The Effect of a Tangential Contact Force Upon the Rolling Motion of an Elastic Sphere on a Plane

1958 ◽  
Vol 25 (3) ◽  
pp. 339-346
Author(s):  
K. L. Johnson
Keyword(s):  
Tangential Force ◽  
Elastic Plane ◽  
Rolling Motion ◽  
Elastic Sphere ◽  
Normal Contact ◽  
Ball Rolling ◽  
Slip Region ◽  
Flat Steel ◽  
Normal Contact Pressure ◽  
Theoretical Results

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane under a normal contact pressure N have been studied for the case where a tangential force T is also sustained at the point of contact. Provided that T < μN (μ = coefficient of friction), the sphere rolls without sliding but exhibits a small velocity relative to the plane, termed “creep.” Following the work of Mindlin and Poritsky, it is shown that creep arises from slip over part of the area of contact, and further, that this slip takes place toward the trailing edge of the contact area. On the assumption of a locked region in which no slip occurs, of circular shape, tangential to the circle of contact at its leading point, surface tractions are found which satisfy the condition of no slip within the locked region and are approximately consistent with the laws of friction in the slip region. The variation of creep velocity with tangential force is thereby determined. Experimental measurements of the creep of a steel ball rolling on a flat steel surface are in reasonable agreement with the theoretical results.

The Effect of Spin Upon the Rolling Motion of an Elastic Sphere on a Plane

1958 ◽  
Vol 25 (3) ◽  
pp. 332-338
Author(s):  
K. L. Johnson
Keyword(s):  
Thrust Bearing ◽  
Theoretical Estimate ◽  
Leading Edge ◽  
Small Extent ◽  
Partial Slip ◽  
Elastic Plane ◽  
Rolling Motion ◽  
Elastic Sphere ◽  
Quantitative Measurements ◽  
Wide Range

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane are examined for the case when the sphere, in addition to its straight rolling motion, has an angular velocity of “spin” Ω about an axis normal to the plane. The action of spin is to twist the area of contact. Surface tractions resulting from this rotation are found, which demonstrate the necessity of partial slip in the area of contact. Previous investigations suggest that this slip cannot occur at the leading edge of the contact circle, so that a system of tractions is found which corresponds to zero stress at the leading point. It is shown that such a system of tractions gives rise to a transverse creep of the sphere in the direction of its rotation Ω. The magnitude of this creep is calculated for small values of Ω, when slip occurs to only a small extent. Experiments have been performed using a simple thrust bearing with plane parallel races. As the bearing rotates, the balls creep radially outward in the predicted manner. Quantitative measurements of this creep agree with the theoretical estimate over a wide range.

scholarly journals Micromechanism of the Breakage of Two Spherical Gypsum Particles under Normal–Tangential Contact Conditions

2021 ◽  
Vol 11 (9) ◽  
pp. 4039
Author(s):  
Yiran Niu ◽  
Lin Li ◽  
Yanwei Zhang ◽  
Shicai Yu ◽  
Jian Zhou
Keyword(s):  
Tangential Force ◽  
Coarse Grained ◽  
Spherical Particles ◽  
Contact Conditions ◽  
Normal Contact ◽  
Tangential Contact ◽  
Theoretical Predictions ◽  
Tangential Forces ◽  
Predicted Values ◽  
The Relationship

Contact breakage of particles makes a large difference in the strength of coarse-grained soils, and exploring the characteristics within the process of the breakage is of great significance. Ignoring the influence of particle shape, the micromechanism of two spherical particles breaking under normal–tangential contact conditions was investigated theoretically and experimentally. Through theoretical analysis, the breakage form, the shape and size of the conical core, and the relationship between the normal and tangential forces at crushing were predicted. Particle contact tests of two gypsum spheres were carried out, in which the breakage forms, features of the conical cores and the normal and tangential forces at crushing were recorded for comparison with the predicted values. The test results and the theoretical predictions showed good agreement. Both the analysis and test demonstrate that the presence of tangential forces causes the conical core to assume the shape of an oblique cone, and the breakage form to change. Moreover, with increasing normal contact force, the tangential force needed for crushing increases gradually first and then decreases suddenly.

An Extension of CEB Elastic-Plastic Contact Model

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Contact Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Normal Contact ◽  
Elastic Plastic ◽  
Force Components ◽  
Plastic Parts

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is by developing the equations governing the shoulder-shoulder contact of asperities based on the Chang, Etsion and Bogy (CEB) model of contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Each force component comprises elastic and elastic-plastic parts. Statistical summation of normal force components leads to the derivation of the normal contact force for the elastic-plastic contact akin to the CEB model. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction.

scholarly journals The effect of sampling interval on the predictions of an asperity contact model of two-process surfaces

2017 ◽  
Vol 65 (3) ◽  
pp. 391-398 ◽  
Author(s):  
P. Pawlus ◽  
R. Reizer ◽  
M. Wieczorowski ◽  
W. Żelasko
Keyword(s):  
Surface Region ◽  
Sampling Interval ◽  
Plasticity Index ◽  
Contact Model ◽  
Asperity Contact ◽  
Normal Contact ◽  
Method Of Calculation ◽  
Surface Separation ◽  
Sampling Intervals ◽  
Flat Steel

AbstractContact of random machined two-process steel textures with a smooth, flat steel surface is discussed in this paper. Two-process surfaces were machined by vapour blasting followed by lapping. An elastic-plastic contact model was applied, assuming distributed radius of asperities. Calculation procedures allowed the mean surface separation, contact pressure, and area fraction to be computed as functions of sampling intervals. Parameters characterizing the summits important in contact mechanics were calculated for different sampling intervals. Plasticity index of two-process textures was calculated using the modified procedure. It was found that the influence of sampling interval on normal contact depended on the rough surface ability to plastic deformation. The use of a traditional method of calculation overestimated the plasticity index. Peaks from plateau surface region governed contact characteristics of two-process surfaces.

scholarly journals The Effect of Multilayer Architecture and Ta Alloying on the Mechanical Performance of Ti-Al-N Coatings under Scratching and Uniaxial Tension

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1307
Author(s):  
Artur Rubinovich Shugurov ◽  
Evgenii Dmitrievich Kuzminov
Keyword(s):  
Uniaxial Tension ◽  
Mechanical Performance ◽  
Multilayer Coating ◽  
High Hardness ◽  
Scratch Testing ◽  
Normal Contact ◽  
Multilayer Architecture ◽  
Normal Contact Pressure ◽  
Steel Substrates ◽  
Metal Layers

The present work is focused on a comparative study of the effect of Ti-Al interlayers and Ta alloying on the mechanical behavior of Ti1−xAlxN coatings under normal contact pressure and in-plane straining. The contact loading of the samples was carried out by scratch testing, while the in-plane tensile straining was performed by uniaxial tension of the coated steel substrates. The Ti0.45Al0.55N and Ti0.43Al0.45Ta0.12N monolithic coatings as well as the Ti0.45Al0.55N/Ti0.45Al0.55 multilayer coatings with different number and thickness of the layers were deposited by DC magnetron sputtering. It was found that the introduction of the ductile Ti0.45Al0.55 layers into the Ti0.45Al0.55N coating and alloying with Ta led to their significant toughening. The improved toughness of the Ti0.43Al0.45Ta0.12N coating coupled with high residual compressive stress and high hardness resulted in its strongest resistance to cracking under scratching and tensile straining among the coatings studied. The multilayer coating with the thickest metal layers exhibited the improved resistance to delamination under in-plane straining.

Contact Stiffness Parameters for Finite Element Modeling of Contact

2019 ◽  
Vol 799 ◽  
pp. 211-216
Author(s):  
Alina Sivitski ◽  
Priit Põdra
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Contact Stiffness ◽  
Influential Factors ◽  
Element Analysis ◽  
Normal Contact ◽  
Element Modeling ◽  
Contact Models ◽  
Machine Elements ◽  
Normal Contact Pressure

Contact modeling could be widely used for different machine elements normal contact pressure calculations and wear simulations. However, classical contact models as for example Hertz contact models have many assumptions (contact bodies are elastic, the contact between bodies is ellipse-shaped, contact is frictionless and non-conforming). In conditions, when analytical calculations cannot be performed and experimental research is economically inexpedient, numerical methods have been applied for solving such engineering tasks. Contact stiffness parameters appear to be one of the most influential factors during finite element modeling of contact. Contact stiffness factors are usually selected according to finite element analysis software recommendations. More precise analysis of contact stiffness parameters is often required for finite element modeling of contact.

Tangential Force Model for the Combined Finite-Discrete Element Method

2019 ◽  
Vol 17 (09) ◽  
pp. 1950068
Author(s):  
Xunnan Liu ◽  
Lanhao Zhao ◽  
Jia Mao ◽  
Tongchun Li
Keyword(s):  
Discrete Element Method ◽  
Contact Interaction ◽  
Contact Force ◽  
Tangential Force ◽  
Numerical Test ◽  
Discrete Element ◽  
Force Model ◽  
Normal Contact ◽  
Tangential Contact ◽  
Element Method

In the past, contact model in the combined finite-discrete element method (FDEM) does not include the influence of the tangential contact interaction, and the deficient model associated with the contact force can seriously degrade the computing accuracy. In order to overcome this defect, an improved FDEM is developed in this work. The potential contact mechanism is implemented to calculate the normal contact force; meanwhile, the force-displacement law by coupling the classical Mohr–Coulomb type frictional algorithm and the rotation transformation algorithm is applied for the accurate computation of the tangential contact force. Consequently, a holonomic system of the calculation algorithm for the contact interaction is proposed, accounting for the influence of the tangential contact force. The performance of the approach is validated with well-known benchmarks including a frictional numerical test, the dynamic response of the block under the seismic excitation, a sliding/toppling test of a joint rock slope, a numerical simulation for joints structure affecting a sliding rock mass and the 2008 Donghekou Landslide trigged by the Wenchuan Earthquake. The results are compared against the experimental data and analytical solutions. Excellent agreements between the computational result and existing measurements show that the proposed approach has an outstanding ability to describe the complex mechanical properties among the separate entities.

scholarly journals Rolling of a rigid ball on a horizontal deformable surface

2004 ◽  
Vol 46 (2) ◽  
pp. 249-264
Author(s):  
Maurice N. Brearley ◽  
Neville J. De Mestre
Keyword(s):  
Finite Strain ◽  
Strain Theory ◽  
Golf Ball ◽  
Rigid Sphere ◽  
Billiard Ball ◽  
Ball Rolling ◽  
Deformable Surface ◽  
Finite Strain Theory ◽  
Theoretical Results

AbstractThe rolling of a ball on a horizontal deformable surface was investigated under the assumptions that the ball was a rigid sphere and the surface was elastic. Finite strain theory was used to develop theoretical results which were found to match observations well in cases where the ball and surface involved were such as to ensure no slipping at the region of contact, including a lawn bowl rolling on a grass rink and a billiard ball rolling on carpet. The theory did not match well the behaviour of a golf ball on a grass green because the ball was too light to enforce the no-slipping condition.

Experimental Investigation of Rolling Contact

1965 ◽  
Vol 32 (4) ◽  
pp. 859-864 ◽  
Author(s):  
Aris C. Spengos
Keyword(s):  
Experimental Investigation ◽  
Contact Area ◽  
Tangential Force ◽  
Leading Edge ◽  
Rolling Contact ◽  
Qualitative Investigation ◽  
Steel Cylinder ◽  
Constant Rate ◽  
Slip Region ◽  
Action Taking

A particular case of rolling contact, that for cylinders having different elastic constants and transmitting a tangential force in the direction of rolling, was experimentally investigated. A steel cylinder, driving a rubber-covered cylinder, was instrumented for the quantitative, as well as qualitative, investigation of the action taking place in the contact area. The results indicate the extent of the locked region at the leading edge of the contact area, the development of the slip region, and the magnitude of the constant-rate slip at the trailing edge of the contact area.

Sign in / Sign up

Export Citation Format

Share Document