Planetary gear sets are preferred in many power transmissions for their advantages such as higher power density, lower radial support loads, lower noise levels, greater kinematic flexibility, and manufacturing error insensitivity compared to counter-shaft gearing. One potential disadvantage of planetary gear sets is power losses due to multiple planet branches, resulting in increased numbers of gear meshes and bearings. The main goal of this study is to theoretically and experimentally investigate the power losses of planetary gear sets.
An experimental power loss database for planetary gear sets is first developed through tightly-controlled experiments. Dependence of power loss on operating conditions is quantified. The influences of number of planets and planet surface roughnesses on planetary power loss are also included in the experimental test matrix.
Sources of planetary gear set power loss are grouped in two categories as load-dependent and load-independent losses. Major components of load-dependent power loss are gear mesh and planet bearing mechanical losses while load-independent power losses are formed by gear and carrier drag, planet bearing viscous losses, and gear mesh pocketing losses. Experimental data is analyzed to separate the load-dependent and load-independent effects, and separate modeling studies are performed corresponding to each. For modeling of the gear mesh mechanical losses, gear and carrier drag losses, and planet bearing viscous losses, well-established modeling methodologies from recent literature are employed. In order to bridge the gaps in the literature, novel models for planet bearing mechanical power loss, and internal and external helical gear mesh pocketing power loss are developed.
For prediction of planet bearing mechanical power losses, a planet bearing load distribution model is first proposed to predict load intensities along the roller contacts due to combined radial force and overturning moment caused by helical gear mesh forces. This model takes into account planet bearing macro-geometry as well as micro-modifications to the roller and race surfaces. Predicted load distributions, bearing kinematic relationships and an elastohydrodynamic rolling power loss model are combined to predict load-dependent power loss of a planet bearing.
A new fluid dynamics model is proposed to predict pocketing power losses at both external (sun-planet), and internal (ring-planet) meshes of a planetary gear set. A numerical procedure and companion discretization scheme are proposed to quantify the pocket volumes, escape areas, and area and volume centroids from the transverse involute geometry of helical gears. Conservation laws of mass, momentum, and energy are applied to the governing multi-degree-of-freedom fluid dynamics system to predict power losses due to squeezing of air, oil, or an air-oil mixture from gear meshes.
Models for key components of planetary power loss are brought together in a single methodology to predict both load-dependent and load-independent power losses of a planetary gear set, including mechanical gear mesh (internal and external) losses, mechanical and viscous planet bearing losses, gear mesh pocketing (internal and external) losses, and gear and carrier drag losses. This methodology is used to simulate the planetary power loss experiments to demonstrate its accuracy within wide ranges of operating, lubrication, surface, and design conditions.