A Method to Derive Friction and Rolling Power Loss Formulae for Mixed Elastohydrodynamic Lubrication

Abstract

Prediction of mechanical power losses of gear pairs requires elastohydrodynamic lubrication (EHL) analyses to be carried out at every discrete contact position. This makes gear efficiency models computationally demanding. As a remedy to this problem, a method is proposed in this study to derive EHL-based friction coefficient and rolling power loss formulae to be used in gear efficiency models. This method employs a large number of EHL analyses covering a full matrix of all key contact parameters, namely normal load, rolling and sliding velocities, radii of curvature, lubricant parameters and surface roughness amplitudes, within typical ranges dictated by gear contacts. Linear regression of the results of the EHL analyses yields friction coefficient and rolling power loss formulae suitable for gear efficiency models. In the EHL model, the hydrodynamic fluid and asperity contact zones are treated in a unified manner. The sliding friction is computed as the sum of the viscous shear within the lubricant and the boundary friction at the local asperity contact spots. The rolling power loss induced by fluid pressure gradient is formulated to include the entire contact zone instead of only the inlet region, since the pressure gradient is substantial within the contact for rough surface condition. The proposed method is demonstrated using an example turbine fluid. Typical measured gear surface roughness profiles are used in the analyses. At the end, the results from the regression formulae are compared to actual EHL predictions to assess their accuracy under various contact conditions.

Modelling of steady-state mechanical power losses in planetary gear trains of automatic transmissions

“…The changes in the normal load were captured via a gear load distribution model while the changes in rolling and sliding velocities were calculated by using the involute geometry. As this method is rather computationally demanding, an alternate method of developing closed-form friction formulae up front by regression of a larger number of EHL analyses covering proper ranges of contact parameter for gears (Xu et al (2007), Li and Kahraman (2011)). The same approach was used by Talbot and Kahraman (2014) which was shown to agree with their earlier experiments (Talbot et al (2012)) well.…”

“…Here κλ μ is the sliding friction coefficient defined for a typical automatic transmission fluid in the manner of Li and Kahraman (2011) …”

“…Here, such a power flow formulation will be combined with EHL based power loss models of gear meshes and planet bearings to predict mechanical losses of planetary gear trains of automatic transmissions Mechanical power loss models for gears and gear trains can be divided into two distinct categories, the first addresses the power losses in simple gear systems like a pair of gears in mesh or a single planetary gear stage. These models may utilize an empirical friction coefficient as reviewed in Martin (1978) or utilize physics-based models to calculate power losses (Xu et al (2007), Li and Kahraman (2010), Li and Kahraman (2011)). The second category of studies utilize a kinematics argument to obtain the power loss or efficiency in complex gear trains by utilizing an assumed gear mesh efficiency value for the individual meshes (Pennestri andFreudenstein (1993), del Castillo (2002), Chen and Angeles (2011)).…”

An experimental characterization of the friction coefficient of a wind turbine gearbox lubricant

“…In addition, the lubricants used are not representative of a wind turbine gearbox lubricant. The VG for the oils used in previous studies is too low (less than 120 mm 2 /s and less than 27.6 mm 2 /s at 40°C, respectively, for the automotive and aerospace lubricants) to allow film‐forming capabilities at the Hertzian region of the rolling‐sliding contacts in wind turbine gearboxes. In fact, He et al recently presented friction test data for a gear oil Mobil 600 XP 68 whose dynamic viscosity at oil temperature of 40°C 0.0597 Pa·s is similar to that of SAE 75W90.…”

“…For example, the prediction of mechanical power loss of a gear pair using a numerical EHD model will require several hundreds of EHD analyses of the defined gear pair. To circumvent this issue, Xu et al 17 and Li and Kahraman 34 have used smooth contact and mixed EHD lubrication theory to derive friction coefficient formulae for automotive (SAE 75W90) and aerospace (Mil-L23699) lubricants, respectively. Recently, Masjedi and Khonsari 35 used a line-contact EHD methodology to derive a curve fit formula for predicting friction coefficients in a rough EHD line-contact lubricated with a nondetergent SAE 30.…”