Finite element modelling of the Ilizarov external fixation system

This study describes a computational method for predicting the mechanical response of any configuration of the Ilizarov external fixation system. Mechanical testing of each of the individual components (ring, threaded rod, and wire) of the Ilizarov system was used to determine the stiffness of each component. Finite element (FE) analysis was then used to model each of the individual components. Each model was tuned to match the mechanical testing. A modular FE modelling system, using a master input file, was then developed where the tuned FE models of the individual components could be generated, positioned, and interconnected to replicate a range of fixator configurations. The results showed that the stiffness predications from the FE modelling of the fixator configurations were consistently 10 per cent higher than the stiffness values obtained from the mechanical testing. The FE modelling system can be used to predict the characteristic response of the fixator configurations and clearly shows the relative changes in that response for variations in the number of components used.     

A simple way to model wires used in ring fixators: analysis of the wire stiffness effect on overall fixator stiffness

The Ilizarov fixator has become widely used in the treatment of complex trauma and deformity correction in the United Kingdom over the last few decades. As such, it has been widely researched. Within this fixator, the characteristic fine wires are the weakest and most flexible component. The wires allow interfragmentary micromotion, which is believed to be beneficial to bone healing. In this paper, a novel and simple numerical model of the stiffness and deflection of the wires when the fixator is subject to axial and torsional loading is presented. A range of wire lengths and pretensions are analysed, and the results compared to the findings of other researchers, with generally good agreement. This indicates that fixator stiffness can be determined simply and without recourse to sophisticated finite element analyses or extensive physical testing. In addition, the model is used to predict the contribution of the wires to the overall stiffness of the fixator.     

Yielding of the clamped-wire system in the Ilizarov external fixator

This study demonstrates that the clamped-wire system used to suspend bones within an Ilizarov external fixator yields when the perpendicular load exceeds 50 N per wire. Cyclic loading was applied to tensioned wires clamped within an Ilizarov ring component, with steadily increasing load amplitude. Wires were tested at four initial tension settings. The amount of energy lost within the clamped-wire system per load cycle was calculated for every test. The results showed that there was a consistent trend to increasing non-recoverable energy loss per load cycle when peak loads exceed 50 N for all initial tension settings. A finite element (FE) model replicating the experimental conditions was performed to investigate the levels of stress within the loaded wires. The FE model analyses showed that high stresses were generated in the wires close to the clamping sites, and that the stress levels could reasonably be expected to exceed the material yield stress when loaded to about 55 N, for all initial tension settings. The results show that material yield, accompanied by some wire slippage through the clamps, is responsible for system yield, in agreement with previous studies. Although the initial wire tension has an appreciable effect on the wire stiffness, it did not affect the elastic load range of the clamped-wire system. To prevent yield of the clamped-wire system in practice, the fixator should be assembled with sufficient wires to ensure that the load transmitted to each wire by the patient does not exceed 50 N.     

Analytical solution of gradually varied flow equation in circular channels using variable Manning coefficient

The direct integration method is used to solve the equation of gradually varied flow (GVF) in open prismatic channels. The GVF is a non-uniform flow with gradual changes in flow depth. In circular channels, Manning roughness coefficient under the partially full flow condition varies with the flow depth, and thus a variable Manning coefficient should be used to calculate the water surface profile. It is accepted that the Manning coefficient varies with flow depth in accordance with Camp’s curve. Given that circular channels have an important application in sewer systems, this research presents a semi-analytical approach for establishing the gradually varied flow profiles in circular channels through application of a variable Manning coefficient. For this, using two approximation expressions, the integrand of the GVF equation is expanded into a finite set of partial fractions and then every term of them is integrated separately. The proposed semi-analytical solution uses a single step for the computation of water surface profiles and provides an accurate and simple way to compute GVF flow profiles.     

The effect of clamping a tensioned wire: implications for the Ilizarov external fixation system

This study demonstrates that clamping a tensioned wire can cause a reduction in wire tension. Tension (about 1275 N) was applied to a wire that was subsequently clamped, using cannulated bolts, to the steel half-ring of an Ilizarov external fixator. The tension in the wire was monitored before, during and after clamping. The apparatus was disassembled and the deformations in the wire caused by the clamps were measured. This experiment was repeated 15 times. When the wire was clamped to the frame, the wire tension was reduced by 22 +/- 7 per cent (mean +/- standard deviation, SD). The drop in wire tension was linearly correlated (r = 0.96; p < 0.001) with the deformation caused by the bolts. A finite element (FE) model of the wire was also constructed. The model was pre-stressed (tensioned), and the clamping effect replicated. This analysis showed that clamping the wire could be considered to squeeze the wire outwards (like toothpaste from a tube) and so reduce its tension during fixator assembly. To assess the magnitude of this effect in the clinical situation, the FE model analysis was repeated to replicate clamping a 1.8-mm-diameter wire to a 180-mm-diameter steel Ilizarov ring component. The analysis showed that for these conditions the tension reduced by 8-29 per cent. The results of this study highlight a general engineering problem: how can a tensioned wire be secured to a structure without an appreciable loss of tension? If the performance of the structure depends on the wire tension, this performance will change when the wire is secured.     

Plastic expansion of a circular hole in sheet metal subjected to biaxial tensile stress

A new yield function proposed by Hill is used to predict the plastic stress and strain distributions in an annulus of sheet metal subjected to a radial tension at its outer periphery. The new yield function has greater generality than the original anisotropic yield function. The theoretical predictions show good correlation with experimental strain distributions measured for sheets of aluminium killed steel, soft aluminium of commercial purity and soft 70/30 brass. There is seen to be a need for the experimental determination of more complete yield loci for sheet metal.     

Numerical modelling of dry-out in pulsating heat pipe using VOF model

Journal of Mechanical Science and Technology - Operational limits are critical in the continuous functioning of a pulsating heat pipe (PHP). A computational fluid dynamics study was conducted to...     

Kinematic modelling of a 3-axis NC machine tool in linear and circular interpolation

Machining time is a major performance criterion when it comes to high-speed machining. CAM software can help in estimating that time for a given strategy. But in practice, CAM-programmed feed rates are rarely achieved, especially where complex surface finishing is concerned. This means that machining time forecasts are often more than one step removed from reality. The reason behind this is that CAM routines do not take either the dynamic performances of the machines or their specific machining tolerances into account. The present article seeks to improve simulation of high-speed NC machine dynamic behaviour and machining time prediction, offering two models. The first contributes through enhanced simulation of three-axis paths in linear and circular interpolation, taking high-speed machine accelerations and jerks into account. The second model allows transition passages between blocks to be integrated in the simulation by adding in a polynomial transition path that caters for the true machining environment tolerances. Models are based on respect for path monitoring. Experimental validation shows the contribution of polynomial modelling of the transition passage due to the absence of a leap in acceleration. Simulation error on the machining time prediction remains below 1%.     

Modelling the evolution of residual stresses during tensile testing of elastoplastic wires subjected to a previous bending operation

During coiling operations high residual stresses are frequently developed in steel wire. In this paper the stress distribution in wires during coiling, unwinding and subsequent tensile testing is modelled for numerous bending degrees, assuming perfect Voce plastic deformation and linear elastic behaviour. The influence of such residual stresses on the observed tensile test data can be deduced. It is shown that coiling with spool radii as used today industrially can lead to measurement of wire properties deviating significantly from the “true” properties of a properly coiled wire. Also, a method is proposed to deduce the original flow behaviour of coiled samples from tensile test curves, hence filtering the effect of the residual stresses.     

Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model

This paper presents an analytical method based on the unequal division shear-zone model to study the machining predictive theory. The proposed model only requires workpiece material properties and cutting conditions to predict the cutting forces during the orthogonal cutting process. In the shear zone, the material constitutive relationship is described by Johnson?CCook model, and the material characteristics such as strain rate sensitivity, strain hardening, and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within the primary shear zone. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of the shear strain rate. The cutting forces are calculated for different machining conditions and flow stress data. Prediction results were compared with the orthogonal cutting test data from the available literature and found in reasonable agreement. In addition, an analysis of the deviation from experimental data for the proposed model is performed, the effects of cutting parameters and tool geometry were investigated.     

Analytical modelling of microstructure changes in the machining of 304 stainless steel

In the machining of hard machined materials, microstructure changes in the machined surface must be taken into account to improve product performance. Therefore, a large number of experimental and finite element method investigations have been carried out to investigate these microstructure changes. However, until now, only a few studies have reported the analytical modelling of microstructure changes. This paper presents a hardness-based analytical model that accounts for both mechanical and thermal effects in predicting microstructure changes during the machining of 304 stainless steel. The model was also validated for a range of cutting speeds, feed rates, and wear widths. The predicted results are in good agreement with the experimentally measured results. Thus, with the analytical model, an accurate prediction of microstructure changes is achieved, which reduces experimental expense and finite element method computational time.     

Identification of external forces in mechanical systems by using LifeCycle model and stress-stiffening effect

This paper presents an optimization-based inverse procedure for the determination of external loads applied to a given mechanical structure, by using information concerning the dynamic behavior of the system and its corresponding finite element model. The influence of the stress-stiffening effect on the dynamic characteristics of structural systems is used to establish a relation between the dynamic responses and the applied external forces. An optimization problem is formulated in which the objective function represents the difference between the measured modal characteristics of the loaded structure and their finite element counterparts. The loading parameters (magnitude, position and direction) assumed as being unknown, are considered as design variables. The identification procedure is illustrated by means of numerical simulations and experimental tests, in which a heuristic technique known as LifeCycle model was used.     

Contact pressure distribution in circular tube expansion using a conical plug

The technique of evaluating contact pressure distributions along a plug metal interface by measuring the deformations in terms of plug surface strains using electrical resistance strain gauges has been explored. To relate the unknown pressure distributions to the strain gauge readings, a finite element model of a plug was used assuming that the normal and shear pressures can be represented as a linear combination of generalized distributions, which have the form of polynomials up to the fourth order.This technique has been suitably applied to a thin brass tube expanding process for a single expansion ratio, and a single conical hollow plug with and without lubricant. To ensure good accuracy in the results, particular care was given to technological plug design and the choice of a number of appropriate strain gauged points on the inside surface of the plug.The more adequate polynomial representations of the normal and shear contact pressures were found by analyzing the degree of randomness in the distribution of the residuals. A comparison was made between experimental pressure distributions and those predicted by the slab method. Results obtained were compared with those derived from the use of a polynomial curve fitting method, besides assuming an average coefficient of friction at the interface.     

自研角度计量转台在圆分度器件校准中的应用

为了实现亚角秒级圆分度器件的高精度校准,建立了基于角度计量转台和自准直仪的角度测量系统,研究了基于无实物基准的圆分度误差检测方法和控制测量系统引入误差的策略。简要介绍了基于真空预载气浮支承和超声马达驱动的自研转台的结构,搭建了整个测量系统。利用圆封闭原理和最小二乘原理分析了圆分度误差的测量算法,讨论了测量过程的误差来源,并分析了抑制各误差源的方法。最后,在构建的测量系统上测量了多齿分度台的圆分度误差,并对测量不确定度进行了分析。实验结果表明：自研计量转台和被校多齿分度台的最大圆分度误差分别为0.12″和0.15″,测量不确定度为0.05″（k=2）。通过比对,表明测量系统能够实现亚角秒级圆分度误差的高精度校准。     

Suppression of a sound field in a wide circular waveguide using an active method

An active process of noise suppression in a wide waveguide with the help of a receiving-emitting device located on the waveguide wall is studied. Using the measurement results of an extraneous field propagating in the waveguide, the amplitudes and phases of auxiliary emitters for suppression of the incident exterior field are determined.     

Detailed modelling of a moving heat source using multigrid methods

The actual contact between solid surfaces is generally rough and time dependent. This roughness can only be correctly described using a 3D model. Moreover, severe thermo-mechanical loading induces high stress and temperature gradients within a thin subsurface layer. Even higher gradients are obtained in the case of surface coatings. Consequently, the problem is strongly multiscale: from contact to coating to roughness, the characteristic dimensions range from millimeter to nanometer.A straightforward discretization of this multiscale problem would exceed the memory and CPU capabilities of current computers. The aim of this work is to propose a more efficient numerical model able to deal with this multiscale problem: using 10⁹ points and 10³ timesteps.This paper traces the history of the numerical solutions of the heat equation from the pioneering work of Carslaw and Jaeger, to the current era.The proposed model is based on multigrid techniques within a finite difference frame work. Localized refinement is implemented to optimize memory and computing time costs. The numerical performance of the solver is presented through a comparison with analytical results using different types of boundary conditions. A multisource contact is studied as a first approximation to real asperity interaction.     

Analytical model for the thermo-hydrodynamic behaviour of a thin lubricant film

The thermo-hydrodynamic behaviour of lubricant films strongly depends on the operating conditions (pressure, speed), on the physical properties of the lubricant, on the temperature level and, furthermore, it is often nonlinear. The thermo-hydrodynamic study of a thin fluid film confined between two parallel planes on relative motion is presented in this paper. The case considered is that of not fully developed thermal conditions and physical properties of the lubricant independent of temperature. A 2D analytical solution is proposed to determine the temperature distribution. The physical parameters affecting the characteristic length, beyond which the flow becomes thermally developed, are determined.     

Control of laminar vortex shedding behind a circular cylinder using tabs

Small, thin flat plates (called tabs hereafter) are attached to the upper and lower surfaces of a circular cylinder to control vortex shedding and reduce the mean drag and lift fluctuations at the Reynolds number of 100. We vary the location and size of the tabs and the distance between the adjacent tabs. The maximum amount of drag reduction by the tabs is 17%. It is found that the tabs perturb twodimensional vortex shedding and introduce spanwise mismatch of vortex shedding, which weakens the strength of vortex shedding or even annihilates vortex shedding. The present result suggests that these tabs are an effective passive device for the control of vortex shedding behind two-dimensional bluff bodies.     

Analysis of thermal performance and thermal stress using two-dimensional thermoelastic model for a 50 MWe external cylindrical solar receiver

Journal of Mechanical Science and Technology - The thermal stress arisen from highly inhomogeneous solar radiation and temperature distribution during operation is mainly responsible for the...