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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

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K II and non-singular T-stresses T x and T y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0 • to 90 • . A compressive T y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T x = T y ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.

Oxidation of iron during hot rolling is inevitable and scale layers are formed on the strip. There are different rate laws of oxidation of iron to predict the scale thickness, in which parabolic rate law and mixed rate law are usually used in hot rolling of strips. As the strip passes through the roll gap, the scale layer can plastically be deformed. Due to limited plasticity of the oxide, cracks through the scale layer can be formed in every roll gap. They open and form new free metallic surfaces which are then oxidized in the interstand. By means of numerical simulations different rate laws of oxidation are compared and the scale deformation with different cases is taken into account. Sensitivity of some rolling parameters to prediction of the scale thickness is discussed in the present paper. Numerical results show that the parabolic rate law overestimates the scale thickness as compared with the mixed rate law and the mixed rate law is not sensitive to the deformation extent of scale.

In 4-high mills the slit model is usually used to determine elastic roll stock deformation, in order to predict the strip profile. In this model, the roll axis deflections obtained by the simple beam theory are satisfactory, but the roll flattening obtained by the elasticity theory of the half-space or the half-plane is inaccurate. In the present paper 5 models are introduced to determine the roll flattening. Change of the roll flattening causes the change of internal pressure between work roll and back-up roll, in turn, the change of strip profile. Therefore influence of the flattening models on the strip crown was investigated. Strip crown difference between these flattening models can reach 60 11m in the present simulation. With the increase of the strip width or the roll force the strip crown difference increases, namely the model error increases. The bending jack force and roll crown have a small influence on the model error. Untersuchung der Modellabweichung bel der Berechnung des Bandprofils in Ouarto-Walzgerusten. In Quarto-Walzgerusten wird das Schnittstellenmodell zur Bestimmung der elastischen Vertormung des Walzensatzes normalerweise benutzt, urn das Bandprofil vorauszusagen. In diesem Modell wird die Walzenbiegung uber die elementare Biegelinientheorie befriedigend beschreiben. Die Walzenabplattung, die uber die Elastizitatstheorie des Halbraums oder der Halbebene berechnet wird, konnte bisher nur ungenugend simuliert werden. In dieser Arbeit werden 5 Modelle vorgestellt, urn die Walzenabplattung zu beschreiben. Der Anderung der Walzenabplattung verursacht eine Anderung des AnpreBdrucks zwischen Arbeits-und StUtzwalze, damit wird das Bandprofil verandert. Deshalb wird der EinfluB der Walzenabplattung-Modelle auf die Bandbombierung untersucht. Der Unterschied der Bandbombierung betraqt je nach verwendetem Modell bis zum 60 11m. Mit zunehmender Bandbreite oder Walzkraft steigt der Unterschied der Bandbombierung, d.h. die Modellabweichung nimmt zu. Die Biegekraft an den Zapfen der Arbeitswalze und Walzenbombierung haben nur einen kleinen EinfluB auf die Modellabweichung.