Closure to “Discussion of ‘Contact Region of a Hard Ball Rolling on a Viscoelastic Plate’” (1968, ASME J. Lubr. Technol., 90, p. 634)

1968 ◽  
Vol 90 (3) ◽  
pp. 634-634
Author(s):  
J. Halaunbrenner ◽  
A. Kubisz
Keyword(s):  
Contact Region ◽  
Viscoelastic Plate ◽  
Ball Rolling ◽  
Hard Ball

Contact Region of a Hard Ball Rolling on a Viscoelastic Plate

1968 ◽  
Vol 90 (1) ◽  
pp. 101-105 ◽  
Author(s):  
J. Halaunbrenner ◽  
A. Kubisz
Keyword(s):  
Contact Area ◽  
Contact Region ◽  
Superposition Principle ◽  
Viscoelastic Plate ◽  
Observation Data ◽  
Relaxation Functions ◽  
Ball Rolling ◽  
Mutually Independent ◽  
Interference Picture ◽  
Hard Ball

In the work presented, the contact region of a glass ball rolling without slip on a flat plate of viscoelastic material at various velocities was recorded. An interference microscope was used. Deformation of the base in the vicinity of the contact area was read from the interference picture obtained due to a narrow air gap between the ball and the base. The material of the base was characterized by creep and relaxation functions at constant temperature of (21 ± 0.5) deg C. The viscoelastic continuum of the base was replaced by the system of mutually independent vertical columns. By a subsequent twofold application of Boltzmann’s superposition principle, the diameter of the contact surface parallel to the velocity vector of the ball and depth of the concave track behind the ball were calculated. The results obtained were compared with observation data. Satisfactory agreement in cases where the shape of the contact area does not differ considerably from a circle (for small and great rolling velocities) was obtained.

Hard Ball Systems and the Lorentz Gas

2000 ◽  
Author(s):  
L. A. Bunimovich ◽  
D. Burago ◽  
N. Chernov ◽  
E. G. D. Cohen ◽  
C. P. Dettmann ◽  
...  
Keyword(s):  
Lorentz Gas ◽  
Hard Ball

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

Analysis of the Contact Deformation of a Radial Tire with Camber Angle

1995 ◽  
Vol 23 (1) ◽  
pp. 26-51 ◽  
Author(s):  
S. Kagami ◽  
T. Akasaka ◽  
H. Shiobara ◽  
A. Hasegawa
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Region ◽  
Contact Deformation ◽  
Contact Pressure Distribution ◽  
Radial Tire ◽  
Ring Model ◽  
Camber Angle ◽  
Contact Free ◽  
Good Agreement

Abstract The contact deformation of a radial tire with a camber angle, has been an important problem closely related to the cornering characteristics of radial tires. The analysis of this problem has been considered to be so difficult mathematically in describing the asymmetric deformation of a radial tire contacting with the roadway, that few papers have been published. In this paper, we present an analytical approach to this problem by using a spring bedded ring model consisting of sidewall spring systems in the radial, the lateral, and the circumferential directions and a spring bed of the tread rubber, together with a ring strip of the composite belt. Analytical solutions for each belt deformation in the contact and the contact-free regions are connected by appropriate boundary conditions at both ends. Galerkin's method is used for solving the additional deflection function defined in the contact region. This function plays an important role in determining the contact pressure distribution. Numerical calculations and experiments are conducted for a radial tire of 175SR14. Good agreement between the predicted and the measured results was obtained for two dimensional contact pressure distribution and the camber thrust characterized by the camber angle.

State of Stress in the Near-Contact Region of a Semiconductor during Metallization Track Electrodegradation

2020 ◽  
Vol 2020 (13) ◽  
pp. 1658-1662
Author(s):  
A. A. Skvortsov ◽  
S. M. Zuev ◽  
M. V. Koryachko ◽  
E. B. Voloshinov
Keyword(s):  
Contact Region ◽  
State Of Stress

Rough Air-Soft Elastohydrodynamic Lubrication

2013 ◽  
Vol 420 ◽  
pp. 30-35
Author(s):  
Khanittha Wongseedakaew ◽  
Jesda Panichakorn
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Modulus Of Elasticity ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Multilevel Methods ◽  
Inlet Temperature ◽  
Film Pressure ◽  
Air Inlet ◽  
Air Film

This paper presents the effects of rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material under the effect of air molecular slip. The time independent modified Reynolds equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness, modulus of elasticity and air inlet temperature are examined. The simulation results showed surface roughness has effect on film thickness but it little effect to air film pressure. When the amplitude of surface roughness and modulus of elasticity increased, the air film thickness decreased but air film pressure increased. However, the air inlet temperature increased when the air film thickness increased.

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