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Journal articles on the topic 'Coefficients of restitution'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Smith, Charles E., and Pao-Pao Liu. "Coefficients of Restitution." Journal of Applied Mechanics 59, no. 4 (1992): 963–69. http://dx.doi.org/10.1115/1.2894067.

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Simplified procedures for predicting post-collision motion in a mechanical system usually incorporate a “coefficient of restitution,” a ratio that must be estimated before the prediction can be completed. Two such ratios have been widely used for some time and a third has been introduced recently by W. J. Stronge. The dependence of these ratios on parameters that characterize various collisions is examined here, using simplifying assumptions about the contact mechanism and with a finite element code. For some collisions all three coefficients of restitution are identical, while significant distinctions can result from other combinations of system configuration, direction of approach velocity, and coefficient of friction.

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2

Cross, Rod. "Coefficients of restitution for a collision." Physics Education 56, no. 6 (2021): 065017. http://dx.doi.org/10.1088/1361-6552/ac1f6e.

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3

Tabakoff, W., and M. F. Malak. "Laser Measurements of Fly Ash Rebound Parameters for Use in Trajectory Calculations." Journal of Turbomachinery 109, no. 4 (1987): 535–40. http://dx.doi.org/10.1115/1.3262144.

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This paper describes an experimental method used to find particle restitution coefficients. The equations that govern the motion of solid particles suspended by a compressible gas flow through a turbomachine depend on the restitution coefficients. Analysis of the data obtained by a laser-Doppler velocimeter (LDV) system of the collision phenomenon gives the restitution ratios as a function of the incidence angle. From these ratios, the particle velocity components after collision are computed and used as the initial conditions to the solution of the governing equations of motion for particle trajectories. The erosion of metals impacted by small dust particles can be calculated by knowing the restitution coefficients. The alloy used in this investigation was 410 stainless steel.

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4

Maghras, E. "Restitution des coefficients d'ondelettes des signaux filtrés." Colloquium Mathematicum 68, no. 2 (1995): 265–83. http://dx.doi.org/10.4064/cm-68-2-265-283.

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5

Wu, C. Y., C. Thornton, and L. Y. Li. "Coefficients of restitution for elastoplastic oblique impacts." Advanced Powder Technology 14, no. 4 (2003): 435–48. http://dx.doi.org/10.1163/156855203769710663.

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6

Ishikawa, H. "Restitution Coefficients in Car-to-Car Collisions." JSAE Review 16, no. 1 (1995): 103. http://dx.doi.org/10.1016/0389-4304(95)94779-m.

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7

Lu, Chung-Jen, and Ming-Chang Kuo. "Coefficients of Restitution Based on a Fractal Surface Model." Journal of Applied Mechanics 70, no. 3 (2003): 339–45. http://dx.doi.org/10.1115/1.1574063.

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Equations of rigid-body mechanics provide a means to predict the post-collision behavior without recourse to highly complex, detailed analysis of deformations during contact. Before the prediction can be completed, the coefficient of restitution, which relates the rebound velocity to the incident velocity, must be estimated properly. The coefficient of restitution depends on the surface topography in addition to the material properties and incident velocity. Recent investigations showed that surface topography can be characterized properly by fractal models. This paper proposes a normal contact model for a fractal surface in contact with a rigid smooth half-space. The fractal surface is constructed based on the Cantor set and composed of elastic-perfectly plastic material. Asymptotic continuous expressions for the load-displacement relations during loading and unloading are derived. Based on these results, we study the effects of surface roughness, material properties and incident velocity on the coefficient of restitution.

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8

Cross, Rod. "Measuring coefficients of restitution with a piezo disk." Physics Education 55, no. 3 (2020): 035008. http://dx.doi.org/10.1088/1361-6552/ab7141.

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9

Arpaz, Ercan. "Determination of restitution coefficients for various granite samples." Arabian Journal of Geosciences 8, no. 7 (2014): 5285–94. http://dx.doi.org/10.1007/s12517-014-1571-z.

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10

Buzzi, Olivier, Anna Giacomini, and Michele Spadari. "Laboratory Investigation on High Values of Restitution Coefficients." Rock Mechanics and Rock Engineering 45, no. 1 (2011): 35–43. http://dx.doi.org/10.1007/s00603-011-0183-0.

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11

Wang, Yanhai, Wei Jiang, Shengguo Cheng, Pengcheng Song, and Cong Mao. "Effects of the impact angle on the coefficient of restitution in rockfall analysis based on a medium-scale laboratory test." Natural Hazards and Earth System Sciences 18, no. 11 (2018): 3045–61. http://dx.doi.org/10.5194/nhess-18-3045-2018.

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Abstract. The reliability of a computer program simulating rockfall trajectory depends on the ascertainment of reasonable values for the coefficients of restitution, which typically vary with the kinematic parameters and terrain conditions. The effects of the impact angle with respect to the slope on the coefficients of restitution have been identified and studied using small-scale laboratory tests. To investigate whether the existing conclusion based on small-scale laboratory tests is valid when the test scale changes as well as the role of rotation in the effect of the impact angle on the coefficients of restitution, this study performed a medium-scale laboratory test using spherical limestone polyhedrons to impact concrete slabs. Free-fall tests are conducted, and the velocities before and after the impact are obtained by a 3-D motion capture system. The comparison of results between our test and the existing small-scale tests verified that several general laws occur when accounting for the effect of the impact angle, regardless of the test scales and conditions. Increasing the impact angle will induce reductions in the normal coefficient of restitution Rn, the kinematic coefficient of restitution Rv and the kinetic energy coefficient of restitution RE, whereas it will lead to increases in the tangential coefficient of restitution Rt. The rotation plays an important role in the effect of the impact angle. A higher percentage of kinetic energy converted to rotational energy always induces a higher normal coefficient of restitution Rn and a lower tangential coefficient of restitution Rt. As the impact angle decreases, the ratio between the rebound angle β and the impact angle α increases, and the percentage of kinetic energy dissipated in rotation as the collision became higher. Considering that the effect of block shape and the detailed impact orientations are not involved in the present study, the test results are valid for trajectory simulation codes based on a lumped-mass model and can be referenced in the trajectory predication of spherical rocks impacting hard surfaces using a rigid body model.

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12

Wang, Jinwu, Changsu Xu, Yanan Xu, et al. "Influencing Factors Analysis and Simulation Calibration of Restitution Coefficient of Rice Grain." Applied Sciences 11, no. 13 (2021): 5884. http://dx.doi.org/10.3390/app11135884.

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It is difficult to determine the coefficient of restitution accurately due to the small size, light weight, and complex influencing factors of rice grain. In the study, the experimental principle of restitution coefficient was described by the impact method, and the restitution coefficients of four typical rice varieties in Northeast China were measured. According to the orthogonal experiment, the primary and secondary factors affecting the restitution coefficient of rice grain were collision material, spring compression (initial collision velocity), moisture content, and rice variety. A single factor test was carried out for the significant factors, and the results showed that: The restitution coefficient of rice grain to a Q235 steel plate, plexiglass plate, seed plate, and rubber plate decreased in turn, and the restitution coefficient gradually decreased with the increase of spring compression (initial collision velocity), and with the increase of water content. The restitution coefficient was obtained by a bench test and simulation test, and the results were 0.429 and 0.423, respectively. The reason for the error was discussed and analyzed, which effectively verified the validity of the measurement of the restitution coefficient of small grain size. This study provides a method for the determination of the restitution coefficient of small grain, and provides a reference for the optimization design of threshing and a cleaning device of the combine harvester and high-speed precision seeder.

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13

Bi, Ran, Shaoying Li, Gou Liu, Jianxi Ren, and Yongjun Song. "Investigating the Effect of Preimpact Energy Dissipation on Coefficient of Restitution regarding the Slope-Boulder Interaction." Advances in Civil Engineering 2021 (April 15, 2021): 1–11. http://dx.doi.org/10.1155/2021/9929119.

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Coefficient of restitution is regarded as a dominating parameter in rockfall research. Generally, small-scale experiments were developed without considering interactions between boulder and slope. However, preimpact moving statuses are essential to evaluate rockfall behaviors. To reveal the effect of preimpact interactions on coefficient of restitution, energy dissipation considering initial velocity, surface type, and slope angle is executed based on medium-scale tests. The results show that (1) as the inclination of initial velocity, higher rebound height, and the declining normal coefficient of restitution occur, a determinable linear function could demonstrate relationships among energy dissipation and all coefficient of restitution; when initial velocity exceeds 5 m/s, the recovery ability shows and produces an increasing trend with respect to the variation of kinematic coefficient of restitution and kinetic energy coefficient of restitution. (2) As the surface material varies, slope hardness and rebound ability influence normal coefficient of restitution, and the surface roughness and rotation feature dominate tangential coefficient of restitution; considering preimpact slope and boulder interactions, four types of coefficient of restitution follow declining trend with different material sequence. (3) Slope angle affects normal coefficient of restitution, and tangential coefficient of restitution relatively descends 18% and inclines 10% when the angle ranges from 30° to 75°; regarding preimpact moving status, it differs from bounce times. The correlation between preimpact energy dissipation and four coefficients of restitution can be represented by the same decreasing linear function, when increasing the slope angle.

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14

Nasrudin, Dindin, Chaerul Rochman, and Herni Yuniarti Suhendi. "KOEFISIEN RESTITUSI: MAKNA FISIS, FORMULA MATEMATIS, DAN REDUKSI DIDAKTIS." Journal of Teaching and Learning Physics 2, no. 1 (2017): 1–9. http://dx.doi.org/10.15575/jotalp.v2i1.5817.

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One of the physics matter that is considered difficult by high school students is the concept of collision in which discuss the coefficient of restitution (e). On that basis, the restitution coefficient becomes one of the studies discussed in Physics Depth II for pre-service physics teacher in one of LPTK in West Java. This paper describes the profile of pre-service physics teacher in understanding the physical meanings of restitution coefficients, how to write mathematical formulas and the appropriate didactic reduction in learning the concept of restitution coefficients in high school students. The population of this research is pre-service physics teacher in one of LPTK in West Java, while the sample is 80 pre-service physics teacher who has taken the subject of Physics Depth II. By using cross-sectional survey method, it was found that (1) the number of respondents who answered the physical meaning of the restitution coefficient in the right category were: 39.7%, the less appropriate category was 22% and the rest of the category was not exactly 38.3%. (2) The mathematical formula of the selected restitution coefficient is 91.3% using TYPE B1, 2.8% using TYPE B2 and the remaining 5.7% using TYPE B4. (3) The didactic reduction chosen by the respondents in learning the concept of restitution coefficient in high school students is 10.2% by returning to the qualitative mean, 66.7% using drawings and sketches, 20.3% using analogy, while the rest using particularization (1.4%) and generalization (1.4%).

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15

Higa, M., M. Arakawa, and N. Maeno. "Measurements of restitution coefficients of ice at low temperatures." Planetary and Space Science 44, no. 9 (1996): 917–25. http://dx.doi.org/10.1016/0032-0633(95)00133-6.

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16

GUTIÉRREZ, E., and D. K. ARROWSMITH. "THE EQUIVALENCE BETWEEN FEEDBACK AND DISSIPATION IN IMPACT OSCILLATORS." International Journal of Bifurcation and Chaos 17, no. 01 (2007): 255–69. http://dx.doi.org/10.1142/s0218127407017306.

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We analyze an important class of engineering systems characterized by the discontinuous motion of a spring-mass constrained by the motion of a feedback-assisted actuator. We show that the combined effects of mechanical restitution coefficient and displacement feedback can be exactly represented by a single equivalent dissipation coefficient. We also show that the topological properties of the surfaces of section of orbits generated by impact oscillators which possess differing proportions of restitution and feedback levels, but whose equivalent dissipation coefficients are equal, are equivalent and universally scalable. The scaling law allows us to interchange the effects of restitution and feedback coefficients and so, effectively, eliminate one of these parameters from the equations of motion. Thus, the topological properties of dissipative feedback-assisted systems can be seen as scaled versions of either purely dissipative, or purely feedback-assisted, oscillators.

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17

Serebryany, Vladimir, Sergey F. Kurtasov, and T. I. Savyolova. "Pole Figure Measurement Plan Influence on Accuracy ODF Coefficients Determined by Modified Harmonic Method." Materials Science Forum 495-497 (September 2005): 1693–0. http://dx.doi.org/10.4028/www.scientific.net/msf.495-497.1693.

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Influences of an X-ray experimental texture plan and of pole figure primary errors on the accuracy of the ODF coefficients are discussed. A modified harmonic method, which is a statistical method of ridge estimates, has been used for ODF restitution from pole figures. The plan of measurement of the pole figures was analysed on the basis of minimization of the primary experimental errors and the errors of the ODF restitution method. Principles of the optimum texture plan construction for hexagonal metals (magnesium example) and for the URD-6 texture diffractometer are considered.

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18

Tang, Hongxiang, Rui Song, Yan Dong, and Xiaoyu Song. "Measurement of Restitution and Friction Coefficients for Granular Particles and Discrete Element Simulation for the Tests of Glass Beads." Materials 12, no. 19 (2019): 3170. http://dx.doi.org/10.3390/ma12193170.

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A slant plate flat throw test system for measuring the restitution coefficient of granular materials and a sliding friction test instrument for measuring the friction coefficient between discrete particles and continuum boundary surface materials are developed. The restitution coefficients of the glass bead particles, the glass beads relative to the glass plate, the composite of glass plate and the rubber membrane and the friction coefficients between the glass beads and the rubber film and the filter paper are measured by the designed methods. Based on the measured restitution coefficient and friction coefficient, the discrete element numerical simulation is carried out for triaxial test and plane strain test. Through comparing the experimental results and the discrete element numerical simulation results, the feasibility and rationality of the designed measurement methods and the discrete element numerical simulation are verified. The measuring methods developed in this paper can be further applied to the tests of other fine particles.

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19

Labiouse, V., and B. Heidenreich. "Half-scale experimental study of rockfall impacts on sandy slopes." Natural Hazards and Earth System Sciences 9, no. 6 (2009): 1981–93. http://dx.doi.org/10.5194/nhess-9-1981-2009.

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Abstract. In the framework of rockfall trajectory modelling, the bouncing phenomenon occurring when a rock block impacts with the slope surface is the most difficult to predict, owing to its complexity and its very limited understanding. To date, the rebound is commonly quantified by means of two coefficients of restitution estimated from a rough description of the ground material. To acquire a better knowledge of the bouncing phenomenon and to investigate the influence of various impact parameters, a comprehensive experimental study was undertaken at the LMR-EPFL (Rock Mechanics Laboratory – Swiss Federal Institute of Technology Lausanne). After a summary of the main conclusions drawn from a small-scale study, the paper focuses on half-scale experiments, describing first the testing device and the data processing and analysing then the influence of several impact parameters. It is observed that the rebound and the commonly-used coefficients of restitution expressed for the mass centre of the block depend not only on slope material characteristics, but also on factors related to the kinematics (slope inclination and impact velocity) and to the block (weight, size and shape). As many trajectory computer codes consider constant coefficients of restitution only function of the outcropping material, the trajectory results should be interpreted with caution and always checked against field observations.

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20

Serero, D., N. Gunkelmann, and T. Pöschel. "Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution." Journal of Fluid Mechanics 781 (September 28, 2015): 595–621. http://dx.doi.org/10.1017/jfm.2015.501.

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A hydrodynamic description of dilute binary gas mixtures comprising smooth inelastic spheres interacting by binary collisions with a random coefficient of restitution is presented. Constitutive relations are derived using the Chapman–Enskog perturbative method, associated with a computer-aided method to allow high-order Sonine polynomial expansions. The transport coefficients obtained are checked against DSMC simulations. The resulting equations are applied to the analysis of a vertically vibrated system. It is shown that differences in the shape of the distributions of the coefficient of restitution are sufficient to produce partial segregation.

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21

Giresini, Linda, Fabio Solarino, Francesca Taddei, and Gerhard Mueller. "Experimental estimation of energy dissipation in rocking masonry walls restrained by an innovative seismic dissipator (LICORD)." Bulletin of Earthquake Engineering 19, no. 5 (2021): 2265–89. http://dx.doi.org/10.1007/s10518-021-01056-6.

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AbstractThis paper presents an innovative anti-seismic device for controlling the out-of-plane rocking motion of masonry walls with traditional tie-rods, called LInear COntrolled Rocking Device (LICORD). LICORD is a low-impact box connected to the extremity of the traditional tie-rod designed to mitigate rocking for medium–high intensity earthquakes. Additionally, the paper widens the knowledge about the dynamic behavior of rocking walls through the interpretation of the results of an extensive experimental campaign performed on masonry specimens composed by clay brick and cementitious mortar. Firstly, the LICORD’s single components are tested to identify their stiffness and damping properties. Secondly, free vibration tests provide actual values of coefficients of restitution on free-standing walls and walls restrained by LICORD, where the walls vary for the height to thickness ratio. For the stockier wall, the ratio of experimental/analytical coefficient of restitution varies from 88 to 98%, whereas for the slender wall, the results are less scattered, with a minimum value of 95% and a maximum value of 96%. The restrained walls are characterized by coefficients of restitution from 5 to 25% less than the values found for unrestrained walls, depending on the equivalent viscous coefficient of the shock absorbers. Moreover, LICORD demonstrated to properly absorb and damp the oscillations of the wall and control its rocking motion, strongly reducing the number of impacts and the rotation amplitudes up to 70%. Considerations about the effect of one-sided motion on the assessment of coefficient of restitution are also given. The equivalent viscous damping coefficients are observed to be on the range 4% (unrestrained wall) and 7–20% for walls restrained by LICORD.

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22

Zhang, Shen, Nan Gui, Xiaoli Huang, et al. "Verifying the tangential and normal restitution coefficients for double-sphere particles." Powder Technology 363 (March 2020): 419–27. http://dx.doi.org/10.1016/j.powtec.2020.01.025.

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23

Zhao, Jing, Dan B. Marghitu, John Schumacher, and Wenzhong Wang. "Impact of Horse Hoof Wall with Different Solid Surfaces." Applied Sciences 10, no. 23 (2020): 8743. http://dx.doi.org/10.3390/app10238743.

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This study aimed to investigate the impact of a horse hoof wall on three solid surfaces: steel, concrete and asphalt. Impact experiments were conducted for different impact angles and different initial impact velocities. The effect of impact surfaces, impact angles and initial impact velocities on the coefficient of restitution and the effective coefficient of friction were tested using one-way ANOVA. Analytical and numerical modeling of the impact were developed. The impact interval was divided into two phases: compression and restitution. For compression, a contact force with a damping term was used. The restitution was characterized by an elastic contact force. The stiffness and damping coefficients of the contact force were estimated from the normal impacts. The simulated velocities after the oblique impacts were compared to the velocities in the in vitro investigation. The coefficient of restitution varied significantly on different surfaces. The effective coefficient of friction was lower on steel compared to concrete and asphalt. The model presented in this study can be applied to refine the impact simulation of the equine hoof during locomotion.

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24

Higa, Michiya, Masahiko Arakawa, and Norikazu Maeno. "Size Dependence of Restitution Coefficients of Ice in Relation to Collision Strength." Icarus 133, no. 2 (1998): 310–20. http://dx.doi.org/10.1006/icar.1998.5938.

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25

Ehsani, Mehran, Salman Movahedirad, Shahrokh Shahhosseini, and Mahshid Ashtiani. "Effects of Restitution and Specularity Coefficients on Solid-Liquid Fluidized Bed Hydrodynamics." Chemical Engineering & Technology 38, no. 10 (2015): 1827–36. http://dx.doi.org/10.1002/ceat.201400744.

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26

Yang, Guidong, Dongmei Huang, Wei Li, Meng Su, and Francesco Pellicano. "Steady-State Dynamical Response of a Strongly Nonlinear System with Impact and Coulomb Friction Subjected to Gaussian White Noise Excitation." Shock and Vibration 2020 (September 28, 2020): 1–11. http://dx.doi.org/10.1155/2020/8837638.

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The paper is devoted to the steady-state dynamical response analysis of a strongly nonlinear system with impact and Coulomb friction subjected to Gaussian white noise excitation. The Zhuravlev nonsmooth transformation of the state variables combined with the Dirac delta function is utilized to simplify the original system to one without velocity jump. Then, the steady-state probability density functions of the transformed system are derived in terms of the stochastic averaging method of energy envelope. The effectiveness of the presented analytical procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different restitution coefficients, amplitudes of friction, and noise intensities on the steady-state dynamical responses are investigated in detail. Results show different intensities of Gaussian white noise can affect the peaks value of the probability density functions, whereas the variations of restitution coefficients and amplitudes of friction can induce the occurrence of stochastic P-bifurcation.

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27

Horabik, Józef, Michał Beczek, Rafał Mazur, Piotr Parafiniuk, Magdalena Ryżak, and Marek Molenda. "Determination of the restitution coefficient of seeds and coefficients of visco-elastic Hertz contact models for DEM simulations." Biosystems Engineering 161 (September 2017): 106–19. http://dx.doi.org/10.1016/j.biosystemseng.2017.06.009.

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28

Borsa, Eugenia, H. Andrés Petit, Juliana Piña, Cecilia I. Paulo, and E. Fabián Irassar. "Influence of the coefficient of restitution on the classification of granite sand using an elutriator." EPJ Web of Conferences 249 (2021): 05006. http://dx.doi.org/10.1051/epjconf/202124905006.

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The objective of this work was to measure the coefficient of restitution of fine granite sand dust (passing sieve ASTM N°30) and to study its influence on the prediction of classification parameters in an elutriator device. Three types of restitution coefficients were evaluated in the computational fluid dynamic model: experimental, elastic, and half the experimental value. The influence of process variables, such as the inclination angle of the equipment and the air inlet velocity, on the efficiency of the obtained fine and coarse fractions was also studied. The results indicate that the coefficient of restitution significantly influences the efficiency parameters calculated for the inclined tests, given the greater contact that exists between the particles and the equipment wall. The experimental value of the coefficient achieved almost total congruence with the coarse fraction collected for the tested velocities. For the vertical tests, the variation of the coefficient did not show significant differences for both collected fractions. The results obtained in this work allowed to gain a deeper insight into the studied gas-solid systems, and to improve the numerical predictions on fine particles classification processes widely used in the ceramic, mining and metallurgical industries.

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29

Cojocaru, Dorian, and Dan B. Marghitu. "Differential Formulation for the Coefficient of Restitution of a Rigid Link." Applied Mechanics and Materials 762 (May 2015): 175–82. http://dx.doi.org/10.4028/www.scientific.net/amm.762.175.

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The differential impact equations of motion are developed using an nonlinear contact force. The nonlinear equations of motion are written using symbolical MATLAB and are solved using numerical techniques. The impact equations are based on the Kogut-Etsion model. The numerical results are obtained for different geometries of the link, different coefficients of friction, and different initial conditions. The coefficient of restitution (COR) is discussed for specific cases. The results can be used for the impact of mobile robots with different type of surfaces.

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30

Hatze, Herbert. "Objective Biomechanical Determination of Tennis Racket Properties." International Journal of Sport Biomechanics 8, no. 4 (1992): 275–87. http://dx.doi.org/10.1123/ijsb.8.4.275.

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Several biodynamical properties of tennis rackets such as vibrational characteristics, direction control, and the coefficient of restitution depend critically on the constraining mode of the handle. The racket response to ball impact differs fundamentally for rigid mechanical clamping of the handle and for hand-held gripping. In order to test objectively the biodynamical characteristics of tennis rackets under standardized but biomechanically realistic conditions, the use of a mechano-electronic replica of the human hand/arm system, termed manusimulator, is suggested. Sample test results of the vibrational characteristics of a specific tennis racket and of the coefficients of restitution of several rackets provide proof of the reproducibility and reliability of the test results so obtained. The results were compared with those obtained using human test players. The latter subjective method yielded data with excessively large coefficients of variation around 84% and was found to be unsuitable for determining tennis racket properties objectively. It is concluded that the standardizable manusimulator testing procedure offers a valuable alternative to subjective testing methods for determining tennis racket parameters.

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31

Popov, Valentin L. "Coefficients of Restitution in Normal Adhesive Impact between Smooth and Rough Elastic Bodies." Reports in Mechanical Engineering 1, no. 1 (2020): 103–9. http://dx.doi.org/10.31181/rme200101103p.

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n 1975, Fuller and Tabor have shown that roughness can destroy macroscopic adhesion. This means that in spite of the presence of adhesion at the microscopic scale, the macrosopic force of adhesion vanishes. The mechanism of vanishing macroscopic adhesion is very simple: during approach of elastic bodies, asperities are elastically deformed so strongly that after unloading they destroy the microscopic adhesive junctions. However, both in the moment of formation of microscopic adhesive junctions in the loading phase and their destruction during unloading, mechanical energy disappears. This means that the microscopic adhesion makes the contact dissipative even if there is no macroscopic force of adhesion. In particular, the force-distance dependency during indentation and pull-off do not coincide with each other showing some "adhesive hysteresis". When a ball rolls on such rough surface, there will be a final energy dissipation due to formation of a new contact at the frontline of the contact and its destruction at the rear part. Thus, microscopic adhesion will lead to appearance of rolling friction in an apparently non-adhesive contact. In the present paper, we calculate the approach and pull-off dependencies of force on distance, the dissipated energy in one loading-unloading cycle and estimate the force of rolling friction due to microscopic adhesion.

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32

KOHNO, Masanori, Katsuya KITASAKO, Yasuo IKEZOE, and Tsuyoshi NISHIMURA. "COEFFICIENTS OF RESTITUTION OF ROCKFALL IMPACTS BASED ON FREE-FALL-REBOUNDING LABORATORY EXPERIMENT." Journal of Japan Society of Civil Engineers, Ser. C (Geosphere Engineering) 71, no. 2 (2015): 81–91. http://dx.doi.org/10.2208/jscejge.71.81.

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33

McGrain, Peter, James Van Dyke, and James Mastro. "Coefficients of Restitution of Balls Used in Team Sports for the Visually Impaired." International Journal of Sport Biomechanics 3, no. 1 (1987): 63–68. http://dx.doi.org/10.1123/ijsb.3.1.63.

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This study examined the coefficients of restitution (e) of selected balls used in team sports for the visually impaired: beep baseball and goal ball. Specifically, a basketball was compared to two men's standard goal balls, and a softball was compared to three different types of beep baseballs. The e for all balls was calculated by dropping each ball five times from heights of 6 ft (1.83 m) and 19.25 ft (5.88 m). A Sony reel-to-reel videotape recorder was used to record rebound heights on a background scale for each ball dropped. Reliability tests of the procedures yielded correlation coefficients (r) of 0.996 and 0.998 for the 6 ft (1.83 m) and 19.25 ft (5.88 m) drops, respectively. Two two-factor analysis of variance (ANOVA) tests yielded significant differences across ball type and height of drop for the basketball and goal balls and for the softball and beep baseballs, respectively (p < 0.001). The es for the more recently developed beep baseballs are close to that of the standard softball, indicating a possible danger to visually impaired participants in beep baseball.

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34

Asteriou, P., H. Saroglou, and G. Tsiambaos. "Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis." International Journal of Rock Mechanics and Mining Sciences 54 (September 2012): 103–13. http://dx.doi.org/10.1016/j.ijrmms.2012.05.029.

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35

Chau, K. T., R. H. C. Wong, and C. F. Lee. "Rockfall Problems in Hong Kong and Some New Experimental Results for Coefficients of Restitution." International Journal of Rock Mechanics and Mining Sciences 35, no. 4-5 (1998): 662–63. http://dx.doi.org/10.1016/s0148-9062(98)00023-0.

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Li, Xue, Ming Dong, Sufen Li, and Yan Shang. "Experimental and theoretical studies of the relationship between dry and humid normal restitution coefficients." Journal of Aerosol Science 129 (March 2019): 16–27. http://dx.doi.org/10.1016/j.jaerosci.2018.12.006.

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37

Inaba, Yuki, Sho Tamaki, Haruhiko Ikebukuro, Koshi Yamada, Hiroki Ozaki, and Kazuto Yoshida. "Effect of Changing Table Tennis Ball Material from Celluloid to Plastic on the Post-Collision Ball Trajectory." Journal of Human Kinetics 55, no. 1 (2017): 29–38. http://dx.doi.org/10.1515/hukin-2017-0004.

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AbstractThe official material used in table tennis balls was changed from celluloid to plastic, a material free of celluloid, in 2014. The purpose of this study was to understand the differences and similarities in the two types of ball materials by comparing their behavior upon collision with a table. The behavior of the balls before and after collision with a table, at various initial speeds ranging from 15 to 115 km/h, was captured using high-speed cameras. Velocities and spin rates before collision and velocities after collision were computed to calculate the coefficients of restitution and friction. Based on the computed variables, the post-collision trajectories of both balls were calculated by integrating the equation of motion of the ball for simulated service, smash and drive conditions with respect to time. The coefficients of restitution were higher for the plastic balls than the celluloid ones when the initial vertical velocities were higher. The coefficients of friction were higher for plastic balls when the initial horizontal contact point velocities were slower. Because of the differences in the material characteristics, the plastic ball trajectories of services with backspin and drives with great topspin were expected to be different from those of celluloid balls. Since the extent of differences between the two ball types varied depending on the initial conditions, testing at various initial conditions was suggested for comparing and understanding the characteristics of the balls.

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38

Li, L.-Y., C.-Y. Wu, and C. Thornton. "A theoretical model for the contact of elastoplastic bodies." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 4 (2001): 421–31. http://dx.doi.org/10.1243/0954406021525214.

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The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. Formulae describing the force-displacement relationship for static contact problems and the coefficient of restitution for dynamic impact problems are derived. The present model can be considered as a modification of Johnson's model by using a more detailed pressure distribution function which is based on finite element analysis (PEA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, finite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coefficients. Good agreements between the model predictions and the FEA results are found.

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Su, Meng, Wei Xu, and Guidong Yang. "Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise." International Journal of Bifurcation and Chaos 28, no. 13 (2018): 1830043. http://dx.doi.org/10.1142/s0218127418300434.

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In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

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Tai, Ching Hui, and Chun Ho Yin. "Application of Finite Element Methods for the Analysis of Restitution Coefficients for Golf Club Heads." Applied Mechanics and Materials 799-800 (October 2015): 589–95. http://dx.doi.org/10.4028/www.scientific.net/amm.799-800.589.

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Finite element methods are applied to investigate the coefficient of restitution (COR) for the head of a golf club. ANSYS commercial finite element software is first applied to determine the COR of two different disc-shaped titanium impact surfaces. These values were then experimentally verified to validate the accuracy of the finite element model. Finally, ANSYS was applied to determine the COR for club heads according to USGA specifications to confirm the reliability of the finite element model. The model is then validated by comparison with experimental results. The model can not only reduce time needed for product design and experimental testing, but can serve as a basis for follow-up studies on ball flight trajectory.

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Koval’nogov, N. N., and R. V. Fedorov. "Numerical analysis of the coefficients of temperature restitution and heat transfer in high-speed flows." Russian Aeronautics (Iz VUZ) 50, no. 3 (2007): 309–16. http://dx.doi.org/10.3103/s1068799807030130.

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Sutkar, Vinayak S., Niels G. Deen, Johan T. Padding, et al. "A novel approach to determine wet restitution coefficients through a unified correlation and energy analysis." AIChE Journal 61, no. 3 (2014): 769–79. http://dx.doi.org/10.1002/aic.14693.

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Kim, Dong Hyun, Ivan Gratchev, Jeroen Berends, and Arumugam Balasubramaniam. "Calibration of restitution coefficients using rockfall simulations based on 3D photogrammetry model: a case study." Natural Hazards 78, no. 3 (2015): 1931–46. http://dx.doi.org/10.1007/s11069-015-1811-x.

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VISWANATHAN, H., N. A. SHEIKH, R. D. WILDMAN, and J. M. HUNTLEY. "Convection in three-dimensional vibrofluidized granular beds." Journal of Fluid Mechanics 682 (August 1, 2011): 185–212. http://dx.doi.org/10.1017/jfm.2011.209.

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We study convective motion in vertically vibrated three-dimensional granular beds by comparing the predictions of a model based on a hydrodynamic description to Navier–Stokes order with experimental results obtained using positron emission particle tracking (PEPT). The three-dimensional conservation equations relating mass, momentum and energy are solved using the finite element (FE) method for a viscous vibrofluidized bed by using only observable system parameters such as particle number, size, mass and coefficients of restitution. The mean velocity profiles from the viscous model show reasonable agreement with the experimental results at relatively low altitudes for the range of experimental values studied, though the velocity fields at higher altitudes were systematically underestimated by the model. We confirm that the convection rolls are influenced by the sidewall coefficient of restitution and demonstrate the scaling relationships that operate, where increasing amplitude of vibration leads to a reduction in the angular velocity of the rolls.

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Alaci, Stelian, Constantin Filote, Florina-Carmen Ciornei, Oana Vasilica Grosu, and Maria Simona Raboaca. "An Analytical Solution for Non-Linear Viscoelastic Impact." Mathematics 9, no. 16 (2021): 1849. http://dx.doi.org/10.3390/math9161849.

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The paper presents an analytical solution for the centric viscoelastic impact of two smooth balls. The contact period has two phases, compression and restitution, delimited by the moment corresponding to maximum deformation. The motion of the system is described by a nonlinear Hunt–Crossley equation that, when compared to the linear model, presents the advantage of a hysteresis loop closing in origin. There is only a single available equation obtained from the theorem of momentum. In order to solve the problem, in the literature, there are accepted different supplementary hypotheses based on energy considerations. In the present paper, the differential equation is written under a convenient form; it is shown that it can be integrated and a first integral is found—this being the main asset of the work. Then, all impact parameters can be calculated. The effect of coefficient of restitution upon all collision characteristics is emphasized, presenting importance for the compliant materials, in the domain of small coefficients of restitution. The results (variations of approach, velocity, force vs. time and hysteresis loop) are compared to two models due to Lankarani and Flores. For quasi-elastic collisions, the results are practically the same for the three models. For smaller values of the coefficient of restitution, the results of the present paper are in good agreement only to the Flores model. The simplified algorithm for the calculus of viscoelastic impact parameters is also presented. This algorithm avoids the large calculus volume required by solving the transcendental equations and definite integrals present in the mathematical model. The method proposed, based on the viscoelastic model given by Hunt and Crossley, can be extended to the elasto–visco–plastic nonlinear impact model.

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Sun, D. C., and Jing Xu. "A Study of the Starting Characteristics of an Unlubricated Journal Bearing." Journal of Tribology 117, no. 2 (1995): 216–23. http://dx.doi.org/10.1115/1.2831230.

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The complicated motion of the journal in an unlubricated bearing in response to an applied torque is analyzed. The theory identifies the conditions for various distinct modes of motion to occur, including the “dry friction whirl” cited in the literature. The crucial dependence of the motion on the friction coefficient and the normal and tangential restitution coefficients, as revealed by the theory, suggest that perhaps these latter parameters of motion can be determined by measuring the journal’s motion in an unlubricated journal bearing.

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Koval’nogov, N. N., and L. M. Magazinnik. "Numerical analysis of the coefficients of temperature restitution and heat transfer in a turbulent dispersed flow." Russian Aeronautics (Iz VUZ) 51, no. 2 (2008): 152–59. http://dx.doi.org/10.3103/s1068799808020086.

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Asteriou, Pavlos, and George Tsiambaos. "Effect of impact velocity, block mass and hardness on the coefficients of restitution for rockfall analysis." International Journal of Rock Mechanics and Mining Sciences 106 (June 2018): 41–50. http://dx.doi.org/10.1016/j.ijrmms.2018.04.001.

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Malzi, Mohamed Jaouad, Aziz Ettahir, Christian Boned, Bernard Lagourette, Kamal Kettani, and Khaoula Amarray. "Critical Study of a Residual Viscosity Correlation of JOSSI: Pure Hydrocarbons Case." Materials Science Forum 986 (April 2020): 61–67. http://dx.doi.org/10.4028/www.scientific.net/msf.986.61.

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The most common residual viscosity correlation used in the petroleum models is JOSSI et al [1] where the residual viscosity is represented by a polynomial function of 4th degree involving the reduced density ρr ([(η-η*)ξ+10-4]1/4=Σ41=0(aiρri)). Based on this formula, it is possible to predict various uncertainties that can be accumulated and thus alter the performance of viscosity restitution which depends on several factors:The quality of the initial adjustment of the coefficients ai;The precision on the density;The accuracy with which are known the characteristics of the constituents of bases;The validity of the rule of the mixtures selected for the determination of the pseudo-critical coordinates Tcm and Pcm and the equivalent molar mass of the mixture.As far as the results are concerned, we reveal that with the new set of coefficients it is possible to obtain a more preciserepresentation compared to that of JOSSI. The method of JOSSI seems to be especially interesting for the viscosities restitution of systems containing light and close paraffins. However, for some pure substances, the opposite situation could be true. Among the four equations-of-state used, it has been found that the cubic equation-of-stateof PENG and ROBINSON should not be used since we would like to generate the density. Finally, we are not expecting a perfect systematic representation. As demonstrated in our model, if for light alkanes one can expect an average deviation ofless than 10%, for certain pure substances the deviation exceeds 20%.

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Zhang, Yuning, and Inna Sharf. "Rigid Body Impact Modeling Using Integral Formulation." Journal of Computational and Nonlinear Dynamics 2, no. 1 (2006): 98–102. http://dx.doi.org/10.1115/1.2389232.

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A three-dimensional single-point impact solution has been developed based on the original work of Keller. The formulation involves an integrated form of Keller’s equations and leads to a different numerical procedure to solve for the after-impact velocities. In this integral formulation, the kinetic and static friction coefficients are differentiated and any of the three hypotheses of the coefficient of restitution can be employed. Furthermore, a singularity problem that may occur in Keller’s solution is avoided with the integral formulation. Numerical examples are given to illustrate the features of the integral formulation and the differences between the two formulations.

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