Out-of-plane flexibilities of dovetail joints in machine tool structures

The paper aims to model the flexibility of a dovetail joint encountered in machine-tool structures. The investigation is concerned with the determination of a flexibility matrix through an approximate semianalytical procedure using finite element analysis. The contact region and the pressure distribution on the two mating surfaces are assumed. The deformation pattern of the male and female parts are separately analysed and from compatibility and equilibrium considerations, the overall deformation pattern of the joint is calculated for the three out of plane external force/moment components. The joint flexibility is represented by a 3 × 3 flexibility matrix. Results are presented for the knee-column joint and the column-overarm joint of a milling machine structure.     

Elastic analysis of pin joints

The advent of large and fast digital computers and development of numerical techniques suited to these have made it possible to review the analysis of important fundamental and practical problems and phenomena of engineering which have remained intractable for a long time. The understanding of the load transfer between pin and plate is one such. Inspite of continuous attack on these problems for over half a century, classical solutions have remained limited in their approach and value to the understanding of the phenomena and the generation of design data. On the other hand, the finite element methods that have grown simultaneously with the recent development of computers have been helpful in analysing specific problems and answering specific questions, but are yet to be harnessed to assist in obtaining with economy a clearer understanding of the phenomena of partial separation and contact, friction and slip, and fretting and fatigue in pin joints. Against this background, it is useful to explore the application of the classical simple differential equation methods with the aid of computer power to open up this very important area. In this paper we describe some of the recent and current work at the Indian Institute of Science in this last direction.     

The brownian excursion area: a numerical analysis

Using an explicit expression for the Laplace transform of the Brownian excursion area generating function, a numerical analysis gives moments, density, and distribution function. An asymptotic formula is given for small argument.     

System theory for numerical analysis

Many numerical schemes can be suitably studied from a system theoretic point of view. This paper studies the relationship between the two disciplines, that is, numerical analysis and system theory. We first see that various iterative solution schemes for linear and nonlinear equations can be suitably transformed into the form of a closed-loop feedback system, and show the crucial role of the internal model principle in such a context. This leads to new stability criteria for Newton's method. We then study Runge-Kutta type methods for solving differential equations, and also derive new stability criteria based on recent results on LMI. A numerical example is given to illustrate the advantage of the present theory.     

IC热阻简化模型的数值分析应用

采用集成电路的热阻简化模型的方法,以DIP封装芯片为例,建立了元件传热的数值模型;分别对两热阻模型和单热阻模型,这两种不同的建模方法在自然对流的情况下进行了稳态分析,并以详细模型的分析结果作为基准进行了对比,获得了使用这两种简化模型进行分析时结果的准确性;对工程师在进行热分析和热设计仿真时,建模方法的选取具有重要的参考价值.     

防坠安全器自动检测的数值算法分析

本文主要对施工升降机安全器的自动检测的数值算法作了系统的研究,主要分析了安全器主要技术参数的计算方法,并且时每种方法进行了理论分析,指出她们的计算精度和误差.     

Computer graphics assisted numerical analysis instruction

A computer assisted instruction package for use in a first course in numerical analysis is discussed. Its use is illustrated by examples from two programs for polynomial interpolation.     

On the numerical analysis of eddy-current problems

Starting from Maxwell's equations, we derive a general variational formulation suitable for eddy-current problems in non-magnetic, non-moving conductors disposed in an arrangement of closed multiply-connected circuits. The related problem of open circuits is considered and the validity of the notion of impedance is discussed. A finite element approach is described and illustrated by two examples, one of them from a real problem in electrical engineering.     

The quantum square well with moving boundaries: A numerical analysis

We present some numerical discussions concerning the infinite square well in one dimension with moving boundaries. Our results show that if the speed of displacement is small, objects of physical relevance like probability density, averaged position or mean value of the energy have a smooth behavior. On the contrary, if this speed becomes large, many irregularities arise, which has a difficult qualitative explanation. These irregularities manifest themselves as sharp bumps on the probability distribution or a chaotic shape on the averaged values of position and energy. None of these patterns is the result of numerical errors and, therefore, we conclude that an unknown and very nontrivial effect is produced at high speeds of the moving wall.     

The queueing system EkMa,b1 and its numerical analysis

In this paper steady-state random-point results for single-server bulk-service system ${}_{\mathrm{k}}\text{M}{}^{\mathrm{a,b}}\text{1}$ are related to imbedded Markov Chain results using the Erlangian technique. Steady-state results, including the expected number in queue at random and arrival epochs, and waiting time distribution are found in terms of the unique root of the characteristic equation. Examples of extensive numerical work are presented in tabular forms.     

Two numerical models for landslide dynamic analysis

Two microcomputer-based numerical models (Dynamic ANalysis (DAN) and three-dimensional model DAN (DAN3D)) have been developed and extensively used for analysis of landslide runout, specifically for the purposes of practical landslide hazard and risk assessment. The theoretical basis of both models is a system of depth-averaged governing equations derived from the principles of continuum mechanics. Original features developed specifically during this work include: an open rheological kernel; explicit use of tangential strain to determine the tangential stress state within the flowing sheet, which is both more realistic and beneficial to the stability of the model; orientation of principal tangential stresses parallel with the direction of motion; inclusion of the centripetal forces corresponding to the true curvature of the path in the motion direction and; the use of very simple and highly efficient free surface interpolation methods. Both models yield similar results when applied to the same sets of input data.Both algorithms are designed to work within the semi-empirical framework of the “equivalent fluid” approach. This approach requires selection of material rheology and calibration of input parameters through back-analysis of real events. Although approximate, it facilitates simple and efficient operation while accounting for the most important characteristics of extremely rapid landslides. The two models have been verified against several controlled laboratory experiments with known physical basis. A large number of back-analyses of real landslides of various types have also been carried out. One example is presented. Calibration patterns are emerging, which give a promise of predictive capability.     

Multi-parameter homotopy for the numerical analysis of mems

The configuration space of electromechanical microdevices inherently includes areas of unstable operation, the analysis of which requires appropriate numerical techniques. Homotopy methods have proven to be suitable for rigid as well as for flexible device structures [Sens. Actuat. A 76 (1999) 9]. In many cases, the electric charge Q located on the actuating electrodes may be used as proper control variable to trace the device characteristics by path continuation. However it shows that, in certain cases, this choice can lead to an undesired, but unavoidable wide spacing of the calculated operating points and, hence, to a rather poor resolution of the device characteristics. We identify the cause of this phenomenon, introduce alternative homotopy parameters and present a new multi-parameter homotopy scheme, which switches automatically and smoothly to the locally most suitable homotopy parameter and, thus, allows for arbitrarily small spacing between the simulated operating points.     

A numerical analysis of muzzle blast precursor flow

A new computational technique, involving the formation of grids by conformal mappings, the use of the λ-scheme and of shock fittings is applied to solve the Navier-Stokes equations which describe the flow field behind the precursor shock consequent to the firing of a gun, until the bullet is entirely out of the barrel. The numerical analysis is presented in detail and reasons for the choice of the technique are discussed. Three examples are presented, discussed and compared with experimental results.     

A numerical analysis of turbulent flow in pipes

The finite element method is used to solve both fully developed and developing turbulent flow in pipes. A particular feature of the approach is the introduction of a special wall element. The purpose of the introduction of such an element is twofold. The first is to avoid using elements with extremely large aspect ratios and the second to attempt a better representation of near wall changes in velocity. The applicability of the method is illustrated by comparing with published experimental and numerical data.     

Minimal cycle bases for analysis of frames with semi-rigid joints

For an efficient force method of frame analysis, special cycle bases should be generated for the formation of localized self-equilibrating systems, leading to sparse flexibility matrices. In this paper, an algorithm is presented using a fundamental cycle basis, where the selected cycles are improved via an algebraic exchange method. Optimal analysis is performed for frames with semi-rigid joints. In this method, flexibility matrices are generated which are highly sparse. An ordering algorithm is also used for profile reduction to acquire an efficient method for the solution of the corresponding equations. Thus a complete force method analysis of semi-rigid frames is formulated and a computer code is developed. Examples are analyzed with the present approach and the results are compared to those of a stiffness method program with semi-rigid joints.     

Frictional contact analysis of spatial prismatic joints in multibody systems

The contact analysis of spatial prismatic joints remains a hard problem due to its complex nature. In this paper, a methodology for the frictional contact analysis of rigid multibody systems with spatial prismatic joints is presented, which is free of calculating the relative motion between the slider and guide, and is particularly suitable to the case of clearances being tiny. Under the assumption of the slider and guide being rigid, we prove that all types of contacts in the joint can be converted to point-to-point contacts. At each of the candidate points, two gap functions are introduced. However, in the proposed method, not the values of these gap functions but the relations between them are essential. In view of the non-colliding contacts being predominant when clearances of joints are tiny, we formulate the contact forces in terms of resultant frictional forces in the joint, resulting in a linear complementarity problem. By the proposed method, details about the contacts including the impact instants can be obtained, although impacts are not taken into consideration explicitly, as indicated by the numerical examples in this paper.     

Elasto-plastic contact stress analysis of joints subjected to cyclic loading

Rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading is carried out. An incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis. For the case of the interference fit, the analysis sequentially carries out insertion of the pin and application of the load on the joint, covering possible initiation of separation (and/or yielding) and progressively the receding/advancing contact at the pin-plate interface. Deformations of both the plate and the pin are considered in the analysis. Numerical examples are presented for the case of an interference fit pin in a large plate under remote cyclic tension, and for an interference fit pin lug joint subjected to cyclic loading. A detailed study is carried out for the latter problem considering the effect of change in contact/separation at the pin-plate interface on local stresses, strains and redistribution of these stresses with the spread of a plastic zone. The results of the study are a useful input for the estimation of the fatigue life of joints.