Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of rest...Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.展开更多
This letter presents a theoretical model of the normal （head-on） collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. Aft...This letter presents a theoretical model of the normal （head-on） collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. After the contact force law between the contacted spheres during a collision is phenomenologically formulated in terms of the compression or overlap displacement under considera- tion of an elastic-plastic loading and a plastic unloading subprocesses, the coefficient of restitution is gained by the dynamic equation of the contact process once an initial impact velocity is input. It is found that the theoretical predictions of the coefficient of restitution varying with the impact velocity are well in agreement with the existing experimental characteristics which are fitted by the explicit formula.展开更多
In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies ...In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies we used MatLab. In simulation to approach to the real case we used an assumption of additional virtual body’s position and velocity for characterizing material of the body which is involved to express the restitution coefficient. The graphic animation program is developed based on ODE for the computer simulation of the proposed graphical method. Additionally, we determined this new characteristic for some sport game balls such as basketball, volleyball, etc.展开更多
In this paper, the dynamics of a transverse plane of a rotary coating disk of a binary mixture system comprising sand and urea particles were simulated using the two-fluid model along with the kinetic theory of granul...In this paper, the dynamics of a transverse plane of a rotary coating disk of a binary mixture system comprising sand and urea particles were simulated using the two-fluid model along with the kinetic theory of granular flow in Fluent 19.1. Although some parameters relating to the material properties and size of the rotary coating disk have been researched, the effects of both drag force and restitution coefficient on the flow characteristics have yet to be examined. Thus, this paper numerically examines the effect of the inclusion of drag models and particle-particle restitution coefficients on particle dynamics in a rotary disk operating in the rolling regime of the granular bed. Three particle-particle drag models were considered: the Schiller-Naumann, Syamlal-O’Brien, and Gidaspow. The Syamlal-O’Brien and Gidaspow models were both able to successfully simulate particle segregation in a perfect rolling regime, whereas the Schiller-Naumann drag model appeared to be unable to predict the segregation of the particles and the rolling flow regime under the assumed conditions. Four different values of the restitution coefficient were also investigated: 0.7, 0.8, 0.9, and 0.95. The higher restitution values of 0.9 and 0.95 were found to substantially affect flow characteristics, ensuring suitable rolling regime behaviour for the bed during the rotational movement. The lower restitution coefficients of 0.7 and 0.8, on the other hand, indicated that irregular velocity vectors could be obtained in the active region of the granular bed.展开更多
The restitution coefficient is an important elementary physical parameter related to the research and development of agricultural machinery.The kinematic model of maize seed in the falling and impacting processes was ...The restitution coefficient is an important elementary physical parameter related to the research and development of agricultural machinery.The kinematic model of maize seed in the falling and impacting processes was developed to measure the restitution coefficient between maize seed and soil.A test bench for measuring the restitution coefficient was designed and built referred to the theory of mirror reflection.The velocities for impacting maize seed were measured and analyzed in a three-dimensional space via high-speed photography,and then restitution coefficients of in different impact conditions were obtained.On this basis,this study took flat dent seed and round seed as samples.Single factor tests were conducted to analyze the influences of these factors on the restitution coefficient.The impact angle,falling height,soil compaction,soil moisture,maize moisture content and different parts of seed were selected as test factors.The corresponding regression equations were obtained by analysis.The results showed that,as the impact angle was bigger than 25°,the restitution coefficient increased with the increase of impact angle.The restitution coefficient had a linear decreasing trend with the increase of falling height.As the soil compaction strength was 200-350 kPa,the restitution coefficient increased with the increase of soil compaction.As the soil compaction strength was larger than 350 kPa,the changing trend of the restitution coefficient was relatively stable.As the soil moisture content was 13.5%-18%,the restitution coefficient decreased with the increase of soil moisture.As the soil moisture content was 18%,the restitution coefficient was the minimum.As the maize moisture content was 11%-16%,the restitution coefficient decreased with the increase of maize moisture content.The rotational motion always occurred in falling process of flat dent seed and round seed.The probabilities of crown part and lateral part of maize seed impacting with soil were the highest,and the restitution coefficient between crown part and soil was higher than that of other parts in the same condition.展开更多
Restitution coefficient(RC)of garlic bulb is an important mechanical property that is required to establish the kinematics model of bulb collision and research the damage mechanism of bulb collision.In this study,kine...Restitution coefficient(RC)of garlic bulb is an important mechanical property that is required to establish the kinematics model of bulb collision and research the damage mechanism of bulb collision.In this study,kinetic equations of bulb collision were established based on Hertz's contact theory.The kinematics characteristics,elastoplastic deformation and contact damage during bulb collision were analyzed by using high-speed photography.The effects of bulb mass,moisture content,collision material,material thickness and release height on the RC were investigated by mixed orthogonal experiments and single-factor experiments.The results showed that the movement of bulb in the compression stage was translation,and the movement in the rebound stage was translation and rotation.During collision,the larger the rotational angular velocity of the bulb was,the smaller the measured RC would be.The contact damage of bulb included internal damage of the tissue,epidermis stretch and tear.The significance of effects of factors on RC decreased with the following sequence:collision material,release height,material thickness,bulb mass,and moisture content.Collision material,release height,material thickness,and bulb mass were significant factors.The RC between the bulb and Q235,nylon,and rubber decreased sequentially.The RC decreased with the increase of release height and bulb mass.The RC increased with the increase of material thickness of Q235,while it decreased with the increase of material thickness of rubber or Nylon.The determination coefficients of the regression equations between the significant factors and the RC were all greater than 0.96.The results will be helpful for damage mechanism analysis and design of garlic production equipment.展开更多
Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed. In the present work, earlier work （Loha, Chattopadhyay, ＆ Chatterjee, 2013） ...Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed. In the present work, earlier work （Loha, Chattopadhyay, ＆ Chatterjee, 2013） was extended to study the effect of the elasticity of particle collision on the hydrodynamic behavior of a bubbling fluidized bed filled with 530-~m particles. The Eulerian-Eulerian two-fluid model was used to simulate the hydrodynamics of the bubbling fluidized bed, where the solid-phase properties were calculated by applying the kinetic theory of granular flow. To investigate the effect of the elasticity of particle collision, different values of the coefficient of restitution were applied in the simulation and their effects were studied in detail. Simulations were performed for two different solid-phase wall boundary conditions. No bubble formation was observed for perfectly elastic collision. The bubble formation started as soon as the coefficient of restitution was set below 1.0, and the space occupied by bubbles in the bed increased with a decrease in the coefficient of restitution. Simulation results were also compared with experimental data available in the literature, and good agreement was found for coefficients of restitution of 0.95 and 0.99.展开更多
The coefficient of restitution is widely used to characterize the energy dissipation rate in numerical simulations involving particle collisions. The challenge in measuring the coefficient of restitution is the strong...The coefficient of restitution is widely used to characterize the energy dissipation rate in numerical simulations involving particle collisions. The challenge in measuring the coefficient of restitution is the strong scatter seen in experimental data that results from varying particle properties, i.e. shape and surface roughness, and from imperfections in the experimental technique. To minimize this scattering, a novel experimental setup was developed based on two synchronized high-speed cameras capturing the collision behaviour of a particle in three dimensions. To measure the wet restitution coefficient, which describes particle impact in the presence of a liquid layer in the contact region, additional accuracy can be achieved by measuring the liquid layer thickness by a high-precision optical confocal sensor. The coefficient of restitution was measured for glass particles with two different diameters, at different relative velocities and liquid layer thicknesses, with a focus on small collision velocities and thin liquid layers, using both the improved （three dimensional） and the conventional （two dimensional） approaches to quantify the improvement of the new method＇s accuracy.展开更多
The restitution coefficient(RC)of cotton stalks is an important elementary physical parameter that is required to establish the crushing mechanical model and research the film residue separation machinery.In this stud...The restitution coefficient(RC)of cotton stalks is an important elementary physical parameter that is required to establish the crushing mechanical model and research the film residue separation machinery.In this study,the calculation method of restitution coefficient considering the rotation motion of stalk-shaped agricultural materials was derived based on the principle of kinematics and the energy restitution coefficient method,and a test bench for measuring the RC was designed and built.The effects of collision material,moisture content,length,diameter,release height,and collision angle respectively on the RC were investigated by single-factor experiments and orthogonal experiments,and the regression models between influence factors and the RC were established.The results showed that Q235 showed the highest value of the RC,and it was followed by cotton stalks and soil lumps,sequentially.The RC of cotton stalks decreased with the increase of moisture content and diameter,while it increased at first and then decreased with the increase of length.As the release height was less than 500 mm,the RC increased with the increased release height.As the collision angle was less than 40°,the RC showed a linear increasing trend.The significance of the effects of factors on RC decreased with the following sequence:collision angle,length,release height,diameter,and moisture content.Length,collision angle,and release height were extremely significant.The contrast test results showed that the values based on Newton’s restitution coefficient method were smaller than that based on the energy restitution coefficient method.The verification test showed that the predicted rebound height of cotton stalks calculated based on the energy restitution coefficient method was closer to the actual rebound height,and the relative error was less than 5%.展开更多
Although the coefficient of restitution was originally thought to be only a material property, the coefficient of restitution also depends upon initial conditions as well as on the frictional effect for oblique collis...Although the coefficient of restitution was originally thought to be only a material property, the coefficient of restitution also depends upon initial conditions as well as on the frictional effect for oblique collisions. The objective of this paper is to demonstrate a method for obtaining the coefficient of restitution for oblique collisions and thereby to provide a theoretical guide for collision experiments. In this paper, we derive expressions for the energetic coefficient of restitution (e*) based on general normal contact deformation law, by which the value of e* can be obtained according to the initial conditions. An example shows that the results calculated by the derived expressions are reasonable.展开更多
基金Supported by Joint Fund of the Ministry of Education of China (Grant No.8091B022203)Youth Talent Support Project (Grant No.2022-JCJQ-QT-059)。
文摘Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.
基金supported by the Innovation Team Fund of the National Natural Science Foundation of China(11121202)
文摘This letter presents a theoretical model of the normal （head-on） collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. After the contact force law between the contacted spheres during a collision is phenomenologically formulated in terms of the compression or overlap displacement under considera- tion of an elastic-plastic loading and a plastic unloading subprocesses, the coefficient of restitution is gained by the dynamic equation of the contact process once an initial impact velocity is input. It is found that the theoretical predictions of the coefficient of restitution varying with the impact velocity are well in agreement with the existing experimental characteristics which are fitted by the explicit formula.
文摘In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies we used MatLab. In simulation to approach to the real case we used an assumption of additional virtual body’s position and velocity for characterizing material of the body which is involved to express the restitution coefficient. The graphic animation program is developed based on ODE for the computer simulation of the proposed graphical method. Additionally, we determined this new characteristic for some sport game balls such as basketball, volleyball, etc.
文摘In this paper, the dynamics of a transverse plane of a rotary coating disk of a binary mixture system comprising sand and urea particles were simulated using the two-fluid model along with the kinetic theory of granular flow in Fluent 19.1. Although some parameters relating to the material properties and size of the rotary coating disk have been researched, the effects of both drag force and restitution coefficient on the flow characteristics have yet to be examined. Thus, this paper numerically examines the effect of the inclusion of drag models and particle-particle restitution coefficients on particle dynamics in a rotary disk operating in the rolling regime of the granular bed. Three particle-particle drag models were considered: the Schiller-Naumann, Syamlal-O’Brien, and Gidaspow. The Syamlal-O’Brien and Gidaspow models were both able to successfully simulate particle segregation in a perfect rolling regime, whereas the Schiller-Naumann drag model appeared to be unable to predict the segregation of the particles and the rolling flow regime under the assumed conditions. Four different values of the restitution coefficient were also investigated: 0.7, 0.8, 0.9, and 0.95. The higher restitution values of 0.9 and 0.95 were found to substantially affect flow characteristics, ensuring suitable rolling regime behaviour for the bed during the rotational movement. The lower restitution coefficients of 0.7 and 0.8, on the other hand, indicated that irregular velocity vectors could be obtained in the active region of the granular bed.
基金the National Science and Technology Support Plan Project(2014BAD06B04).
文摘The restitution coefficient is an important elementary physical parameter related to the research and development of agricultural machinery.The kinematic model of maize seed in the falling and impacting processes was developed to measure the restitution coefficient between maize seed and soil.A test bench for measuring the restitution coefficient was designed and built referred to the theory of mirror reflection.The velocities for impacting maize seed were measured and analyzed in a three-dimensional space via high-speed photography,and then restitution coefficients of in different impact conditions were obtained.On this basis,this study took flat dent seed and round seed as samples.Single factor tests were conducted to analyze the influences of these factors on the restitution coefficient.The impact angle,falling height,soil compaction,soil moisture,maize moisture content and different parts of seed were selected as test factors.The corresponding regression equations were obtained by analysis.The results showed that,as the impact angle was bigger than 25°,the restitution coefficient increased with the increase of impact angle.The restitution coefficient had a linear decreasing trend with the increase of falling height.As the soil compaction strength was 200-350 kPa,the restitution coefficient increased with the increase of soil compaction.As the soil compaction strength was larger than 350 kPa,the changing trend of the restitution coefficient was relatively stable.As the soil moisture content was 13.5%-18%,the restitution coefficient decreased with the increase of soil moisture.As the soil moisture content was 18%,the restitution coefficient was the minimum.As the maize moisture content was 11%-16%,the restitution coefficient decreased with the increase of maize moisture content.The rotational motion always occurred in falling process of flat dent seed and round seed.The probabilities of crown part and lateral part of maize seed impacting with soil were the highest,and the restitution coefficient between crown part and soil was higher than that of other parts in the same condition.
基金This work was supported by the National Natural Science Foundation of China(Grant No.51805282)Funds for Central Universities,China(XDJK2018AC001)National Key R&D Program of China(2017YFD0701305-02).
文摘Restitution coefficient(RC)of garlic bulb is an important mechanical property that is required to establish the kinematics model of bulb collision and research the damage mechanism of bulb collision.In this study,kinetic equations of bulb collision were established based on Hertz's contact theory.The kinematics characteristics,elastoplastic deformation and contact damage during bulb collision were analyzed by using high-speed photography.The effects of bulb mass,moisture content,collision material,material thickness and release height on the RC were investigated by mixed orthogonal experiments and single-factor experiments.The results showed that the movement of bulb in the compression stage was translation,and the movement in the rebound stage was translation and rotation.During collision,the larger the rotational angular velocity of the bulb was,the smaller the measured RC would be.The contact damage of bulb included internal damage of the tissue,epidermis stretch and tear.The significance of effects of factors on RC decreased with the following sequence:collision material,release height,material thickness,bulb mass,and moisture content.Collision material,release height,material thickness,and bulb mass were significant factors.The RC between the bulb and Q235,nylon,and rubber decreased sequentially.The RC decreased with the increase of release height and bulb mass.The RC increased with the increase of material thickness of Q235,while it decreased with the increase of material thickness of rubber or Nylon.The determination coefficients of the regression equations between the significant factors and the RC were all greater than 0.96.The results will be helpful for damage mechanism analysis and design of garlic production equipment.
文摘Collision between particles plays an important role in determining the hydrodynamic characteristics of gas-solid flow in a fluidized bed. In the present work, earlier work （Loha, Chattopadhyay, ＆ Chatterjee, 2013） was extended to study the effect of the elasticity of particle collision on the hydrodynamic behavior of a bubbling fluidized bed filled with 530-~m particles. The Eulerian-Eulerian two-fluid model was used to simulate the hydrodynamics of the bubbling fluidized bed, where the solid-phase properties were calculated by applying the kinetic theory of granular flow. To investigate the effect of the elasticity of particle collision, different values of the coefficient of restitution were applied in the simulation and their effects were studied in detail. Simulations were performed for two different solid-phase wall boundary conditions. No bubble formation was observed for perfectly elastic collision. The bubble formation started as soon as the coefficient of restitution was set below 1.0, and the space occupied by bubbles in the bed increased with a decrease in the coefficient of restitution. Simulation results were also compared with experimental data available in the literature, and good agreement was found for coefficients of restitution of 0.95 and 0.99.
文摘The coefficient of restitution is widely used to characterize the energy dissipation rate in numerical simulations involving particle collisions. The challenge in measuring the coefficient of restitution is the strong scatter seen in experimental data that results from varying particle properties, i.e. shape and surface roughness, and from imperfections in the experimental technique. To minimize this scattering, a novel experimental setup was developed based on two synchronized high-speed cameras capturing the collision behaviour of a particle in three dimensions. To measure the wet restitution coefficient, which describes particle impact in the presence of a liquid layer in the contact region, additional accuracy can be achieved by measuring the liquid layer thickness by a high-precision optical confocal sensor. The coefficient of restitution was measured for glass particles with two different diameters, at different relative velocities and liquid layer thicknesses, with a focus on small collision velocities and thin liquid layers, using both the improved （three dimensional） and the conventional （two dimensional） approaches to quantify the improvement of the new method＇s accuracy.
基金This work was financially supported by the funding of the Southern Xinjiang Key Industry Innovation and Development Support Program(Grant No.2020DB008)the Graduate Education Innovation Project of Xinjiang Uygur Autonomous Region(Grant No.XJ2022G085)+1 种基金the Open Fund of Jiangsu Province and Education Ministry Co-sponsored Synergistic Innovation Center of Modern Agricultural Equipment(Grant No.XTCX2006)the National Natural Science Foundation of China(Grant No.52065058).
文摘The restitution coefficient(RC)of cotton stalks is an important elementary physical parameter that is required to establish the crushing mechanical model and research the film residue separation machinery.In this study,the calculation method of restitution coefficient considering the rotation motion of stalk-shaped agricultural materials was derived based on the principle of kinematics and the energy restitution coefficient method,and a test bench for measuring the RC was designed and built.The effects of collision material,moisture content,length,diameter,release height,and collision angle respectively on the RC were investigated by single-factor experiments and orthogonal experiments,and the regression models between influence factors and the RC were established.The results showed that Q235 showed the highest value of the RC,and it was followed by cotton stalks and soil lumps,sequentially.The RC of cotton stalks decreased with the increase of moisture content and diameter,while it increased at first and then decreased with the increase of length.As the release height was less than 500 mm,the RC increased with the increased release height.As the collision angle was less than 40°,the RC showed a linear increasing trend.The significance of the effects of factors on RC decreased with the following sequence:collision angle,length,release height,diameter,and moisture content.Length,collision angle,and release height were extremely significant.The contrast test results showed that the values based on Newton’s restitution coefficient method were smaller than that based on the energy restitution coefficient method.The verification test showed that the predicted rebound height of cotton stalks calculated based on the energy restitution coefficient method was closer to the actual rebound height,and the relative error was less than 5%.
文摘Although the coefficient of restitution was originally thought to be only a material property, the coefficient of restitution also depends upon initial conditions as well as on the frictional effect for oblique collisions. The objective of this paper is to demonstrate a method for obtaining the coefficient of restitution for oblique collisions and thereby to provide a theoretical guide for collision experiments. In this paper, we derive expressions for the energetic coefficient of restitution (e*) based on general normal contact deformation law, by which the value of e* can be obtained according to the initial conditions. An example shows that the results calculated by the derived expressions are reasonable.
