The magnitude and variation of tooth pair compliance affects tooth loading and gear dynamics significantly. This paper presents an improved fillet/foundation compliance analysis based on the theory of Muskhelishvili applied to circular elastic rings. Assuming linear and constant stress variations at root circle, the above theory makes it possible to derive an analytical formula for gear body-induced tooth deflections which can be directly integrated into gear computer codes. The corresponding results are in very good agreement with those from finite element models and the formula is proved to be superior to Weber’s widely used equation, especially for large gears.

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A model is presented which makes it possible to predict power losses in a six-speed manual gearbox. The following sources of dissipation, i.e., power inputs in the model, are considered: (i) tooth friction; (ii) rolling element bearings; (iii) oil shearing in the synchronizers and at the shaft-free pinion interfaces; and (iv) oil churning. Based upon the first principle of Thermodynamics for transient conditions, the entire gearbox is divided into lumped elements with a uniform temperature connected by thermal resistances which account for conduction, convection, and radiation. The numerical predictions compare favorably with the efficiency measurements from the actual gearbox at different speeds and torques. The results also reveal that, at lower temperatures (about 40°C), power loss estimations cannot be disassociated from the accurate prediction of temperature distributions.

A series of formulas are presented which enable accurate predictions of churning losses for one pinion characteristic of automotive transmission geometry. The results are based on dimensional analysis and have been experimentally validated over a wide range of speeds, gear geometries, lubricants, and immersion depths. The case of a pinion-gear pair in mesh has been considered, and it has been proved that, depending on the sense of rotation, the superposition of the individual losses of the pinion and of the gear leads to erroneous figures. A new formula devoted to a pinion and gear rotating anticlockwise has been derived and validated by comparison with experimental evidence.

A model based upon a finite element procedure is introduced for analyzing the influence of tooth friction on spur and helical gear dynamics. The equations of motion are solved by combining a time-step integration method with several iterative algorithms aimed at satisfying normal and tangential contact conditions. Comparisons between simulated and measured quasi-static bearing forces are satisfactory and largely validate the theoretical developments. Results also reveal the potentially significant contribution of tooth friction to gear vibration and noise. Simulations are then extended to high speeds and the interest of considering both transmission error and tooth friction excitations to achieve silent gears is discussed. [S1050-0472(00)02804-X]

An original displacement-based formulation of tooth friction power losses in spur and helical gears is established, which can account for the influence of tooth profile modifications. Several analytical formulas are derived enabling friction losses to be easily estimated for a wide range of gears at the design stage. Numerous comparisons with both the classic formulas in the literature and the results of numerical simulations are presented, which confirm the accuracy of the proposed approach.

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