This paper is concerned with the determination of the normal force-displacement （NFD） relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed...This paper is concerned with the determination of the normal force-displacement （NFD） relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM.展开更多
Spiral springs have a wide range of applications in various fields.As a result of the complexity of friction,few theoretical analyses of spring belts under static loading have been carried out.Considering the piecewis...Spiral springs have a wide range of applications in various fields.As a result of the complexity of friction,few theoretical analyses of spring belts under static loading have been carried out.Considering the piecewise smooth property of the whole contact area,a simplified static model of spiral springs under loading is established in this paper.Besides,three main stress and friction distribution areas of the spring belt are proposed,namely,internal,transitional,and external regions.Since the outermost side of the spring is not subject to any pressure,a recursive method is adopted from the outside to the inside.The model provides the parameter conditions,i.e.,the internal and external forces are independent or dependent.Therefore,the case that the whole contact region of the spring belt has one subregion,two subregions,and three subregions is obtained.The model gives a theoretical basis for the parameter optimization of spiral springs.展开更多
We study experimentally and theoretically the planar dynamics of purely rolling prisms on a rough ramp, where the rolling motion is interrupted intermittently by edge impacts. The experiments were carried out for pris...We study experimentally and theoretically the planar dynamics of purely rolling prisms on a rough ramp, where the rolling motion is interrupted intermittently by edge impacts. The experiments were carried out for prisms made of different materials and having different geometries. We found that the angular velocities of the rolling prisms are material-independent, but they change significantly with their geometry. We modelled the dynamics of edge impacts by considering a socalled detachment front propagating across the contact interface. The detachment front represents the moving boundary between a detached region and a stress region that coexist within the interface plane. The theoretical analysis indicates that the detachment front can be characterized by a scale number, whose value converges to 0.4050 for prisms having large number of edges. A new jump rule for edge impacts is then developed, by which we can accurately reproduce the experimental observations, and explain why the motion of the prism is material-independent.展开更多
In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the...In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the Lagrangian equations of the first type to establish the nonlinear differential algebraic equations(DAEs),leaving nine coupled differential equations,six contact equations,two holonomic constraint equations and four nonholonomic constraint equations.We then present a complete description of hands-free circular motions,in which the time-dependent variables are eliminated through a rotation transformation.We find that the circular motions,similar to those of the bicycle moving on a horizontal surface,nominally fall into four solution families,characterized by four curves varying with the angular speed of the front wheel.Then,we numerically investigate how the topological profiles of these curves change with the parameter of the revolution surface.Furthermore,we directly linearize the nonlinear DAEs,from which a reduced linearized system is obtained by removing the dependent coordinates and counting the symmetries arising from cyclic coordinates.The stability of the circular motion is then analyzed according to the eigenvalues of the Jacobian matrix of the reduced linearized system around the equilibrium position.We find that a stable circular motion exists only if the curvature of the revolution surface is very small and it is limited in small sections of solution families.Finally,based on the numerical simulation of the original nonlinear DAEs system,we show that the stable circular motion is not asymptotically stable.展开更多
The study of soil and rigid body system interactions is very important for the exploration of the Moon and Mars worldwide.The discrete element method(DEM)is a relatively accurate simulation method to study dry sand so...The study of soil and rigid body system interactions is very important for the exploration of the Moon and Mars worldwide.The discrete element method(DEM)is a relatively accurate simulation method to study dry sand soil mechanical properties.However,it is not suitable for bodies that are in mutual contact,connected due to constraints or have complex inertia properties due to their geometry.An efficient combination of the two-dimensional discrete element and multibody dynamic modeling method is proposed to solve the problem,in which the contacts and frictions among the granular spheres and the multibody system,including the smooth and rough rigid bodies,are taken into account.In this work,the soil field is modeled by a two-dimensional DEM,and the dynamics of the constrained rigid body system are modeled by the Cartesian method.A detection algorithm is developed to address the interactions between spherical discrete elements and roughly shaped rigid bodies.The advantage of this coupled method is that it enables the simultaneous capture of both responses.Finally,the program is verified by simulation experiments of the three-ball collision and the collision among the rectangular bars and the three balls.Based on this,the movement of the toothed wheel in the granular matter is analyzed,and the results show that the wheel with six teeth and 30°inclination has the fastest forward speed.In extraterrestrial objects,the wheel grip worsens,but the forward speed first increases and then decreases with decreasing gravity acceleration and loads on wheels,which proves that the coupled two-dimensional DEM and multibody dynamic program is effective in solving engineering problems.展开更多
The onset of frictional motion couples complex spatiotemporal dynamics of discrete contacts with different orders of magnitude at time and length scales.In order to reveal how these individual scales affect the fricti...The onset of frictional motion couples complex spatiotemporal dynamics of discrete contacts with different orders of magnitude at time and length scales.In order to reveal how these individual scales affect the frictional sliding,we establish a 2D multiscale spring-block model for the frictional sliding at an elastic slider-rigid interface.In this model,the rupture of frictional interface is described by three different types of locally microscopic motion:pinned,sliding and dislocated states.By using realistic boundary conditions,our numerical results can precisely reproduce the loading curves found in previous experiments.The precursor events,corresponding to a discrete sequence of rapid crack-like fronts propagating partially in the contact zone,can also be shown in our simulation.From the analysis of the microscopic motion,we characterize the evolution of the real contact area and the corresponding interface motion at the mesoscale level,and show that the evolution corresponds to four distinct and inter-related phases:detachment,fast and slow slip motion,as well as the rest of slip.These mesoscale behaviors are completely consistent with the existing experimental results and their physical mechanisms can be explained by the detailed information of the numerical simulation.The study is established on a bottom-up multiscale model which provides a comprehensive picture about the complex spatiotemporal dynamics of frictional sliding.展开更多
The dynamic dashpot models are widely used in EDEM commercial software.However,most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force inclu...The dynamic dashpot models are widely used in EDEM commercial software.However,most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact velocity.Moreover,the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact phase.These two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular chain.Therefore,this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular matters.First,the entire contact process is divided into three different phases:elastic,elastoplastic,and full plastic phases.The Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic phase.Hertz contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma‐Liu(ML)model in each time step.Second,the whole contact behavior is treated as a linear mass‐spring‐damper model,and the damping factor is obtained by solving the single‐degree‐freedom underdamped vibration equation.The new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors,which not only removes the initial im-pact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic phase.Finally,a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental data.The simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.展开更多
基金The project supported by the National Natural Science Foundation of China(10272002:60334030)
文摘This paper is concerned with the determination of the normal force-displacement （NFD） relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM.
基金the National Natural Science Foundation of China(No.11972055)the National Defense Science and Technology Fund in the Technical Field of the Foundation Strengthening Plan(No.2020-JCJQ-JJ-009)the Civil Aerospace Pre-research Project(No.D020206)。
文摘Spiral springs have a wide range of applications in various fields.As a result of the complexity of friction,few theoretical analyses of spring belts under static loading have been carried out.Considering the piecewise smooth property of the whole contact area,a simplified static model of spiral springs under loading is established in this paper.Besides,three main stress and friction distribution areas of the spring belt are proposed,namely,internal,transitional,and external regions.Since the outermost side of the spring is not subject to any pressure,a recursive method is adopted from the outside to the inside.The model provides the parameter conditions,i.e.,the internal and external forces are independent or dependent.Therefore,the case that the whole contact region of the spring belt has one subregion,two subregions,and three subregions is obtained.The model gives a theoretical basis for the parameter optimization of spiral springs.
基金supported by the National Natural Science Foundation of China (No. 11572017)
文摘We study experimentally and theoretically the planar dynamics of purely rolling prisms on a rough ramp, where the rolling motion is interrupted intermittently by edge impacts. The experiments were carried out for prisms made of different materials and having different geometries. We found that the angular velocities of the rolling prisms are material-independent, but they change significantly with their geometry. We modelled the dynamics of edge impacts by considering a socalled detachment front propagating across the contact interface. The detachment front represents the moving boundary between a detached region and a stress region that coexist within the interface plane. The theoretical analysis indicates that the detachment front can be characterized by a scale number, whose value converges to 0.4050 for prisms having large number of edges. A new jump rule for edge impacts is then developed, by which we can accurately reproduce the experimental observations, and explain why the motion of the prism is material-independent.
基金National Natural Science Foundation of China(Grants 11932001 and 11702002).
文摘In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of revolution.We employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the Lagrangian equations of the first type to establish the nonlinear differential algebraic equations(DAEs),leaving nine coupled differential equations,six contact equations,two holonomic constraint equations and four nonholonomic constraint equations.We then present a complete description of hands-free circular motions,in which the time-dependent variables are eliminated through a rotation transformation.We find that the circular motions,similar to those of the bicycle moving on a horizontal surface,nominally fall into four solution families,characterized by four curves varying with the angular speed of the front wheel.Then,we numerically investigate how the topological profiles of these curves change with the parameter of the revolution surface.Furthermore,we directly linearize the nonlinear DAEs,from which a reduced linearized system is obtained by removing the dependent coordinates and counting the symmetries arising from cyclic coordinates.The stability of the circular motion is then analyzed according to the eigenvalues of the Jacobian matrix of the reduced linearized system around the equilibrium position.We find that a stable circular motion exists only if the curvature of the revolution surface is very small and it is limited in small sections of solution families.Finally,based on the numerical simulation of the original nonlinear DAEs system,we show that the stable circular motion is not asymptotically stable.
基金supported by the Key Program of National Natural Science Foundation of China(Grant No.11932001)the General Program of National Natural Science Foundation of China(Grant Nos.11772186 and 11772188)for which the authors are grateful.This research was also supported by the Key Laboratory of Hydrodynamics(Ministry of Education).
文摘The study of soil and rigid body system interactions is very important for the exploration of the Moon and Mars worldwide.The discrete element method(DEM)is a relatively accurate simulation method to study dry sand soil mechanical properties.However,it is not suitable for bodies that are in mutual contact,connected due to constraints or have complex inertia properties due to their geometry.An efficient combination of the two-dimensional discrete element and multibody dynamic modeling method is proposed to solve the problem,in which the contacts and frictions among the granular spheres and the multibody system,including the smooth and rough rigid bodies,are taken into account.In this work,the soil field is modeled by a two-dimensional DEM,and the dynamics of the constrained rigid body system are modeled by the Cartesian method.A detection algorithm is developed to address the interactions between spherical discrete elements and roughly shaped rigid bodies.The advantage of this coupled method is that it enables the simultaneous capture of both responses.Finally,the program is verified by simulation experiments of the three-ball collision and the collision among the rectangular bars and the three balls.Based on this,the movement of the toothed wheel in the granular matter is analyzed,and the results show that the wheel with six teeth and 30°inclination has the fastest forward speed.In extraterrestrial objects,the wheel grip worsens,but the forward speed first increases and then decreases with decreasing gravity acceleration and loads on wheels,which proves that the coupled two-dimensional DEM and multibody dynamic program is effective in solving engineering problems.
基金supported by the National Natural Science Foundation of China(Grant 1193200).
文摘The onset of frictional motion couples complex spatiotemporal dynamics of discrete contacts with different orders of magnitude at time and length scales.In order to reveal how these individual scales affect the frictional sliding,we establish a 2D multiscale spring-block model for the frictional sliding at an elastic slider-rigid interface.In this model,the rupture of frictional interface is described by three different types of locally microscopic motion:pinned,sliding and dislocated states.By using realistic boundary conditions,our numerical results can precisely reproduce the loading curves found in previous experiments.The precursor events,corresponding to a discrete sequence of rapid crack-like fronts propagating partially in the contact zone,can also be shown in our simulation.From the analysis of the microscopic motion,we characterize the evolution of the real contact area and the corresponding interface motion at the mesoscale level,and show that the evolution corresponds to four distinct and inter-related phases:detachment,fast and slow slip motion,as well as the rest of slip.These mesoscale behaviors are completely consistent with the existing experimental results and their physical mechanisms can be explained by the detailed information of the numerical simulation.The study is established on a bottom-up multiscale model which provides a comprehensive picture about the complex spatiotemporal dynamics of frictional sliding.
基金The National Natural Science Foundation of China,Grant/Award Numbers:1193200,12172004Boya Postdoctoral Fellowship of Peking University。
文摘The dynamic dashpot models are widely used in EDEM commercial software.However,most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact velocity.Moreover,the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact phase.These two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular chain.Therefore,this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular matters.First,the entire contact process is divided into three different phases:elastic,elastoplastic,and full plastic phases.The Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic phase.Hertz contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma‐Liu(ML)model in each time step.Second,the whole contact behavior is treated as a linear mass‐spring‐damper model,and the damping factor is obtained by solving the single‐degree‐freedom underdamped vibration equation.The new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors,which not only removes the initial im-pact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic phase.Finally,a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental data.The simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.
