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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 1 st to 4 th 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. Modal analysis is a basis of transient dynamic analysis, load prediction, spectrum analysis, modal superposition method for response (to determine the fatigue life, dynamic strength etc.), vibration control, vibration acoustic character- istics estimation and control, fault vibration and prediction and dynamic optimization design (3-5). Obtained the natural frequency of the structure by modal analysis can avoid the occurrence of resonance phenomenon, and provide some measures to reduced vibration, shock and noise. It is difficult to establish a real constraint conditions and the incentives are very complex during the finite element constraint modal analysis for the spiral bevel gear wheel, because of the spiral bevel gear wheel with very complex constraint conditions, while the free modal itself reflects the spiral bevel gear wheel inherent dynamic characteristics (6-9), so the free modal analysis of a mini bus main reducer spiral bevel gear wheel has been done in this paper.

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