Page 416 - Marks Calculation for Machine Design

P1: Naresh
January 4, 2005
15:28
Brown.cls
Brown˙C09
APPLICATION TO MACHINES
398
By analogy with the discussion for internal combustion engines where the torque varies
with the angle of rotation, the change in the inertial energy levels of the punch press system
is equal to the work done on or by the system. Therefore, Eq. (9.57) is applicable here where
the torque varies with angular velocity. Expanding the difference in angular velocities in
Eq. (9.57) as it was done in Eq. (9.58), the work done becomes
1 2 2 1 2 2
Work = I sys ω max − ω min = I sys ω − ω 1
2
1→2 2 2
1 ω 2 + ω 1
= I sys (ω 2 + ω 1 )(ω 2 − ω 1 ) = I sys (ω 2 − ω 1 ) (9.73)
2 2

= I sys ω m (ω 2 − ω 1 ) = I sys ω 1 C f ω 1
= I sys C f ω 2
1
Solving for the mass moment of inertia of the system (I sys ) in Eq. (9.73) gives
Work
1→2
I sys = 2 (9.74)
C f ω
1
which is very similar to Eq. (9.62) for internal combustion engines. However, the mass
moment of inertia of a punch press system (I sys ) is actually determined using Eq. (9.69),
once the torque (T 2 ) has been found by trial and error using Eq. (9.67).
U.S. Customary SI/Metric
Example 4. A punch press requires a certain Example 4. A punch press requires a certain
punching torque during only 4 percent of the punching torque during only 4 percent of the
punching cycle, which is (1 s). Determine the punching cycle, which is (1 s). Determine the
required mass moment of inertia of the system required mass moment of inertia of the system
(I sys ) and the coefficient of fluctuation (C f ), (I sys ) and the coefficient of fluctuation (C f ),
where where
T punch = 150 ft · lb T punch = 225 N · m
t 2 = 1s t 2 = 1s
P rated = 5hp P rated = 4kW
ω rated = 1,725 rpm ω rated = 1,725 rpm
ω syn = 1,800 rpm ω syn = 1,800 rpm
solution solution
Step 1. Convert the rated power (P rated ) from Step 1. Convert the rated power (P rated ) from
horsepower (HP) to (ft · lb/s). kilowatts (kW) to (N · m/s).
ft · lb N · m
550 1,000
s s
P rated = 5HP × P rated = 4kW ×
HP kW
ft · lb N · m
= 2,750 = 4,000
s s
Step 2. Convert the rated angular velocity Step 2. Convert the rated angular velocity
(ω rated ) from (rpm) to (rad/s). (ω rated ) from (rpm) to (rad/s).
rev 2 π rad 1 min rev 2 π rad 1 min
ω rated = 1,725 × × ω rated = 1,725 × ×
min rev 60 s min rev 60 s
= 180.6 rad/s = 180.6 rad/s