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1. Introduction
The efficiency of the gear transmissions may have significant influence not only on the direct operating costs and the operating lives but also on the environmental impact associated to power loss. The efficiency of involute gears is usually high, but uncontrolled friction phenomena may result in surface defects arising after operating periods shorter than the expected ones. These defects will produce higher losses, noise, vibrations, and heat generation during the operation, which may result in the complete failure of the transmission even.
Classic, simple models of efficiency of spur gears available in technical literature [1–5] are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. Neither of them is accurate, but the efficiency of spur gears is high, and very accurate calculations were not required in the past. However, the rapidly rising trend of transmitted power to size ratio may make more accurate models suitable. In this sense, variations of the friction coefficient along the path of contact can be neglected if average values are considered [2, 3, 5]. Nevertheless, errors induced for considering uniform load sharing between couples of teeth in simultaneous contact may be high, especially if errors are expressed in terms of power losses.
Empirical models for load distribution and constant friction coefficient have been used in some studies, as ones of Michlin and Myunster [6] and Höhn et al. [7]. A preliminary authors’ study using a nonuniform load distribution model can be found in [8]. Other models using nonuniform friction coefficient models have been reported by Anderson et al. [9–11], Vaishya and Houser [12], Lehtovaara [13], and Diab et al. [14]. More complex models using the elastohydrodynamic lubrication theory to formulate the variation of the friction coefficient avoiding the necessity of experimental results have been developed by Martin [15] and...