Study on the force chain characteristics with coal dust layer and the three-body contact stiffness

To explore the influence of the meso-mechanical behaviors of the wet coal dust layers on the contact stiffness of mechanical bonding surfaces,a three-body contact model incorporating an interface with wet coal dust was constructed based on breakage theory.The model considered the mechanical surface morphology and contact characteristics of the wet coal dust.The force chain evolution laws of the wet coal dust layer were elucidated under the effects of gap filling and the cover layer,and the bearing characteristics of the three-body contact bonding surfaces were revealed by quantitative analyses of the number,length,collimation coefficient,and coordination number of the force chains within the wet coal dust layer.Finally,the three-body normal contact stiffness under various preload forces was computed and experimentally validated.The results demonstrate that the external load transfer path of the three-body contact bonding surfaces was from mechanical surface(macroscopic stress)to wet coal dust layer(mesoscopic force chains)and then to mechanical surface(peaks and valleys).The interactions among these three elements contributed to transforming the distributions of the macroscopic stresses and mesoscopic force chains to the locations at the peaks and valleys of the mechanical surface.Among them,the proportion of short force chains in the wet coal dust layer increased from approximately 0.8%–91%,while the proportion of long force chains exhibited an opposite changing trend.The force chain collimation coefficient initially increased and subsequently stabilized,reaching a maximum value of 0.93.A large number of broken,small particles in the wet coal dust layer mainly served to fill the gaps among large particles.The maximum relative error between the experimental and simulated values on the three-body contact stiffness is 7.26%,indicating that the simulation results can be an approximate substitute for the experimental results with a certain degree of accuracy and practicality.The research results are of great significance for understanding the contact characteristics of mechanical surfaces containing particulate media.

Contact stiffness and damping of spiral bevel gears under transient mixed lubrication conditions

Existing studies primarily focus on stiffness and damping under full-film lubrication or dry contact conditions.However,most lubricated transmission components operate in the mixed lubrication region,indicating that both the asperity contact and film lubrication exist on the rubbing surfaces.Herein,a novel method is proposed to evaluate the time-varying contact stiffness and damping of spiral bevel gears under transient mixed lubrication conditions.This method is sufficiently robust for addressing any mixed lubrication state regardless of the severity of the asperity contact.Based on this method,the transient mixed contact stiffness and damping of spiral bevel gears are investigated systematically.The results show a significant difference between the transient mixed contact stiffness and damping and the results from Hertz(dry)contact.In addition,the roughness significantly changes the contact stiffness and damping,indicating the importance of film lubrication and asperity contact.The transient mixed contact stiffness and damping change significantly along the meshing path from an engaging-in to an engaging-out point,and both of them are affected by the applied torque and rotational speed.In addition,the middle contact path is recommended because of its comprehensive high stiffness and damping,which maintained the stability of spiral bevel gear transmission.

NORMAL CONTACT STIFFNESS OF THE ELLIPTIC AREA BETWEEN TWO ASPERITIES

A new expression for contact deformation is given, and the normal contact stiff- ness between single asperities is derived according to Hooke＇s law. A contact model between two ellipsoidal asperities is simulated by the FE method, the result compared with the theoretical solution. It is found that the curves of the normal contact stiffness versus the included angle in the principal curvature direction show similar trends and evolve as a cosine feature. The effects of the parameters on normal contact stiffness are found to show that normal contact stiffness increases and reaches the upper limit gradually with an increase in these parameters.

A Modified Elastoplastic Contact Stiffness Model Considering Continuous Smooth Contact Characteristics and Substrate Deformation

The contact stiffness of the joint surface directly affects the static and dynamic mechanical behavior,and accuracy of the machine tool.A new elastoplastic contact stiffness model is proposed by considering continuous and smooth contact characteristics and substrate deformation.First,the interpolation interval of cubic Hermite polynomials is improved to meet the continuous and smooth change of contact parameters during asperity deformation.Then,the micro-contact mechanism considering substrate deformation is explored by establishing an asperity-substrate system model.Furthermore,combined with statistical principles,a new contact stiffness model of the joint surface is established.Finally,the correctness of the built model is verified by comparing with experimental data and different contact models.The simulation results show that the model changes continuously and smoothly in the three deformation regions.The substrate deformation mainly affects the asperities in the elastic contact stage.The smoother is the surface,the more significant is the influence of substrate deformation.

Reduction of friction by normal oscillations.I.Influence of contact stiffness

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane.In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period,so that the sample starts to 'jump'.It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters-a dimensionless sliding velocity and dimensionless oscillation amplitude.This function in turn depends on the shape of the contacting bodies.In the present paper,analysis is carried out for two shapes:a flat cylindrical punch and a parabolic shape.Here we consider 'stiff systems',where the contact stiffness is small compared with the stiffness of the system.The role of the system stiffness will be studied in more detail in a separate paper.

Elastohydrodynamic Lubrication Interface Stiffness and Damping Considering Asperity Lateral Contact

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.

Active Compliance Control of a Position‑Controlled Industrial Robot for Simulating Space Operations

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.

Evaluating Local Elasticity of the Metal Nano-films Quantitatively Based on Referencing Approach of Atomic Force Acoustic Microscopy

Traditional technique such nanoindenter（NI） can＇t measure the local elastic modulus at nano-scale（lateral）. Atomic force acoustic microscopy （AFAM） is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper（Cu） film with 110 nm thickness, zinc（Zn） film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples （it＇s elastic modulus is known）, and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values Mcu--105-130 GPa, Mzn = 88.44 GPa and Molass = 50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160 pm, 225 μm and 520 μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.

Stability analysis of the rotating tribological pair system on circular-disc end faces

In order to study the stability of friction and contact of the rotating tribological pair system,considering the influence of the changeable factors on the stability,the system dynamics analysis model based on the Lagrange equation is firstly established.The surface contact stiffness model is determined on the basis of the fractal theory.The model of the friction torque with velocities is created by using the Stribeck friction effect.The Lyapunov indirect method is employed to explore the eigenvalue problem of the system state equation.The effects of the applied load,the fractal dimension,the fractal scaling coefficient and the Stribeck coefficient on the system stability are investigated in detail.The numerical simulation results demonstrate that the tribological pair system is prone to causing system instability at low speed,and the system instability boundary value decreases when the Stribeck coefficient decreases.The fractal dimension and the fractal scaling coefficient impact the system stability slightly when fractal dimensions are large,and the system instability can be reduced by properly increasing the surface smoothness.Moreover,the system instability evidently increases with the increase in the applied load and the Stribeck coefficient.These achievements can provide a reference and theoretical support for the analysis of the dynamic performance of the tribological pair system.

Equivalent Kelvin Impact Model for Seismic Pounding Analysis of Bridges

Based on Hertz contact theory, a method to determine the parameters of Kelvin impact model for seismic pounding analysis of bridges is proposed. The impact stiffness of Kelvin model is determined by the ratio of maximum impact force to maximum contact deformation, which is calculated based on Hertz contact theory with considering the vibration effect. The restitution coefficient which has great influence on the damping coefficient of Kelvin impact model is investigated by numerical analysis. Numerical results indicate that the impact stiffness of Kelvin impact model increases with the increment of the Hertz contact stiffness, approaching velocity or the length ratio of short to long girders. Vibration effect has remarkable influence on the impact stiffness and cannot be neglected. The restitution coefficient decreases when approaching velocity increases or the length ratio of short girder to long girder decreasing. The practical ranges of impact stiffness and restitution coefficient are obtained as 3 × 10^8--6 × 10^8 N/m and 0.6-3.95 respectively.

A semi-analytical approach to the elastic loading behaviour of rough surfaces

The elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area;2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads;and 3) average gap shows an exponential relationship with load only in moderate load range.

Ionic liquids on uncharged and charged surfaces: In situ microstructures and nanofriction

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][BF_(4)](BB)and[BMIM][PF_(6)](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.