Experimental investigation and FEM analysis of resonance frequency behavior of three-dimensional, thin-walled spur gears with a power-circulating test rig

摘要

This paper is a fundamental study on resonance frequency behavior of three-dimensional, thin-walled spur gears from experimental tests and finite element analyses. Firstly, "power-circulating form" test rig is built for vibration tests of the thin-walled gears at the speed range 500-3000 rpm and then strain phase method is presented in this paper to identify the resonance mode shapes of the thin-walled gears when they are running in a complete resonance state. It is found that when wall thickness of the gear is very thin, vibrations of the thin-walled gear are the 2nd, the 3rd, the 4th order bending vibrations of the rim and the 2nd, the 3rd and the 4th bending vibrations of the web. When the wall thickness is increased, the 2nd, the 3rd and the 4th order bending vibrations of the web disappear and only the 2nd, the 3rd and the 4th order bending vibrations of the rim are remained. Effects of gear wall thickness, teeth mesh stiffness and assembly errors on resonance frequency behavior of the thin-walled gears are also investigated experimentally and peak speeds of the thin-walled gears are measured. It is found that there are several frequency components existing at the same peak speeds of the thin-walled gears. Torsional vibration frequencies of the test rig system are analyses by building an equivalent lump-mass model system. Natural frequencies and mode shapes of the lump-mass model system are analyzed. It is found that calculated natural frequencies of the equivalent lump-mass model system are not found in the measured resonance frequencies of the thin-walled gears. Structural vibrations of the thin-walled gears are also analyzed by using three-dimensional, finite element method (3D-FEM) with 20-noded isoparametric element. It is found that natural frequencies and mode shapes of the thin-walled gear structure calculated by FEM are well agreement with the ones measured by experiments. Effects of tooth module, web thickness, web position, rim thickness, face width and gear hub on natural frequencies of the thin-walled gears are investigated by FEM calculations. It is found that rim and web thickness have greater effects on structural frequencies of the thin-walled gears than other parameters. Tooth module also exerts an effect on the natural frequencies of the thin-walled gears. Finally, close and duplicated frequency phenomenon happened in structural vibrations of the thin-walled gears are stated in this paper.