FEM in Numerical Analysis of Strains Distributions and Mashing Modyfication in Planetary Cycloidal Gear
by
Antoni John
Silesian University of Technology, Department for Strength of Material and Computational Mechanics, Konarskiego 18A, 44-100 Gliwice,Poland,
Coauthors: Manfred Chmurawa (Silesian University of Technology, Institute of Transport, Krasinskiego 8, Katowice, OBRDiUT,"DETRANS", Bytom, Poland)

In heavy industry, high speed engines are used for many types of machines it requires application high ratio mechanical gears. The most frequently planetary gears with involute meshing are used. It causes that sliding friction appear. Currently, a group of advanced cycloidal gears exists, where only the rolling friction appears and it causes lower level of energy dissipation. Relatively, the smallest mechanical gear with high ratio at one stage and high efficiency is the cycloidal planetary gear (CPG) known as cyclo gear. The main problem in cycloidal planetary gears is the load distribution in mashing area with respect to stress distribution and initial backlash. Outline of planet wheel is an equidistant of shortened epicycloid. The complicated geometry and loads cause the analytical solving very difficult or even impossible. It is reason the numerical methods, mainly finite element method (FEM) should be applied. Individual stages of the modelling process are presented below. Knowledge of calculating planetary gears and numerical methods enables including following precise assumptions: real, elastic planet wheel described by its geometry and material features neglecting simplifying assumptions to calculate forces between teeth and reactions basing on strains resulting from rotation angles of rigid planet wheel and rigid plate of straight line mechanism, substitution of concentrated force R for distribution and configuration of forces resulting from pressure of active rolls of eccentric bearing as the function of radial clearance g. The model of meshing as the shape of equidistant of shortened epicycloid was created in two main steps: generation of the curve points (equidistant) on the basis of parametric equations with given tolerance every 0, 050 or 0, 10, connection of curve points in one closed shape basing on interpolation of set of curve points. In the paper it has been presented a trial of implementation of FEM for calculation distribution of reduced stresses and displacements in high effort points of planetary gear. Applied numerical method in higher level approximates calculation model to conditions in real gear. Values of forces has been calculated for given size of cycloidal gear with ratio i = 19, power N = 3, 7 kW and rotational speed nh = 750 rpm. Meshing of toothed wheels with elements of CPG is characterized by coplanar forces and can be modeled in coplanar state of stress. FEM has been used for calculation for which series of interacting models has been worked out with implementation of surface elements 2D.

Conclusions Mating of planet wheels with elements of CPG can be modelled in 2D strain state by FEM with implementation of 4- or 8-node elements 2D solid The major influence on distribution of loads in planet wheels has the construction of wheel which depends on ratio and number and diameters of bearing holes. FEM enables visualisation of distribution of stresses sred and distribution of strains di practically in every point in planet wheel. Obtained distributions enable fast identification of highly loaded parts of the wheel and pointing local highest stresses. Strain distribution in mashing area can be used to shaping the initial backlash in cyclo gear. Obtained results of calculations can be a base to work out more precise strength calculations concerning mainly contact strength and fatigue life of toothed wheels of cycloidal gear.

Date received: January 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-60.