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.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

Contact area of a ball rolling on an adhesive viscoelastic material

Wear ◽  
1978 ◽  
Vol 51 (2) ◽  
pp. 375-384 ◽  
Author(s):  
M. Barquins ◽  
D. Maugis ◽  
J. Blouet ◽  
R. Courtel
Keyword(s):  
Viscoelastic Material ◽  
Contact Area ◽  
Ball Rolling

A Study of the Effect of m and n Coefficients of the Hertzian Contact Theory on Railroad Vehicle Dynamics

2007 ◽  
Author(s):  
J. P. Pascal ◽  
Khaled E. Zaazaa
Keyword(s):  
Contact Area ◽  
Contact Region ◽  
Local Deformation ◽  
Hertzian Contact ◽  
Vehicle Dynamic ◽  
Railroad Vehicle Dynamics ◽  
Original Table ◽  
Data Points ◽  
Railroad Vehicle ◽  
Contact Ellipse

For the wheel/rail contact problem, the Hertz theory for two elastic bodies in contact is commonly used to determine the shape and dimensions of the contact area and the local deformation of the wheel and rail surfaces at the contact region. The shape of the contact area is assumed to be elliptical. The ratio of the contact ellipse semi-axes is equal to the ratio of two non-dimensional contact area coefficients, known as m and n coefficients. Hertz presented a table of these two coefficients, determined as a function of an angular parameter, θ. Most railroad vehicle dynamic codes use this table with online interpolation to determine the contact ellipse semi-axes. Recently, it was found that this original table may be too coarse, and that more data points are needed within the table for solving the wheel/rail contact accurately. This paper discusses the effect of the accuracy of the m and n coefficients in solving for wheel/rail contact, and demonstrates this effect with two numerical examples that show the resulting differences in the dynamic behavior of railroad vehicles dependent on this accuracy. A new table with more data points is presented that is recommended for use in railroad vehicle dynamic codes that employ the Hertzian contact for solving the wheel/rail contact interaction. This modified table was originally derived by Jean-Pierre Pascal as a part of collaborative research between the Federal Railroad Administration (FRA) and the French Ministry of Transportation.

Fixturing Effects in the Thermal Modeling of Laser Cladding

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. F. Gouge ◽  
P. Michaleris ◽  
T. A. Palmer
Keyword(s):  
Surface Roughness ◽  
Laser Cladding ◽  
Contact Area ◽  
Contact Region ◽  
Thermal Modeling ◽  
Model Error ◽  
Effective Contact ◽  
Contact Conductivity

Fixturing of components during laser cladding can incur significant conductive thermal losses. However, due to the surface roughness at contact, interfacial conduction is impeded. The effective contact conductivity, known as gap conductance, is much lower than the contacting material conductivities. This work investigates modeling conduction losses to fixturing bodies during laser cladding. Two laser cladding experiments are performed using contrasting fixturing schemes: one cantilevered substrate with a minimal substrate-fixture contact area and one with a substrate bolted to a work bench, with a significant substrate-fixture contact area. Using calibrated gap conductance values, error for the cantilevered fixture model decreases from 20.5% to 6.49% in the contact region, while the bench fixtured model error decreases from a range of 60–102% to 11–45%. The improvement in accuracy shows the necessity of accounting for conduction losses in the thermal modeling of laser cladding, particularly for fixturing setups with large areas of contact.

scholarly journals Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour

2008 ◽  
Vol 5 (25) ◽  
pp. 835-844 ◽  
Author(s):  
Jongho Lee ◽  
Carmel Majidi ◽  
Bryan Schubert ◽  
Ronald S Fearing
Keyword(s):  
Elastic Modulus ◽  
Contact Area ◽  
Shear Force ◽  
Contact Region ◽  
Pure Shear ◽  
Shear Loading ◽  
High Shear ◽  
Polypropylene Fibres ◽  
True Contact Area ◽  
True Contact

Gecko-inspired microfibre arrays with 42 million polypropylene fibres cm −2 (each fibre with elastic modulus 1 GPa, length 20 μm and diameter 0.6 μm) were fabricated and tested under pure shear loading conditions, after removing a preload of less than 0.1 N cm −2 . After sliding to engage fibres, 2 cm 2 patches developed up to 4 N of shear force with an estimated contact region of 0.44 cm 2 . The control unfibrillated surface had no measurable shear force. For comparison, a natural setal patch tested under the same conditions on smooth glass showed approximately seven times greater shear per unit estimated contact region. Similar to gecko fibre arrays, the synthetic patch maintains contact and increases shear force with sliding. The high shear force observed (approx. 210 nN per fibre) suggests that fibres are in side contact, providing a larger true contact area than would be obtained by tip contact. Shear force increased over the course of repeated tests for synthetic patches, suggesting deformation of fibres into more favourable conformations.

scholarly journals Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory

2020 ◽  
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi ◽  
Kassem Mustapha
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Decay Rate ◽  
Viscoelastic Plate ◽  
Plate Equation ◽  
Infinite Memory ◽  
Time Stepping ◽  
Energy Decay Rate ◽  
Relaxation Functions ◽  
General Energy

Abstract In this paper, a weakly dissipative viscoelastic plate equation with an infinite memory is considered. We show a general energy decay rate for a wide class of relaxation functions. To support our theoretical findings, some numerical illustrations are presented at the end. The numerical solution is computed using the popular finite element method in space, combined with time-stepping finite differences.

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