Page 419 - Marks Calculation for Machine Design

P1: Naresh
January 4, 2005
15:28
Brown.cls
Brown˙C09
U.S. Customary MACHINE ENERGY SI/Metric 401
Step 11. Calculate the slope (a) of the motor Step 11. Calculate the slope (a) of the motor
curve in the linear region using Eq. (9.70) as curve in the linear region using Eq. (9.70) as
T 1 15.2ft · lb T 1 22.1N · m
a = = a = =
ω 1 − ω syn (1,725 − 1,800) rpm ω 1 − ω syn (1,725 − 1,800) rpm
15.2 ft · lb ft · lb 22.1 N · m N · m
= =−0.203 = =−0.295
−75 rpm rpm −75 rpm rpm
Step 12. Using the slope (a) found in step 11, Step 12. Using the slope (a) found in step 11,
the times (t 1 ) and (t 2 ), and the torques (T 1 ) and the times (t 1 ) and (t 2 ), and the torques (T 1 ) and
(T 2 ) in Eq. (9.69), calculate the mass moment (T 2 ) in Eq. (9.69), calculate the mass moment
of inertia of the system (I sys ) as of inertia of the system (I sys ) as
a (t 2 − t 1 ) a (t 2 − t 1 )
I sys = I sys =
T 2 T 2
ln ln
T 1 T 1

ft · lb N · m
−0.203 (1 − 0.04) s −0.295 (1 − 0.04) s
rpm rpm
= =
ln (1.5ft · lb/15.2ft · lb) ln (2.25 N · m/22.1N · m)
ft · lb · s N · m · s
(−0.203)(0.96) (−0.295)(0.96)
rpm rpm
= =
ln (0.099) ln (0.102)
−0.195 ft · lb · s −0.283 N · m · s
= =
−2.316 rpm −2.285 rpm
ft · lb · s 1 rpm N · m · s 1 rpm
= 0.084 × = 0.124 ×
rpm 2 π rad rpm 2 π rad
60 s 60 s
60 60
2
2
= (0.084) (ft · lb · s ) = (0.124) (N · m · s )
2 π 2 π
slug · ft kg · m

= 0.8 ft · · s 2 = 1.2 · m · s 2
s 2 s 2
= 0.8 slug · ft 2 = 1.2kg · m 2
Remember that the mass moment of inertia Remember that the mass moment of inertia
(I sys ) found in step 12 is for the entire system (I sys ) found in step 12 is for the entire system
that includes the flywheel. that includes the flywheel.
9.3.4 Composite Flywheels
The flywheel shown in Fig. 9.8 is the simplest of designs, that is, a solid circular disk. This
is probably the easiest and the most economical design to produce; however, it is not the
most efficient use of material, and therefore, weight. This has been known for quite some
time, as the design of more efficient flywheels became almost an art in the nineteenth
century, carrying on to the twentieth century and now to the new millennium.
Better designs are achieved by moving material from near the axis of rotation and placing
it as far as practical from the axis. (Remember, mass moment of inertia is a measure of the
distribution of mass, and mass farther away from the axis counts more than the same amount
of mass near the axis.) The traditional theme of more efficient flywheels is shown in Fig. 9.13,