應用昆式進給函式於工具機S型加減速設計研究

A quintic feedrate function for S-curve acceleration/deceleration tool control in CNC machining

陳鈞煌(Jin-Hung Chen)

指導教授 ： 葉賜旭

國立臺北科技大學/機電學院/機電整合研究所/碩士(2011年)

摘要

近十年來工具機S型加減速演算法的研究越來越重要，因為S型加減速演算法提供刀具更平順的進給運動、縮短了加工時間、維持加工品質和延長刀具的壽命。在本篇研究中應用昆式函式來規畫加減速，並以給定的進給速度、加速度和Jerk的極限值來實現S型加減速演算法。此篇研究分析了昆式進給函式的運動學上的特性然後藉由進給速度的差異、給定的加速和Jerk的限制條件發展一套有系統的方法來決定加減速的時間，使得完整定義的昆式進給函式在加減速期間可以被限制在軸向極限加速度和軸向極限Jerk值以內，以減少由刀具路徑上不連續點對軸向進給伺服機構造成不利的影響，最後經由在CNC工具機上的實驗驗證此方法的可行性。

關鍵字

加減速 ； 昆式函式 ； 進給函式 ； CNC工具機

並列摘要

A quintic feedrate function for achieving S-curve acceleration and deceleration (ACC/DEC) in computer numerical control (CNC) machining is developed and demon-strated through experiments using a biaxial planar motion system to provide the neces-sary motion control given limited inputs of feedrate, feed acceleration, and feed jerk. Smoother feed motions such as S-curve ACC/DEC has become important in CNC ma-chining to shorten machining time, maintain machining quality and prolong the life of cutting tools. The kinematic characteristics of the proposed quintic feedrate function for S-curve ACC/DEC control are analyzed in detail, and a systematic scheme for deter-mining the ACC/DEC time by referring to the inputs of feedrate difference, feed acce-leration, and feed jerk constrains is presented. The results of experiments using the con-trol algorithm demonstrate the feasibility of the approach for improving the smoothness of cutting tool motion in practical CNC machining.

並列關鍵字

acceleration/deceleration ； quintic function ； feedrate function ； CNC machine tools

參考文獻

[1] Altintas, Y., Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, UK, 2000.

[2] Alintas, Y.; Erkormaz, K.,” Feedrate optimization for spline interpolation in high speed machine tools,” CIRP Annals-Manufacturing Technology, 52(1), 2003, 297-302.

[4] Dewes, R. C.; Aspinwall, D. K.,” Review of ultra high speed milling of hardened steels,” Journal of Materials Processing Technology, 69(1-3), 1997, 1-17.

[5] Erkorkmaz, K.; Altintas, Y.,” High speed CNC system design. Part I: Jerk li-mited trajectory generation and quintic spline interpolation,” International Jour-nal of Machine Tools and Manufacture, 41(9), 2001, 1323-1345.

[6] Erkorkmaz, K.; Altintas, Y.,” Quintic spline interpolation with minimal feed fluctuation,” Journal of Manufacturing Science and Engineering, Transactions of the ASME, 127(2), 2005, 339-349.