Contact geometry estimation and precise radial force prediction for the radial-axial ring rolling process

In the present research work, the modular parametric design plug-in Grasshopper, available in Rhinoceros 5, is utilized as a pre-processor for the estimation of the projection of the contact length between ring and tools in the radial-axial ring rolling process. The estimated lengths, for each round of the process, are then used in a slip line based force model for the precise estimation of the radial forming force. The proposed method allows reducing the inaccuracies of the traditional approaches since it supersedes the concept of common thickness draft on both mandrel and main roll side, allowing a more precise estimation of the projection of the contact arc between ring and tools, considered to have a unique value on both mandrel side and main roll side. The fulfillment of this last assumption ensures the forming force to have the same value regardless it is calculated on the mandrel side or on the main roll side. The model has been validated by cross-comparing the analytical results with those of laboratory experiment and finite element simulation. The developed analytical model has been also applied to three different study cases where the previous literature models for the calculation of the projection of the contact arc have shown inaccuracies, demonstrating that the proposed approach can overcome these limitations. The positive cross comparisons among laboratory experiment, FEM simulations, and analytical estimations prove the reliability of the proposed approach, as well as its good integration with authors’ previous analytical algorithms.     

Mechanical analysis of edge bending mode for four-roll plate bending process

A mathematical model is developed for simulating the mechanics of edge bending mode for four-roll plate bending process. The governing differential equations for large deflection of elastic-perfectly plastic thin plate is derived and solved semi-analytically. The physical quantities important for operation, such as the shift of plate contact angle with rolls, the forces applied on rolls and the position setup of side roll, etc. are all evaluated and shown graphically as the function of the desired finished curvature of plate. Various effects of bender system parameters on these physical quantities are also studied. Received 12 January 1998     

An approximate method of calculating the kinetics of the drying process

An approximate method is presented for the calculation of the kinetics involved in the process of drying moist materials, this method based on the determination of the newly introduced Rebinder number and on the drying-rate relationships.     

An approximate solution for two-dimensional estuaries

The steady flow in a slightly stratified two-dimensional estuary is considered. An approximate form of the salinity which contains an unknown constant and which satisfies the prescribed boundary conditions is assumed. From a simplified form of the equations of motion the streamfunction is obtained. The unknown constant is then found by applying Galerkin's method the salt continuity equation.     

折边锥体封头的一种精确展开法

对折边锥体封头展开成扇环的解析法作了探讨，总结出折边锥体封头展开的一组精确计算公式。     

基于有限元的三辊行星轧制力预测及分析

为预测三辊行星轧制力,建立了三维热力耦合有限元模型,用均匀设计法安排有限元模拟样本,采用基于LM算法的BP神经网络学习有限元轧制力结果,确定了轧制参数与轧制力的映射关系,并根据训练后的神经网络分析了摩擦系数、轧辊偏转角和轧辊转速对轧制力影响．预测结果表明：摩擦系数和轧辊偏转角对轧制力影响是多方面的,在高轧辊转速时,较大的摩擦系数有利于降低轧制力．     

An approximate kinetic theory for accelerated testing

Accelerated testing is the attempt to accelerate the degradation processes that occur in a material system by applying a high stress. Typically accelerated testing requires extrapolating results from a feasible regime for laboratory or factory experimentation to a natural setting of interest. Usually the models used for this extrapolation either arise from assuming a single rate limiting step in the physical or chemical degradation process or as purely empirical relations. This paper presents a general theory for the design and interpretation of accelerated testing derived by considering a simple theory of how processes may trade off as stress decreases and time increases. Some of the main results of the theory are counter to current accepted practice. In particular, careful step stress experiments (experiments in which stress is perturbed during the accelerated aging) are shown to be necessary for identifying acceleration functions, and the possibility of predicting how long experiments need to be run prior to beginning the experiments is indicated.     

An approximate nonlinear dynamic theory for plates

Summary In this paper an approximate theory for the moderately large motion of transversely isotropic (orthotropic) plates is presented. Unlike other methods used in the past, the method used here involves no artificial assumptions. The method of approach begins with the equations of a partially non-linear elasticity theory and utilizes a method of asymptotic integration to arrive at successive two-dimensional approximations of increasing accuracy. The first approximation theory obtained here is the dynamic counterpart of Karman's plate theory. It includes the effect of rotatory inertia.     

An approximate method for evaluating hypersingular integrals

This paper describes a new method for direct numerical evaluation of multidimensional hypersingular integrals assigned on smooth curves and surfaces. These integrals arise when the boundary integral equations are used to solve problems of mechanics, electrodynamics, aerodynamics, etc. The hypersingular integrals are considered, in the sense of Hadamard, as finite parts. The main advantage of the proposed method is the numerical computation of the hypersingular integrals by the direct application of the developed cubature formulas, thus requiring little analytical pre-work. The method is not restricted to the type of problem however and may be easily applied to any hypersingular integrals. The convergence of the proposed technique has been proved and error estimates are given. An illustrative example demonstrates the accuracy and efficiency of the method.     

An iterative improvement for non-conforming bending elements

A method is described whereby the formulation for non-conforming bending elements includes the work dissipated across the inter-element boundaries. For the examples considered, this correction is shown to lead to a significant improvement in accuracy at little extra cost. Since the solution procedure is based on an iterative technique, the method would be particularly suitable if applied to non-linear problems.     

小直径厚壁管材变曲率弯曲回弹预测

为快速、准确地预测管材变曲率的弯曲回弹,建立变曲率弯曲回弹预测的解析模型.基于ABAQUS平台建立小直径厚壁管材变曲率弯曲成形及回弹数值模拟模型,通过试验验证了所建模拟方法的可靠性.将变曲率回弹问题转化为离散定曲率回弹问题进行研究,通过近似纯弯曲回弹实验,建立管材定曲率弯曲回弹前后半径之间的函数关系式,将变曲率弯管轴线双圆弧拟合逼近离散,针对离散化的回弹弯管进行G1连续拼接,依据轴线复杂程度,构建拼接修正函数,建立管材变曲率弯曲回弹预测解析模型.通过2个试验算例验证该解析模型能够有效预测小直径厚壁管材平面变曲率弯曲回弹.回弹的准确预测是有效控制弯管回弹缺陷的前提,用于指导后续模具型面修正,补偿回弹误差,保证弯管几何精度.     

An approximate solution for toughness-dominated near-surface hydraulic fractures

Asymptotic solutions for fracture opening, volume and specific surface energy for small and large fracture radii are presented from the literature. By comparison to numerical simulation of static circular fractures subject to constant and uniform internal pressures, it is found that a good approximation for fracture opening, for intermediate fracture radii, is obtained from a power mean (with exponent 1/2) of the small and large fracture radii limiting cases. The power mean equation for fracture opening is used to derive corresponding equations for fracture volume, specific surface energy and mode I and II stress intensities. These are then combined to form an approximate solution to describe the propagation of circular toughness-dominated near-surface hydraulic fractures, suitable for small, large and intermediate fracture radii. The approximate solution is shown to closely approximate results from equivalent numerical simulation.     

An approximate yield criterion for voided nonlinear materials

An approximate yield criterion (Eq. (40)) for voided nonlinear materials is proposed in which the effect of material hardening is directly included. The matrix is assumed to be a power-law material and approximate velocity fields for the matrix are employed to derive the yield function. Analysis indicates that the shape of yield surface in stress space expands along with increasing strain-hardening exponent N. For N = 0, the Gurson yield function is derived. And as N = 1, an analytical expression of the yield function in the form of ellipsoid is obtained. Furthermore, as 0 < N < 1, an appropriate expression for the yield function is suggested. A comparison between the approximate yield function and Cock's model (1989) is carried out. The agreement of the two models is very good.     

An approximate solution for the flow in viscous couplings

The creeping flow between two discs and in a slotted disc-plate system where one of the discs rotating is considered. The equations of motion and continuity are simplified by an order of magnitude estimation and the assumption that the gap between the discs is small. For the disc-disc system the equations of motion are decoupled and can be integrated to give a zeroth order solution which is introduced into the equations. There are integrated again to give a first order solution which depends on the Reynolds number. It is shown that a disc rotating and axially movable in a narrow gap will centre itself. The integration of the equtions of motion for the slotted disc-plate system leads to a Poisson equation with Neumann boundary conditions for the pressure. The boundary conditions are obtained with the assumption that the mass flows in radial direction are zero and the pressure gradients in circumferential direction are opposite equal. The differential equations are discretized and solved by a multigrid method. Velocities, pressure and torque are calculated. The superposed pressure distributions of the front and back side of a segment gives a resulting force exerted on the segment in axial direction.     

An annular segment finite element for plate bending

A stiffness matrix for a finite element having the planform of an annular segment is derived using the displacement approach. Numerical problems involved in the derivation are discussed and rapid convergence to exact solutions is demonstrated on three sample problems. It is concluded that the new element will be of great value to engineers concerned with the analysis of slabs of bridge decks curved in plan.     

An improved three-noded triangular element for plate bending

A new three-noded triangular element for plate bending is described. The element is based on an earlier stress-smoothed triangular element due to Razzaque,¹ but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high-performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen² are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general-purpose finite element program.     

An efficient quadrilateral element for plate bending analysis

A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the following considerations: (i) suppression of all kinematic deformation modes, (ii) the element has a favourable value for the constraint index in the thin plate limit, (iii) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.     

An approximate method of analysis for notched unidirectional composites

An approximate method is proposed for the analysis of unidirectional, filamentary composite materials having slit notches perpendicular to the fibers and subjected to tension parallel to the fibers. The approach is based on an engineering model which incorporates important effects of material heterogeneity by considering average extensional stresses in the fibers and average shear stresses in the matrix. Effects of interfacial failure and matrix plasticity at the root of the notch are considered. Predictions of the analysis are in reasonably good agreement with previous analytical models and experimental data for graphite/epoxy.     

An approximate method for evaporation problem with mushy zone

In the present paper, a simple mushy zone model is used to track the moving boundaries in an evaporation problem in which the vapor is removed upon formation. Two main parameters for the mushy zone model are analyzed as well as their effect on the movement of the moving boundaries and the thickness of the mushy zone. A new approximate method is developed for analysis and tracking the moving boundaries appears throughout the process. The proposed method mainly based on applying the boundary integral equation corresponding to each phase in such a way that the associated boundary and initial conditions as well as energy equations at the moving boundaries achieved with minimum error and low number of iterations. The results of the present paper seem to be good because there are neither analytical or numerical solutions available.     

Numerical simulation of rotating bending process for U-tubes in heat exchangers

Heat exchangers comprise thousands of tubes having U-shaped portions. Rotating bending method has been widely utilized to make U-bends. Although this method shows an excellent performance, cracks have been frequently detected in the U-bends due to residual stresses induced by bending. In this paper, the bending process is simulated based on elastic–plastic finite element analyses in order to investigate the magnitude and distribution of the residual stresses including the effects of operating pressure. Analyses results show that the residual stress increases as the radius of U-bend decreases and that operating pressure has a detrimental effect in terms of stress corrosion cracking at the intrados of U-bend. It is thought that these results can be utilized for the estimations of fracture mechanics parameters such as limit load, stress intensity factor and J-integral, prevention of the cracking, and establishment of the optimum inspection strategy for the heat exchanger tubes.