五軸CNC工具機動態誤差與幾何誤差之誤差分析與模擬

Analysis and Simulation of Dynamic and Geometry Error for Five-axis CNC Mahcine Tool

陳志安(Jr-An Chen)

指導教授 ： 林明宗

國立虎尾科技大學/工程學院/機械與機電工程研究所/碩士(2010年)

https://doi.org/10.6827/NFU.2010.00037

摘要

五軸工具機發展至今已有數十年的時間，其加工精度受到靜態誤差與動態誤差所影響。縱觀市售的商用五軸量測系統(包含荷蘭IBS Precision Engineering公司的R-Test、德國Etalon公司的LaserTRACER及美國API公司的Laser tracker III等)單價偏高且尚未能完全分離五軸工具機之靜態幾何誤差，因此本研究採用國立虎尾科技大學精密機械技術研發中心所開發之五軸光學量測校正系統作為量具，並針對五軸工具機的靜態幾何誤差與伺服動態誤差進行研究與分析。
在不考慮熱變形誤差的情況下，本論文使用齊次座標轉換矩陣建立五軸工具機之順向與逆向運動學方程式，同時亦建構出五軸工具機之幾何誤差模型及伺服動態模型，該幾何誤差模型包括了43個靜態誤差，伺服動態模型則考慮五軸伺服控制系統之速度、位置、速度前餽等控制器參數以及各軸伺服動態模型。隨後分析此幾何誤差模型之參數靈敏度，利用逆向運動方程式設計規劃NC路徑(如：BK1、BK2、BK4等)，並透過Matlab軟體進行誤差模擬與分析。最後在商用五軸工具機機台上進行實機操作與量測，再利用量測誤差與模擬數據進行比對與驗證，並補償五軸工具機之靜態誤差及調整控制器參數，藉此來調校五軸工具機，提升加工精度。

關鍵字

五軸工具機 ； 齊次座標轉移矩陣 ； 幾何誤差 ； 動態誤差 ； 逆向運動學

並列摘要

The five-axis machine tool has been developed over a period of decades. The precision of its processes is affected by static error and dynamic error. This research is going to make the study and survey which is aimed at static error and dynamic error. In the comprehensive survey of the commercial measuring system on present market conditions, this technology is the high unit price and imperfect. So we used five-axis machine tool optical measuring system form PMC of NFU, and analysis and simulation of dynamic and geometry error for five-axis CNC machine tool.
First of all, disregarding the thermal deformed error, this paper brings up an algorithm of the geometry error for five-axis machine tool, which is using Homogeneous Transformation Matrix to establish the kinematic formula of the five-axis machine, so as to structure a model of its geometry error. This model indicated 43 Static errors. And then, by using the kinematic formula to produce NC code and analyze the parameter sensitivity of the geometry error model, we designed the proper NC route such as BK1, BK2, BK4. After that, we simulated and tested the NC route through Matlab software. At last, we performed the operation and measurement of five axis machine (model TTTRR), in order to compare and verify the measured signal and the hypothesized data, and to use as regulating the five-axis machine tool, and raise the precision of its processes.

並列關鍵字

Five-axis machine tool ； HTM ； Geometry error ； Dynamic error ； Inverse kinematics

參考文獻

[56] 王冠中, “開發一具有即時預視功能之混合型NC碼插補器”, 國立虎尾科技大學機械與機電工程研究所, 碩士論文, 2010.

[1] V. S. B. Kiridena and P. M. Ferreira, “Kinematic Modeling of Quasistatic Errors of Three-Axis Machining Centers,” International Journal of Machine Tools and Manufacture, vol. 34, no. 1, pp. 85-100, 1994.

[2] V. S. B. Kiridena and P. M. Ferreira, “Parameter Estimation and Model Verification of First order Quasistatic Error Model for Three-Axis Machining Centers,” International Journal of Machine Tools and Manufacture, vol. 34, no. 1, pp. 101-125, 1994.

[3] V. S. B. Kiridena and P. M. Ferreira, “Computational Approaches to Compensating Quasistatic Errors of Three-Axis Machining Center,” International Journal of Machine Tools and Manufacture, vol. 34, no. 1, pp. 127-145, 1994.

[4] V. S. B. Kiridena and P. M. Ferreira, “Mapping the Effects of Positioning Errors on the Volumetric Accuracy of Five-Axis CNC Machine Tools,” International Journal of Machine Tools and Manufacture, vol. 33, no. 3, pp. 417-437, 1993.