A Note on Interpreting Tool Temperature Measurements from Thermography

Thermography (thermal imaging) is a well-established experimental method for studying cutting tool temperature distributions. In one form, cutting edge temperatures within the chip / tool contact area are deduced from thermal images of tool faces normal to the cutting edge but offset from the contact region. In general practice, the offset is made as small as possible (<< 1 mm) and it is assumed that the observed temperature is the same as that within the contact. In this short communication an approximate analytical model is developed for the influence of the offset on the observed temperature. The predictions from the model are compared with previously unpublished existing results on the machining of Ti alloys (Ti6Al4V and Ti5Al4V) and on steel (AISI 4140). It is shown that ignoring the offset may introduce underestimates of cutting edge temperature of ≈ 30% or more. This is large compared to the usually considered uncertainties of ± 5% from camera and tool emissivity calibration. There is a need for a dedicated study of this effect.     

Effect of small harmonic oscillations during the steady rolling of a cylinder on a plane

If a wheel rolling over a rail transmits a tangential traction, frictional microslip occurs in part of the contact area, resulting in energy dissipation and localized wear. If the applied forces oscillate in time, the resulting wear will be non-uniform, resulting in ‘corrugations’ that can grow with progressive passes, depending on the dynamics of the overall system. In this paper, a linear perturbation method is used to obtain closed-form expressions for the receptance of a two-dimensional rolling contact subjected to small oscillations in normal force and rotational speed superposed on a mean value in the limit of large coefficient of friction. Corresponding expressions are also obtained for the amplitude and phase of the energy dissipation in the contact, which is expected to correlate with the local wear rate.The results are compared with a simpler Winkler model of the contact and with other models that have been used for the analysis of rail corrugation. Surprisingly good agreement is obtained with numerical results due to Gross-Thebing for the receptances due to oscillations in rotational speed.     

Evaluation of friction coefficient using indentation model of Brinell hardness test for sheet metal forming

This work presents an indentation model of the Brinell hardness test, which is a rigid ball-deformable plane contact model (RB-DP model), to elucidate the sliding friction mechanism of sheet metal forming. In the proposed model, the friction force can be defined as a combination of shear (shearing effect) and plough (ploughing effect) forces. The real contact area ratio α is determined from the RBDP model under sliding condition. Moreover, the lateral contact area ratio A _c /A _r can be specified as a function of the real contact area ratio α. Based on Meyer’s law and Hertz contact problem, the maximum contact area ratio α _u , a limiting condition of the real contact area ratio α, can be described as a function of the strain hardening exponent n. Additionally, a limiting condition applies: the strain hardening exponent n must be less than 0.64 in the present model. The present friction model reveals that the friction coefficient μ _d is a function of strain hardening exponent n, the real contact area ratio α and the maximum contact area ratio α _u . The calculated friction coefficient μ _d agrees with the published experimental results.     

A numerical investigation of the sinusoidal model for elastic layers in line contact

Distributions of normal stresses and surface deformations, induced when an elastic layer of finite thickness is indented by a frictionless rough rigid flat or cylindrical indenter, are calculated numerically. It is assumed that the punch has a sinusoidal roughness superimposed on its nominal profile. Two cases will be examined, namely when the elastic layer is either bonded to a rigid backing or resting on a frictionless rigid backing (unbonded). Chebyshev polynomials of the first kind T_n(x) are utilized to model both the unknown pressure and the given deformation over the contact area. The governing elasticity equation is thereby reduced to a finite set of linear equations and hence a complete solution is found. The present numerical method is simple, accurate and valid in the full range of Poisson's ratio 0 v 0.5. Moreover, a set of semi-analytical solutions for the contact pressure is obtained for both thin unbonded and bonded elastic layers. The numerical results compared favourably with the asymptotic solutions. The effects of the layer thickness, layer compressibility and roughness amplitude parameters on the contact stresses and deformations are considered.     

Calculation of Longitudinal Oscillations in a Cylinder of Finite Dimensions

Longitudinal (symmetrical) oscillations of a thin disk and a cylinder of infinite length have been analyzed using the linear elasticity theory. Dispersion equations have been obtained under the simplifying assumption that the normal stress component averaged over the cylindrical surface of a disk of finite dimensions turns to zero. Solutions obtained using iterative techniques have shown that the parameters calculated by both models can be matched to one another at a critical value of the height-to-diameter ratio (h/d) of 0.85. Calculations of the dispersion coefficient at different values of the Poisson ratio with an accuracy sufficient for practical applications have been tabulated for h/d ranging between 0.05 and 10.0.     

An investigation into the generation of corrugation by transient spin creep

It has been suggested that short wavelength corrugation of railway track may arise from a mechanism in which the fluctuating spin moment normal to the contact patch preferentially wears some wavelengths of an initially aperiodic roughness on the rail. This hypothesis has been investigated in the laboratory in a rolling contact disc machine. After running for a total of 7 × 10⁶ cycles the experimental discs were worn to a uniform roughness throughout the appropriate wavenumber range. We therefore believe that it is unlikely that the proposed mechanism is sufficiently selective to produce corrugation. Corrugations of a longer wavelength were produced by a wear mechanism involving the dynamics of the disc machine.     

Multiple Slips in Atomic-Scale Friction: An Indicator for the Lateral Contact Damping

The occurrence of multiple jumps in 2D atomic-scale friction measurements is used to quantify the viscous damping accompanying the stick–slip motion of a sharp tip in contact with a NaCl(001) surface. Multiple slips are observed without apparent wear for normal forces between 13 and 91 nN. For scans parallel to [100] directions, the tip jumps between minima of the substrate corrugation potential in a zigzag fashion. An algorithm is applied to determine histograms of lateral force jumps which characterize multiple slips. The same algorithm is used to classify multiple slips occurring in calculated lateral force maps. Comparisons between simulations and experiments indicate that the nanometer-sized contact is underdamped at intermediate loads (13–26 nN) and becomes slightly overdamped at higher loads. The proposed procedure is a novel way to estimate the lateral contact damping which plays an important role in the interpretation of measurements of the velocity and temperature dependence of friction, of slip duration, and of the reduction of friction by applied perpendicular or parallel oscillations.     

Short-pitch rail corrugation: A possible resonance-free regime as a step forward to explain the “enigma”?

Rail corrugation has been noticed at least for 100 years, but (particularly short pitch one in the range 20–80 mm) has been considered an enigma because measured corrugation wavelength did not relate well with wear-instability models. The apparently large number of governing parameters has resulted in many independent efforts to generate models, which do not entirely correspond to the collected experimental evidence, and therefore there is still some uncertainty over the possible critical factors dominating the phenomenon.We show in the paper that there is a simple possible mechanism of corrugation in longitudinal direction, apparently not noticed before in the literature by other authors, which does not necessarily correspond to a resonance in the system, not even the pinned–pinned resonance associated with the effect of discrete supports, but may depend on geometrical and loading conditions (normal load, creepage ratio, shape of the contact area, etc.), in general overall agreement with experiments.Additionally, some approximate calculations including discrete supports, using a typical concrete sleepers vertical receptance of BR use, show no evidence of corrugation mechanism at the pinned–pinned resonance, at least in the longitudinal direction. A full comparison between lateral and longitudinal mechanisms would depend on the particular value of the lateral creepage vs. longitudinal creepage, system-specific. The present “resonance-free” mechanism is a possible alternative for the data which fall outside the pinned–pinned resonance range.     

材质气孔率和气孔大小与表面粗糙度的数学模拟与特征

为提高光学系统的成像质量,研究了光学系统中镜片表面粗糙度与镜片材质中的颗粒大小、缺陷、气孔率、气孔大小的关系.通过几何方法,建立了气孔率与气孔大小和数量的关系模型,分别给出了单位体积和单位面积中气孔率与气孔大小和数量的关系表达式.最后用数学方法建立了材质中气孔率、气孔大小与表面粗糙度的定量模型,给出了表面粗糙度与材质气孔率和气孔大小的关系表达式,表明表面粗糙度近似与材质中的气孔率成正比,与气孔大小成正比.     

Simplified theories of flat rolling-I. The calculation of roll pressure, roll force and roll torque

The classical theories of rolling continue to be widely used in practice although finite element methods can provide a more detailed analysis of the deformation during rolling. Both a homogeneous deformation solution and an inhomogeneous method for calculating the roll pressure are reformulated as a development of the classical theories of flat rolling. The new solutions do not require the gradient of the stress-strain curve d(2k)/dφ. This simplifies the computations, leads to consistent estimates of the main rolling parameters including the calculation of the roll torque and allows more general yield stress functions to be readily included in solutions for hot or cold rolling. Data for the rolling of annealed copper is used to establish the consistency and accuracy of the new solutions.     

Autoradiographic studies on the mode of growth in jejunal crypt cells of the mouse

The structures of primary concern in Part A are varieties—the generalization in higher dimensions of smooth curves and surfaces. Fixed orientation random s-sections (s-dimensional flat sections) of a fixed t-variety (t-dimensional variety) in R^d (d-dimensional space) are considered in Section 2. The t-variety induces a density-cum-orientation distribution which is related to corresponding sectional quantities. The by now classical basic formula; of stereology are all special cases of the simple multi-dimensional formula (2.16). Next (Section 3), statistics of the variety of intersection of several statistically homogeneous random varieties are related to the corresponding statistics of the parent varieties. Part B is concerned with the analysis by random s-sections of fixed aggregates of t-dimensional opaque particles (i.e. varieties for 1 ≤ t ≤ d — 1, domains for t = d) embedded within an opaque specimen. Fixed orientation random sections are considered in Section 5, and isotropically oriented ones in Sections 6–10. It is shown in Section 7 that the mean particle ‘caliper diameter’, a key quantity, may in theory be estimated by isotropic slice sectioning. The theory is particularly rich when the particles are convex, witness the arrays of useful formula; in Sections 8–10. Crofton's remarkable ‘second theorem’ comes into its own in Section 9, permitting simple estimates from isotropic test lines of mean area squared to mean perimeter (when d = 2) and mean volume squared to mean surface area (when d = 3); in fact, the formulæ of Sections 7–9 suggest estimates for both mean and variance of the areas (when d = 2) and volumes (when d = 3) of aggregates of embedded convex particles. Further results for aggregates of convex polytopes are given in Section 10. Certain general considerations and principles relating to estimation from random sections in the practical cases, i.e. d ≤ 3, are included in the final Section 11. Equations which are the specializations of multi-dimensional formulæ to the practical cases are asterisked. A feature is the attention given to the proper probabilistic specification of random sections through the specimen, a matter that seems largely to have been ignored.     

Friction at Small Displacement

Low contact resistance between metal surfaces is often observed in spite of interposed lubricant and/or oxide films. To study this effect an apparatus is used with which normal force and tangential microdisplacement are applied between a small lead rider and a gold flat with various surface film conditions. Simultaneous oscillograph records are made of forces, displacement, and contact resistance. A unique low compliance force transducer allows direct recording of the frictional behavior during microdisplacement.

Under nonoxidized and nonlubricated conditions, and with either oxide or stearic acid lubricant film alone, friction is high and contact resistance is low. With oxide and lubricant together, friction is much lower and slide is smooth, but contact resistance remains low and Ohm's law is obeyed.

The results are consistent with Greenwood's theory of contact resistance for a cluster of minute metallic contact spots within the load-supporting area. The contact resistance of such a cluster is indistinguishable, for practical purposes, from that given by complete metallic contact.     

On non-symmetrical plane contacts

Plane elastic contact problems are considered, with particular emphasis on asymmetrical punch profiles, in the case of ‘complete’, ‘partially complete’ and ‘incomplete’ contact. An explicit, analytical solution is presented for the case of a single area of contact where the overlap is described by a generic spline function, and examples presented. The interior stress field and strength of the contact, under full or partial slip conditions, are also discussed, and some example shown for representative cases. It is found also that the direction of sliding has a significant effect for the strength of non-symmetrical contacts.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

Study on the Effect of Track Curve Radius on Friction-Induced Oscillation of a Wheelset–Track System

Abstract

The purpose of this article is to investigate the correlation between the friction-induced oscillation of a wheelset–track system and curve radius and to explain a general phenomenon of rail corrugation based on the viewpoint of friction-induced oscillation. The typical phenomenon of rail corrugation in metros is that corrugation generally arises when the curve radius is quite small, whereas it rarely occurs when the curve radius is larger or on a straight track. Different multibody models of the vehicle–track system and finite-element models of the multiple-wheelset–track system with different curve radii are established, respectively. According to the creep force analyses and unstable vibration analyses, the correlation between the creep force and friction-induced oscillation can be identified. Then the effect of the track curve radius on the friction-induced oscillation of the wheelset–track system can be summarized, which provides an explanation of the typical phenomenon of corrugation.     

Technique of Determination of the Piezoelectric Modulus d 33 and Investigation of the Limits of its Use

The classification of the piezoelectric modulus measurement methods for different loading regimes is investigated. It is established that the quasi-static methods make it possible to determine the static piezoelectric constants with the minimum errors. An improved method of measuring the piezoelectric modulus d ₃₃ in the quasi-static regime is developed. The method ensures the minimum effect of changes in the domain orientation and transition processes. Dependences of d ₃₃ on the level of mechanical stresses _n are obtained for TsTS-19, TsTS-23, and TsTBS-3 piezoceramics and it is shown that their nature depends of the ferro-rigidity of the piezoceramics composition. Features of the dependences d ₃₃( _n ) associated with the variation of the contact area of piezoelectric elements in the process of measurements and the effect of changes in the domain orientation are revealed. It is shown that the lower boundary of the compression force amounts to 2 MPa for TsTS-19. It is also established that the optimum dimension of the piezoelectric elements in determining d ₃₃ must satisfy the condition 0:45 < < 1:75. It is calculated that the error in measurements of d ₃₃ in accordance with the method proposed is 4.5% with the confidence probability of 95%.     

Preliminary investigation of the effect of dimple size on friction in line contacts

The scale of surface texture is becoming an important issue of surface texture design, particularly for the condition of low speed and high load. Experiments were carried out to investigate the effect of dimple size on friction under line contact condition. The patterns of dimples distributed as square array were fabricated on the surface of brass disks. Each pattern has the same area density of 7%, the same depth over diameter ratio h/d of 0.03, and dimple diameter d varying from 20 to 60 μm. The frictional tests of the brass disk sliding against a stationary cylindrical surface of bearing roller were conducted. It was found that the pattern with dimple diameter of 20 μm presented the effect of friction reduction. For the further understanding of the effect of dimple size under line contact condition, numerical simulations were also carried out to evaluate the hydrodynamic pressure within the contact of cylindrical and plane surfaces. The effects of dimple size and radius of the cylinder on the load carrying capacity were evaluated and discussed.     

地铁线路上一种钢轨波磨现象的成因分析

针对地铁线路直缓点附近区间上的一种特殊钢轨波磨现象,根据现场条件建立车辆-轨道系统数值模型,并对模型的有效性进行了验证;运用数值模型分析上述线路区间的轮轨界面黏滑特性,解释了该类钢轨波磨的形成原因;结合轮轨系统动力响应特性,分析促使钢轨波磨生成和发展的波长固定属性的成立条件。结果表明：在线路直缓点附近区间,导向轮对和从动轮对内外侧轮轨界面均会发生横向黏滑运动,而轮轨界面发生纵向黏滑运动的概率较低,且黏滑运动的交替发生,导致了钢轨表面初始波磨的形成;当导向轮对和从动轮对内外侧车轮经过线路直缓点时,外侧轮轨接触表现为轮缘-轨距角接触,且接触形式的改变造成了轮轨系统法向力的波动,说明直缓点的存在赋予了轮轨横向黏滑运动的相位同步特征,能够保持钢轨波磨的波长固定属性,因此,钢轨波磨最终形成并不断发展,而且内轨表现为轨面波磨,外轨表现为侧面波磨,这与实测区间波磨现象一致。     

Fretting fatigue strength estimation considering the fretting wear process

In fretting fatigue process the wear of contact surfaces near contact edges occur in accordance with the reciprocal micro-slippages on these contact surfaces. These fretting wear change the contact pressure near the contact edges. To estimate the fretting fatigue strength and life it is indispensable to analyze the accurate contact pressure distributions near the contact edges in each fretting fatigue process.So, in this paper we present the estimation methods of fretting wear process and fretting fatigue life using this wear process. Firstly the fretting-wear process was estimated using contact pressure and relative slippage as follows:

W=K×P×S,