In a self locking brake, the force required to apply the brake is

Concept:

When the frictional force is great enough to apply the brake with no external force, then the brake is said to be a self-locking brake.

The figure shows the brake drum.

From the equilibrium of forces,

F × l + μR_N × b = R_N × a

F × l = R_N × a - μR_N × b

R_N (a - μb) = F × l

\(R_N=\frac{Fl}{(a-μ b)}\)...........................(1)

Braking torque on Drum is given as, T_B = F_f × R ⇒ T_B=μR_N × R

\(\therefore T_B=μ\times \frac{Fl}{(a-μ b}\times R\)

For self-locking brake:

From equation (1), the expression for the force "F" required to apply the brake is obtained as, \(F=\frac{R_N(a-μ b)}{l}\)

And if a < μ b, then F will be negative or zero. This means that no external force is required to apply the brake and hence the brake is self-locking.

Self-energizing brakes

When the frictional force helps the applied force in applying the brake, such types of brakes is said to be self-energizing brakes.

The brake should be self-energizing and not the self-locking.