Modal Analysis of Double-Helical Planetary Gears With Numerical and Analytical Approach

Abstract

The vibration modal properties of double-helical planetary gear (DHPG) system with three-dimensional motion are investigated with a combined use of numerical and analytical approach in this paper. The lumped-parameter model of the DHPG considering stiffness coupled between the left gear and the right gear is developed. Load-sharing with journal bearings is accepted in this planetary gear system, so that four stiffness coefficients can be applied to describe the dynamic behavior between the planet gear and the carrier. The model has three planar degrees of freedom for the carrier and an added axial degree of freedom for all gears, considering the effect of axial dynamic forces. The vibration equations are obtained according to Lagrange equation. A modal type distribution map is plotted initially to simplify modal classification. With the application of this modal type distribution map, all vibration modes are categorized distinctly into three essentially different types of modes including planet mode (PM), rotational-axial mode (RAM), and planer-translational mode (PTM). Unique characteristics of these vibration modes, such as, eigenvalue number, multiplicity of natural frequencies and deflection relations, are deduced and proved analytically. For each type of vibration modes, the reduced-order eigenvalue problems are derived.