scholarly journals Coefficient of Restitution Interpreted as Damping in Vibroimpact

1975 ◽  
Vol 42 (2) ◽  
pp. 440-445 ◽  
Author(s):  
K. H. Hunt ◽  
F. R. E. Crossley
Keyword(s):  
Energy Loss ◽  
Relative Motion ◽  
Sine Wave ◽  
Coefficient Of Restitution ◽  
Damping Term ◽  
Physical Experiments ◽  
Voigt Model ◽  
Special Case ◽  
Two Bodies

During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith’s work. A damping term λxnx˙ is here introduced; for a sphere impacting a plate Hertz gives n = 3/2. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.

Rigid Body Collisions

1989 ◽  
Vol 56 (1) ◽  
pp. 133-138 ◽  
Author(s):  
Raymond M. Brach
Keyword(s):  
Energy Loss ◽  
Classical Problem ◽  
Negative Energy ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
Interaction Process ◽  
Energy Losses ◽  
Conservation Of Energy ◽  
Special Case ◽  
Two Bodies

A general approach is presented for solving the problem of the collision of two rigid bodies at a point. The approach overcomes the difficulties encountered by others on the treatment of contact velocity reversals and negative energy losses. A classical problem is solved; the initial velocities are presumed known and the final velocities unknown. The interaction process between the two bodies is modeled using two coefficients. These are the classical coefficient of restitution, e, and the ratio, μ, of tangential to normal impulses. The latter quantity can be a coefficient of friction as a special case. The paper reveals that these coefficients have a much broader intepretation than previously recognized in the solution of collision problems. The appropriate choice of values for μ is related to the energy loss of the collision. It is shown that μ is bounded by values which correspond to no sliding at separation and conservation of energy. Another bound on μ combined with limits on the coefficient e, provides an overall bound on the energy loss of a collision. Examples from existing mechanics literature are solved to illustrate the significance of the coefficients and their relationship to the energy loss of collisions.

Application of Dry-Friction Whip and Whirl Solution Methods to Systems With Support Asymmetry

2018 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Relative Motion ◽  
General Model ◽  
Dry Friction ◽  
Current Work ◽  
General Sense ◽  
Continuous Contact ◽  
Solution Methods ◽  
Asymmetric Rotor ◽  
Two Bodies

Dry-friction whip and whirl occurs when a rotor contacts a stator across a clearance annulus. In a general sense, the relative motion between the two bodies is described by a circular precessing motion. While this problem is generally well understood, the author is unaware of any papers that discuss the problem for systems having asymmetric rotor or stator supports. The current work will investigate a general model to describe dry-friction whip and whirl for the case of continuous contact between a rotor and stator in the presence of asymmetry. This paper will show that for light asymmetry, the rotor and stator motions are elliptical; however, the relative motion between the two bodies remains circular.

Determination of Relative Damping at Various Prestresses

1960 ◽  
Vol 33 (2) ◽  
pp. 282-301
Author(s):  
Th Kempermann ◽  
R. Clamroth
Keyword(s):  
Energy Loss ◽  
Phase Angle ◽  
Loss Factor ◽  
Short Review ◽  
The Other ◽  
Simple Function ◽  
History Of ◽  
Tan Δ ◽  
Special Case

Abstract After a short review of the history of the development of the concept of damping, the definitions—one in words, the other in the form of an equation—given in DIN 53513 are discussed, and their usefulness for measurements at various values of prestress is investigated. It is evident that the mathematical definition given in the Standard applies only in the special case when prestress and alternating stress are equal. For the complete range of prestress, the phase angle δ or some simple function of δ, such as the loss factor, tan δ, should be measured. If it is desired not to relinquish the percentage statement of the energy loss, then a new definition for the relative damping is proposed which is independent of the prestress, just as is tan δ. The dependence upon the prestress of the damping values under discussion is demonstrated in an experimental section, for various types of elastomers.

Formulas for Entraining Velocity in Lubricated Line Contacts

2002 ◽  
Vol 124 (4) ◽  
pp. 856-858
Author(s):  
Enrico Ciulli
Keyword(s):  
Relative Motion ◽  
Physical Meaning ◽  
Point Of View ◽  
Lubricated Contacts ◽  
Line Contacts ◽  
Two Bodies

The knowledge of the entraining velocity is necessary for the investigation of lubricated contacts. The entraining velocity is the average of the surface velocities of the two bodies in contact relative to the contact itself; its estimation can be actually not always immediate. In this work the general case of two pairing cylindrical surfaces in planar relative motion is analyzed from a kinematical point of view. Formulas for the evaluation of the entraining velocity are presented that are directly applicable to any case of connected members of a mechanism. The physical meaning of the terms of the proposed formulas is also briefly investigated from a lubrication point of view.

Wave-Energy Conversion Through Relative Motion Between Two Single-Mode Oscillating Bodies

1999 ◽  
Vol 121 (1) ◽  
pp. 32-38 ◽  
Author(s):  
J. Falnes
Keyword(s):  
Energy Conversion ◽  
Relative Motion ◽  
Wave Energy ◽  
Load Force ◽  
Wave Forces ◽  
Equivalent System ◽  
Wave Excitation ◽  
Excitation Force ◽  
Two Bodies ◽  
Wave Excitation Force

Wave-energy converters (WECs) need a reaction source against which the wave forces can react. As with shore-based WECs, sometimes also floating WECs react against a fixed point on the seabed. Alternatively, for a floating WEC, force reaction may be obtained by utilizing the relative motion between two bodies. A load force for energy conversion is assumed to be applied only to this relative motion. It is assumed that either body oscillates in one mode only (mostly, the heave mode is considered here). The system, if assumed to be linear, is proved to be phenomenologically equivalent to a one-mode, one-body system, for which the wave excitation force equals the force which is necessary to apply between the two bodies in order to ensure that they are oscillating with zero relative motion. It is discussed how this equivalent excitation force and also the intrinsic mechanical impedance of the equivalent system depend on the mechanical impedances for the two separate bodies, including the radiation impedance matrix (which combines radiation resistances and added masses). The equivalent system is applied for discussing optimum performance for maximizing the absorbed wave energy. It is shown that, for an axisymmetric system utilizing heave modes, it is possible to absorb an energy amounting to the incident wave power on a crest length which equals the wavelength divided by 2π, even though the power take-off is applied to the relative motion only. Moreover, it is shown that it is possible to obtain an equivalent excitation force which exceeds the wave excitation force on either body.

The translation of two bodies under the free surface of a heavy fluid

1950 ◽  
Vol 46 (3) ◽  
pp. 453-468 ◽  
Author(s):  
A. Coombs
Keyword(s):  
Free Surface ◽  
Large Range ◽  
Three Dimensional ◽  
Finite Depth ◽  
Arbitrary Cross Section ◽  
Wave Resistance ◽  
Vertical Force ◽  
First Approximation ◽  
Special Case ◽  
Two Bodies

1. Many investigations have been made to determine the wave resistance acting on a body moving horizontally and uniformly in a heavy, perfect fluid. Lamb obtained a first approximation for the wave resistance on a long circular cylinder, and this was later confirmed to be quite sufficient over a large range. In 1926 and 1928, Havelock (4, 5) obtained a second approximation for the wave resistance and a first approximation for the vertical force or lift. Later, in 1936(6), he gave a complete analytical solution to this problem, in which the forces were expressed in the form of infinite series in powers of the ratio of the radius of the cylinder to the depth of the centre below the free surface of the fluid. General expressions for the wave resistance and lift of a cylinder of arbitrary cross-section were found by Kotchin (7) using integral equations, and the special case of a flat plate was evaluated. He continued with a discussion of the motion of a three-dimensional body. More recently, Haskind (3) has examined the same problem when the stream has a finite depth.

scholarly journals A Control System For Constrained Wave-Powered Oceanographic Buoys

2020 ◽  
Vol 2 (1 (Nov)) ◽  
pp. 51-61
Author(s):  
Shangyan Zou ◽  
Ossama Abdelkhalik
Keyword(s):  
Relative Motion ◽  
Wave Energy ◽  
Control Strategy ◽  
Real Data ◽  
Nonlinear Damping ◽  
Irregular Waves ◽  
Coastal Observatory ◽  
Switching Control Strategy ◽  
Displacement Constraints ◽  
Two Bodies

Wave energy can be used to power oceanographic buoys. A new switching control strategy is developed in this paper for a two-body heaving wave energy converter that is composed of a floating cylinder and two rigidly connected submerged hemispheres. This control strategy is designed to prevent excessive displacement of the floating buoy that may occur due to the actuator force. This control strategy switches the control between a multi-resonant controller and a nonlinear damping controller, depending on the state of the system, to account for displacement constraints. This control strategy is developed using a one-degree-of-freedom dynamic model for the relative motion of the two bodies. Estimation of the relative motion, needed for feedback control, is carried out using a Kalman filter. Numerical simulations are conducted to select the proper mooring stiffness. The controller is tested with stochastic models of irregular waves in this paper. The performance of the controller with different sea states is discussed. Annual power production using this control strategy is presented based on real data in 2015 published by Martha's Vineyard Coastal Observatory.

Experimental Study on the Possibilities to Decrease the Coefficient of Restitution after Impact

2012 ◽  
Vol 217-219 ◽  
pp. 1659-1662 ◽  
Author(s):  
Todor Nikolov Penchev ◽  
Ivan Lyubomirov Altaparmakov ◽  
Dimitar Nedelchev Karastojanov
Keyword(s):  
Experimental Study ◽  
Laboratory Test ◽  
Experimental Research ◽  
Rocket Engine ◽  
Coefficient Of Restitution ◽  
Compressed Air ◽  
Pile Driving ◽  
Additional Force ◽  
Forging Die ◽  
Two Bodies

Technological processes such as forging, die forging, pile driving, etc., are realized as a result of a collision between two bodies. The bodies’ rebound after the collision takes place due to the use of part of the energy of the hit for their elastic deformation. The paper presents results from an experimental research on the possibilities of the decrease of rebound, by the use of an additional force during the hit. A laboratory test-stand is described in which an additional force is created by the use of a cold rocket engine, working with compressed air.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1996 ◽  
Vol 63 (4) ◽  
pp. 974-984 ◽  
Author(s):  
N. Sankar ◽  
V. Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid-body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

scholarly journals Rheology of an Ice-Floe Field

1984 ◽  
Vol 5 ◽  
pp. 23-28 ◽  
Author(s):  
Iain Bratchie
Keyword(s):  
Sea Ice ◽  
Energy Loss ◽  
Strain Rate ◽  
Yield Curve ◽  
Sine Wave ◽  
Two Dimensional ◽  
Number Density ◽  
Yield Curves ◽  
Develop Theory ◽  
Ice Strength

The aim of the paper is (1) to develop theory to describe sea ice as a collection of finite-sized floes and (2) to construct a rheology based on this description.Successful sea-ice models have considered the ice to be a two-dimensional continuum with a nonlinear plastic rheology, a two-dimensional yield curve being used to determine the internal ice stresses as functions of the strain-rate (Hibler 1979). In this paper, the shape but not the size of such a yield curve is derived from an idealized picture of floes as moving discs, randomly distributed in a plane. The expected collision rate, which determines the energy loss, is calculated in terms of the average floe size, the areal floe-number density, and the strain-rate. For the case in which the ice strength is low, the dependence of the energy loss upon the strain-rate implies a lens-shaped yield curve, the curved portions being parts of a sine wave. This compares with circular, tear drop-shaped and elliptical yield curves that have been used in sea-ice models to date (Coon 1974, Colony 1976, Hibler 1979). The applicability of the derived yield curve to cases where the ice strength is not low and significant ridging takes place, such as in a continuous ice cover is discussed.

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