Global optimization design method for maximizing the capacity of V-belt drive

Abstract

An optimization model is constructed to formulate the maximization problem on the capacity of V-belt drive. The concavity, the monotonicity and the global optimality condition are studied for the objective function, and it is proved that the feasible region of the model is bounded, closed and convex under some design conditions. Then, a solution method, called an optimal segment algorithm, is developed to find the global maximizer of the model. Under four different design conditions, solution methods are presented respectively. Some real case studies are employed to demonstrate that the model and the algorithm in this paper are promising. V-belt, global optimization, capacity of drive, optimal segment algorithm Citation:Zhang S J, Wan Z, Liu G L. Global optimization design method for maximizing the capacity of V-belt drive.Owing to the superiority in structural simplicity, operating stability, high impact strength, relatively large transmission power and low production cost, the V-belt drive is widely used to transmit power in various mechanical elements [1,2]. It is helpful to simplify the mechanical structure, save resources and reduce the production cost if the driving capacity of a single V-belt is maximized under some given design conditions so that the number of the belts is minimized in the system of V-belt drive. The design methods for the system of V-belt drive include the conventional design and the optimal design. In the framework of conventional design (see, for example, [3]), the type of V-belt is first chosen from a given design table based on the transmission power and the rotation rate of the small pulley, then the diameters of both the big and the small pulleys are determined, and the central distance as well as the length of V-belt are estimated in some range according to the structure of the drive system. Subsequently, after verifying the constraints on the speed and the wrap angle of the small pulley, the standard rating power of a single V-belt is gotten from a specific design table. Finally, taking account of the modification of factors such as transmission ratio, the wrap angle and the length of the belt, we obtain the transmission power of the single V-belt, and compute the number of the needed belts. The principle in this approach is that a feasible design scheme is given by checking whether the constraints are satisfied or not. Thus, the obtained solution can not be guaranteed to be a local or global optimal solution. Recently, there are a lot of attempts to obtain an optimal design for the system of V-belt drive. and the references therein, the theory and the basic design methods are addressed systemically and comprehensively. Some specific software for V-belt design are developed by some companies. For example, the software, Ciclo VBelt, is often used in engineering. In summary, according to different objectives, the optimal models of V-belt

Two-step based sampling method for maximizing the capacity of V-belt driving in polymorphic uncertain environment

“…Then, a global optimization algorithm, called the optimal line segment algorithm, is developed to find a global maximizer of the constructed model. It is shown in Zhang et al [36] that the obtained solution by the proposed optimization method can improve the capacity of V-belt driving in some case studies. However, there is no report of contributions on the optimal design of V-belt driving by polymorphic uncertain optimization methods.…”

“…The other parameters are specified as those in references [36] and [40] 3.598]. For different choices of the satisfaction level a, the lower and the upper bounds of optimum and its corresponding optimal objective value by the proposed method are obtained and presented in Table 2.…”

“…In Č epon et al [35], a deterministic model is constructed to identify the contact parameters between the belt and the pulley based on experimental data. In Zhang et al [36], a deterministic model is constructed to maximize the capacity of V-belt driving. Then, a global optimization algorithm, called the optimal line segment algorithm, is developed to find a global maximizer of the constructed model.…”

Interval Solution for Nonlinear Programming of Maximizing the Fatigue Life of V-Belt under Polymorphic Uncertain Environment

“…It is well known that V-belt driving is widely used in all kinds of machines. Some deterministic models have been established to optimize the volume or the driving capacity of a V-belt drive system (see, e.g., [1,2]). In [3], the effect of angular speed on the behavior of V-belt drive system is studied by finite element method.…”

“…In [4], a deterministic model is constructed to identify the contact parameters between belt and pulley based on experimental data. In [1], a global optimization algorithm, called optimal line segment algorithm, is developed to find a global maximizer of the deterministic model for maximizing the carrying power of V-belt drive. In addition, in [5], a deterministic model is constructed to maximize the fatigue life of V-belt and a global optimal solution is found by the algorithm developed in [1].…”