A revised Lewis bending fatigue stress capacity model for spur gears is presented and used to study the influence of mesh friction on root stress. It took the original Lewis formula and made modifications for dynamic loads, shear stress, and mesh friction in spur gear design. The study reveals that mesh friction may increase bending stress by up to 6% in enclosed cylindrical gear drives when an average mesh friction coefficient of 0.07 is assumed. A possible increase of 15% in root stress may occur in open gear drives when the mesh friction coefficient is taken as 0.15, a value considered to be representative for properly maintained open drives. To account for mesh frictional load and other factors directly influencing mesh friction, a friction load factor of 1.1 is suggested and introduced to gear service load estimation for enclosed gear drives and 1.15 for open gear drives.

A single expression for estimating the nominal pitting strength of steel materials, based on surface hardness, is developed from first principles for a reliability of 99% at 107 load cycles. It requires the hardness values to be measured in Vicker's hardness scale. The expression may be used for any steel material processed by hot rolling, cold drawing, quenching and tempering or case-hardening. The formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the expression are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources as indicated in Tables 3 and 4. The expression predicts lower values at low hardness but higher values at high hardness. The variance is between - 15.21% and 10.13% for through-hardened steels. For case-hardened steels, the variances range from 14.23% to 20.26% between the estimates and available data. These variances appear to be reasonable considering the many factors involved in pitting resistance. The main advantage of this study is that pitting strength of new steel materials may be estimated for initial design sizing without long and costly contact fatigue testing which of course is necessary for design validation. Also, the estimation method developed may be applied to other materials, metallic and non-metallic. Suggestions are made for estimating some pertinent pitting strength adjustment factors when considering field or service pitting strength.

An attempt is made to predict the pitting strength of cast iron and copper alloy materials from their compressive yield or compressive proof strength for a reliability of 99% at 107 load cycles. The compressive yield or compressive proof strength is related to the tensile strength of ductile cast iron and copper alloy materials by a proportionality factor. Two proportionality factors are used for brittle cast iron materials. The pitting strength formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the predictions are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources. The predicted values for gray cast irons had variances in the range of -11.28% to 25%. Ductile cast iron pitting strength estimates deviated from those of AGMA by -30.28% to 1.73% and 16.76% to 36.34% for Austempered ductile irons. The variances obtained for cast bronze were from 11.17% and 14.73%, but the sample size was small. These variances appear to be reasonable due to the many factors that can influence pitting resistance. Since pitting strength data for many grades of cast iron and copper alloys are not available (especially in the public domain), they may be estimated by the expressions developed in this study for initial design sizing. Also, the pitting strength of new cast iron and copper alloy materials could likewise be estimated for initial design sizing. This will eliminate long and costly contact fatigue testing at the initial design phases, which of course is necessary for design validation.

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Helical bevel gears have inclined or twisted teeth on a conical surface and the common types are skew, spiral, zerol, and hypoid bevel gears. However, this study does not include hypoid bevel gears. Due to the geometric complexities of bevel gears, commonly used methods in their design are based on the concept of equivalent or virtual spur gear. The approach in this paper is based on the following assumptions, a) the helix angle of helical bevel gears is equal to mean spiral angle, b) the pitch diameter at the backend is defined as that of a helical gear, and c) the Tredgold's approximation is applied to the helical gear. Upon these premises, the contact stress capacity of helical bevel gears is formulated in explicit design parameters. The new contact stress capacity model is used to estimate the contact stress in three gear systems for three application examples and compared with previous solutions. Differences between the new estimated results and the previous solutions vary from -3% and -11%, with the new estimates being consistently but marginally or slightly lower than the previous solution values. Though the differences appear to be small, they are significant because the durability of gears is strongly influenced by the contact stress. For example, a 5% reduction in contact stress may result in almost 50% increase in durability in some steel materials. The equations developed do not apply to bevel crown gears.