This paper presents optimized nonlinear analytical procedure for the slipping and sticking motion of extensible belt pulley systems. The procedure initially assumes a general spline representing the changes in the internal moment along the slipping zones. This assumption enables one to get the shear force values along the belt length. Also this assumption enabled us to discover an entrance slipping zone of the belt pulley contact with all variables changing along this zone. The contact between the belt and the pulley has thus three stages that lead to more realistic prediction of the belt system variables and more accurate values for the angles in the belt pulley sliding zones. The change in the angular velocity of the driven pulley with respect to the driving pulley, the change in the cross section dimensions, and the belt stretch are predicted. The analytical model gives highly nonlinear equations which are solved by numerical optimization procedure and validated by the solution obtained using absolute nodal coordinate formulation (ANCF) finite element method. The results obtained demonstrate that the present formulation leads to more accurate prediction for the belt tension, friction and normal forces. This paper presents the analytical results of several models which are presented and would enable better prediction for the critical loads for several cases.

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