An experimental and theoretical investigation of power losses in planetary gearboxes

Abstract

Gearboxes based on planetary gear sets are preferred for their advantages, such as higher gear ratios, improved self-centering capabilities, kinematic flexibility, favorable bearing support conditions and higher power densities with less noise in a more compact size. The multiple-planet branches of planetary gear sets are usually symmetric about their axes so they are a more suitable choice in the design of a drivetrain configuration where there is high demand for low-speed high torque, high-speed low torque or both operating conditions. Meeting the design requirements for such drivetrain configurations can result in a compromise between the reliability and efficiency of the gearbox. The main goal of this study is to experimentally and theoretically investigate the power losses of planetary gearboxes.

A planet–sun gear mesh power loss model is first developed to quantify the influence of micro and macro geometry on a single planet–sun gear mesh power loss. Also, several base oil types were investigated to understand their influence on planet gear bearing power loss. Understanding and quantifying the influence of base oil types and viscosity on planet gear bearing power loss is essential as it dictates the effective film thickness at the rolling element-raceway contacts. To account for power losses in a wind turbine gearbox, the planet–sun gear mesh power loss model was further developed to include a non-uniform load distribution model to allow the prediction of the varying gear tooth loads at the planet–sun and planet–ring gear mesh.

Also included is an adjusted local friction coefficient model to allow for the prediction of local friction coefficient values at each contact point on the line of action (LOA). Power losses were grouped into two main categories: load-dependent and load-independent power losses. Load-independent power losses were identified to be non-consequential for wind turbine gearboxes, while load-dependent power losses dictate the total power loss of a wind turbine gearbox. A parametric study helped in identifying several geometrical parameters that can be optimized in a wind turbine gearbox to allow improved energy savings.

Considering that the next generation gearboxes for wind turbines and heavyduty off-road working machines have a planetary gear set incorporated with a permanent magnet synchronous machine, the two groups of power losses initially defined for conventional planetary gearboxes had to be extended to accommodate the power losses arising because of the conventional mechanical gear interaction with permanent magnet electric motors. For this, a methodology for predicting power losses in an integrated planetary gearbox was developed and validated with measurement data from a prototype integrated gearbox. A good correlation between prediction and measurement was successfully achieved and load-dependent power losses were identified as the most dominating power loss components, with a major contribution emerging from the electrical components.

Realizing that the friction coefficient values at the gear and rolling element contacts play a major role in predicting the efficiency of wind turbine gearboxes is the first motivation for developing new closed-form formulae for predicting friction coefficients. The second is that no formula exists for predicting the instantaneous friction coefficient values for wind turbine gearbox contacts. As such, a new family of closed-form friction coefficient formulae is proposed to allow a more realistic prediction of friction coefficient values for wind turbine gearbox rolling– sliding contacts. The new closed-form friction coefficient formulae are based on a comprehensive experimental friction coefficient measurement database which takes into account a wide range of rolling and sliding speeds, surface roughnesses, oil temperature and lubrication conditions.