Abstract: This paper deals with the design sensitivity analysis of natural frequencies of gear-shaft systems. A method is proposed for establishing the dynamical equation, and the transmission ratio of gears is involved in the dynamical equation by a transmission ratio matrix, which makes the establishing of dynamical equation easier. The formulation of design sensitivity of natural frequencies is derived with respect to design parameters including stiffness of shafts, transmission ratio and inertia of gear or other elements on the shafts. An example is given to illustrate the procedure. The method proposed is of practical importance in the optimization design of gear-shaft systems.

Key words: Gear transmission, Natural frequency, Optimization, Sensitivity, Torsional vibration