Optimum designs of operating curves for rotating shaft systems with limited power supplies

A rotating shaft system may happen not to be operated beyond the critical speed in the case of a limited power supply and even if it can pass through the critical speed. It often yields comparatively a large transient dynamic responses. To solve these problems, an optimum design method of the operating curve is shown here for a rotating shaft system with a limited power supply. The operating curve is conveniently expressed by the cubic spline function and position vectors to determine the spline function are taken as design variables. By the gradient - based optimization method, the operating curve is so optimized as to reduce the transint dynamic responses around the critical speed. Several numerical examples are demonstrated and discussed.