# Theory of gear meshing stiffness

The comprehensive meshing stiffness of gear is the elastic response of the comprehensive Meshing Effect of each pair of teeth in the whole meshing area, which is directly related to the elastic deformation of single tooth, the comprehensive elastic deformation of single pair of teeth and the coincidence degree of gear system itself. For the spur gear system with coincidence degree greater than 1 and less than 2, the gear includes single tooth meshing area and double tooth meshing area in one meshing cycle. In the single tooth meshing region, the gear comprehensive meshing stiffness (km) can be defined as:

In the formula: KP is the stiffness of the driving gear, kg is the stiffness of the driven gear, KH is the Hertz contact stiffness, and the calculation expression of the Hertz contact stiffness is as follows:

In the formula, e is elastic modulus, B is tooth width, V is Poisson’s ratio.

In the double tooth meshing area, the method to calculate the combined meshing stiffness of two pairs of gears is to add the meshing stiffness of two pairs of gears together. In the double tooth meshing region, the gear comprehensive meshing stiffness (km) can be expressed as follows:

In the formula: KP1 is the stiffness of the driving gear in the first pair of meshing teeth, kg1 is the stiffness of the driven gear in the first pair of meshing teeth, KP2 is the stiffness of the driving gear in the second pair of meshing teeth, and kg2 is the stiffness of the driven gear in the second pair of meshing teeth.

If the stiffness of the whole gear system changes due to the pitting fault of the driven gear tooth surface in the gear system, the stiffness kg pitting of the gear with pitting fault is used to replace the stiffness kg of the healthy gear to calculate the meshing stiffness of the gear system with pitting fault. In order to calculate the comprehensive time-varying meshing stiffness of a gear system, it is necessary to calculate the meshing stiffness of a single gear separately, and the meshing stiffness of a single gear can be indirectly calculated by the measured gear root strain. 