Scaling law of gear transmission system obtained from dynamic equation and finite element method

Abstract When the size of the gearbox is too large, the test will be difficult to carry out. It is an effective method to replace prototype with scale model. The original contribution of the paper is that the dynamic similarity theory is introduced into gear transmission system, and a method to predict the dynamic characteristics of gear system is proposed. The scale model of gear transmission system is designed by using dynamic equation and similarity theory, and the scaling law of dynamic response is obtained. By unifying the units of vector, the problem that the similarity ratio of the matrix in the dynamic equation can not be obtained is solved. Taking the parallel shaft gear transmission system as an example, the dynamic responses of different scale models and full size models are calculated by the node finite element method. The validity of scaling law is verified by the free vibration response and forced vibration response of the system. The numerical value and trend of the dynamic response of the full size model at different speeds can be obtained from the scale model.