Question

A single self-energizing long shoe drum shoe uses a molded lining of friction coefficient 0.45 and maximum allowable pressure of 150 psi as the friction material. If the angle subtended by the shoe is 120°, with θ1 = 0, find the face width required for the shoe to stop a torque of 3800 lb.in. The drum diameter is 12-in.

Answer 1

A = 10.83 in² , w = 3.29 in

Step-by-step explanation:

For this exercise we must use the rotational equilibrium condition

Σ τ = 0

in this case they give us the external torque τ = 3800 lb in.

τ - τ’= 0

τ = τ'

where τ‘ is the torque exerted by the brake shoe that is given by the friction force

τ’ = fr r sin θ

indicates that θ= 120º and the radius is half the diameter of the drum

r = 6 in

the friction force is given by the expression

fr = μ N

substitute

τ = μ N r sin θ (1)

to find the normal let's use Newton's second law on the perpendicular pressure axis

Σ F = 0

N - f = 0

N = f

The applied force can be found using the definition of pressure

P = f / A

where A is the area of ​​the footing

f = P A

let's substitute

N = P A

let's substitute in 1

τ = μ P A r sin θ

`A= (\tau )/(\mu \ P \ r \ sin\ \theta )`

let's calculate

A = 3800 / (0.45 150 6 sin 120)

A = 10.83 in²

to find the size of the shoe we must assume a specific shape, suppose the shoe is square

A =w²

w = √A

w = 3.29 in