# friction

Friction , also known as friction or frictional resistance , is a force that acts between bodies or particles that touch each other. The frictional force then makes it difficult for the bodies to move against each other. In order to create or maintain movement, work is necessary. If friction occurs during movement, part of the work or kinetic energy is converted into frictional heat by dissipation and / or used for wear .

When considering friction processes, a distinction is made between external friction and internal friction . The outer friction occurs in friction between the contacting outer surfaces of solids. The internal friction occurs between adjacent particles in forming processes within solids, liquids and gases. In physical models, frictional forces are often neglected if they are relatively small and / or difficult to quantify. Tribology (friction theory) deals with the scientific investigation of friction processes .

## Types of friction

### External friction

Weight and normal force of a box on a flat surface

External friction is also known as solid body friction because it occurs between the contact surfaces of touching solid bodies. It is divided into static friction and dynamic friction , both of which are also known as Coulomb friction in honor of the physicist Charles Augustin de Coulomb . They do not always appear strictly separate from one another. They can occur simultaneously or alternately; for example, the stick-slip effect is a periodic transition between static and dynamic friction. Application-related terms are rolling friction , drilling friction and rope friction .

The maximum frictional force when adhering and the frictional force when gliding increase with the normal force with which the body presses perpendicularly on the surface or, conversely, the surface perpendicularly onto the body. Where the normal force comes from, whether z. B. solely on weight, through springs (clutch), hydraulic pressure ( disc brake ), the curve pressure in excessive curves or other processes is irrelevant here. Often the dependence is approximately linear and the frictional force is independent of the size of the contact area (see Amonton's laws ): ${\ displaystyle F _ {\ mathrm {R}} ^ {\ mathrm {max}}}$${\ displaystyle F _ {\ mathrm {R}}}$ ${\ displaystyle F _ {\ mathrm {N}}}$

${\ displaystyle F _ {\ mathrm {R}} ^ {\ mathrm {max}} \ leq \ mu _ {0} \ cdot F _ {\ mathrm {N}} \ qquad F _ {\ mathrm {R}} \ approx \ mu \ cdot F _ {\ mathrm {N}}}$.

The coefficient of friction µ depends on the nature of the surfaces. The coefficient for sticking ( ) is generally greater than that for sliding ( ). Their values ​​are determined experimentally. The inequality comes from the fact that a frictional force can never collide. ${\ displaystyle \ mu _ {0}}$${\ displaystyle \ mu}$

#### Static friction

In many cases, adherence between bodies in contact is desirable. Everyday life would not work at all without static friction. Furniture would not stay in place, vehicles parked on the street (the wheels blocked) could be moved by the wind alone. You couldn't put your foot “firmly” on the ground, all driven vehicle wheels would “spin”, so no traction would be possible. In technical applications, in addition to the weight force that usually acts, a technically generated pressure is used between the contact surfaces, for example by means of tensioned springs in a friction clutch .

Sticking is a state of rest in which the actual static friction force is always opposite to the parallel component of the external force. There is neither wear nor energy loss. Adhesion is a combination of form- locking on a small scale , through roughness as a 3rd to 5th order deviation in shape , which would be destroyed by movement, and molecular frictional locking on a small scale through molecular forces of attraction, i.e. adhesion .

#### Sliding friction

Sliding friction occurs on the contact surfaces between bodies that move relative to one another. The sliding friction force is usually less than the static friction force with the same normal force. According to Amontons' and Coulomb's laws, it is independent of the speed. With some material combinations, creep occurs, so that the frictional force becomes speed-dependent.

Fig. 1, 2 Static friction : The external force F and the static friction force F H are equal → The body does not move.
Fig. 3 Static friction : as in Fig. 1, but here the maximum static friction force F H, crit is reached. Since the external force is greater than the limit of adhesion, the body is accelerated.
Fig. 4 Sliding friction : the body slips with constant speed, the external force is less than F H, crit . The external force F is equal to the sliding friction force F R .
Only the forces in the direction of movement are shown.

#### Rolling friction

Rolling friction occurs when a body rolls on a surface. In the model, rolling friction can be explained by the deformation of a body that is not ideally rigid . Rolling friction is described by the dimensionless rolling friction coefficient. This is defined as the ratio of the rolling friction length and the radius of the rolling element: ${\ displaystyle d}$${\ displaystyle R}$

${\ displaystyle \ mu _ {\ mathrm {R}} = {d \ over R}}$

#### Rolling friction

If sliding and rolling friction are superimposed, this is referred to as rolling friction. This is the typical description model for bodies of revolution on a track, for example a wheel on a roadway.

#### Drilling friction

Drilling friction occurs at the point of support of a body rotating around the vertical axis on a plane. Since the drilling friction acts during a rotating movement, the drilling friction is given as torque :

${\ displaystyle M _ {\ mathrm {B}} = \ mu _ {\ mathrm {B}} \ cdot F _ {\ mathrm {N}}}$

The coefficient of drilling friction has the dimension of a length and can be interpreted as the radius of the apparent support washer, i.e. as the resulting lever arm of the moments of area. In general, however, it can not be calculated as the product of a constant mean radius of the support surface and a material constant. ${\ displaystyle \ mu _ {\ mathrm {B}}}$

#### Rope friction

The Euler-Eytelwein formula describes the friction of a rope wrapped around a round body, on which forces act on both sides, and indicates the conditions under which the rope adheres.

### Internal friction

Internal friction causes the viscosity of materials and fluids and influences deformations and flows. In addition to the movement of particles in a substance, internal friction also describes the frictional resistance of bodies moving in fluids and the attenuation of sound waves. Typically, internal friction (viscosity) increases with temperature in gases and decreases in liquids. In simple cases a quantitative description is possible with the means of statistical physics .

At temperatures close to zero , some liquids lose their internal friction completely (see superfluidity ).

In contrast to mechanics, in which friction is neglected as long as possible, internal friction is firmly contained in the standard theory of hydrodynamics , the Navier-Stokes equations (hence Stokes friction ). These non-linear equations can generally only be solved numerically. In the case of a small Reynolds number Re, i.e. if the advection of momentum versus momentum transport through viscosity can be neglected, there are closed solutions for simple geometries and Newtonian fluids :

This applies, for example, to a thin layer of lubricant between surfaces moving against one another. The friction is then proportional to the shear rate , i.e. the speed . The same conditions apply to the case of a small sphere in a viscous fluid, see Stokes' law . With dominant impulse advection, on the other hand, the dissipation is proportional to the square of the speed, see flow resistance . ${\ displaystyle v}$

The plastic deformation of solids is usually very non-linear and therefore cannot be easily described by viscosity. Even with smaller forces or tensions, there are deviations from the ideal elasticity as another type of internal friction in the solid, which, however, cannot simply be understood as viscosity. Correspondingly, the equation of internal friction and viscosity is limited to fluids.

## Frictional energy

According to the law of conservation of energy , no energy is lost through friction. This also applies when energy disappears from a system under consideration because it has been converted into thermal energy with an increase in entropy . A sliding hockey puck comes to a standstill because friction converts its kinetic energy into heat, which increases the thermal energy of the puck and the surface of the ice. Since this heat quickly dissipates , subject to early philosophers, including Aristotle , the fallacy that moving objects without losing influence a driving force energy.

When an object is moved along a path on a surface, the frictional work done is calculated from the product of the path and the force acting along the path, according to the definition of the work. If the force or the coefficient of friction are not constant over the path, a curve integral must be applied. ${\ displaystyle C}$${\ displaystyle {W} _ {\ mathrm {fric}} \,}$

Assuming complete conversion into thermal energy, the following applies

${\ displaystyle {W} _ {\ mathrm {fric}} = E _ {\ mathrm {th}} = \ int _ {C} \ mathbf {F} _ {\ mathrm {fric}} (\ mathbf {x}) \ cdot \ mathrm {d} \ mathbf {x} \ = \ int _ {C} \ mu _ {\ mathrm {k}} \ \ mathbf {F} _ {\ mathrm {n}} (\ mathbf {x} ) \ cdot \ mathrm {d} \ mathbf {x} \,}$

in which

${\ displaystyle \ mathbf {F} _ {\ mathrm {fric}} \,}$ the frictional force,
${\ displaystyle \ mathbf {F} _ {\ mathrm {n}} \,}$the normal force ,
${\ displaystyle \ mu _ {\ mathrm {k}} \,}$the coefficient of sliding friction (within the integral, as it can vary from place to place, e.g. due to material changes along the path),
${\ displaystyle \ mathbf {x} \,}$ represents the position of the object.

The energy lost from a system through friction is a classic example of thermodynamic irreversibility .

## Friction conditions in lubrication technology

The optimization of friction processes is the subject of tribology .

In the case of solid body friction, the surfaces sliding on each other touch each other. In the process, raised surfaces are leveled (abrasion or wear ). If the material pairing is unfavorable and the surface pressure is high , the surfaces will weld together ( adhesion ). Solid friction occurs, for example, when using dry lubricants ( graphite , Teflon ), if no lubricant is used or if the lubrication fails. This state of friction is therefore also referred to as dry friction and can be significantly reduced by using linear ball bearings . Almost frictionless movements can be realized through an aerostatic bearing ( air bearing ).

The mixed friction may occur with lubrication with insufficient lubrication or at the beginning of the movement of two friction partners. The sliding surfaces touch each other at certain points. The frictional force in the mixed friction range is speed-dependent and can be observed on plain bearings . The friction force / torque decreases with increasing sliding speed until pure fluid friction occurs and separates the friction surfaces. As the sliding speed continues to rise, the frictional force / torque increases again. In the mixed friction area, the wear decreases similarly with the frictional torque, until the sliding speed has reached the almost wear-free fluid friction. The mixed friction is therefore always undesirable in continuous operation, but is sometimes unavoidable or its avoidance is so complex that the cost incurred for wear repairs into account.

The fluid friction occurs when a permanent between the sliding surfaces lubricating film forms. Typical lubricants are oils, water, but also gases (see air bearings ). The sliding surfaces are completely separated from each other. The resulting friction is based on the fact that the lubricant molecules slide on each other. So that these shear forces only lead to an acceptable increase in temperature of the lubricant, the heat generated must be dissipated in a suitable way. Fluid friction is the desired state of friction in bearings and guides when durability, high sliding speed and high load capacity are required. An important example is the pressure oil lubrication of the bearing shells between the crankshaft and the connecting rod in the car engine ( hydrodynamic plain bearing ).

The transition from mixed friction to fluid friction is represented by the Stribeck curve , the minimum of frictional force / torque of the curve marks the transition to pure fluid friction.

## literature

• Gerd Fleischer (Ed.): Basics of friction and wear . German publishing house for basic industry, Leipzig 1983.
• Bo Persson: Sliding Friction. Physical Principles and Applications . Springer, 2002, ISBN 3-540-67192-7 .
• Ernest Rabinowicz: Friction and Wear of Materials . Wiley-Interscience, 1995, ISBN 0-471-83084-4 .
• Frank Philip Bowden, David Tabor: The Friction and Lubrication of Solids . Oxford University Press, 2001, ISBN 0-19-850777-1 .
• Valentin L. Popov: Contact Mechanics and Friction. A text and application book from nanotribology to numerical simulation . Springer-Verlag, 2009, ISBN 978-3-540-88836-9 .