Constraint and Load Handling To simplify the calculation, a single pair of meshing tooth contacts in the two contact gears is selected as the actual analytical model of the gear contact. It is specified that the displacement of the driven gear boundary node is zero, so the driven gear applies a fixed constraint to fix the driven tooth root surface. For the driving gear, in order to transmit the driving torque acting thereon to the driven wheel, the rigid body rotational degree of freedom must be retained, so that a linear distributed surface stress is applied to the driving gear to form a force constraint of the gear teeth. The external load is applied by converting the drive torque into equal node forces acting on certain nodes of the drive wheel in the direction of motion. According to the above modeling method, the author has compiled a three-dimensional contact stress boundary element analysis modeling program for spur gears.

By using the program, the gradient boundary element mesh can be automatically generated by inputting the basic parameters of the tooth profile, that is, the number of teeth of the main and driven gears, the modulus, the pressure angle, the tooth width, the elastic modulus of the material, and the Poisson's ratio. It is feasible to calculate the three-dimensional contact problem of the spur gear with the stress analysis program of this paper. The analysis results show that the boundary element method is simple, accurate and reliable for analyzing the stress of gears. The author uses the boundary element to make a detailed analysis of the contact area stress of the gears that are in contact with each other. This has practical significance for understanding the gear contact stress and exploring the real cause of the tooth surface failure. As an analysis of gear contact and extrusion, it is beneficial and necessary to understand the distribution of static pressure and load distribution.

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