Identification of System Parameters for Ball End Milling

轉子系統具球銑刀銑削之系統参數鑑別

蕭庭郎(Ting-Nung Shiau) ； 陳冠宏(Kuan-Hung Chen) ； 洪銘宏(M. H. Huang) ； 張哲榮(Jer-Rong Chang)

《中國機械工程學刊》 30卷2期 (2009/04) Pp. 95-105

https://doi.org/10.29979/JCSME.200904.0003

摘要

本論文研究轉子系統具有球銑刀切削之系統參數鑑別，系統參數包含切削力係數及等效參數（質量、阻尼及勁度），切削力係數包含剪力係數及邊緣力係數，然而剪力係數可推算切削力參數，它們包含剪應力，磨擦角度及切屑厚度比，在切削力係數鑑別是運用遞回最小平方演算法與平均切削力法，以端銑刀加工的實驗值來進行切削力係數之鑑別，經由鑑別得邊緣力係數及切削力參數，可預測球銑刀及端銑刀加工之切削力，在等效參數鑑別方面，是從預測切削力及量測刀尖振動量，運用傅立業轉換過濾法、延伸卡曼過濾法及直接卡曼過濾法來進行鑑別運算。從實驗量測與鑑別理論估算之切削力及刀尖振動量可以進行圖形比對，去證實本文所提出鑑別方法之可靠性，關於實驗方面，切削力之數值直接由動力計量測，而刀尖振動量是由兩個雷射位移計量測之值推算得知。經鑑別鋁材(AL6061-T6)的剪力係數隨著每刃進給增加而減小，但是邊緣力係數則是增加，而經換算切削參數之剪應力隨著每刃進給增加而減小，但是磨擦角度及切屑厚度比則呈現定值，使用這些切削參數及邊緣力係數可成功預測端銑刀及球銑刀之切削力，藉由使用遞回最小平方演算法估算切削力幾乎與實驗量測數據一致，而使用傅立業轉換過濾法及延伸卡曼過濾法可有效率鑑別等效參數，它們所預估刀尖振動量非常類似於實驗量測值。

並列摘要

In this paper, the system parameters including the cutting force coefficients and the equivalent parameters (mass, damping and stiffness) are identified. The cutting force coefficients including the shear force coefficients and the edge force coefficients are identified from the end milling by using the recursive least square method (RLS) and the average cutting force method (ACF). The cutting parameters including the shear stress, friction angle, and chip ratio are thus derived from the identified shear force coefficients. Then the cutting forces in the end milling and the ball end milling are predicted from the cutting parameters and the edge force coefficients. The equivalent mass, damping and stiffness parameters of the rotor system are identified by using Fourier transform filter (FTF), the extended Kalman filter (EKF), and the direct Kalman filter (DKF) through the predicted cutting forces and the measured displacements of the tool tip. The cutting forces and the tool tip displacements measured from the experiment are also carried out and compared graphically with those from the identification estimation to verify the reliability of the proposed identification methods. About the experiment, the cutting forces are measured with the dynamometer, and the tool tip displacements are derived from the measured data using two laser displacement sensors. The identified shear force coefficients decrease and the identified edge force coefficients increase as the feed per flute increases for AL6061-T6. The derived cutting parameters show that the shear stress decreases and the friction angle and the chip ratio remain almost constant as the feed per flute increases. Using these edge force coefficients and cutting parameters, the cutting forces in ball end milling and end milling can be successfully predicted. The predicted cutting forces by using the RLS are almost coincident with the experimental results. The equivalent mass, damping and stiffness parameters can be effectively identified by using the FTF and the EKF, which predict the tool tip displacements similar to the experimental measurements.

並列關鍵字

Identification ； system parameters ； cutting parameters ； ball end milling