Be Summer 2022

Seat No.: ________ Enrolment No.
___________
GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–VI (NEW) EXAMINATION – SUMMER 2022
Subject Code:3162001 Date:01/06/2022
Subject Name:Design of Mechanisms
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
Q.1 (a) State different factors affecting the selection of materials. 03

(b) A machine component is subjected to a flexural stress which fluctuates between +300 04
MN/m2 and –150 MN/m2. Determine the value of minimum ultimate strength according
to 1. Gerber relation; and 2. Modified Goodman relation. Take, yield strength =
0.55*Ultimate strength; Endurance strength = 0.5*Ultimate strength; and factor of safety
= 2.
(c) A rotating shaft of 16 mm diameter is made of plain carbon steel (fyt = 400 N/mm2). It is 07
subjected an axil tensile load of 5000 N, a steady torque of 50 Nm and maximum bending
moment of 75 Nm. Calculate the factor of safety available based on:
(i) Maximum normal stress theory; and
(ii) Maximum shear stress theory
If the factor of safety is 1.686, find the required yield strength of the material using
distortion energy theory of failure. Assume remaining data same.
Q.2 (a) Name the various alloying elements in ‘alloy’ steels. 03

(b) A column of uniform cross section is shown in Figure. If the permissible tensile stress 04
for the column material is 70 MPa, determine the width ‘t’ of the column.
(c) Explain the procedure for the design of a socket and spigot cotter joint with sketch. 07
OR
(c) The layout of a transmission shaft carrying two pulleys B and C and supported on 07
bearings A and D is shown in Figure. Power is supplied to the shaft by means of a vertical
belt on the pulley B, which is then transmitted to the pulley C carrying a horizontal belt.
The maximum tension in the belt on the pulley B is 2.5 kN. The angle of wrap for both
the pulleys is 180° and the coefficient of friction is 0.24. The shaft is made of plain
1
carbon steel 30C8 (Syt = 400 N/mm2) and the factor of safety is 3. Determine the shaft
diameter on strength basis.
Q.3 (a) Define stress concentration and endurance limit. 03

(b) The maximum load on a petrol engine push rod 300 mm long is 1400 N. It is hollow 04
having the outer diameter 1.25 times the inner diameter. Spherical seated bearings are
used for the push rod. The modulus of elasticity for the material of the push rod is 210
kN/mm2. Find a suitable size for the push rod, taking a factor of safety of 2.5.
(c) A bell crank lever is to be designed to raise a load of 5 kN at the short arm end. The arm 07
lengths are 150 mm and 500 mm. The permissible stresses for lever and pin materials in
shear and tension are 60 N/mm2 and 90 N/mm2 respectively. The bearing pressure on
the pin is to be limited to 12 N/mm2. Assume the lever cross section as t*4t.
OR
Q.3 (a) What is coupling? Give its classifications. 03
(b) A foot lever is 1 m from the centre of shaft to the point of application of 800 N load. 04
Find: 1. Diameter of the shaft, 2. Dimensions of the key, and 3. Dimensions of
rectangular arm of the foot lever at 60 mm from the centre of shaft assuming width of
the arm as 3 times thickness. The allowable tensile stress may be taken as 73 MPa and
allowable shear stress as 70 MPa.
(c) The C-frame of a 100 kN capacity press is shown in Figure. The material of the frame is 07
grey cast iron FG200 and the factor of safety is 3. Determine the dimensions of the frame.
Q.4 (a) What are the types of keys? 03

(b) A cast iron pulley transmits 20 kW at 300 r.p.m. The diameter of pulley is 550 mm and 04
has four straight arms of elliptical cross-section in which the major axis is twice the
minor axis. Find the dimensions of the arm if the allowable bending stress is 15 MPa.
Mention the plane in which the major axis of the arm should lie.
(c) For supporting the travelling crane in a workshop, the brackets are fixed on steel columns 07
as shown in Figure. The maximum load that comes on the bracket is 12 kN acting
vertically at a distance of 400 mm from the face of the column. The vertical face of the
bracket is secured to a column by four bolts, in two rows (two in each row) at a distance
of 50 mm from the lower edge of the bracket. Determine the size of the bolts if the
permissible value of the tensile stress for the bolt material is 84 MPa. Also find the cross-
section of the arm of the bracket which is rectangular.
2
OR
Q.4 (a) A manufacturer is interested in starting a business with five different models of tractors 03
ranging from 7.5 to 75 kW capacities. Specify power capacities of the models. There is
an expansion plan to further increase the number of models from five to nine to fulfill
the requirement of farmers. Specify the power capacities of the additional models.
(b) What do you understand by self-locking screw? Explain the condition for self-locking. 04
(c) In a machine tool application, the tool holder is pulled by means of an operating nut 07
mounted on a screw. The tool holder travels at a speed of 5 m/min. The screw has single-
start square threads of 48 mm nominal diameter and 8 mm pitch. The operating nut exerts
a force of 500 N to drive the tool holder. The mean radius of the friction collar is 40 mm.
The coefficient of friction at thread and collar surfaces is 0.15. Calculate (i) power
required to drive the screw; and (ii) the efficiency of the mechanism.
Q.5 (a) State the advantages and disadvantages of gear drive over other types of drives. 03
(b) What are the different type of failures taking place in gear drives? 04
(c) A single row deep grove ball bearing is subjected to following work cycle: 07
Radial Axial Thrust Service

Elem. Time Radial Race Speed
load load Factor Factor
no % Factor Rotating (rpm)
Fr Fa Y Ks
X
1 20 5.0 kN 1.5 kN 0.56 2.0 Inner 1.50 720
2 50 7.0 kN 1.0 kN 1.00 0.0 Outer 1.25 1440
3 10 7.5 kN 0.5 kN 0.56 1.8 Inner 1.50 720
NO NO
4 20 - - Inner - 360
LOAD LOAD
If the dynamic capacity of bearing is 108 KN. Calculate
i. The rotating life of bearing in hours
ii. The average speed of operation
iii. The life of bearing in hours if reliability required is 95 %.
OR
Q.5 (a) Describe the factors affecting the endurance limit. 03
(b) Define the static and dynamic load carrying capacity of rolling contact bearing. 04
(c) Following data is given for a steel spur gear transmitting 7.5 kW power running at 1440 07
rpm to a machine running at 480 rpm. Approximate centre distance = 240 mm,
Allowable bending stress for pinion and gear are 200MPa and 160 MPa respectively.
Surface hardness is 450 BHN. Tooth system is 20⁰ full depths involutes. Design a spur
gear drive for above application. Take, C = 11860 *e and e = 0.064
0.912 2 ∗ 𝑍𝑔
𝑦𝑃 = 0.154 − 𝑍 Q = 𝑍 +𝑍
𝑝 𝑔
𝐹𝑆 = 𝑓𝑏 ∗ 𝑏 ∗ 𝑦 ∗ 𝜋 ∗ 𝑚 𝐹𝑤 = 𝑑𝑝 × 𝑄 × 𝑘 × 𝑏 𝑓𝑒𝑠 = 2.75∗BHN - 68.65
21 𝑉 (𝑐 𝑏 + 𝐹𝑡 ) 𝑓𝑒𝑠 2 𝑠𝑖𝑛∅ 1 1
𝐹𝑑 = 𝐹𝑡 + [21 𝑉 𝑚+ ] K= [𝐸 + 𝐸 ]
𝑚 √𝑐 𝑏+𝐹𝑡 1.4 𝑝 𝑔
*************
3

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Seat No.: ________ Enrolment No.

GUJARAT TECHNOLOGICAL UNIVERSITY

Q.1 (a) State different factors affecting the selection of materials. 03

Q.2 (a) Name the various alloying elements in ‘alloy’ steels. 03

Q.3 (a) Define stress concentration and endurance limit. 03

Q.4 (a) What are the types of keys? 03

Radial Axial Thrust Service

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