Abstract
The features of the propagation of dynamic stresses in a conveyor belt, the material properties of which correspond to the Maxwell element model, are considered. Analytical expressions are presented for calculating the dynamic elastic modulus, the loss modulus, and the angle of mechanical loss depending on the frequency of longitudinal oscillations in the belt of an extended transport conveyor. To analyze the dynamic stress propagation process, dimensionless parameters are introduced that characterize the specific features of the viscoelastic process in a conveyor belt, the material properties of which correspond to the Maxwell element model. The transition to the dimensionless Maxwell element model is made and the analysis of the relationship between stress and deformation of a conveyor belt element for extremely large and small values of dimensionless parameters is made. The substantiation of the scope of the Maxwell element model is given. It is shown that at sufficiently high frequencies of longitudinal stress oscillations in a conveyor belt, at which the oscillation period is much less than the characteristic oscillation decay time, the relationship between stress and deformation of the conveyor belt element corresponds to Hooke's law. A qualitative analysis of the relaxation time was carried out for a conveyor belt material, the properties of which correspond to the Maxwell element model. The analysis of the propagation of dynamic stresses in the conveyor belt for the characteristic operating modes of the transport conveyor is carried out. The conveyor operating mode with a constant deformation rate of the belt element; the mode in which a constant load is suddenly applied to the belt element; the conveyor operating mode with an instantly applied load to the belt element were investigated. It was determined that in cases where the characteristic process time significantly exceeds the stress relaxation time in the conveyor belt or the longitudinal oscillation period is much less than the stress relaxation time in the conveyor belt, the Maxwell element model can be replaced with a sufficient degree of accuracy by the Hooke element model.
Highlights
One of the characteristics of a transport conveyor, which determines its operational capabilities, is the strength of the conveyor belt [1, 2]
The problem of constructing simple analytical dependencies between the stress and deformation of the belt element is urgent, which would simplify the solution of the wave equation and make it possible to form constraints on phase coordinates when designing algorithms for optimal speed control of the belt, the material properties of which correspond to the Maxwell element model
All this allows us to assert the feasibility of conducting a study on the construction of approximate Maxwell element models with their subsequent use to calculate the propagation of longitudinal oscillations in a conveyor belt
Summary
One of the characteristics of a transport conveyor, which determines its operational capabilities, is the strength of the conveyor belt [1, 2]. Switching speed modes leads to acceleration or deceleration of the conveyor belt, and, to the emergence of dynamic stresses in the belt. This imposes additional restrictions on the speed modes of the transport system. For more complex elastic element models, among which the Maxwell element model should be distinguished, the solution of the wave equation is associated with additional difficulties In this regard, the problem of constructing simple analytical dependencies between the stress and deformation of the belt element is urgent, which would simplify the solution of the wave equation and make it possible to form constraints on phase coordinates when designing algorithms for optimal speed control of the belt, the material properties of which correspond to the Maxwell element model
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