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This paper aims to assess the wear reliability characteristics of the piston/cylinder pair based on the wear failure prediction using numerical and experimental techniques for the water hydraulic state. This is due to the complex forces and contact states acting in the piston, hence, making it difficult to establish a numerical model for wear failure prediction. The Hertzian contact and Elastic-Plastic mechanical equivalence are proposed in numerically modelling the friction fatigue mechanism based on asperity damage for piston/cylinder pair. An experimental analysis is conducted for the reciprocating ceramic peek-2507 steel tribopair to validate the effectiveness of the prediction model. The error between the numerical and experimental models is assessed to be less than 10% with a coefficient of determinant R2 of 0.99. The numerical wear data were scattered within the 10% confidence interval, indicating the high survivability of the predicted data. In addition, the reliability characteristics based on the volume of wear predicting in risk monitoring using the Weibull probability distribution function are proposed to model the reliability and probability of failure for the piston/cylinder pair. From the volume of wear prediction from the computed Mean-Volume-To-Failure (MVTF) = 17.8 mm3, the probability of failure based on the numerical modelling is estimated to be at 0.52. Hence, the proposed numerical model is suitable for predicting the wear volume in the water hydraulic state for various conditions. [Display omitted] [ABSTRACT FROM AUTHOR]

Multi-layer CrTiN/CrCN and CrTiN/TiCN coatings were deposited on 2379 and SLD steels by cathodic arc physical vapor deposition (arc-PVD) in different thicknesses. Coatings are mechanically, physically, and chemically characterized by nanoindentation, optical microscope, atomic force microscope (AFM), and scanning electron microscope/energy-dispersive X-ray (SEM/EDX) analyses. The crystal structure of the coatings was investigated by X-ray diffraction (XRD) analysis. Wear and friction characterizations were performed via reciprocating tribometer tests under 2.4 and 3.0 GPa Hertzian contact pressures at the unlubricated conditions. Results showed that CrTiN/CrCN coatings demonstrated excellent wear resistance and friction coefficient (COF) at elevated contact pressures both on 2379 and SLD steels. [ABSTRACT FROM AUTHOR]

The impact response of shear deformable sandwich cylindrical shells composed of two face layers and a functionally graded (FG) porous core is investigated. The mass density and elastic moduli of FG porous core are assumed to vary along the thickness in terms of the coefficients of mass density and foam, whose relationships are determined by employing the typical mechanical characteristics of an open-cell metal foam. Governing equations are derived using the first-order shear deformation shell theory and Hamilton's principle. The contact force is achieved based on linearized Hertzian contact law. The Duhamel integration is applied to find the transverse displacement of porous sandwich shell. Results show that the core thickness, impact velocity, foam type, foam coefficient, and masses of impactor and shell play important roles on the impact response of sandwich porous shells. [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]

The calculation of the wheel–rail contact forces is one of the most difficult yet time-consuming processes in multibody system (MBS) simulations for a vehicle-track interaction system. The classical combination of the Hertzian model with the FASTSIM algorithm is the most widely used model in MBS code for railway application and the 'exact' solver CONTACT is seldom used due to its high computational cost. A trade-off solution between accuracy and computational efficiency is the simplified and approximate non-Hertzian approach. This paper attempts to compare the influence on MBS simulation for rail vehicle system dynamics of the varied combinations of the classical contact models (i.e. Hertz model and FASTSIM), well-known simplified non-Hertzian model (Kik–Piotrowski model) recently developed improved simplified non-Hertzian models i.e. Extended Kik–Piotrowski and Kalker Book of Tables for Non-Hertzian contact (KBTNH), and the CONTACT algorithm. The results show that all non-Hertzian approaches deviate from the classical Hertzian solutions in both local contact and global dynamics and the KBTNH model provides better agreement with CONTACT than the FASTSIM algorithm for non-elliptic contact conditions considered in this study. A detailed analysis of the causes and influences of the difference due to varied contact models is presented. [ABSTRACT FROM AUTHOR]

In this work, solitary wave solutions of particle mechanical metamaterials are studied, in which the mass-in-mass structure with local resonators is considered. The Hertzian contact theory is used to describe adjacent particles in a precompressed granular chain. The governing wave equations are decoupled, and the expressions of bright, dark, and peaked solitary waves are derived, respectively. According to the results, both the wave velocity and prestress can affect the propagation of solitary waves. The amplitudes of bright and peaked solitary waves are smaller when a larger prestress is applied, which are different from the dark solitons. Furthermore, the wave widths become larger as the prestress increases. [ABSTRACT FROM AUTHOR]

In the hydrodynamic line contact, there is a very thin layer physically adsorbed to the solid surface. When the surface separation is sufficiently small, the Hertzian contact zone will be completely filled with the boundary layer, while in most of the inlet zone still occurs continuum hydrodynamics, which lies between the mated adsorbed layers. The present paper studies this mixed hydrodynamics by a multiscale analysis. The boundary layer flows are simulated by the flow factor approach model. The intermediate continuum fluid flow is simulated by the continuum fluid model. The flow equations are given respectively for the boundary layers and for the intermediate continuum fluid. The final governing equation has been obtained relating the surface separation to the solid surface speeds and the carried load. The calculation results show that for a high rolling speed the hydrodynamic behavior in the contact agrees with the classical hydrodynamic theory; however for a critically low rolling speed it gives the surface separation greatly higher than that calculated from the classical hydrodynamic theory, showing the significant adsorbed layer effect. [ABSTRACT FROM AUTHOR]

Two models are compared for calculating the surface separation in a multiscale elastohydrodynamic lubricated line contact for the same operating conditions. In the studied line contact, the surface separation is very low so that the effect of the adsorbed boundary layer is significant. Model I principally takes the continuum fluid film as intervening between the two adsorbed boundary layers. Model II takes the continuous phase transition both along the flow direction and across the whole surface separation; in this model, in the Hertzian contact zone there is only the adsorbed boundary layer, while in most of the inlet zone there is only the continuum fluid film (by neglecting the adsorbed boundary layer). The analytical results show that for the same case these two models give the close surface separations. The equivalence of these two models is shown. [ABSTRACT FROM AUTHOR]

Blast mitigation continues to be a popular field of research when military vehicles are concerned. The main problem is coping with the vehicle global motion consequences following an explosion. The paper presents a potential application of the linear vacuum packed particle (VPP) damper as a supplementation for a viscous shock absorber in a traditional blast mitigation seat design. The paper also presents field test results for the underbelly blast explosion, comparing them to the laboratory tests carried out on the impact bench. To collect accelerations, the anthropomorphic test device, i.e. the Hybrid III dummy, was used. A set of numerical simulations of the modified blast mitigation seat with the additional VPP linear damper were revealed. The VPP damper was modeled according to the Johnson-Cook model of viscoplasticity. The Hertzian contact theory was adopted to model the contact between the vehicle and the ground. The reduction of the dynamic response index (DRI) in the case of the VPP damper application was also proved. [ABSTRACT FROM AUTHOR]

Countless biophysical studies have sought distinct markers in the cellular mechanical response that could be linked to morphogenesis, homeostasis, and disease. Here, an iterative-fitting methodology visualizes the time-dependent viscoelastic behavior of human skin cells under physiologically relevant conditions. Past investigations often involved parameterizing elastic relationships and assuming purely Hertzian contact mechanics, which fails to properly account for the rich temporal information available. We demonstrate the performance superiority of the proposed iterative viscoelastic characterization method over standard open-search approaches. Our viscoelastic measurements revealed that 2D adherent metastatic melanoma cells exhibit reduced elasticity compared to their normal counterparts—melanocytes and fibroblasts, and are significantly less viscous than fibroblasts over timescales spanning three orders of magnitude. The measured loss angle indicates clear differential viscoelastic responses across multiple timescales between the measured cells. This method provides insight into the complex viscoelastic behavior of metastatic melanoma cells relevant to better understanding cancer metastasis and aggression. Parvini, Cartagena and Solares introduce an iterative viscoelastic approach based on the generalized Maxwell and Kelvin-Voigt models. The results showed that metastatic melanoma cells had lower elasticity than normal fibroblasts and melanoma cells were less viscous than the fibroblasts over a large frequency range, enhancing the understanding of cellular responses at different frequencies. [ABSTRACT FROM AUTHOR]

This work investigated the elastic responses of a composite laminate shell subjected to a transverse low-velocity impact. The governing equation based on the equations of motion of both the impactor and target was developed to detetrmine the impact force. The displacement of the shell subjected to unit impulse loading was solved using the finite element method. A non-linear differential equation in terms of the indentation depth was derived by incorporating the Hertzian contact law and theory of convolution. Runge-Kutta method was employed to solve the non-linear integro-differential equation, leading to the determination of the impact force at the point of contact between the impactor and the composite shell. The elastic responses including the displacement and stress of the composite laminate shell were evaluated using the finite element method by exerting the impact force on the apex of the composite shell. Present approach was verified with the analytical, experimental and numerical results reported in the existing literatures. The influences of stacking sequence of the composite laminate shell on the impact responses were examined through a series of parametric studies. In addition, impact responses of the spherical shells with different materials such as steel, aluminum and glass were studied. [ABSTRACT FROM AUTHOR]

We show that Hertzian particle contacts are the underlying cause of the as-yet-unexplained noninteger power laws in weakly nonlinear rheology. In the medium amplitude oscillatory shear (MAOS) region, the cubic scaling of the leading order nonlinear shear stress (σ 3 ∼ γ 0 m 3 , m 3 = 3) is the standard expectation. Expanding on the work by Natalia et al. [J. Rheol. 64, 625–635 (2020)], we report an extensive data set of noncubical, noninteger power law scalings m 3 for particle suspensions in two immiscible fluids with a capillary attractive interaction, known as capillary suspensions. Here, we show that distinct power law exponents are found for the storage and loss moduli and these noninteger scalings occur at every secondary fluid concentration for two different contact angles. These compelling results indicate that the noninteger scalings are related to the underlying microstructure of capillary suspensions. We show that the magnitude of the third harmonic elastic stress scaling m 3 , elastic originates from Hertzian-like contacts in combination with the attractive capillary force. The related third harmonic viscous stress scaling m 3 , viscous is found to be associated with adhesive-controlled friction. These observations, conducted for a wide range of compositions, can help explain previous reports of noninteger scaling for materials involving particle contacts and offers a new opportunity using the variable power law exponent of MAOS rheology to reveal the physics of particle bonds and friction in the rheological response under low deformation instead of at very high shear rates. [ABSTRACT FROM AUTHOR]

Polymer hybrid ball bearings' balls and rings consist of different materials. Rings have been manufactured viskoelastic material. The traditional ball bearings ball-ring contact analyse with Hertzian contact theory but polymer hybrid ball bearings has not been analyse with the Hertzian contact theory. Polymer ring-ball contact has been analysed with elasto-plastic contact model instead of Hertzian contact theory. Elasto-plastic contact model has two model which are indentation and flattening. These model have been evaluated contact area as elastic region, elasto-plastic region or plastic region. Elastic contact region evaluate the same as Hertzian contact theory. Ball bearings has long lifetime to run elastic region and away from resonance condition. Friction has been caused the systems temperature to rise while the shaft-bearing system run. This condition has been caused to drop elastic modulus and stiffness of polymer bearing. Elastic modulus has been affect the bearings force capacity and stiffness. Stiffness affect the natural frequency of systems. For researching temperature effect on elastic modulus and vibration characteristic of ball bearings mathematical model has been created. Radial deep groove ball bearings geometric and material properties have been used in mathematical model. Simulations have been done via MATLAB software program. As a result, elastic modulus and natural frequency of systems' decreases with temperature rise. Although force capacity related with elastic modulus, force capacity increase with temperature rise because of critic deformation. [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]

Low shear strength (30 MPa) organic films were grown in situ on Pt0.9Au0.1 surfaces via cyclic sliding contact in dry N2 with trace concentrations of ambient hydrocarbons. We present a systematic investigation of the stress- and time-dependent film formation. Steady-state friction coefficients were found to be as low as µ ~ 0.015 and inversely proportional to contact pressure, revealing non-Amontonian behavior. Above a Hertzian contact pressure of ~500 MPa, shear strength dropped, indicating an activated process. Raman spectroscopy identified non-uniformity in areal coverage and relative order with contact pressure. Regions of steady-state low-friction behavior exhibited spectra similar to DLC coatings. Atomic force microscopy was used to study the formation and growth of films at the nanoscale. Stress- and time-dependent measurements suggested a sublinear increase of film volume with time, and a transition from growth to wear at a Hertzian contact pressure of ~1.2 GPa. [ABSTRACT FROM AUTHOR]

• A novel method for the gear mesh stiffness calculation of plastic gear pair is established. • The influences of meshing deformation on the mesh behavior of plastic gear pair are investigated. • An iterative algorithm is utilized for the accurate calculation of gear mesh stiffness. • The proposed method is verified by the finite element method. The accurate calculation of the mesh stiffness for a plastic gear pair is significant for analyzing its transmission performance. During the meshing process, factors such as gear tooth meshing deformation and thermal effect will cause variations of the meshing position and tooth load particularly for plastic gears. These increase the difficulty for the accurate calculation of the gear mesh stiffness for plastic gear pair. To address this issue, the instantaneous gear tooth meshing deformation is obtained based on the potential energy method. Then, the effects of the above factors on the contact condition of a meshing tooth pair are analyzed, based on which the actual mesh position is accurately obtained via an iterative algorithm. Under the commonly-used elastic contact assumption, the contact stiffness at the new meshing position is calculated based on the Hertzian contact theory, and the algorithm of the mesh stiffness calculation for a plastic gear pair is derived by analyzing the influence of the elastic approach of meshing tooth on load distribution mechanism of gear pair. Compared with previous analytical methods, the proposed algorithm for mesh stiffness calculation shows higher accuracy, and it can also properly analyze the effect of load and other parameters on the mesh behavior of plastic gear pair, which can provide a theoretical basis for the performance analysis of plastic gear transmission system. [ABSTRACT FROM AUTHOR]

In this paper, the predicted generation mechanism, chatter stability, and characteristics of the unique regenerative chatter with the burnishing process in wiper-turning operations are verified experimentally. It was found in the first part of the paper that the vibration regenerates in the burnishing process by the wiper part of the insert causing a novel type of chatter. In this second part, this chatter phenomenon is investigated in an experimental manner to verify its mechanism. The specific burnishing force, which is a gain factor characterizing the burnishing process, is determined by the Hertzian contact law. In addition, the specific cutting force is measured by a cutting test, the compliance of the flexible structure is measured by a hammering test, and the residual compliance is measured by a static indentation test. Then, experiments are conducted where the tilt angle and the feed rate are varied to find the critical stability. The conducted chatter experiments prove that the predicted generation mechanism, critical stability, and characteristics are true. • Regenerative chatter in turning with burnishing process has been experimentally verified. • Specific burnishing force is identified by the Hertzian contact law. • The predicted large phase shift is confirmed experimentally, e.g. 329.8 deg. • Tilt angle of insert has a large effect on chatter stability since burnishing width changes. • Feed rate does not have much effect on stability since burnishing width is nearly constant. [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]

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.

Elastic-plastic response of M-plane single crystal sapphire was explored via a nano-indenter with a Berkovich tip. Elastic-plastic transition was observed with eight different points (ranging from 0.30 to 0.55 mN) subject to respective peak load. Mechanical properties i.e., Oliver-Pharr hardness and elastic modulus were also determined in the onset elastic and elastic-plastic regions. Stable value of elastic modulus estimated from Oliver-Pharr nanoindentation experiments was around 430 ± 15.0 GPa. However, Oliver-Pharr hardness in purely elastic and elastic–plastic (ISE) regions was approximately 2.19 and 2.0 times greater than the non-ISE hardness values respectively. Values of hardness in the non-ISE region were also in compliance with the depth independent hardness calculated through Nix-Gao and proportional specimen resistance models. Additionally, principal stresses and maximum shear stress were estimated on pop-in burst using Hertzian contact theory. Values of the critical resolved shear stress (CRSS) and maximum possible shear strength were also calculated at the first pop-in burst. Moreover, plastic zone size enhanced 1.36 times by shifting of critical load from 0.30 to 0.55 mN. Multiplication of Schmid factor and interplanar spacing indicated two slip systems i.e., prism {01 1 ‾ 1 ‾ } <10 1 ‾ 1 ‾ > and pyramidal {11 2 ‾ 0} < 1 ‾ 100>, which are verified in the Transmission electron microscopy (TEM) images. Estimated values of maximum contact pressures at respective critical loads were much lower in comparison to phase transformation pressure of sapphire. Maximum tensile stress was also calculated using Hertzian contact theory relations. Obtained value of maximum tensile strength was 3.58 times lower than cleavage fracture stress at the first pop-in. [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]

This paper established geometric coordination equations of deep groove ball bearings (DGBB) and 4-point ball bearings (4PBB) in which the contact sliding state is defined specifically. Combined with the classic Hertzian contact theory, a set of five nonlinear equations was established. The discrete Newton method algorithm was used to solve this nonlinear equation. According to the calculation results, the load-displacement curve of the bearing was obtained. Theoretically, the load-displacement relationship of different parameters (such as DGBB or 4PBB, clearance, raceway curvature, etc.) was compared. Then a test bench for measuring the load-displacement relationship was established, the axial load-displacement relationship and tilting load-displacement relationship were measured. Afterward, the axial load-displacement and the tilting load-displacement curves of the sample bearings with five different design parameters were measured and compared with the theory. Finally, three ways to decrease the bearing's displacement under load were concluded from the study. [ABSTRACT FROM AUTHOR]

Purpose: To explore fracture strength and failure behaviour of minimally invasive CAD-CAM composite resin overlay restorations. Methods: Eighty bi- and tri-layer cylindrical overlay model including the restoration bonded over bovine tooth dentin (Groups D) and enamel-dentin (Groups E) were assembled (diameter 9 mm). Restorations were milled from CAD-CAM composite resin blocks (Brilliant Crios, Coltène/Whaledent AG) in different thicknesses (0.5mm, 1mm, 1.5mm, 2mm) and equally distributed in four Groups D and four Groups E (n=10). All specimens were submitted to an Hertzian load-to-failure contact test with spherical indenter. Critical loads were recorded in Newton and data were analysed using Kruskal-Wallis test for multiple and Mann-Whitney test for 2-samples comparisons (p < 0.05). Fragments were examined using SEM. The stress distribution for specimens with restorations of 0.5 mm and 2 mm was also investigated with FEA. Results: For all specimens, the mean static loads in Newton increased with an increase in restoration thickness. On contrary, restorations with the same thickness displayed higher resistance values when bonded over enamel than dentin, except for the 2-mm thick restorations. A damage competition was detected between cone/median cracks originating at the loading contact area of the restorations and radial cracks beginning at their inner surface, with the former prevailing in restorations bonded on enamel and the latter being dominant for restorations bonded on dentin. Conclusions: For bonded ultra-thin resin composite restorations (0.5 mm to 1.5 mm) enamel as bonding substrate assures higher critical loads to fracture than dentin. This influence gradually decreases as restoration thickened. [ABSTRACT FROM AUTHOR]

• A comprehensive stiffness model of intermediate bearing is presented. • A reduced model of dual rotor-bearing-casing coupling system is developed. • The effects of typical parameters on the vibration of the system are discussed. • The mechanism of the comprehensive stiffness and system vibration is revealed. This paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark- β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity. [ABSTRACT FROM AUTHOR]

The dynamics of granular materials have been studied for many years, however, they have recently drawn attention for their unique response to acoustic excitation, and thus their potential applications in acoustics and noise and vibration control. For example, porous granules like zeolite and activated carbon have been applied to enhance the performance of loudspeakers at low frequencies. The reliable prediction of the acoustic behavior of these materials requires accurate characterization, which can be accomplished from a practical point-of-view by making standing wave tube measurements. But, to help with the interpretation of those types of measurements, in this article, the Biot poro-elastic theory is applied to describe the sound propagation in granules stacked in a cylindrical sample holder, as in a standing wave tube. The originality of the present work is the extension of the Biot model to accommodate materials like granular activated carbon (GAC) that are porous at multiple levels, and a finite difference (FD) implementation that incorporates the depth-dependent stiffness of the granular materials predicted by the Janssen's model and Hertzian contact theory. The model predictions are compared with measurements of GAC and light-weight glass bubble stacks, with the simulation results accurately matching the measured features of material absorption. • A FD method was built to predict the acoustic response of granular material. • The model considers the elasticity and inner particle pores of granules. • The approach was validated with measurements of two types of granules. [ABSTRACT FROM AUTHOR]

• Contact line calculation for face gear drives. • Analytical curvature calculation for face gear drives. • Calculation of the topological contact stress based on the Hertzian line contact. • Definition of an equivalent involute virtual cylindrical gear pairing. • Calculation examples for validation of the contact stress calculation methods. Face gear drives are angular gear units in which an involute pinion meshes with a face gear wheel. Spur and helical face gear drives are possible with or without center offset. Face gear drives can be manufactured on conventional gear cutting machines. Furthermore, the pinion is free to move axially and such displacements have no effect on the contact pattern. This makes them a promising gearing for various applications. Due to the lack of established calculation standards, the design of face gear drives is a challenge and often results in oversizing or early failures. This may also be why face gear drives have not yet established themselves in power transmissions. Instead, the main application can be found in kinematic/auxiliary drives. In this paper, two methods for contact stress calculation for face gear drives with any configuration between helix angle and center offset are developed. Calculation examples compare the two methods and confirm the applicability. Overall, this study provides a new standard-capable easy-to-program calculation method for the contact stress based on existing standards for cylindrical gears. [ABSTRACT FROM AUTHOR]

Bistable systems have been of great research interest due to their rich dynamics arising from a variety of excitations. This study presents an investigation into the nonlinear dynamics of a continuous bistable beam subjected to a form of vibro-impact forcing. A fixed–fixed Euler–Bernoulli beam, precompressed to achieve bistability, is considered, while a shaker with sinusoidally-prescribed velocity applies transverse impact forcing. By varying excitation parameters such as frequency and amplitude, the system response can be tuned. The study begins by employing a Galerkin expansion to the continuous equation of motion, using the buckling modes to remove buckling level dependence and ensure equilibrium symmetry. A Hertzian contact law is chosen to model the collision between the shaker and the buckled beam. The rich dynamics of this system are then explored through numerical and experimental analyses. The focus lies on investigating the emergence of intrawell and interwell dynamics that arise with varying excitation frequency, amplitude, and location. Moreover, we evaluate the significance of including higher-order modes in the modeling of bistable beam dynamics, particularly near snapthrough. This research provides valuable insights into the behavior of continuous bistable structures under vibro-impact forcing, contributing to the understanding and control of such systems in engineering applications. • Novel multi-mode model studies nonlinear dynamics of a buckled beam with impact. • Experiment and computational results reveal rich excitation-dependent dynamics. • More modes are required to model high frequencies and off-center excitation. • Shaker frequency, amplitude, and location strongly influence buckled beam response. [ABSTRACT FROM AUTHOR]

• Time delays and relative approach of the impactors affect the contact forces. • The relative position and trajectories of the impactors influence the delamination. • The coefficient of friction and impactor size decides the critical angle for gross slip. The impacts occurring in real scenarios can be arbitrary, simultaneously impacting at different trajectories, giving rise to complexity in analysing the impact phenomena. This necessitates the implementation of a robust numerical finite element (FE) model capable of modelling such multiple impacts. The present paper investigates the multiple oblique low velocity impacts (OLVIs) on a clamped GLARE plate by spherical impactors exploring the influence of obliquity and their relative trajectories as well as the time delay between the OLVIs on the impact response and the extent of interfacial delamination. A 3D FE code has been developed considering the Hertzian contact model for modelling the normal component of contact and the theory of Mindlin and Deresiewicz is used for modelling tangential component considering friction. Results show that in addition to the obliquity of the impactors and the coefficient of friction, their relative trajectories, sizes and instant of their occurrences significantly influence the contact force histories, contact durations and the delamination at the interfaces. [ABSTRACT FROM AUTHOR]

The wealth of soft contact tribological (SCT) investigations utilising ball-on-disc tribometers assume Hertzian contact model to describe substrate deformation. We hypothesise this is invalid for soft-adhesive viscoelastic discs with a finite thickness. Here, we uniquely use the wear transducer in the mini-traction machine to indirectly measure the load-dependent deformation and fluid film thickness of rigid-soft, soft-rigid, and soft-soft contacts across a range of loads, speeds and viscosities. Macroscopic deformation within these configurations and compliance of the respective tribopairs vary considerably, which is not predicted by the Hertzian model. We consider how to account for these deformation effects in SCT. [Display omitted] • MTM wear transducer measures film thickness in EHL regime for soft contacts (ball-disc). • MTM wear transducer measures substrate deformation in BL-ML regime. • Hertzian contact mechanics is invalid for viscoelastic substrates with finite thickness. • A large effective gap arises in BL-ML regime due to the deformation of VE substrates (disc). [ABSTRACT FROM AUTHOR]

• Based on the Hertzian contact distribution and creep-slip characteristics, the fatigue life of spinning bearings is predicted using the damage parameter theory of the critical plane method and the L-P theory. • The deviation rate between the finite element simulation and the theoretical calculation results is 6.61% • The rotation speed, friction coefficient and external load affect the fatigue life of spinning bearings, and better lubrication and excellent contact surface to extend the life. • A rotary bearing life experimental device verified the reliability of the theoretically calculated deviation rate is 3.86%. In order to ensure the longer working life of rolling guide bushing, this work proposed a fatigue life prediction model of spinning bearings based on the Hertzian contact distribution and creep-slip characteristic. The influence of different parameters on the fatigue life of spinning bearings was analyzed according to the damage parameter theory of the critical plane method and the L-P theory. Finally, the fatigue life prediction model of spinning bearings was verified through the finite element simulation combined with the experiments. The reliability results show that creep-slip characteristic and deformation lead to the contact zone stress of the spinning bearing firstly increases, decreases subsequently to zero and then increases to the peak value. The increase of rotational speed will make the fatigue life of the spinning bearing firstly increases and then decreases. With the increase of friction coefficient, its fatigue life will become smaller and smaller, and the increase of the external load will decrease its fatigue life. Meanwhile, the prediction error rate of the fatigue life prediction model proposed in this study is 4.60%, which is within the error tolerance. This study provides certain methods and ideas for fatigue life prediction of spinning bearings, and lays a theoretical foundation for the design of highly reliable spinning bearings. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system. [ABSTRACT FROM AUTHOR]

Since fatigue life is the pivotal parameter in rolling element bearings, an enhancement in fatigue life has been enviable always. The flexibility of rolling elements can aid in reduction of contact stresses which eventually can increase fatigue life of rolling element bearings and that led to the hollow roller concept, however hollow roller concept encountered limitations in applications due to its catastrophic fractures at relatively lower loading conditions. Thus, the concept of end hemispherical cavities (EHC) roller, which possesses enough strength against such catastrophic failures along with probability of higher fatigue life than solid roller, has been treated further. Correspondingly, the present paper discusses the methodology for predicting fatigue life of rolling element bearings and employs the understanding of fatigue life models for comparing performance of EHC roller concept with other variants from fatigue life aspect. The simulations were performed for variants considered ensuing validation of methodology by exercising analytical results of Hertzian contact pressure. The stressed volume and the magnitude of decisive stress were emphasized to gauge performance of variants. Attained results indicated that EHC roller concept has prospects of transcending fatigue life of solid roller. [ABSTRACT FROM AUTHOR]

The dynamic response of delaminated twisted stiffened cylindrical shell under low-velocity impact of multiple masses is presented. The impactors are considered to impact at two arbitrary locations simultaneously or at different time, wherein the contact forces of the impactor are computed by using the modified Hertzian contact law. Multipoint constraint algorithm is used to create rectangular inter-ply delamination. An eight-noded isoparametric shell element is combined with a three-noded isoparametric beam element to model the stiffened panel. The governing equations are derived from Lagrange's equation of motion and solved by Newmark's constant acceleration algorithm to perform the parametric study. [ABSTRACT FROM AUTHOR]

• A semianalytical Hertzian frictional contact model in 2D is developed with a penalty factor. • The penalty factor increases with contact width and Poisson's ratio, and is bounded between 0 and 1. • The Hertzian contact stresses and partial slip effects are explicitly considered. • The proposed contact model is validated with finite element analyses and DEM simulations. The Hertzian contact model is prominent for characterizing the contact behaviors of particles in three dimensions (3D), while its two-dimensional (2D) version in the tangential direction has not been well-established yet. In this work, a semianalytical Hertzian frictional contact model in 2D is developed, with an analytical solution for the normal contact behavior and a semianalytical solution with a variable penalty factor for the tangential contact behavior. Numerical analyses with finite element simulations are performed to characterize the penalty factor and validate the proposed contact model. The results show that the penalty factor increases with the contact width and Poisson's ratio based on which an empirical equation of the penalty factor is provided. Using the penalty factor calculated from the empirical equation, the contact behaviors evaluated from the proposed contact model match fairly well with those of finite element simulations. The proposed contact model is implemented in a discrete element code. Quantitative analyses of a bi-axial compression test on polydispersed particles demonstrate the stability and effectiveness of the proposed contact model. The proposed contact model could be useful to the computational mechanics of particles in 2D and parallel-axis cylinders with strip contacts in 3D. [ABSTRACT FROM AUTHOR]

• Temperature dependence of contact mechanical properties is characterized by theory. • The theoretical models are expressed in terms of some basic material properties. • Nature and underlying physical control mechanisms at high temperatures are revealed. • Excellent agreements are obtained between model calculations and measurements. The novel theoretical models for the temperature dependence of the contact mechanical properties of the particulate composites in Hertzian contact are proposed in this paper, based on an assumption of the temperature-independent constant energy storage capacity for a specific brittle particulate composite, associating with the material yielding, and the theory of Hertzian contact. The yield stress, critical loads for the onset of the brittle and quasi-plastic damage modes, indentation strength, and the more commonly used fracture strength of the composites are expressed in terms of the basic material properties—the temperature-dependent Young's modulus and specific heat capacity, and the critical flaw size. The models enable the priori and quantitative predictions of the contact damage behavior of the composites during the whole process of the Hertzian contact. The models are validated by comparing against the experimental measurements of the temperature-dependent contact mechanical properties of the particulate-reinforced ultra-high temperature ceramic matrix composites in the temperature range of 25 ∼ 800 °C, which were found probably to be the only reported experimental studies of the particulate composites. The temperature dependence of the contact damage behavior of the composites is revealed to be mainly governed by the temperature-dependent Young's modulus and specific heat capacity, and the change of the flaw size above a certain temperature point. The models provide additional adequate methods for the determination of the nature and the underlying physical control mechanisms of the damage behavior of the composites at high temperatures. [ABSTRACT FROM AUTHOR]

From the perspective of spontaneous combustion control in coal mining, this study conducted a progressive axial loading test of broken coal using a self-designed multi-field coupling oxidation test system. The evolutionary characteristics of the bulking factor under different loading conditions of stress, stress–temperature, and stress–moisture were obtained. Subsequently, factors affecting the bulking properties of broken coal in the synchronous compression and deformation stage were analyzed theoretically using the four-particle accumulation model and Hertzian contact deformation principle. The research results are summarized as follows: (1) in the process of axial loading, the bulking factor of broken coal generally decreased, but showing three stages; (2) under the stress-moisture coupling effect, when the axial force was 0 kN and the external water content increased from 0 to 6.75%, the water wedge effect increased the bulking factor of broken coal by 2.17%; (3) under the stress-temperature coupling effect, when the axial force was 47.1 kN and the temperature increased from room temperature (23.3 °C) to 100 °C, the bulking factor of broken coal decreased by 5.08%; and (4) in the synchronous compression and deformation stage (at the axial stress of 94.2 kN), the theoretical analysis revealed that the bulking factor decreased gradually with increasing stress, temperature, and external water content, which was consistent with the test results. The abovementioned test results established the basic theory and provide practical support for subsequent recognition of the spontaneous combustion of confined coal. [ABSTRACT FROM AUTHOR]

Electrical capacitance method has been applied in measuring the elasto-hydrodynamic lubrication film thickness in rolling element bearings since 1970s, due to its feasibility of measuring film thickness directly in metallic components and its simple theory. In the current article, a summary on the evolution of the method and the corresponding issues relating to the film thickness measurements is given. The evolution of electrical capacitance method and other developed electrical capacitance methods in measuring the film thickness are discussed. Especially, the two existing methods of converting measured capacitance into film thickness are highlighted. One is to calculate the capacitance in the Hertzian contact area and the dielectric constant of the lubricant. The other is to apply calibration tests which are then used to transfer the measured capacitances into film thicknesses. The strengths and weaknesses of the two methods are also explored and discussed based on published researches. [ABSTRACT FROM AUTHOR]

Assume a rigid sphere that is slightly pushed towards an elastic half space. The applied force on the half space can be easily calculated using the basic theoretical tools provided by the Hertzian contact mechanics theory. It should be noted that the aforementioned analysis is valid under the condition that the deformation depth is significantly smaller compared to the sphere's radius (h ≪ R). So, a significant question arises; what if the sphere is pushed deeper in the elastic half space (e.g. h > R)? In this paper, the aforementioned question is answered and a relative discussion regarding the application of the results is presented. [ABSTRACT FROM AUTHOR]

The strength of a particle is one of the most crucial characteristics within a comminution process due to the mechanical stresses experienced by each particle. In this study, the K9 glass spheres and ceramic spheres were subjected to a breakage test. The test includes the breakage of up to 240 particles under compression to obtain the distribution of the breakage probability depending on the crushing force and breakage energy. The breakage test was conducted for five particle size fractions from each individual material. Thus obtained 10 crushing force distributions and corresponding 10 breakage energy distributions were fitted with lognormal distribution function. The parameters in the lognormal were analyzed including the effect of the material and particle size. Following this, the relationship between the crushing force and breakage energy was analyzed based on the Hertzian elastic contacts model and Tomas's elastic-plastic contact model, respectively. Additionally, particle strength in terms of crushing force and breakage energy were compared and found to be size dependent. Finally, a simple transformation algorithm of distributions is developed. According to this algorithm the crushing force distribution can be transformed into breakage energy distribution and vice versa. The findings facilitate a better understanding of the particle strength distribution under compression and will help to improve the comminution process design, control and optimization. [ABSTRACT FROM AUTHOR]

We study experimentally, numerically, and theoretically the dynamics of a one dimensional array of repelling magnets. We demonstrate that such systems support solitary waves with a profile and propagation speed that depend on the amplitude. The system belongs to the kind of nonlinear lattices studied in [Friesecke and Matthies, Physica D 171, 211-220 (2002)] and exhibits a sech2 profile in the low energy regime and atomic scale localization in the high energy regime. Such systems may find potential applications in the design of novel devices for shock absorption, energy localization and focusing. Furthermore, due to the similarity of the magnetic potential with the potentials governing atomic forces, the system could be used for a better understanding of important problems in physics and chemistry. [ABSTRACT FROM AUTHOR]

Almost all solid surfaces have roughness on different length scales, from macro, micro to nano. In the conventional fractal contact model, the macroscopic Hertzian contact theory is employed to predict the contact load-area relation for all sizes of contact spots. However, when the contact radius of an asperity shrinks to nanometers, surface tension may greatly alter the contact behavior. In the present paper, we address surface effects on the contact between a rigid sphere and an elastic half space, and we demonstrate that the contact load-area relation is size-dependent, especially for nanosized asperities. Then, the refined contact relation is incorporated into the Majumdar-Bhushan fractal contact model. It is found that the presence of surface tension requires higher load than the conventional fractal contact model to generate the same real contact area. [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]

Sintering of alumina from 1500°C to 1650°C and tribo‐mechanical properties at room temperature had been investigated using nano CuO as a sintering aid. Bulk density gradually increases with sintering temperature from 1500°C to 1600°C and is optimized at 1600°C, beyond this, bulk density does not significantly increase at 1650°C. The addition of 2 wt% CuO showed the best result on densification. Densification of about 97.74% was attained at 1600°C with the incorporation of 2 wt% CuO. Nano CuO at grain boundaries forms CuAl2O4 liquid which modifies the morphology of the grain and improves mechanical properties. The formation of self‐lubricating tribo‐film on the wear track results in a low coefficient of friction <0.2 and reduces specific wear rate. 4 wt% CuO addition increases contact tensile stress (σmax) by 51.2% and high Hertzian contact pressure (Pmax≈1.51 GPa) causes plastic deformation of wear track. The re‐solidified strengthening bond phase on the wear track simultaneously increases in friction coefficient and wear resistance with CuO addition. The optimizing effect of CuO addition shows that 2 wt% significantly decreases wear rate, and increases hardness and fracture toughness. [ABSTRACT FROM AUTHOR]

In this paper, the low velocity impact analysis of carbon nanotube (CNT)/carbon fiber (CF)-reinforced hybrid nanocomposite plates is presented using variational differential quadrature (VDQ) method due to its numerical essence and the framework of implementation. The hybrid nanocomposite plate deformation is formulated based on classical plate theory and the contact force between the plate and projectile is estimated using Hertzian contact law. Also, a new micromechanics approach is presented to calculate the effective mechanical properties of the CNT/CF polymer hybrid nanocomposites. Five important factors including, random orientation and random distribution of CNTs, CNT/polymer interphase region, waviness and transversely isotropic behavior of CNT are incorporated in the micromechanical analysis. The accuracy of the present approach is verified with the available open literature results showing a clear agreement. The effects of various factors such as volume fraction and non-straight shape of CNT, CNT/polymer interphase region, CF volume fraction, random and regular arrangement of CFs, plate geometrical parameters and impactor velocity on the low velocity impact behavior of the CNT/CF-reinforced hybrid nanocomposite plates are studied. [ABSTRACT FROM AUTHOR]

High levels of contact stress between mating teeth can damage the contact surface and hall structure of spur gears, driving research that has aimed to minimize this stress. This study analyzed the effects of the profile shift factor (x) on the contact stress between a pair of spur gear teeth. Five profile shift factors were considered, from x = 0 (standard spur gear) to x=0.2. For each case, theoretical results were calculated based on the Hertzian contact theory and ISOequations of contact stress and subsequently compared with results generated in the ANSYS Workbench software using the finite element method. Modal analysis was performed to compare the mode shape frequencies of all profile shift factor values. The harmonic responses indicate that the stresses generated by our geometry are less than the maximum material stress. [ABSTRACT FROM AUTHOR]

The impact between a rotating link and a solid flat surface is considered. For the impact, we consider three distinct periods: elastic period, elastoplastic period, and restitution period. A Hertzian contact force is considered for the elastic period. Nonlinear contact forces developed from finite element analysis are used for the remaining two phases. The tangential effect is taken into account considering a friction force that combines the Coulomb dry friction model and a viscous friction function of velocity. Simulations results are obtained for different friction parameters. An experimental setup was designed to measure the contact time during impact. The experimental and simulation results are compared for different lengths of the link. [ABSTRACT FROM AUTHOR]

This paper investigates the tool-workpiece contact mechanism in the disc polishing process, where the soft polishing disc touches the rigid freeform workpiece with a small tilt angle. The developed contact force model can explain how the contact parameters, including the disc contact depth, the disc tilt angle, the radii of curvature of the disc and the workpiece, affect the normal contact force. Under some reasonable geometric and mechanical assumptions of the disc and the workpiece, an approximated contact force equation is derived in a simple power-law form similar to the Hertzian contact model. The contact force is found to be positively related to the disc contact depth and the disc radius, while negatively related to the disc tilt angle and the workpiece normal curvature that is orthogonal to the feed direction. Both finite element simulations and experiments verify the effectiveness of the proposed contact force model. Furthermore, the material removal process is analyzed and a model-based process parameter planning method is developed to achieve uniform material removal considering the variation of workpiece curvatures. • Contact modeling between a soft tilted disc and a rigid freeform workpiece. • The disc penetration depth, tilt angle, and workpiece curvature are considered. • The contact force formula is derived in a simple power-law form. • The contact stiffness can be derived from the force formula. [ABSTRACT FROM AUTHOR]

It is traditionally considered that, due to the Hertzian contact force-deformation relationship, the stiffness of rolling bearings has stiffening characteristics, and gradually researchers find that the supporting characteristics of the system may stiffen, soften, and even coexist from them. The resonant hysteresis affects the stability and safety of the system, and its jumping effect can make an impact on the system. However, the ball bearing contains many nonlinearities such as the Hertzian contact between the rolling elements and raceways, bearing clearance, and time-varying compliances (VC), leading great difficulties to clarify the dynamical mechanism of resonant hysteresis of the system. With the aid of the harmonic balance and alternating frequency/time domain (HB-AFT) method and Floquet theory, this paper will investigate the hysteretic characteristics of the Hertzian contact resonances of a ball bearing system under VC excitations. Moreover, the linearized dynamic bearing stiffness of the system will be presented for assessing the locations of VC resonances, and the nonlinear characteristics of bearing stiffness will also be discussed in depth. Our analysis indicates that the system possesses many types of VC resonances such as the primary, internal, superharmonic, and even combination resonances, and the evolutions of these resonances are presented. Finally, the suppression of resonances and hysteresis of the system will be proposed by adjusting the bearing clearance. [ABSTRACT FROM AUTHOR]