Free Modal Analysis for the Pinion of Logarithmic Spiral Bevel Gear with 20CrMnTi

Abstract

In order to obtain the pinion's natural frequencies and mode shapes of a new kind of spiral bevel gear (SBG) which is logarithmic spiral bevel gear (LSBG) in the unconstrained state for the purpose of dynamic characteristics study, select the low carbon alloy steel 20CrMnTi (China specification) with good mechanical properties, which the carbon content is 0.17%-0.23%, the elastic modulus E=2.06675×1011Pa, the Poisson's ratio is 0.25, and the density is 7.85×103kg/m3, the finite element model of LSBG pinion which consist of 35100 nodes, 19889 Solid187 tetrahedron FEM elements is established by using free meshing method based on LSBG pinion's physical model in this paper. Solve the modal parameters of the first 6 orders, draw the main vibration mode shape according to the first 6 orders natural frequencies respectively. The first 6 orders critical revolution speeds are calculated by the first 6 orders corresponding natural frequencies, and the LSBG pinion allowable work revolution speeds are 117074.16 revolutions per minute. The free modal analysis of the conventional SBG pinion with the same parameters is done for comparison with LSBG pinion. The results show the LSBG pinion's nature frequency and the critical revolution speed are both lower than that of conventional SBG. The conclusions reflect the vibration response characteristics of LSBG pinion, and provide theoretical basis for dynamic response, structure design and optimization of LSBG pinion.