Lateral motion of the endless flat belt in a two-pulley belt system

An analytical model of the lateral motion of the endless belt in a two-pulley belt system is proposed. This model can be used to forecast the transient and steady lateral motion of the belt when the tilted angle of the steering pulley is time-variant and it is valuable in the design and assessment of belt lateral position controllers. The responses of the belt to variations in the tilted angle of the steering pulley according to a piecewise step function are solved using the delay differential equation solver dde23 in MATLAB. The validity of the model is confirmed by experiments. The simulation and experimental results show that the belt tends to move to the side with a shorter center distance. In the steady phase of the step responses, the lateral belt velocities at different positions tend to be coincident with each other. A closed-form expression of the steady belt lateral velocity is derived. The expression shows the steady belt lateral velocity is proportional to the input tilted angle and the belt speed, and it increases with an increase in the center distance and the pre-load tension and a decrease in the radius of the pulleys and the belt bending stiffness.