Study of Torsional Vibration under a Transient Regime in a Gear Mechanism

Abstract

This study develops a conceptual model of a gear transmission system (branched system) to determinate its natural frequencies and modes of torsional vibration, as well as to analyze the system response to a sinusoidal impulsive force that simulates the starting stage (transitional state). The methodology consists at first in a bibliographical review and the study of torsional vibrations, natural frequencies and modes of vibration, conceptual models of torsional systems and torsional vibrations in the starting stage. Subsequently, a conceptual model of the transmission mechanism was developed by obtaining the system of differential equations of motion with three degrees of freedom using the Lagrange equations. For that, three cases of analysis were defined, considering variations in the parameters of rigidity, inertia and transmission ratio for each case. Further, we created algorithms in MATLAB to produce the characteristic curves that allow us to study the behavior of natural frequencies, modes of torsional vibration and system response under transient state. Lastly, we analyzed the equivalent system of three degrees of freedom by the finite element method (FEM) to obtain the natural frequencies of torsional vibration using SolidWorks. The results show that increasing the transmission ratio and keeping the other parameters constant, the response amplitude in the motor shaft section reaches maximum values compared with amplitudes obtained varying these parameters. In the section of the driven shaft, the amplitude decreases until being smaller than the impulsive force amplitude. Likewise, the increase of the transmission ratio and drive shaft rigidity rise the natural frequency of the system. The application of FEM is an alternative method for the dynamic analysis of torsional systems; its results are similar to those obtained by the analytical method. It is very important to consider the measurement and control of torsional vibrations in the predictive maintenance program of rotary machines in industry in order to avert mechanical failures due to torsional stresses leading to fatigue failures.