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Gear shaping causes processing characteristics on gear tooth surfaces (PCGTS), e.g., gear tooth surface deviation (GTSD) and processing textures (PT), which can affect gear meshing performances. Gear shaping simulation is operated to obtain PCGTS with different indexing feeds. An improved contact stiffness method of gear tooth surfaces is developed based on a wedge-shaped contact form to obtain tooth contact stiffness with PT caused by gear shaping. An improved time-varying meshing stiffness (TVMS) method for gears manufactured by gear shaping is developed to calculate TVMS of gears with GTSD and PT under different indexing feed conditions. Effectiveness of the improved TVMS method is validated using the finite element method. Analysis results of the proposed contact stiffness method of gear tooth surfaces indicate that PT caused by gear shaping can aggravate fluctuations of gear tooth contact stress. Analysis results of the proposed TVMS method for gears also indicate that GTSD of gear tooth surfaces caused by gear shaping can reduce their TVMS. The proposed TVMS method of gears can effectively analyze TVMS of gear tooth surfaces via gear shaping and evaluate processing settings of gear shaping to improve gear meshing performances. • An improved contact stiffness model considering processing textures is proposed. • A time-varying meshing stiffness (TVMS) method for gears is developed. • Gear shaping simulation is used to obtain processed gear tooth surfaces. • TVMS results with different indexing feeds are obtained. • Effectiveness of the improved TVMS method is verified by finite element method. [ABSTRACT FROM AUTHOR]

The cable bracket is one of the crucial components of high-speed Electric Multiple Units (EMUs), which is fixed to the axle box by bolts to support the cable. As an important parameter of the joint surface, contact stiffness significantly affects the dynamic response and service life of the cable bracket. However, it is difficult to directly measure the contact stiffness of the joint surface. As a result, an identification method is proposed in this investigation to identify the contact stiffness. A finite element model incorporating both normal and tangential stiffness parameters is developed. According to the finite element model and modal testing results, an improved particle swarm optimization algorithm is employed to identify the contact stiffness of the joint surface. The effect of the contact stiffness on the vibrations of the cable bracket is investigated. The findings indicate that pre-tightening torque significantly influences the contact stiffness of the cable bracket. The contact stiffness has a great effect on the vibrations of the cable bracket. Optimal contact stiffness notably reduces vibrations of the cable bracket, thereby extending its service life. [ABSTRACT FROM AUTHOR]

Material deformation due to nanoindentation is well known. However, the deformation of a material, indentation cavity, and piled-up region drastically increases and nanohardness significantly decreases if the nanoindentation is performed in such a way that the deformation of one nanoindentation affects the others. This situation arises in various materials when they are subjected to tribological application such as pantograph assembly in electric trains and contact between the electrical power supply plug and pins. This situation has been addressed in this study and the quantitative reduction in nanohardness has been evaluated in detail. In this work, the nanoindentation was performed on the laser powder bed fusion (LPBF) CuCrZr alloy specimen under a load condition of 4500μN. This test was conducted at 100 points with an array of 10×10 at a 1μm pitch value. Two significant findings were identified in this work. First, the indentation impression was smaller and the corresponding nanohardness and contact stiffness values were higher in the first column of 10 nanoindentations and the first row of 10 nanoindentations. The remaining 80 nanoindentations displayed contrasting behavior compared to the initial 20 nanoindentations due to the prior deformation of nearer regions. Nanohardness value decreased parabolically from the low deformation to the high deformation region. This finding was validated by increasing the pitch to 15μm under the 4500μN load conditions. The piled-up region around the impression of indentation changed from a semi-circular shape at a 15μm pitch value to a cone shape at a 1μm pitch value. These findings will be beneficial for industries during the design of materials and will help reduce material failures resulting from tribological activities. [ABSTRACT FROM AUTHOR]

The central rod-fastened rotor of gas turbine exhibits pronounced noncontinuous characteristics due to the large number of contact interfaces between the compressor and turbine disks. It is necessary to establish an accurate dynamic modeling method for the central rod-fastened rotor that fully considers the contact surface effect. In this work, the contact behavior of the rough surface is characterized by the fractal theory. The normal and tangential contact stiffness models are developed, and the influence of fractal parameters is discussed. Besides, the finite element model for the central rod-fastened rotor is established by developing an improved contact element considering the equivalent stiffness segment of Hirth couplings. Finally, the proposed model is verified by conducting the modal testing and measuring the first four modes of natural frequencies and modal shapes of the central rod-fastened rotor. The results show that the numerical results are in good agreement with the experimental ones, and the fractal contact model can effectively predict the connection stiffness of Hirth couplings, which in turn improves the simulation accuracy for the modal characteristics of the central rod-fastened rotor and provides a dynamic modeling approach with high efficiency and less computational complexity. [ABSTRACT FROM AUTHOR]

• Specific modal vibration caused by bolted joint in rotor-AMBs system. • Accurate macroscopical rotor-AMBs mechatronic model with microscopic contact model. • Modelling of partial separation in the contact interface due to the AMBs supporting. • A novel time-variant additional stiffness matrix related to contact status. • Influence of bolted joint parameters on system response validated by experiments. Rotor-active magnetic bearings (rotor-AMBs) systems nowadays have been widely used in fluid machinery and the impeller and the shaft are commonly connected by bolted joint. However, when a certain pre-tightening force is applied to the bolted joint and the interface contact between the shaft and the impeller is formed, causing flexible modal vibrations when rotor is levitated. The mechanism of this modal vibration needs to be revealed to ensure stable operation of the machine. In traditional modelling, the effect of the interface contact is equated to an additional stiffness matrix by massless spring units, whose certain contact stiffness is uniformly distributed over the interface. Particularly, the calculation of contact stiffness and the effect of AMBs are neglected, resulting in the inaccurate response compared to experiments. Based on traditional modelling, we consider that there is partial separation in the contact interface due to the AMBs supporting and a novel additional stiffness matrix related to contact status is proposed by calculating the real-time contact area. The contact stiffness is calculated by microscopic contact model based on fractal theory and surface topography measurement. Finally, numerical simulation shows that the interface contact influences the system robustness and the unstable mode is excited. The increase of pre-tightening torque and contact radius both will increase the steady vibration amplitude, with the former being the major contributor. Moreover, the influence and order of the vibration are quantitatively validated by the experiments. [ABSTRACT FROM AUTHOR]

Abstract The cable bracket is one of the crucial components of high-speed Electric Multiple Units (EMUs), which is fixed to the axle box by bolts to support the cable. As an important parameter of the joint surface, contact stiffness significantly affects the dynamic response and service life of the cable bracket. However, it is difficult to directly measure the contact stiffness of the joint surface. As a result, an identification method is proposed in this investigation to identify the contact stiffness. A finite element model incorporating both normal and tangential stiffness parameters is developed. According to the finite element model and modal testing results, an improved particle swarm optimization algorithm is employed to identify the contact stiffness of the joint surface. The effect of the contact stiffness on the vibrations of the cable bracket is investigated. The findings indicate that pre-tightening torque significantly influences the contact stiffness of the cable bracket. The contact stiffness has a great effect on the vibrations of the cable bracket. Optimal contact stiffness notably reduces vibrations of the cable bracket, thereby extending its service life.

Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness. [ABSTRACT FROM AUTHOR]

The impact of contact between two elastic–plastic bodies is highly complex, with no established theoretical contact model currently available. This study investigates the problem of an elastic–plastic sphere impacting an elastic–plastic half-space at low speed and low energy using the finite element method (FEM). Existing linear contact loading laws exhibit significant discrepancies as they fail to consider the impact of elasticity and yield strength on the elastic–plastic sphere. To address this limitation, a novel linear contact loading law is proposed in this research, which utilizes the concept of equivalent contact stiffness rather than the conventional linear contact stiffness. The theoretical expressions of this new linear contact loading law are derived through FEM simulations of 150 sphere and half-space impact cases. The segmental linear characteristics of the equivalent contact stiffness are identified and fitted to establish the segmental expressions of the equivalent contact stiffness. The new linear contact loading law is dependent on various factors, including the yield strain of the half-space, the ratio of elastic moduli between the half-space and sphere, and the ratio of yield strengths between the half-space and sphere. The accuracy of the proposed linear contact loading law is validated through extensive Finite Element Method simulations, which involve an elastic–plastic half-space being struck by elastic–plastic spheres with varying impact energies, sizes, and material combinations. [ABSTRACT FROM AUTHOR]

In mixed elastohydrodynamic lubrication (EHL), the load distribution between the gear meshing surfaces is shared by the oil film and the asperities of the gear's rough surface. Based on the load‐sharing concept, this paper proposes a time‐varying meshing stiffness (TVMS) model for gears with mixed EHL. The initial step involves the utilization of the Greenwood‐Williamson model to calculate the contact stiffness of surface asperities, while the lubricating film is assessed using a curve‐fitting formula to investigate the influence of gear surface morphology on TVMS. Subsequently, the incorporation of gear fillet foundation deformation and friction enables accurate TVMS determination. The proposed method is employed to examine the meshing stiffness of the gear pair under both dry lubrication and EHL conditions. Comparative analysis reveals favorable agreement between the proposed model and experimental results obtained under dry lubrication, thereby highlighting the superior performance of the proposed approach. Moreover, the time‐varying friction coefficient under EHL is computed, and the impacts of gear surface morphology parameters, temperature, speed, and load on lubrication conditions and TVMS are investigated. The findings presented in this paper contribute significantly to advancements in gear design and performance. [ABSTRACT FROM AUTHOR]

The validity of different available contact models is tested against experimental data for contact normal loading of artificially shaped granite stones. Three elastic models and two plastic models were tested with different combinations of contact shape (spherical, conical and flat) and roughnesses. It was found that the deviation from the Hertz model increased with surface roughness with a generally better representation of the data achieved by using models which consider surface roughness and the fractality of the surface. The validity of all these models seems to be limited to before excessive plastic deformations start taking place, after which the contact seems to deform under constant stiffness. [ABSTRACT FROM AUTHOR]

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems. [ABSTRACT FROM AUTHOR]

Mechanical joint interfaces are widely found in mechanical equipment, and their contact stiffness directly affects the overall performance of the mechanical system. Based on the fractal and elastoplastic contact mechanics theories, the K-E elastoplastic contact model is introduced to establish the contact stiffness model for mechanical joint interfaces. This model considers the interaction effects between micro-asperities in the fully deformed state, including elasticity, first elastoplasticity, second elastoplasticity, and complete plastic deformation state. Based on this model, the effects of fractal parameters on normal contact stiffness and contact load are analyzed. It can be found that the larger fractal dimension D or smaller characteristic scale coefficient G will weaken the interaction between micro-asperities. The smoother processing surfaces lead to higher contact stiffness in mechanical joint interfaces. The applicability and effectiveness of the proposed model are verified by comparing it with the traditional contact model calculation results. Under the same load, the interaction between micro-rough surfaces leads to an increase in both overall deformation and contact stiffness. The accuracy of the predicted contact stiffness model is also validated by comparing it with experimental results. [ABSTRACT FROM AUTHOR]

Contact tests on machined and natural granite showed that extensive plastic deformation which extends to the core shape is happening before the cross-over from the behaviour of an elastic rough surface to the Hertzian behaviour of an elastic smooth contact when all asperities have yielded in the surface. The plastic deformation, which was found to take place when the estimated maximum stresses at the contact reaches about 0.6 of the material hardness, affects the behaviour during normal loading as the material will start to deform at constant stiffness after reaching these stresses. The plastic deformation during lateral loading also affects the applicability of lateral loading models. The data yielded a much lower lateral stiffness which is around one order of magnitude less than that predicted by the available contact models. [ABSTRACT FROM AUTHOR]

The principle of reflection of ultrasonic waves at lubricated interfaces has been widely studied in recent years using different models. In this work, two different models (the spring model and the resonance model) were used to verify the influence of the acoustic properties of four different lubricating oils. A simple three-layer configuration was used, where carefully prepared, well-controlled gaps between stainless steel plates were established to accommodate a drop of oil. Optical measurements showed that the gaps formed were: gap 1 = 11 µm, gap 2 = 85 µm, gap 3 = 100 µm, and gap 4 = 170 µm. The smaller gap (11 µm) was found to be in the limit measurement range using the spring model for the sensor used in this work (14 MHz), whereas the resonance method was used for the thicker gaps. For the resonance model, the use of the phase spectra helped the identification of the resonance frequencies. The results showed good agreement between the measured thicknesses and the nominal gap values. There was little effect of the acoustic properties of the oils on the measured values, with the largest discrepancies found for the oil with the highest speed of sound (PAO4). This new way to characterize oil properties in a thin gap, where the material and geometry of the contact are fully characterized, enables us to compare different measurement methods and understand their sensitivity when testing similar materials of the same class of lubricants, as small deviations are crucial in real-life applications. [ABSTRACT FROM AUTHOR]

Mixed lubrication interfaces are widespread in engineering. The measurement of contact stiffness is a challenge for device performance evaluation. The ultrasonic reflection method is an effective method, but the difficulty of accurate construction of the acoustic model limits the measurement accuracy. In this study, an improved acoustic model is proposed to analyze the contact stiffness of the mixed lubrication interface. The model is constructed using a quasi-static spring model, virtual material model, statistical microcontact model, and multilayer acoustic model. The mixed lubrication interface is equivalent to a homogeneous and isotropic virtual material layer. Then, the mechanical, geometric, and acoustic parameters of the virtual layer are determined by introducing thickness coefficients. The contact stiffness is obtained with the proposed model and compared with the quasi-static spring model and the virtual material layer model. The reflection coefficient of the interface can also be calculated using a multilayer acoustic model based on the calculated parameters. The proposed model is verified by comparing the predicted reflection coefficients with the published experimental results. [ABSTRACT FROM AUTHOR]

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

The stick–slip friction observed in an atomic force microscope (AFM) experiment has been widely studied using the Prandtl-Tomlinson (PT) model or molecular dynamics (MD) simulations. However, the mechanisms of friction energy dissipation in AFM are still not well understood. Our detailed MD simulations of a benchmark system, a Pt metal tip sliding on the Au (111) surface, provide a method of computing the contact stiffness and damping between the tip apex and the metal surface. We revealed that the contact stiffness is largely dependent on the very first contact layer atoms of the tip apex, but essentially independent of the temperature and the atomic mass of the AFM tip, and is also less dependent on the normal load if the contact geometry remains unchanged in elastic contact. Furthermore, by connecting the atomic relaxation rate to the damping coefficient, an important parameter gauging the friction dissipation in the PT model but the choice of which is usually empirical, we demonstrate that this damping coefficient is dependent on the atomic structure of the tip apex and the intrinsic relaxation rate of the individual atoms in the contact layer. We use such mechanisms to calculate the two parameters and carry out Langevin dynamics simulation within the framework of the PT model for two friction systems: a small Pt tip consisting of 3956 Pt atoms and a large polycrystalline Pt tip consisting of 18,365 Pt atoms. Our simulation results show that both tip apexes are underdamped in a stick–slip friction. We also demonstrate that the results from the Langevin dynamics simulation using these two critical parameters compared remarkably well with the straightforward MD simulation results in a range of sliding velocity (V = 0.01 – 1 m/s). [ABSTRACT FROM AUTHOR]

Elastohydrodynamic lubrication (EHL) point contact occurs between two rough surfaces at the mesoscopic level, while the interaction of rough surfaces involves contact between asperities at the microscale level. In most cases, the contact between asperities within an interface takes the form of lateral contact rather than peak contact. Regions devoid of contact asperities are filled with lubricating oil. However, conventional models often oversimplify lateral contact forms as interactions between asperities and a smooth, rigid plane. These simplifications fail to accurately represent the true contact conditions and can lead to inaccuracies in the analysis of EHL's contact performance. To address this issue, we have developed a novel EHL interface model comprising two rough surfaces. This model allows us to explore the influence of asperity height, contact angle, and contact azimuth angle on EHL interface performance. [ABSTRACT FROM AUTHOR]

This data article describes the extensive experimental dataset of friction hysteresis measured during the round robin test of the original research article [1]. The round robin test was performed on the two different fretting rigs of Imperial College London and Politecnico di Torino, and consisted of recording comparable friction hysteresis loops on specimen pairs manufactured from the same batch of raw stainless steel. The reciprocating motion of the specimens was performed at room temperature under a wide range of test conditions, including different normal loads, displacement amplitudes, nominal areas of contact and excitation frequencies of 100 Hz and 175 Hz. Friction forces and tangential relative displacements for each specimen pair were recorded and stored as hysteresis raw data. Each hysteresis loop was post-processed to extract friction coefficient, tangential contact stiffness and energy dissipated, whose evolution with wear was thus obtained and stored as well. MATLABⓇ scripts for post-processing and plotting data are included too.The dataset can be used by researchers as a benchmark to validate theoretical models or numerical simulations of friction hysteresis models and wear mechanisms, and also to study the physics of friction hysteresis and its contact parameters. This friction data can also be used as input in models for nonlinear dynamics applications as well as to provide information on the contact measurement uncertainty under fretting motion. Other applications include using this data as a training set for machine learning applications or data-driven models, as well as supporting grant applications.

The dual-drive ball screw pair serves as a crucial element within the fixed gantry machine tool with cross-rail movement. When in service, the dual-drive ball screw pair experiences variations in axial load, impacting the contact load distribution of the ball screw pair. A calculation model for determining the axial load offset of the dual-drive ball screw pair is proposed to investigate the variation in axial load. The impact of the geometric error associated with the guide rail and the position of the slide are considered. This paper presents the contact load distribution model for the dual-drive ball screw pair. This study investigates the contact load and contact angle distribution of the dual-drive ball screw pair during the machine tool in service. Additionally, based on fractal theory, the stiffness models of individual micro-convex body and contact surfaces have been established. This study provides a comprehensive analysis of the contact stiffness of the ball screw pair, considering the influence of guide rail geometric error and slide position. In addition, the three-dimensional surface morphology of ball screw pair is obtained by experiments. This paper investigates the contact stiffness distribution of dual-drive ball screw pair during service. [ABSTRACT FROM AUTHOR]

Contact stiffness–contact stress mapping relationship is the key to ultrasonic stress measurement. The interaction of asperities at the rough interface is very complicated. The complexity of the asperity interaction and the irregularity of the lubricant film distribution make it difficult for the existing acoustic models to accurately construct the mapping relationship. Therefore, this paper conducts experimental research on the contact stiffness of the lubricating interface, and constructs the contact stiffness–contact stress mapping relationship of the lubricating interface considering the influence of plastic deformation. The critical contact pressure is determined and used to analyze the influence of plastic deformation and elastic deformation on contact stiffness. The change of equivalent oil film thickness and stiffness under load was also analyzed, and the optimized analysis formula is obtained. Based on the load sharing concept, the contact stiffness–contact stress mapping relationship of lubricating interface was constructed. Finally, the proposed acoustic model was experimentally verified. [ABSTRACT FROM AUTHOR]

Grinding is the most important method in machining, which belongs to the category of precision machining processes. Many mechanical bonding surfaces are grinding surfaces. Therefore, the contact mechanism of grinding a joint surface is of great significance for predicting the loading process and dynamic characteristics of precision mechanical products. In this paper, based on the collected grinding surface roughness data, the profile parameters and topography characteristics of the asperity were analyzed, the rough surface data were fitted, the asperity profile was reconstructed, and the parabola y = nx2 + mx + l of the cylindrical asperity model was established. After analyzing the rough surface data of the grinding process, the asperity distribution height was fitted with a Gaussian distribution function, which proved that asperity follows the Gaussian distribution law. The validity of this model was confirmed by the non-dimensional processing of the assumed model and the fitting of six plasticity indices. When the pressure is the same, the normal stiffness increases with the decrease in the roughness value of the joint surface. The experimental stiffness values are basically consistent with the fitting stiffness values of the newly established model, which verifies the reliability and effectiveness of the new model established for the grinding surface. In this paper, a new model for grinding joint surface is established, and an experimental platform is set up to verify the validity of the model. [ABSTRACT FROM AUTHOR]

In order to study the dynamic response of hydraulic cylinders under complex load conditions, the modal characteristics of hydraulic cylinders were simulated and calculated by comprehensively considering the combined effects of preload and oil fluid dynamics. The contact in the finite element model was specially processed to ensure that the local degrees of freedom of the piston in the structure were maintained during the modal simulation calculation process. After the static characteristics were calculated, the relevant data was imported into the modal simulation module to achieve coupling analysis under preload. By verifying the contact stiffness factor, the boundary conditions of the model were effectively optimized. The natural frequencies of the model were compared and analyzed under different piston strokes, and the mechanism of dynamic response was obtained. Through modal testing, the results indicated that the simulation results had high accuracy and reliability. [ABSTRACT FROM AUTHOR]

A simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δf, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δf and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δf and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment. [ABSTRACT FROM AUTHOR]

The inherent membrane tension of biological materials could vitally affect their responses to contact loading but is generally ignored in existing indentation analysis. In this paper, the authors theoretically investigate the contact stiffness of axisymmetric indentations of elastic solids covered with thin tensed membranes. When the indentation size decreases to the same order as the ratio of membrane tension to elastic modulus, the contact stiffness accounting for the effect of membrane tension becomes much higher than the prediction of conventional contact theory. An explicit expression is derived for the contact stiffness, which is universal for axisymmetric indentations using indenters of arbitrary convex profiles. On this basis, a simple method of analysis is proposed to estimate the membrane tension and elastic modulus of biological materials from the indentation load-depth data, which is successfully applied to analyze the indentation experiments of cells and lungs. This study might be helpful for the comprehensive assessment of the mechanical properties of soft biological systems. This paper highlights the crucial effect of the inherent membrane tension on the indentation response of soft biomaterials, which has been generally ignored in existing analysis of experiments. For typical indentation tests on cells and organs, the contact stiffness can be twice or higher than the prediction of conventional contact model. A universal expression of the contact stiffness accounting for the membrane tension effect is derived. On this basis, a simple method of analysis is proposed to abstract the membrane tension of biomaterials from the experimentally recorded indentation load-depth data. With this method, the elasticity of soft biomaterials can be characterized more comprehensively. [Display omitted] [ABSTRACT FROM AUTHOR]

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The dynamic stability of machining processes is influenced by the dynamic stability of the workpiece and fixture assembly. This effect has not yet been sufficiently considered. Achieving dynamic stability by simply applying a large amount of clamping force is a basic method and involves damages such as elastic deformation of relatively thin workpieces, damage to the clamping surfaces, and high wear of fixture components resulting in malfunction. In spite of this, to the best knowledge of the present authors, the contact stiffness between workpiece and fixture as an influencing parameter has not been sufficiently paid attention by researchers and these parameters have not been taken into account in the equations of dynamic stability. The contact stiffness itself is influenced by the machining parameters. In the present study, the changes in contact stiffness in different machining conditions are investigated as a partial undertaking to fill the gap existing in the modeling of the machining dynamics. In this paper, by defining the mathematical model of the workpiece-fixture system and calculating the matrices of contact stiffness and fixture stiffness, the results of changes in various machining parameters in the stiffness of the workpiece-fixture system have been investigated. The results showed that high contact stiffness cannot be provided simply by applying the maximum force of the clamps. Rather, by increasing the spindle speed, the contact stiffness will increase significantly. Furthermore, by increasing the spindle speed, further increase in the contact stiffness will be achieved with lower feed rates, which will not be economically viable. [ABSTRACT FROM AUTHOR]

In the existing finite element models of ultrasonic shot peening, most of them ignore the influence of elastic and plastic deformation of the projectile on the numerical simulation results. There are few reports on the influence of the friction coefficient between the surface of the projectile and the surface of the sprayed material on the numerical prediction results of ultrasonic shot peening. Therefore, taking pure copper as the research object, the influence of friction coefficient and projectile deformation on pure copper by ultrasonic shot peening was studied by combining the ultrasonic shot peening experiment and numerical simulation process. Firstly, a three-dimensional finite element model of single ultrasonic shot peening was established based on ABAQUS platform. Then, the single ultrasonic shot peening experiment was designed, and the influence of shot peening distance on velocity was analyzed according to the experimental conditions. The experimental conditions were input into the simulation model, and the experimental and simulation results were compared from the aspects of shot velocity and indentation morphology. Finally, under the condition of friction coefficient of 0.1,0.2,0.3,0.4 and 0.5, the ultrasonic shot peening numerical simulation of pure copper specimens was carried out by respectively using rigid shot, elastic shot and elastic-plastic shot. The surface morphology and residual stress of the treated surface were analyzed. The obtained results show that when the friction coefficient between the shot and the pure copper is larger than 0.2, the influence of the friction coefficient on the morphology of indentations and residual stress formed by ultrasonic peening of pure copper is no longer significant. With the increase of the contact stiffness between the shot and the pure copper, the indentation size, the depth of the compressive residual stress field, the maximum compressive residual stress and the surface tensile residual stress induced by ultrasonic shot peening of pure copper increase accordingly. The research results have important guiding significance for the numerical modeling of ultrasonic shot peening. [ABSTRACT FROM AUTHOR]

A new approach in the calibration process of DEM samples of structured sand is presented. Micromechanical‐based experimental data are interpreted to develop a failure model and a range of input parameters in the DEM analyses are incorporated considering strong and a weak bonds in the simulated samples. Subsequently, the numerical samples correspond to analog mature structured soil/sandstone in terms of both compositional and textural maturity, and the study focused on the small‐to‐medium strain shear modulus and on providing multi‐scale insights of the simulated materials. The heterogeneity of the structured sand is incorporated based on Gaussian and Weibull distributions of the contact properties and four major parameters are examined including bonding amount/content, bonding strength, heterogeneity, and confining pressure. The numerical results showed, at the macroscopic level, agreement with respect to a number of element‐size experiments on sandstones which were re‐analyzed in the present work, in terms of stiffness—pressure relationship, stiffness reduction, and occurrence of the yield point associated with the initiation of bond breakage. It was shown that even though the bond strength and amount of bonds are important influencing factors on the macroscopic behavior of the structured sand, the incorporation of heterogeneity can significantly alter the interpretations of the microscopic involved mechanisms. This unveils that the implementation of "average" input parameters cannot capture well the contributing mechanisms which influence the deformation characteristics of structured soils and sandstones. [ABSTRACT FROM AUTHOR]

The stability of workpiece inside fixture influences the dynamics of machining. Although, the workpiece is uniquely and deterministically positioned and grasped by the fixture, it undergoes small displacements due to the contact compliance resulting from the frictional slip under the external loads and vibrations. The frictional slip of workpiece, along or around the main axes relative to the fixture components is a major cause of instability and the main element influencing the contact stiffness between the workpiece and the fixture. In the present study, a procedure has been developed to evaluate the contact stiffness by employing mathematical and experimental tools. The grasp matrices defined in analytical model were obtained by a combination of calibration and measurement of forces, displacements, and friction coefficient. The contact stiffness was also determined by modal analysis of the assembly of workpiece and fixture and the results were compared. It was evidenced that the dry friction existing in the contact areas between the workpiece and fixture elements could lead to the stick-slip instability, detrimental to the dynamics of machining. The main contribution and novelty of the present study can be outlined, as follows. The contact stiffness between workpiece and fixture was modeled and measured. The frictional slip was modeled and measured in addition to the physical compliances. Dry friction between workpiece and fixture was detected as a source of stick-slip. Procedures were developed to calibrate and measure all forces and displacements. Modal analysis was done as a complementary tool to verify the results. [ABSTRACT FROM AUTHOR]

Mechanical joint interfaces are widely found in mechanical equipment, and their contact stiffness directly affects the overall performance of the mechanical system. Based on the fractal and elastoplastic contact mechanics theories, the K-E elastoplastic contact model is introduced to establish the contact stiffness model for mechanical joint interfaces. This model considers the interaction effects between micro-asperities in the fully deformed state, including elasticity, first elastoplasticity, second elastoplasticity, and complete plastic deformation state. Based on this model, the effects of fractal parameters on normal contact stiffness and contact load are analyzed. It can be found that the larger fractal dimension D or smaller characteristic scale coefficient G will weaken the interaction between micro-asperities. The smoother processing surfaces lead to higher contact stiffness in mechanical joint interfaces. The applicability and effectiveness of the proposed model are verified by comparing it with the traditional contact model calculation results. Under the same load, the interaction between micro-rough surfaces leads to an increase in both overall deformation and contact stiffness. The accuracy of the predicted contact stiffness model is also validated by comparing it with experimental results.

The impact of contact between two elastic–plastic bodies is highly complex, with no established theoretical contact model currently available. This study investigates the problem of an elastic–plastic sphere impacting an elastic–plastic half-space at low speed and low energy using the finite element method (FEM). Existing linear contact loading laws exhibit significant discrepancies as they fail to consider the impact of elasticity and yield strength on the elastic–plastic sphere. To address this limitation, a novel linear contact loading law is proposed in this research, which utilizes the concept of equivalent contact stiffness rather than the conventional linear contact stiffness. The theoretical expressions of this new linear contact loading law are derived through FEM simulations of 150 sphere and half-space impact cases. The segmental linear characteristics of the equivalent contact stiffness are identified and fitted to establish the segmental expressions of the equivalent contact stiffness. The new linear contact loading law is dependent on various factors, including the yield strain of the half-space, the ratio of elastic moduli between the half-space and sphere, and the ratio of yield strengths between the half-space and sphere. The accuracy of the proposed linear contact loading law is validated through extensive Finite Element Method simulations, which involve an elastic–plastic half-space being struck by elastic–plastic spheres with varying impact energies, sizes, and material combinations.

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.

Soft fingertips have distinct intrinsic features that allow robotic hands to offer adjustable and manageable stiffness for grasping. The stability of the grasp is determined by the contact stiffness between the soft fingertip and the object. Within this work, we proposed a line vector representation method based on the Winkler Model and investigated the contact stiffness between soft fingertips and objects to achieve control over the gripping force and fingertip displacement of the gripper without the need for sensors integrated in the fingertip. First, we derived the stiffness matrix of the soft fingertip, analyzed the contact stiffness, and constructed the global stiffness matrix; then, we established the grasp stiffness matrix based on the contact stiffness model, allowing for the analysis and evaluation of the soft fingertip's manipulating process. Finally, our experiment demonstrated that the variation in object orientation caused by external forces can indicate the contact force status between the fingertip and the object. This contact force status is determined by the contact stiffness. The position error between the theoretical work and tested data was less than 9%, and the angle error was less than 5.58%. The comparison between the theoretical contact stiffness and the experimental results at the interface indicate that the present model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experiment data. [ABSTRACT FROM AUTHOR]

It is well known that the elastoplastic properties of materials are important indicators to characterize their mechanical behaviors and are of guiding significance in the field of materials science and engineering. In recent years, the rapidly developing nanoindentation technique has been widely used to evaluate various intrinsic information regarding the elastoplastic properties and hardness of various materials such as metals, ceramics, and composites due to its high resolution, versatility, and applicability. However, the nanoindentation process of indenting materials on the nanoscale provides the measurement results, such as load-displacement curves and contact stiffness, which is challenging to analyze and interpret, especially if contained in a large amount of data. Many numerical methods, such as dimensionless analysis, machine learning, and the finite element model, have been recently proposed with the indentation techniques to further reveal the mechanical behavior of materials during nanoindentation and provide important information for material design, property optimization, and engineering applications. In addition, with the continuous development of science and technology, automation and high-throughput processing of nanoindentation experiments have become a future trend, further improving testing efficiency and data accuracy. This paper critically reviewed various numerical methods for evaluating elastoplastic constitutive properties of materials based on nanoindentation technology, which aims to provide a comprehensive understanding of the application and development trend of the nanoindentation technique and to provide guidance and reference for further research and applications. [ABSTRACT FROM AUTHOR]

Background: The contact force–deformation relation between two spheres is one fundamental property which determines the mechanical response of the colliding bodies. In general, collisions of solid spheres occur in a very short time, so a highly accurate and a non-contact measurement method is required. Objective: In this study, a concept for the experimental determination of contact force–deformation curves of two colliding spheres is presented. Thereby two identical steel spheres collide by using a pendular setup and the sphere's velocities are measured by Laser Doppler Vibrometers (LDVs). Methods: The displacements are obtained by integrating the velocity with time and the accelerations are obtained by differentiating the velocity with time. From these values, the deformation and the contact forces can be calculated. Then, the elastic results are compared with the Hertzian theory of impact and experiments are conducted with elasto-plastic spheres. Results: Although the deformations are in good agreement with these analytical values, the influence of numerical differentiation is observed in the contact force. However, it is shown that the elastic contact force–deformation curve of two colliding spheres can be obtained with reasonable accuracy by using LDVs. For elasto-plastic spheres the coefficient of restitution became smaller than for the purely elastic case, and the force–deformation curve with hysteresis are measured. Conclusions: The results of this study are considered to be reasonable as far as comparisons with those for elastic collisions. Therefore, more detailed verification by numerical analysis, such as finite element analysis, is desirable. [ABSTRACT FROM AUTHOR]

The macroscopic relative motion solid-liquid interface widely exists in the contact motion pairs of machine tools and other mechanical equipment. In order to accurately obtain the tangential contact stiffness and damping parameters, the Savkoor asperity adhesion-sliding friction contact model is used to analyze the contact area and the corresponding tangential force changes of a single pair of solid contact asperity in the four typical phases of contact growth, contact stagnation, crack adhesion and crack propagation. According to the hypothesis of Gaussian distribution of asperity on rough surface, the contact model of single-pair asperities is extended to the whole joint. The tangential contact stiffness and damping models of solid-solid interface in macroscopic relative motion are obtained. For the fluid contact part, the oil film pressure distribution and film thickness are obtained by solving part of the film Reynold’s equation, and then the fluid tangential stiffness and damping model is established. The tangential contact stiffness and damping of the whole solid-liquid interface are obtained by analyzing the stiffness and damping of solid and fluid parts, and the effects of normal load and moving velocity on tangential contact stiffness and damping are obtained by simulation. The results show that the tangential contact stiffness and damping of solid-liquid interface increase with the increase of normal contact load and decrease with the increase of moving velocity.

In the process of plunge cylindrical grinding, it is difficult to directly measure the contact stiffness between the grinding wheel and the workpiece. In order to solve this problem, a simplified method for qualitatively determining the contact stiffness between the grinding wheel and the workpiece is proposed, and the grinding parameters are optimized. Based on the dynamic model of plunge cylindrical grinding process, the transfer function of grinding process is deduced, and the mathematical model of the time constant and contact stiffness is established. A simplified method for qualitative determination of grinding contact stiffness is proposed. Further, multiple tests are conducted by controlling the wheel feed speed and the workpiece speed. According to the experimental results, the variation of the system time constant and the grinding force with the grinding parameters are analyzed. The relationship model between the contact stiffness and the grinding parameters is established by regression analysis, and the optimal values of the wheel feed speed and the workpiece speed in the specific grinding process are determined under the condition of meeting the machining requirements.

Abstract An industrial robot with a six-axis force/torque sensor is usually used to produce a zero-gravity environment for testing space robotic operations. However, using traditional force control methods, such as admittance control, causes position-controlled industrial robots to undergo from force divergence owing to intrinsic time delay. In this paper, a new force control method is proposed to eliminate the force divergence. A hardware-in-the-loop (HIL) simulator with an industrial robot is first presented. The free-floating satellite dynamics and the motion mapping from the satellites to simulator are both established. Thus, the effects of measurement delay and dynamic response delay on contact velocity and force are investigated. After that, a real-time estimation method for contact stiffness and damping is proposed based on the adaptive Kalman filter. The measurement delay is compensated by a phase lead model. Moreover, the identified contact parameters are adopted to modify contact forces, and thus the dynamics response delay can be compensated for. Finally, a co-simulation and experiments were conducted to verify the force control method. The results show that contact stiffness and damping could be identified exactly and that the simulation divergence could be prevented. This paper proposes an active compliance control method that can deal with force constrained tasks of a position-controlled robot in unknown environments.

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Presliding contacts play an important role in stiffness, damping, and thus dynamic response of assembled structures. Load-dependent nonlinearities in presliding contacts still hinder predictive modeling. Classical models apply only to smooth elastic contacts and a small subset of materials. Recently, the authors tested high density polyethylene (HDPE) inside a scanning electron microscope (SEM) and observed that nonlinearity trends in tangential stiffness and damping deviate from the predictions of the classical models. This discrepancy was attributed to HDPE's nonlinear viscoplastic response. The aim of this study is to model aforementioned experiments numerically and investigate the influence of nonlinear material response on the presliding response of spherical contacts. A finite element model of a rigid spherical indenter pressed and sheared on a nonlinear viscoplastic half-space is constructed. The indenter geometry and boundary conditions are set in accordance with the experiments, and the constitutive model is tuned to the measured indentation responses. The tuned model delivers a shear response in agreement with the experiments. Accumulated plastic deformations are also found to correlate well with the wear profiles. The model further reveals that nonlinear viscoplasticity dominates tangential stiffness and dissipation at high normal preloads. Our results confirm further that nonlinear material response contributes significantly to the load-dependent nonlinearities in viscoplastic presliding contacts. [ABSTRACT FROM AUTHOR]

Double-row tapered roller bearings have been widely used in various equipment recently due to their compact structure and ability to withstand large loads. The dynamic stiffness is composed of contact stiffness, oil film stiffness and support stiffness, and the contact stiffness has the most significant influence on the dynamic performance of the bearing. There are few studies on the contact stiffness of double-row tapered roller bearings. Firstly, the contact mechanics calculation model of double-row tapered roller bearing under composite loads has been established. On this basis, the influence of load distribution of double-row tapered roller bearing is analyzed, and the calculation model of contact stiffness of double-row tapered roller bearing is obtained according to the relationship between overall stiffness and local stiffness of bearing. Based on the established stiffness model, the influence of different working conditions on the contact stiffness of the bearing is simulated and analyzed, and the effects of radial load, axial load, bending moment load, speed, preload, and deflection angle on the contact stiffness of double row tapered roller bearings have been revealed. Finally, by comparing the results with Adams simulation results, the error is within 8%, which verifies the validity and accuracy of the proposed model and method. The research content of this paper provides theoretical support for the design of double-row tapered roller bearings and the identification of bearing performance parameters under complex loads. [ABSTRACT FROM AUTHOR]

Rockfill is a common irregular granular material used in most dam construction projects. The purpose of this paper is to investigate the distribution and size-dependent properties of the mechanical parameters describing the elastic properties and crushing strength of rockfill particles. These statistics can be used as a reference to calibrate the input parameters of numerical models when studying the macroscopic behavior of rockfill with particle breakage using the discrete element method. A series of limestone particles ranging in diameter from 20 to 240 mm were measured in this study using a single particle compression test. The elastic modulus, elastic contact stiffness, tensile stress and fracture force were then determined by characterizing each experimental force–displacement curve. Classical statistical methods were used. It has been shown that Weibull, lognormal and logistic functions can all represent the distributional features of the elastic modulus, tensile stress and fracture force, with the lognormal function being the optimal type here. As the grain size increases, the elastic modulus and tensile stress decrease, while the fracture force rises. Empirical models of power functions effectively reproduced these size-dependent laws. Meanwhile, the relationship between these parameters was also established. Finally, the lognormal function was adopted to express the randomness of the maximum elastic contact stiffness. Some suggestions were made after discussing the positive association between the maximum elastic contact stiffness and grain size. Moreover, the evaluation of the loading strain rates of individual particles tested shows that the present conclusions are applicable to quasi-static case. [ABSTRACT FROM AUTHOR]