Types of friction and wear

TO Category:

Maintenance of road vehicles

Types of friction and wear

Depending on the kinematic features of the relative movement of bodies, the following types of friction are distinguished: sliding friction, rolling friction and spinning friction.

Rotation friction is the least studied, therefore, when solving practical problems, they try to reduce this type of friction to sliding or rolling friction.

With the relative displacement of deforming bodies, the tangency between them occurs not at points, but in zones called contact areas. At these contact sites, a very diverse physical and mechanical phenomena can occur, for example: elastic and plastic deformations of particles, molecular adhesion of particles, adsorption of thin layers of gas, dispersion of colloidal particles, etc. Some scientists, when studying this issue, counted more than 20 such phenomena, moreover, many of them found themselves in a reciprocal relationship. The quantitative and qualitative relationships between these phenomena occurring on the elastic areas of two contacting (rubbing) bodies largely depend on the presence of a liquid or gaseous layer between them - a lubricant.

Therefore, depending on the presence or absence of lubrication, as well as the nature of the rubbing surfaces, they are distinguished:
a) pure friction that occurs on rubbing surfaces in the absence of impurities on them in the form of a liquid or gas layer. Practically pure friction is very difficult to achieve; it can only be realized in a vacuum;
b) dry friction appears in the absence of lubrication and contamination between the rubbing surfaces;
c) boundary friction, in which the rubbing surfaces are separated by a layer of grease no more than 0.1 microns thick. The boundary film has special properties and does not obey the general laws of the hydrodynamics of viscous fluids; therefore it should not be mixed with a normal sized oil film;
d) liquid friction, in which the rubbing surfaces are completely separated by a layer of liquid of the required size, which does not allow contact between the rubbing bodies and takes the entire load;
e) semi-dry friction, when, in the presence of a lubricating layer between the rubbing surfaces, individual protrusions of the surfaces come into direct contact (i.e., simultaneously boundary and dry friction);
f) semi-fluid friction - such that most of the load is transferred by the oil film, and a smaller part is perceived directly by the contact of the rubbing surfaces (i.e., simultaneously liquid and boundary or liquid and dry friction).

In technology, semi-dry and semi-fluid friction are most often encountered at the same time, of which the first is usually taken for dry, and the second for liquid.
Let us recall the basic laws and mathematical dependences of dry and liquid friction.

The main provisions of the law of dry sliding friction are:
1. The sliding friction force on the plane is directly proportional to the normal pressure in a certain range of speeds and loads.
2. The direction of the sliding friction force is opposite to the relative speed of the rubbing bodies.
3. The exact position of the point of application of the sliding friction force is unknown.
4. Friction depends on the material and the state of the rubbing surfaces.
5. With an increase in the speed of movement, the friction force in most cases decreases, approaching a certain constant value.
6. With increasing specific pressure, the friction force in most cases increases.

The laws of dry rolling friction in the first approximation were derived by Coulomb.

The main provisions of this law are:
1. The rolling friction is directly proportional to the normal pressure and inversely proportional to the radius of the roller
where N - normal pressure, kg;
R is the radius of the roller, cm;
X is the rolling friction coefficient, see.
2. The rolling friction force is directed in the opposite direction relative to the speed.
3. The exact position of the point of application of the rolling friction force is unknown.

With liquid friction, there is no direct contact between surfaces moving relative to each other, since there is a layer of liquid between them. At relative motion surfaces in this case, there is a shift of individual layers of the liquid relative to each other and therefore the friction in the liquid layer is reduced to viscous shear. The founder of the hydrodynamic theory of lubrication is the outstanding Russian scientist N.P. Petrov. The main essence of this theory is as follows.

The main value in fluid friction is the coefficient m), i.e., the coefficient of internal friction or the coefficient of absolute viscosity. Therefore, the smallest thickness of the liquid layer must be greater than the irregularities of the two contacting surfaces A and B, otherwise there will be direct contact between them.

It follows from the hydrodynamic theory of lubrication that, to maintain the normal thickness of the oil layer, the friction surfaces may not be strictly parallel, and the journals of the shaft and bearing may not be concentric. This conclusion can be made on the basis of the properties of the wedge-shaped lubricant layer, which are as follows.

With the wedge-shaped oil layer between the two sliding surfaces A and B, the oil adheres to these surfaces due to its oiliness. This phenomenon leads to the fact that the flow rate of the oil is significantly reduced, and the pressure inside the oil layer increases accordingly. This pressure, as shown by experimental data, at the narrowest point of the wedge-shaped shape reaches 200 kg / cm2 and causes a large lifting force, due to which body A floats, providing the necessary thickness of the oil layer separating surfaces A and B.

Rice. 1. Schemes of fluid friction

Based on the properties of the wedge-shaped lubricant layer, it can be assumed that when the machine is started, when the shaft begins to rotate, the wedge-shaped lubricant layer will be absent, and therefore, the condition for liquid lubrication will also be absent, i.e., semi-dry or semi-liquid friction will occur.

Back in 1883, N.P. Petrov gave the following basic provisions of fluid friction.
1. The lubricating fluid between the rubbing surfaces must be kept in the gaps.
2. In the lubricant layer with the relative sliding of the lubricated surfaces, internal pressure should arise and be maintained, which balances the external load pressing the rubbing surfaces against each other.
3. The lubricating fluid must completely separate the rubbing surfaces.
4. The layer of liquid located between the rubbing surfaces must have a thickness not less than a certain minimum limit.

Friction and wear are closely related. Wear is the result of friction work. According to a number of scientists working in this field, there is still no generally accepted definition of friction wear in the technical literature. By the definition of prof. MM Khrushchov, wear of machine parts is an undesirable gradual change in their dimensions in the process of work, which occurs under the action of forces on their rubbing surfaces.

The wear that occurs during the operation of machines can be subdivided into natural and emergency.

Natural wear of machine parts occurs as a result of the action of friction forces and is determined by the working conditions of the parts, the quality of the material, the nature of the processing, etc. These wear are inevitable and appear as a result of a relatively long period of operation of the machine.

Accidental wear is the result of rapidly increasing natural wear and tear and disruption of the normal operation of the machine, violation of the rules of maintenance, operation and repair of machines. These wear are almost always characterized by sharp deformations of parts, destruction of individual components, assemblies and the entire machine.

Deterioration of machines encountered in practice is very diverse in form of manifestation, for reasons of occurrence, character of growth and many other signs.

The most common type of normal wear and tear is mechanical wear.

Prof. AK Zaitsev, taking into account the nature of the phenomena and processes occurring during wear, gives the following classification of mechanical wear: wear class I - purely mechanical; Class II - physical and mechanical; III class - chemical and mechanical; IV class - complex.

Purely mechanical wear (metal erosion) is accompanied by a change in the shape and volume of rubbing parts without significant manifestations of chemical processes. This type of wear is the result of frictional forces that arise when the surfaces of parts move relative to each other.

Depending on the type of friction, purely mechanical wear is divided into three main types: wear from sliding friction, from rolling friction and complex wear, which manifests itself with the simultaneous action of sliding friction and rolling friction.

Wear from sliding friction is most widespread in units and assemblies of road machines; it occurs, for example, on the surfaces of the journals of shafts and bearings, piston rings and cylinders, valve stems and guide bushings, etc.

The most visible wear from rolling friction is wear in ball and roller bearings, which are common in road vehicles.

A typical example of complex wear in road vehicles is wear caused by gear teeth.

Physical and mechanical wear occurs when mechanical wear is accompanied by physical changes in rubbing parts. These changes are closely related to the internal processes taking place in the parts, which usually lead to a change in their hardness, rigidity, fragility and to the appearance of work hardening. An example of such wear is jaw wear on rock crushers.

Chemical and mechanical wear (metal corrosion) is characterized by the fact that mechanical wear is accompanied by chemical processes. An example of such wear is corrosion, in the presence of which mechanical wear is greatly enhanced and accelerated. The phenomenon of corrosion is essential in the wear of parts of road machines and engines.

Corrosion occurs as a result of the action of organic acids in the lubricant or formed during the combustion of fuel, as well as as a result of the action of gases at high temperatures, water vapor, etc.

During the operation of road vehicles, the following types of corrosion occur: atmospheric, soil, electrochemical, liquid and corrosion at high temperatures.

Atmospheric and soil corrosion is caused by humidity in the air or soil, especially in the presence of carbon dioxide, ammonia, etc.

Electrochemical corrosion occurs when a galvanic pair is formed upon contact of two different metals, i.e. one metal with a more negative potential serves as the anode and the other as the cathode. Metal with a more negative potential will generally corrode.

Liquid corrosion occurs in steam-water systems due to the presence of oxygen-enriched air in the water. At the same time, the water contains minerals that give solutions of mineral salts, acids and alkalis. Such aqueous solutions are electrolytes that, interacting with metal, cause active corrosion.

Corrosion at high temperatures is caused by heating the metal and exposing it to heat. Corrosion activity in this case largely depends on the quality of the metal and its ability to oxidize at high temperatures, for example, corrosion observed in the upper part of the cylinders of internal combustion engines. From a study of the combustion process of fuel in engines, it follows that particles of incomplete combustion products, strongly oxidized by a sudden drop in temperature, adhere to the cylinder walls, and the oxygen contained in them affects the metal.

Complex wear occurs when mechanical wear is accompanied by both chemical and physical processes. Comprehensive wear includes such wear of engine exhaust valves, when, under the influence of high temperatures, partial (surface) combustion of the metal occurs, its structure and mechanical properties change, and the chemical process resulting from the action of gases causes metal corrosion. The valve loses its qualities so much that at a certain moment its head completely burns out, and sometimes even breaks off.

Abrasive wear is a type of purely mechanical wear, which is caused by the presence of abrasive particles in the mating rubbing parts.

During the operation of road machines, individual parts and interfaces have direct contact with the ground, for example, motor grader knives, bulldozers and scrapers, caterpillar parts, etc., operating in the most difficult conditions. In these cases, abrasive particles are critical in terms of wear.

When grinding cylinders and valves with insufficient cleaning after processing, some of the abrasive dust remains in the engine cylinders.
The main conductor of the ingress of abrasive materials into the engine cylinders is its intake system. If the engine has even the most advanced air cleaner, a certain amount of dust still gets into it.

Abrasive dust entering the engine cylinders mixes with the oil and forms a kind of lapping paste, which significantly increases the wear of parts (pistons, rings, valves, etc.).

Abrasive wear is the most common among parts of road machines operating with sand, crushed stone, concrete, slag, etc. Metal wear in this case occurs under the influence of grains of various abrasive materials, which are pressed into the base of the metal of the part and form a groove in it (Fig. . 2). The extruded metal in the form of beads is located on both sides of this groove. Since the structure of the metal is largely inhomogeneous, cracks appear in the displaced metal, which weaken it and create an opportunity for abrasive grains to gradually deform and destroy it. At the bottom of the resulting groove, work-hardening occurs, due to which the hardness of the metal increases significantly.

Rice. 2. Trace of abrasive grain on a rubbing surface

V last years Much attention has been paid to abrasive wear, since the wear resistance of parts to this type of wear is essential for extending the service life of machines and their reliability in operation. Noteworthy are the studies in the field of abrasive wear, carried out by Cand. tech. Sciences M. M. Tenenbaum. Of undoubted interest is his point of view on the issue of active abrasive action of solid abrasive particles in the contact of rubbing parts.

Tenenbaum points out that the same amount of abrasive substance in contact with solids, depending on various factors causes various destruction of the surface of these bodies in volume. For example, the activity of the abrasive action of a certain amount of quartz sand grains in contact between two bodies depends largely on the nature of the interaction of these grains with two bodies. If the abrasive grain, without collapsing, is pressed into the surface layer of the part, then there is a kind of partial isolation of the grain in the contact of the mating parts and their caricature. This caricature of the surface layers of the mating parts with abrasive particles increases their wear in comparison with the wear of parts in the conjugation of which there are no abrasive particles.

As noted in the research, the greatest wear is obtained when the abrasive grains in contact between two mating parts are crushed. The energy required to crush the abrasive grains is transferred through small-area contact areas of the surface layer, which causes the destruction of certain volumes of the material of the parts. The newly formed particles of quartz abrasive will have their own specific geometry, which will promote a high concentration of contact stresses in the surface layers of rubbing parts, which in turn will cause increased wear of the surfaces.

Thus, when the same amount of abrasive grains are crushed in contact, the wear of the mating parts under certain conditions will be much greater, since the abrasive action will be accompanied by a higher activity. Only this can basically explain that solid bronze bearings wear out the shaft journal more than babbit bearings under conditions of the same grease contamination.

In literary sources, there are very often opinions that a mating pair of parts made of steel and nylon during abrasive wear has a higher wear resistance than the mating of metal parts. This is due to the fact that nylon partially absorbs abrasive grains and thereby reduces the activity of abrasive wear.

As a result of these phenomena, it can be concluded that the effect of abrasive particles in conjunction with parts can be different depending on the state of these particles and the material of the mating parts. The wear resistance of mating parts to abrasive wear can be increased by selecting parts with increased wear resistance or by selecting parts from materials of relatively low wear resistance, but capable of absorbing abrasive particles.

Institute structural mechanics Academy of Sciences of the Ukrainian SSR held great job on the study of wear of parts of cars, tractors and agricultural machines. As a result of the work of this institute, prof. BI Kostetskiy established fundamentally different types of wear of parts, obeying the laws of a certain process.

BI Kostetskiy gives the following classification of the types of wear of machine parts: seizure wear of the first kind; adhesion wear of the II kind, or thermal; oxidative wear; abrasive and speckled wear.

Due to the fact that each part has a leading type of wear, it will have the most wearable surface wherever this type of wear occurs. A clearly pronounced type of wear usually determines the wear resistance of the part, the nature and rate of its wear. For example, the leading type of wear of heavily loaded gear teeth is pox-like, and the accompanying types of wear are thermal and oxidative. Pointed wear determines the wear resistance of the gear teeth and appears in the zone of the initial tooth circumference, while the other two types of wear - thermal (on the tooth root) and oxidative (on the gear tooth head) - are not decisive in relation to the overall wear resistance of the gear teeth under certain operating conditions.

TO Category: - Maintenance of road cars

Objective: to consolidate knowledge of the types of friction and wear.

Exercise:.

1. Study theoretical material.
2. Fill in table 1.
3. Answer security questions.

Control questions:

1. Factors that determine the rate of wear?

2. What are the main ways to reduce the intensity of mechanical abrasion do you know?

3. Which frictional force is greater than rolling or sliding friction?

Table 1

Theoretical part.

Friction- the main reason for the wear of machine parts. The problems of friction, wear and lubrication are studied by the science of tribology, based on the fundamental laws of physics, chemistry, continuum mechanics, thermodynamics and materials science.

Distinguish between friction:

Slides,

Rolling,

The rolling friction force is about 10 times less than the sliding friction force.

Types of friction... During the operation of machines, the friction surfaces of the parts are in different conditions. Depending on whether or not there is lubrication between the rubbing surfaces, the following types of friction are distinguished.

Friction without lubrication occurs in the absence of all types of lubricant on the friction surfaces of both solid bodies.

Boundary friction two solids occurs when a thin layer of lubricant on the friction surfaces does not exceed the height of the roughness of the contacting surfaces.

Fluid friction occurs between two bodies completely separated by a layer of liquid (lubricant). The lack of contact between the surfaces protects them from destruction.

Wear- the process of destruction and separation of material from the surface of a solid during friction and (or) an increase in its permanent deformation, which manifests itself in a gradual change in the size and (or) shape of the body.

Wear types... Under conditions of all types of friction, the rubbing surfaces are destroyed, that is, the surfaces wear out.

Wear classification

According to GOST 23.002 - 78, there are 3 main types of wear:

1) mechanical (abrasive, hydro and gas abrasive, erosion, hydro and gas erosion, cavitation, fatigue, fretting, jamming);

2) corrosion-mechanical (oxidative, fretting corrosion);

3) under the action of electric current (electroerosive).

Mechanical wear occurs as a result of the action of solid particles on rubbing surfaces. This group should include such types of wear as abrasive, hydro- and gas-abrasive, fatigue, cavitation, erosion.

Abrasive wear- wear as a result of mechanical action through the cutting and scratching action of hard particles or particles in the presence of a relative speed of movement.

Hydro and gas abrasive wear appears as a result of the action of solids or particles entrained by the flow of liquid or gas.

Fatigue wear causes a change in the friction surface or individual areas as a result of repeated deformation of microvolumes of the material, leading to the appearance of cracks and separation of particles.

Cavitation wear surface occurs with a relative increase in the speed of movement of a solid in a liquid, i.e., under conditions of hydrodynamic cavitation - disruption of the continuity of the intra-fluid.

Erosive wear occurs as a result of exposure to a liquid or gas stream.

Molecular mechanical wear is a result of simultaneous mechanical and molecular or atomic forces.

Corrosion-mechanical wear is wear due to friction of the metal that has entered into chemical interaction with the environment.

The factors that determine the rate of wear include:

Type of friction (sliding, rolling, rolling with slippage);

Friction type (dry, boundary, hydrodynamic);

Environment (air, water, gas, soil, etc.);

Contact type of friction pairs (point, line, plane, cylinder, sphere);

The nature of the movement (uniform, continuous, etc.);

Movement type (rotational, translational, reciprocating);

The nature of the load (constant, unsteady, alternating sign);

Load value;

The speed of movement of the rubbing surfaces;

Temperature conditions.

The main ways to reduce the intensity of mechanical abrasion:

1) Structural:

Ensuring rational rigidity and pliability of parts (floating parts, springs, springs, gaskets, etc.).

Selection of rational friction pairs:

The combination of a hard material with a soft material (eliminates galling) - straight [hardened movable

Caliper - raw fixed bed] and reverse [chromed sleeve - unhardened cast iron ring, hardened shaft - babbitt insert] pairs;

Combination of hard material with hard material (high wear resistance);

Elimination of the combination of materials of the same name and soft with soft;

The use of porous, powder antifriction materials.

Replacement of sliding friction pairs with rolling ones;

Creation of conditions for fluid friction.

2) Technological:

Ensuring optimal roughness,

Compliance with manufacturing accuracy and hardening of friction surfaces.

3) Operational:

Unloading of working surfaces;

Compliance with the rules of operation, maintenance and repair of machines.

We encounter friction when we move some bodies relative to each other (kinetic friction) or try to set in motion bodies that are at rest (static friction). Friction occurs when two bodies moving relative to each other touch their outer surfaces (external friction) or when structural elements of a body (atoms, molecules) move relative to each other (internal friction). Internal friction can occur in liquids, gases and solids. The classification of the types of friction is presented in table. 2.5. In addition to mechanical friction, thermal, electrical, magnetic and other phenomena take place. Table 2.5

Kinetic friction(friction of movement) - occurs when any bodies move relative to each other.

Static friction(friction at rest) - occurs when a stationary body begins to move from a state of rest.

External friction- occurs when two bodies moving relative to each other touch their outer surfaces.

Internal friction- when the elements of the body structure (atoms, molecules) move relative to each other. Occurs in solids, liquids and gases.

Friction without lubricant(dry friction) - friction of two bodies in the absence of any type of lubricant introduced on the friction surface.

Friction with lubricant(fluid friction) - friction of two bodies in the presence of any type of lubricant introduced on the friction surface.

Sliding friction- friction of motion of two rigid bodies, in which the velocities of the bodies at the points of contact are different in magnitude and direction, or in magnitude or direction (Fig. 2.1).

Rolling friction- friction of motion of two rigid bodies, at which their velocities at the points of contact are the same in magnitude and direction (Fig. 2.2) Fig. 2.2

Boundary friction- friction in the presence of a film of boundary lubrication.

Analyzing the above definitions different types friction can formulate a general definition of the process of friction.

Lubricant- the material introduced to the friction surface to reduce the friction force (F TP) and the intensity of wear (oil - surfactant cannot be completely squeezed out. At low temperatures, severe wear occurs due to oil crystallization).

When moving (or moving) bodies come into contact with other bodies, as well as with particles of matter environment forces arise that impede such movement. These forces are called frictional forces... The action of friction forces is always accompanied by the transformation of mechanical energy into internal energy and causes heating of bodies and their environment.

Exists external and internal friction(otherwise called viscosity). External this type of friction is called, in which forces arise at the points of contact of solids that impede the mutual movement of bodies and are directed tangentially to their surfaces.

Internal friction(viscosity) is the type of friction, which consists in the fact that in mutual displacement. layers of liquid or gas between them, tangential forces arise that prevent such a movement.

External friction is subdivided into static friction (static friction) and kinematic friction... Friction at rest occurs between immobile rigid bodies when any of them are attempted to move. Kinematic friction exists between mutually contacting moving rigid bodies. Kinematic friction, in turn, is subdivided into sliding friction and rolling friction.

Friction forces play an important role in human life. In some cases, he uses them, and in others he fights with them. Friction forces are electromagnetic in nature.

Rest friction

Observations show that the force of friction at rest is always directed in the opposite direction to the external force acting on the body, striving to set this body in motion. Until a certain moment, the force of friction at rest increases with an increase in the external force, balancing the latter. The maximum value of the static friction force is proportional to the modulus of the force F d of the pressure exerted by the body on the support.

According to Newton's third law, the force F d of the body pressure on the support is equal in magnitude to the force N of the support reaction. Therefore, the maximum static friction force is proportional to the support reaction force. For the modules of these forces, the following ratio is valid:

F p = f p N, (2.19)

where f p is a dimensionless coefficient of proportionality, called static friction coefficient... The value of this coefficient depends on the material and the state of the rubbing surfaces.

The value of the coefficient of friction at rest can be determined as follows. Let the body (flat bar) lie on the inclined plane AB (Fig. 23). Three forces act on it: the force of gravity F, the force of friction at rest F p and the reaction force of the support N. The normal component F p of the force of gravity is the force of pressure F d produced by the body on the support, i.e.

F H = F d. (2.20)

The tangential component F t of gravity is a force tending to move the body down an inclined plane.

At small angles of inclination a, the force F t is balanced by the static friction force F p and the body is at rest on an inclined plane (the force N of the support reaction according to Newton's third law is equal in magnitude and opposite in direction to the force F d, that is, it balances it).

We will increase the angle of inclination a until the body begins to slide down the inclined plane. In this moment

F t = F пmax (2.21)

Substituting expressions (2.20) and (2.21) into formula (2.19), we obtain

f p = F t / F n (2.22)

From fig. 23 shows that

F t = Fsin a = mg sin a; F n = Fcos a = mg cos a.

f n = sin a / cos a = tg a. (2.23)

Measuring the angle a, at which the sliding of the body begins, we can use formula (2.25) to calculate the value of the coefficient of friction at rest f p.

Types of kinematic friction

Sliding friction occurs when one solid slides over the surface of another. The sliding friction law has the form

F c = f c N, (2.24)

where F c - modulus of sliding friction force; f c - dimensionless coefficient of sliding friction; N is the modulus of the support reaction force. The value of f c depends on what substances the rubbing surfaces are made of and on the quality of their processing. If the surfaces are smoother, the f c c value increases again. This happens because the molecules of bodies with smooth surfaces come close to each other and the forces of molecular attraction between them cause the bodies to "stick", preventing them from sliding. Rolling friction occurs when solid bodies of a circular shape roll (without sliding) on ​​the surface of other solid bodies.will decrease. However, the roughness of surfaces can be reduced only up to a certain limit, since for very smooth (for example, polished) surfaces, the value of f

The reason for the appearance of rolling friction is as follows. By gravity, the round solid(for example, a ball or wheel) located on a flat surface is deformed, as a result of which it rests not on one point, but on a platform of larger or smaller dimensions. This leads to the fact that when the body begins to roll, point A of application of the reaction of support is displaced slightly forward from the vertical passing through the center of gravity of the body, and the line of action of the reaction force of support R deviates slightly back from this vertical (Fig. 24). In this case, the normal component R n = N of the support reaction compensates for the force of gravity F (i.e. R n = -F), and not the compensated tangential component R t of the support reaction is directed against the movement of the body and plays the role of the rolling friction force F k. The modulus of force rolling friction F k is determined by the law

F k = K k N / r (2.25)

where K to is the dimensionless rolling friction coefficient; N = R n - modulus of the normal component of the support reaction force; r is the radius of the rolling body.

If we compare the coefficients of all types of external friction for any two materials from which the contacting bodies are made, we will see that f p> f c> K k, i.e., other things being equal the largest is the static friction, and the smallest is the rolling friction.

The role of lubricant

In order to reduce external friction between the contacting surfaces of solids, a lubricant is introduced, that is, a viscous liquid that adheres to solids and forms a layer of greater or lesser thickness between their surfaces. In this case, friction no longer occurs between solids, but between layers of lubricant, which leads to a significant decrease in the friction force. External friction is called dry if there is no lubrication at all, hydrodynamic if the lubricant layer is thick, boundary if the lubricant layer is very thin.

Resistance forces to the movement of bodies in liquids and gases

Resistance force motion also arises when solids move in liquids and gases. In this case, there is no rest friction at all, since in a liquid or gas an arbitrarily small force can bring the body out of the state of rest, imparting acceleration to it.

The resistance force arising in a liquid or gas is always directed against the movement of the body, tangentially to its surface and depends on the speed of the body. At low speeds, the drag force F c is proportional to the speed, and at high speeds - F cproportional to the square of the speed.

In gases, due to their low density, the body can develop high speed, therefore the resistance force F c = -k 1 v 2. In liquids, the density of matter is high, the body cannot develop high speed, and therefore Fc = -k 2 v. In the last formulas, the proportionality coefficients k 1 and k 2 depend on the type of liquid or gas and their temperature.

Observations show that the force of resistance to motion in liquids or gases also largely depends on the shape of the moving body. The geometric shape of the body, at which the force of resistance to motion from the side of the medium is small, is usually called streamlined.

There are several types of friction in nature. In the case of touching a solid body and others like them, dry friction occurs, which is divided into:

• Rest friction;
• Sliding friction;
• Rolling friction.

If a solid begins to come into contact with a liquid or gas, non-dry friction occurs.

Static friction force

Consider a ball lying on a surface. Forces act on him:

• Gravity F, where m is body mass and g is acceleration free fall, which is a constant.
• Support reaction force N.

Let's try to act on the ball with a force parallel to the surface on which it is located. As a result, our ball did not budge, which suggests that another force is acting on it as well. It is called the static frictional force, and is opposite in direction to the force with which we acted on the ball. It is equal in magnitude to the applied force.

Thus, the following formula can be written:

There is also a value that characterizes the dependence of the static friction force and the reaction force of the support. It is called the coefficient of friction at rest and is denoted by μ0

The maximum value of the static friction force that acts on the ball can be calculated using the formula:

Sliding friction force

Let us apply force again to the considered ball. This time, our ball starts moving along the surface it is on. And in this case, from the side of the surface, a force acts on the ball, which is called the sliding friction force. This force prevents the ball from moving and is directed in the opposite direction of movement.

The sliding friction force is also proportional to the support reaction force:

Ftr.slid. = Μ * N

Rolling friction force

This type of friction occurs when the ball rolls to some other body, or when it rolls over the surface. Just like sliding friction, it is directed in the opposite direction to motion.

Not dry friction

This type of friction occurs when a solid moves in a liquid or gaseous medium. This force is also directed in the direction opposite to the movement and prevents it. The magnitude of the resistance force depends on the speed with which the body moves in the medium.

If the body is moving at low speed, the drag force can be calculated using the following formula:

Fresistance = k * v

k- resistance coefficient, v- the value of the relative speed.

If the value of the relative velocity has sufficient great importance, then the resistance force must be calculated using the following formula.