Calculation of toothed gear mechanisms in machines and assemblies considering the effect of lubricants

Abstract

The basic criteria of operational efficiency of most toothed gear mechanisms is the contact endurance of the conjugated surfaces of the teeth and the flexural endurance of teeth legs. In this case, the calculation based on contact stresses is the principal one in terms of determining the geometrical dimensions of toothed gear mechanisms, while the calculation of tooth bending is performed for validation.It is known that in order to prolong longevity and improve operational efficiency and load capacity of toothed mechanisms, different lubricants are used. However, given the insufficient body of research into the influence of a lubricant on contact endurance of the active surfaces of teeth, traditional methods for the calculation of toothed gears (for example, GOST 21354-87) equate a lubricant influence coefficient to unity, that is, a perfect case is considered when friction is absent. Such an approach leads to the inaccurate evaluation of load capacity of toothed gears that can be a reason for both their premature failure and the overestimation of their geometrical dimensions.In this work, we have solved the contact problem on a contact between two bodies of arbitrary shape, close to half-planes, at the finite friction coefficient; it was found that the value of the resulting contact stress exceeds the stress, calculated according to the known Hertz solution, by 6 %.The proposed procedure for the calculation of toothed gears in terms of contact strength at the finite friction coefficient, without assumptions about the smallness of the contact area and the shape of borders, makes it possible to estimate load capacity of the toothed gears considering the influence of lubrication and the existence of friction between the conjugated surfaces of the teeth.We have derived the analytical expression for a lubricant influence coefficient based on the solution to the contact problem of pressure from a rigid stamp on the elastic half-plane in terms of the coefficient of friction between the conjugated surfaces of toothed gears. That allows the estimation of the true load capacity of toothed gears under the influence of various lubricants, which is of great theoretical and practical importance when designing machines and assemblies