Search

When cutting flexible metal workpieces, the mechanical characteristics of the fixture play a crucial role in suppressing deformation and vibration. Previously, the influence of fixture design elements on workpiece vibration has been studied with the aim of gaining a fundamental understanding of the phenomenon. Meanwhile, there has been limited research on the contact area between the fixture and workpiece, and there is a need for further research to understand the phenomenon and establish design guidelines for fixtures. In this paper, an experimental approach is proposed to characterize the relationship between stress on the contact surface and the resulting displacement. The main goal is to analyze the influence of contact surface shape and material on the deformation (or vibration) of the fixture and the workpiece. To this end, an on-machine measurement device was introduced. This device was used to obtain displacement-load curves without setup errors for materials such as PTFE, MC nylon, and aluminum alloy, as well as contact surface shapes such as flat or conical. From the obtained curves, the repeatability stability of the fixture was qualitatively evaluated. When using MC nylon, the plastic deformation was minimal even when loads were applied multiple times under flat conditions or conical conditions with a tip angle of 170° or more. This indicates that these contact conditions are stable as fixtures. On the other hand, when using PTFE, buckling occurred due to its low Young's modulus, and the workpiece was damaged when using aluminum alloy. This suggests that these materials are not suitable for use as fixtures in this paper. For a more quantitative evaluation, an assessment based on contact stiffness was conducted. The displacement-load curves were modeled using a power-law function, following existing elastoplastic models. The contact stiffness was calculated from the slope of the tangent line to the displacement-load curve at maximum load. When using MC nylon as the material, the contact stiffness was found to be a maximum of 6×106 N/m. Furthermore, the rate of change of contact stiffness during loading and unloading was used to quantitatively evaluate the fixture stability. [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]

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.

• 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]

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]

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]

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.

In order to study the contact stiffness of the bonding surface in more detail from the perspective of fractal theory, on the basis of the M-B fractal model and the Hertz theory, a domain expansion factor is introduced to represent the fractal dimension to establish the normal and tangential contact stiffness fractal models of the bonding surface, respectively. The model comprehensively considers the effects of load, fractal dimension and material parameters on the contact stiffness. At the same time, the change trend of the contact stiffness of the joint surface and each parameter is obtained through numerical simulation.The change trend of normal contact stiffness and normal load is the same, which is opposite to the fractal characteristics and length scale coefficient, but the change trend of the fractal dimension is more complicated, no longer monotonic. The changetrend caused by tangential contact stiffness and the above parameters is similar to that caused by normal contact stiffness.

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]

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]

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

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.

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]

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.

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]

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]

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

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.

Evaluation of bolt tightening plays an important role to keep a performance of a mechanical structure. Lack of the fastening force induces slack and falling of the tightening bolt. Excessive fastening force induces a plastic deformation of screw thread and causes the decline of the fastening force. Therefore, guarantee of the bolt tightening is an important subject in order to secure the mechanical structure against unforeseen accidents. However, most of preceding studies are restricted within qualitative evaluation of the slackness. In the field of industrial manufacturing, quantitative evaluation of the bolt tightening is strongly required. In this paper, the authors propose a technique for quantitative evaluation of bolt tightening, and in this technique, the flank of the screw thread is assumed to contact through a contact stiffness. The transmissivity and reflectivity of an ultrasonic pulse wave through the flank are derived as a function of contact stiffness, and the contact stiffness is capable of being identified from experimentally acquired amplitude of ultrasonic pulse wave. The contact stiffness is quantitatively identified and the surface pressure on the screw thread is estimated by the identified contact stiffness through the results of the preceding study. The proposed technique treats an ultrasonic pulse perpendicularly transmits a fastening bolt, and is applied to an experimentally acquired ultrasonic pulse which enters a side surface of nut and transmits a bolt-nut fastening element. The identified contact stiffness is shown to be adequate for the given fastening force to the bolt-nut fastening element, and validity of the proposed technique is demonstrated.

As a critical element of time-varying mesh stiffness (TVMS), contact stiffness of a gear drive has been defined based on simplified Hertzian contact stiffness or semi-empirical nonlinear Hertzian contact stiffness in previous works. This study proposes a general contact stiffness model for elastic bodies through piecewise linear interpolation of contact pressure. The TVMS of a spur gear drive is determined through potential energy method and proposed contact stiffness model verified by Hertzian contact theory and finite-element method. Then, the influence of applied load on contact stiffness is studied, and the differences among proposed contact stiffness, simplified Hertzian contact stiffness, and nonlinear Hertzian contact stiffness are analyzed. Results show that contact stiffness increases with the applied load, and the TVMS based on the proposed contact stiffness model is the smallest among the three contact stiffness models. Effects of tooth width and input torque on the TVMS are further discussed. The TVMS becomes bigger with increased tooth width and input torque, but the increase rate decreases as tooth width or input torque increases. These findings indicate that reasonable matching of design parameters is beneficial for increasing load capacity and optimizing the dynamic performance of gear systems. [ABSTRACT FROM AUTHOR]

We consider analytical, numerical, and experimental approaches developed to describe the mechanical contact between a rigid indenter and an elastic half-space coated with an elastic layer. Numerical simulations of the indentation process were performed using the recently generalized boundary element method (BEM). Analytical approximation of the dependence of contact stiffness on the indenter diameter was used to verify the results of BEM simulations. Adhesive contacts of hard indenters of different shapes with soft rubber layers have been experimentally studied using specially designed laboratory equipment. The comparison of the results from all three implemented methods shows good agreement of the obtained data, thus supporting the generalized BEM simulation technique developed for the JKR limit of very small range of action of adhesive forces. It was shown that the half-space approximation is asymptotical at high ratios of layer thickness h to cylindrical indenter diameter D; however, it is very slowly. Thus, at the ratio h/D = 3.22, the half-space approximation leads to 20% lower contact stiffness compared with that obtained for finite thickness using both an experiment and simulation. [ABSTRACT FROM AUTHOR]

The vibration from the road inevitably causes the microscopic dynamic contact of the contact interface inside the proton exchange membrane fuel cell (PEMFC), and the dynamic characteristics of the contact interface have an obvious influence on the dynamic behavior of the whole stack. In this paper, the normal and tangential contact between bipolar plate (BP) and membrane electrode assembly (MEA) is investigated by fractal theory, and the variation of contact stiffness with fractal dimension, characteristic length and loading force is studied comprehensively. Then, through the virtual material method, a dynamic model of the fuel cell stack reflecting the contact characteristics is established. It is found that the natural frequencies of the stacks considering the contact stiffness are lower than those not considering it. The larger the contact stiffness corresponding to the fractal dimension and characteristic length, the higher the natural frequency of the stack, and the effect of fractal parameters on the surface roughness is explored. Increasing the total clamping force can increase the stack global modal frequency, but it will decrease the cell local modal frequency. [Display omitted] • Fractal theory is first used to study the contact stiffness between BP and GDL. • The effect of BP and GDL surface fractal parameters on surface roughness is studied. • A more accurate dynamic model of PEMFC based on virtual materials is established. • Effect of contact properties on the dynamic performance of PEMFC is investigated. [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.

Modal analysis carried out within the Finite-Element-Analysis leads to natural frequencies and mode shapes. Using adjacent solids in linear dynamics generates a computational contact problem with several configuration parameters. Contact stiffness is of importance as it affects the accuracy and convergence behaviour of the results. Thus, an overlarge value leads to a locking phenomenon and causes ill-conditioned system matrices. This paper investigates whether recommendations for appropriate contact stiffnesses in static mechanics are also applicable to modal analysis. In fact, it can be observed that a significantly smaller contact stiffness than stated in the literature is also well suited for modal analysis. Furthermore, choosing the optimum range for the numerical contact stiffness for modal analysis depends on the order of the natural frequency and the corresponding vibration mode. The results of the simulations are validated against experimental modal analysis of a sample with identical elastic properties. The verified contact settings in the present paper permit a more realistic consideration of contact constraints in modal analysis. [ABSTRACT FROM AUTHOR]

Understanding and modeling the contact behavior of particles provides enhanced constitutive laws in discrete-based simulations as well as a strong linkage between micro- and macroscopic behavior of granular materials. In the present study, we studied the influence of a polymer-based additive composed of Methocel cellulose ether on the tribological response of rough particles with grain-scale experiments. We performed both monotonic and cyclic tests on pairs of particles subjected to repeated shearing so that to explore the additional influence of abrasion in relation to previous loading history. Each sample was tested at first in a dry state and consecutively was immersed into the polymer-based fluid. The test results indicated increased friction at the contacts of the particles when immersed in the polymer-based additive, suggesting promising applications of the Methocel cellulose ether in improving the stability of geo-systems. For the shearing tests in a dry state, abrasion influences were amplified at higher magnitudes of normal load, whereas the polymer additive acted as a fluid film (or thin coating) mitigating in this way the continuous abrasion due to repeated shearing. We incorporated the Mindlin and Deresiewicz (M–D) contact model in a modified form to analyze the tangential response of the particles. It was found that the power of the modified M–D model was directly correlated with the natural logarithm of the microslip displacement threshold, when this threshold was normalized with respect to the normal load. Based on the analysis of the closed loops from the cyclic tests, the energy dissipation was found to be reduced when the samples were immersed in the polymer fluid compared with the tests in a dry state. The test results from the present work offer some insights into the micromechanical-based analysis of particulate materials and the interactions of rough particles in the presence of polymeric fluids with potential applications in contact mechanics modeling using discrete-based tools. These results also contribute to unveiling the prevailing micromechanisms in order to understand (or interpret) bulk behavior, thus the database from the present work may provide helpful guidance in understanding granular material behavior and the interactions between particles with polymer-based additives. [ABSTRACT FROM AUTHOR]

In situ changes in the nanofriction and microstructures of ionic liquids (ILs) on uncharged and charged surfaces have been investigated using colloid probe atomic force microscopy (AFM) and molecular dynamic (MD) simulations. Two representative ILs, [BMIM][BF4] (BB) and [BMIM][PF6] (BP), containing a common cation, were selected for this study. The torsional resonance frequency was captured simultaneously when the nanoscale friction force was measured at a specified normal load; and it was regarded as a measure of the contact stiffness, reflecting in situ changes in the IL microstructures. A higher nanoscale friction force was observed on uncharged mica and highly oriented pyrolytic graphite (HOPG) surfaces when the normal load increased; additionally, a higher torsional resonance frequency was detected, revealing a higher contact stiffness and a more ordered IL layer. The nanofriction of ILs increased at charged HOPG surfaces as the bias voltage varied from 0 to 8 V or from 0 to —8 V. The simultaneously recorded torsional resonance frequency in the ILs increased with the positive or negative bias voltage, implying a stiffer IL layer and possibly more ordered ILs under these conditions. MD simulation reveals that the [BMIM]+ imidazolium ring lies parallel to the uncharged surfaces preferentially, resulting in a compact and ordered IL layer. This parallel "sleeping" structure is more pronounced with the surface charging of either sign, indicating more ordered ILs, thereby substantiating the AFM-detected stiffer IL layering on the charged surfaces. Our in situ observations of the changes in nanofriction and microstructures near the uncharged and charged surfaces may facilitate the development of IL-based applications, such as lubrication and electrochemical energy storage devices, including supercapacitors and batteries. [ABSTRACT FROM AUTHOR]

Contact operations of free-floating satellite robots are difficult and risky and therefore, they must be thoroughly tested and verified by ground-based facilities. A hardware-in-the-loop (HIL) simulation system with industrial robots is commonly used for simulating space robotic operations. However, a great challenge is to handle simulation divergence due to intrinsic time delay between the measured forces and the simulation driven reaction of the robot. This paper presents a novel hybrid force/velocity control method for compensating the time delay of a HIL simulation. A real-time identification method for contact stiffness and damping is proposed based on the adaptive Kalman filter. Then, an energy observer is designed to monitor the energy flow and an energy controller (EC) is established. The EC acts a variable damping and thus the contact damping is amended. Therefore, a compensation strategy based on parameter identification and damping amendment is proposed to eliminate the effects of time delays. Finally, numerical simulations and experimental results show that the simulation divergence due to time delay can be prevented. Moreover, space robotic operations with high fidelity of both contact force and contact velocity are reproduced by the proposed method.

In order to establish the tangential contact stiffness and damping model of the solid–liquid interface by tangential exciting vibration force under mixed lubrication, the finite difference method was firstly used to solve the average flow equation considering the effect of roughness on the lubrication effect, and the bearing capacity, shear force, and friction coefficient of the oil film were obtained, and thereby the dynamic tangential contact stiffness and damping of the oil film under tangential harmonic excitation were calculated. Then, according to the relationship between the normal deformation and the load of the solid contact microconvex body in the elastic/elastic–plastic/plastic deformation stage, integrating the tangential stick–slip theory, considering the effect of fluid lubrication on the solid contact friction coefficient, and tangential dynamic excitation, the tangential contact stiffness and damping of the microconvex body in three deformation stages were calculated. Furthermore, the dynamic tangential contact stiffness and damping of the solid–liquid interface were obtained by summing the solid surface contact part and the solid–liquid contact part in parallel according to the assumption of microconvex Gaussian distribution. Finally, through simulation analysis and experiments, the variation of the tangential dynamic contact stiffness and damping of the solid–liquid interface with normal load, tangential exciting frequency, and displacement amplitude was revealed and verified. [ABSTRACT FROM AUTHOR]

A dynamics model of high-speed angular contact ball bearings under the lubrication condition is established， in the calculation of contact deformation and contact stiffness between ball bearing and inner/outer ring， the influence of lubricating oil entrainment and squeeze during high-speed rotation is considered. Through the coupling iteration of contact angle and contact stiffness， the calculation method of axial and radial stiffness of high-speed angular contact ball bearings considering lubrication effect is obtained. The results show that after considering the lubrication effect， the contact angle between the ball and the inner/outer ring decreases， and the axial/radial stiffness of the bearing increases. The increase in the axial load increases the axial/radial stiffness， and the lower the axial load， the more obvious the effect of lubricating oil. The increase in the radial load makes the axial stiffness increase and the radial stiffness decrease. As the number of rollers increases，the axial/radial stiffness increases，and the effect of lubricating oil is more obvious; Compared with 4019 lubricant， 4106 lubricant increases bearing axial/radial stiffness. The axial/radial stiffness of ceramic ball bearings is greater than steel ball bearings， and has an approximately linear relationship with the speed.

In order to explore the dynamic characteristics of the circumferential rod fastening rotor-bearing system, a numerical model of three-dimensional Gaussian random rough surface was established by using the method of autocorrelation function. Moreover, the geometric model of rough surface was generated by Ansys APDL. Abaqus software was used to simulate the contact of rough surface, and the contact stiffness of rough surface under different preloads was obtained. The finite element model of the circumferential rod fastening rotor-bearing system of a certain type of gas turbine considering the contact stiffness was also established. The dynamic characteristics of the system with different preloads and clearances of bearing assembly were calculated. It is shown that critical speed of rotor-bearing system increases nonlinearly with the increase of preload, and the amplitude of unbalance response increases with the increase of preload and clearance of bearing assembly as the rotor has passed the critical speed.

Mecanum wheels (MWs) are valuable components to automated guided vehicles (AGVs) and autonomous mobile robots (AMRs) for their versatile motion capabilities. Such characteristics are associated with the series of rubber-covered rollers obliquely attached around the circumference of the wheel rim. The rollers take turns in contact with the ground while MW is rotating. Even though MWs were designed and appear perfectly circular, vehicles equipped with MWs often exhibit periodic bouncing motion. Such a phenomenon hinders the application of MW in factories, such as panel manufacturing. This article sought the cause of the non-uniform contact stiffness associated with MWs and attempted to improve its design to mitigate the vibration problem. A hard-kill topology optimization scheme was proposed where interfacial elements between the steel core and the rubber layer can switch the material property to steer the contact stiffness toward the desired value. Nonlinear finite element analyses on the detailed 3D geometry of the roller system involving neo-Hookean material and contact simulation were performed for accurate numerical estimation in the optimization process. Due to elastic deformation, dual contacts occur at the transition of adjacent rollers; as a result, the total contact stiffness increases significantly compared to the other regions. The proposed optimization scheme successfully reached a design of uniform contact stiffness for the entire circumference of MW, including transition zones between adjacent rollers. Prototypes of the optimized MW were fabricated. Experiments on the vibration of an AGV with the old and the new MWs were conducted. The new MWs effectively reduced vibration amplitudes by approximately 30%. [ABSTRACT FROM AUTHOR]

Particle dampers' dissipative characteristics can be difficult to predict because of their highly non-linear behavior. The application of such devices in deformable vibrating systems can require extensive experimental and numerical analyses; therefore, improving the efficiency when simulating particle dampers would help in this regard. Two techniques often proposed to speed up the simulation, namely the adoption of a simplified frictional moment and the reduction of the contact stiffness, are considered; their effect on the simulation run-time, on the ability of the particle bed to sustain shear deformation, and on the prediction of the dissipation performance is investigated for different numerical case studies. The reduction in contact stiffness is studied in relation to the maximum overlap between particles, as well as the contacts' duration. These numerical simulations are carried out over a wide range of motion regimes, frequencies, and amplitude levels. Experimental results are considered as well. All the simulations are performed using a GPU-based discrete element simulation tool coupled with the multi-body code MBDyn; the results and execution time are compared with those of other solvers. [ABSTRACT FROM AUTHOR]

The spindle and grinding wheel flange (GWF) adopt double positioning of a tapered surface and end face. Due to the processing quality, the contact state of the spindle–GWF interface cannot be determined accurately. Based on the theory of finite element and the Yoshimura integral method, an analysis method for the contact stiffness of the spindle–GWF interface was established. In addition, the effects of the spindle–GWF interface's original clearance and tightening torque on the contact pressure, final contact state and contact stiffness of the spindle–GWF interface were investigated and experimentally verified. It was found that the final contact state of the spindle–GWF changed when the tightening torque increased, especially when the original contact state was tapered contact, and the final contact state changed significantly after assembly. The contact pressure and contact stiffness of the spindle–GWF interface are increased by increasing the tightening torque. The radial stiffness is more affected by the end clearance variation compared to the axial and angular stiffness. When the original contact state is tapered contact, the radial stiffness of the interface is at maximum in three contact states. This research provides theoretical guidance for GWF assembly on gear-grinding machines. [ABSTRACT FROM AUTHOR]

The article deals with the solution of the problem of improving the quality of torque transmission connections of spindle units of multi-purpose machines. The aim of the work is to determine the contact stiffness of the spindle-mandrel joints of various types, based on the conducted simulation experiments of the assembly and disassembly process of auxiliary tools of various structural forms, in conditions of reusable replacements. A comparative analysis of the mathematical expectations of contact stiffness of traditional and non-traditional conical profile split joints based on an equiaxial contour with a number of faces equal to three under external loading conditions is performed. The results obtained allow us to predict the quality indicators of multi-purpose machines in the design of quick-release connections.

In order to calculate the contact stiffness of cycloid-pin gear more accurately and guide its practical application， a method for calculating the contact stiffness of cycloid-pin gear based on Monte Carlo was proposed. In this method， the tooth profile functions of cycloid gear before and after the cycloid gear profile modification are established， and the influence of gear profile modification on the contact stiffness of cycloid gear is investigated. Taking RV-40E reducer of industrial robot as an example， the calculation example shows that the contact stiffness of cycloid gear will be changed if the gear tooth profile is modified for cycloid gear， and the contact stiffness of the cycloid-pin gear wheel will first decrease， then increase and then decrease with the increase of the amount of modification.

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

• A new stiffness coefficient with roughness is proposed. • A new hysteresis damping factor is derived. • A new contact force model is formulated. • The effectiveness of the new contact model is verified by the experimental data. This investigation aims to validate the effect of the rough contact surface on the dynamic responses of the multibody system based on the fractal theory. Firstly, a two-dimensional rough surface is described using the Weierstrass-Mandelbrot (W-M) function based on the fractal theory. The contact properties of a single asperity are estimated based on the Morag and Etsion (ME) model and Hertz law. The novel contact stiffness with roughness is derived from the size distribution function of the Majumdar and Bhushan (M-B) model. Secondly, a new hysteresis damping factor is derived to represent the energy dissipation during contact. Subsequently, a more general contact force model is proposed based on a nonlinear spring-damper vibration system, in which the novel contact stiffness is associated with the new hysteresis damping factor. The simulation results show that the newly introduced contact force model is a more generalized contact model and the existing contact force models are a special case under the condition of an ideal contact surface. Finally, the new contact force model is utilized to predict the dynamic responses of the one-dimension granular chain and the slider-crank mechanism with a clearance joint, which is validated by the experimental data. [ABSTRACT FROM AUTHOR]