_Converted_BPNN to predict the thermal positioning error of the X-axis, Y-axis and Z-axis feed axis of the machine-tool, and reduced the number of temperature sensors from 19 to 8, reducing the cost of the sensor and improving the prediction accuracy. The maximum absolute error is reduced from 138.9 (μm) to within 10.78 (μm), and the root mean square error is less than 2.51 (μm).

並列關鍵字

Thermal Positioning Error ； Machine-Tool Feed Axis ； Machine Learning

參考文獻

[1] J. Bryan, International status of thermal error research (1990), CIRP annals, 39 (1990) 645-656.

[2] S.N. Grama, A. Mathur, A.N. Badhe, A model-based cooling strategy for motorized spindle to reduce thermal errors, International Journal of Machine Tools and Manufacture, 132 (2018) 3-16.

[3] Z. Ge, X. Ding, Design of thermal error control system for high-speed motorized spindle based on thermal contraction of CFRP, International Journal of Machine Tools and Manufacture, 125 (2018) 99-111.

[4] W.-H. Ye, Y.-X. Guo, H.-F. Zhou, R.-J. Liang, W.-F. Chen, Thermal error regression modeling of the real-time deformation coefficient of the moving shaft of a gantry milling machine, Advances in Manufacturing, 8 (2020) 119-132.

[5] W. Feng, Z. Li, Q. Gu, J. Yang, Thermally induced positioning error modelling and compensation based on thermal characteristic analysis, International Journal of Machine Tools and Manufacture, 93 (2015) 26-36.