The Efficiency of a Hypoid Axle – A Thermally Coupled Lubrication Model
The final drive unit in road vehicles, such as medium and heavy trucks, and four-wheel-drive and rear-wheel-drive passenger cars, usually consists of a hypoid or spiral bevel geared transmission and differential, housed in a self-contained, dip-lubricated axle. Such units are subjected to very variable duty—including extreme combinations of speed, gradient, applied torque and external temperature—and are typically cooled by natural and forced convection on the exterior surface. On the other hand, there are appreciable internal power losses due to gear friction and churning and to bearing and seal losses. These losses are highly dependent upon the lubrication regime of the internal components and hence to the thermal behaviour of the entire axle.
In the present paper, we describe a thermally coupled model of axle lubrication. The torque and speed demand is first found from a specified duty (“drive cycle”) which includes terrain as well as speed-versus-time and external temperature data. The evolution of sump oil and component temperatures is followed, and increments of energy loss evaluated in each time-step. Elastohydrodynamic film thickness is determined for the hypoid gear set, using a development of Buckingham’s method, and friction losses calculated using a simple oil rheological model based on tribometer (MTM) testing. Churning, seal and bearing (speed-dependent) losses are found using empirical algorithms. Energy losses over complete drive cycles for different lubricants are derived, enabling the relative fuel economy for different oils to be evaluated.
Results show that (i) the bulk temperature rise of the axle is highly dependent on the specified vehicle duty and (ii) the efficiency can be strongly influenced by choices available to the lubricant formulator. Taken together, these findings suggest that specialist axle lubricant formulations for particular vehicle types and applications will be attractive as a route to optimum fuel economy.
Keywords: Hypoid, Friction, Elastohydrodynamic, Lubrication