Comparison of EHL central stress fitting formula and Hertz formula in gear line contact

The following figure shows the comparison of EHL central stress and maximum Hertz stress calculated by fitting formula under different speeds and loads. The viscosity is included in the formula. In order to make the research more in line with the engineering practice, the viscosity is selected here. Other calculation parameters are: α ‘= 2.2 × 10-8 m2 / N, e’ = 226 GPA, r = 0.02 M. the linear velocity V1, V2 and V3 of the three calculation conditions are 1.0 m / s, 60 m / s and 150 m / s, respectively.

It can be seen from the figure that the calculated value of EHL central stress fitting formula is very close to that calculated by Hertz formula. The larger the load and the lower the speed, the smaller the relative error between them. Under the condition of high speed and light load with 150 m / s online speed and 0.1 GPA Hertz stress, the maximum relative error is 12%, but the absolute error is only 0.012 GPa. In a wide range of parameters, the relative errors between the EHL central stress fitting formula and Hertz formula are within 10%.

Because Hertz contact can be regarded as a special case of EHL when the speed and viscosity of lubricating oil are equal to zero, it can be considered that the fitting formula of EHL central stress which takes into account the speed, oil viscosity, load and other factors is more consistent with the actual working condition of gear contact stress under EHL condition than Hertz formula, and the fitting formula can completely match Hertz’s The same formula is used as the basis of gear contact strength design.