The Convergence of Normalized Vehicular Rolling Friction Coefficient (Crr) by Dynamic High-Speed Imaging and Least Square Optimization Techniques

Abstract

The paper describes a simple, small scale and low cost yet comprehensive approach to quantifying the Coefficient of Rolling Resistance/Friction (Crr) also known as the Rolling Resistance Coefficient in automobiles. Crr is usually defined as the amount of force required to overcome the hysteresis of the material during tire rotation, where reduced Crr tires can save 1.5–4.5% of automotive fuel consumption. Automotive Standards from the Society of Automotive Engineers use to quantify Crr namely SAE J2452 and SAE J1269 were briefly introduced. Methods of coast down and speed trap tests were conducted under varying body weighted conditions to find the coefficient value, where a high speed camera monitored the motion of the vehicle. The experiment produced different equations of motion which were then solved analytically by numerical analysis techniques to converge on the rolling friction coefficient. A scaled model was used to run dynamic tests and the Reynolds Number (Re) was used to establish a relationship between model and full scale vehicle velocities. Initial guesses in the least square optimization iterations provided coefficient values where drag forces were normalized by assuming constant drag coefficient (CD of 0.40) and then neglecting its contribution during vehicle motion due to the test model size, resulting in a mean Crr of 0.0116. The study results were compared with 3 studies and also against an automotive Crr model. Schmidt 2010 Dynatest Green Road report shares a high 43% error, while the National Academy of Sciences, 2006 and Gillespie, 1992 yielded errors of 10.5% and 7.2%. The recent mathematical model of Ehsani 2009 yielded an average Crr value error of 2.3% (with individual test averages of 0.80%). Direct scaling and multiplying abilities were attributed for quantifying the normalized value in the study.