# Comparison of gear design results based on EHL central stress formula and Hertz stress formula

1 Influence of speed

The main parameters are as follows: helix angle β = 8.11 °, η 0 = 0.15 PA · s, α = 20 °, μ = 2.52, Ze = 189.8 mpa1 / 2, [σ H] = 800 MPa, k = 1.5. The diameter required for the gear to meet the contact strength requirements is calculated with the formula when the speed changes from 1 m / s to 30 m / s. The results are shown in Fig. 1.

The curves of ①, ② and ③ in Fig. 1 are the variation diagram of gear diameter designed based on EHL central stress and gear diameter with speed designed based on Hertz formula when the transmission power is 5kW, 20kW and 100kW respectively. It can be seen from the figure that the calculation results of the two methods are almost the same. The maximum relative error of the three groups is only 4.4%.

2 Power effect

The three groups of curves (1, 2 and 3) in Fig. 2 show the variation of design results with power based on EHL central stress formula and Hertz formula when the linear velocity is 1 m / s, 10 m / s and 30 m / s, respectively. It can be seen that there is no difference between the two results. The maximum relative error of the three groups is only 3.5%.

3 Effect of lubricant viscosity

Lubrication is very important for gears, so the influence of lubricant viscosity on gear design results is specially calculated. The results are shown in Fig. 3.

In Fig. 3, the curves of ①, ② and ③ correspond to three working conditions of low speed light load (1 m / s, 5 kW), medium speed medium load (10 m / s, 20 kW) and high speed heavy load (30 m / s, 100 kW). It can be seen from the figure that the change of lubricating oil viscosity has no effect on the design result based on Hertz formula, but has little influence on the design result based on EHL center stress, but it is very small. In Figure 3, the maximum relative error between the design results based on EHL center stress and that based on Hertz formula is 5.7%.

Based on the above, it can be concluded that the gear contact strength design formula based on EHL central stress fitting formula can be used in gear design and meet the engineering needs. 