Modal Analysis of Worm and Worm Gear Based on ANSYS Workbench

To establish the three-dimensional model of the worm and worm gear by using SolidWorks. On the worm and worm gear modal analysis is carried out by using finite element analysis software ANSYS Workbench. Obtain the first 6 order natural frequency and vibration mode characteristics of worm and worm gear. Modal analysis laid the foundation for further study on dynamics analysis, Also for the worm and worm gear structure optimization design provides a reference.


Introduction
Worm and worm gear mechanism used to transmit motion and power between the two crossed axis, high transmission ratio can be achieved, and also can achieve self locking [1] .The research object of this paper is a pair of ordinary cylindrical worm and worm gear which is applied in automobile automatic clutch.Due to Vibration will cause structural resonance or fatigue, lead to damage of the clutch structure, for the worm and worm gear are easy to produce resonance problems, to prevent the resonance, modal analysis is necessary for the worm and worm gear.
ANSYS Workbench is a new generation product development platform , which is a large scale general finite element analysis software with structure, fluid, electric field, magnetic field, sound field analysis, with CAD seamless interface, Parametric modeling tools of a new generation, achieved data share and exchange, its powerful analysis function can accurately reflect the actual object state [2] .

Establishment of Finite Element Model
As the new interface of ANSYS, ANSYS Workbench can achieve seamless connection with CAD system, it is very convenient to make the CAD model import into the ANSYS Workbench [3] .The worm and worm gear model is saved as STP format file, And then imported to the ANSYS Workbench Geometry, before modal analysis, first of all, to set the material and its properties, in this paper, the material of worm is No.45 steel, density ρ 1 =7.85g/cm3, modulus of elasticity E 1 =209GPa, Poisson's ratio μ 1 =0.269; the material of worm gear is POM, density ρ 2 =1.39g/cm3, modulus of elasticity

The Constraint Conditions
Using different constraints will have a direct impact on the results of the analysis, different constraint conditions, the modal parameters obtained are also different [4] .For the worm, it can only around its own axis (Z axis) rotation, therefore, to restrict the worm around X, Y axis rotation and move along the X, Y, Z axis; for the worm gear, also it can only around its own axis (Z axis) rotation, limit the other direction freedom.In the modal: for the worm, add Cylindrical Support, and the Tangential is set to Free, and add the Displacement constraint in the worm one side end face, restrictions on the movement of the axial; for the worm gear, add the Fix Support in its rotation center, limit its around X, Y axis of rotation and movement, and add the Displacement constraint on the worm gear end surface, limit the movement along the Z axis.

Modal analysis of worm and worm gear 4.1 Overview of Modal Analysis
Modal analysis is a numerical technique to calculate the vibration characteristics of structure, the structure vibration characteristics including natural frequency and vibration mode.Modal analysis is the basic of dynamics analysis, also is the foundation of other dynamics analysis, such as the response spectrum analysis, random vibration analysis and the harmonic response analysis.
Modal analysis can make structure design to avoid the resonance, help to solve the control parameter in other dynamic analysis [5] .

The Basic of Modal Analysis
No damping modal analysis is a classical eigenvalue problem.The basic equation of dynamics problems is: In the equation( 1): > @ M --mass matrix; > @ K --stiffness; t x --acceleration vector; t --the displacement vector Free vibration of structure is simple harmonic vibration, the displacement as a sinusoidal function.> @ > @ ^`0 x M w K  [6] .

The Result of Modal Analysis
Obtained the worm and worm gear the first 6 order natural frequency and vibration type in this paper, the natural frequency and vibration type description are shown in table The first torsion The second torsion The third torsion The first bending The second bending The third bending

MATEC Web of Conferences
For accurate modeling of the worm and worm gear by using SolidWorks, the model imported into ANSYS Workbench, the model was meshed and added constraints, to obtain the first 6 order natural frequency and vibration mode, and the vibration modes are described.The results of this analysis for the following dynamic analysis and structure optimization design provides an important basis, also laid the foundation for more in-depth study on the vibration and noise problems, to provide a reference and basis for the practical experiment.

E 2 4 MATEC
Fig. 1.The finite element model of the worm and worm gear

Table 1 .
1,table 2. The first 6 order modal shape of worm and worm gear are shown in fig. 2. The first 6 order natural frequency and vibration type description of worm

Table 2 .
The first 6 order natural frequency and vibration type description of worm gear