This paper reports stick-slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention （NIED）, Tsuk...This paper reports stick-slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention （NIED）, Tsukuba, Japan. The apparatus consists of the existing shaking table as the shear-loading device up to 3,600 kN, the main frame for holding two large rectangular prismatic specimens with a sliding area of 0.75 m^2 and for applying normal stresses an up to 1.33 MPa, and a reaction force unit holding the stationary specimen to the ground. The shaking table can produce loading rates v up to 1.0 m/s, accelerations up to 9.4 m/s^2, and displacements d up to 0.44 m, using four servocontrolled actuators. We report results from eight preliminary experiments conducted with room humidity on the same gabbro specimens at v = 0.1-100 mm/s and an = 0.66-1.33 MPa, and with d of about 0.39 m. The peak and steady-state friction coefficients were about 0.8 and 0.6, respectively, consistent with the Byerlee friction. The axial force drop or shear stress drop during an abrupt slip is linearly proportional to the amount of displacement, and the slope of this rela- tionship determines the stiffness of the apparatus as 1.15 × 10^8 N/m or 153 MPa/m for the specimens we used. This low stiffness makes fault motion very unstable and the overshooting of shear stress to a negative value was recognized in some violent stick-slip events. An abrupt slip occurred in a constant rise time of 16-18 ms despite wide variation of the stress drop, and an average velocity during an abrupt slip is linearly proportional to the stress drop. The use of a large-scale shaking table has a great potential in increasing the slip rate and total displacement in biaxial friction experiments with large specimens.展开更多
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...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.展开更多
An innovative physical simulation apparatus, including high speed camera, red thermal imaging system, and mechanical quantity sensor, was used to investigate the friction heat generation and atom diffusion behavior du...An innovative physical simulation apparatus, including high speed camera, red thermal imaging system, and mechanical quantity sensor, was used to investigate the friction heat generation and atom diffusion behavior during Mg-Ti friction welding process. The results show that the friction coefficient mainly experiences two steady stages. The first steady stage corresponds to the Coulomb friction with material abrasion. The second steady stage corresponds to the stick friction with fully plastic flow. Moreover, the increasing rates of axial displacement, temperature and friction coefficient are obviously enhanced with the increase of rotation speed and axial pressure. It can also be found that the there exists rapid diffusion phenomenon in the Mg-Ti friction welding system. The large deformation activated diffusion coefficient is about 105 higher than that activated by thermal.展开更多
The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance jo...The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively.The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem(LCP) algorithm and the trial-and-error algorithm.Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.展开更多
Although atomic stick–slip friction has been extensively studied since its first demonstration on graphite,the physical understanding of this dissipation-dominated phenomenon is still very limited. In this work, we p...Although atomic stick–slip friction has been extensively studied since its first demonstration on graphite,the physical understanding of this dissipation-dominated phenomenon is still very limited. In this work, we perform molecular dynamics（MD） simulations to study the frictional behavior of a diamond tip sliding over a graphite surface. In contrast to the common wisdom, our MD results suggest that the energy barrier associated lateral sliding（known as energy corrugation） comes not only from interaction between the tip and the top layer of graphite but also from interactions among the deformed atomic layers of graphite. Due to the competition of these two subentries, friction on graphite can be tuned by controlling the relative adhesion of different interfaces.For relatively low tip-graphite adhesion, friction behaves normally and increases with increasing normal load. However,for relatively high tip-graphite adhesion, friction increases unusually with decreasing normal load leading to an effectively negative coefficient of friction, which is consistent with the recent experimental observations on chemically modified graphite. Our results provide a new insight into the physical origins of energy corrugation in atomic scale friction.展开更多
A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is ...A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid modeling method, dynamic equations of the system, which include all states（before, during, and after the collision）are obtained. Simulation results of a concrete example are compared with the results obtained from two other models： a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.展开更多
This paper, using Karnopp's model of friction force and phase plane method, studies the stick-slip motion of the flexible drive mechanism. It is explained that a sudden drop of friction force is the essential sour...This paper, using Karnopp's model of friction force and phase plane method, studies the stick-slip motion of the flexible drive mechanism. It is explained that a sudden drop of friction force is the essential source of stick-slip motion when the sliding is impending. A new criterion for occurrence of stick-slip motion is established. The stick-slip region and the stable region in a parameter plane are separated by a critical parameter curve. Moreover, for the stick-slip motion of the flexible drive mechanism without viscous damping, a parameter expression is obtained. The results may be used in design of the flexible drive mechanism.展开更多
A disc-pad friction system is modelled as that two moving pads act symmetrically on an annular beam with flexible boundary condition.Simulation procedure is proposed to deal with the moving interactions and calculatio...A disc-pad friction system is modelled as that two moving pads act symmetrically on an annular beam with flexible boundary condition.Simulation procedure is proposed to deal with the moving interactions and calculation is carried out by using the finite difference method,which shows that only the first-order mode vibration of the beam can be induced.Then the partial differential equation of motion of the disk is reduced to a first-order mode vibration system with time-varying stiffness.As the disk speed is decreased below the critical speeds,the relative equilibrium of the pad on the disk loses its stability and stick-slip type limit cycle vibrations are resulted in all directions′movements.Acceleration of the disk motion on the frictional instability is also investigated.The period of stick-slip vibration with large amplitude will be shortened with higher moving deceleration.展开更多
Incorporating rate and state friction laws, stability of linearly stable （i.e., with stiffness greater than the critical value） spring-slider systems subjected to triggering perturbations was analyzed under variable...Incorporating rate and state friction laws, stability of linearly stable （i.e., with stiffness greater than the critical value） spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical mag- nitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/（b - a） when k = kcr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %-16 % for a relatively large ct = 0.56 with （b - a）/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip- law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k 〉 kcr（V,）, a spring-slider system with the slowness law is much more stable than with the slip law,suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~ 10 orders of magnitude.展开更多
We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous （SD） oscillator proposed by the Cao et al. and the classical moving belt. The movin...We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous （SD） oscillator proposed by the Cao et al. and the classical moving belt. The moving belt friction is modeled as the Coulomb friction to formulate the mathematical model of the proposed self-excited SD oscillator. The equilibrium states of the unperturbed system are obtained to show the complex equilibrium bifurcations. Phase portraits are depicted to present the hyperbolic structure transition, the multiple stick regions, and the friction-induced asymmetry phenomena. The numerical simulations are carried out to demonstrate the friction-induced vibration of multiple stick-slip phenomena and the stick-slip chaos in the perturbed self-excited system. The results presented here provide an opportunity for us to get insight into the mechanism of the complex friction-induced nonlinear dynamics in mechanical engineering and geography.展开更多
This paper sums up the research situation. At the influence of friction, a simulator exists the phenomenon of low-speed stick-slip. The character of low-speed of simulator is affected seriously. According to the phase...This paper sums up the research situation. At the influence of friction, a simulator exists the phenomenon of low-speed stick-slip. The character of low-speed of simulator is affected seriously. According to the phase plane method, algebra analyzing method and Lyapunov theory, the paper gives a criterion about overcoming low-speed stick-slip. Making use of the criterion, we can conclude the relationship between system parameters and low-speed stick-slip, and determine the condition where the parameters of PID controller should satisfy, for the purpose of overcoming low-speed stick-slip and has not the phenomenon of low-speed stick-slip. This method is simple and easy to carry out and the experiments show that the condition is correct.展开更多
Two stochastic models on simple random system with friction were developed. One of them was a discrete model by a two-dimensional mean map applied to describe random stick-slip motion. The numerical examples show, tha...Two stochastic models on simple random system with friction were developed. One of them was a discrete model by a two-dimensional mean map applied to describe random stick-slip motion. The numerical examples show, that external noise can reduce the complexity of the system behavior. Secondly, a probability model described was established with coexistence of stick-slip and slip motions. The numerical results point out that this model possesses pure stochastic behavior.展开更多
This study investigates controlled micro/nano manipulation of polydimethylsiloxane (PDMS) using Atomic Force Microscopy (AFM). Lithographic results revealed stick-slip phenomena along the slow scan direction. Varying ...This study investigates controlled micro/nano manipulation of polydimethylsiloxane (PDMS) using Atomic Force Microscopy (AFM). Lithographic results revealed stick-slip phenomena along the slow scan direction. Varying the normal loading force, scan size, scan number and contact conditions allowed the control of certain lithographic outcomes e.g., channel spacing. The PDMS surface experienced significant in-plane deformation in response to the tip-induced lateral force. This displacement increased with increasing loading force, creating greater spacing between channels in the slow scan direction. Simultaneous generation of a lateral displacement in the fast scan direction caused a decrease in channel length with increasing loading force due to an increase in static friction with normal force, resulting in a greater surface relaxation, and shorter track length of dynamic friction. By controlling both the loading force and the number of scans over an area, frictional tiers were produced.展开更多
基金supported by the NIED research project titled‘‘Development of the Earthquake Activity Monitoring and Forecasting,’’the JSPS KAKENHI Grant No.23340131the State Key Laboratory of Earthquake Dynamics,Institute of Geology,CEA(LED2014A06)
文摘This paper reports stick-slip behaviors of Indian gabbro as studied using a new large-scale biaxial friction apparatus, built in the National Research Institute for Earth Science and Disaster Prevention （NIED）, Tsukuba, Japan. The apparatus consists of the existing shaking table as the shear-loading device up to 3,600 kN, the main frame for holding two large rectangular prismatic specimens with a sliding area of 0.75 m^2 and for applying normal stresses an up to 1.33 MPa, and a reaction force unit holding the stationary specimen to the ground. The shaking table can produce loading rates v up to 1.0 m/s, accelerations up to 9.4 m/s^2, and displacements d up to 0.44 m, using four servocontrolled actuators. We report results from eight preliminary experiments conducted with room humidity on the same gabbro specimens at v = 0.1-100 mm/s and an = 0.66-1.33 MPa, and with d of about 0.39 m. The peak and steady-state friction coefficients were about 0.8 and 0.6, respectively, consistent with the Byerlee friction. The axial force drop or shear stress drop during an abrupt slip is linearly proportional to the amount of displacement, and the slope of this rela- tionship determines the stiffness of the apparatus as 1.15 × 10^8 N/m or 153 MPa/m for the specimens we used. This low stiffness makes fault motion very unstable and the overshooting of shear stress to a negative value was recognized in some violent stick-slip events. An abrupt slip occurred in a constant rise time of 16-18 ms despite wide variation of the stress drop, and an average velocity during an abrupt slip is linearly proportional to the stress drop. The use of a large-scale shaking table has a great potential in increasing the slip rate and total displacement in biaxial friction experiments with large specimens.
文摘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.
基金Projects (51101126, 51071123) supported by the National Natural Science Foundation of ChinaProjects (20110491684, 2012T50817) supported by the China Postdoctoral Science FoundationProject (20110942K) supported by the Open Fund of State Key Laboratory of Powder Metallurgy of Central South University, China
文摘An innovative physical simulation apparatus, including high speed camera, red thermal imaging system, and mechanical quantity sensor, was used to investigate the friction heat generation and atom diffusion behavior during Mg-Ti friction welding process. The results show that the friction coefficient mainly experiences two steady stages. The first steady stage corresponds to the Coulomb friction with material abrasion. The second steady stage corresponds to the stick friction with fully plastic flow. Moreover, the increasing rates of axial displacement, temperature and friction coefficient are obviously enhanced with the increase of rotation speed and axial pressure. It can also be found that the there exists rapid diffusion phenomenon in the Mg-Ti friction welding system. The large deformation activated diffusion coefficient is about 105 higher than that activated by thermal.
基金Project supported by the National Natural Science Foundation of China(No.11772021)
文摘The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively.The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem(LCP) algorithm and the trial-and-error algorithm.Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.
基金support from the National Natural Science Foundation of China (Grants 11272177, 11422218, 11432008)the National Basic Research Program of China (Grants 2013CB933003, 2013CB934201 and 2015CB351903)+2 种基金the Tsinghua University Initiative Scientific Research Programthe Thousand Young Talents Program of Chinathe financial support from China Postdoctoral Science Foundation (Grant 2014M562055)
文摘Although atomic stick–slip friction has been extensively studied since its first demonstration on graphite,the physical understanding of this dissipation-dominated phenomenon is still very limited. In this work, we perform molecular dynamics（MD） simulations to study the frictional behavior of a diamond tip sliding over a graphite surface. In contrast to the common wisdom, our MD results suggest that the energy barrier associated lateral sliding（known as energy corrugation） comes not only from interaction between the tip and the top layer of graphite but also from interactions among the deformed atomic layers of graphite. Due to the competition of these two subentries, friction on graphite can be tuned by controlling the relative adhesion of different interfaces.For relatively low tip-graphite adhesion, friction behaves normally and increases with increasing normal load. However,for relatively high tip-graphite adhesion, friction increases unusually with decreasing normal load leading to an effectively negative coefficient of friction, which is consistent with the recent experimental observations on chemically modified graphite. Our results provide a new insight into the physical origins of energy corrugation in atomic scale friction.
基金supported by the National Natural Science Foundation of China(Grants 11272155,11132007,and11502113)the 333 Project of Jiangsu Province in China(Grant BRA2011172)the Fundamental Research Funds for Central Universities(Grant 30920130112009)
文摘A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid modeling method, dynamic equations of the system, which include all states（before, during, and after the collision）are obtained. Simulation results of a concrete example are compared with the results obtained from two other models： a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.
文摘This paper, using Karnopp's model of friction force and phase plane method, studies the stick-slip motion of the flexible drive mechanism. It is explained that a sudden drop of friction force is the essential source of stick-slip motion when the sliding is impending. A new criterion for occurrence of stick-slip motion is established. The stick-slip region and the stable region in a parameter plane are separated by a critical parameter curve. Moreover, for the stick-slip motion of the flexible drive mechanism without viscous damping, a parameter expression is obtained. The results may be used in design of the flexible drive mechanism.
基金supported by the National Natural Science Foundation of China (Nos.51575378, 11272228 and 11332008)
文摘A disc-pad friction system is modelled as that two moving pads act symmetrically on an annular beam with flexible boundary condition.Simulation procedure is proposed to deal with the moving interactions and calculation is carried out by using the finite difference method,which shows that only the first-order mode vibration of the beam can be induced.Then the partial differential equation of motion of the disk is reduced to a first-order mode vibration system with time-varying stiffness.As the disk speed is decreased below the critical speeds,the relative equilibrium of the pad on the disk loses its stability and stick-slip type limit cycle vibrations are resulted in all directions′movements.Acceleration of the disk motion on the frictional instability is also investigated.The period of stick-slip vibration with large amplitude will be shortened with higher moving deceleration.
基金supported by the National Natural Science Foundation of China under Grant Nos.40574080 and 41274186
文摘Incorporating rate and state friction laws, stability of linearly stable （i.e., with stiffness greater than the critical value） spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical mag- nitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/（b - a） when k = kcr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %-16 % for a relatively large ct = 0.56 with （b - a）/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip- law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k 〉 kcr（V,）, a spring-slider system with the slowness law is much more stable than with the slip law,suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~ 10 orders of magnitude.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372082 and 11572096)the National Basic Research Program of China(Grant No.2015CB057405)
文摘We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous （SD） oscillator proposed by the Cao et al. and the classical moving belt. The moving belt friction is modeled as the Coulomb friction to formulate the mathematical model of the proposed self-excited SD oscillator. The equilibrium states of the unperturbed system are obtained to show the complex equilibrium bifurcations. Phase portraits are depicted to present the hyperbolic structure transition, the multiple stick regions, and the friction-induced asymmetry phenomena. The numerical simulations are carried out to demonstrate the friction-induced vibration of multiple stick-slip phenomena and the stick-slip chaos in the perturbed self-excited system. The results presented here provide an opportunity for us to get insight into the mechanism of the complex friction-induced nonlinear dynamics in mechanical engineering and geography.
基金This project was supported by the National Fund of Defense Pre research.
文摘This paper sums up the research situation. At the influence of friction, a simulator exists the phenomenon of low-speed stick-slip. The character of low-speed of simulator is affected seriously. According to the phase plane method, algebra analyzing method and Lyapunov theory, the paper gives a criterion about overcoming low-speed stick-slip. Making use of the criterion, we can conclude the relationship between system parameters and low-speed stick-slip, and determine the condition where the parameters of PID controller should satisfy, for the purpose of overcoming low-speed stick-slip and has not the phenomenon of low-speed stick-slip. This method is simple and easy to carry out and the experiments show that the condition is correct.
文摘Two stochastic models on simple random system with friction were developed. One of them was a discrete model by a two-dimensional mean map applied to describe random stick-slip motion. The numerical examples show, that external noise can reduce the complexity of the system behavior. Secondly, a probability model described was established with coexistence of stick-slip and slip motions. The numerical results point out that this model possesses pure stochastic behavior.
文摘This study investigates controlled micro/nano manipulation of polydimethylsiloxane (PDMS) using Atomic Force Microscopy (AFM). Lithographic results revealed stick-slip phenomena along the slow scan direction. Varying the normal loading force, scan size, scan number and contact conditions allowed the control of certain lithographic outcomes e.g., channel spacing. The PDMS surface experienced significant in-plane deformation in response to the tip-induced lateral force. This displacement increased with increasing loading force, creating greater spacing between channels in the slow scan direction. Simultaneous generation of a lateral displacement in the fast scan direction caused a decrease in channel length with increasing loading force due to an increase in static friction with normal force, resulting in a greater surface relaxation, and shorter track length of dynamic friction. By controlling both the loading force and the number of scans over an area, frictional tiers were produced.
