應用機器學習於工具機軸向熱變位預測

Application of machine learning in the prediction of axial thermal displacement for machine tool

王宇鋐(Yu-Hung Wang)

指導教授 ： 廖洺漢

共同指導教授 ： 蔡孟勳(Meng-Shiun Tsai)

國立臺灣大學/工學院/機械工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202200262

摘要

滾珠螺桿進給系統為CNC工具機的關鍵零組件，主要負責刀具或工作台的移動與定位，機台在加工過程中，進給系統的驅動元件與傳動元件的生熱會傳導至螺桿，使其溫升引起軸向熱變形，進而影響加工精度，而熱變形所導致的加工誤差，約佔總體加工誤差的40%以上。雖然機台可經由安裝光學尺來避免螺桿熱變形造成的加工誤差，但由於光學尺本身造價昂貴，若三個軸向皆安裝光學尺會使機台成本提高不少。因此，開發較具經濟效益的進給軸向熱變位補償模型就成為一個值得研究的議題。
　　根據目前的相關文獻，補償模型可分為理論模型(Theoretical model)與經驗模型(Empirical model)兩種類型，其中理論模型需要仰賴繁瑣費時的實驗鑑別出熱傳係數，才能達到準確的預測效果；經驗模型則僅需於機台上佈署溫度感測器，並建立溫升量測資料與熱變位的函數關係，所以後者的建模流程較易應用於產業界中。此外，近來機器學習演算法對於迴歸預測問題具有高準確度的優勢，適合用來擬合溫升與熱變位的函數關係。因此，本論文會透過經驗建模的方式建立補償模型，並應用機器學習常見的多元線性迴歸(Multiple linear regression)與支持向量迴歸(Support vector regression)於模型中。
　　一般量測進給軸的熱變位主要是採用雷射干涉儀，其缺點為量測所需時間較長，造成螺桿因冷卻而縮短的現象被放大，進而導致熱變形的量測資料失真。因此為了降低此效應的影響，本論文會基於結合光學尺與馬達編碼器的軸向熱變形量測架構，量測各個實驗工況下螺桿的熱變形與各部件跟環境的溫升，並藉此分析出溫度點溫升與螺桿熱變位的特性，建立以機器學習為基礎的熱變位預測模型。為了提升模型的預測效果，本論文使用窮舉法篩選最佳溫度點組合作為模型的輸入。最後比較分別以多元線性迴歸與支持向量迴歸建立模型的預測效果差異，由結果可知兩者皆能有效預測長時間複合工況的軸向熱變位，其中又以多元線性迴歸建立的模型的準確度較高，能將最大熱變位誤差從24 μm補償至5 μm，並同時降低各量測位置因熱變位引起的誤差達55%至80%。

關鍵字

滾珠螺桿 ； 軸向熱變位 ； 光學尺 ； 機器學習 ； 多元線性迴歸 ； 支持向量迴歸

並列摘要

The ball screw feed drive system is the key component of the CNC machine tool, which is mainly responsible for the transmission and positioning of the tool or worktable. However, during the processing, the heat generated by the drive elements and transmission elements of the feed system is transferred to the screw causing thermal deformation and reducing machine accuracy. Furthermore, the error caused by the thermal deformation is main source of machining error. Although the linear scale can be installed on the machine tool to avoid machining errors caused by axial thermal deformation of the screw, the cost of the linear scale is too expensive. Therefore, the development of a compensation model for axial thermal displacement has become a topic worthy of study.
At present, there are two ways to establish compensation models: Theoretical model and Empirical model. In order to have an accurate prediction results, the theoretical model requires many tedious and time-consuming experiments to identify heat transfer coefficients. On the other hands, the empirical model only needs to establish the function between the temperature rise and thermal displacement, so the empirical modeling process is easier to apply in the industry. In addition, because machine learning algorithms have the advantage of high accuracy for regression prediction problems, it is suitable for fitting the function between temperature rise and thermal displacement. Therefore, this article will establish a compensation model through empirical modeling, and apply multiple linear regression and support vector regression, which are common in machine learning, in the model.
Therefore, in order to reduce the influence of thermal deformation measurement data distortion caused by cooling effect, this article will use an axial thermal deformation measurement structure based on a linear scale and a motor encoder to the thermal deformation of the screw and the temperature rise of each component and the environment under each experimental condition. Based on the measurement data collected under these conditions, the characteristics of the temperature rise at each temperature measurement point and the thermal displacement of the screw are analyzed. Then, we build a machine learning-based thermal displacement prediction model based on the results of the analysis. Furthermore, in order to improve the prediction performance of the model, this article uses the best combination of temperature points selected by the exhaustive method as the input of the model. Finally, we compare the differences between the prediction performance of the models established by multiple linear regression and support vector regression. It can be seen from the results that both of them can effectively predict the axial thermal displacement of long-term composite conditions. It is worth mentioning that the model established by MLR has higher accuracy, and this model can compensate the maximum thermal error from 24 μm to 5 μm, and also reduce the machining error caused by thermal displacement at each measurement position by 55% to 80%.

並列關鍵字

Ball screw ； axial thermal displacement ； linear scale ； machine learning ； multiple linear regression ； support vector regression

參考文獻

[1]A. S. Yang et al., “Thermal Deformation Estimation for a Hollow Ball Screw Feed Drive System,” p. 6, 2013.

[2]D. J. H. GmbH, “Accuracy of Feed Axes,” p. 12.

[3]R. Ramesh, M. A. Mannan, and A. N. Poo, “Thermal error measurement and modelling in machine tools.: Part I. Influence of varying operating conditions,” International Journal of Machine Tools and Manufacture, vol. 43, no. 4, pp. 391–404, 2003.

[4]J. Yang, X. Mei, B. Feng, L. Zhao, C. Ma, and H. Shi, “Experiments and simulation of thermal behaviors of the dual-drive servo feed system,” Chin. J. Mech. Eng., vol. 28, no. 1, pp. 76–87, 2015.

[5]H. Shi, C. Ma, J. Yang, L. Zhao, X. Mei, and G. Gong, “Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools,” International Journal of Machine Tools and Manufacture, vol. 97, pp. 60–71, 2015.