To improve the performance accuracy of a conical journal bearing system, the surface error needs to be considered in the analysis since a tiny difference in dimensional values can alter the performance; the consideration of surface error may degrade the performance behavior of bearing. However, a better way to overcome such degradation may be to make use of magnetohydrodynamics (MHDs) of fluid. Therefore, the present work is planned to investigate the impact of taper error and MHD lubricant in recessed conical hybrid journal bearing. In this article, the Reynolds equation is derived under stated assumptions along with frictional power loss expression and finally solved using the finite element analysis, Newton–Raphson method, and generalized minimum residual method. The conducted research helped in determination of optimum values of recess width, land width ratio, and restrictor design parameter, and also obtaining the results corresponding to distinct performance indices. The outcome of these results may inspire practicing designers for the development of better tribo components.

In the present study, the dynamic behavior of the last stage low-pressure steam turbine blade with fir-tree root at different conditions of blade root flank faces and their interfaces with rotor groove have been analyzed. Modal analysis has been done using a finite element approach to evaluate natural frequencies and evaluation of Campbell diagram generated under these conditions. For this, both healthy and defective blade have been taken. Since the variable crack size of fir-tree root flank has been taken, the excitation pattern has been evaluated due to stiffness variation of the cracked blade. This analysis provides the basis of excitation pattern of cracked blades due to inherent character and critical stressed zone. The outcome of this study forms the guidelines and checks during the fitting of blades in rotor assembly and its checks during health audit, overhaul, overspeed balancing test, and frequency turning.

The performances of the tribo-pairs are greatly influenced by introducing the grooved surfaces. Developments of the newer type of lubricants have made a great impact on the performance of fluid film bearings. This article investigates the non-Newtonian behavior of electrorheological lubricant on the performance of grooved hybrid spherical journal bearing. The effect of different arrangements of grooves, i.e., partially grooved or fully grooved on the bearing surface, has been studied. The finite element method is used to numerically simulate the results. Furthermore, a parametric study is performed for optimizing the groove attributes. The present work demonstrates that the different grooved arrangements have a substantial influence on the bearing performance. It is revealed that the provision of grooves on the bearing surface decreases frictional losses and enhances the stiffness coefficients of the bearing. Furthermore, numerically simulated results indicate that the electrorheological lubricant enhances the value of minimum fluid film thickness and the stiffness coefficients ( S ¯ x x a n d S ¯ y y ) of spherical hybrid journal bearing. Improved bearing performance can be achieved by using the optimized grooved attributes together with the electrorheological lubricant.

To harness higher axial load capacity, a larger cone angle is used in conical bearings, resulting in an increase in the surface area which in turn increases the frictional power loss. The use of microgrooves in journal bearing helps in controlling this loss. Therefore, the present work is aimed to analyze conical hybrid journal bearing (i.e., combination of hydrostatic and hydrodynamic modes of operation) consisting of microgrooves along with shear thinning and piezo-viscous behavior of the lubricant. In this study, the microgroove attributes have been optimized by obtaining the solution of a Reynolds equation using finite element method and generalized minimum residual scheme (GMRES). These optimized groove attributes are used for numerically simulating the performance of the conical bearings. It has been observed that the best features of microgrooves and shear thinning behavior of the lubricant can be extracted to achieve better performance of the bearings. The results presented in this study are believed to be beneficial to the bearing designers and practising lubrication engineers.

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

In this paper, the effective strength and elastic properties of carbon nanotube reinforced composites are evaluated using a representative volume element with a number of carbon nanotubes embedded in the matrix. This concept is used to predict the mechanical properties of multiple, unidirectional, aligned, and also randomly dispersed carbon nanotube reinforced composites. To characterize these nanocomposites, a continuum model has been developed for large-scale analysis. The effective Young’s and shear moduli of the composites are determined using finite element analysis under the effect of elastic deformation. The role of design parameters like length and volume fraction of carbon nanotubes, tensile and shear strength as well as type of loading conditions are analyzed for multiple carbon nanotubes based composites. The discontinuous and continuous types of carbon nanotubes, with aligned and random distribution, are evaluated. The results show that the continuous and aligned carbon nanotubes produce the largest tensile modulus, compared to the discontinuous and aligned as well as discontinuous and randomly oriented carbon nanotubes along the longitudinal direction.

The multirecess noncircular hybrid journal bearings have been receiving wide importance in order to overcome the adverse effects on performance characteristics of multirecess circular journal bearings. During the lifetime of a machine, bearings are quite often required to be operated over a number of years and are subjected to several start and stop operations. As a consequence of this, the bush becomes progressively worn out and thereby changing the clearance space between journal and bearing. The present paper presents an analytical study investigating the effect of wear along with both aligned and misaligned conditions of journal on the performance of a capillary compensated three-lobe three-pocket hybrid journal bearing system for the various offset factors δ = 0.8,1.0, and 1.2. The wear caused on the bearing surface due to the transient (start/stop) operations has been modeled using Dufrane’s wear model. The modified Reynolds equation governing the flow of lubricant in the clearance space of a three-lobe multirecess worn hybrid journal bearing system along with both aligned and misaligned conditions of journal has been solved using an iterative scheme based on FEM. The influence of offset factor ( δ ) , the wear depth parameter ( δ ¯ w ) , and journal misalignment factors ( σ ¯ , δ ¯ ) on the performance of the three-lobe three-pocket hybrid journal bearing and three-pocket circular hybrid journal bearing system have been investigated. The results have been presented for the capillary compensated three-lobe three-pocket hybrid journal bearing system. The simulated results suggest that a bearing with a higher value of offset factor ( δ > 1 ) provides better static and dynamic performance characteristics as compared with a three-pocket circular journal bearing but the bearing with offset factor ( δ < 1) is predominantly affected by the wear defect and misalignment of journal. The numerically simulated results suggest that the wear defect and offset factors significantly affect the bearing performance. Therefore, it becomes imperative to account for the influence of wear and offset factors during the design process so as to generate accurate data of bearing performance. The numerically simulated results have been presented in terms of maximum fluid-film pressure, minimum fluid-film thickness, lubricant flow rate, direct fluid-film stiffness, damping coefficients, and stability threshold speed margin. The present study demonstrates that the performance of bearing is significantly affected by wear along with both aligned and misaligned conditions of journal and the loss is partially compensated by keeping the offset factor δ > 1 .

In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

The present work aims to analytically study the performance of misaligned four-pocket, membrane compensated, hybrid journal bearing system operating with micropolar lubricant. In the present study, the flow characteristic of the lubricating oil containing additives and contaminants has been modeled using Erigen’s micropolar theory. The journal misalignment which may occur as a result of noncentral loading, improper assembly, shaft deflection due to elasticity and thermal distortions, etc. has been accounted for in the present study by defining a pair of misalignment parameters in vertical and horizontal directions (i.e., δ and σ).The modified Reynolds equation governing the flow of micropolar lubricant in the clearance space of a misaligned bearing has been solved using FEM and Newton Raphson method along with the appropriate boundary conditions. The numerically simulated results suggest that the effect of journal misalignment is to cause degradation in bearing performance, whereas the influence of micropolar effect of lubricant is to enhance the bearing performance. Therefore, it is imperative to account for the effect of misalignment and lubricant behavior during the design process in order to generate accurate bearing characteristics data.

In this paper, fault diagnosis of high speed rolling element bearings due to localized defects using response surface method has been done. The localized defects as spalls on outer race, on inner race, and on rolling elements are considered for this study. The mathematical formulation accounted for tangential motions of rolling elements and inner and outer races with the sources of nonlinearity such as Hertzian contact force and internal radial clearance. The nonlinear stiffness is obtained by the application of Hertzian elastic contact deformation theory. The mathematical formulation predicts discrete spectrum having peaks at the characteristic defect frequencies and their harmonics. Experimentation has also been performed to validate the results obtained from the mathematical model and it shows that the model can be successfully used to predict amplitude ratios among various spectral lines with localized surface defects. Combined parametric effects have been analyzed and their influence has been considered with design of experiments and surface response methodology is used to predict the dynamic response of a rotor bearing system.

Carbon nanotubes (CNTs) have been regarded as an ideal reinforcements of high-performance composites with enormous applications. In this paper, the effects of pinhole defect are investigated for carbon nanotube based nanocomposites using a 3D representative volume element (RVE) with long CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with pinholes in it. These defects are considered on the single wall (CNTs). The mechanical properties such as Young’s modulus of elasticity are evaluated for various pinhole locations and number of defects. The influence of the pinhole defects on the nanocomposite is studied under an axial load condition. Numerical equations are used to extract the effective material properties for the different geometries of RVEs with nondefective CNTs. The field-emission microscopy (FEM) results obtained for nondefective CNTs are consistent with the analytical results for cylindrical RVEs, which validate the proposed model. It is observed that the presence of pinhole defects significantly reduces the effective reinforcement when compared with nondefective nanotubes, and this reinforcement decreases with the increase in the number of pinhole defects. It is also found from the simulation results that the geometry of RVE does not have much significance on the stiffness of nanocomposites.

Fracture mechanics at the nanoscale level is a very complex phenomenon, whereas the macroscale fracture mechanics approach can be employed for nanoscale to simulate the effect of fracture in single-walled carbon nanotubes (SWCNTs). In this study, an extended finite element method is used to simulate crack propagation in carbon nanotubes. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space frame structures. The nanostructure is analyzed using the finite element method, and the modified Morse interatomic potential is used to simulate the nonlinear force field of the C–C bonds. The model has been applied to single-walled zigzag, armchair, and chiral nanotubes subjected to axial tension. The contour integral method is used for the calculation of the J-integral and stress intensity factors (SIFs) at various crack locations and dimensions of nanotubes under tensile loading. A comparative study of results shows the behavior of cracks in carbon nanotubes. It is observed that for the smaller length of nanotube, as the diameter increased, the stress intensity factor is linearly varied while for the longer nanotube, the variation in stress intensity factor is nonlinear. It is also observed that as the crack is oriented closer to the loading end, the stress intensity factor shows higher sensitivity to smaller lengths, which indicates more chances for crack propagation and carbon nanotube breakage. The SIF is found to vary nonlinearly with the diameter of the SWCNT. Also, it is found that the predicted crack evolution, failure stresses, and failure strains of the nanotubes correlate very well with molecular mechanics simulations from literature.

The objective of the present paper is to study analytically the influence of wear on the performance of a capillary-compensated, four-pocket, hybrid journal bearing system operating in a turbulent regime by considering various geometric shapes of recess. The present study deals with bearings having four different geometric shapes of recess, i.e., square, circular, elliptical, and triangular recessed bearings. The wear on the bearing surface is modeled using Dufrane’s abrasive wear model. The Reynolds equation based on Constantinescu’s turbulent lubrication theory has been solved using finite element method along with a restrictor flow equation as a constraint together with appropriate boundary conditions. The numerically simulated results have been presented for a wide range of nondimensional external loads, wear depth parameters, and Reynolds numbers. The numerically simulated results suggest that the combined influence of wear, turbulence, and geometric shape of recess significantly affects the bearing performance. It has been observed that a triangular recessed bearing provides a greater value of minimum fluid film thickness when operating in a turbulent regime. It is also noticed that direct fluid film stiffness coefficients get reduced significantly when bearings operate in a turbulent regime compared with a laminar regime. Further, it is observed that from the viewpoint of fluid film stiffness, a square recessed bearing is found to be most suitable when operating in a turbulent regime.

This paper deals with the dynamic analysis of carbon nanotube with surface deviation along its axis. The type of carbon nanotube used in this analysis is a single-walled carbon nanotube that is doubly clamped at a source and a drain and this type of nanotube is used to represent a single mode resonator. In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. The resonant frequency of the doubly clamped single walled carbon nanotube (SWCNT) with deviation (waviness) has been investigated. The results showed the sensitivity of the single-walled carbon nanotubes having different waviness to different masses (attached at the center of a doubly clamped SWCNT) and different lengths. The sensitivity of resonant frequency shifts to tube length and waviness has been demonstrated. The vibration signature exhibits superharmonic and subharmonic responses with different levels of mass. The vibration spectra of CNT with varying attached mass from 10 − 5 fg to 10 − 3 fg show dense signature near peak of excitation. It is found that with the increase in mass attached to CNT with 60 nm length, the peak excitation appears in the vibration signature in chaotic nature with reduced vibration amplitude.