Dynamic modeling of belt drives using the elastic/perfectly-plastic friction law
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Belt drives are used in numerous applications to transmit power between various machine elements. One limitation of the use of belt drives is the poor convergence of complex models which did not make them applicable for manufacturing use in industry. A source of convergence failure is the sharp changes in the solution. It is believed that the inclusion of an Elastic/Perfectly-Plastic (EPP) friction law into the belt/pulley contact mechanics can yield mathematical models with enhanced accuracy. This new friction model more accurately captures the true behavior of an elastic belt that exhibits microslip prior to fully-developed slip than previous regularized friction models. The Elastic/Perfectly-Plastic friction model was applied to a two-pulley flat belt system, and the equations of motions were derived using Hamilton's Principle. The results from the analytical model were compared to results from a finite element model. It was found that, unlike Coulomb's Law, the solutions with the EPP model had no slope discontinuities in the normal force. The elimination of these slope discontinuities could potentially help alleviate convergence issues for more complex models. It was also found that if the EPP spring stiffness is too small, then the belt cannot undergo the prescribed tension change. If it is too large, then the EPP model approaches Coulomb's Law and sharp changes appear. The Elastic/Perfectly-Plastic friction model was also applied to a v-belt model. It was found that the solutions and convergence properties with the EPP friction model were similar to the solutions with the Coulomb friction model. When compared to Coulomb's Law, the range of possible high tensions for a given low tension was reduced slightly for the EPP friction. Convergence fails due to sharp changes of the inclination angle and the sliding angle. Because the sharp changes occur when the belt exits the pulley, the EPP friction model cannot smooth the slope discontinuities.