Transcendental inverse eigenvalue problems in damage parameter estimation

In this paper the author has introduced transcendental eigenvalue problems for estimating the damage parameters in the continuous structure from measured eigenvalues or natural frequencies. For simplicity axially vibrating rods are considered in which single or multiple damage parameters due to open cracks or notches are simulated by linear springs that are representative of the loss in stiffness or axial rigidity at the location of cracks. Transcendental eigenvalue problems (direct and inverse) associated with rod having multiple damage parameters have been formulated and solved. The numerical method for solving such eigenvalue problems are developed which overcomes the requirements of closed form characteristic frequency equations that are often unavailable. The modeling and solution approach developed here is utilized for evaluating the spectrum of rods with multiple damage parameters as well as for identifying the locations and severity of the damage parameters purely from the eigenvalues. Numerical examples and simulations corresponding to various damage configurations are presented and verified against experimental evidence. It is demonstrated that the solution of transcendental inverse eigenvalue problems can be successfully used for estimating the damage parameters by using only few and selected eigenvalues corresponding to the measured resonant and anti-resonant frequencies of the rod.     

Modeling of EMI response of damaged Mindlin–Herrmann rod

To ensure high sensitivity to incipient damages, electromechanical impedance (EMI) is measured at high frequencies for damage detection. In the working high-frequency range, very high vibration modes, of the order of the thousandth mode or higher, of a structural member are likely to be activated. This imposes a great difficulty on the accurate modeling of EMI response of a structure. In this paper, the reverberation matrix method (RMM) is adopted to study the dynamics of a Mindlin–Herrmann rod with surface piezoelectric patches. The rod is inhomogeneous along the axial direction so that damage-induced reduction of cross-section or Young's modulus could be easily incorporated in the model. A piecewise-homogeneous rod model is subsequently introduced to approximate the inhomogeneous rod, along with a shear lag model of interfacial bonding between the lead zirconate titanate (PZT) patches and the host rod. An analytical expression for the electric impedance (or admittance) of the coupled model of PZT patch-bonding layer-host rod system is derived. Comparison with other established results is presented. Parametric investigations are also performed to show the dynamic properties of the coupled smart structural system. The analysis in this paper provides necessary theoretical basis for damage detection of rod via the EMI signatures.     

Quality control of rolled rods by the electromagnetic-acoustic technique

Special features of testing of metal rods by the electromagnetic-acoustic technique were studied using rod waves (Pochhammer wave s ₀, torsional wave T ₀) and bulk waves (longitudinal l and transverse t waves of radial direction). It was shown that rod waves can detect not only a discontinuity but also a change in the chemical composition or length of rods. Bulk waves make it possible to perform nondestructive testing and structural analysis and to find a change in diameter. A combination of pivoting and bulk waves makes it possible to find the anisotropy of elastic properties and evaluate the texture of rolled metal.     

Wear of dental enamel

Teeth wear for a number of reasons. One of the causes for wear is the use of abrasive tooth pastes. A study is reported in which enamel was damaged by single pass sliding of a diamond indenter. In single crystals of fluorapatite, wear occurs by flaking out of chips of material and severely fractured substrate is left behind. On the other hand teeth are made of small rods of polycrystalline hydroxyapatite of the order of 5 μm in diameter oriented perpendicular to the tooth surface. This rod structure of human teeth prevents large scale flaking out of material. Apparently the subsurface cracks do not extend from one rod to the other so that subsequent passes do not result in severe wear. Small abrasive particles may do considerable damage to rods, but the overall effect is small. Large abrasive particles with high loads cause separation of rods, and cracks appear to propagate but without severe permanent damage.     

Three-dimensional vibration analysis of thick, tapered rods and beams with circular cross-section

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, tapered rods and beams with circular cross-section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u_r, u_θ, and u_z in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four- digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3-D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler–Bernoulli beam theory.     

ON THE NATURE OF MACHINING CRACKS IN GROUND CERAMICS: PART I: SRBSN STRENGTHS AND FRACTOGRAPHIC ANALYSIS

ABSTRACT

Machining cracks in ground sintered reaction-bonded silicon nitride (SRBSN) rods and bars were analyzed by fractographic techniques. Grinding flaw sizes were as small as 12 µm and as large as 80 µm and correlated strongly with grinding direction and wheel grit size. Some grinding treatments had no deleterious effect on strength since the machining cracks were very small and fracture occurred from the material's inherent flaws. The telltale signs of machining damage may be detected with conventional low power optical microscopy using simple fractographic techniques. The telltale signs are summarized in a new series of schematic drawings which will aid pattern recognition for engineers and fractographers.     

利用复合激励的无盲点管道裂纹漏磁检测新方法

管道是石油和天然气工业的重要组成部分,而轴向裂纹是管道安全运营的重要隐患。传统的漏磁检测技术(MFL)对管道中轴向裂纹的检测灵敏度不高,从而形成检测盲区。本文提出了一种利用复合激励的MFL检测新方法,可实现对轴向和周向缺陷的同步检测。首先,利用U型磁轭对管壁进行交直流复合磁化;直流磁化场直接作用于周向裂纹并形成有效的MFL检测信号,而交流磁化场则在管壁内形成垂直于磁化方向的均匀涡流场;当该涡流场受到轴向裂纹干扰时,将形成二次感生磁场的扰动,因此,新方法通过对管壁表面的漏磁场及二次感生磁场检测,同时获得周向和轴向两个方向的探测能力;最后开展仿真和实验,并分析了新方法中作用于轴向和周向裂纹的磁化场、涡流场和二次感生磁场的分布。结果表明,新方法只需通过一次扫描,即可以获得缺陷的轴向和周向特征,实现了对裂纹的无盲点检测。     

水平井抽油杆柱力学模型的建立与分析

首先分析水平井筒里抽油杆柱的运动状态,考虑柱塞与悬点运动的不一致性,找出杆柱受力最大和最小的位置时刻,根据井筒中抽油杆柱的空间几何关系,考虑抽油杆的约束条件和井斜角、方位角的变化等边界条件后,建立抽油杆柱的力学模型,并对模型进行相关分析,对杆柱的优化设计和优化配套防偏磨的工艺具有一定的指导意义.     

复杂裂纹涡流检测与评估方法研究

钢轨表面及上表面产生的滚动接触疲劳裂纹通常以斜裂纹或多角度复杂裂纹的形态存在,对其检测和评估是个难题。 基于此,采用基于无线能量传输的涡流检测方法(WPT-ECT),设计新的探头结构并结合神经网络算法对裂纹进行检测和评估。 首先,有别于现有 WPT-ECT 方法,采用增大激励频率,而非串并联电容的方式,构造谐振电路;其次,根据复杂裂纹的特点,设计 由两个八字形激励线圈和两个矩形接收线圈组成的方向性探头结构;最后,充分提取检测信号的特征,并运用径向基神经网络 算法对裂纹进行识别。 仿真和实验结果表明,所提出的探头结构对任何角度的缺陷均敏感。 同时,RBF 算法对斜裂纹、T 裂纹、 Y 裂纹和 1. 2 mm 提离下的 T 裂纹的识别准确率分别为 92. 00% 、 95. 27% 、96. 64% 和 89. 50% 。     

基于双轴 TMR 电磁传感器的裂纹检测方法研究

针对单一激励交流电磁探头检测任意方向裂纹容易出现漏检问题,设计了用于检测奥氏体不锈钢表面斜裂纹的新型双激励传感器,建立了奥氏体不锈钢表面裂纹交流电磁场检测仿真模型,开发了基于新型双激励传感器和高分辨率隧道效应磁阻传感器的金属平板表面裂纹检测系统。基于理论模型和试验系统研究了试件上裂纹走向和裂纹宽度对传感器拾取到磁场分量幅值的影响规律,研究了裂纹检测与方向判定方法。仿真和实验结果表明,利用磁场分量B_x、B_y畸变特征能够以相同的灵敏度检测出试件表面尺寸为15 mm×0.2 mm、深度大于3 mm的微小裂纹,并实现裂纹方向判定。引入宽度补偿参数后减小了横向、纵向裂纹判定误差,判定误差最大为3.9°。     

Finite element analysis of coating adhesion failure in pre-existing crack field

Abstract

The influence of a pre-existing crack field on coating adhesion failure in a steel surface coated with a 2 μm thick titanium nitride (TiN) coating was investigated by finite element method modelling and simulation. The stress and strain fields were determined in contact conditions with a spherical diamond tip sliding over the coated surface at a loading of 8 N. One crack in or at the coating increased the maximum tensile stresses with six times from 82 to 540 MPa when the crack was vertical through the coating or L shaped and with nine times when the crack was horizontal at the coating/substrate interface. A simulated multicrack pattern relaxed the tensile stresses compared to single cracks. The results indicate that a cracked coated surface needs to have about five to nine times higher adhesive and cohesive bonds to resist the same loading without crack growth compared to a crack free surface. For optimal coated surface design, the strength of the adhesive bonds between the coating and the substrate in the vertical direction needs to be 50% higher than the cohesive bonds within the coating and the substrate in the horizontal direction. The first crack is prone to start at the top of the coating and grows vertically down to coating/substrate interface, and there it stops due to the bigger cohesion within the steel material. After this, there are two effects influencing that the crack will grow in the lateral direction. One is that steel cohesion is normally bigger than the coating/interface adhesion, and the second is that there are higher tensile stresses in the horizontal than in the vertical cracks. Several vertical cracks can stop the horizontal crack growth due to stress relaxation.     

Thermodynamic Differences of Different Friction Pairs in a Multidisc Clutch Caused by Spline Friction: Numerical Simulation and Experimental Verification

Abstract

Considering the spline friction, the dynamic model of a multidisc clutch is established that permits the calculation of the contact pressure and friction torque acting at each friction surface; the thermal model is then developed to investigate the temperature difference between different friction pairs. The corresponding test bench is established, where the effect of inertia on the torque error is analyzed in detail. The simulated and measured results are compared to validate the numerical model and confirm the existence of spline friction. The results indicate that spline friction can lead to the attenuation of contact pressure on friction pairs along the axial direction. Therefore, there exists a significant temperature gradient in the axial direction, and the maximum temperature appears in the second separate plate near the piston. Moreover, the friction torque of a single pair decreases along the axial direction. Thus, as the number of friction pair increases, the total friction torque increases nonlinearly, and the average torque of single friction pair decreases gradually.     

Combined rod and tube extrusion: Numerical solution of axi-symmetric slip-line fields and associated velocity fields

Numerical method of construction of axi-symmetric slip-line fields and associated velocity fields in the form of computographic plots of axial and radial velocity components, earlier given by the authors for rod extrusion and tube extrusion, was extended to the solution of two types of combined rod and tube extrusions: (i) where the rod and tube are extruded in opposite direction to each other and (ii) where, both the rod and tube move in the same axial direction as the punch movement during the extrusion process. Computographic plots of slip-line fields and associated velocity fields in the (r, z) plane are given and the deficiencies noticed in the solutions are highlighted. The results of specific punch pressures are observed to compare well with those estimated, using simple upper bound analysis and the experimental work of the authors.     

Angular dose variations from 320 kV rod pinch diode flash X-ray experiments on the modified Kali-1000 Pulsed Power System

This paper highlights the angular distribution of radiation dose emitted from a rod-pinch diode. The typical RP diode employed used a small diameter (1–2 mm) anode rod extended through a cathode aperture (5–8 mm). The diode chamber is maintained at 2 × 10^–5 Torr vacuum by a rotary backed diffusion pump. Experiments performed on a modified Kali-1000 Pulsed Power System (300 kV, 30 kA, 100 ns) were aimed at optimizing the source by maximizing the figure of merit (dose at 1 m in rad/spot diameter² in mm²) with minimizing of the diode impedance. The typical electron beam parameters used in the experiments are 240–320 kV, 6.5–27.5 kA, 100 ns, with a few hundreds of kA/cm² current density. The radiation emitted from a rod-pinch diode is measured using thermoluminescence dosimeters at an angular interval of 15° on either side of the rod in horizontal and vertical plane with different aspects ratio ranging from 2.5 to 10.0. Experimentally found that the radiation dose produced from the rod pinch diode configuration is maximum in the axial direction and decreases with angular variation on either side of the axis in horizontal and vertical planes, which indicates the directivity of the source. Maximum radiation dose at 1 m distance on the axial line is ranging from 42 to 307 mR.     

An Electron Microscope Study of Rolling Contact Fatigue

Progressive changes in the surface topography of the running track in a rolling contact fatigue tester were studied by using replica techniques and the electron microscope. Early in the life of a specimen, micron she cracks appeared on the stressed surface. With further running more cracks appeared, but those existing did not grow to any extent except for isolated cases. When the lubricant was changed, the time to form the first few cracks and the rate of formation of additional cracks correlated well with the fatigue performance.

Etching of the ball tracks showed that the surface cracks observed were almost always located at the chrome carbide to martensite interface.

It is postulated that corrosion fatigue may contribute to the differences between the fatigue performance of lubricants as much or more so than elastohydrodynamic effects.     

不锈钢表面裂纹方向电磁检测方法

针对传统交流电磁场检测表面不定方向裂纹容易出现漏检的问题,研究了旋转磁场下感应电流方向、裂纹方向变化对平板表面裂纹检测幅值的影响,推导了裂纹走向角度与平面磁场分量波谷幅值的关系表达式,从检测机理角度提出了裂纹方向判定方法及影响因素.建立了奥氏体不锈钢表面裂纹交流电磁场检测有限元仿真模型,开发了基于双U形激励和高分辨率隧...     

Contact Fatigue under Oscillatory Normal Load

Experimental studies were made wherein contact fatigue was brought about by a cyclic variation of normal load applied to the contact between a ball and a flat specimen. Curves of flat-specimen temperature versus time showed that a rapid temperature rise occurred in the initial stage of crack formation rather than after the appearance of fully developed spalls; thus the temperature criterion appeared to provide an early indication of fatigue. Fatigue failure was observed in unlubricated as well as lubricated contact, but with much longer life when unlubricated.

Toroidal rings of hardened and softened material were noted both on and below the contact surface. These hardness variations bore symmetrical relationship to the contact geometry and were apparently related to the stress pattern.

It was found that the fatigue cracks did not initiate in the most severely hardened material but in the material adjacent to it. Further, the slope of the cracks tended to follow the boundary of the hardened region in general direction. Propagation of microcracks in this general direction appeared to be influenced by the prior austenitic grain boundaries. These microcracks at times appeared to propagate along carbide stringers.     

厚壁筒双轴向表面裂纹尖端应力强度因子影响因素的研究

在现有文献对平面结构任意分布多裂纹间相互作用影响因素及厚壁筒轴向表面单裂纹尖端应力强度因子分析的基础上,提出了包含裂纹尖端应力强度因子影响因素的厚壁筒双轴向表面裂纹尖端应力强度因子公式.根据有限元方法,利用ANSYS软件对不同厚壁筒壁厚比、不同裂纹深度比及不同裂纹夹角情况下双轴向表面裂纹尖端应力强度因子进行了计算,分析...     

Forced vibration of composite cylindrical helical rods

The dynamic behavior of composite cylindrical helical rods subjected to time-dependent loads is theoretically investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial laminated rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, the anisotropy of the rod material, effect of the rotary inertia, axial and shear deformations are considered in the formulations. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem accurately. The solutions obtained are transformed to the time domain using an appropriate numerical inverse Laplace transform method. The free vibration is then taken into account as a special case of forced vibration. The results obtained in this study are found to be in a good agreement with those available in the literature.     

Biotribocorrosion: Some electrochemical observations from an instrumented hip joint simulator

36 mm Metal-on-Metal heads and cups were tested in a hip joint simulator instrumented with a 3-electrode electrochemical cell. This facilitated in situ monitoring of the tribological depassivation of the bearing surface. Subsurface analysis of the different regions of the femoral head was analysed using transmission electron microscopy. It was found that tribological depassivation increased the rate of corrosion, but subsequently decreased at around 450,000 cycles. Observations of the subsurface microstructure revealed the formation of nano-crystallites and the presence of micro-scale subsurface cracks.