friction in turning pairs – friction circle

FRICTION IN TURNING PAIRS – FRICTION CIRCLE

• Consider a journal bearing (which forms a turning pair) is shown in Fig.6.15(a), in which stationary part is known as bearing and rotating part is known as journal or shaft. 

• When a shaft rotates in a bearing some power is lost due to friction between the shaft and bearing surface. When the shaft (journal) is stationary and bearing is unlubricated, then the point of contact is at A, as shown in Fig.6.15(a). The load W is balanced by the normal reaction RN. The point A is also known as seat or point of pressure.

• When the shaft (journal) starts rotating (say, in the clockwise direction), then the point of contact shifts from A to B, as shown in Fig.6.15(b). In this case the lubrication is used to reduce friction which forms a thin layer between shaft and bearing, which rises boundary friction.

• At point B (Fig.6.15(b)), the two forces acting on the shaft are: (i) the normal reaction RN, and (ii) the frictional force μ RN, which act in the opposite direction of rotation and tangential at B. The resultant reaction produced by the bearing will be R which is inclined at an angle ϕ with RN.

Let

W = Vertical load on the shaft (journal),

r = Radius of the shaft (journal),

RN = Normal reaction exerted by bearing surface on the shaft,

μ = Coefficient of friction between shaft and bearing,

R = Resultant reaction,

ϕ = Friction angle i.e., angle between R and RN, and

ω = Angular velocity of the shaft.

For the equilibrium of the journal, we have

W = R

These two forces W and R form a couple (as they are not in same line of action) which opposes the torque required to produce the motion. This couple is known as friction couple or frictional torque.

Frictional torque is given by

If a circle is drawn with O as centre and OC = r sin ϕ as radius, then the circle is known as the friction circle of the bearing (as shown in dotted circle in Fig.6.15(b)).

Power lost is friction is given by