FRICTION CASE STUDY

FRICTION  CASE STUDY

Properties of Friction.: Friction is the resistance to motion that takes place when one body is moved upon another, and is generally defined as “that force which acts between two bodies at their surface of contact, so as to resist their sliding on each other.”

 According to the conditions under which sliding occurs, the force of friction, F, bears a certain relation to the force between the two bodies called the normal force N. The relation between force of friction and normal force is given by the coefficient of friction, generally denoted by the Greek letter μ. Thus

FIG 1

F = μ × N and μ =F / N

where :
N : normal force
F : force of friction
μ : coefficient of friction
we will consider frictional resistance between dry surfaces. Figure 1  shows a block of material resting on a dry horizontal surface. Initially, it is in a state of static equilibrium with its weight, W acting downwards balanced by the reaction, N of the horizontal surface acting upwards. When a small horizontal pulling force, P is applied to the block, nothing much happens to begin with.
The frictional resistance, F is able to balance the pulling force and the block stays in static equilibrium. As the pulling force is increased, the frictional resistance increases to balance it.
Eventually a value ofthe pulling force is reached above which the frictional resistance cannot rise. This is known as the limiting frictional resistance and at this point, the block starts to slide over the surface. 
Once an object starts to slide, it is found that the frictional resistance to motion is slightly less than the limiting value, and that the pulling force needed to maintain motion is slightly less than that required to get things moving. The reason for this is thought to be that there are irregularities, such as peaks and valleys, in even the smoothest of surfaces. When at rest, the peaks on the two surfaces are in contact and the weight, W is carried on a very small area, as shown in Figure 2.

FIG 2

As a result of the pressure, the surfaces become welded together at the contact points and the bonds have to be broken before sliding can take place. This accounts for the fact that once sliding
has begun, the force necessary to maintain the motion, which is called kinetic frictional resistance, is less than that to overcome static friction or ‘stiction’ as it is sometimes called.

1-- If a body sliding on a flat horizontal surface as in Figure 2, and the forces which act upon
The first law states that frictional resistance is proportional to the force between the surfaces

F =constant×W

The constant is the coefficient of friction, μ for the two surfaces.

F =μ×W

The coefficient of friction depends on the surface roughness and texture, as stated in the second law. It has two values for any two particular surfaces. One is the coefficient of static friction, which is
also called the limiting coefficient of friction. This enables the value of the force required to overcome ‘stiction’ to be calculated. The other is the coefficient of kinetic friction which has a slightly lower value, and enables the value of the frictional resistance in motionto be calculated.

Figure 3.shows that the two active forces, P and W, produce a resultant reaction, RR which is inclined at an angle 𝜙 to the normal. This is called the angle of friction, whose tangent is equal to the coefficient of friction m. That is,

tan 𝜙 = F/  W =μ

FIG 3

It should be noted that the laws of friction only apply within reasonable limits. If the force between the surfaces is excessive, or the area of contact is very small or the sliding velocity is high,
excessive amounts of heat energy will be generated. This can cause the temperature at the interface to rise to a level where seizure occurs, and the surfaces become welded together. This can easily
happen in internal combustion engines if the supply of lubricating oil to the cylinders should fail. In these circumstances, the pistons become welded to the cylinder walls. figure 4,

FIG 4

2-- If a body is placed on an inclined plane figure 5 , the friction between the body and the plane will prevent it from sliding down the inclined surface, provided the angle of the plane with the horizontal is not too great. There will be a certain angle, however, at which the body will just barely be able to remain stationary, the frictional resistance being very nearly overcome by the tendency of the body to slide down. This angle is termed the angle of repose, and the tangent of this angle equals the coefficient of friction. The angle of repose is frequently denoted by the Greek letter θ. Thus, μ = tan θ.

FIG 5

A greater force is required to start a body moving from a state of rest than to merely keep
it in motion, because the friction of rest is greater than the friction of motion.
Laws of Friction.
The laws of friction for unlubricated or dry surfaces are summarized in the following statements.
1) For low pressures (normal force per unit area) the friction is directly proportional to the normal force between the two surfaces. As the pressure increases, the friction does not rise proportionally; but when the pressure becomes abnormally high, the friction increases at a rapid rate until seizing takes place.
2) The friction both in its total amount and its coefficient is independent of the areas in contact, so long as the normal force remains the same. This is true for moderate pressures only. For high pressures, this law is modified in the same way as in the first case.
3) At very low velocities the friction is independent of the velocity of rubbing. As the velocities increase, the friction decreases.
Lubricated Surfaces: For well lubricated surfaces, the laws of friction are considerably different from those governing dry or poorly lubricated surfaces.
1) The frictional resistance is almost independent of the pressure (normal force per unit area) if the surfaces are flooded with oil.
2) The friction varies directly as the speed, at low pressures; but for high pressures the friction is very great at low velocities, approaching a minimum at about two feet per second linear velocity, and afterwards increasing approximately as the square root of the speed.
3) For well lubricated surfaces the frictional resistance depends, to a very great extent, on the temperature, partly because of the change in the viscosity of the oil and partly because, for a journal bearing, the diameter of the bearing increases with the rise of temperature more rapidly than the diameter of the shaft, thus relieving the bearing of side pressure.
4) If the bearing surfaces are flooded with oil, the friction is almost independent of the nature of the material of the surfaces in contact. As the lubrication becomes less ample, the coefficient of friction becomes more dependent upon the material of the surfaces.
Influence of Friction on the Efficiency of Small Machine Elements.Friction between machine parts lowers the efficiency of a machine. Average values of the efficiency, in per cent, of the most common machine elements when carefully made are ordinary bearings,  roller bearings, ; ball bearings, spur gears with cut teeth,including bearings, bevel gears with cut teeth, including bearings, belting, from  to  high-class silent power transmission chain, roller chains,
Coefficients of Friction.
Tables 1 and 2 provide representative values of static friction for various combinations of materials with dry (clean, unlubricated) and lubricated surfaces. The values for static or breakaway friction shown in these tables will generally be higher than the subsequent or sliding friction. Typically, the steel-on-steel static coefficient of 0.8 unlubricated will drop to 0.4 when sliding has been initiated; with oil lubrication, the value will drop from 0.16 to 0.03.
Many factors affect friction, and even slight deviations from normal or test conditions can produce wide variations. Accordingly, when using friction coefficients in design calculations, due allowance or factors of safety should be considered, and in critical applications, specific tests conducted to provide specific coefficients for material, geometry, and/or lubricant combinations.

Rolling Friction.
When a body rolls on a surface figure 6 , the force resisting the motion is termed rolling friction or rolling resistance. :

FIG 6

resistance to rolling, in pounds = (W× f) ÷ r.

where 
W = total weight of rolling body or load on wheel, in pounds;
 r = radius of wheel, in inches;
 f = coefficient of rolling resistance, in inches. 

The coefficient of rolling resistance, f, is in inches and is not the same as the sliding or static coefficient of friction given in Tables 1 and 2, which is a dimensionless ratio between frictional resistance and normal load. Various investigators are not in close agreement on the true values for these coefficients and the foregoing values should only be used for the approximate calculation of rolling resistance.
Friction in screw threads
Single and multi-start screw threads are used for power transmission in screw jacks, presses and machine tools. A square section screw thread can be regarded as an inclined plane which ascends in

a spiralling direction figure 7

FIG 7

Turning the screw has the effect of moving the load up or down the incline whose angle is the helix angle, 𝚹 of the thread. The distance moved by the load for one revolution of the thread is called the lead. For a single-start thread the lead, l is equal to the pitch, p and for a two-start thread, l=2 p etc. If d, is the thread diameter, the helix angle can be found from

For a single-start thread, l=p and the helix angle is given by

The tangential force, P required to raise the load W by a horizontal force

Where :

P : required tangential force  (N)

W  : mas to be raised 

The torque required to raise the load is given by
torque =tangential force×effective radius

Experiments to determine the coefficient of friction
There are two experimental methods which are commonly used to Bdetermine the coefficient of friction. The first method lends itself to finding the limiting coefficient of friction whilst the second can, with care, give both the limiting and kinetic coefficients
Method 1
Apparatus: Horizontal surface and slider faced with the two materials under investigation, free-running pulley, slotted and stackable masses, length of cord and a hanger for the slotted masses.
Procedure:
1. Weigh the slider and make a note of its mass.
2. Assemble the apparatus as shown in Figure 8 making sure that the plane surface and the slider           are clean and dry.
3. Place a stackable mass of 0.5 kg on the slider and add slotted masses to the hanger until the                   tension     in the cord just overcomes static friction.

FIG 8

4. Make a note of the total sliding mass and the total hanging mass.
5. Repeat the last two operations for increments of 0.5 kg on the slider until at least six sets of                  readings have been taken.
6. Plot a graph of hanging mass against sliding mass and calculate the value of its gradient.                 The results should give you a straight line graph as shown in Figure 9. There may be a little scattering of the points and if so, draw in the line of best fit.

FIG 9

Theory: The total mass of the slider and slotted masses,Mis directly proportional to its weight, W. This is the normal force between the surfaces in contact. Similarly, the total hanging mass is directly proportional to its weight. This is the force, F necessary to overcome static friction. The gradient of the graph shown in Figure 9 thus gives a mean value of the limiting coefficient of friction. That is

Method 2

Apparatus: Adjustable inclined plane faced with one of the materials under test and fitted with a protractor to measure the angle of inclination. Slider whose lower surface is faced with the other material and whose upper surface contains a spigot for holding stackable masses (Figure10).

FIG 10

Procedure:

1. Weigh the slider and make a note of its mass. Make sure that the inclined plane surface and the            slider are clean and dry.

2. With the plane horizontal, place the slider at the end opposite the hinge with a mass of 0.5 kg on           the slider.

3. Slowly incline the plane and note the angle,𝚹 at which the slider starts to move.

4. Adjust the angle of the plane so that the slider continues to slide slowly down with a steady                  velocity and again note the value of the angle,𝚹.

5. Repeat the procedure with increasing values of mass on the slider and tabulate the results.

6. For each set of results, calculate the tangent of the angle at which the slider starts to move and the       tangent of the angle at which the slider moves with a slow and steady velocity.

Theory: Figure 11 shows the forces acting on the slider. The weight of the slider and masses can be resolved into two components, one which acts normal to the incline and one which acts

parallel to the incline. In the limit as motion commences, and when the slider is moving with a steady velocity, the forces normal to the plane and parallel to the plane will be equal and opposite.

Normal reaction, R = W cos 𝚹

and

Frictional resistance, F = W sin𝚹

FIG 11

The coefficient of friction is given by

coefficient of friction =  frictional resistance / normal reaction

The mean value of the tangents of the angle at which motion commences gives a mean value of the limiting coefficient of friction between the surfaces. Similarly, the mean value of the

tangents of the angle at which the slider moves at a steady velocity gives a mean value of the coefficient of kinetic friction

Applications of Friction
In some applications, a low coefficient of friction is desirable, for example, in bearings, pistons moving within cylinders, on ski runs, and so on. However, for such applications as force being transmitted by belt drives and braking systems, a high value of coefficient is necessary.
Advantages and Disadvantages of Frictional Forces
Instances where frictional forces are an advantage include:
(i) Almost all fastening devices rely on frictional forces to keep them in place once secured, examples being screws, nails, nuts, clips and clamps.
(ii) Satisfactory operation of brakes and clutches rely on frictional forces being present.
(iii) In the absence of frictional forces, most accelerations along a horizontal
surface are impossible; for example, a person’s shoes just slip when walking is attempted and the tyres of a car just rotate with no forward motion of the car being experienced.
Disadvantages of frictional forces include:
(i) Energy is wasted in the bearings associated with shafts, axles and gears due to heat being generated.
(ii) Wear is caused by friction, for example, in shoes, brake lining materials and bearings.
(iii) Energy is wasted when motion through air occurs (it is much easier to cycle with the wind rather than against it).