The investigation of dynamics of misaligned units in vehicle transmission

Abstract

In the article the problems related to the dynamics of a mechanic system on misalignment of shafts in radial direction are presented. The object of the investigation is a two-shaft system connected with an elastic centrifugal ring coupling. Using equations of static equilibrium it was found that an internal moment of resistance to rotation appears in the coupling connecting the radially misaligned shafts. Using Dalamber's principle for the rotational movement the differential equation that describes the rotation of the second shaft has been developed. It was shown that after the perfonnance of the corresponding actions and the introduction of a new variable the said equation is transformed in to an equation which character virtually coincides with the equation describing free oscillations of a mathematical pendulum. Because the value of misalignment of shafts in the radial direction is small in comparison with other parameters, a small parameter method was used for the solution of this equation. The found solutions show that rotational vibrations with the double frequency of rotational movement are excited in the misaligned mechanical system with an elastic centrifugal ring coupling. The restrictions of the application of a small parameters method have been explored and the limits of its application have been found.