The Motion of a Compliantly Suspended Rigid Body Constrained by Multipoint Frictional Contact

2005 ◽  
Vol 127 (4) ◽  
pp. 623-632
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Friction Force ◽  
Coefficient Of Friction ◽  
Coulomb Friction ◽  
Frictional Contact ◽  
The Body ◽  
Elastic Behavior ◽  
Inertial Forces ◽  
Active Constraints ◽  
The Coefficient Of Friction

This paper addresses methods for determining the motion of an elastically suspended rigid body in frictional contact at multiple distinct locations. The methods developed assume that: (1) The motion of the support from which the body is suspended and the elastic behavior of the suspension are known; (2) inertial forces are negligible (motion is quasi-static); and (3) the contact is characterized by Coulomb friction. The derived coupled set of spatial rigid body equations is used to determine both the unknown direction of the friction force (at each point of contact) and the unknown motion of the rigid body. The uniqueness of the set of active constraints when considering multipoint contact is also addressed. We show that, for any passive compliant system, if the coefficient of friction at each contact is upper bounded, the set of active constraints is unique. A procedure to determine both the set of active constraints and the motion of the constrained body is provided.

The Spatial Motion of a Compliantly Suspended Rigid Body Constrained by Multi-Point Frictional Contact

2003 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Friction Force ◽  
Coulomb Friction ◽  
Frictional Contact ◽  
The Body ◽  
Elastic Behavior ◽  
Inertial Forces ◽  
Spatial Motion ◽  
Frictional Surfaces

This paper addresses methods for determining the motion of an elastically suspended rigid body interacting with frictional surfaces at multiple locations. The methods developed assume: 1) that the motion of the base from which the body is suspended and the elastic behavior of the suspension are known, 2) that inertial forces are negligible (motion is quasi-static), and 3) that the interaction is characterized by Coulomb friction. The derived coupled sets of spatial rigid body equations are used to determine both the unknown direction of the friction force (at each point of contact) and the unknown motion of the rigid body.

Determining the Set of Active Constraints When a Rigid Body Compliantly Interacts With Multiple Frictional Contacts

2004 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Elastic Properties ◽  
Coefficient Of Friction ◽  
Coulomb Friction ◽  
Frictional Contact ◽  
Contact Point ◽  
Frictional Contacts ◽  
Active Constraints ◽  
The Coefficient Of Friction ◽  
Individual Contact

In this paper, the motion of an elastically suspended rigid body unilaterally constrained by frictional contact at multiple locations is studied. In this problem, each individual contact may or may not constrain the body’s motion. The set of actual active constraints is determined by: 1) the commanded motion of the body’s compliant support, 2) the coefficient of friction at each contact point, 3) the number and geometry of all potentially constraining surfaces, and 4) the elastic properties of the support. Here, the investigated problem is restricted to quasistatic motion and the interaction is characterized by Coulomb friction. We show that, for a passive compliant system, if the coefficient of friction at each contact is upper bounded, the set of active constraints is unique. A procedure to determine both the set of active constraints and the motion of the constrained body is provided.

The Motion of a Compliantly Suspended Rigid Body Constrained by a Frictional Surface

2001 ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Friction Force ◽  
Coulomb Friction ◽  
Unilateral Constraint ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Elastic Behavior ◽  
Frictional Surface ◽  
Elastic Suspension ◽  
Controlled Motion

Abstract In this paper, the quasistatic motion of an elastically suspended, unilaterally constrained rigid body is studied. The motion of the rigid body is determined, in part, by the position controlled motion of its support base and the behavior of the elastic suspension that couples the part to the support. The motion is also determined, in part, by contact with a frictional surface that both couples the rigid body to unilateral constraint surfaces and generates a friction force. The unknown friction force, however, is determined in part by the unknown direction of the rigid body motion. We derive a solvable set of equations that simultaneously determines both the friction force and the resulting rigid body motion. This set of equations requires that the friction and motion at the point of contact are oppositely directed. Solution involves the use of rigid body kinematics, the Coulomb friction coefficient, the commanded motion of the support, and the spatial elastic behavior of the coupling.

Stresses Due to Tangential and Normal Loads on an Elastic Solid With Application to Some Contact Stress Problems

1953 ◽  
Vol 20 (2) ◽  
pp. 157-166
Author(s):  
J. O. Smith ◽  
Chang Keng Liu
Keyword(s):  
Plane Strain ◽  
Coefficient Of Friction ◽  
Contact Area ◽  
Normal Load ◽  
Elastic Solid ◽  
Real Variable ◽  
The Body ◽  
Shearing Stress ◽  
Tangential Load ◽  
The Coefficient Of Friction

Abstract The results of two-dimensional approach using real variable method to Hertz’s problem of contact of elastic bodies are presented. Both normal and tangential loads are assumed to be distributed in Hertzian fashion over the area of contact. The magnitude of the intensity of the tangential load is assumed to be linearly proportional to that of the normal load when sliding motion of the body is impending. The stresses in the elastic body due to the application of these loads on its boundary are presented in closed form for both plane-stress and plane-strain cases. A numerical value of f = 1/3 is assumed for the linear proportionality (coefficient of friction) between the tangential and normal loads in order that the distribution of stresses may be illustrated. The significance of the stress distribution, across the contact area and in the body, is also discussed. It is shown that when the combination of loads considered in the paper are applied at the contact area of bodies in contact the maximum shearing stress may be at the surface instead of beneath the surface. For example, for plane strain, if the coefficient of friction is f = 1/3, the maximum shearing stress is at the surface and is 43 per cent larger than the maximum shearing stress, which would be below the surface, that occurs when the normal force acts alone. The effect of range of normal stress and of shearing stress on the plane of maximum shear and on the plane of maximum octahedral shear on failure by progressive fracture (fatigue) is discussed.

ON THE FRICTION OF INFLATED RUBBER TIRES ON ICE

1958 ◽  
Vol 36 (5) ◽  
pp. 599-610 ◽  
Author(s):  
C. D. Niven
Keyword(s):  
Friction Force ◽  
Coefficient Of Friction ◽  
Sliding Friction ◽  
Rolling Friction ◽  
The Other ◽  
Slow Speed ◽  
Dry Ice ◽  
Load Axis ◽  
Cold Room ◽  
The Coefficient Of Friction

The friction on ice of some small inflated rubber tires was measured on a turntable in a cold room. When rolling-friction force was plotted against load, the relation was either linear or slightly curved away from the load axis; such curvature implies that Thirion's Law does not hold for rolling friction. On the other hand when sliding-friction force was plotted against load the curvature was toward the load axis as would be expected if Thirion's Law applied. The coefficient of friction can go as low as 0.01 or even lower for a hard-pumped tire when the temperature is near 0 °C, but at −1 °C. rolling friction on dry ice is quite appreciable. The results refer only to measurements at very slow speed.

scholarly journals A Contact Characteristic of Roller Bearing with Palm Oil-based Grease Lubrication

2021 ◽  
Vol 89 (2) ◽  
pp. 139-149
Author(s):  
Yap Jun Heng ◽  
Nurul Farhana Mohd Yusof ◽  
Lee Ann Yen ◽  
Shazlina Abd Hamid ◽  
Nurul Nadzirah Mohd Yusof
Keyword(s):  
Finite Element ◽  
Coefficient Of Friction ◽  
Palm Oil ◽  
Frictional Contact ◽  
Roller Bearing ◽  
Rolling Contact ◽  
Von Mises Stress ◽  
The Coefficient Of Friction ◽  
Contact Characteristic ◽  
Von Mises

Grease lubricants are widely used in rolling contact applications to reduce friction between two rolling surfaces. Improper lubrication may cause high contact stress and deformation to the bearings and lead to machine failure The purpose of this study is to investigate the coefficient of friction produced by newly developed palm oil-based grease and to investigate the contact characteristics in lubricated roller bearings. In this work, the coefficient of friction of new greases was evaluated experimentally and the values were compared with the conventional mineral oil-based grease to investigate the friction performance. The friction test was performed using a four-ball tester. The finite element model was developed based on the roller bearing geometry and the simulation was carried out the evaluate the contact characteristic. The experimental result shows that the palm oil grease formulation A had the least coefficient of friction, followed by palm oil grease formulation B, mineral grease and food grade grease. This indicates that palm oil-based grease has the potential to be applied in rolling contact applications due to low friction characteristics. Finite element analysis shows that the maximum von Mises stress and total deformation for frictional contact are higher than the frictionless contact. For the frictional contact analysis with various lubricant COF, similar values were obtained with von Mises stress at 400.69 MPa and 3.4033×10-4 mm deformation. The finding shows that the small difference in grease COF did not affect the rolling contact. The finding also shows that the newly developed biodegradable grease has a similar performance in terms of rolling contact friction and contact characteristic in a condition that the bearing is operating in normal condition.

A quasistatic frictional contact problem for viscoelastic materials with long memory

2020 ◽  
Vol 27 (2) ◽  
pp. 249-264
Author(s):  
Abderrezak Kasri ◽  
Arezki Touzaline
Keyword(s):  
Contact Problem ◽  
Coefficient Of Friction ◽  
Frictional Contact ◽  
Time Discretization ◽  
Contact Boundary ◽  
Long Term Memory ◽  
Viscoelastic Materials ◽  
Existence Of A Solution ◽  
Frictional Contact Problem ◽  
The Coefficient Of Friction

AbstractThe aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

The Effect of Magnesium Carbonate (Chalk) on Geometric Entropy, Force, and Electromyography During Rock Climbing

2016 ◽  
Vol 32 (6) ◽  
pp. 553-557 ◽  
Author(s):  
Matthew A. Kilgas ◽  
Scott N. Drum ◽  
Randall L. Jensen ◽  
Kevin C. Phillips ◽  
Phillip B. Watts
Keyword(s):  
Coefficient Of Friction ◽  
Body Position ◽  
Muscular Activity ◽  
Magnesium Carbonate ◽  
Rock Climbing ◽  
The Body ◽  
Movement Sequence ◽  
The Coefficient Of Friction ◽  
Hands And Feet ◽  
Static Coefficient Of Friction

Rock climbers believe chalk dries the hands of sweat and improves the static coefficient of friction between the hands and the surface of the rock. The purpose of this study was to assess whether chalk affects geometric entropy or muscular activity during rock climbing. Nineteen experienced recreational rock climbers (13 males, 6 females; 173.5 ± 7.0 cm; 67.5 ± 3.4 kg) completed 2 climbing trails with and without chalk. The body position of the climber and muscular activity of the finger flexors was recorded throughout the trial. Following the movement sequence participants hung from a standard climbing hold until they slipped from the climbing structure, while the coefficient of friction and the ratio of the vertical forces on the hands and feet were determined. Although there were no differences in the coefficient of friction (P = .748), geometric entropy (P = .359), the ratio of the vertical forces between the hands and feet (P = .570), or muscular activity (P = .968), participants were able to hang longer after the use of chalk 62.9 ± 36.7 s and 49.3 ± 25.2 s (P = .046). This is advantageous because it may allow for prolonged rests, and more time to plan the next series of climbing moves.

Friction Coefficients and Surface Properties for Laser Sintered Parts

2013 ◽  
Author(s):  
Daniel B. Roppenecker ◽  
Rebecca Grazek ◽  
Johannes A. Coy ◽  
Franz Irlinger ◽  
Tim C. Lueth
Keyword(s):  
Coefficient Of Friction ◽  
Flexural Modulus ◽  
Selective Laser Sintering ◽  
Influence Factors ◽  
The Body ◽  
Material Behavior ◽  
Basic Material ◽  
Layer By Layer ◽  
Stl File ◽  
The Coefficient Of Friction

Today different types of established rapid prototyping (RP) systems are available. In a Selective Laser Sintering (SLS)-process a CAD-model is designed and converted into a STL-file (Standard Tessellation Language). Next the body information is sliced into layers and transferred to the production system. By melting the powder-material using a laser beam, parts can be created layer by layer. Afterwards the parts are cleaned and several finishing treatments can be applied. The primarily aim in using RP was to reduce the product development time and to create design models. Nowadays whole assemblies and complex parts can be produced altogether in one manufacturing step with RP-systems. To ensure a save part construction due to calculation formulas and basic material constants, predictable design calculations are necessary. Concerning SLS-materials like polyamide PA 2200 components, only specific mechanical values like the tensile and flexural modulus have been identified. To fill this gap concerning tribological characteristics and to reach the next level of rapid manufacturing the key aspects of this article are the determination of the coefficient of friction μ0 of SLS-parts made of polyamide PA 2200 concerning several influence factors. An anisotropic material behavior, a decrease of the coefficient of friction μ0 with increasing contact pressure, larger contact areas and more intensive finishing treatment could be detected. Due to the knowledge of the identified material properties, now friction loaded components can be configured and used as functional machine parts.

Influence on Friction Force of Adhesion Force between Vulcanizates and Sliders

1994 ◽  
Vol 67 (5) ◽  
pp. 797-805 ◽  
Author(s):  
Kunio Mori ◽  
Satoshi Kaneda ◽  
Kentaro Kanae ◽  
Hidetoshi Hirahara ◽  
Yoshiyuki Oishi ◽  
...  
Keyword(s):  
Free Energy ◽  
Surface Free Energy ◽  
Friction Force ◽  
Coefficient Of Friction ◽  
Adhesion Force ◽  
High Surface ◽  
Low Surface Energy ◽  
Polar Groups ◽  
Slider Surface ◽  
The Coefficient Of Friction

Abstract The effects of vulcanizate and slider surface free energy—as well as the adhesion force (P) between them—on friction the force (F) and the coefficient of friction (μ) has been investigated. SBR and NBR vulcanizates were prepared using three molds differing in surface free energy. The mold with a high surface free energy gave a vulcanizate surface possessing polar groups. The mold with low surface energy gave a vulcanizate surface with many nonpolar groups. The coefficient of friction increased with the surface free energy of SBR and NBR vulcanizates. With SBR vulcanizate (surface free energy, 31.3 mJ·m−2) and teflon slider (surface free energy, 28.1 mJ·m−2) combination having the least surface free energy, the coefficient of friction was constant at greater than a 0.2N load. With vulcanizates and an aluminum slider with high surface free energy, friction force could be detected even at zero load because of the adhesion force at the interface. Friction force increased linearly with adhesion force between vulcanizates and sliders when the physical properties of the vulcanizates and net work chain density were constant. The present results clearly demonstrate the contribution of adhesion force to the friction of vulcanizates.

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