past year exam 2.4

Question

3.1. A grinding wheel with a diameter of 200mm rotates at a speed of 2500r/min and exerts a tangential force of 60N on a work piece. If the motor rotates at a speed of 1500r/min with a machine efficiency of 85%, calculate the following: 3.1.1. the output at the grinding wheel 3.1.2. the input power of the motor 3.1.3. the torque on the spindle of the motor 3.2. calculate the power consumed at the following operations: 3.2.1. a lathe operation during the cutting force applied to the cutting tool is 1000 N and the rotational speed of the workpiece with a diameter of 350mm is 350r/min. 3.2.2. A shaper operation involving a cutting force by 750N and a stroke length of 120mm long taking 8 seconds to complete.

Answer 1

3.1.1 )

Grinding wheel diameter d_r = 200 mm

d_r = 200/1000 = 0.2 m

r = d/2 = 0.2/2 = 0.1 m

Grinding wheel Speed N_r = 2500 rpm

tangential force F = 60 N

Motor speed of N = 1500 rpm

machine efficiency η = 85%

η = 0.85

The output at the grinding wheel P_g =

Drive ratio DR = motor rpm / driven mechine rpm

Torque of mechine T = rF

Substitute r = 0.1 and F = 60 N

T = (0.1)(60)

T = 6 N-m.

Power P = 2πNT/60

Substitute T = 6 and N_r = 2500

P = 2π(2500)(6) / 60

P = 1570.8 W

The output at the grinding wheel P_g is 1570.8 W

Answer 2

3.1.2 )

Grinding wheel diameter d_g = 200 mm

d_g = 200/1000 = 0.2 m

Grinding wheel Speed N_g = 2500 rpm

Tangential force F = 60 N

Motor speed of N = 1500 rpm

Machine efficiency η = 85%

η = 0.85

The input power of the motor P_i = ?

d_g N_g = d N

d = d_g N_g/N

d = 0.2 * 2500 / 1500

d = 0.333

r = d/2 = 0.33/2 = 0.1667

Torque of mechine T = rF

Substitute r = 0.1667 and F = 60 N

T = (0.167)(60)

T = 10.002 N-m.

Power output P = 2πNT/60

Substitute T = T = 10.002 and N = 1500

P = 2π(1500)(10.002) / 60

P = 1571.11 W

But P_i = P/η

Substitute η = 0.85 and P = 1571.11

P_i = 1571.11/0.85

P_i =  1848.37

The input power of the motor is 1848.37 W

Answer 3

3.1.3)
Grinding wheel diameter d_r = 200 mm

d_r = 200/1000 = 0.2 m

r = d/2 = 0.2/2 = 0.1 m

Grinding wheel Speed N_r = 2500 rpm

tangential force F = 60 N

Motor speed of N = 1500 rpm

machine efficiency η = 85%

η = 0.85

The torque on the spindle of the motor T =

Torque of mechine T = rF

Substitute r = 0.1 and F = 60 N

T = (0.1)(60)

T = 6 N-m.

The torque on the spindle of the motor is 6 N-m

Answer 4

3.2.1 )

Workpiece diameter d = 350 mm

d = 350/1000 = 0.35 m

r = d/2 = 0.35/2 = 0.175 m

Workpiece Speed N = 350 rpm

Lathe cutting force F = 1000 N

The power consumed P = ?

Torque of mechine T = rF

Substitute r = 0.175 and F = 1000 N

T = (0.175)(1000)

T = 175 N-m.

Power P = 2πNT/60

Substitute T = 175 and N = 350

P = 2π(350)(175) / 60

P = 6414.1 W

The power consumed is 6414.1 W

Answer 5

3.2.2 )

Stroke length x = 120 mm

x = 120/1000 = 0.12 m

Workpiece cutting time t = 8 sec

t = 8/60 = 0.133 min

For 0.133 minutes time  It gives 1 revolution for peremeter formed by stroke.

Peremeter p = 2πx = 2π(0.12)

p = 0.754 m

RPM = peremeter / time in minutes

RPM = 0.754 / 0.133

RPM = 5.67 = N

Cutting force F = 750 N

The power consumed P = ?

Torque of mechine T = xF

Substitute x = 0.12 and F = 750 N

T = (0.12)(750)

T = 90 N-m.

Power P = 2πNT/60

Substitute T = 90 and RPM = N = 350

P = 2π(350)(90) / 60

P = 3298.67 W

The power consumed is 3298.67 W