Coupled belt-pulley mechanics in serpentine belt drives

Belt vibration and slip are primary concerns in the design of serpentine belt drives. Belt-pulley coupling is essential for the analysis. This work investigates issues to advance the understanding of belt-pulley mechanics.; Closed-form eigensolution approximations for an axially moving beam with small bending stiffness are given. This model is the first order approximation for the transverse vibration of each span in a serpentine belt drive. Perturbation techniques for algebraic equations and the phase closure principle are used. The eigensolutions are interpreted in terms of propagating waves.; For a complete serpentine belt drive, a hybrid continuous-discrete model is built. Incorporation of belt bending stiffness introduces linear belt-pulley coupling. This model can explain the transverse span vibrations caused by crankshaft pulley fluctuations at low engine idle speeds where other coupling mechanisms do not. For the steady state analysis, a novel transformation of the governing equations to a standard ODE form for general-purpose BVP solvers leads to numerically exact steady solutions. A closed-form singular perturbation solution is developed for the small bending stiffness case. A coupling indicator based on the steady state is defined to quantify the undesirable belt-pulley coupling. A spatial discretization is developed to find the free vibration eigensolutions. In contrast to prior formulations, this discretization is numerically robust and free of missing/false natural frequency concerns. New dynamic properties induced by bending stiffness are characterized. Dynamic response calculations using the discretized model follow naturally. The effects of major design variables are investigated. This provides knowledge to help optimize structural design, especially to reduce large belt transverse vibration.; Finally, to better predict the belt-pulley contact interactions applicable to serpentine belt drives an improved model is established for the steady state mechanics. Bending stiffness is considered while other factors in the literature such as belt-pulley friction and belt inertia are retained. An iterative solution based on general-purpose BVP solvers is presented to determine the belt deflections and the distributions of speed, tension, and friction along the belt as well as the belt-pulley contact points and adhesion/slip zones on the pulleys. Key design criteria like maximum transmissible moment and power efficiency are examined.