# Importance of contact finite element model of spiral bevel gear to finite element calculation

The finite element analysis model is very important for finite element calculation. The models and boundary conditions are different, and the conclusions are inconsistent or even quite different. It mainly depends on whether it can truly reflect the stress and constraints of the entity. The finite element analysis model methods proposed in many articles divide elements and nodes in a standard rule subdomain, and then map them into the mesh of the actual model by isoparametric transformation and other methods. This is only suitable for the finite element calculation of general problems. In the contact problem of gears, the initial clearance of the tooth surface needs to be calculated accurately, and the initial clearance is calculated by the tooth surface coordinates. Therefore, the coordinates of the mesh nodes of the tooth surface can not be approximately generated by isoparametric transformation. In addition, the generation of possible contact points on the meshing tooth surface must be considered, which can only be solved with accurate meshing tooth surface coordinates according to the method in Chapter 3.

The denser the grid of the calculation model, the higher the calculation accuracy, and the computer capacity and calculation time will be greatly increased. It is necessary to reasonably calculate the mesh density of the model, which mainly depends on the following factors:

(1) Computer memory capacity,

(2) Computer operation speed.

For the gear contact problem, it is necessary to accurately solve the shape of the contact area and the pressure distribution. It may be that the preset of contact point pairs is very important. If there are too few preset contact point pairs, the iterative solution of the formula will diverge and the result will be distorted. If there are too many preset contact point pairs, the iterative time of the formula will be too long. The calculation shows that the maximum initial clearance is less than 0.1mm, which is the most reasonable. Only when the initial clearance is less than this value can it be the contact point pair. At the same time, the coordinate value of the contact point pair shall be obtained. The coordinate value of the contact point pair shall not exceed the contact tooth surface, otherwise it shall be eliminated.

When dividing the unit, first mesh the large and small gears, and number the unit and node according to the principle of minimum bandwidth. Then, the coordinates of possible contact point pairs on the pinion tooth surface are solved by using the grid node coordinates of the gear tooth surface, and then replaced by the node coordinates of the pinion tooth surface grid. The alternative method is to search the nearest node in the tooth surface grid coordinates with the generated contact point coordinates, and record the node number of the nearest node, that is, the node number of the corresponding contact point pair.

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