Free Modal Analysis for Spiral Bevel Gear Wheel Based on the Lanczos Method

Xiang Tieming*, 1, 2, Zhou Shuiting1, Yi Liao1
1 School of Mechanical & Automotive Engineering, Xiamen University of Technology, Xiamen, 361024, China
2 College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, 361021, China

© 2015 Tieming et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Xiamen University of Technology, Xiamen city, Fujian Province, 361024, China; Tel: +86 0592-6291072; E-mail:


In order to obtain the spiral bevel gear wheel natural frequencies and mode shapes in the unconstrained state for the purpose of dynamic characteristics study, the spiral bevel gear wheel three-dimensional solid model of a mini-bus main reducer is established in this paper. The finite element model of spiral bevel gear wheel which consists of 32351 nodes, 18436 solid187 tetrahedrons finite element method elements is established by using free grid meshing method in this paper. Extract the first 6 orders modals parameters such as natural frequencies and main vibration mode shapes by using the Lanczos method. The new 1st to 4th orders modals are formed by comparing and merging 2 orders repeated modals. In order to verify the effectiveness of the finite element analysis results, the experiment modal test based on the impulse force hammer percussion transient single-point excitation and multi-point response analysis method has been done. The maximum difference value of natural frequency between experimental modal test result and finite element modal analysis results is 29.86 Hz, the maximum error rate is 0.41%, which confirmed the result of finite element method is effective and reliable. The conclusions reflect the vibration response characteristics of spiral bevel gear wheel, and provide theoretical basis for dynamic response, structure design and optimization of spiral bevel gear wheel.

Keywords: Experiment modal test, free modal, Lanczos method, mode shape, natural frequency, spiral bevel gear.