Velocity Restitution Coefficient Research Articles

An Analysis of Factors Affecting Flowslide Deposit Morphology Using Taguchi Method

Flowslides, as one type of landslides, are becoming a research hotspot due to their high speed and long runout distance, which can cause tremendous damage and economic loss. The scale of damage and deposit morphology of flowslide is closely related to factors like deposit volume, slope height, and slope angle. In order to assess the influence of these factors, a sandbox apparatus is developed, and the Taguchi method is used to design an experimental scheme to analyze the results of factors affecting the deposit morphology of flowslide. The results show that the factor that has the greatest impact on flowslide deposit morphology is slope angle, followed by the influence of volume and slope height. As slope angle increases, the maximum width, maximum length, area, and length‐width ratio of the deposit first increase and then decrease. In addition, there should be a critical angle in the changes of deposit morphology that is between 60° and 70° under the experimental conditions. When the volume is 5.4 × 10−3 m3, the slope angle is 70°, the slope height is 0.90 m, and the changes of deposit morphology of the flowslide are the largest. In this study, considering the slope angle as a single variable, there is a single upheaval for a slope angle of 40° and 50° and a double upheaval at 60° and 70°. The formation mechanism of the upheaval is analyzed based on the Mohr‐Coulomb criterion and considered properties of the material. The apparent friction coefficient of a flowslide is spatially and lithologically different and increases nonlinearly as the slope angle increases. The initial benchmark of the slope angle and apparent friction coefficient curve are affected by the friction coefficient of the material; the position of the inflection point at which the curve increases rapidly is affected by the coefficient of velocity restitution.

Development and application of a model test system for rockfall disaster study on tunnel heading slope

To study the motion law of rockfall which collapses from the tunnel heading slope and the dynamic response of the open-cut tunnel to the impact, a large-scale three-dimensional model test system is developed by taking the heading slope above a tunnel exit of the under-constructed Chengdu–Lanzhou Railway as the study object. The system consists of high-strength model test bench, three-dimensional release device of falling blocks, a high-speed video camera and fiber Bragg grating-monitoring device, etc. Test bench whose largest exterior dimension is 3.4 m × 2 m × 2.5 m (length × width × height) is made of high-strength steel framework and tempered glass as body material to realize the visibility of the test process. The block-releasing device is mainly composed of a releasing box, three groups of slide rails, hydraulic cylinder and gas cylinder, by which can satisfy the requirements of the initial slip angles of rockfall in various test conditions. The high-speed video camera is adopted to capture the trajectory of the rockfall and video-processing software is used to calculate the motion parameters. Fiber Bragg grating-monitoring device is adopted to collect the information about force and deformation of the open-cut tunnel under the impact of rockfall and to study the dynamic response of the structure. Similar materials of slopes, falling blocks and open-cut tunnel are developed based on the existing geo-mechanical materials. Construction of the models and the arrangement of fiber Bragg grating-monitoring devices are explained systematically in the paper. The results of rockfall impact tests show that the mass, release height and impact angle of rock blocks have significant effects on the velocity restitution coefficient of blocks after impacting on the open-cut tunnel structure. The normal restitution coefficient of the block’s velocity is basically between 0.3 and 0.45. The model test system is reliable and can be applied in subsequent model test researches of rockfall disasters.

Model of the Relationship between the Velocity Restitution Coefficient and the Initial Car Velocity during Collision

Abstract This article contains the results of statistical research of velocity restitution coefficient variations when a motor car hits a concrete wall during crash tests performed by different researchers, for the purpose of deriving an equation of the relationship between the velocity restitution coefficient and the initial impact velocity. The derived expression is innovative as it has no prototype. The analysis of its adequacy has shown acceptable deviations from the calculated values of the velocity restitution coefficient obtained by other researchers.

Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls

In this paper, we analyze the capabilities of a generalized kinematic (Newton’s like) restitution law for the modeling of a planar rigid block that impacts a rigid ground. This kinematic restitution law is based on a specific state transformation of the Lagrangian dynamics, using the kinetic metric on the configuration space. It allows one to easily derive a restitution rule for multiple impacts. The relationships with the classical angular velocity restitution coefficient r for rocking motion are examined in detail. In particular, it is shown that r has the interpretation of a tangential restitution coefficient. The case when Coulomb’s friction is introduced at the contact impulse level together with an angular velocity restitution is analyzed. A simple chain of aligned balls is also examined, illustrating that the impact law applies to various types of multibody systems.

Correlation between solid particle erosion of cermets and particle impact dynamics

Since the erosion rate depends on energy exchange between particle and material, a reformulation and solution of the equations of two solid bodies collision is presented and adapted to the calculation of the energy absorbed by a material surface during impact of a spherical particle onto a plain target. It has been observed that energy loss is a strong function of dynamic coefficients named as coefficient of velocity restitution after impact, k, and coefficient of dynamic friction, f. The new method and experimental equipment for the coefficients determination are described. It was shown that energy consumption during application may be an appropriate guide for the material selection in the conditions of erosive wear.

Energy of a single bead bouncing on a vibrating plate: experiments and numerical simulations.

The energy of a single bead bouncing on a vibrating plate is determined in simulations and experiments by tracking the bead-plate collision times. The plate oscillates sinusoidally along the vertical with the dimensionless peak acceleration Gamma, and the bead-plate collisions are characterized by the velocity restitution coefficient epsilon. Above the threshold dimensionless peak acceleration Gamma(s) approximately 0.85, which does not depend on the restitution coefficient, the bead energy is shown to initially increase linearly with the vibration amplitude A, whereas it is found to scale like v(2)(p)/(1-epsilon), where v(p) is the peak velocity of the plate, only in the limit Gamma>>Gamma(s). The threshold Gamma(s) is shown to decrease when the bead is subjected, in simulations, to additional nondissipative collisions occurring with the typical frequency nu(c). As a consequence, the bead energy scales like v(2)(p)/(1-epsilon) for all vibration strengths in the limit nu(c)>>nu(*)(c). From the experimental and numerical findings, an analytical expression of the bead energy as a function of the experimental parameters is proposed.

Joint tripode fixe d'une transmission automobile. Modèle de chocs et essais industriels

An automotive transmission is made of a fixed tripod joint close to the wheel and a plunging tripod joint close to the engine linked together by an intermediate shaft. The fixed tripod joint is excited by the shudder vibrations generated by the longitudinal movement of the intermediate shaft. The axial stop at the fixed joint level is obtained by a star clamp of large stiffness fixing the joint on the shaft and a spring under a stop whose stiffness and position permit the joint optimisation considering vibrations. The proposed mechanical model built with a mass spring system is used to predict shocks between the star clamp and the tripod, star clamp and stop and stop and tulip. The velocity restitution coefficient after shock steel on steel of 0.9 was used and the six state equations were numerically integrated using a Runge and Kutta algorithm. This model was used to show the star clamp-tripod separation and determined the relevant positions of deformation gauges on an instrumented transmission for the measurement of internal efforts.

Investigation of impact of solid particles against hardmetal and cermet targets

The objective of the present work is to investigate and discuss some features of the surface damage and material removal process during particle-wall collision of the solid particles and hardmetal and cermet targets. The restitution parameters of TiC-base cermets, WC–Co hardmetals and glass of different composition and properties have been investigated. In order to clarify the details of the impact of glass spheres and corundum particles of irregular shape on a solid half-space, the process of interaction of solid particle with target was studied using a Laser Doppler Anemometer (LDA) measuring technique. Targets were impacted with particles over the range of impact velocities (7–50 m s −1) at impact angle 67°. The experimentally observed variations of the coefficient of velocity restitution as a function of the test material properties, impact velocity and hardness ratio ( H m/ H a) are adequately explained on the basis of a theoretical model. Systematic studies of the influence of the impact variables on the collision process have been carried out.

Dynamics of A Nonharmonically Forced Impact Oscillator.

The model consists of a mass attached to a linear spring and a linear viscous dashpot impacting a rigid obstruction with a coefficient of velocity restitution. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out by using the piecewise linear feature.

On averaging in systems with a variable number of degrees of freedom

An averaging procedure is established for systems with a variable number of degrees of freedom which arise when considering vibrocollisional oscillations with zero velocity restitution coefficient. Compared with the method of staged integration /1, 2/ the approach presented, associated with non-analytical changes in the variables /3, 4/, widens the class of systems that can be considered. Unlike the classical averaging method /5–7/ there is a reduction in the degenerate degrees of freedom because of the specific degeneracy of the problem.

4671005 Trigger mechanism : Arnold Jewell assigned to Jewell Arnold; Goddard James

A novel type of periodic motions in which a part of the trajectory is composed of an infinite sequence of collision-collisionless segments, is investigated for the systems with collisions. The problem of existence in the dynamic systems with collision interactions of such a sequence was studied in [1]. (∗) In analogy with other piecewise continuous systems, this sequence of motions is called “slippage”. The case of an infinite sequence of collisions occurring in a dynamic model of a clock movement was studied in [2], while the case arising in the process of impulsive braking with dry friction was studied in [3] under the name of quasi-plastic collision.The problem of constructing the boundaries of the slippage region in the phase space is solved as well as that of defining the region of existence of stable periodic motions with a slippage region, in the parametric space of a single-mass vibrating striker.The results of numerical computations are given for the oscillations occurring in the presence of an external periodic force, which are of greatest practical importance.Numerous investigations of the dynamic models of the systems with impulsive interactions have shown the existence of modes of varying complexity, the complexity determined by the ratio of the periodicity of the motion to the periodicity of the driving force and by the number of impacts per single period of motion. It was found that the increase in complexity is accompanied by appreciable narrowing of the regions of existence and stability of the mode in the parametric space.The regions of existence of stable periodic motions with an infinite convergent sequence of collisions defined in the parametric space of the vibrating striker, and of a simplest system containing two colliding pairs [4], were found to be of the same order as the corresponding regions of the one-impact modes. This indicates the practical importance of the motions with slippage for the systems with collisions. The presence of such motions makes possible an interpretation of a number of experimental results within the framework of the Newton's hypothesis. Such would be e. g. the finite duration of impact of a vibrohammer when the velocity restitution coefficient is different from zero [5 – 7] or the manner in which the escapement of a marine chronometer interacts with a shock bearing, the interaction consisting of the first, not completely elastic collision followed by a second inelastic collision, with subsequent motion under a kinematic constraint [8].

Impacting under harmonic excitation

The steady state response of a one dimensional linear oscillator impacting under harmonic excitation on to rigid obstructions with a coefficient of velocity restitution is investigated. Numerical experiments are discussed and an expression of the steady state velocity for one sided impacting is derived. The variation of impacting velocity with excitation frequency for symmetric two sided impacting steady states is analyzed. It is shown that steady states cannot exist below a minimum frequency whilst for frequencies in the band for which the steady state amplitude exceeds the clearance, a unique steady state can exist. For greater frequencies, two possible steady states exist for a given excitation frequency.

Periodic motions of a vibrating striker including a slippage region: PMM vol. 35, n≗ 5, 1971, pp. 892–898

A novel type of periodic motions in which a part of the trajectory is composed of an infinite sequence of collision-collisionless segments, is investigated for the systems with collisions. The problem of existence in the dynamic systems with collision interactions of such a sequence was studied in [1]. (∗) In analogy with other piecewise continuous systems, this sequence of motions is called “slippage”. The case of an infinite sequence of collisions occurring in a dynamic model of a clock movement was studied in [2], while the case arising in the process of impulsive braking with dry friction was studied in [3] under the name of quasi-plastic collision. The problem of constructing the boundaries of the slippage region in the phase space is solved as well as that of defining the region of existence of stable periodic motions with a slippage region, in the parametric space of a single-mass vibrating striker. The results of numerical computations are given for the oscillations occurring in the presence of an external periodic force, which are of greatest practical importance. Numerous investigations of the dynamic models of the systems with impulsive interactions have shown the existence of modes of varying complexity, the complexity determined by the ratio of the periodicity of the motion to the periodicity of the driving force and by the number of impacts per single period of motion. It was found that the increase in complexity is accompanied by appreciable narrowing of the regions of existence and stability of the mode in the parametric space. The regions of existence of stable periodic motions with an infinite convergent sequence of collisions defined in the parametric space of the vibrating striker, and of a simplest system containing two colliding pairs [4], were found to be of the same order as the corresponding regions of the one-impact modes. This indicates the practical importance of the motions with slippage for the systems with collisions. The presence of such motions makes possible an interpretation of a number of experimental results within the framework of the Newton's hypothesis. Such would be e. g. the finite duration of impact of a vibrohammer when the velocity restitution coefficient is different from zero [5 – 7] or the manner in which the escapement of a marine chronometer interacts with a shock bearing, the interaction consisting of the first, not completely elastic collision followed by a second inelastic collision, with subsequent motion under a kinematic constraint [8].

Slippage in dynamic systems with collision interactions: PMM vol. 31, no. 3, 1967, pp. 533–536

The distinctive featr-es of the phase space of a multidimensional d namic x system with collision interactions a : investigated under the usual idealizations. e existence of certain configurations of the phase space is established. Motions near these configurations (called “slippa e” motions) constitute convergent infinite sequences of collision-collisionless domains. l collisions occurring outside these configurations cannot be completely inelastic and have a velocity restitution coefficient different from zero. This model of slippage is a generalization of the idealization of collision interactions proposed in [l] on the basis of an experimental study of interactions in a chronometer. This idealization takes account of two collisions: the not completely elastic first collision and the second inelastic collision with subsequent motion under a kinematic constraint. This “improved” dynamic model of systems with collision interactions made possible the investigation of complex periodic and nonperiodic modes of operation through analog and digital computer simulation [2 and 31.