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The aim of this work is to estimate Hertzian contact stresses in EN31 alloy steel and to obtain the line of best fit using statistical analysis. In refrigerant screw compressors, EN31 is used as a material of construction for cylindrical roller bearings. The Hertzian contact with friction between the outer surface of the inner race of the rolling contact bearing & the outer surface of the cylindrical roller is simulated using pin-on-disk tribometer. Measurement of friction coefficient was carried out by sliding different cylinders of hardened EN31 material against the hardened EN31 disk of the pin-on-disk tribometer. A total 16 tests, each of 1 minute time duration, are performed for the estimation of friction coefficient with varying loads from 20 N to 100 N and speeds in the range of 50 RPM to 200 RPM. The magnitude of Von Mises stress induced in the inner race of the bearing is estimated using Gauss quadrature method with the help of a self-developed MS Excel program. Statistical analysis showed that the stress magnitude increases with the increase in the load & decreases with an increase in speed. [ABSTRACT FROM AUTHOR]

A new method of machining ultrasonic cavitation abrasive flow based on phase control technology was proposed for improving the machining efficiency of the inner wall of TC4 (Ti-6Al-4V) titanium alloy tubes. According to ultrasonic phase control theory and Hertzian contact theory, a model of ultrasonic abrasive material removal rate under phase control technology was established. Using COMSOL Multiphysics 6.1 software, the phase control deflection effect, acoustic field distribution, and the size of the phase control cavitation domain on the inner wall surface were examined at different transducer frequencies and transducer spacings. The results show that the inner wall polishing has the most excellent effect at a transducer frequency of 21 kHz and spacing of 100 mm. In addition, the phased deflection limit was explored under the optimal parameters, and predictive analyses were performed for voltage control under uniform inner wall polishing. Finally, the effect of processing time on polishing was experimented with, and the results showed that the polishing efficiency was highest from 0 to 30 min and stabilized after 60 min. In addition, the change in surface roughness and material removal of the workpiece were analyzed under the control of the voltage applied, and the experimental results corresponded to the voltage prediction analysis results of the simulation, which proved the viability of phase control abrasive flow polishing for the uniformity of material removal of the inner wall of the tube. [ABSTRACT FROM AUTHOR]

ABSTRACT The accuracy and efficiency of the wheel‐rail adhesion model are important to the wheel‐rail rolling contact issues. The purpose of this study is to develop a simplified non‐Hertzian wheel‐rail adhesion model under interfacial contaminations to predict the wheel‐rail adhesion coefficient. Firstly, a non‐Hertzian full elasto‐hydrodynamic lubrication (EHL) model was developed and applied to determine the wheel‐rail contact pressure and film thickness under interfacial contaminations. Then, the empirical formula of central film thickness available to non‐Hertzian wheel‐rail normal contact relating to train speeds, axle loads and material parameters were proposed based on a large number of non‐Hertzian full EHL simulation for smooth surface under interfacial contaminations using linear regression. The empirical non‐Hertzian central film thickness formula and minimum film thickness formula for wheel‐rail contact obtained in this paper show certain differences from the formulas based on Hertzian contact. Using the proposed non‐Hertzian central film thickness formula, a simplified non‐Hertzian wheel‐rail contact adhesion model was developed, and the adhesion coefficient was obtained at different speeds and compared with the field test data. The numerical results showed good agreement with field test data. [ABSTRACT FROM AUTHOR]

This study investigates the impact of Carbon Nanotubes (CNTs) and Graphene Platelets (GPLs) on the low-velocity impact behavior of curved beams. Nanofillers (CNT or GPL) are evenly distributed within each layer, but their volume fraction varies from layer to layer, creating a functionally graded pattern. The Halpin–Tsai micromechanical model is employed to predict the effective properties of the nanocomposites. The contact force between the plate and projectile is estimated using Hertzian contact law. The First-order Shear Deformation Theory (FSDT), Hamilton’s principle, finite element and Newmark integration methods are employed to model the problem. The effects of different initial velocity and mass of the impactor on the impact behavior are investigated. The analysis also takes into account the impact of different weight fractions of nanoparticles and investigates four unique reinforcement patterns: X, O, U, and V. Curved beams reinforced with GPL showed less center deflection compared to those reinforced with CNT at the same weight fraction. As the weight fraction increased, the difference in center deflection between GPL and CNT reinforcements became less significant, ultimately leading to their deflection responses converging at a weight fraction of 0.75. [ABSTRACT FROM AUTHOR]

We study a fully passive and robust mechanism to mitigate the transient response of resonantly base-excited single- and multi-DOF structures by drastically reducing the portion of input energy that enters into the structures from base excitations. Unlike traditional approaches which are essentially resonance-driven and rely on adding either linear or nonlinear, typically dissipative, secondary attachment(s) to a main (primary) structure, the presented approach is based on incorporating intentional strong non-smooth nonlinearities due to Hertzian interactions. We show that these nonlinear interactions effectively "stiffen" the system and drive the structural response out of resonance by breaking the monotonic increase of input energy for the resonantly excited structure. To elucidate this mechanism, first we consider a resonantly base-excited single-floor frame structure incorporating a single-sided clearance. Subsequently the study is extended to a three-floor frame structure with an internal flexible core, featuring double-sided asymmetrical clearances, subjected to resonant excitation by ground acceleration. Three distinct structural configurations are considered, namely, a linear model serving as a reference for the unprotected structure, and two nonlinear configurations incorporating purely elastic and inelastic Hertzian contacts. Moreover, the influence of the type of contact stiffness magnitude is explored across a wide range, spanning from soft to stiff Hertzian contacts. For both the single- and three-floor structures, the results reveal an unexpectedly favorable regime of contact stiffness, characterized by multiple beneficial attributes, wherein soft, and even purely elastic, contacts exhibit a significant reduction in both input energy and acceleration levels along with an enhancement in the dissipation rate compared to the linear case. It was observed that the occurrence of contacts facilitates energy transfer to and from the primary structure, acting as a mechanism to drive the system out of resonance, and disrupting the monotonic increase in input energy when the base excitation is applied. As the contact stiffness increases, the amount of input energy further decreases and the dissipation rate is enhanced; however, this mitigation performance is accompanied by a modest rise in floor acceleration levels attributed to the stiff impacts. Surprisingly, it was found that for a fixed contact stiffness, the amount of input energy increases when inelasticity in the Hertzian contacts is added. The present study underscores the importance of intentional strong nonlinearities in structural vibration mitigation. Further applications of this concept are discussed. [ABSTRACT FROM AUTHOR]

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage. [ABSTRACT FROM AUTHOR]

Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine's chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat kernels during peeling, this study established a continuous damage model based on Hertzian contact theory and continuous damage theory. The model's accuracy was validated through experiments, culminating in the calculation of critical parameters for wheat peeling. This study focused on different wheat varieties (Ningmai 22 and Jichun 1) and kernel sizes (the thicknesses of the small, medium, and large kernels were standardized as follows: Ningmai 22—2.67 ± 0.07 mm, 2.81 ± 0.07 mm, and 2.95 ± 0.07 mm; Jichun 1—2.98 ± 0.11 mm, 3.20 ± 0.11 mm, and 3.42 ± 0.11 mm). Continuous compression tests were conducted using a mass spectrometer, and critical damage parameters were analyzed and calculated by integrating the theoretical model with experimental data. The test results showed that the average maximum crushing force (Fc) for small, medium, and large-sized kernels of Ningmai 22 was 96.71 ± 2.27 N, 110.17 ± 2.68 N, and 128.41 ± 2.85 N, respectively. The average maximum crushing deformation (αc) was 0.65 ± 0.08 mm, 0.68 ± 0.13 mm, and 0.77 ± 0.17 mm, respectively. The average elastic–plastic critical pressure (Fs) was 50.21 N, 60.13 N, and 59.08 N, respectively, and the average critical values of elastic–plastic deformation (αs) were 0.37 mm, 0.38 mm, and 0.39 mm, respectively. For Jichun 1, the average maximum crushing force (Fc) for small-, medium-, and large-sized kernels was 113.34 ± 3.15 N, 125.28 ± 3.64 N, and 136.15 ± 3.29 N, respectively. The average maximum crushing deformation (αc) was 0.75 ± 0.11 mm, 0.83 ± 0.15 mm, and 0.88 ± 0.18 mm, respectively. The average elastic–plastic critical pressure (Fs) was 58.11 N, 64.17 N, and 85.05 N, respectively, and the average critical values of elastic–plastic deformation (αs) were 0.45 mm, 0.47 mm, and 0.52 mm, respectively. The test results indicated that during mechanical compression, if the deformation is less than αs, the continued application of the compression load will not result in kernel crushing. However, if the deformation exceeds αs, continued compression will lead to kernel crushing, with the required number of compressions decreasing as the deformation increases. If the deformation surpasses αc, a single compression load is sufficient to cause kernel crushing. Since smaller wheat kernels are more susceptible to breakage during processing, the peeling pressure (F) within the chamber should be controlled to remain below the average elastic–plastic critical pressure (Fs) of small-sized wheat kernels. Additionally, the kernel deformation (α) induced by the flow rate and loading in the chamber should be kept below the average elastic–plastic critical deformation (αs) of small-sized wheat kernels. This paper provides a theoretical foundation for the structural design and optimization of processing parameters for wheat peeling machines. [ABSTRACT FROM AUTHOR]

The rock uniaxial compressive strength (UCS) has significant implications for underground engineering support design. Traditional methods mainly rely on laboratory tests, which are costly, time-consuming, and unable to meet the real-time adjustment of underground engineering support plans and construction safety requirements. To address the real-time acquisition issue of rock UCS in tunnel engineering sites, this paper proposes a method for predicting the rock UCS based on computer drilling jumbo measurement while drilling (MWD) data. First, by applying the principle of energy conservation and the Hertzian contact theory, a theoretical relationship between MWD data and the rock UCS is established. Second, a method for filtering MWD data was proposed, determining energy transfer efficiencies for percussion (ηP), rotation (ηR), and feed (ηF) are 51%, 41%, and 42%, respectively. The proposed relationship model was validated using a dataset of 398 experimental samples, resulting in an R2 of 0.92 and an RMSE of 5.76 MPa, demonstrating the correctness of the model and its applicability for predicting the rock UCS. Finally, the relationship model is applied to the Xiwuling Tunnel, forming a three-dimensional visualization evaluation method for the tunnel rock UCS based on MWD data. The results of 6 sets of samples in the DK42+253 section demonstrated an R2 of 0.91 and an RMSE of 4.12MPa between predicted UCS and laboratory-measured UCS. These findings affirm the reliability of the method, providing valuable support for tunnel construction and design. Highlights: The theoretical relationship between MWD data and rock UCS is deduced. 398 groups of laboratory tests were carried out to verify the accuracy of the model. A three-dimensional visualization evaluation method of tunnel UCS is proposed. A valuable reference is provided for tunnel construction and design. [ABSTRACT FROM AUTHOR]

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears' steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise. [ABSTRACT FROM AUTHOR]

The paper presents a parallel between the calculation of deformations for uniaxially compressed rubber spheres, by direct measurement on the experimental stand. Generalities about rubber, definition, properties, main characteristics and examples of use, are presented. The authors' original experimental study is then presented to study the deformability of rubber spherical bodies and to analyze the deviations of rubber behavior from Hertzian model. An experimental rig was designed for this purpose. Its operation and the working method used, as well as the force-strain characteristics for different experimental situations (spheres'arrangement and support) are presented, that being the compression of two or three rubber spheres, with three different ways of supporting them. Considering that a model that accurately describes the behavior of rubber the spheres are made of is the Money-Rivlin model, which is characterized by two constants, C10 and C01, these constants were determined by a simple method, using the hardness of the material as a basic element hyperelastic, measured on the Shore A scale. After determining the material constants, the deformation values were also determined by numerical modeling with the help of Ansys software. For validation, the experimental curve for the deformation of a rubber sphere on a plane and the numerical curve for the similar situation with the experimentally determined mechanical characteristics, were plotted on the same graph. Finally, the conclusions resulting from the conducted research are presented: - highlighting two ways of evaluating the deformation of rubber spheres, experimentally and numerically, determining the specific Mooney-Rivlin constants of the material through a simple, efficient and valid method, - a way to calculate deformations for this case of loading rubber spheres is to model them as an axisymmetric contact (reducing the model to a quarter), - by finite element method, because it uses a lower number of finite elements and saves significant resources, both the calculation method and the experimental methods used are validated by a good correspondence between the experimental curve and numerical results. [ABSTRACT FROM AUTHOR]

Hypothesis: Sample-spanning particle networks are used to induce structure and a yield stress, necessary for 3D printing of porous ceramics and paints. In capillary suspensions, a small quantity of immiscible secondary fluid is incorporated into a suspension. By further adding nanoparticles with a range of hydrophobicities, the structure of the bridges and microparticle-microparticle contacts is expected to be modified, resulting in a tunable yield stress and shear moduli. Moreover, the compressibility of these samples, important in many processing and application steps, is expected to be sensitive to these changes. Experiment: The nanoparticle hydrophobicity was altered and their position relative to the microparticles and the bridges was examined using confocal microscopy where the correlation between bridge size and network structure was observed. A step-wise uniaxial compression test on the confocal was conducted to monitor the microparticle movement and structural changes between capillary suspension networks with and without nanoparticles. Findings: Our observation suggests that nanoparticles induce the formation of thin liquid films on the surface of the microparticles, mitigating contact line pinning and promoting internal liquid exchange. Additionally, nanoparticles at microparticle contact regions further diminish Hertzian contact, enhancing the capacity for rearrangement. These effects enhance microparticle movement, narrowing the bridge size distribution. Nanoparticles added to capillary suspensions : The nanoparticles either homogeneously aggregate around the microparticles or stabilize the liquid-liquid interface. These capillary nanosuspensions readily rearrange and compress, opening new opportunities for tunable design of porous ceramics, printed electronics, and low-fat spreadable chocolate. • Nanoparticles in capillary suspensions aggregate on microparticles or stabilize interfaces depending on the wettability. • Nanoparticles induce thin layers of liquid films, promoting internal liquid exchange, and reducing Hertzian contacts. • Capillary nanosuspensions demonstrate a reduction in elastic moduli and less pronounced peak in the viscous modulus. • The structures of capillary nanosuspensions rearrange more easily when subjected to compression. [ABSTRACT FROM AUTHOR]

AbstractModeling the knee is an important factor in increasing the quality of life of both healthy individuals and patients. Nevertheless, the intricate nature of the knee makes this problem complicated. In this study, an extension to an established planar knee joint model with Hertzian contact pairs is proposed with contact mechanics based on polynomial chaos expansion surrogate. Firstly, the finite element (FE) model is made representing a contact pair of sphere-to-plane type with two layers on both bodies, corresponding to the cartilage and the bone. Five variables corresponding to both geometry and material parameters are used to parametrize this model. Then, 128 distinct variants of the FE model are created based on a quasi-Monte Carlo sequence. This dataset is used to train and validate the surrogate. The trained surrogate is proven to have predictive capabilities with an average nRMSE of 0.2% in randomized test/train splits. When included in a model of the knee and tested under parameter uncertainties in Monte Carlo simulations, it results in nRMSE of 58% for angular coordinate compared to the original model with Hertzian pair. This signifies the high influence of contact formulation on the model output and the need for more physically based models in knee contact modeling. [ABSTRACT FROM AUTHOR]

Through evolutionary processes, helicoidal structures have been proven to exhibit exceptional load‐carrying capacity and impact resistance performance. To date, extensive experimental and numerical studies have been carried out on their impact behaviors, while few relevant analytical studies have been reported even though it is urgently needed for the preliminary assessment of structure design and optimization. In this work, based on the first shear deformation theory (FSDT) and the improved linearized Hertzian contact method, an analytical model for low velocity impact (LVI) performances of helicoidal laminates with arbitrary layups is developed. Therein, the post‐impact damage is taken into account according to continuum damage mechanics (CDM). Comparisons of load‐carrying capacity and energy‐absorbed performance between the proposed model prediction and the existing experimental data\numerical results have been made for verification. Besides, LVI behaviors of conventional laminates with unidirectional distribution andcross‐ply arrangement are discussed. Moreover, the role of rotation angle, impact velocity and the plate dimension on helicoidal laminates' LVI performances are analyzed quantitatively. There is evidence that helical layouts are better able to absorb energy and delay the in‐plane damage. Highlights: The LVI responses of bio‐inspired single‐helicoidal (SH) and double‐helicoidal (DH) composite laminate are studied.An effective model to predict the LVI responses considered the post‐impact damage is developed.A comparison of the LVI performance of single‐helicoidal structures with various lay‐up schemes is carried out.DH structure has better low velocity impact resistance than SH structure when the rotation angle shares the same. [ABSTRACT FROM AUTHOR]

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil. The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders. [ABSTRACT FROM AUTHOR]

Even though the influence of impact energy on the low velocity impact of laminated plate is well reported, the influence of relative mass of the impactor has not been addressed extensively. This work investigates the effect of impactor mass relative to that of target and other associated factors like impactor velocity and the target plate size on the impact response of a GLARE plate. A 3 D finite element analysis incorporating Newmark-β method and Hertzian contact is used considering appropriate contact stiffness to evaluate the contact force. Results show that the impactor mass significantly influences the contact force and interfacial delamination. [ABSTRACT FROM AUTHOR]

Structural vibration has always been a major concern in the engineering field. A dynamic vibration absorber in the form of contacts with adjustable stiffness (CDVA) offers effective vibration suppression and can improve conventional dynamic vibration absorbers with high sensitivity to frequency deviation and difficulty in adjusting the frequency. In this research, first, based on the theoretical model of the contact between a rubber ball and an inner cone, the feasibility of changing the axial contact state to change the structure's natural frequency was verified using an ANSYS simulation. A theoretical model of the static contact stiffness between the ball and the inner cone was constructed using Hertzian contact theory and Hooke's law, and a theoretical model of the cubic nonlinear elastic restoring force was used to characterize the stiffness properties of the rubber ball during compressive rebound. The steady-state frequency response equations of the main vibration structure were derived using the averaging method in conjunction with the two-degree-of-freedom dynamics model, and the stability of the solutions to the frequency response equations was obtained in conjunction with the stability determination criterion. Then, the impact of the CDVA's design parameters on the nonlinear dynamic response of the primary vibration structure was simulated and analyzed. The resulting findings can serve as guidance for designing dynamic vibration absorber parameters. Based on the principles of ball-inner cone contact, a dynamic vibration absorber structure was proposed. A design test was conducted to verify the correctness of the contact stiffness model, and an experimental study was carried out to investigate the law of change in the dynamic stiffness and damping of the principle structure of CDVA under dynamic excitation conditions. Finally, the vibration test platform of the solidly supported beam structure was constructed, and vibration suppression tests of the CDVA in different compression states were conducted to investigate the tunability and feasibility of CDVA vibration suppression. The results showed that the dynamic vibration absorber had good vibration absorption characteristics and could be used for single-mode vibration suppression of multimodal main structures. [ABSTRACT FROM AUTHOR]

This study focuses on investigating the behavior of slider–crank mechanisms with different bearing failures using a vibration analysis technique. The reliability and lifespan of bearings are crucial for such mechanisms, which convert rotary motion to reciprocating motion. Previous research primarily addressed ball-bearing failures, neglecting needle bearings due to their specific applications. To bridge this gap, our experimental setup integrated both roller and ball bearings within a slider–crank mechanism. Vibration data were collected during normal operation, as well as under failure conditions of the ball and roller bearings. By analyzing the vibration signatures during simultaneous multiple failures, we gained insights into the nature of vibrations in the system. Furthermore, a mathematical model based on Hertzian contact was employed to calculate the theoretical frequency of ball bearings; however, due to the variable motion of the needle bearing, a novel mathematical model was proposed to estimate the defective impulse frequency, considering the inter-impact time between two impacts. The experimental results were compared with the healthy crank mechanism setup to draw meaningful conclusions. This research contributes to a comprehensive understanding of bearing failures in slider–crank mechanisms and provides valuable insights for designing reliable and long-lasting systems. [ABSTRACT FROM AUTHOR]

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke's law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer. [ABSTRACT FROM AUTHOR]

A stress-dependent porosity and permeability model is proposed to predict the microstructure evolution and the physical properties and mechanical behavior of deformable hydrate-bearing sediments (HBS) with various hydrate growth patterns under engineering disturbance. First, according to Hertzian contact theory and the proposed mesoelastic–plastic damage model (Gurson-DP model), the correction formula of the pore size under the influence of the effective confining pressure and the overburden pressure is given, and the stress-dependent porosity model is derived. Second, the fractal capillary bundle model is used to describe the stress-dependent permeability of HBS with different hydrate saturations considering the grain-cementing hydrate and the universal-growth hydrate. Finally, the proportions of hydrates with various growth patterns, such as pore filling (PF), wall coating (WC), and grain cementing (GC), are determined based on the equivalent flow assumption to reasonably evaluate the hydrate growth habit in HBS. This paper comprehensively studies the stress-dependent porosity and permeability models of deformable HBS and thus, provides a theoretical basis for quantitative evaluation and prediction of the physical properties (such as porosity and permeability) and mechanical behavior of HBS. [ABSTRACT FROM AUTHOR]

Considering the influence of manufacturing parameters, precisely predicting the post-grinding tooth surface topography is of great significance for improving transmission performance and service life of face gear transmission. However, it faces numerous challenges in practical applications, encompassing factors like abrasive grain size, grain distribution, grinding wheel inclination, and machine tool vibrations. Simultaneously, the establishment of prediction models presents complexities and precision-related difficulties. To predict the tooth surface topography more accurately, this paper proposes a method for predicting surface topography of face gear grinding based on dynamic contour interference sampling. Based on Hertzian contact theory, coupled with abrasive grain interference sampling, the motion trajectories of abrasive grains within discrete grinding width intervals are simulated. Thus, by considering the overlap regions of grinding width between adjacent grinding trajectories, a more accurate prediction of tooth surface topography is achieved. The method delves deeply into the impact of grinding depth on the deformation patterns within the grinding contact region. To validate the accuracy of the proposed method, face gear grinding experiments were designed and conducted, with the experimental results being compared against the predicted outcomes. The experimental results indicate that the topography prediction model, which accounts for grinding trajectory interference, closely aligns with the actual tooth surface topography. [ABSTRACT FROM AUTHOR]

Charge transfer between the particle and wall occurs after each collision in powder handling operations, called "contact electrification". In the present study, a LIGGGHTS code was developed by adding the Hertzian contact area formula and condenser model to predict the particle charge after every impact. The simulation results showed that, the particle with a higher impact velocity became saturated under fewer collisions. Considering that the charging constant depends on the impact velocity and initial particle charge, the Average Relative Error (ARE) of simulation prediction significantly decreased from 22 and 16% to 10.6 and 11% for Rubber particles at impact velocities of 4.8 and 2.8 m/s, respectively. Therefore, the current modified LIGGGHTS code has a great potential to predict the impact charge of particle-wall collision. [ABSTRACT FROM AUTHOR]

In this article, we focus on utilising electrical impedance spectroscopy (EIS) for the assessment of global and contact impedances in roller bearings. Our primary objective is to establish a quantitative prediction of lubricant film thickness in elasto-hydrodynamic lubrication (EHL) and investigate the impedance transition from ohmic to capacitive behaviour as the system shifts from boundary lubrication to EHL. To achieve this, we conduct measurements of electrical impedance, bearing and oil temperature, and frictional torque in a cylindrical roller thrust bearing (CRTB) subjected to pure axial loading across various rotational speeds and supply oil temperatures. The measured impedance data is analysed and translated into a quantitative measure of lubricant film thickness within the contacts using the impedance-based and capacitance-based methods. For EHL, we observe that the measured capacitance of the EHL contact deviates from the theoretical value based on a Hertzian contact shape by a factor ranging from 3 to 11, depending on rotational speed, load, and temperature. The translation of complex impedance values to film thickness, employing the impedance and capacitance method, is then compared with the analytically estimated film thickness using the Moes correlation, corrected for inlet shear heating effects. This comparison demonstrates a robust agreement within 2% for EHL film thickness measurement. Monitoring the bearing resistance and capacitance via EIS across rotational speeds clearly shows the transition from boundary to mixed lubrication as well as the transition from mixed lubrication to EHL. Finally, we have observed that monitoring the electrical impedance appears to have the potential to perform the run-in of bearings in a controlled way. [ABSTRACT FROM AUTHOR]

Functionally graded (FG) composites reinforced by carbon nanotubes (CNTs) have received extensive attention due to their excellent mechanical properties. The impact responses of FG‐CNT nanocomposites are analyzed by the developed meshless method. The temperature‐dependent material properties are expressed by way of the extended rule of mixture. The kinematics of the composite plate is established on the basis of the first‐order shear deformation theory. The modified Hertzian contact law is adopted to evaluate the impact loading between the plate and the impactor. The dynamic balance equations of the plate are constructed and computed by the Systemic Smoothed Particle Hydrodynamics (SSPH) method with strengthened prediction ability. The impacting behaviors of the FG‐CNT nanocomposite plate, as well as the parametric effects, are analyzed by the developed model and the suitability is clearly demonstrated. Highlights: Impact of FG‐CNTRC is firstly solved by a self‐developed meshless SPH model.Strong capacity of the SPH impact model is clearly demonstrated.More CNTs close to the strike face would improve the impact resistance. [ABSTRACT FROM AUTHOR]

The bending stiffness of transmission line conductors can vary significantly, ranging from maximum stiffness when behaving monolithically to minimum stiffness when wires behave loosely. This large range makes it challenging to estimate stiffness accurately at intermittent bending stages. To address this issue, a mathematical model that accounts for both frictional forces between wires in the same layer and the clenching effects of helical wires from preceding layers is proposed in this paper. The proposed model estimates cable bending stiffness as a function of axial load and curvature for multilayered strands by considering slip caused by wire behavior. To evaluate the bending stiffness, experiments were conducted on Panther and Moose Indian Power Transmission line conductors. The proposed slip model considers Coulomb frictional effects and clenching effects caused by Hertzian contact forces, filling the void in the estimation procedure. Additionally, the model considers the wire stretch effect, a parameter not previously accounted for in cable research. The predicted numerical results of the proposed model were found to vary within a maximum of 7% from the experimental tests. The proposed mathematical model thus offers a more accurate and comprehensive way of estimating the bending stiffness of transmission line conductors, addressing the existing limitations in the estimation procedure. [ABSTRACT FROM AUTHOR]

Taking the involute spur gear pairs with profile shift as the research object, the mesh stiffness calculation models including nonlinear Hertzian contact stiffness, tooth profile curve, fillet foundation stiffness with structure coupling effect were established based on the potential energy method. Considering the influences of gear profile shifts, the calculation formulas for tooth profile curve, half tooth angle of base circle and half tooth angle of dedendum circle in mesh stiffness calculation were revised. The fillet foundation stiffness models were revised by considering tooth surface frictions. The pressure angle models of gear mesh point were derived by considering geometric eccentricity errors. The effects of profile shifted, tooth surface frictions and geometric eccentricity errors on mesh stiffness were studied. The results show that the center distance, stiffness amplitude and contact ratio of the profile shifted gear pairs have great changes. Owing to the profile shift, the moment when the direction of frictional force changes on a pair of meshing gears no longer occurs within the single tooth meshing interval, thereby affecting the characteristics of the mesh stiffness. Geometric eccentricity increases the peak-to-peak values of the mesh stiffness, and at the same time, sideband frequencies with intervals corresponding to the rotational frequencies appear in the frequency domain of the meshing stiffness. In the presence of eccentricity errors in both the driving and driven gears, a new sideband frequency arises with an interval equal to the difference in rotation frequency. Considering the combined effects of three factors, the mesh stiffness characteristics may be significantly influenced. The research results provide the references for further researches of the dynamics of profile shifted gears. [ABSTRACT FROM AUTHOR]

Contact damage in materials is critical in engineering applications because it influences mechanical resistance, such as wear, erosion, and impact failure. Indentation tests were performed using a tungsten carbide ball indenter (Hertzian contact) on the surfaces of glass–ceramics containing hexagonal CaAl2Si2O8 or mica crystals (fluorophlogopite), both of which have a layered structure. The stress–strain relation and the permanent deformation on the surface, as well as the observation of the microcrack zone by X‐ray computed tomography using synchrotron radiation, revealed that the glass–ceramic with hexagonal CaAl2Si2O8 showed ductility similar to the quasi‐plastic behavior previously observed in the mica glass–ceramic. The yield stresses of the glass–ceramics were estimated from the stress deviating from the stress–strain relation assuming complete elastic response between the ball and the sample. The ratio of the yield stress to Young modulus (Y/E) of the glass–ceramic with hexagonal CaAl2Si2O8 was determined to be higher than that of the mica glass–ceramic. [ABSTRACT FROM AUTHOR]

Contact electrification phenomena are commonly observed in many handling powder process, in which the charge transfers between contacting particle and wall during collisions. In this work, a condenser model and Hertzian contact area formula were added to an LIGGGHTS code so as to predict the polymer particle charge after a single impact with a metal plate. The simulated impact charge of several single polymer particles was successfully predicted after a single collision on a metal plate with determined values for C0, achieving an average relative error (ARE) less than 10%. An assumption that the value of charging constant parameter (k) changes with the impact velocity reduced the ARE value significantly from 20% and 9% to 2% and 0.3% for PS and Nylon 66, respectively. As a main result, the current modified LIGGGHTS code can successfully estimate the impact charge of a single particle after colliding with a wall. [ABSTRACT FROM AUTHOR]

Subsurface rolling contact fatigue (RCF) failure occurs beneath heavily loaded hard contacts like gears, bearings, and cams. This study investigates microstructural decay beneath a RCF-tested surface in AISI/SAE 52100 bearing steel tempered at 240 ℃. RCF tests were conducted at 100 ℃ with a maximum Hertzian contact pressure of 4 GPa for four stress cycles. Microstructural characterization utilized scanning electron microscopy, electron backscatter diffraction, transmission Kikuchi diffraction, and transmission electron microscopy. Due to high tempering temperature, white etching bands (WEBs) were observed without preceding dark etching regions. The microstructural decay sequence involved: (1) formation of elongated ferrite and ferrite microbands, (2) complete dissolution of tempered carbides and partial dissolution of residual cementite, (3) formation of WEBs composed of nano-sized ferrite grains (100–300 nm) transformed from ferrite microbands, and (4) appearance of lenticular carbides. Within the WEBs, most nano-sized grains had high-angle grain boundaries, while the fraction of low-angle grain boundaries increased in later stages of RCF. Lenticular carbides formed alongside elongated ferrite and coalesced nano-sized ferritic grains. [ABSTRACT FROM AUTHOR]

• A novel dual-rotor-bearing-casing coupling model for aero-engine is established based on the finite element method. • The casing is discretized by the shell element and the modified Craig–Bampton method is utilized for model reduction. • The coupled bending-torsional effect has been studied in detail. • A nonlinear bearing model and the rub-impact effect was introduced in this study. In this study, a novel modeling method for a dual-rotor-bearing-casing system is proposed based on the finite element method (FEM) and the model reduction method. The dual-rotor system is modeled using Timoshenko beam and rigid disc elements, while the casing is modeled using shell elements. To reduce the number of degrees of freedom (DOFs), the modified Craig–Bampton method is used to downscale the finite element model of the casing. In addition, the Hertzian contact force and the DOFs of the bearing outer race and pedestal are considered in the bearing model. Through a specific assembly method, a dynamic model of the dual-rotor-bearing-casing is established at the expense of slight increase in the number of DOFs. Based on this dynamic model with fewer DOFs, the effects of two disc imbalances and the rub-impact fault between the low-pressure (LP) turbine and casing are then introduced as an application of the proposed model. The calculation results indicate that the critical speeds of each order of the whole aero-engine model are significantly lower than those of the casing-free model. In the amplitude-frequency diagram, the peak of the critical speed of the whole aero-engine model is found to appear earlier, and the extent of rightward bending is larger. The study also includes parametric analysis to examine the effects of parameters such as the coefficient of friction, the casing-disc contact stiffness, and the casing-foundation connection stiffness. After introducing the nonlinear bearing model, a large number of fractional frequency components are found in the frequency-domain diagram, the dynamic characteristics of the model become more complicated. The coupled bending-torsional effect has also been studied in detail, the calculation results show that it is reasonable to ignore the torsional deformation. [ABSTRACT FROM AUTHOR]

The sealing reliability of collet connectors is essential within underwater production systems. This paper is based on the lens gasket sealing mechanism and Hertzian contact theory, establishing mechanical models for the core sealing components in preloaded and working states and analyzing the minimum required axial preload force for sealing. According to the sealing principles of the connector, the force characteristics of each sealing element are analyzed in both preloaded and working states. The interplay of forces between these elements is subsequently determined. Furthermore, the amplification of axial preload force within the sealing structure is confirmed through simulations of contact characteristics. Finally, the accuracy of theoretical and simulated results is confirmed through experimental validation. [ABSTRACT FROM AUTHOR]

Purpose: Track irregularities contribute a large impact on the vibrations of a railcar. Therefore, this research is about assessing the impact of track irregularities on the rail vehicle vibration in the case of Addis Ababa Light Rail Transit Service. To assure the comfort of passengers in the railcar, it is important to monitor and identify rail irregularities that lead to rail-car uncomfortable vibrations. The objective of this research is to establish a method that uses rail irregularity measurement data and railcar design parameters to determine the railcar vibrations levels and frequency spectrum. Method: To achieve the objective, the analytical vibration equations of the half-railcar model with twelve degrees of freedom were derived and solved using MATLAB. The impact of periodic track irregularities on a bogie's primary rubber-made suspension materials was also analyzed in MATLAB. On the other hand, a 3D bogie lumped model with the railcar mass via secondary suspension and with Hertzian contact effects neglected in finite element model was analyzed to validate the analytical modal equations. The natural frequencies provided by 3D Finite Element Method (FEM) with full dimensions are compared with those obtained using lumped parameter model analytically. Results: The frequency of the car-body that corresponds to bounce motion provided by lumped parameter model was 14.89Hz, while the frequency obtained from modal analysis by FEM was 13.829Hz. Then, conformity of the frequencies in both models provided confidence in the correctness of the analytical model. The displacement of the railcar found was low and cannot cause fatigue to the vehicle components. Conclusion: As the significance of this research, rail irregularities that lead to a car-body vibration frequency spectrum that produces an uncomfortable ride can be carefully investigated to eliminate their effect, with reference to ISO 2631, which defines the methods for measuring human vibration levels and their effects on comfort. Their effect must be eliminated in the railway lines by either correcting the track or using appropriate railcar suspension parameters. [ABSTRACT FROM AUTHOR]

Previous works on the thermal modelling for face gear grinding usually used Hertzian contact theory and ignored the material removal mechanism. By contrast, a comprehensive force–thermal model was founded on the wheel–gear geometry and material mechanism for economical and efficient prediction of grinding temperature field in this work. In the process of grinding face gear, a force model was established on the basis of single-grain model under the action of grinding fluid. The temperature analytical model for face gear was derived considering the contribution of the cross-sectional area of the undeformed chip thickness to the heat flux. Moreover, energy partition ratio to workpiece was optimized by applied the idea of averaging to solving formulas. The temperature field responses to different grinding conditions were simulated and investigated. The aftereffect of grinding parameters on the temperature fields on the tooth surface and the reason for variations in the grinding temperature to different grinding positions of face gear was analysed. The experimental results with newly measurement method are highly consistent with the simulation results with the error of −6.10% to −13.69%, thereby validating the proposed model. This work provides theoretical support for obtaining a uniform grinding temperature during grinding face gear and to obtain a high tooth surface integrity. [Display omitted] • Comprehensive force–thermal modelling for face gear grinding. • Mechanical properties of abrasive grain and workpiece materials with grinding fluid. • Temperature field responses to face gear grinding conditions. • Analysis of grinding condition to temperature field. [ABSTRACT FROM AUTHOR]

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Purpose: The curved and tribologically highly stressed surfaces of bearing components pose a major challenge for steel alloys or tribological resistant coatings like tetrahedral amorphous carbon (ta-C) coatings which in particular have an increased risk of delamination due to the significantly increased residual stresses. A possibility to prevent coating failure is the use of dopants while maintaining or even increasing tribological properties. This study aims to compare the tribological behavior of several doped diamond-like-carbon coatings with an undoped ta-C coating under varying slip conditions and Hertzian pressure up to 1800 MPa. Design/methodology/approach: For this purpose, the tribological behavior was studied using of a ball-on-disc tribometer and a two-disc test rig under mixed/boundary conditions. The tests were conducted with coated specimens against uncoated 100Cr6 steel. Additionally, the influence of lubrication additives was studied due to the use of two fully formulated PAO-based oils, one without and one with molybdenum containing additives. The friction was measured in situ, and the wear was analyzed trough laser scanning microscopy and tactile measurement. Findings: It was shown that the use of doped ta-C coatings exhibited a tendency for a more favorable tribological behavior compared to undoped ta-C coatings, with no general dependence on the lubricants used. The use of the most suitable coatings reduced the wear of the steel counter-body considerably. Originality/value: To the best of the authors' knowledge, this is the first approach of testing the tribological behavior of these doped ta-C coatings, developed for friction efficiency, in dependency on lubrication additives under the given load collective. The approach is relevant to determine whether the friction reduction and the wear inhibition of these coatings are suitable for higher contact pressures and load cycles. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2022-0336/ [ABSTRACT FROM AUTHOR]

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Hard and brittle materials are widely used in many frontier fields because of their better properties, and their efficient precision polishing methods are attracting much attention. The research on surface quality of optical lenses with surface finishing requirement not only involves surface roughness, but also surface form accuracy. The generated surface profile is a key factor affecting the surface form accuracy and overall smoothness. From experience, both processing mechanism of adopted method and toolpath have effects on the generated surface profile. For this, the paper presents a theoretical and experimental study of the generated surface profile of spiral toolpath in axial ultrasonic vibration-assisted polishing (UVAP). Based on classical Preston equation, Hertzian contact theory and the axial vibration-assisted processing principle, a prediction calculation model for generated surface profile of spiral toolpath is proposed. The model can specifically analyze the dwell-time distribution characteristics of periodically varying contact pressure and sliding velocity in the areas near/far-from the curvature center of curve toolpath, accurately predict the surface profile shape and material removal rate (MRR), and scientifically reveal the assisted processing principle. Accordingly, a series of experiments are conducted to verify the rationality of the proposed model and the polishing performance of axial UVAP. Compared to conventional methods, the predictions can more reasonably and accurately present the real surface profile characteristics, both high MRR and superior surface quality are obtained. This study would aid in achieving a deterministic processing technology of higher efficiency and better surface quality, laying a crucial theoretical basis for the global polishing of optical lens. [ABSTRACT FROM AUTHOR]

In this paper, a novel method to analyze the mechanical behavior of the coin-tap test using the principle of pounding mechanics is proposed. Based on the Hertzian contact theory, the linearized contact law is applied to simplify the mathematical model of the coin-tap test. By modeling the stiffness of the defect as an equivalent spring in a serial connection with the contact stiffness, the impact force and impact time can be theoretically derived. The derived expressions show that, the closer the defect is to the surface of the structure, the longer the impact duration time and the smaller the impact force will be. In addition, with the increase of defect radii, the peak force and duration of the impact will decrease and increase, respectively. Another innovation of this paper is that an equivalent impact stiffness (EIS)-based damage index (DI) is proposed to reveal the severity and location of the near-surface damages. Two validation experiments were carried out to validate the influences of the damage's radii and under-surface depths. In the first experiment, the impact force and time of the central point for eight plates are measured to validate the accuracy of the proposed model. In the second experiment, 18 points on the horizontal centerline of eight specimens were tapped at an interval of 1 cm. The recorded pounding force and time were processed by EIS-based DI. Experimental results show that the EIS-based DI can effectively predict the position and severity of the defects and it holds the potential for practical application. [ABSTRACT FROM AUTHOR]

Rolling bearings operated at small oscillation angles or exposed to vibrations during standstill show typical damage after only a short period of operation. This can be false brinelling damage, so-called standstill marks or classic fretting damage (fretting corrosion, tribo-oxidation). It is important to differentiate here according to the amplitude-ratio x/2b, which indicates the ratio between the rolling element Motion (x) and the Hertzian contact half-axis (b). Depending on this ratio, suitable laboratory test methods must be used to test the lubricating grease practically for the particular application. For this purpose, the Fafnir wear test, according to the standard of the American Society for Testing and Materials ASTM D4170, is also listed in the current high-performance multi-use specification of the National Lubricating Grease Institute (NLGI) as a release test for lubricating greases. In Europe, the SNR-FEB2 test is frequently used, which is also required to release greases in the blade bearings of wind turbines, among other things. In the case of standstill marks due to very small oscillation angles or vibrations, the Mannheim Tribology Competence Center (KTM) has developed a special test now established in the industry. The oscillating angles vary in these three different standard tests in the range from ±6° in the Fafnir test to ±3° in the SNR-FEB2 test to ±0.5° in the KTM standstill marking test; the x-to-2b ratios range from 5.5 (Fafnir) to 3.4 (SNR) to 0.5 (KTM). This paper will explain the scientific basis for these special operating and test conditions and compare test results of specially prepared model greases in these three standard rolling bearing tests, two test variations and a classical fretting test under oscillating sliding friction (ASTM D7594). The paper's main objective is to show that the suitability of grease for such an application depends strongly on the prevailing operating conditions. Different tests in this field are, therefore, not interchangeable. Good results in one test do not automatically mean good results in a similar test at first glance. Therefore, selecting the right test for the application is important. [ABSTRACT FROM AUTHOR]

Advanced ball bearing simulations require the use of accurate tribological models, starting with the calculation of the ball-race contact load and pressure in potentially truncated contacts. Ball—cage and cage—guiding ring contact stiffness models are suggested using the Hertzian contact stiffness and/or a structural stiffness. The central ball-race film thickness, a hydrodynamic rolling force, and normal load increase are calculated using relationships respecting miscellaneous lubrication regimes, including iso-viscous-rigid or piezo-viscous-elastic. A drag force acting at the ball center is included, and its magnitude discussed for claiming that the contribution from drag to the final rolling resistance is smaller than the one from hydrodynamic rolling acting at the ball-race contact. The central film thickness and sliding speed are used for defining shear rate, shear stress, and, hence, final sliding force, using a nonlinear visco-elastic-plastic lubricant rheological model including viscosity, elastic lubricant shear modulus, and limiting shear stress, which are all functions of the pressure and temperature. Elastic effects are approximated using a simple nonlinear visco-plastic model with apparent viscosity. The temperature is defined as the sum of the operating temperature and several other sources of temperature increase. It is observed that when adopting Roelands viscosity model and a simple nonlinear visco-plastic model, the final lubricant traction coefficient and its gradient with respect to sliding speed decrease as the rolling speed increases, mostly reducing the need for a lubricant elastic shear modulus. Appropriate experimental results are highlighted to support these analytical models. [ABSTRACT FROM AUTHOR]

Purpose: Axle box bearings are the crucial components of high-speed trains (HSTs). Based on Gupta's model, a dynamic model of cylindrical roller bearing is presented to describe the dynamic behaviour of the axle box bearing more realistically, with the coupling effects of local defects and wheel-rail disturbances considered. Methods: The Hertzian contact force and lubrication traction between the raceway and the roller are taken into account, as well as the gravity of the car body and the wheel-rail contact force. The local defects are described as the time-varying deflection excitations applied to the outer raceway, inner raceway and rollers respectively. By transforming the power spectrum of track irregularity into time-domain, the random excitation is input as external excitation. The fourth-order Runge-Kutta method is used to solve the equations of motion. Results: The dynamical behaviors of the bearing with different defects are analyzed. Besides, the effects of vehicle speed on bearing acceleration are studied. Conclusion: The outer raceway and inner raceway failure are coupled strongly with the track irregularity, whereas such coupling effect for roller failure is relatively small. [ABSTRACT FROM AUTHOR]

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson's ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin's theorem and Barber's extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant's approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem. [ABSTRACT FROM AUTHOR]

Dynamic interaction between train wheel and high-speed slab is an important issue when evaluating the contact force at the wheel–rail interface under the influence of an irregularity either on the train wheel or on the rail. In this paper, an influence of amplitude of irregularity along with the vehicle speed on the dynamics of wheel–rail interaction for high-speed railway tracks is being analyzed. For this purpose, single-wheel high-speed railway (HSR) track interaction models are developed using the bond graph modeling technique. The HSR track model consists of two layers of beam, i.e., rail and concrete slab. Both the rail and slab track is modeled using the Euler–Bernoulli beam theory. The Hertzian contact theory at the wheel–rail interface has been considered for this analysis. The vertical dynamic interaction between a train wheel and a high-speed slab track is compiled in the time domain using a bond graph approach coupled with a technique known as modal superposition. Irregularity present on the wheel is characterized as smooth, moderate, and severe depending upon the variation of irregularity amplitude. An expeditious increase of maximum contact force has been observed between the speed range of 200 and 250 km/h. Beyond the speed of 250 km/h, there is a gradual increment of contact force up to its peak value. When the train speed is beyond 288 km/h, there is a gradual decrease in maximum contact force. This kind of several other useful dynamic responses in terms of wheel acceleration and wheel–rail overlap are also evaluated. [ABSTRACT FROM AUTHOR]

In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined. [ABSTRACT FROM AUTHOR]

Linear ball guideways (LBGs) have several advantages for the precise positioning control of machine tools. However, the ball-groove contact behaviour leads to poor dynamic compliance, which induces a significant nonlinear behaviour of the guideway and a poor chatter stability. The nonlinearity complicates the chatter prediction due to the dependence of the contact stiffness. This approach aims to offer an industrially orientated method of estimation of chatter stability for structures based on LBG. Consequently, the present study first employs Hertzian contact theory to describe the ball-groove contact behaviour in the LBG of a lathe machine. Two static models are presented, both predict the LBG stiffness under different cutting loads. The first model describes is simplified, ignores the effects of the contact force on the deformation of the guideway components, even with that limitation depicts the main behaviour of the system. The second model is more precise and adopts a dynamic substructuring cosimulation method to incorporate the effects of structural deformation into the analysis. For both models, a linearisation approach is employed to analyse the dynamic behaviour of the system under static loading and define the dynamic compliance. The chatter frequencies of the LBG are estimated using the second model and are shown to be in good agreement with the experimental results. In general, the results of the analysis show that fundamental shifts in the frequency response of the LBG occur under specific values of the cutting force and gravity load. In other words, the results confirm that this method provides sufficient estimation of nonlinear behaviour of machine tool based on the LBG. [ABSTRACT FROM AUTHOR]

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The modeling of tilting-pad journal and thrust bearings presents a level of complexity beyond that of bearings with a fixed-arc geometry, particularly with regard to their dynamic influences. With tilting-pad bearings, the theory surrounding their fluid film must be complemented with the representative modeling of the pad dynamics. What has been recognized in recent decades is the significance of the pad support, in particular the flexibility of the pivot region of the pad. The typical model for including the stiffness of the pivot is based on the Hertzian contact theory. Some researchers have noted that the Hertzian theory does not permit sufficient flexibility in the pivot region. It has been suggested that the contact mechanics at the pivot would be better represented as a pairing of rough surfaces. The modeling used here is based on a statistical asperity micro-contact theory for rough surface line contact that has been extended to include contact stiffness. This model has been applied to the determination of the effective dynamic properties of tilting-pad bearings. The results show that pivot stiffness can be as low as one third of the stiffness determined by the Hertzian theory. A comparison to published experimental results confirms the significance of the rough surface modeling, particularly for the line contacts associated with rocker-back tilting pads. [ABSTRACT FROM AUTHOR]

We derive an extension of the Maugis-Dugdale-Johnson-Greenwood model for 2D adhesive Hertzian contact to viscoelastic materials. This results in extremely simple approximate results for the maximum amplification of the pull-off due to viscoelastic effects, for arbitrary form of the viscoelastic linear properties. In particular, we assume that the initial loading state is fully relaxed, and unloading occurs at very large pulling speeds. We show that the maximum amplification (of the order of E I / E R 2 / 3 , the ratio between instantaneous and relaxed modulus to the 2/3 power) is only reached for large and soft cylinders, namely, large enough (relaxed) Tabor-Maugis parameters λ of the order of the order of E I / E R , and therefore typically much larger than the Tabor-Maugis parameters to have a "short-range" JKR adhesion regime in quasi-static conditions, which is λ ∼ 1. The results agree well with recent numerical ones by Muser-Persson, but there is an shift factor in the Tabor-Maugis parameter which requires further study and may depend on initial contact area. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)