| Summary: | 博士 === 國立中正大學 === 機械工程所 === 98 === The dynamic response of a rotating multi-span shaft with rigid supports or elastic supports subjected to an axially moving force is investigated. This study can be applied on the dynamic behaviors of a rotating workpiece subjected to cutting forces along the longitudinal axis, for example, turning, grinding, and other rotating mechanisms subjected to applied moving forces. The assumed mode method is employed to analyze the deflection of flexible shaft and two types of assumed mode functions are used. One is eigenfunctions and the other is polynomial functions. In general, the conventional assumed mode method (AMM) uses eigenfunctions. Although using the eigenfunctions can accurately obtain numerical results, the calculate process is so complex for solving the eigenfunctions of system, especially for the shaft with multi-span or elastic supports. Therefore, the assumed mode method based on the eigenfunctions is only applied on the single-span shaft with simply supports in this study. As for the multi-span shaft, the polynomial is chosen as the assumed mode functions. Since there are no geometric requirements on the polynomial expansion and no nodes exist at some positions, the method can be directly applied on the multi-shaft with elastic supports. However, for the multi-shaft with rigid supports, the transformation matrix composed of geometric constraint equations is proposed to force system equations of motion to satisfy the zero deflection constraints at the supporting positions. And the system dynamic response is solved by the Runge-Kutta method. In this study the assumed mode method with polynomial functions is also called global assumed mode method (GAMM). To ensure the validity of the method, this study performs the convergent test of the dynamic response with respect to the number of assumed mode functions and gives a comparison of natural frequencies obtained with the present method and finite element method. The numerical results indicate that the global assumed mode method shows good performance to deal with the multi-span shaft and avoids the complex process for obtaining system eigenfunctions. Moreover, the effects of the rotational speed of shaft, moving speed of force, number of spans, stiffness of elastic support, and various boundary conditions on dynamic response are investigated.
In the last chapter, the dynamic response of a screw in grinding is analyzed by using the assumed mode method based on the eigenfunctions. The screw is modeled as a simply supported Timoshenko beam and the grinding force is regarded as a moving regenerative force. The force describes the nonlinear interactions including the effects of wheel wear, time-delay, and the possibility of contact loss between the grinding wheel head and screw. In addition, The effects of the depth of cut and the rotational speeds of grinding wheel and screw on dynamic response are studied.
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