past year exam 2.3

Question

3.1. A 250mm diameter shaft is revolving in a bearing and exerting a force of 75kN on the bearing. The coefficient of friction between the shaft and the bearing is 0,02 and the shaft rotates at 350r/min. Calculate the power lost due to friction 3.2. in a cutting tooth operation on a milling machine, the horizontal force exerted by the milling cutter is 1,5kN. The milling cutter has a diameter of 125mm and roatates at 70r/min. The feed of the milling cutter is 0,175mm per tooth and the cutter has 45 teeth. Calculate the following if the average feed is equal to the tangential cutting force: 3.2.1. the cutting speed of the milling cutter 3.2.2. the power consumed during the cutting action of the milling cutter 3.2.3. the power consumed for the feed of the milling machine

Answer 1

3.1)

The diameter of the shaft is 250 mm .

The radius of the shaft is [ r₂ ]  125 mm .

Amount of force exerted by shaft on bearing is (F) 75 kN .

 The coefficient of friction between the shaft and the bearing is ( μ) 0.02 .

The shaft rotates at the speed of 350 r/min .

The shaft rotates at the speed of 350 r/min = ( 350/60 ) = 5.8333 revolutions per second . 

The axial load W is the amount of force exerted by shaft on bearing  .

So the axial load W is 75 kN .

The frictional torque T is given by 

T = (2/3)μW [ r₂³ / r₂² ]

T = (2/3)μW [ r₂ ] 

T = (2/3)(0.02) (75 * 1000 ) [ 0.00125 ]

 T = (0.667)(0.02) (75) [ 125 ]

T = (0.0133) (9375)

T = 125 .

So the frictional torque is 125 Nm .

Thus the power loss is p = Tω .

p = Tω 

p = T * 2π ( revolutions per second ) 

p = 125 * 2π ( 5.8333 )

p = 125 * (36.6519 )

p = 4581.489 W .

So thus  the power loss is 4581.489 W . 

 

Answer 2

3.2.1)

Horizontal force of the milling cutter = 1.5 kN

Milling cutter diameter d = 125 mm

d = 125/1000

d = 0.125 m

Milling cutter speed RPM = 70 rpm

Milling cutter feed f = 0.175 mm per tooth

Number of teeth t = 45.

The cutting speed of the milling cutter N = ?

RPM = cutting speed/πd

Cutting speed = (RPM)πd

Cutting speed = 70×π×0.125

Cutting speed = 27.49 rev/min

The cutting speed of the milling cutter is 27.49 rev/min