Class: 4th Year
Subject: Design of Machine Elements
and Theory of Machines
Time: 3-hours
Examiner: Oday. I. A
Date: /6/2007
University of Baghdad
College of Engineering
Nuclear Engineering Department
Final Examination (2006– 2007)
First Attempt
THEORY OF MACHINES: Answer three questions only,
Question One
A belt drive consists of two V-belts in parallel, on grooved pulleys of the same size. The angle of the
groove is (30º). The cross-sectional area of each belt is (750 mm2) and (   0.12) . The density of the belt
material is (1.2 Mg/m3) and the maximum safe stress in the material is (7 M N/m2). Calculate the power that
can be transmitted between pulleys (300 mm) diameter rotating at (1500 r.p.m). Find also the shaft speed in
(rev/min) at which the power transmitted would be a maximum.
Question Two
An effort of (150-Kg) is required to just move a certain body up an inclined plane of angle (12º),
force acting parallel to the plane. If the angle of inclination was (15º), the effort required would be (172-Kg).
Find the weight of the body and the coefficient of friction.
Question Three: Attempt two of the following questions,
(a) A cylinder of weight (W) and radius (r) rolls without slipping on a cylindrical surface of radius (R), as
shown in Fig. (1-a). Determine its differential equation of motion for small oscillations about the lowest
point. For no slipping ( r  R ) .
(b) Determine the spring stiffness for the system of spring shown in Fig. (1-b).
(c) Modal the system shown in the Fig. (1-c) by a block attached to a single spring of an equivalent stiffness.
Question Four:
Power is transmitted from an electric motor to a machine tool by an open belt drive. The
effective diameter of the pulley on the motor shaft is (150 mm) while that on the machine tool is (200 mm)
with a center distance of (600 mm). If the motor speed is (1440 r.p.m) and the maximum permissible belt
tension is (900N), then the maximum power transmissible is (6 Kw). It is necessary that the power
transmissible be increased to (6.75 Kw), using the same pulleys, center distance and motor speed. The belt is
treated with a special preparation that increases its coefficient of friction by (10 per cent) of its existing
value; in addition a jockey pulley may be fitted. Determine (a) The existing coefficient of friction (b) The
new angle of lap.
1
θ
R
Fig. (1-a)
r
Φ
K
K1
K
K
3K
K2
K
m
2K
o
2K
a
2K
b
Fo
Fig. (1-c)
Fig. (1-b)
DESIGN OF MACHINE ELEMENTS: Answer three questions only,
Question One
Design a pair of (20º) stub tooth helical gears to transmit a power of (20 Kw), the speed on the pinion is
(10000 r.p.m). The center distance between the pinion and gear is to be (200 mm) and velocity ratio should
be about (4:1), both gears are of steel for which the endurance limit of material is (160 N/mm 2) and have a
helix angle (45º). Then check the gears for wear. Given:
 es  620 N / mm 2 , E  210 * 10 3 N / mm 2
6
( 5 m / sec  V  10 m / sec)
6 V
15
Cv 
( 10 m / sec  V  20 m / sec)
15  V
0.75
Cv 
( V  20 m / sec)
0.75  V
 2 es sin n  1
1  , tan  tan .cos  ,Y   ( 0.175  0.841 )
K

n


N
1.4
 E p Eg 
Question Two
a) In a Fig. (2-a). Determine the safe static load (P) that can be applied to the steel member, if the design
2
2
2
stresses are (70 N / mm ) in tension, (42 N / mm ) in shear and (112 N / mm ) in bearing. Data:
(t1  6 mm, t 2 11, d  40 mm, D  60 mm) .
b) Find the thickness for the machine part as shown in Fig. (2-b). When (P) is completely reversed
Cv 
(P=20KN). ( e  255 N / mm , y  630 N / mm , N  2, Kta  1.83, Ktb 1.5) .
Question Three:
2
2
A rotating shaft as shown in Fig. (3) is subjected to a reversed load P   2700 N  , find
the dimension (L), if the stress at the fillet is equal to the stress at the center.
Question Four:
A circular shaft, (50 mm) in diameter, is welded to a support by means of a fillet weld as
shown in Fig. (4). Determine the size of the weld, if the permissible shear stress in the weld
is limited to (100 N/mm2).
2
t
r=10 mm
D
P
100 mm
t2
30º
50 mm
t1
d
250 mm
150 mm
Fig. (2-b)
P
Fig. (2-a)
P
L/2
Kt=1.6
A
B
62.5 mm
(dia)
Bearing
50 mm
(dia)
375 mm
L
375 mm
Fig. (3)
200 mm
10 KN
Fig. (4)
3
50 mm (dia.)