In the field of engineering technology, the method of finite element analysis has been widely used. It has involved many fields. At first, it was mainly used in structural static analysis, and now it has been extended to many complex problems such as structural dynamics, acoustics, hydrodynamics and so on. For the finite element analysis of spiral bevel gear, the solution steps are as follows:

(1) Create three-dimensional geometric model of spiral bevel gear;

(2) The geometric model of spiral bevel gear is discretized;

(3) Determine the load, displacement, speed and other boundary conditions of spiral bevel gear;

(4) The stiffness matrix and equilibrium equation for this problem are created;

(5) Solving equations;

(6) The calculation results are obtained, sorted and analyzed.

The contact between multiple parts is a highly nonlinear behavior with boundary conditions. In the process of contact, there are geometric nonlinearity, material nonlinearity and contact surface nonlinearity at the same time. The contact of spiral bevel gear changes with the rotation or deformation of the gear. The contact problem of spiral bevel gear is complex. In the calculation and analysis, it is necessary to accurately track the movement of tooth pairs in the contact area and the interaction between tooth pairs. At every moment in the low-speed loading process of spiral bevel gear, the system is close to a balanced state, and a series of near balanced states constitute the whole meshing process of the gear. Static meshing refers to the meshing process close to the equilibrium state. Static meshing does not consider the influence of gear pair inertia, but mainly investigates the meshing characteristics of gear pair during loading, such as the variation law of tooth surface and tooth root stress. The purpose of static finite element analysis on the meshing performance of spiral bevel gear is to observe the variation law of tooth surface contact stress and tooth root bending stress of the gear under low-speed operation. It can also check the correctness of the established finite element model and verify whether it is consistent with the actual meshing law of spiral bevel gear, Thus, it lays a foundation for further high-speed dynamic transient meshing simulation.

The static analysis ignores the influence of damping and inertia on the results, and mainly investigates the mechanical analysis of the model under constant static load. Contact problem is a typical nonlinear problem. The logical flow of contact algorithm created based on Newton iterative method in ABAQUS.

ABAQUS divides the analysis and calculation process into multiple load increment steps, and judges whether the dependent node is open on the contact pair by observing the interaction state between all contact surfaces on each increment step. Only after the reasonable solution of each incremental step is obtained through multiple iterations, can the next incremental step be solved. The sum of all incremental step responses constitutes the approximate solution of nonlinear analysis. P represents the contact pressure value on the slave node; H represents the distance of the slave node invading the master surface. If a node is closed, you need to determine whether the node is bonded or sliding. The software imposes corresponding constraints on the closed nodes, releases the constraints of each node after changing the contact state, and then carries out iterative solution.

The software checks the change of contact conditions on the slave node before checking the force or torque balance of the two spiral bevel gears in contact. If the gap of the contact pair becomes zero or negative after iteration, the contact pair will change from open state to closed state. If the contact force of the contact pair is negative, the contact pair needs to change from closed state to open state. After the first iteration, the software needs to modify the contact constraints and try the second iteration. Repeat this process before completing the iteration without changing the contact state. Check the convergence after the first balance iteration. The software will perform another iterative solution after the convergence check fails. ABAQUS / standard repeats the entire iterative process before convergence. There is no default physical quantity unit in ABAQUS software. In the process of analysis and calculation, we must meet the unity of each physical quantity unit.

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