Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

Dividing the transit wind speeds into intervals as a favorable methodology for analyzing the relationship between wind speed and the aerodynamic impedance of vegetation in semiarid grasslands

In grassland ecosystems,the aerodynamic roughness(Z0)and frictional wind speed(u*)contribute to the aerodynamic impedance of the grassland canopy.Thus,they are often used in the studies of wind erosion and evapotranspiration.However,the effect of wind speed and grazing measures on the aerodynamic impedance of the grassland canopy has received less analysis.In this study,we monitored wind speeds at multiple heights in grazed and grazing-prohibited grasslands for 1 month in 2021,determined the transit wind speed at 2.0 m height by comparing wind speed differences at the same height in both grasslands,and divided these transit wind speeds at intervals of 2.0 m/s to analyze the effect of the transit wind speed on the relationship among Z0,u*,and wind speed within the grassland canopy.The results showed that dividing the transit wind speeds into intervals has a positive effect on the logarithmic fit of the wind speed profile.After dividing the transit wind speeds into intervals,the wind speed at 0.1 m height(V0.1)gradually decreased with the increase of Z0,exhibiting three distinct stages:a sharp change zone,a steady change zone,and a flat zone;while the overall trend of u*increased first and then decreased with the increase of V0.1.Dividing the transit wind speeds into intervals improved the fitting relationship between Z0 and V0.1 and changed their fitting functions in grazed and grazing-prohibited grasslands.According to the computational fluid dynamic results,we found that the number of tall-stature plants has a more significant effect on windproof capacity than their height.The results of this study contribute to a better understanding of the relationship between wind speed and the aerodynamic impedance of vegetation in grassland environments.

Grey Relation between Nonlinear Characteristic and Dynamic Uncertainty of Rolling Bearing Friction Torque

The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

A comprehensive comparative investigation of frictional force models for dynamics of rotor−bearing systems

Vibrations of a rotor-bearing system(RBS)can be affected by the frictional forces between the components of the inherent bearings.Thus,an in-depth investigation of the influences of the frictional moments of the bearings on the vibrations of the RBS can be helpful for understanding the vibration mechanisms in the rotating machinery.In this study,an improved dynamic model of a RBS considering different frictional force models is presented.A comparative investigation on the influences of the empirical and analytical frictional force models on the vibration characteristics of the RBS is proposed.The empirical frictional force models include Palmgren’s and SKF’s models.The analytical frictional force model considers the rolling friction caused by the radial elastic material hysteresis,slipping friction between the ball and races,viscosity friction caused by the lubricating oil,and contact friction between the ball and cage.The influences of the external load and rotational speed on the vibrations of the RBS are analyzed.The comparative results show that the analytical frictional force model can give a more reasonable method for formulating the effects of the friction forces in the bearings on the vibrations of the RBS.The results also demonstrate that the friction forces in the bearings can significantly affect the vibrations of the RBSs.

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem （NCP）. An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.

Simulation and experimental study of dynamic recrystallization process during friction stir vibration welding of magnesium alloys

A two-dimensional cellular automaton(CA)model was utilized to analyze the effect of mechanical vibration on microstructure evolution of AZ91 alloy during friction stir welding(FSW).The simulated results,namely grain topology,grain size distribution,average grain size,and also the dynamic recrystallization(DRX)fraction were compared with measured data.The adequate comparability between FEM and experimental data shows that the CA method can be applied to the analysis of the microstructure progression during the friction stir welding of AZ91 alloy.It is concluded that the dislocation density during the friction stir vibration welding(FSVW)is higher than that in the FSW process and the process of nucleation and grain growth is faster for samples during FSVW compared to FSW.The grain size modification and DRX phenomenon with various vibration frequencies were also simulated in detail during FSVW.It is found that vibration makes nucleation start earlier and decreases the proportion of the incubation period and the percentage of recrystallization as vibration frequency improves.

Modeling joints with clearance and friction in multibody dynamic simulation of automotive differentials

Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatics, cylindrics or universal joints.In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the friction is presented. This formulation has been used to represent the link between the planet gears and the planet carrier in an automotive differential model. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301303]

Robot Zero-Moment Control Algorithm Based on Parameter Identification of Low-Speed Dynamic Balance

This paper proposes a zero-moment control torque compensation technique.After compensating the gravity and friction of the robot,it must overcome a small inertial force to move in compliance with the external force.The principle of torque balance was used to realise the zero-moment dragging and teaching function of the lightweight collaborative robot.The robot parameter identification based on the least square method was used to accurately identify the robot torque sensitivity and friction parameters.When the robot joint rotates at a low speed,it can approximately satisfy the torque balance equation.The experiment uses the joint position and the current motor value collected during the whole moving process under the low-speed dynamic balance as the excitation signal to realise the parameter identification.After the robot was compensated for gravity and static friction,more precise torque control was realised.The zero-moment dragging and teaching function of the robot was more flexible,and the drag process was smoother.

Effect of Friction on Dynamic Response of A Power Split Transmission System

The tooth surface friction stiffness and friction torque coefficient equations of cylindrical gear are derived.On the basis of factors such as time varying friction coefficient and mesh stiffness,support stiffness,torsional stiffness and comprehensive error,the dynamic equations of the gear trains with bending torsional coupling are established.Using the Fourier series method,the total response of the system is obtained,and the influence of friction on it is analyzed.The results show that when the spur gear enters the meshing,the frictional amplitude of the tooth surface is larger than that of the gear when it is withdrawn from engagement,and the meshing force fluctuates greatly.The frictional force and dynamic meshing force of the herringbone gear tooth surface are relatively stable,and the fluctuation amplitude is much smaller than that of the spur gear.The amplitude of the bearing vibration is not affected by the friction,but the friction has a certain influence on the bearing force of the output shaft.The first order natural frequency of the split stage and the power confluence stage has a large influence on the vibration of the bearing force.In general,the natural frequency of the power confluence stage has a large proportion of influence.

The Dynamic Tribological Performance of One Certain Resin-based Friction Materials under Different Temperature Conditions

A fixed-point observation method was designed to research the dynamic tribological performance of one certain resin-based friction materials. The friction test was performed through a constant speed friction tester under various temperature conditions. It was found that the dynamic tribological performance of materials has a good consistency with the dynamic evolution of worn surfaces. At lower temperatures, the friction coefficient and wear rate were constant, resulted from the stable worn surfaces. At higher temperatures, the friction coefficient increased gradually, while the wear rate decreased, due to the increasing contact area and Fe concentration. A fade occurred above 250 ℃, which can be explained by the degradation of binders.

A DYNAMIC MODEL FOR A DISC EXCITED BY VERTICALLY MISALIGNED,ROTATING,FRICTIONAL SLIDERS

This paper presents a dynamic model for a disc subjected to two sliders rotating in the circumferential direction over the top and bottom surfaces of the disc.The two sliders are vertically misaligned and each is a mass-spring-damper system with friction between the slider and the disc. The moving loads produced by misaligned sliders can destabilise the whole system.Stability analysis is carried out in a simulated example.This model is meant to explain the friction mechanism for generating unstable vibration in many applications involving rotating discs.

DYNAMIC FRICTION:Ⅰ.EXPERIMENTAL OBSERVATIONS OF ROCK FRICTION

Dynamic friction is a critical process of crustal earthquake ruptures. Recent experimenta1 and theoretica1 progress in rock friction have demonstrated that most continental earthquakes are associated with stick-slip in the brittle field of the crust and that only dynamic instability with fast slip is related to seismicity. Dynamic stability will be influenced by frictional parameters a-b, a, stiffness K, characteristic displacement L, slip rate history (velocity weakening), normal stress history (pressure strengthening), and temperature, which is described by the frictional constitutive laws. Velocity-weakening (a-b<0) can cause dynamic instability if the medium stiffness is below the critical stiffness (X/Kc<1), while velocity-strengthening enhances the frictional stability.The most recent experimental evidence of rock friction will be systematically reviewed in this paper.

Numerical Calculation of Dynamic Response for Multi-Span Non-Uniform Beam Subjected to Moving Mass with Friction

In order to simulate the coupling vibration of a vehicle or train moves on a multi-span continuous bridge with non-uniform cross sections, a moving mass model is used according to the Finite Element Method, the effect of the inertial force, Coriolis force and centrifugal force are considered by means of the additive matrices. For a non-uniform rectangular section beam with both linear and parabolic variable heights in a plane, the stiffness and mass matrices of the beam elements are presented. For a non-uniform box girder, Romberg numerical integral scheme is adopted, each coefficient of the stiffness matrix is obtained by means of a normal numerical computation. By applying these elements to calculate the non-uniform beam, the computational accuracy and efficiency are improved. The finite element method program is worked out and an entire dynamic response process of the beam with non-uniform cross sections subjected to a moving mass is simulated numerically, the results are compared to those previously published for some simple examples. For some complex multi-span bridges subjected to some moving vehicles with changeable velocity and friction, the computational results, which can be regarded as a reference for engineering design and scientific research, are also given simultaneously.

Frictionally excited thermoelastic dynamic instability of functionally graded materials

The perturbation method is applied to investigate the frictionally excited thermoelastic dynamic instability (TEDI) of a functionally graded material (FGM) coating in half-plane sliding against a homogeneous half-plane. We assume that the thermoelastic properties of the FGM vary exponentially with thickness. We also examine the effects of the gradient index, sliding speed, and friction coefficient on the TEDI for various material combinations. The transverse normal stress for two different coating structures is calculated. Furthermore, the frictional sliding stability of two different coating structures is analyzed. The obtained results show that use of FGM coatings can improve the TEDI of this sliding system and reduce the possibility of interfacial failure by controlling the interfacial tensile stress.

An experimental study on the effects of friction modifiers on wheel-rail dynamic interactions with various angles of attack

By modifying friction to the desired level,the application of friction modifiers(FMs)has been considered as a promising emerging tool in the railway engineering for increasing braking/traction force in poor adhesion conditions and mitigating wheel/rail interface deterioration,energy consumption,vibration and noise.Understanding the effectiveness of FMs in wheel–rail dynamic interactions is crucial to their proper applications in practice,which has,however,not been well explained.This study experimentally investigates the effects of two types of top-of-rail FM,i.e.FM-A and FM-B,and their application dosages on wheel–rail dynamic interactions with a range of angles of attack(AoAs)using an innovative well-controlled V-track test rig.The tested FMs have been used to provide intermediate friction for wear and noise reduction.The effectiveness of the FMs is assessed in terms of the wheel–rail adhesion characteristics and friction rolling induced axle box acceleration(ABA).This study provides the following new insights into the study of FM:the applications of the tested FMs can both reduce the wheel–rail adhesion level and change the negative friction characteristic to positive;stick–slip can be generated in the V-Track and eliminated by FM-A but intensified by FM-B,depending on the dosage of the FMs applied;the negative friction characteristic is not a must for stick–slip;the increase in ABA with AoA is insignificant until stick–slip occurs and the ABA can thus be influenced by the applications of FM.

Effect of interlayer bonded bilayer graphene on friction

We study the friction properties of interlayer bonded bilayer graphene by simulating the movement of a slider on the surface of bilayer graphene using molecular dynamics.The results show that the presence of the interlayer covalent bonds due to the local sp^(3) hybridization of carbon atoms in the bilayer graphene seriously reduces the frictional coefficient of the bilayer graphene surface to 30%,depending on the coverage of interlayer sp^(3) bonds and normal loads.For a certain coverage of interlayer sp3bonds,when the normal load of the slider reaches a certain value,the surface of this interlayer bonded bilayer graphene will lose the friction reduction effect on the slider.Our findings provide guidance for the regulation and manipulation of the frictional properties of bilayer graphene surfaces through interlayer covalent bonds,which may be useful for applications of friction related graphene based nanodevices.

Nano-scale Interfacial Friction Behavior between Two Kinds of Materials in MEMS Based on Molecular Dynamics Simulations

The aim of this article was to provide a systematic method to perform molecular dynamics simulotion or evaluation for nano-scale interfacial friction behavior between two kinds of materials in MEMS design. Friction is an important factor affecting the performance and reliability of MEMS. The model of the nano-scale interracial friction behavior between two kinds of materials was presented based on the Newton＇ s equations of motion. The Morse potential function was selected for the model. The improved Verlet algorithm was employed to resolve the model, the atom trajectories and the law of the interfacial friction behavior. Comparisons with experimental data in other paper confirm the validity of the model. Using the model it is possible to simulate or evaluate the importance of different factors for designing of the nano-scale interfacial friction behavior between two kinds of materials in MEMS.

An Improved Dynamic Friction Rejection Attitude Stability Control Strategy

The attitude stability control of under actuated spacecraft that used two reaction wheels in the presence of dynamic friction disturbance is handled. A novel improved control approach with a combination of a singular control law based on quaternion and extended state observer (ESO) is employed to establish a stabilization control so as to restrain the effect of friction. The corresponding simulation results demonstrate the highly stable accuracy and performance compensated dynamic friction. Furthermore if there is a non zero initial condition in under actuated axis the attitude stability can be enhanced with a magnetic torquer. Simulations for a nano spacecraft denote a potential application value in pointing accuracy using two reaction wheels and a magnetic torquer.

SURFACE DYNAMIC FRICTION OF POLYMER GELS

The sliding friction of various kinds of hydrogels has been studied and it was found that the frictional behaviors ofthe hydrogels do not conform to Amonton's law F=μW which well describes the friction of solids. The frictional force andits dependence on the load are quite different depending on the chemical structures of the gels, surface properties of theopposing substrates, and the measurement condition. The gel friction is explained in terms of interracial interaction, eitherattractive or repulsive, between the polymer chain and the solid surface. According to this model, the friction is ascribed tothe viscous flow of solvent at the interface in the repulsive case. In the attractive case, the force to detach the adsorbing chainfrom the substrate appears as friction. The surface adhesion between glass particles and gels measured by AFM showed agood correlation with the friction, which supported the repulsion-adsorption model proposed by the authors.