Page 418 - Marks Calculation for Machine Design

P1: Naresh
January 4, 2005
Brown˙C09
Brown.cls
400
U.S. Customary 15:28 APPLICATION TO MACHINES SI/Metric
Try 2.5 ft · lb Try 4.5 N · m
24 24

? 134.8 ? 202.9
2.5 = 15.2 4.5 = 22.1
150 − 2.5 225 − 4.5
? 24 ? 24
2.5 = 15.2 (0.914) 4.5 = 22.1 (0.920)
? ?
2.5 = 15.2 (0.115) = 1.75 4.5 = 22.1 (0.136) = 3.00
(too high) (too high)
Try 1.5 ft · lb Try 2.25 N · m
24 24

? 134.8 ? 202.9
1.5 = 15.2 2.25 = 22.1
150 − 1.5 225 − 2.25
? 24 ? 24
1.5 = 15.2 (0.908) 2.25 = 22.1 (0.911)
? ?
1.5 = 15.2 (0.098) = 1.49 2.25 = 22.1 (0.106) = 2.35
(close enough) (close enough)
Therefore, the torque (T 2 ) is Therefore, the torque (T 2 ) is
T 2 = 1.5ft · lb T 2 = 2.25 N · m
Step 9. Substitute the torque (T 2 ) found in Step 9. Substitute the torque (T 2 ) found in
step 8, the rated torque (T rated ) = (T 1 ), the rated step 8, the rated torque (T rated ) = (T 1 ), the rated
angular velocity (ω rated ) = (ω 1 ), and the given angular velocity (ω rated ) = (ω 1 ), and the given
synchronous speed (ω syn ) in Eq. (9.66) to find synchronous speed (ω syn ) in Eq. (9.66) to find
the corresponding angular velocity (ω 2 ). the corresponding angular velocity (ω 2 ).
ω syn − ω 2 ω syn − ω 2
T 2 = T 1 T 2 = T 1
ω syn − ω 1 ω syn − ω 1
1.5ft · lb = (15.2ft · lb) 2.25 N · m = (22.1N · m)
(1,800 rpm) − ω 2 (1,800 rpm) − ω 2
× ×
(1,800 − 1,725) rpm (1,800 − 1,725) rpm
1.5ft · lb (1,800 rpm) − ω 2 2.25 N · m (1,800 rpm) − ω 2
= =
15.2ft · lb 75 rpm 22.1ft · lb 75 rpm
(0.099)(75 rpm) = (1,800 rpm) − ω 2 (0.102)(75 rpm) = (1,800 rpm) − ω 2
7.4 rpm = (1,800 rpm) − ω 2 7.6 rpm = (1,800 rpm) − ω 2
ω 2 = 1,793 rpm ω 2 = 1,792 rpm
Step 10. Substitute the angular velocity (ω 2 ) Step 10. Substitute the angular velocity (ω 2 )
found in step 9 and the angular velocity (ω 1 ) in found in step 9 and the angular velocity (ω 1 ) in
Eq. (9.72) to find the coefficient of fluctuation Eq. (9.72) to find the coefficient of fluctuation
(C f ) as (C f ) as
ω 2 − ω 1 (1,793 − 1,725) rpm ω 2 − ω 1 (1,792 − 1,725) rpm
C f = = C f = =
ω 1 1,725 rpm ω 1 1,725 rpm
68 rpm 67 rpm
= = 0.039 = = 0.039
1,725 rpm 1,725 rpm