Question

An engine shaft running at 120 r.p.m. is required to drive a machine shaft by means of a belt. the pulley on the engine shaft is of 2 m diameter and that of the machine shaft is 1 m diameter. if the belt thickness is 5 mm; determine the speed of the machine shaft

Answer 1

N1=120 r.p.m. N2=? D1=2m D2 =1m t= 0.005

Your answer is = 223.22 r.m.p

Answer 2

Answer:

The speed of the machine shaft, N₂ = $239.4rpm$.

Explanation:

The speed of the engine shaft, N₁ = $120rpm$

The diameter of the engine shaft, d₁ = $2m$

The diameter of the machine shaft, d₂ = $1m$

The thickness of the belt, t = $5mm$ = $0.005m$

The speed of the machine shaft, N₂ =?

As we know,

• The velocity of the engine shaft = the velocity of the machine shaft
• $d_{1} N_{1} =d_{2} N_{2}$

As given, the thickness of the belt is also present that we cannot neglect.

Therefore,

• $(d_{1} +t )N_{1} =(d_{2} + t ) N_{2}$
• $N_{2} = \frac{(d_{1} +t )N_{1} }{(d_{2} + t )}$
• $N_{2} = \frac{(2 +0.005 )120 }{(1 + 0.005 )}$
• $N_{2} = \frac{(2.005 )120 }{(1.005 )}$
• $N_{2} = 239.4rpm$

Hence, the speed of the machine shaft, N₂ = $239.4rpm$.