Sliding friction

Slip friction. (Coulom friction or dry friction) It is defined as the friction of contact surfaces of solid bodies in the absence of a separating layer of lubricating fluid


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  • 1 History
  • 2 Experiment
  • 3 Static friction
  • 4 Kinetic friction
  • 5 Slip friction problems
  • 6 Source


The theory of sliding friction is sometimes called Coulomb friction, even though the fundamental relationships involved are known prior to COULOMB. The laws governing the behavior of sliding friction are based mainly on the experiments carried out by C0UL0MB in 1781 and on the works of MORIN between 1831 and 1834


Fig. 2. Experiment

The experiment will consist of the application of a horizontal pulling force T that will vary continuously from zero to a value sufficient to set the block in motion and give it an appreciable speed. The diagram for the solid free block corresponding to any value of T is shown in Figure 66b, and the force tangential frictionthat the plane exerts on the block is indicated with the letter F. This friction force will always have the direction of movement and sense contrary to it or to the tendency to movement of the body on which it acts. There is also a normal force N that in this case is equal to P, and the resulting force R that the supporting surface exerts on the block is the resultant of N and F. Figure 66c shows an enlargement of the irregularities of the surfaces. rough to help understand the mechanical action of friction. Support is necessarily intermittent and occurs on ridges without polish. The directions of the reactions acting on the block R1, R2, R3, etc., can be considered normal to the contact surface at the respective ridge.

The total normal force N is only the sum of the normal components of the reactions and the total friction force F is the sum of the tangential components of the reactions. When the surfaces are in relative motion, the contacts come closer to the ridges of the roughness, and the tangential components of the reactions will be smaller than when the surfaces are at rest with respect to each other. This consideration explains the known fact that the force T necessary to maintain movement is less than that required to set the block in motion when the irregularities are almost engaged.

Now suppose that the aforementioned experiment is carried out and that the friction force F as a function of T is measured. Figure 66d shows the experimental relationship obtained. When T is null, equilibrium requires no friction force. As T grows, the friction force must be equal to T as long as the block does not slide. During this period the block is in equilibrium and all the forces acting on the block must satisfy the equilibrium equations.

Finally, a value of T is reached that causes the block to slide in the direction and direction of the applied force. At this very moment the friction force decreases abruptly and slightly to a somewhat lower value. It then remains essentially constant for a certain period and then decreases further with increasing speed when it is higher.

Static friction

The zone to the slip point is called the static friction domain, and the value of the friction force is determined by the equations of equilibrium. This force can have any value between zero and the maximum value in the limit, inclusive. For a given pair of unpolished surfaces, this maximum value of static friction Fe turns out to be proportional to the normal force N.

Thus, Fe = feN where f is the proportionality constant that is called the static friction coefficient. Please note that this equation only describes the maximum value or limit of the static friction force, but not a lower value. Then this equation will apply only to cases where movement is known to be imminent.

Kinetic friction

Fig. 3.Kinetic friction cone

Once slippage occurs, we are faced with kinetic friction conditions. Kinetic friction (also called dynamic) involves a force somewhat less than the maximum static friction force. The kinetic friction force F also turns out to be proportional to the normal force.

Thus, F = feN where f is the coefficient of kinetic friction. It follows that f. is somewhat less than f. As the speed of the block increases, the coefficient of kinetic friction decreases somewhat and when reaching high speeds, the lubricating effect of the air layer between the surfaces can be appreciated. The friction coefficients depend largely on the exact condition of the surfaces, as well as on the speed, and are subject to a large margin of uncertainty.

The two equations for the friction force are usually written simply in the form You will be aware of the problem when they are implicit or the limit static friction with its corresponding static friction coefficient, or the kinetic friction with its corresponding kinetic coefficient. We insist that many problems carry with them a static friction force less than the maximum value for imminent movement and, therefore, in such a case the friction equation cannot be used. In figure 66c it can be seen that in the case of rough surfaces, large angles formed by the reactions with the direction of the normal are more possible than in the case of smoother surfaces. So that, the coefficient of friction measures the roughness of a pair of surfaces in contact and incorporates a geometric property of these rough contours. It makes no sense to speak of the friction coefficient of such a surface. The direction of the resultant R measured, in figure 66b, from the direction of N, is determined by tga = F / N. When the friction force reaches its maximum static value, the angle u reaches its maximum value 4.

Thus, tg 4 = f. When slippage occurs, the angle a will take a value 4 corresponding to the kinetic friction force.

Analogously, It is customary to simply write tga = F / N, tg = f (42) where the application to the static limit case or the kinetic case is inferred from the problem to be solved. Angle 4 is called a static friction angle, and angle 4 a kinetic friction angle. This angle clearly defines, for each case, the limit position of the total reaction R between the two surfaces in contact. If the movement is imminent, R must be a generatrix of a semi-angle revolution straight cone at vertex 4, as indicated in figure 67. If the movement is not imminent, R will be inside the cone. This semi-angle cone 4 is called the static bearing cone and represents the locus of the possible positions of the reaction R for the motion in-motion. If movement occurs,

Another experiment shows that the friction force is independent of the area of ​​the contact surface. This is true as long as the pressure is not too great. For high pressures the characteristics of the surfaces vary and the friction coefficient increases.

Slip friction problems

There are three types of sliding friction problems that commonly occur in mechanics. In the first type, one must look for the condition of imminent movement. In the problem statement it should be clear that the limit static friction requirement must be used.

In the second type of problem there is no need for imminent movement, and therefore the friction force may be less than that given by equation 41 with the coefficient of static friction. In this case the friction force will be determined by the equilibrium equations only. In such a problem it may be asked whether the existing friction is sufficient or not to keep the body at rest. To answer this, it must be assumed that there is equilibrium and from the equations of equilibrium the friction force necessary to maintain this state can be calculated. This friction force can then be compared to the maximum static friction that surfaces can withstand, calculated from equation 41 where f = f. If F is less than the one given by equation 41, it follows that the assumed friction force can be supported and therefore the body is at rest. If the calculated value of F is greater than the limit value, it follows that the given surfaces cannot withstand as much friction force and therefore there is movement and friction will be kinetic. The third type of problem involves relative movement between the surfaces in contact and in this case the coefficient of kinetic friction is applied. In this case, equation 41 with f = f ,, will always directly give the kinetic friction force. The preceding discussion is applicable to all dry surfaces in contact and, to a certain limit, to partially lubricated moving surfaces. Table D2 in Appendix D gives some typical values ​​of friction coefficients. These values ​​are only approximate and are subject to considerable variations, depending on the exact conditions prevailing. However, they can be used as typical examples of the magnitudes of friction effects.

When a practical calculation involving friction is required, it is often desirable to determine the appropriate coefficient of friction through an experiment in which the conditions of the problem surfaces are reproduced as accurately as possible.


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