Torsional Vibration Modal Analysis Method Of Long Cascade Shaft System Based On Effective Inertia Concept

With the increase of power and parameters of the steam turbine,the diameter of the blade at the end of the unit is also increasing gradually.In this case,it will lead to calculation error if the long cascade still simplified as a rigid body to calculate the torsional vibration mode and frequency of the steam turbine,and also can not quantify the damping effect of the cascade on the shaft torsional vibration.In this paper,the concept of effective inertia is put forward from the modal mass and the effective mass,and the formula of calculating the effective inertia with kinetic energy,frequency and reaction is derived.Then,combine with the finite element technology,the method to calculate the effective inertia through the modal analysis is found.On base of above,a method to obtain the rule about effective inertia of arbitrary structure long cascade with different torsional vibration frequency is proposed.Finally,on the basis of this rule,a torsional vibration modal analysis method is proposed,which replaces the long cascade model with effective inertia value.Through the comparison and analysis,it is proved that the method can be used to calculate the torsional vibration mode of the branch system model and improve the accuracy.It can also be applied to the finite element technology of simplify shaft system and reduce the complexity and resource consumption without significantly affecting the accuracy of the finite element analysis.Through the work in this paper,the torsional vibration modal analysis of the shaft with long cascade structure has been further studied,and a method is proposed which can help to solve the problem that the branch system is difficult to modal the shape of the bending and twisting blades and consider the damping.At the same time,it avoids the problem of large consumption of finite element model,and provides a new solution to reduce the complexity and resource consumption of the model under the premise of ensuring the accuracy of calculation.