| The contact fatigue strength design of involute cylinder gearing is based on Hertz theory. However, this theory is only suitable for the frictionless, static dry contact between two smooth surfaces, which is inconsistent with the reality of industrial gear drive. As everybody knows that the friction is inevitably produced by the relative slide between two teeth faces. In addition, all teeth faces are rough and mesh in the lubrication state. So the bearing load is shared between the lubricant film and rough peaks on teeth faces, which implies that the overwhelming majorities of gear drives are operated under the state mixed elastohydrodynamic lubrication. Therefore, the current study is of both theoretical significances and practical values.The model for computing the frictional coefficient between teeth faces at the state of mixed elastohydrodynamic lubrication is first established and more than 80 sets of numerical calculations are completed. The computational results show that when the film thickness ratio λ<1.6 frictional coefficient μ is drastically decreased as λ rises; Thereafter it decrease smoothly when λ≤4. 5; When λ >4. 5, however, it goes up again with λ, which indicates that the excessive film thickness ratio (the excessive lubricant viscosity ) will deteriorate gear wear. In addition, the formulae for determining the frictional coefficient are formed through the regression analyses of computational results.Mixed EHL numerical computation is emphasis and difficulty for the current paper. The difficulty lies in the slow convergence rate.To overcomethe difficulty the paper has made an analysis of convergency of Reynolds equation using functional theory. Based on this analysis the computational speed is increased by 6-30 times as much but the computational accuracy is just the same as the others', which is gained from a reasonable discrete of the computational domain and the adoption of fast iteration method as well as a careful choice of the computational initial values. Applying the revised program, the paper has completed about 40 mixed EHL numerical computations. The computational results show that both the pressure distribution and film thickness distribution fluctuate obviously and a serious stress concentration occurs within subsurface for rough tooth face comparing with those for smooth tooth face. Due to teeth roughness average film thickness for rough tooth face hav,r increases instead of decreasing comparing to the hav,s for smooth tooth face and the difference range between two is related to film thickness ratio λ:The computational results also show that subsurface maximumprincipal shear stress τmax,r for rough tooth face is always greater than theτmax,s for smooth teeth. The difference range between the two decreaseswith an increament of film thickness ratio λ. When λ >2.3, however, theratio between the two tends to become constant:More than 100 sets of EHL numerical calculations are also completed by the paper and based on the regression analyses of computational results the quantitative relations between the gearing contact stress and the gearing parameters are given. And then the paper defines a non-dimensionalparameter-- the lubrication state parameter Jr.It can be seen that the parameter is determined by gearing design parameters and lubricant' properties whose value affects the form of pressure and subsurface stress distributions. When Jr <12.0 the difference in pressure and subsurface stress distributions between Hertz contact and the lubrication contact is trivial, merely having slight stress concentrations near tooth face beneath the pressure peak; When Jr ≥12.0, however, the difference is marked, a notable pressure peak occurring at exit end of contact zone and having serious stress concentrations near tooth face beneath the peak.In order to verify the above theoretical results six sets of fatigue tests with rollers are conducted and the experimental results support better the theoretical results. Both the theoretical and experimental results indicate that there is a parabolic relation between gearing contact fatigue life and the lubrication state parameter Jr. When Jr< 9.0 the fatigue life N is increased as the lubricant viscosity or rotational speed rise; When Jr≥ 9.0, however, the fatigue life N is decreased as the viscosity or speed rise. Especially when Jr≥ 12. 0, the fatigue life N when gears are lubricated is less than the life for dry contact. The current results show that in order to get an optimum gearing fatigue life the lubricant's viscosity should be determined byBased on the above results the paper considers that the two factors have some limitations recommended by the current design standard of gearing contact fatigue strength (ISO/TC60 423E) which gives the lubrication factor ZL and speed one Zv in order to consider the lubrication effect. But the values of the above two factors are monotonously going up as the viscosity and the speed rise respectively. The reason for this was that the above factorswere acquired from the inference of a few experimental results and are in lack of theoretical bases. So they have some limitations. To overcome the limitations the synthetic lubrication factor ZLv and roughness factor ZR are raised. The factor ZLv has considered the synthetic effects of the number of teeth, module, load, rotational speed, material and lubricant's properties and the orther factor ZR reflects an important effect of surface roughness on gearing contact stress. Two factors are then used to revise the current formula for designing gearing contact fatigue strength so as to make design results more objective, scientific and safe.The defects of the current study lie in that quantitative verifications are insufficient because the test data are limited. In addition, the temperature effect is simplified in numerical calculations and theoretical research is roughly assumed the isotemperature condition. It is one of the research objectives to probe into the mixed thermal EHL of involute gear drives when energy equation is included in numerical computations.
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