Dry Friction and Wear Characteristics of Impregnated Graphite in a Corrosive Environment

Tribological properties of impregnated graphite are greatly influenced by preparation technology and working conditions and it’s highly susceptible to corrosion environmental impacts,but the experimental research about it are few.In this paper,three kinds of impregnated graphite samples are prepared with different degree of graphitization,the tribological properties of these samples in the dry friction environment and in a corrosive environment are analyzed and contrasted.The tribo-test results show that the friction coefficient of samples is reduced and the amount of wear of samples increase when the graphitization degree of samples increases in dry friction condition.While in a corrosive environment（samples are soaked N2O4）,the friction coefficient and amount of wear are changed little if the graphitization degree of samples are low.If the degree of graphitization increase,the friction coefficient and amount of wear of samples increase too,the amount of wear is 2 to 3 times as the samples tested in the non-corrosive environment under pv value of 30MPa？m/s.The impregnated graphite,which friction coefficient is stable and graphitization degree is in mid level,such#2,is more appropriate to have a work in the corrosion conditions.In this paper,preparation and tribological properties especially in corrosive environment of the impregnated graphite is studied,the research conclusion can provide an experimental and theoretical basis for the selection and process improvement of graphite materials,and also provide some important design parameters for contact seal works in a corrosive environment.

Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchronization

Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics.

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.

The equilibrium stability for a smooth and discontinuous oscillator with dry friction

In this paper,we investigate the equilibrium stability of a Filippov-type system having multiple stick regions based upon a smooth and discontinuous（SD） oscillator with dry friction.The sets of equilibrium states of the system are analyzed together with Coulomb friction conditions in both（ f_n,f_s） and（x,˙x） planes.In the stability analysis,Lyapunov functions are constructed to derive the instability for the equilibrium set of the hyperbolic type and La Salle＇s invariance principle is employed to obtain the stability of the nonhyperbolic type.Analysis demonstrates the existence of a thick stable manifold and the interior stability of the hyperbolic equilibrium set due to the attractive sliding mode of the Filippov property,and also shows that the unstable manifolds of the hyperbolic-type are that of the endpoints with their saddle property.Numerical calculations show a good agreement with the theoretical analysis and an excellent efficien y of the approach for equilibrium states in this particular Filippov system.Furthermore,the equilibrium bifurcations are presented to demonstrate the transition between the smooth and the discontinuous regimes.

Neimark-Sacker(N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance

An oscillator with dry friction under external excitation is considered. The Poincar@ map can be established according to the series solution near equilibrium in the case of 1：4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker （N-S） bifurcations may occour. The theoretical results are verified with the numerical simulations.

Dry Friction and Wear Characteristics of Rare-Earth/MoSi_2 Composite

The dry friction and wear characteristics of rare earth/MoSi 2 composite against 45 steel under different loads were investigated by using an M 200 type friction and wear tester. SEM and XRD were used to analyze the morphology of the friction surface and the phase of worn piece in order to reveal the wear mechanism of rare earth/MoSi 2 composite. Results show that the relationships of friction coefficient, μ , or wear rate, W , of MoSi 2 and RE/MoSi 2 composite to loads, p , can be fitted well with the following function: μ (or W )= a+bp+cp 2+dp 3+ep 4 , where a, b, c, d and e are fitting constants depending on materials and confidence. MoSi 2 and rare earth/MoSi 2 composite have excellent wear resistance. When load is in the range of 80～120 N, the wear rate of RE/MoSi 2 composite is lower than that of MoSi 2 material by about 65%. The main wear mechanism of rare earth/MoSi 2 composite is adhesive wear.

A Damping Characteristics Calculation Method of Metal Dry Friction Isolators

The dry friction ring-type vibration isolator is considered as an isotropic continuous medium. A method of dry friction hysteresis loop calculation is proposed based on friction force analysis of contact beam. The friction force is modeled as an equivalent distributed moment to use the finite element method （FEM） to calculate the dry friction vibration isolator hysteresis loop, so the damping characteristics can be obtained. A comparison of the hysteresis loop calculation results and the experimental results shows the average relative error is 2.7 %, it proves the calculation method is feasible.

NONLINER VIBRATION ANALYSIS OF THE PLATE WITH DRY FRICTION SUPPORT CONDITION

The rigid-interface friction model is usually used in the nonlinear vibrationof the rectangular plate with dry friction support edges. The present study provides an extensionby using a hysteretic spring friction model and taking account of the stick-slip motion of theplate. Results for a range of problem parameters have been obtained. The results show that thenonlinear frequency response behavior of the system can be quite different from the rigid-interfacefriction model. The effects of the stiffness at friction interfaces and the stick-slip motion on thenonlinear vibration of the plate are significant and hence cannot be neglected.

Study on Dry Friction and Wear Properties of TiAl Alloy

A Ti-50Al alloy has been prepared by vacuum pressure casting.The full lamellar microstructure (FL) has been formed upon heat treating at 1400 ℃ and then furnace cooling.The frictional wear behavior of the alloy at the room temperature has been tested and its wear mechanism has been studied.The results show that with the increase of the load and sliding speed,the wear rate of the as-cast Ti-50Al alloy rises and the friction coefficient declines.When sliding speed is lower than 1.0 m/s the wear rate of the FL Ti-50Al alloy increased with the load and sliding speed,but the friction coefficient is relatively invariable at about 0.5.The wear mechanism is mainly of abrasive wear and adhesive wear.When sliding speed is higher than 1.5 m/s,the wear mechanism has changed to mainly oxidization wear so that the wear rate of the FL Ti-50Al alloy declines significantly and the friction coefficient increases.Compared to the as-cast alloy,the FL Ti-50Al alloy has better wear resistance.

Dry friction and wear properties of intermetallics MoSi_2

The dry friction and wear properties of intermetallics MoSi 2 against 45 steel under different loads were investigated with M 2 type friction and wear tester. Scanning electric microscope (SEM) equipment with microprobe was employed to analyze the morphology of the friction surface. Results show that the dry friction and wear properties are deeply affected by load. The wear rate of MoSi 2 at the load of 80?N is the maximum which is 36.1?μg/m. On the condition of the load of 150?N, MoSi 2 material has the better friction and wear properties: friction coefficient is 0.28 and wear rate is 10.6?μg/m. With the load increasing, the main friction mechanisms change from microslip and plastic deformation to adhesive effect, and the main wear mechanisms change from plough groove wear and oxidation fatigue wear to adhesive wear.

APPROXIMATE ANALYTICAL SOLUTION OF THE SELF-EXCITED VIBRATION OF PIECEWISE-SMOOTH SYSTEMS INDUCED BY DRY FRICTION——The Vibration Mechanism of the Chinese Cultural Relic Dragon Washbasin

Based on our previous work, a mathematical model of piecewise-smooth systems is established by means of phase-plane orbit analysis, and it is then used to study the intersting phenomena of Chinese cultural relic Dragon Washbasin. The mechanism of nonlinear damping is analyzed; the approximate analytical solution of self-excited vibration of piecewise-smooth nonlinear systems induced by dry friction is derived by means of KB Method, the results of which agree well with that of the numerical solution. Therefore, the method presented in this paper is proved to be very efficient in analyzing the self-excited vibration of piecewise-smooth systems induced by dry friction.

SELF-EXCITED VIBRATION CAUSED BY DRY FRICTION BETWEEN TWO ELASTIC STRUCTURES——Vibration Mechanism of the Chinese Cultural Relic Dragon Washbasin

Based on our previous work([1]), self-excited vibration of a multi-degree-of-freedom system caused by dry friction between two elastic structures is investigated using the Chinese cultural relic dragon washbasin as an example. Some new characteristics of the self-excited vibration in this kind of system are found. The conditions under which self-excited vibration occurs at low-order or high-order modes are discussed. Effects of changes in parameters of the system on the self-excited vibration are analyzed. The vibration mechanism of the water droplets spurting phenomenon of the Chinese cultural relic dragon washbasin is further explained. This investigation presents a new idea for modeling the self-excited vibration caused by dry friction interaction between two elastic structures.

Dry friction and wear performance of SiC 3D continuous ceramic frame reinforced 7075Al alloy

The dry friction and wear behavior of 7075 Al alloy reinforced with SiC 3D continuous ceramic network against Cr12 steel was studied with oscillating dry friction and wear tester under the testing conditions of 70 ℃, 30 min, and the load range of 40-100 N. The experimental result shows that the characteristic of abrasive wear and oxidation wear mechanisms are present for 3D continuous SiC/7075 Al composite. 3D continuous network ceramic as the reinforcement can avoid composite from the third body wear that usually occurs in traditional particle reinforced composite. Under low load, the composite with low volume fraction of ceramic reinforcement exhibits better wear resistance due to the homogeneous reinforcement distribution with small pore size; on the contrary, under high load, the composite with high reinforcement volume fraction exhibits better wear resistance because of the coarse frame size. Hard SiC frame leads to the wear of Cr12 steel mainly. The frame with high volume fraction corresponds to the high Fe content.

Dynamics Modeling and Numerical Analysis of Rotor with Elastic Support/Dry Friction Dampers

The elastic support/dry friction damper is a type of damper which is used for active vibration control in a rotor system.To establish the analytical model of this type of damper,a two-dimensional friction model-ball/plate model was proposed.By using this ball/plate model,a dynamics model of rotor with elastic support/dry friction dampers was established and experimentally verified.Moreover,the damping performance of the elastic support/dry friction damper was studied numerically with respect to some variable parameters.The numerical study shows that the damping performance of the elastic support/dry friction damper is closely related to the stiffness distribution of the rotor-support system,the damper location,the pressing force between the moving and stationary disk,the friction coefficient,the tangential contact stiffness of the contact interface,and the stiffness of the stationary disk.In general,the damper should be located on an elastic support which has a large vibration amplitude in order to achieve a better damping performance,and the more vibration energy in this elastic support concentrates,the better performance of the damper will be.The larger the tangential contact stiffness of the contact interface,and the stiffness of the stationary disk are,the better performance of the damper will be.There will be an optimal value of the friction force at which the damper performs best.

Analytical Method Determining Resonant Response of Blade with Dry Friction Damper

This paper presents an analytical method for determining the steady state response of blade with dry friction damper. A complete vibration cycle is divided into four successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined by using analytical solution forms. An analytical solution of the system periodic motion can be formed by combining the four intervals’ solutions. Numerical simulation shows that there are two response peaks in passage through the resonant frequencies of the system without the friction damper and with the friction damper fully stuck respectively. The amplitude of the first peak can be reduced up to 90% by adjusting the value of normal pressure force between the damper’s contacting surfaces. Whereas to determine the optimum pressure force, reduction of amplitudes of two peaks should be considered together.

Dry Friction Characteristics of Ti-6Al-4V Alloy under High Sliding Velocity

Tribological behaviours of Ti-6Al-4V alloy pins sliding against GCr15 steel discs over a range of contact pressures （0.33-1.33 MPa） and sliding velocities （30-70 m/s） were investigated using a pin-on-disc tribometer under unlubricated conditions. The wear mechanisms and the wear transition were analyzed based on examinations of worn surfaces using SEM, EDS and XRD. When the velocity increases, the friction coefficient and the wear rate of the Ti-6Al-4V alloy show typical transition features, namely, the critical values of sliding velocities for 0.33 and 0.67 MPa are 60 and 40 m/s, respectively. The experimental results reveal that the tribological behaviours of Ti-6Al-4V alloys are controlled by the thermal-mechanical effects, which connects with the friction heat and hard particles of the pairs. A tribolayer containing mainly Ti oxides and V oxides is formed on the worn surface of Ti-6Al-4V alloy.

Dry Friction with Various Frictions Laws: From Wave Modulated Orbit to Stick-Slip Modulated

Choices of excitation signals are important in engineering sciences and in physical simulations;a sufficient excitation can be critical in modelling a complicated nonlinear dynamic system. The discontinuous dynamic of a non-linear, friction-induced with two idealized periodical forced oscillators is studied. The dry friction in the system follows the classical Coulomb law, and various friction characteristics of dry friction laws in engineering sciences. To capture the presence of the two driving forces, the system must be studied as a function of their frequency-modulated and its equivalent amplitude modulated waveforms. Our numerical investigation shows a rich dynamical behaviour including periodic, quasi-periodic motions, thus a variable dynamics phenomenon among others;such as modulated waves, modulated stick-slip, periodic oscillation, and periodic stick-slip. It seems that such excitation forces can be used to conveniently identify the existence of nonlinearity, dry friction effects, and strength degradation in the system. The results achieved via the Coulomb’s law are compared with those obtained via two others particular friction laws: the complete model with Stribeck effect and Coulomb viscosity.

A semi-analytical multi-harmonic balance method on full-3D contact model for dynamic analysis of dry friction systems

Dry friction damping structures are widely-used in aero-engines to mitigate vibration.The nonlinear nature of friction and the two-dimensional in-plane motion on the contact interface bring challenges to accurately and efficiently predict the forced response of frictionally damped structures.The state-of-the-art Multi-Harmonic Balance Method(MHBM)on quasi-3D contact model in engineering cannot precisely capture the kinematics on the friction interface although the efficiency is high.The full-3D contact model can describe the constitutive relationship of the interface in a more accurate manner;however,the efficiency and convergence are not guaranteed for large-scale models.In this paper,a semi-analytical MHBM on full-3D contact model is proposed.The original Trajectory Tracking Method(TTM)for evaluating the contact force is reformulated to make the calculation more concise and the derivation of the Analytical Jacobian Matrix(AJM)feasible.Based on the chain rule of derivation,the AJM which is the core to upgrade the performance is deduced.Through a shrouded blade finite element model,the accuracy and efficiency of the proposed method are compared with both the MHBM on full-3D contact model with numerical Jacobian matrix and the MHBM on quasi-3D contact model with AJM.The results show that the AJM improves significantly the efficiency of the MHBM on full-3D contact model.The time cost of the proposed method is in the same order of magnitude as that of the MHBM on quasi-3D contact model.We also confirm that the full-3D contact model is necessary for the dynamic analyses of shrouded blades.If one uses the quasi-3D model,the estimation relative error of damping can even reach 31.8%in some cases.In addition,the AJM also brings benefits for stability analysis.It is highly recommended that engineers use the MHBM on full-3D contact model for the dynamic analysis and design of shrouded blades.

Dry friction damping mechanism of flexible microporous metal rubber based on cell group energy dissipation mechanism

Flexible microporous metal rubber (FMP-MR) is a high-damping material that dissipates energy by dry friction through internal spiral metal wires in contact with each other. However, the FMP-MR energy dissipation mechanism is not fully understood owing to its disordered grid interpenetrating structure. In this work, computer-aided preparation technology is used to accurately reconstruct the complex spiral network structure of FMP-MR multipoint random contact, and a cell group model with an energy dissipation mechanism is proposed to obtain the dynamic energy distribution of the contact friction in both space and time dimensions. By judging the effective contact point, a global displacement ablation phenomenon of hooked staggered porous materials is induced. The macro- and micro-equivalent frictions are introduced to effectively explain the characteristics of the strong energy dissipation in FMP-MR under fretting excitation. A real and effective damping hysteresis constitutive model is then constructed to dynamically capture the mapping relationship between the complex nonlinear topological structure effect of the materials and spatial random contact dry friction in real time. The results indicate that the contact behavior between turns of the FMP-MR wire follows a clear quasi-Gaussian distribution under an external load, forcing the topological results to change. The energy dissipation of the materials revealed peak energy consumption lagging behind the loading limit for a certain distance, which can be determined by the effective contact point and contact dry friction slip. The consistency between the quasi-static compression tests and constitutive curves of the model was quantitatively verified through residual analysis. The data demonstrated the differential behavior of the FMP-MR meso-structure to follow a phased growth law during loading with different action mechanisms in the guiding, main growth, and relaxation stages of the energy consumption displacement curve. In summary, these findings provide an acceptable theoretical basis for the damping energy consumption mechanism and lifetime prediction of FMP-MR.

Solving the transient response of the randomly excited dry friction system via piecewise RBF neural networks

Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization.