A fundamental approximation in MATLAB of the efficiency of an automotive differential in transmitting rotational kinetic energy



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The VCOST budgeting tool uses a drive cycle simulator to improve fuel economy predictions for vehicle fleets. This drive cycle simulator needs to predict the efficiency of various components of the vehicle's powertrain including any differentials. Existing differential efficiency models either lack accuracy over the operating conditions considered or require too great an investment. A fundamental model for differential efficiency is a cost-effective solution for predicting the odd behaviors unique to a differential. The differential efficiency model itself combines the torque balance equation and the Navier-Stokes equations with models for gear pair, bearing, and seal efficiencies under a set of appropriate assumptions. Comparison of the model with existing data has shown that observable trends in differential efficiency are reproducible in some cases to within 10% of the accepted efficiency value over a range of torques and speeds that represents the operating conditions of the differential. Though the model is generally an improvement over existing curve fits, the potential exists for further improvement to the accuracy of the model. When the model performs correctly, it represents an immense savings over collecting data with comparable accuracy.