Friction forces arise when the surfaces of two solid bodies are in direct contact. There are forces of friction - rest, sliding and rolling. When a body does not slide on the surface of another body, but rolls, then in this case resistance is exerted by the rolling friction force. Rolling friction is ten times less than sliding friction. Let's look at the mechanism of this force.

Rolling is easier than pulling

AT Everyday life We enjoy the benefits of rolling almost daily:

• Heavy, bulky items can be easily moved by placing round rollers or pipes under them. For example, to move a cast-iron blank weighing 1 ton on asphalt, you need to apply a force of 200 kgf - only powerful strongmen are capable of this. And even a child can roll the same blank on a trolley, because this requires a force of no more than 10 kgf;
• All vehicles moving on the surface of the earth use wheels;
• To facilitate the lifting of heavy objects to a height, a wheel-shaped block has been used for a long time;
• Roller and ball bearings are used in all applications where minimum friction in rotating parts is required.

Of course, the invention of the wheel is one of the most outstanding achievements of human civilization.

Rice. 1. Examples of the rolling friction force.

So, the rolling friction force is the force that occurs when a body rolls on a surface without slipping. The essential point in this definition is the exclusion of slippage, because during slippage, friction increases tenfold!

Why does rolling friction occur?

A round object (disk, ball, cylinder) is slightly pressed into the surface during rolling, forming a “pit and tubercle”. It turns out that a rolling body with its own weight creates an obstacle (a tubercle) for itself, and overcomes it, as if rolling all the time uphill. In this case, the body itself is also slightly deformed.

The second reason is the cohesive force (adhesion) that occurs between the surfaces at the moment of contact. Adhesion occurs as a result of intermolecular interaction.

Rice. 2. Occurrence of rolling friction force.

The harder the surface on which the body rolls, the smaller the “hole” (indentation) will be and, therefore, the rolling friction force will be smaller. Rolling resistance is less than sliding friction because the contact area is usually very small and therefore Normal strength, which presses the body to the surface, is also small and insufficient to prevent the body from moving.

For railway transport, where the wheels and rails are steel, rolling friction is many times less than that of truck tires. If the body itself and the surface were absolutely solid, then the friction force would be zero.

What determines and what is the force of rolling friction

If a round body, for example, a wheel with a radius R rolls on the surface, then for the formula for the rolling friction force F t fair following expression:

$ F_t = N * (μ\over R) $ (1),

N— pressing force, N;

μ — coefficient of rolling friction, m/N.

It follows from the formula that F t increases with body weight and decreases with increasing wheel radius R. This is understandable: the larger the wheel, the less important for it are the roughness of the surface (tubercles) on which it rolls.

Rolling friction coefficient μ has the dimension $[m/N]$ in contrast to the coefficient of sliding friction k, which is dimensionless.

Rice. 3. Formula for the rolling friction force.

Bearings

To reduce sliding friction, a lubricant was first invented, which made it possible to achieve a reduction in friction by 8-10 times. It was only at the end of the 19th century that the idea arose to replace sliding friction with rolling friction in a bearing. This replacement is carried out by ball and roller bearings. When the wheel or motor shaft rotates, the balls (or rollers) roll along the sleeve (ball cage), and the shaft or wheel axle rolls along the balls. In this way, it was possible to reduce friction tenfold.

What have we learned?

So, we learned what the rolling friction force is. We considered two main mechanisms that cause this force. According to formula (1), the rolling friction force increases with body weight and decreases with increasing wheel radius. Roller and ball bearings find their application in most devices that have rotating parts.

Topic quiz

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Friction(frictional interaction) - the process of interaction of bodies during their relative motion (displacement) or when the body moves in a gaseous or liquid medium.

The branch of physics that deals with the study of friction processes is called tribology(mechanics of frictional interaction).

Friction is usually divided into:

• dry when interacting solids are not separated by any additional layers / lubricants (including solid lubricants) - a very rare case in practice; characteristic distinguishing feature dry friction - the presence of a significant static friction force;
• boundary when the contact area may contain layers and areas of various nature (oxide films, liquid, and so on) - the most common case in sliding friction;
• liquid(viscous), arising from the interaction of bodies separated by a layer of a solid body (graphite powder), liquid or gas (lubricant) of various thicknesses - as a rule, occurs during rolling friction, when solid bodies are immersed in a liquid, the magnitude of viscous friction is characterized by the viscosity of the medium;
• mixed when the contact area contains areas of dry and liquid friction;
• elastohydrodynamic(viscoelastic) when internal friction in the lubricant is of decisive importance. Occurs with an increase in the relative speeds of movement.

Friction force- this is a force that occurs at the point of contact of bodies and prevents their relative movement.

Causes of the friction force:

• roughness of contacting surfaces;
• mutual attraction of the molecules of these surfaces.

Sliding friction is the force arising from the translational movement of one of the contacting / interacting bodies relative to the other and acting on this body in the direction opposite to the direction of sliding.

rolling friction- the moment of forces arising from the rolling of one of the two contacting / interacting bodies relative to the other.

Friction of rest- the force that arises between two contacting bodies and prevents the occurrence of relative motion. This force must be overcome in order to set two contacting bodies in motion relative to each other.

The friction force is directly proportional to the normal reaction force, that is, it depends on how strongly the bodies are pressed against each other and on their material, therefore the main characteristic of friction is coefficient of friction, which is determined by the materials from which the surfaces of the interacting bodies are made.

Wear- a change in the size, shape, mass or state of the surface of the product due to the destruction (wear) of the surface layer during friction.

The operation of any machine is inevitably accompanied by friction during the relative movement of its parts, so it is impossible to completely eliminate wear. The amount of wear in direct contact of the surfaces is directly proportional to the work of the friction forces.

Abrasion is partly caused by the action of dust and dirt, so it is very important to keep the equipment clean, especially its rubbing parts.

To combat wear and friction, some metals are replaced with others that are more stable, thermal and chemical treatment of rubbing surfaces, precision machining are used, and metals are replaced with various substitutes, the design is changed, lubrication is improved (they change appearance, additives are introduced), etc.

In machines, they strive to prevent direct sliding friction of solid surfaces, for which they are either separated by a layer of lubricant (liquid friction), or additional rolling elements (ball and roller bearings) are introduced between them.

The basic rule for the design of rubbing machine parts is that a more expensive and difficult to replace element of a rubbing pair (shaft) is made from a harder and more wear-resistant material (hard steel), and simpler, cheaper and easily replaceable parts (bearing shells) are made from relatively soft material with a low coefficient of friction (bronze, babbitt).

Most machine parts fail precisely due to wear, so reducing friction and wear even by 5-10% gives huge savings, which is of exceptional importance.

Link List

1. Friction // Wikipedia. – http://ru.wikipedia.org/wiki/Friction.
2. Wear (technology) // Wikipedia. - http://ru.wikipedia.org/wiki/Wear_(technology) .
3. Friction in machines, friction and wear in mechanical engineering // Project-Tekhnar. Progressive auto-technologies. – http://www.studiplom.ru/Technology/Trenie.html .

Questions to control

1. What is friction?
2. What are the types of friction?
3. What causes friction force?
4. How is friction classified according to the acting forces?
5. What is wear and how is it dealt with?

Consider a cylindrical roller resting on a horizontal plane (Fig. 67, a). Let us apply a force S to its center and observe the state of the rink with a gradual increase in this force. Experience shows that the movement of the roller does not begin immediately, but only after the force S reaches a certain limit value.

However, from the balance equations of the skating rink, compiled even taking into account the static friction force, a completely different conclusion follows - the movement should begin with an arbitrarily small force S. Indeed, for a flat system of forces: P (roller weight), N (normal reaction of the support), T - the friction force of rest and the applied force S in the state of equilibrium, all three equilibrium equations must be satisfied: .

In our case, the third equation has the form (R is the radius of the roller) and is satisfied only when ; when equilibrium is impossible, and the skating rink comes into motion with an arbitrarily small force .

The reason for the contradiction lies in the fact that not all the forces acting on the roller from the bearing surface were taken into account. The contact of real bodies is always carried out along a certain area, as a result of which another pair of forces arises with a moment opposite to the direction of the possible rolling of the body on the supporting surface (Fig. 67, b).

When the moment of rolling friction is taken into account, the equation of moments relative to the point O takes on the form , which removes the contradiction that has arisen. It follows from this equation that while there is no rolling, the moment of friction is equal to the moment of the moving force. By gradually increasing the force S, one can come to such a limiting state when the slightest increase in the force S causes the roller to roll along the support. In this state of limit equilibrium, the rolling friction moment takes on its greatest value

The value having the dimension of length is called the coefficient of rolling friction and is determined from the experiment or from technical reference books.

The rolling friction moment thus varies within

taking on a value only when rolling occurs.

The name defines the entity.

Japanese proverb

The rolling friction force, as shown by centuries of human experience, is approximately an order of magnitude less than the sliding friction force. Despite this, the idea of ​​a rolling bearing was formulated by Virlo only in 1772.

Consider the basic concepts of rolling friction. When the wheel rolls on a fixed base and when turning through an angle, its axis (point 0) shifts by an amount, then such a movement is called pure rolling without slippage. If the wheel (Fig. 51) is loaded with force N, then to make it move it is necessary to apply a torque. This can be done by applying a force F to its center. In this case, the moment of force F relative to the point O 1 will be equal to the moment of rolling resistance.

Fig.51. Pure rolling pattern

If the wheel (Fig. 51) is loaded with a force N, then to make it move, it is necessary to apply a torque. This can be done by applying a force F to its center. In this case, the moment of force F relative to the point O 1 will be equal to the moment of rolling resistance.

Rolling friction coefficient is the ratio of driving torque to normal load. This value has the dimension of length.

Dimensionless characteristic - rolling resistance coefficient is equal to the ratio of work driving force F on the unit path to normal load:

where: A is the work of the driving force;

The length of a single path;

M is the moment of the driving force;

The angle of rotation of the wheel corresponding to the path.

Thus, the expression for the coefficient of friction in rolling and sliding are different.

It should be noted that the adhesion of the rolling body to the track should not exceed the friction force, otherwise the rolling will turn into sliding.

Consider the movement of a ball along the track of a rolling bearing (Fig. 52a). Both the largest diametral circle and smaller circles of parallel sections are in contact with the track. The path traveled by a point on circles of different radii is different, that is, there is slippage.

When a ball or roller rolls along a plane (or inner cylinder), contact occurs at a point or along a line only theoretically. In real friction units, under the action of working loads, the contact zone is deformed. In this case, the ball contacts in a certain circle, and the roller contacts in a rectangle. In both cases, rolling is accompanied by the appearance and destruction of frictional bonds, as in sliding friction.

The roller, due to the deformation of the raceway, travels a path that is less than the length of its circumference. This is clearly seen when a rigid steel cylinder is rolling on a flat elastic rubber surface (Fig. 52b). If the load causes only elastic deformations e, then the rolling track is restored. With plastic deformations, the raceway remains.

Fig.52. Rolling: a - a ball along a track, b - a cylinder along an elastic base

Due to the inequality of the paths (along the circumference of the roller and along the supporting surface), slippage occurs.

It has now been established that there is almost no reduction in sliding friction (from slippage) by improving the quality of the processing of contact surfaces or the use of lubricants. It follows from this that the rolling friction force is due to a greater extent not to slip, but to the dissipation of energy during deformation. Since the deformation is mainly elastic, the rolling friction loss is the result of elastic hysteresis.

Elastic hysteresis consists in the dependence of deformation under the same loads on the sequence (multiplicity) of actions, that is, on the loading history. Part of the energy is stored in the deformable body, and when a certain energy threshold is exceeded, a wear particle is separated - destruction. The greatest losses occur when rolling on a viscoelastic base (polymers, rubber), the smallest - on high-modulus metal (steel rails).

The empirical formula for determining the rolling friction force is:

where: D is the diameter of the rolling element.

Analysis of the formula shows that the friction force increases:

With increasing normal load;

With a decrease in the size of the rolling body.

With an increase in rolling speed, the friction force changes little, but wear increases. Increasing the speed of movement due to the diameter of the wheel reduces the force of rolling friction.

The force of friction in terrestrial conditions accompanies any movement of bodies. It occurs when two bodies come into contact, if these bodies move relative to each other. The friction force is always directed along the contact surface, in contrast to the elastic force, which is directed perpendicularly (Fig. 1, Fig. 2).

Rice. 1. The difference between the directions of the friction force and the elastic force

Rice. 2. The surface acts on the bar, and the bar acts on the surface

There are dry and non-dry types of friction. Dry type of friction occurs when solids come into contact.

Consider a bar lying on a horizontal surface (Fig. 3). It is affected by the force of gravity and the reaction force of the support. Let's act on the bar with a small force , directed along the surface. If the bar does not move, then the applied force is balanced by another force, which is called the static friction force.

Rice. 3. Force of static friction

The static friction force () opposite in direction and equal in magnitude to the force tending to move the body parallel to the surface of its contact with another body.

With an increase in the “shearing” force, the bar remains at rest, therefore, the static friction force also increases. With some, sufficiently large, force, the bar will begin to move. This means that the static friction force cannot increase to infinity - there is an upper limit, more than which it cannot be. The value of this limit is the maximum static friction force.

Let's act on the bar with a dynamometer.

Rice. 4. Measuring the friction force with a dynamometer

If the dynamometer acts on it with a force, then it can be seen that the maximum static friction force becomes greater with an increase in the mass of the bar, that is, with an increase in the force of gravity and the reaction force of the support. If accurate measurements are taken, they will show that the maximum static friction force is directly proportional to the reaction force of the support:

where is the modulus of the maximum static friction force; N– support reaction force (normal pressure); - coefficient of static friction (proportionality). Therefore, the maximum static friction force is directly proportional to the force of normal pressure.

If we conduct an experiment with a dynamometer and a bar of constant mass, while turning the bar on different sides (changing the area of ​​​​contact with the table), we can see that the maximum static friction force does not change (Fig. 5). Therefore, the maximum static friction force does not depend on the contact area.

Rice. 5. The maximum value of the static friction force does not depend on the contact area

More accurate studies show that static friction is completely determined by the force applied to the body and the formula.

The static friction force does not always prevent the body from moving. For example, the static friction force acts on the sole of the shoe, while imparting acceleration and allowing you to walk on the ground without slipping (Fig. 6).

Rice. 6. Force of static friction acting on the sole of the shoe

Another example: the static friction force acting on a car wheel allows you to start moving without slipping (Fig. 7).

Rice. 7. The static friction force acting on the car wheel

In belt drives, the static friction force also acts (Fig. 8).

Rice. 8. Force of static friction in belt drives

If the body is moving, then the friction force acting on it from the side of the surface does not disappear, this type of friction is called sliding friction. Measurements show that the force of sliding friction is practically equal in magnitude to the maximum force of static friction (Fig. 9).

Rice. 9. Force of sliding friction

The force of sliding friction is always directed against the speed of the body, that is, it prevents movement. Consequently, when the body moves only under the action of the friction force, it imparts negative acceleration to it, that is, the speed of the body is constantly decreasing.

The magnitude of the sliding friction force is also proportional to the force of normal pressure.

where is the modulus of the sliding friction force; N– support reaction force (normal pressure); – coefficient of sliding friction (proportionality).

Figure 10 shows a graph of the dependence of the friction force on the applied force. It shows two different areas. The first section, in which the friction force increases with an increase in the applied force, corresponds to static friction. The second section, where the friction force does not depend on the external force, corresponds to sliding friction.

Rice. 10. Graph of the dependence of the friction force on the applied force

Coefficient of sliding friction approx. equal to the coefficient rest friction. Typically, the coefficient of sliding friction is less than unity. This means that the sliding friction force is less than the normal pressure force.

The coefficient of sliding friction is a characteristic of two bodies rubbing against each other, it depends on what materials the bodies are made of and how well the surfaces are processed (smooth or rough).

The origin of static and sliding friction forces is due to the fact that any surface at the microscopic level is not flat, there are always microscopic inhomogeneities on any surface (Fig. 11).

Rice. 11. Surfaces of bodies at the microscopic level

When two bodies in contact are attempting to move relative to each other, these inhomogeneities are caught and prevent this movement. With a small amount of applied force, this engagement is sufficient to prevent the bodies from moving, so static friction arises. When external force exceeds the maximum static friction, then the engagement of the roughness is not enough to hold the bodies, and they begin to shift relative to each other, while the force of sliding friction acts between the bodies.

This type friction occurs when bodies roll over each other or when one body rolls on the surface of another. Rolling friction, like sliding friction, imparts negative acceleration to the body.

The occurrence of the rolling friction force is due to the deformation of the rolling body and the supporting surface. So, a wheel located on a horizontal surface deforms the latter. When the wheel moves, the deformations do not have time to recover, so the wheel has to climb a small hill all the time, which causes a moment of forces that slows down the rolling.

Rice. 12. Occurrence of rolling friction force

The magnitude of the rolling friction force, as a rule, is many times less than the sliding friction force, all other things being equal. Due to this, rolling is a common type of movement in engineering.

When driving solid body in a liquid or gas, a resistance force acts on it from the side of the medium. This force is directed against the speed of the body and slows down the movement (Fig. 13).

The main feature of the resistance force is that it occurs only in the presence of relative motion of the body and its environment. That is, the static friction force in liquids and gases does not exist. This leads to the fact that a person can move even a heavy barge that is on the water.

Rice. 13. Resistance force acting on a body when moving in a liquid or gas

The resistance force modulus depends on:

From the size of the body and its geometric shape (Fig. 14);

Conditions of the body surface (Fig. 15);

Properties of a liquid or gas (Fig. 16);

The relative speed of the body and its environment (Fig. 17).

Rice. 14. Dependences of the modulus of resistance force on the geometric shape

Rice. 15. Dependences of the resistance force modulus on the state of the body surface

Rice. 16. Dependences of the resistance force modulus on the properties of a liquid or gas

Rice. 17. Dependences of the resistance force modulus on the relative velocity of the body and its environment

Figure 18 shows a graph of the dependence of the resistance force on the speed of the body. At a relative velocity equal to zero, the drag force does not act on the body. With an increase in the relative velocity, the resistance force first grows slowly, and then the growth rate increases.

Rice. 18. Graph of the dependence of the resistance force on the speed of the body

At low values ​​of the relative speed, the drag force is directly proportional to the value of this speed:

where is the value of the relative velocity; - resistance coefficient, which depends on the type of viscous medium, the shape and size of the body.

If the relative speed has enough great importance, then the resistance force becomes proportional to the square of this speed.

where is the value of the relative velocity; is the drag coefficient.

The choice of formula for each specific case is determined empirically.

A body of mass 600 g moves uniformly along a horizontal surface (Fig. 19). In this case, a force is applied to it, the value of which is 1.2 N. Determine the value of the coefficient of friction between the body and the surface.