OPTIMAL CONVERGENCE RATE OF THE LANDAU EQUATION WITH FRICTIONAL FORCE

The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.

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.

Use of opposite frictional forces by animals to increase their attachment reliability during movement

Many animals have the natural ability to move on various surfaces,such as those having different roughness and slope substrates,or even vertical walls and ceilings.Legged animals primarily attach to surfaces using claws,soft and hairy pads,or combinations of them.Recent studies have indicated that the frictional forces generated by these structures not only control the movement of animals but also significantly increase the reliability of their attachment.Moreover,the frictional forces of various animals have opposite characteristics and hierarchical properties from toe-to-toe and leg-to-leg.These opposite frictional forces allow animals to attach securely and stably during movement.The coordination of several attachment(adhesion)modes not only helps animals adhere,which would be impossible in single mode,but also increases the overall stability of the attachment(adhesion)system.These findings can help the design of highly adaptable feet for bionic robots in the near future.

Simulating Calculation of Frictional Force between Mold and Billet

Assumption about the inner surface of mold is made according to the forming mechanisms of frictional force. The frictional force between billet and mold can be analysed by calculating the thermal shrinkage and the shearing strength of the meniscus.The model is used to calculate the maximum drawing speed at different conditions. The results are very satisfactory.

Improved hybrid position/force controller design of a flexible robot manipulator using a sliding observer

An improved hybrid position/force controller design of a flexible robot manipulator is presented using a sliding observer. The friction between the end effector and the environment is considered and compensated. For systematic reasons the controller is designed taking into consideration the rigid link subsystems and the flexible joints. The proposed control system satisfies the stability of the two subsystems and copes with the uncertainty of robot dynamics. A sliding observer is designed to estimate the time derivative of the torque applied as input to the rigid part of the robot. For the stability of the observer, it is assumed that the uncertainty of the observed system is bounded. A MRAC algorithm is used for the estimation of the friction forces at the contact point between the end effector and the environment. Finally simulation and experimental results are given, to demonstrate the effectiveness of the proposed controller.

Fundamental Characteristics of Reduction System for Seismic Response using Friction Force

A new device of reduction for seismic response using friction force was developed. In this paper, fundamental characteristics of reduction system for seismic response using this device were investigated by excitation experiment using artificial seismic waves. The peak acceleration amplitude on this system has decreased to about 50-90% over the input waves. Although a spectral peak around the frequency of 0.5Hz that is the natural period of this system was identified, the value of a spectral peak was decreased using bearings with the high friction force. This device is useful for reduction of seismic response.

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first- and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theoretical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is complicated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.

Analysis and Experimental Study on the Friction Force at the Binding Point of Flexible Cable on Satellite

Mainly for the problem that the friction force generated by the existing process of bind-ing,fixing and fastening the flexible cable on the satellite is unknown,the friction force analysis and experimental research on the binding point of the flexible cable are carried out.The equivalent model of the cable bundle bound by nylon cable ties is established,the force on the binding point is analyzed,and the empirical formula for calculating the friction force at the binding point is estab-lished.The formula shows that the friction force is related to the cable bundle diameter,the number of winding cycles of silicone rubber tape,the width of nylon cable ties,and the binding force.The friction force tests of the cable diameter of 5.06 mm,8.02 mm,24.02 mm,38.04 mm under different winding turns of tape were carried out,which was compared with the theoretical calculation value.It is concluded that the calculation accuracy of the theoretical model is more than 95%,which can estimate the actual friction force value accurately.This provides a reference and basis for the theoretical and experimental research on the friction force of the flexible cable binding point on satellite.

Dynamical Analysis of Rub-impact Rotor System with Asymmetric Oil Film Force

Considering the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force, a dynamical model of rub-impact rotor system is established, then the nonlinear dynamical behavior is studied by numerical analysis method. The effect of rotation speed, nonlinear stiffitess ratio and speed effect factor on brifurcation and chaotic behavior for rub-impact rotor system is comprehensively analyzed. The analysis results show that the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on the dynamical behavior of the rotor system has close relation with rotation speed. The chaotic behavior exists in a wider parameter region, and the chaotic evolution rule is more complicated. The research provides a reliable theory basis and reference for diagnosing some faults of the rotor system.

Study on the Sliding Displacement of a Sliding Structure Subjected to Multi directional Earthquake Excitation

Transient dynamic analysis is used to study the effect of the bidirectional interaction of friction on the response of sliding displacement of a sliding structure subjected to bidirectional earthquake ground motion. The analysis varies the parameters of amplitude ratio of earthquake excitation, the period of the superstructure, and the coefficient of friction in the sliding support. Numerical results show that the sliding structure is significantly influenced by the interaction of frictional forces. So the sliding displacement may be underestimated and the acceleration of the superstructure may be overrated if the bidirectional interaction of frictional forces is neglected.

Sliding Wear Performance Evaluation of Red Mud (RM), RM + Fly Ash (FA) and RM + FA + Al Coatings on Mild Steel

The research paper focuses on evaluating the dry sliding wear behaviour of plasma sprayed coatings like red mud (RM), RM + 5% Fly Ash (FA) and RM + 5% FA + 5% Al on mild steel cylindrical shape substrate. Spraying was done at 10 kW operating power level. A conventional pin on disc wear tester is adopted for wear analysis. The wear test was performed at track diameter of 50 mm and sliding speed of 60 rpm (0.157 m/s) with normal load of 10 N. The duration of sliding varies from 54 minutes for pure red mud coating to a maximum value of 102 minutes for RM + 5% FA + 5% Al composite coating. A significant decrease in wear rate (in terms of mass loss) is observed by reinforcement of fly ash and aluminium to red mud, which might be due to improved interfacial properties.

Influence of friction on buckling of a drill string in the circular channel of a bore hole

Enhancement of technology and techniques for drilling deep directed oil and gas bore hole is one of the most important problems of the current petroleum industry.Not infrequently, the drilling of these bore holes is attended by occurrence of extraordinary situations associated with technical accidents. Among these is the Eulerian loss of stability of a drill string in the channel of a curvilinear bore hole. Methods of computer simulation should play a dominant role in prediction of these states. In this paper, a new statement of the problem of critical buckling of the drill strings in 3D curvilinear bore holes is proposed. It is based on combined use of the theory of curvilinear elastic rods, Eulerian theory of stability, theory of channel surfaces, and methods of classical mechanics of systems with nonlinear constraints. It is noted that the stated problem is singularly perturbed and its solutions have the shapes of localized harmonic wavelets. The calculation results showed that the friction effects lead to essential redistribution of internal axial forces, as well as changing the eigenmode shapes and sites of their localization. These features make the buckling phenomena less predictable and raise the role of computer simulation of these effects.

A review of down-hole tubular string buckling in well engineering

Down-hole tubular string buckling is the most classic and complex part of tubular string mechanics in well engineering. Studies of down-hole tubular string buckling not only have theoretical significance in revealing the buckling mechanism but also have prominent practical value in design and control of tubular strings. In this review, the basic principles and applicable scope of three classic research methods （the beam-column model, buck- ling differential equation, and energy method） are intro- duced. The critical buckling loads and the post-buckling behavior under different buckling modes in vertical, inclined, horizontal, and curved wellbores from different researchers are presented and compared. The current understanding of the effects of torque, boundary condi- tions, friction force, and connectors on down-hole tubular string buckling is illustrated. Meanwhile, some unsolved problems and controversial conclusions are discussed. Future research should be focused on sophisticated description of buckling behavior and the coupling effect of multiple factors. In addition, active control of down-hole tubular string buckling behavior needs some attention urgently.

Mechanical behavior of drillstring with drag reduction oscillators and its effects on sliding drilling limits

Practice has proved that drag reduction oscillators can decrease the axial friction and increase wellbore extension effectively in sliding drilling operations.However,the complicated mechanical behavior of drillstring with drag reduction oscillators has not been revealed sufficiently.In this paper,the mechanical model of drillstring with drag reduction oscillators is established by considering the friction nonlinearity.Further introducing the initial conditions,boundary conditions and continuity conditions,the finite differential equation of drillstring vibration is obtained and solved.The new model has been applied to a case study,in which the drag reduction effects of drillstring with and without oscillators are compared and the effects of relevant factors on drag reduction are analyzed.The results show that the hook loads increase obviously by reducing downhole average friction coefficient for drillstring with oscillators.Increasing vibration amplitude of the drag reduction oscillator can decrease axial friction,but the vibration frequency is nearly irrelevant to drag reduction.Increasing number of drag reduction oscillators can decrease axial friction,but may lead to large hydraulic power loss and high risk of drillstring fatigue.Therefore,there is an optimal number of drag reduction oscillators.The re search re sults are of significant guiding significance for optimal design and safety control in sliding drilling operations.

EXPERIMENTAL INVESTIGATION ON PARTICLE EFFECT IN PISTON RING-CYLINDER LUBRICATION

To study the tribological properties of the piston ring-cylinder liner in liquid-solid lubrication, the experiment is carried out on a modified piston ring-cylinder liner tester. Two kinds of liquid-solid lubricants are used, one with ultra-dispersed diamond （UDD） nano-particles suspending in pure lubricant, the other with micro-sized MoS2 particles. The particle concentrations are 0%, 0.02% and 0.1% by weight. The experimental temperature is 30℃ and 75℃ respectively. The results show that with the presence of ultra-dispersed diamond particles, the load when scuffing failure occurs is increased. For the lubricant contains MoS2 particles, the scuffing load is decreased. The liquid-solid lubricant also affects the thermal behavior of piston ring-cylinder liner. The surface bulk temperatures of cylinder liner specimen are measured. It has been seen that liquid-solid lubricant used in this research tends to improve the thermal properties generally and the measured friction forces also decreases with the presence of UDD nano-particles. The surface bulk temperature when scuffing occurs is also measured. The results show that the size effect and environment temperature have obvious influence on scuffing load and scuffing temperature. With some new findings, this work is an important complement to the existing research on particle effect on lubrication, because the existing results only show one aspect of this problem.

Friction phenomena in a two-dimensional Frenkel-Kontorova model

By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.

Self-contained Capsubot Propulsion Mechanism

In this paper, a self contained capsubot （capsule robot） propulsion mechanism is investigated. The proposed capsubot works on the principle of internal force-static friction. A modified linear DC motor is used to drive the capsubot. A novel acceleration profile is proposed for the moving part （linear cylinder） based on the principle. A significant feature of the proposed capsubot is that it is legless, wheelless, and trackless. The developed capsubot with a proposed propulsion mechanism demonstrates a very good average velocity. The propulsion mechanism has the potential to be used for the propulsion of a wireless-controlled self-propelling capsule endoscope. Simulation and experimental results demonstrate the performance of the self-contained capsubot with the proposed acceleration profile.

SYNTHESIS OF PERFLUORO-1-OCTANESULFONATED FULLERENE AND THE FRICTION PROPERTIES OF ITS THIN FILM

A star-shaped compound of perfluoro-1-octanesulfonated fullerene was synthesized. The measurement of the friction for its spin-coating film by friction force microscopy (FFM) reveals that the films possess lower friction force compared to that of the star-shaped C-60-polystyrene films.

Theoretical Features of the Process Cleaning Zone between Sections of Raw Cotton from Weed Impurities

The article proposes to use the Euler equations to describe the motion of a stationary stream in the cleaning zones, which allows us to determine the laws of the distribution of pressure, density and speed along the arc of contact of the moving layer of raw cotton with the surface of the mesh during impact with spikes on the pulp. It was found that the pressure, density and flow velocity along the cleaning arc as a result of the hammer spikes change stepwise with decreasing pressure and density and increasing flow velocity along this arc.

Dynamics of Interaction of a Single Fiber with a Headset of a Sampling Drum

The article presents an analysis of the dynamics of interaction of a single fiber with the sampling drum of a headset during pneumomechanical spinning. The regularity is investigated and the equation of the movement of fibers on the surface of the tooth of the sampling drum headset is obtained. It was found that the dependences of the movement of fibers along the tooth at different angles of inclination, the distribution of fiber tension along the arc, and the distribution of fiber speeds in the region of the sampling arc have an increase property. As a result of the analysis of the tension and speed of the fibers, it was found that with the increase in the sampling zone, the tension force and speed of the fiber increase.