# Numerical - Flat pulley, given β & α

Q.  A V-belt pulley transmits power to flat belt pulley. If the coefficient of friction is 0.25 then which pulley governs the design? (β = 21o & α = 0.2)
- Published on 19 Oct 15

a. Flat pulley
b. V-belt pulley
c. Both a. and b.
d. None of the above

#### Discussion

• Sravanthi   -Posted on 05 Oct 15
Given: Co-efficient of friction (μ) = 0.25, β = 21o & α = 0.2

Generally, pulley having lower friction capacity governs the design.
Formula: 1) For flat pulley: θv = π - 2 α
2) For V-pulley: μ' θv = (μ θv ) / sin β & θv = π - 2 α

Substituting the given values we get,

1) Flat pulley
θf = π + 2 α
θf = π + (2 x 0.2) = 3.541 rad

μf θf = 0.885

2) V-pulley

θv = π - 2 α = 2.741 rad
μ' θv = (μ θv ) / sin β
= (0.25 x 2.741) / sin 21
= 1.912

μf θf < μ' θv

Hence, flat belt pulley governs the design.

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