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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]

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]

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]

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]

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]

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]

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]

Dynamics models of planetary gear sets (PGSs) are usually established to predict their dynamic behavior and load-sharing characteristics. The accurate modeling of bearing support stiffness is essential to study their dynamics. However, in most of the existing PGS dynamic models, the effect of characteristics coupling the rolling bearing time-varying nonlinear stiffness with the translational property of PGSs on the dynamic responses was completely neglected. To investigate this problem, a refined dynamic model for PGSs is proposed considering the coupled relationship between the radial translation of the rotating components and the time-varying nonlinear support stiffness of the ball bearing. The refined dynamic model simultaneously considers the coupled effect of the time-varying characteristic caused by the orbital motion of the rolling elements and the nonlinear characteristic caused by Hertzian contact between the rolling elements and raceways of the ball bearing. Comparisons between the simulations and experimental results are presented, which indicate that the PGS vibration spectrums yielded by the proposed time-varying nonlinear stiffness model are much closer to the actual scenarios than those of traditional models. The analysis results provide theoretical guidance for fault monitoring and diagnosis of the rolling bearings used in the PGS. [ABSTRACT FROM AUTHOR]

The deformations that occur during composite forming processes are governed by the friction between the fabrics and tooling material on the mesoscopic level. The effect of normal load and multi-plies on the frictional behavior of the carbon plain weave is investigated by simulating the friction between the fabric and metal semi-cylinder tool by using the experimental method. The periodic wavy friction-displacement curve between the metal tool and fabric is caused by the interwoven structure of the fabric. Both the increase in the normal load and the number of layers cause an increase in the real contact area during friction, leading to an increase in the friction force. The real contact area is calculated based on the Hertzian contact model and the self-designed testing method. The friction force values obtained from multiplying the real contact area with shear strength are closely aligned with the measured results. [ABSTRACT FROM AUTHOR]

Traveling wave rotary ultrasonic motors (TRUMs) are widely used in various industrial processes due to their attractive features, such as compact structure, high accuracy, and fast response. However, the major limiting factors of the operational performance of TRUMs under high-voltage excitation are the nonlinear behavior caused by the nonlinearities of the piezoelectric materials and the friction between the stator and rotor of the motor. In this study, a nonlinear dynamics model and an identification method are presented to directly design the driver circuit for suppressing the nonlinear behavior under high voltage excitation. Firstly, by studying the time–frequency characteristics of the isolated electrode voltage, a single-sided Hertzian contact forced oscillator model of TRUMs is established, involving the nonlinearities of the piezoelectric material and friction. Secondly, a harmonic balance nonlinear identification is proposed in the time domain for TRUMs. The influence of the voltage and preload on the nonlinear phenomena is discussed. Lastly, a novel driver circuit is proposed to suppress the nonlinearities using feedback from the isolated electrode. Experiments showed that the total harmonic distortion decreased by 89.4% under 500 Vpp. The proposed drive circuit design method is used to find a high excitation voltage and preload to achieve greater motor output power. [ABSTRACT FROM AUTHOR]

Optimising the performance of materials requires, among other things, the characterisation of residual stresses during the design stage. Raman spectroscopy offers access to these residual stresses at the micrometre scale when this inelastic light scattering is active in these materials. In this case, the relationship between the Raman mode shift and the pressure must be known. High-pressure cells with diamond anvils or bending instruments coupled to Raman spectrometers are habitually used to determine this relationship. In this article, we propose a new method that involves a Hertzian contact to obtain this relationship. A device that compresses an alumina ball against a transparent glass plane is connected to a Raman spectrometer. Under these conditions, the contact pressure can be as high as 1.5 GPa. The contact between the glass plane and the ball is observed through a diaphragm. Several hundred Raman spectra are recorded depending on the contact diameter. The spectral profiles obtained represent the shift in the Raman modes of alumina and glass along the contact diameter. Hertz's theory accurately describes the pressure profile as a function of position for elastic materials. Therefore, the contact diameter can be measured by fitting the spectral profile with a function identical to the Hertz profile. We then deduce the maximum pressure. Next, the calculated pressure profile along the contact diameter is correlated with the spectral profile. We obtain a pressure dependence of the Raman mode with a coefficient equal to 2.07 cm − 1 /GPa for the Eg modes of alumina at 417 cm − 1 , which is in good agreement with the literature. In the case of glass, we refine the measurement of the Q3 mode shift at 1096 cm − 1 in the studied pressure range compared to the literature. We find a coefficient of 4.31 cm − 1 /GPa. This work on static contacts opens up promising prospects for investigations into dynamic contacts in tribology. [ABSTRACT FROM AUTHOR]

The objective of this study was to explore the mechanical properties of AlCrSiN and AlTiSiN coatings deposited on Inconel and steel substrates after thermal treatments of 500 °C and 800 °C. Nanoindentation was used to measure the hardness and elastic modulus of the coatings, and microindentation was used for observing the contact damage with Hertzian contact loadings. Microscratch and Mercedes tests were used to evaluate the adhesive strength between coating and substrate with both progressive and static loads, respectively. The surface damage was inspected by optical microscopy and scanning electron microscopy (SEM). Focus ion beams (FIB) were used to mill the cross-sections in order to detect the extent and mode of failure. The results show that AlCrSiN coatings and Inconel substrates exhibit better mechanical performance, even after thermal treatments. [ABSTRACT FROM AUTHOR]

Tribological coatings are widely used in industry, particularly when the conventional oil lubrication of sliding surfaces has to be replaced by maintenance-free contacts. This work studies the tribological performance of waterborne tribological coatings based on three binders of the polyaryletherketone (PAEK) family: polyetherketone (PEK), PEEK, and polyetherketoneketone (PEKK). Even though PEEK is a well-known commercial solution for this type of tribological coatings, PEK and PEKK have never been studied in such a context. PTFE particles were added to all coatings as a solid lubricant. High thermal resistance of the binder materials was confirmed, with decomposition starting above 550 °C, under either N2 or O2 atmosphere. XRD analysis showed that PEK and PEEK are semi-crystalline after being subjected to the coating curing conditions, while PEKK is amorphous. The coatings were successfully applied with thicknesses of 20–30 µm. Tribological measurements showed that the PEK-based coating possesses a coefficient of friction (COF) of 0.08 under high load and pressure conditions (hertzian point contact), which is lower than the reference PEEK-based coating (around 0.11). The PEKK-based coating showed an impressive wear resistance with almost no wear measured compared to the 105 µm wear obtained for PEEK-based coating, while showing a similar COF. These results suggest that PEK and PEKK seem to be interesting alternatives to PEEK and should be further studied for use in tribological coatings. [ABSTRACT FROM AUTHOR]

Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz's hypotheses do not hold. This paper summarizes Hertz's theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz's theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz's hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made. [ABSTRACT FROM AUTHOR]

AE detection and analysis usually requires a specific, costly platform due to its particular burst nature and high-frequency content. This experimental study investigates the relationship between low-demand acoustic emission parameters (AE) and the occurrence of stick–slip (SS) at the Hertzian linear contact. Hence, the correlation of basic AE characteristics (amplitude, energy, and evolution in time) with stick–slip characteristics (static and kinetic friction coefficients, amplitude, energy, and evolution in time) is pursued. Tribological tests were conducted on cylinder–plane specimens under dry friction conditions with different loads at different low driving speeds and Hertzian contact pressures at a constant stiffness. The AE, normal, and friction forces were recorded simultaneously on the experimental stand. At the cylinder–plane interface, the jumps specific to the stick–slip phenomenon (friction coefficient—COF) were followed after a few milliseconds by AE jump peaks. The results of the experiments show that the amplitude and energy generated by AE were sensitive to the occurrence of the stick–slip phenomenon, while the AE and COF energies in the stick and slip phases had the same law of variation based on the driving velocities. The results show that the amplitude and energy of the sampled low-frequency AE signals were enough to detect the friction in SS and demonstrate the potential of AE as a tool for detecting and monitoring the tribological behaviour of SS at the linear Hertzian contact. [ABSTRACT FROM AUTHOR]

This paper focuses on the influence of radial internal clearance on the dynamics of a rolling-element bearing. In the beginning, the 2—Degree of Freedom (DOF) model was studied, in which the clearance was treated as a bifurcation parameter. The derived nonlinear mathematical model is based on Hertzian contact theory and takes into consideration shape errors of rolling surfaces and eccentricity reflecting real operating conditions. The analysis showed characteristic dynamical behavior by specific clearance range, which reflects others in a low or high amplitude and can refer to the optimal clearance. The experimental validation was conducted with the use of a double row self-aligning ball bearing (SABB) NTN 2309SK in which the acceleration response was measured by various rotational velocities. The time series obtained from the mathematical model and the experiment were analyzed with the recurrence quantification analysis. [ABSTRACT FROM AUTHOR]

The goal of this study was to explore the self-guided machining mechanism of boring and trepanning association (BTA) deep hole drilling and realize precise control of the machining quality. The motion analysis method was used to analyze the center motion trajectory of the drill during the entrance, and the self-guiding mechanism and hole-forming mechanism of BTA deep hole drilling were revealed. Considering the bending deformation of the drilling tube and the tool structure parameters, according to the elastic-plastic deformation theory and Hertzian contact theory, a novel analytical model of the extrusion contact between the guide pads and the hole wall of the BTA deep hole drilling was established for the theoretical prediction of the extrusion deformation and the machining hole diameter. Combined with the finite element method (FEM) simulation model, the variation law of the contact inclination angle, contact stress, and extrusion deformation of the guide pads and the hole wall with the drilling conditions were studied. The total extrusion deformation between the guide pad and the hole wall was between 10 and 50 μm. The maximum error between the FEM simulation results and the test results was 18.1%, and the maximum error between the analytical model results and the test results was 23.6%. The simulation and experimental results showed that the established extrusion contact model could accurately predict the extrusion deformation of the hole wall and the machining hole diameter. [ABSTRACT FROM AUTHOR]

In rolling or gear contacts, truncation of the contact ellipse can occur, for example, when an undercut extends into the contact area. For an elastic calculation approach, the edge constitutes a mathematical singularity, which is revealed by a theoretically infinitely high pressure peak. However, when elastic–plastic material behavior is taken into account, the pressure peak is limited by local hardening and yielding of the material, leading to plastic deformations. As a result, those calculations are rather challenging and the results partly unexpected due to the discontinuity contained in the geometry. Nevertheless, to the authors' knowledge, hardly any published studies exist on elastic–plastic simulations of truncated contact ellipses. Therefore, a numerical study concerning the contact of a rigid ball with an elastic–plastic plane is presented. Due to an undercut in the plane, a quarter of the theoretical Hertzian contact ellipse is cut off. The aim of the study is to investigate the influence of the undercut angle on the pressure distribution and the elastic and plastic deformation at the edge. The use of FEM shows that the undercut angle has a significant effect on the characteristics of the contact. The results obtained using FEM are then used as a reference for comparison with a semi-analytical method (SAM). It is shown that the SAM, based on the half-space, provides comparable results only for very small undercut angles. [ABSTRACT FROM AUTHOR]

Locating bearing track rollers are used, for example, in monorail transport systems to enable relative movement between the rail and the shuttle. Due to the two-point contact, both radial and axial forces can be transmitted simultaneously. Since friction is involved, the state of the art does not provide any calculation rules for the dimensioning and design. The development of a calculation model with sophisticated commercial software brings its difficulties since no plausibility check is possible using existing models. For this reason, a model based on analytical descriptions including the Hertzian and the elastic half space theories is presented in this paper. It bridges the gap between very simple approaches and widely developed commercial software. With this model, the contact forces, friction forces, surface tensions, relative velocities and subsurface stresses can be calculated for both free and driven rolling. The main advantages are that the model is easy to apply, and thus comparisons between different track roller designs can be made quickly. [ABSTRACT FROM AUTHOR]

The work hardening behaviour of GCr15 bearing steel during rolling contact fatigue (RCF) is investigated. Ball-on-rod RCF tests and micro-indentation tests are performed to obtain various subsurface hardness profiles in rod specimens. It is found that orthogonal shear stress is responsible for work hardening under Hertzian contact and that the extent of hardness increase is positively associated with the stress level and number of cycles. A dislocation-based work hardening model is established by combining the Kocks–Mecking theory, the bearing steel plasticity equation and the Taylor relation. The proposed model is capable of predicting hardness changes with any given rolling contact stress state and number of cycles. The modelling results are compared against the experimental results, with good agreement obtained. This research also provides a methodology for studying the work hardening of different types of bearing steels undergoing RCF, from experiment to modelling. [ABSTRACT FROM AUTHOR]

In order to eliminate the calculation error of the Hertzian elastohydrodynamic contact stress due to the asymmetry of the contact region of the helix raceway, a non-Hertzian elastohydrodynamic contact stress calculation method based on the minimum excess principle was proposed. Firstly, the normal contact stresses of the screw raceway and the nut raceway were calculated by the Hertzian contact theory and the minimum excess principle, respectively. Subsequently, the Hertzian solution and the non-Hertzian solution of the elastohydrodynamic contact stress could be determined by the Reynolds equation under different helix angles and screw speeds. Finally, the friction torque test of the double-nut ball screws was designed and implemented on a self-designed bed for validation of the proposed method. The comparison showed that the experimental friction torque was the good agreement with the simulated friction torque, which verified the effectiveness and correctness of the non-Hertzian elastohydrodynamic contact stress calculation method. Under the large helix angle, the calculation accuracy of asperity contact stress for the non-Hertzian solution was more accurate than that of the Hertzian solution at the contact region of ball screws. Therefore, the non-Hertzian elastohydrodynamic contact stress considering the asymmetry of the raceway contact region could more accurately analyze the wear depth of the high-speed ball screws. [ABSTRACT FROM AUTHOR]

Dynamic analysis of a combination of misaligned rotors, the disturbance of the Cardan joint and the rotor–stator rubbing within a restricted clearance space in a viscous fluid is complex and can result in persistent vibration anomalies that are often misunderstood. It becomes increasingly important to gain some insights into how the transmission of coupled motion responds dynamically under a variety of conditions. This paper introduces an efficient simulation of the misaligned multi-degree-of-freedom rotor's model, which was developed to predict the transient dynamic behaviours of a driveshaft deflection. The model accounts for tight clearance as a function of contact deformation according to nonlinear Hertzian contact theory. The paper also examines recent research by considering the influence of parameters such as eccentric masses, applied torques and flexible coupling joint perturbation introduced in the proposed rotor system. The simulation results indicated that the viscous fluid surrounding the driveshaft had sufficient torsional flexibility to dampen the rubbing impact to the driven shaft displacement. In addition, the torsional fluctuations of the flexible coupling abruptly increased, and then significantly impacted the vibration of the submerged driveshaft. Parametric studies involving the interconnected rotor models indicated that the effects of fluid on a close-bounds contact area can create partial disturbance reduction. The high rubbing contact is shown to be lost through the Hooke's joints during power transmission. The speed-frequency spectrum maps provide valuable information on all the modelled excitations over the frequency of the twice-running speed resonance in a viscous medium. Further, nonlinear characteristics are reconstructed through orbit shapes and can be adopted in the condition monitoring of rotors in engineering practice. [ABSTRACT FROM AUTHOR]

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro (e.g., rolling bearings considering Hertzian contact restoring force between rolling elements and bearing raceways) or micro (e.g., the micro cantilever probe system of atomic force microscopy) scale mechanical systems, and contact resonance could cause serious problems of wear, contact fatigue, vibration, and noise, which has attracted widespread attention. In the present paper, the softening/hardening stiffness characteristics of continuous and one-sided contact power-form nonlinear spring models are addressed, respectively, by the analysis of the monotone features of resonant frequency-response skeleton lines. Herein, the period-n solution branch and its stability characteristics are obtained by the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory. Compared with previous studies, this paper will furtherly clarify the influences of externally normal load, the power form exponent term, and excitation amplitude on the softening/hardening stiffness characteristics of general power-form spring systems. In addition, for a power-form system with a one-sided contact, the phenomena of primary and super/sub-harmonic hysteretic resonances inducing period-doubling, folding bifurcation, the coexistence of multiple solutions are demonstrated. Besides, it gives the evolution mechanism of two types of intermittency chaos in a one-sided contact system. The overall results may have certain basic theoretical significance and engineering values for the control of vibration and noise in contact mechanical systems. [ABSTRACT FROM AUTHOR]

Wheel flats induce high-impact loads with relevance for the safety of the vehicle in operation as they can contribute to broken axles, hot axle boxes, and damaged rolling bearings and wheels. The high loads also induce damage in the track components such as rails and sleepers. Although this subject has been studied numerically and experimentally over the last few years, the wheel flat problem has focused on ballasted tracks, and there is a need to understand the phenomena also for slab tracks. In this research, a numerical approach was used to show the effects of the wheel flats with different geometric configurations on the dynamic behavior of a classical ballasted track and a continuous slab track. Several wheel flat geometries and different vehicle speeds were considered. The nonlinear Hertzian contact model was used because of the high dynamic variation of the interaction of the load between the vehicle and the rail. The results evidenced that, for the same traffic conditions, the dynamic force was higher on the slab track than on the ballasted one, contrary to the maximum vertical displacement, which was higher on the ballasted track due to the track differences regarding the stiffness and frequency response. The results are useful for railway managers who wish to monitor track deterioration under the regulatory limits. [ABSTRACT FROM AUTHOR]

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system's response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators. [ABSTRACT FROM AUTHOR]

In early design phases of ball typed constant velocity joints (CVJ), which are widely used for the uniform transmission of rotational movement in driveshafts, the knowledge of the interactions between the components is essential. Therefore, a simulation model for a multi-body analysis is developed to consider general, transient operating conditions of the joint in the development process. The model is derived using the example of a plunging joint of the rear prop shaft, which has a straight track geometry and two track angles. On this basis, a two-dimensional, analytical contact determination between balls and tracks can be carried out, which reduces the required computation times compared to a general contact determination. Although rigid bodies are used for numerical analysis, local elastic deformations between the contact bodies are possible on the basis of Hertzian contact theory. For a higher level of detail, frictional forces are also taken into account via the Coulomb friction law, which is adapted for numerical use. To validate the simulation model, the influences of the numerical parameters are discussed and the numerical results are compared with the analytical results of the statically undeflected joint condition. Finally, the created simulation model is utilised to present the numerical joint analysis using two examples of joint kinematics analysis. [ABSTRACT FROM AUTHOR]

This paper presents the change of non-dimensional characteristics and thermal behavior of different sized tilting pad journal bearings (TPJBs) with the same Sommerfeld number. A three-dimensional (3D) TPJB numerical model is provided considering the thermo-elastic hydro-dynamic (TEHD) lubrication model with pad thermal-elastic deformation. The pivot stiffness is assumed to be the combination of linear and cubic stiffness based on the Hertzian contact theory. The TPJBs in a configuration of load between pad (LBP) with the same Sommerfeld number having seven different sizes are simulated, and their non-dimensional dynamic and static characteristics and thermal behavior are compared. Pad thermal and elastic deformation are both taken into account. If the changes in lubricant viscosity, thermal deformation, and elastic deformation of journal/pads due to viscous shearing are ignored, the bearings with identical Sommerfeld numbers should show the same performance characteristics. However, the heat generation at the bearing clearance during operation (a) induces a decrease in viscosity and heat transfer to journal/pads and (b) results in a thermal deformation. Furthermore, the elastic deformation of the tilting pads and pivots also affects the bearing dynamic performance. For the same Sommerfeld number, the numerical analyses provide how the viscous shearing and elastic deformation lead to a change in bearing performance. For the small bearings with the same Sommerfeld number, the non-dimensional characteristics did not change significantly, where the heat generation was small being compared to the large sized bearing. The largest change in non-dimensional characteristics occurred when the maximum temperature of the oil film increased by 30 °C or more compared to the lubricant supply temperature. The root cause of the change in the non-dimensional characteristics is the viscous shearing in the oil film, and the thermal deformation of the structures surrounding the oil film acts in combination. These results provide insight into the Sommerfeld number, which can be used for the early stage of bearing design. [ABSTRACT FROM AUTHOR]

An approximate solution for a contact problem of profiles which are not axially symmetrical but deviate only slightly from the axial symmetry is found in a closed explicit analytical form. The solution is based on Betti's reciprocity theorem, first applied to contact problems by R.T. Shield in 1967, in connection with the extremal principle for the contact force found by J.R. Barber in 1974 and Fabrikant's approximation (1986) for the pressure distribution under a flat punch with arbitrary cross-section. The general solution is validated by comparison with the Hertzian solution for the contact of ellipsoids with small eccentricity and with numerical solutions for conical shapes with polygonal cross-sections. The solution provides the dependencies of the force on the indentation, the size and the shape of the contact area as well as the pressure distribution in the contact area. The approach is illustrated by linear (conical) and quadratic profiles with arbitrary cross-sections as well as for "separable" shapes, which can be represented as a product of a power-law function of the radius with an arbitrary exponent and an arbitrary function of the polar angle. A generalization of the Method of Dimensionality Reduction to non-axisymmetric profiles is formulated. [ABSTRACT FROM AUTHOR]

Tilting pad journal bearings (TPJB) are used in turbomachinery for their stability at high speeds. For design purposes, it is necessary to preliminarily investigate the turbomachine rotor dynamic behavior by simulation. The dynamic characteristics of all components must be known as precisely as possible and experimental validation of each single model is required. While a lot of work has been carried out on bearings, the ball-and-socket stiffness is still estimated by means of Hertzian formulas. Recently, some authors have used the finite element method, but it seems that nothing has been done experimentally to date. This paper describes the test rig designed to determine the stiffness of a TPJB ball-and-socket pivot by equipping the grippers of a tensile universal testing machine with specifically designed interfaces. A methodology for evaluating the stiffness from the experimental results is reported. Preliminary compression results are presented and compared with the analytical ones obtained using Hertz's formula showing significant differences for the ball-and-socket conformal contact. [ABSTRACT FROM AUTHOR]

This paper reports a novel pocket-textured surface for improving the tribological properties of point contact under starved lubrication by possibly storing and releasing oil, and homogenizing the surface contact pressure. The ball-on-disk experimental results confirmed the coefficient of friction (COF) and wear reduction effect of such pocket-texturing. The maximum reduction rate was 40% compared with a flat surface under the same operating conditions. Analyses on experimental results attributed the oil storage effect and enhanced the secondary lubrication effect within the starved lubrication state, to become the main mechanism. In addition, the plate elasticity and the Hertzian contact principles were employed to estimate the pressure and the load acting on the surface. The experimental results and numerical analysis substantiated the design of pocket-textured surface, making it likely to enlarge about 50% of contact surface and to reduce 90% of equivalent stress in comparison to those of conventional surfaces. [ABSTRACT FROM AUTHOR]

In applications requiring high load carrying capacity, conforming contacting pairs with a relatively large contact footprint are used. These include circular arc, Novikov, and Wildhaber gears found, for example, in helicopter rotors. Closely conforming contacts also occur in many natural endo-articular joints, such as hips, or their replacement arthroplasty. The main determining factors in contact fatigue are the sub-surface shear stresses. For highly loaded contacts, classical Hertzian contact mechanics is used for many gears, bearings, and joints. However, the theory is essentially for concentrated counterforming contacts, where the problem is reduced to a rigid ellipsoidal solid penetrating an equivalent semi-infinite elastic half-space. Applicability is limited though, and the theory is often used inappropriately for contacts of varying degrees of conformity. This paper presents a generic contact mechanics approach for the determination of sub-surface stresses, which is applicable to both highly conforming as well as concentrated counterforming contacts. It is shown that sub-surface shear stresses alter in magnitude and disposition according to contact conformity, and lead to the different modes of fatigue failure noted in practice. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing interest in the use of highly nonlinear solitary waves (HNSWs) for nondestructive evaluation and structural health monitoring applications. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as granular particles in Hertzian contact. The easiest setup consists of a built-in transducer in drypoint contact with the structure or material to be inspected/monitored. The transducer is made of a monoperiodic array of spherical particles that enables the excitation and detection of the solitary waves. The transducer is wired to a data acquisition system that controls the functionality of the transducer and stores the time series for post-processing. In this paper, the design and testing of a wireless unit that enables the remote control of a transducer without the need to connect it to sophisticated test equipment are presented. Comparative tests and analyses between the measurements obtained with the newly designed wireless unit and the conventional wired configuration are provided. The results are corroborated by an analytical model that predicts the dynamic interaction between solitary waves and materials with different modulus. The advantages and limitations of the proposed wireless platform are given along with some suggestions for future developments. [ABSTRACT FROM AUTHOR]

The complex nature of slip-rolling contacts in many applications such as gear tooth flanks, rolling bearings, and heavy machinery often makes determining the friction and wear properties, as well as the fatigue resistance, of tribosystems difficult. The establishment of the tribological profile of a tribocouple under high Hertzian contact pressure and under slip-rolling will allow for the measurement and comparison of friction and wear coefficients as well as slip-rolling resistance by continuously monitoring the wear rate, coefficient of friction, temperature, oil film thickness, and/or electrical contact resistance using high-resolution signal analysis (HRA). A twin disc system can provide insight into the adhesive behavior of material and lubricant products such as alternative base oils and additives, ceramics, alloys, and thin film coatings. The strength and endurance of these products are often characterized through fatigue and resistance tests, which apply high Hertzian contact pressures to the rolling contact until seizure or failure is obtained. The further observation of the formation of tribofilms on the surface of contact yields information about the reactivity and thermochemical properties of additives. This review aims to illustrate how the implementation of different screening methodologies can be used as a meaningful tool for assessing the aforementioned tribological profile properties for the development of slip-rolling tribosystems. [ABSTRACT FROM AUTHOR]

The ankle is one of the most complicated joints in the human body. Its features a plethora of elements with complex behavior. Their functions could be better understood using a planar model of the joint with low parameter count and low numerical complexity. In this study, an accurate planar model of the ankle with optimized material parameters was presented. In order to obtain the model, we proposed an optimizational approach, which fine-tuned the material parameters of two-dimensional links substituting three-dimensional ligaments of the ankle. Furthermore, the cartilage in the model was replaced with Hertzian contact pairs. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the structure exhibited angular displacements in the range of the ankle joint and that their range was higher in dorsiflexion than plantarflexion. The structure also displayed a characteristic ramp up of the angular stiffness. The results obtained from the optimized model were in accordance with the experimental results for the ankle. Therefore, the proposed method for fine-tuning the material parameters of its links could be considered viable. [ABSTRACT FROM AUTHOR]

The paper probes slip differential heat of magnetorheological fluids (MRFs) subjected to shear mode operation and its effect on the structure. To begin, we present a novel model for measurement of slip differential heat to describe temperature rise of MRFs mainly caused by friction between magnetorheological particles. It includes two stages: (1) The micro-macro analysis of slip differential heat of MRFs including force, movement and heat between neighboring particles based on magnetic dipole and Hertzian contact theories, and (2) the further application to two basic disc-type and cylinder-type magnetorheological clutches combined with finite element simulations involving electromagnetic field and thermal analysis. The model takes into account the effect of each of the main influencing factors, such as the input current of excitation coil, the rotational speed difference of the clutches, the size and volume fraction of particles, the saturation magnetization of particles, and the structural size of the clutches, etc., on the slip differential heat of MRFs. Then the thermal structure analysis of MRFs comprising thermal deformation and equivalent thermal stress is carried out. Moreover, the effect of typical governing parameters on the slip power of MRFs and the influence of slip differential heat on the structure of MRFs are investigated individually. We show that such a model is effective in reflecting the temperature-slip time relation of MRFs. It is shown that the input current and the rotational speed difference have great effect on the slip power, and the slip differential heat has a certain influence on the micro-structure of MRFs. [ABSTRACT FROM AUTHOR]

Film thickness is the most important parameter of a lubricated contact. Its evaluation in a cam-follower contact is not easy due to the continuous variations of speed, load and geometry during the camshaft rotation. In this work, experimental apparatus with a system for film thickness and shape estimation using optical interferometry, is described. The basic principles of the interferometric techniques and the color spaces used to describe the color components of the fringes of the interference images are reported. Programs for calibration and image analysis, previously developed for point contacts, have been improved and specifically modified for line contacts. The essential steps of the calibration procedure are illustrated. Some experimental interference images obtained with both Hertzian and elastohydrodynamic lubricated cam-follower line contacts are analyzed. The results show program is capable of being used in very different conditions. The methodology developed seems to be promising for a quasi-automatic analysis of large numbers of interference images recorded during camshaft rotation. [ABSTRACT FROM AUTHOR]

In this study, ballistic experiments were performed to determine the critical velocity of a Twaron® 2040 high-performance yarn transversely impacted by round projectiles. Four different round projectiles possessing a radius of curvature of 2 µm, 20 µm, 200 µm and 2 mm were used in this study. Load cells were mounted to the grips to measure the load history of the yarn upon impact. A high-speed camera was incorporated into the ballistic experimental setup to capture the failure process of the yarn upon impact. A scanning electron microscope was utilized to perform post-mortem failure analysis on the recovered specimens. The results showed that as the radius of curvature of the projectile increased, the critical velocity also increased. The critical velocities for all cases were bounded between those predicted from the Euler–Bernoulli beam and Smith models. Upon impact above the upper limit of the critical velocity, the axial loads revealed a demonstrative reduction. The failure surfaces changed from shear to fibrillation as the radius of curvature increased. For those specimens that failed in shear, Hertzian contact model was used to predict the critical velocity. [ABSTRACT FROM AUTHOR]