The basic theory of gear meshing stiffness is deduced by energy method

(a) Axial compression effect (b) Bending effect (c) Shear effect

According to the theory of mechanics of materials and elasticity, a beam/bar with equal section length of Z is taken as an example, as shown in Fig. (a). Under the action of a tensile or compression load, within the elastic deformation range of the material, the amount of deformation is Ai. Assuming that the beam/bar is always in static equilibrium during the deformation process, the theoretical formula 2 can be deduced according to the linear deformation to obtain the deformation amount Al. The work done by load F can be completely converted into the potential energy of the beam/bar, as shown in Formula 3. Substituting Formula 1 and Formula 2 into Formula 3, the incremental potential energy function of the beam/bar related to various geometric parameters and loads can be deduced. Similarly, the incremental functions of work and potential energy under the bending effect (Fig. (b)) and shear effect (Fig. (c)) are shown in Formula 4 and Formula 5, respectively.


F — acting load, N;

E — elastic modulus of the material, N/m2;

G — shear modulus of the material, N/m2;

A– Cross-sectional area of beam/bar interaction surface, m2;

I– moment of inertia of beam/bar action, m4.