Finite element analysis of edge lamination during hot rolling process of aluminium alloy

Summary The rigid-plastic finite element method is applied to the analysis of the three-dimensional deformation behaviour, in particular the forming of edge lamination during the multi-pass hot roughing process of aluminium. the calculation is carried out for various rolling conditions and reduction schedules, and their influence on the edge lamination is examined. The results suggest that the crop loss due to the edge lamination can be reduced by increasing the roll diameter, the reduction per pass and the initial width of the slab.     

Note on axial-shear and contour vibrations of prisms

Exact solutions of the equations of the linear theory of elasticity are given for axial-shear modes of vibration of an isotropic, prismatic bar whose normal section is an equilateral triangle or has the equilateral triangle as a module. A family of contour modes is also described for bars with a rhombic section formed of two equilateral triangles and with sections having the rhombus as a module.     

Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.     

Three-dimensional vibration analysis of prisms with isosceles triangular cross-section

This paper studies the three-dimensional (3-D) free vibration of uniform prisms with isosceles triangular cross-section, based on the exact, linear and small strain elasticity theory. The actual triangular prismatic domain is first mapped onto a basic cubic domain. Then the Ritz method is applied to derive the eigenfrequency equation from the energy functional of the prism. A set of triplicate Chebyshev polynomial series, multiplied by a boundary function chosen to, a priori, satisfy the geometric boundary conditions of the prism is developed as the admissible functions of each displacement component. The convergence and comparison study demonstrates the high accuracy and numerical robustness of the present method. The effect of length-thickness ratio and apex angle on eigenfrequencies of the prisms is studied in detail and the results are compared with those obtained from the classical one-dimensional theory and the 3-D finite element method. Sets of valuable data known for the first time are reported, which can serve as benchmark values in applying various approximate beam and rod theories.     

Area rule for integral quantities

In hydrodynamics and aerodynamics there is an area rule for nearly axisymmetric bodies. It states that the drag [1–3], the coefficient of heat transfer and the ablation [4], and also the wake parameters [5] of a three-dimensional body are equal to the analogous quantities for an axisymmetric body which has the same distribution of the cross sectional area along the axis. In some cases, the area rule holds for bodies which depart strongly from axial symmetry [6]. It is shown in the present paper that equality also holds for other integral quantities and not only in hydrodynamic problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–159, July–August, 1981.We thank Yu. B. Lifshits for helpful comments.     

Energy considerations for frictional impacts

Many machine and mechanism processes are accompanied by impacts with friction. They arise by short-time contacts between two or more bodies, and they generate energy losses mainly due to friction in tangential contact directions. During the last two decades, a couple of impact models based on the theory of rigid body contact were established connected with the names of Moreau, Frémond, and Glocker, which all work quite satisfactorily with respect to practical applications, although some examples indicate deviations requiring more investigations with respect to the impact models and the type of examples considered. We shall focus on Glocker’s model, for which some experimental verifications are available by Beitelschmidt. A missing link are energy considerations, which are available, but nevertheless do not provide us with a complete information for all possible cases. The paper tries to fill a bit this gap by founding the investigations on a combined phenomenological and theoretical basis.     

Wake and cavitation characteristics of equilateral prisms at incidence

The characteristics of flow past a two-dimensional equilateral prism are experimentally studied at different angles of incidence to the approach flow. Tests were conducted in a water tunnel suitable for cavitation studies. The presence of cavitation facilitated excellent visual observations of the wake region. The mean separation pressure coefficients and the vortex-shedding frequency were determined at various degrees of cavitation for five different orientations of the prism. The latter determines, to a large extent, the vibration characteristics of the system in which the prismatic elements are located.     

Algorithms for Nanoindentation Strain Rate Jump Testing and Analysis

Experimental Mechanics - Understanding the dynamics of deformation processes is of interest for determining the dominant thermally activated processes during plasticity [1] and fracture [2, 3]....     

On the three-dimensional vibrations of elastic prisms with skew cross-section

Three-dimensional (3-D) free vibration of an elastic prism with skew cross-section is investigated using an elasticity-based variational Ritz procedure. Specifically, the associated energy functional minimized in the Ritz procedure is formulated using a simple coordinate mapping to transform the solid skew elastic prism into a unit cube computational domain. The displacements of the prism in each direction are approximately expressed in the form of variable separation. As an enhancement to conventional use of algebraic polynomials trial series in related solid body vibration studies in the associated literature, the assumed skew prism displacement, u, v and w in the computational ξ–η–ζ skew coordinate directions, respectively, are approximated by a set of generalized coefficients multiplied by a finite triplicate Chebyshev polynomial series and boundary functions in ξ–η–ζ to ensure the satisfaction of the geometric boundary conditions of the prism. Upon invoking the stationary condition of the Lagrangian energy functional for the skew elastic prism with respect to the assumed generalized coefficients, the usual characteristic frequency equations of natural vibrations of the skew elastic prism are derived. Upper bound convergence of the first eight non-dimensional frequencies accurate to four significant figures is achieved by using up to 10–15 terms of the assumed skew prism displacement functions. First known 3-D vibration characteristics of skew elastic prisms are examined showing the effects of varying prism length ratios (ranging from skew solids to skew slender beams), as well as, varying cross-sectional side ratios and skewness, which collectively can serve as benchmark studies against which vibration modes predicted by classical Euler and shear deformable skew beam theories as well as alternative methodologies used in elastic prism vibrations of mechanical and structural components.     

滚轴承刚度分析程序

本文介绍了一种用Fortran语言编写的滚动轴承刚度分析程度,它基于作者近年来研究的刚度分析理论,具有兼容性好,输入简单,输出直观的特点,并已通过了很多实例验算,结果良好。     

Experimental and theoretical investigation of galloping of transversely inclined slender prisms

Galloping is characterized by large and periodical oscillations which may lead to collapse of slender structures. This study is the first attempt of a comprehensive experimental and theoretical investigation of galloping of transversely inclined prisms. A modified quasi-steady model is proposed with a constant term to estimate the galloping of a transversely inclined prism, which is later experimentally investigated by conducting a static Synchronous Multi-Pressure Sensing System (SMPSS) test and an aeroelastic test in a boundary layer wind tunnel. The galloping responses of the prisms were measured in the aeroelastic test, while the aerodynamic force coefficients were determined from the SMPSS test. These experimental results were subsequently utilized to validate the quasi-steady model. Based on the proposed model, the galloping responses of the prisms were predicted and compared with the experimental results. The experimentally measured and theoretically predicted galloping responses are discussed with respect to aerodynamic damping ratios, onset galloping wind speeds, distributed pressure coefficients, point pressure spectra and vortex shedding frequencies. Interesting findings are summarized.     

On the Cox-Merz rule for magnetic dispersions

The Cox-Merz rule can be a useful, empirical tool for relating steady and oscillatory shear flow property measurements. Here we test its applicability for magnetic dispersions. Neither the rule nor a previously published modification of it applies for the dispersions, but we demonstrate that the steady shear viscosity and the magnitude of the complex viscosity are nonetheless related. Received: 30 August 2000 Accepted: 21 December 2000     

Closed-form weight function for edge crack problems

An accurate crack surface opening displacement formula for edge cracks in finite bodies has been derived, and was subsequently used to develop wide-range closed-form weight functions for edge cracks. The analytical weight function is general and can be easily used to determine accurate stress intensity factors and crack surface opening displacements for arbitrarily loaded edge cracks with high efficiency. Examples have been given for problems of edge crack(s) with a number of typical load conditions for illustration.     

A novel analytical model based on arc tangent velocity field for prediction of rolling force in strip rolling

Accurate prediction of rolling force is an effective method to improve strip quality in rolling process. To achieve this goal, a novel arc tangent velocity field model based on the upper bound method is proposed to evaluate the rolling force. The mathematical expression of rolling force is derived from the virtual work principle and maximum plastic work principle. Comparing the experimental results with the proposed analytical model prediction, it has been found that this model is good for estimation of rolling force. Meanwhile, the finite element method is also used to simulate the rolling process to verify the validity of the analytical model. It is shown that this model can be used for prediction of rolling force in practice.

     

A multibody approach for dynamic investigation of rolling systems

Summary In the classical multibody models which are used for vehicle dynamics, the contact forces applied to the wheels are considered as external forces and must be supplied in analytical from for each particular application. Moreover, when geometrical constraints arise because several wheels are in contact with a non-planar rolling path, they also have to be specified analytically.This paper presents a multibody model where each wheel-ground contact is considered as an internal joint of the system. Some of the geometrical constraints are taken into account by means of closed-loops and generated automatically by a programme. The remaining constraints have a simple expression and allow the contact forces and the characteristics of the rolling-path to be introduced in a straightforward manner. The equations of motion of a two-wheel system moving in a plane on a non-rectilinear path are derived to illustrate the method.

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Versuch der Berechnung der Fahrzeugdynamik mittels eines Mehrkörpersystemmodells

Übersicht In den klassischen Mehrkörpersystemmodellen, welche man in der Fahrzeugdynamik verwendet, werden die Kräfte, die vom Kontaktpunkt her auf die Räder einwirken, als äußere Kräfte betrachtet und müssen bei jeder besonderen Anwendung in analytischer Form gegeben werden. Hinzu kommt noch, daß im Falle, wo geometrische Zwangsbedingungen auftreten, weil mehrere Räder mit einem unebenen Fahrweg in Kontakt sind, diese auch analytisch bestimmt sein müssen.Dieser Artikel stellt ein Mehrkörpersystemmodell vor, in welchem jeder Rad-Bodenkontakt als eine interne Bindung des Systems betrachtet wird. Einigen dieser geometrischen Zwangsbedingungen wird mittels sogenannter geschlossener kinematischer Schleifen Rechnung getragen, und sie werden automatisch mit Hilfe eines Rechnerprogramms generiert. Die restlichen Zwangsbedingungen haben eine einfache Form und erlauben eine gesetzmäßige Eingabe der Kontaktkräfte sowie der Charakteristiken des Fahrweges. Die Bewegungsgleichungen eines Zweiradsystems, welches sich in einer Ebene auf einem nicht-geradlinigen Fahrweg fortbewegt, werden abgeleitet, um diese Methode zu illustrieren.

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This research has been partially supported by Constructions Ferroviaires et Métalliques, B.N.