# Strength and axial stiffness check of spiral bevel gear planetary gear box

The basic ideas of finite element analysis are summarized as follows

1) The continuous structure is discretized into a calculation model composed of various elements. After discretization, the elements are connected with each other through nodes.

2) By using the idea of piecewise interpolation, the finite element equations are established, and the original function problem of infinite degree of freedom is transformed into the function problem of finite degree of freedom.

3) The basic equations and boundary conditions of the original function problem are equivalent transformed by using the variational principle or the weighted residual method. The ordinary differential equations or algebraic equations are established, and the approximate values are obtained by using the numerical solution method.

If the axial force of reducer box is too large, the box will be deformed and the transmission precision will be reduced. The grid division of the box and the 20KN load diagram of the box are shown in Fig. 1.

Figure 2 shows the equivalent stress and axial deformation of the box. The maximum equivalent stress of the box is 332.03 MPa. The yield strength of 7075 aluminum alloy box material is σ s = 455 MPa ≥ 332.03 MPa, and the box meets the strength requirements.

The maximum axial deformation of the output shaft is 0.00927 mm, and the axial stiffness k = 2.16 × 109n / m ≥ 1 × 108n / m. the box meets the stiffness requirements, and its deformation does not affect the normal operation of the transmission device. 