本文欲模擬車床加工中，均勻圓柱之工件的動態響應。預想之加工情況，為等速循環之連續切削，刀具作用於工件上之力可視作一移動之外力，除了對工件產生週期之側向力之外，對工件之軸向也會造成張力與壓力作用。文中將等速移動之側向力與軸向力表示為週期性之函數，利用傅立葉展開法，分析車削多個週期後，工件之動態響應。 理論上，工件可視為一旋轉之雷立夫樑，受到週期性運動相依之側向力，與週期性之軸向力。本文使用漢米爾頓定理，推導出此系統之運動方程式，並無因次化，代入以傅立葉展開之外力函數，再以格勒金法離散化系統運動方程式。接著，針對各個模態，以多重尺度法與數值方法做穩定性分析，以討論在各種條件下，系統之穩定特性。之後，以阮奇庫塔法，求解系統之微分方程組，得到位移響應，並經由快速傅立葉轉換得到頻譜圖，分析位移響應之頻譜特性。最後，再顯示穩定狀態下，旋轉樑隨時間之變形。 This paper formulates the processing of the lathe. In this process, a turning tool moves along the workpiece repeatedly. It could be seem as a periodically moving load which includes radial motion-dependent force and axial tension and compression distributed forces. To analyze the dynamic response of the workpiece after numerous turning cycles, those external forces are periodic functions in the forms of Fourier series. A rotating Rayleigh beam with periodically radial and axial forces was considered. The governing equations were derived by Hamilton's principle and expressed in a dimensionless form. The equation of motions was turned into discrete equations by Galerkin's method. For each mode, the stability of the rotating beam was analyzed by the method of multiple scales and Floquet theory. The differential equations were also solved by Runge-Kutta method. The phenomena of stability analysis and spectrum analysis are discussed. Finally, the time responses of the beam are showed and discussed.
