# Dynamics of Machines ```College of Engineering
Quiz
Department: Mechanical Engineering Subject: Dynamics of Machines (ME 243/221)
Date
: 24/04/2014
QN. 1. A shaft carrying 3 masses m1, m2, m3 at radii r1=1.135m&lt; 113.40, r2= 0.822m&lt;48.80, and
1.04m &lt;251.40. The values of masses m1, m2, 1nd m3 are 1.2 Kg, 1.8 Kg, and 2.4 Kg respectively.
Two masses are needed to dynamically balance the system using correction planes A and B.
The distances of planes 1, 2, 3, and B from reference plane A are given below.
A
1
2
3
B
0.854
1.701
2.396
3.097
Find out the mass radius product (mArA, and MBrB) and angular locations of correction masses
to dynamically balance the system.
QN. 2. Prove that the primary force and primary torque, and secondary forces and Torque for ‘
n’ in line cylinders are given by
Fp= mB r w2 [coswt∑ 𝐶𝑜𝑠∅𝑛 − 𝑆𝑖𝑛𝑤𝑡 ∑ 𝑠𝑖𝑛∅𝑛 ] MB reciprocating mass, Fp: primary Force
Tp= mB r w2 [coswt∑ 𝑎𝑛 𝐶𝑜𝑠∅𝑛 − 𝑆𝑖𝑛𝑤𝑡 ∑ 𝑎𝑛 𝑠𝑖𝑛∅𝑛 ] Tp primary Torque, an: distance of masses
from 1st plane.
Fs= = mB r w2 [cos2wt∑(𝐶𝑜𝑠 2 ∅𝑛 − 𝑆𝑖𝑛2 ∅𝑛 ) − 2𝑆𝑖𝑛𝑤𝑡 ∑(𝑠𝑖𝑛∅𝑛 𝐶𝑜𝑠∅𝑛 ) ]
Fs is Secondary force and TS is secondary Torque
Ts = mB r w2 [cos2wt∑ 𝑎𝑛 (𝐶𝑜𝑠 2 ∅𝑛 − 𝑆𝑖𝑛2 ∅𝑛 ) − 2𝑆𝑖𝑛𝑤𝑡 ∑ 𝑎𝑛 (𝑠𝑖𝑛∅𝑛 𝐶𝑜𝑠∅𝑛 ) ]
QN3. The turning moment diagram of an engine represented below. Each mm2 area represents
3 N-m of energy. If resisting
(mean) torque is uniform,
determine the mass of the
flywheel to keep the speed of
flywheel 218-222rpm. The
radius of gyration is 1.25 m.
Suction stroke =400 mm2.,
Compression stroke= 1600
mm2, Expansion stroke =
8000mm2 and exhaust stroke=
500mm2.
suction
Compressio
n
π
Exhaust
2π
3π
Expansion
4π
```