The implementation of multiple drives for belt conveyors can solve the problems associated with motor overpower and the excessive tension of conveyor belts powered by a single drive. However, multiple drives can suffer from uneven driving power allocation. Among various factors, the selection of the type of conveyor belt particularly affects the power allocation. The current study aims to investigate the influence of the elastic modulus of a conveyor belt on the power allocation of multi-drive conveyors. Based on the Kelvin-Voigt viscoelastic model, a discrete model of an entire machine is established. Kelvin-Voigt software is used to simulate the working conditions of conveyor belts with different elastic moduli under full loads. The driving forces of individual rollers are obtained and then compared. Compared to other types of belts, a steel wire core conveyor belt, whose elastic modulus is relatively high, effectively improves the stability of the conveyor belt under a full load after start-up to achieve a reasonable power allocation. The results of this study provide a foundation for conveyor belt selection for multi-drive conveyors.
Belt conveyors have been extensively applied to bulk material delivery applications in various industries, such as the metallurgy and mining industries, the coal chemistry industry and the food processing industry. In modern industrial enterprises, bulk transportation accounts for approximately 30% of production costs . In response to policies related to energy conservation and consumption reduction, belt conveyors are being developed to accommodate heavy loads, long distances and high speed [2–4].
As the driving force produced by the traditional single-roller belt conveyor cannot satisfy the requirement for long-distance driving, scholars have proposed the multi-roller driving method [5–7]. However, this method tends to cause uneven power allocation among the rollers [8, 9], which results in either overloaded or underloaded individual electric motors, thereby increasing production costs and wasting resources .
Numerous factors can affect the power allocation of multi-drive conveyors, such as the topography of the system, drive spacing, elastic modulus of the conveyor belt, wrap angle of the drive pulleys (the central angle corresponded by the arc length of the roller that is wrapped by the conveyor belt), friction coefficient between the conveyor belt and driving roller, and mechanical performance of the driving device . Among these factors, scholars have focused on the start-up time , start-up acceleration curve [12–14], and tensioner performance [15–18] while ignoring the performance of the conveyor belt.
A conveyor belt is typically made of a viscoelastic material, which extends elastically under tension. While running in different segments (except for the driving roller segment), the belt has to overcome various resistances, causing its tension to increase continuously. Correspondingly, the belt gradually extends, its speed gradually increases, and its tension and extension at the joining end of the driving roller increase. Because the peripheral velocity of the roller is constant, the belt elongates and slides along the opposing direction of the roller rotation, which leads to the creep of the conveyor belt on the roller . This condition in turn affects the transfer of the peripheral force of the driving roller, i.e., power allocation. To improve the performance of the conveyor, the extension and slide of the belt should be reduced to a minimum. However, the elastic extensions of conveyor belts vary according to type.
The elastic modulus of the conveyor belt is the ratio between the stress and strain of the belt; it is an important index for assessing the capability of the belt to resist elastic deformation. A higher elastic modulus often indicates that a greater stress is required to cause elastic deformation of a belt and that the rigidity of the belt will be greater. For a certain type of conveyor belt, the elastic modulus remains constant . To date, numerous studies on conveyor belts have been reported. These studies have mainly focused on the resistance of a belt while running. The resistance between the belt and the rollers accounts for approximately 60% of the total resistance during belt operation [5, 7, 14, 15]. The elastic modulus of the bottom cover of the belt is also an important factor for running resistance. Given the same specifications of the conveyor belt, an increased rigidity of the bottom cover of the belt, i.e., the adoption of the bottom cover with a higher elastic modulus, can effectively reduce the indentation area of the supporting roller on the belt, thereby reducing the running resistance [21–23].
Multi-roller driving serves as an extension of single-roller driving, which is, theoretically, a result of the increasing surrounding angle between the belt and the roller. Multi-roller driving arrangements can take multiple forms, and the basic forms include double-head roller driving and single-head and tail roller driving. With the increase in the conveying distance and conveyed volume of conveyor belts, central line friction driving and combinations of the two basic arrangements have been developed to satisfy the requirements for large traction forces . Due to its balanced power allocation, multi-roller driving effectively reduces the motor power of the main output under the condition of uneven power allocation, which reduces the maximum tension of the conveyor belt, thereby elongating the service life of the belt. However, the manner in which the elastic modulus of the conveyor belt influences the power allocation and the extent of this influence remains unreported.
Using typical double-head driving conveyor belts as the study object, this study investigates the influence of the elastic modulus of the belt on the driving force of the rollers. For the dynamic analysis of long-distance belt conveyors, the commonly used modeling methods include the Maxwell model, the Kelvin-Voigt model, the Standard model, and the Maxwell-Kelvin model. The Maxwell model connects springs and damping in series; however, it is applicable for only the stress analysis of the belt. Although the Standard model and Maxwell-Kelvin model can satisfactorily reflect the viscoelasticity of the belt, they are disadvantageous because they require too many parameters and a complex modeling process [6, 17]. The Kelvin-Voigt model connects springs and dampers in parallel. This model reflects not only the stress of the belt but also the deformation of the belt. Furthermore, the modeling process of the Kelvin-Voigt model is simple. Therefore, to achieve the goal of this study, the Kelvin-Voigt viscoelastic model is taken as the unit model of the conveyor belt, and a dynamic model of the belt conveyor is established. However, the Kelvin-Voigt model places particular emphasis on the belt dynamics caused by belt viscoelasticity. Belt indentation is introduced into the simulation model in the form of a resistance parameter. AMEsim simulation software is used for the dynamic analysis of the discrete model of the whole machine. DIN is used to simulate the friction coefficient, and the point-by-point tension method is utilized to calculate the resistance. Loading is performed according to the variation in the starting acceleration during the start-up process when the belt is under a full load, and sine acceleration is used in this study. By measuring the strains at the belt approach point and the runaway point from the drive roller, the driving force values for individual rollers of the conveyor belts with different elastic moduli are obtained. Actual measurements are performed to obtain the power ratio between the driving rollers; then, the actual results and the simulation results are compared.
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