GUJARAT TECHNOLOGICAL UNIVERSITY - mytoolbag.inmytoolbag.in/media/GTUPAPERS/1/2/MECHANICAL/S5/TOM.pdf · 4. R L Norton, Kinematics and Dynamics of Machinery, McGraw -Hill. 5. Kenneth

GUJARAT TECHNOLOGICAL UNIVERSITY

MECHANICAL ENGINEERING (19)

THEORY OF MACHINES

SUBJECT CODE: 2151902

B.E. 5th SEMESTER

Type of course: Under Graduate

Prerequisite: None.

Rationale: Theory of Machines is a fundamental course for Mechanical engineers to understand the

working principals of any machine. This course is essential to understand the motion,

transmission of the motion and the forces responsible for the motion

Teaching and Examination Scheme:

Teaching Scheme Credits Examination Marks

Total

Marks L T P C

Theory Marks Practical Marks

ESE

(E)

PA (M) PA (V) PA

(I) PA ALA ESE OEP

3 0 2 5 70 20 10 20 10 20 150

Content:

Sr.

No.

Content Total

Hrs % Weightage

1 Gyroscope:

Principle of gyroscope, Definition of axes, active and reactive couples; Roll,

Yaw and Pitch motions; Gyroscopic effect in a rotor, two wheelers, Four

wheelers, ship and aeroplane.

10 20%

2 Friction Devices: Clutches, Brakes and Dynamometers

Classification of clutches, torque transmission capacity, considerations for

uniform wear and uniform pressure theory, single plate and multi-plate

clutch, centrifugal clutch, Energy equation and thermal considerations.

Classification of brakes, Braking effect, Analysis of Brakes: Block Brake,

Band Brake, Band and Block Brake, Internal expansion shoe brake; Braking

analysis of four wheelers.

Classification of Dynamometers, Analysis of Dynamometers: Prony brake,

Rope brake, Hydraulic, Belt Transmission, Epicyclic-Train and Bevis-Gibson

torsion.

12 30%

3 Flywheels:

Significance of flywheel, Turning moment and crank effort diagrams for

reciprocating machines, coefficient of fluctuation of speed and energy,

Limiting velocity of flywheel, Design of flywheels for engines and punching

machines.

5 15%

4 Governors:

Necessity of governor, Classification of Governors, Working principle of

centrifugal governors, Concept of control force, Control force diagram,

Stability of governor, Condition for stability, Concept of isochronism,

Sensitivity of governor, Characteristics of governors, Hunting of governors.

** 5%

** Should be covered during practical session only.

Suggested Specification table with Marks (Theory):

Distribution of Theory Marks

R Level U Level A Level N Level E Level C Level

10 15 15 10 10 10

Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate C: Create and

above Levels (Revised Bloom’s Taxonomy)

Note: This specification table shall be treated as a general guideline for students and teachers. The actual

distribution of marks in the question paper may vary slightly from above table.

Reference Books:

1. S S Rattan 4/e, Theory of Machines, McGraw-Hill.

2. J.Uicker , Gordon R Penstock & J.E. Shigley, Theory of Machines and Mechanisms, Oxford.

3. A G Ambekar, Mechanism and Machine Theory, PHI.

4. R L Norton, Kinematics and Dynamics of Machinery, McGraw-Hill.

5. Kenneth J Waldron , Gary L Kinzel, Kinematics, Dynamics and Design of Machinery, Wiley.

6. Meriam, J L and Kraige, L G, Engineering Mechanics: Dynamics, Wiley.

Course Outcome:

After learning the course the students should be able to:

1. Analyse effect of gyroscopic couple on vehicles, ships and aeroplanes.

2. Design flywheels for IC engines and punching press.

3. Apply fundamentals of dynamics analysis to various mechanical systems.

4. Design and analyse clutches and brakes.

5. Perform power measurement using dynamometers.

6. Analyse governors.

List of Experiments:

1. Performance on gravity controlled governors.

2. Analysis of gyroscopic effect.

3. Performance on spring controlled governors.

4. Analysis of clutch.

5. Analysis of brakes.

6. Power measurement using dynamometers.

7. Dynamic force analysis of 4-bar mechanism and slider crank mechanism (Analytical Methods)

8. Design of Flywheel for IC engine and Punch press.

5 Introduction to Dynamics:

Newton’s Laws of Motion, Applied and constraint forces, Free-body

diagrams, conditions for equilibrium, Two and Three forces members, Four

force members, Friction forces, Static force analysis with friction. Centroid

and Centre of Mass, Mass Moments and products of inertia, Inertia forces and

D’alembert’s Principle. Planar rotation about fixed centre, Shaking forces and

moments, Complex algebra approach, Equation of motion. Application of

concepts to dynamic analysis of slider-crank mechanism and 4-bar

mechanism.

Spatial: Measuring mass moment of Inertia, Transformation of Inertia axes,

Euler’s equation of motion, Impulse and momentum, Angular impulse and

momentum.

15 30%

9. Measurement of mass moment of inertia.

10. Measurement of radius of gyration of various components.

Design based Problems (DP)/Open Ended Problem:

1. Carryout mechanism analysis using CAD tools.

2. Write program for analysis of mechanism.

3. Conceptualize a system to replace a clutch.

4. Perform analysis of braking system for various vehicles.

Major Equipment:

1. Governors.

2. Dynamometers.

ACTIVE LEARNING ASSIGNMENTS: Preparation of power-point slides, which include videos,

animations, pictures, graphics for better understanding theory and practical work – The faculty will allocate

chapters/ parts of chapters to groups of students so that the entire syllabus to be covered. The power-point

slides should be put up on the web-site of the College/ Institute, along with the names of the students of the

group, the name of the faculty, Department and College on the first slide. The best three works should

submit to GTU.

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V (NEW) - EXAMINATION – SUMMER 2017

Subject Code: 2151902 Date: 12/05/2017 Subject Name: Theory of Machines Time: 02:30 PM to 05:00 PM Total Marks: 70 Instructions:

1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

Marks

Q-1 Short Questions 14

1 The gyroscopic effect due to rotating parts of a turbo jet engine of an air craft on

a curved course depend on

(a) Flight velocity (b) flight altitude (c) radius of curve (d) Flight velocity and

radius of curve

2 The axis of spin, the axis of precession, axis of applied gyroscope couple are

contained in

(a) One plane (b) two plane (c) three planes perpendicular to one another

3 The rotor of a ship rotates in clockwise direction when viewed from the stern and

the ship takes a left turn. The effect of the gyroscopic couple acting on it will be

(a) to raise the bow and stern (b) to lower the bow and stern

(c) to raise the bow and lower the stern (d) to lower the bow and raise the stern

4 If the angle of the cyclist with normal increases the cyclist should have

(a) Higher speed (b) same speed as before (c) lower speed

5 Write the conditions for a dynamically equivalent system.

6 When brakes are applied to all the four wheels of a moving car, the distance

travelled by the car before it is brought to rest, will be

(a) maximum (b) minimum (c) zero

7 Which of the following is an absorption type dynamometer?

(a) prony brake dynamometer (b) epicyclic-train dynamometer (c) torsion

dynamometer

8 The ratio of the maximum fluctuation of speed to the mean speed is called

(a) fluctuation of speed (b) maximum fluctuation of speed

(c) coefficient of fluctuation of speed (d) none of these

9 The ratio of the maximum fluctuation of energy to ________ the, is called

coefficient of fluctuation of energy.

(a) minimum fluctuation of energy (b) work done per cycle

10 The angle of inclination of the plane, at which the body begins to move down the

plane, is called

(a) angle of friction (b) angle of repose (c) angle of projection

11 In a screw jack, the effort required to lift the load W is given by

(a) P = W tan (α – φ) (b) P = W tan (α + φ)

(c) P = W cos (α – φ) (d) P = W cos (α + φ)

12 The frictional torque transmitted by a disc or plate clutch is same as that of

(a) flat pivot bearing (b) flat collar bearing

(c) conical pivot bearing (d) trapezoidal pivot bearing

13 The frictional torque transmitted by a cone clutch is same as that of

(a) flat pivot bearing (b) flat collar bearing

(c) conical pivot bearing (d) trapezoidal pivot bearing

14 Draw the turning moment diagram of a single cylinder double acting steam

engine.

Q.2 (a) Explain following

1. Sensitiveness of Governors

2. Isochronous Governors

04

(b) How stability of four wheels automobile is affected due Gyroscopic couple and

centrifugal force. Explain with necessary expression.

04

(c) Each road wheel of a motor cycle has a mass moment of inertia 1.5 kg-m2. The

rotating parts of the engine of a motor cycle have a mass moment of inertia of

0.25 kg-m2. The speed of the engine is 5 times the speed of the wheels and is in

the same sense. The mass of motor cycle with the rider is 250 kg and the centre

of gravity is 0.6 m above the ground level. Find the angle of heel if motor cycle

is travelling at 50 km per hour and is taking turn of 30 m radius. Wheel diameter

is 0.6 m.

06

OR

(c) The turbine rotor of a ship having a mass 0f 200 kg rotates at 2000 rpm and its

radius of gyration is 0.30 m. if the rotation of rotor is clockwise looking from the

aft, determine the gyroscopic couple set by the rotor when

1. Ship takes left turn at a radius of 300 meters at a speed of 30 km/hr,

2. Ship pitches with the bow rising at an angular velocity of 1 rad/sec and

3. Ship rolls at an angular velocity of 0.1 rad/sec

06

Q.3 (a) Derive the expression of maximum fluctuation of energy for multi-cylinder

engine and coefficient of fluctuation of energy. 06

(b) A vertical single petrol engine 150 mm diameter and 200 mm stroke has a

connecting rod 350 mm long. The mass of the piston is 1.6 kg and the engine

speed is 1800 rpm. On the expansion stroke with crank angle 30o from top dead

centre, the gas pressure 750 X 103 N/m2. Determine the net thrust on the piston.

08

OR Q.3 (a) Derive an expression of fluctuation of energy for flywheel used in punching

press. 06

(b) The following data relate to a horizontal reciprocating engine:

Mass of reciprocating part: 120 kg, crank length = 90 mm, engine speed = 600

rpm, mass = 90 kg, length between centres = 450 mm, distance of centre of mass

from big end centre =180 mm, radius of gyration about an axis through centre of

mass = 150 mm. determine.

1. Inertia torque due to reciprocating parts

2. Correction couple.

08

Q.4 (a) Determine the retardation of a four wheel car when the brakes are applied to the

rear wheel. 04

(b) Explain working of epicyclic train dynamometer. 03 (b) A differential band brake, as shown in Fig. has an angle of contact of 225°. The

band has a compressed woven lining and bears against a cast iron drum of 350

mm diameter. The brake is to sustain a torque of 350 N-m and the coefficient of

friction between the band and the drum is 0.3. Find the necessary force (P) for

the clockwise and anticlockwise rotation of the drum.

07

OR Q.4 (a) Determine the retardation of a four wheel car when the brakes are applied to the

front wheel. 04

(b) Explain working of Bevis Gibson flash light torsion dynamometer. 03 (b) A vehicle moving on a rough plane inclined at 10° with the horizontal at a speed

of 36 km/h has a wheel base 1.8 metres. The centre of gravity of the vehicle is

0.8 metre from the rear wheels and 0.9 metre above the inclined plane. Find the

distance travelled by the vehicle before coming to rest and the time taken to do

so when 1. The vehicle moves up the plane, and 2. The vehicle moves down the

plane. The brakes are applied to all the four wheels and the coefficient of friction

is 0.5.

07

Q.5 (a) Derive an expression of radius of gyration for connecting road. 05 (b) Using graphical method determine the required value of T2 and various forces on

link for equilibrium of the system.

09

OR Q.5 (a) Discuss the effect of friction on the forces acting at joints of mechanism. 05

(b) Determine the magnitude and direction of the forces which must be applied to

link 2 to maintain equilibrium. Neglect friction. O2A = 3 cm, AB = 7 cm, AC =

14 cm, BC = 8 cm.

09

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V(New) • EXAMINATION – WINTER 2016

Subject Code:2151902 Date:24/11/2016

Subject Name:Theory of Machines

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.

MARKS

Q.1 Short Questions 14

1 For any flywheel what is more important, mass or mass moment of inertia?

2 Define Free body diagram. 3 In which type of clutch no pedal is required for engagement or disengagement of

drive?

4 Governor is used with which type of engines only. 5 In a rope brake dynamometer why cooling water is required? 6 Are we using flywheels with electric motors in mixer grinder? Why? 7 Which are the various types of brakes?

8 What is the meaning of “Stern” for naval ship?

9 For which engine the size of flywheel will be small, either 2 cylinder engine or 4

cylinder engine producing same power. Why?

10 Define Precession axis.

11 Hunting of governor is useful or not? Why?

12 Give one advantage of Gyroscopic couple.

13 Illustrate constraint force with proper fig.

14 Give statement of D’alembert’s principle.

Q.2 (a) Give only two differences and one similarity between Brake and Dynamometer. 03

(b) Explain basic terms used for gyroscopic with proper diagram. 04

(c) Discuss the gyroscopic effect and stability of a four wheel vehicle moving along a

curved path. 07

OR

(c) A car is of total mass 1800 kg has the track width 160 cm. Each wheel having an

effective diameter 60 cm and the mass moment of inertia 2.5 kg m2. The mass

moment of inertia of rotating parts of the engine is 1.4 kg m2. The engine axis is

parallel to the rear axle and the crankshaft rotates in the same sense as the road

wheels. The gear ratio of the engine to the rear wheel is 3. The centre of mass of the

car is 50 cm above the road level. If the car is rounding a curve of 60 m radius at a

speed of 110 km/h, determine the load distribution on the inner and outer wheels.

07

Q.3 (a) Short note on Flywheel material. 03

(b) Explain various applications of flywheel. 04

(c) What is the function of a dynamometer? List various types of dynamometers. Explain

any one with neat sketch. 07

OR

Q.3 (a) For a rope brake dynamometer with flywheel dia. of 1 m, speed of the engine 180

rpm, dia. of rope is 10 mm, dead weight 50 kg, reading of spring balance is 120 N,

then find the brake power of the engine.

03

(b) Give advantages and disadvantages of hydraulic dynamometer. 04

(c) The T- diagram of an engine consists of intercepted areas which are +40, -85, +79, -

68, +96 and -62 mm2 in one cycle taken in the given order. The torque axis scale is 1

mm = 75 N-m and crank angle scale is 1 mm = 50. Mean speed of the engine is 500

rpm. Design the rim of the flywheel for the following data:

(a) Limiting rim speed at mean radius = 30 m/s.

(b) The fluctuation of speed = 2 % around mean speed.

07

2

(c) Width to thickness ratio for rectangular rim section is 1.5 which contributes

100% of MI of flywheel.

(d) Material density is 7200 kg/m3. Neglect the flywheel effect of hub and arms.

Q.4 (a) Define Centroid and centre of gravity. Give difference between two. 03

(b) Explain working principle of centrifugal governor with suitable diagram. 04

(c) 100 kW is transmitted at 3000 rpm by a multiplate disk friction clutch. The plates are

having friction surface with coefficient as 0.07 and the axial intensity of pressure

should not exceed 1.5 bar. External radius is 1.25 times the internal radius and the

external radius is 12.5 cm. Determine the number of plates needed to transmit the

required torque assuming uniform wear.

07

OR

Q.4 (a) State and explain parallel axis theorem. 03

(b) What is a function of a governor? How does it differ from that of a flywheel? Also

explain the terms sensitiveness, hunting and stability relating to governors.

04

(c) Determine the time required to accelerate a counter shaft of rotating mass 500 kg and

radius of gyration of 200 mm to the full speed of 250 rpm from rest through a single

plate clutch of internal and external radii 125 mm and 200 mm, taking coefficient of

friction as 0.3 and axial spring force of 600 N. Assume that only one side of clutch is

working.

07

Q.5 (a) State Newton’s three laws of motion. 03

(b) Explain the concept of Free body diagram with proper example. 04

(c) A steel forging consists of a 60 x 20 x 20 mm rectangular prism and two cylinders of

20 mm diameter and 30 mm length as shown in Fig. Determine the moments of

inertia of the forging with respect to the co-ordinate axes passing from centroid of

prism. Density of steel is 7850 kg/m3.

07

OR

Q.5 (a) State Lami’s theorem and give suitable example. 03

(b) A wheel rotates with constant angular acceleration and describes 100 radians during

time of 5 seconds. After that it has constant angular velocity for 5 seconds and it

describes 80 radians. Find the initial angular velocity and the angular acceleration.

04

(c) In slider crank mechanism, the crank is 300 mm long and connecting rod 850 mm

long. The piston is of 90 mm in diameter and gas pressure acting on the piston is 5

MPa. When the crank has moved through 450 from I.D.C. find

(a) Thrust in connecting rod

(b) Reaction from guide ( side thrust on piston)

(c) Torque acting on the crankshaft and

(d) Radial load on main bearing

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V (NEW) - EXAMINATION – SUMMER 2016

Subject Code:2151902 Date:06/05/2016 Subject Name:Theory of Machines Time:02:30 PM to 05:00 PM Total Marks: 70 Instructions:


Q.1 (a) Illustrate the effect of Gyroscopic couple on a car. 06

(b) The ship is propelled by a turbine rotor having mass of 6 tonnes and speed of 2400

rpm. The direction of rotation of the rotor is clockwise when viewed from the stern.

The radius of gyration of the rotor is 450 mm. Determine the gyroscopic effect

when

1. The ship steers the left in curve of 60 m radius at a speed of 33.48 km/hr.

2. The ship pitches 7.5 degree above and 7.5 degree below the normal

position and the bow is descending with its maximum velocity. The

pitching motion is simple harmonic with periodic time of 18 seconds.

3. The ship rolls and at the instant, its angular velocity is 0.035 rad/sec

counter clockwise when viewed from the stern.

08

Q.2 (a) Describe with the help of a neat sketch the principles of operation of an internal

expanding shoe. Derive the expression for the braking torque. 06

(b) A car moving on a level road at a speed 50 km/h has a wheel base 2.8 meters,

distance of C.G. from ground level 600 mm, and the distance of C.G. from rear

wheels 1.2 meters. Find the distance travelled by the car before coming to rest

when brakes are applied, 1. to the rear wheels, 2. to the front wheels, and 3. to all

the four wheels. The coefficient of friction between the tires and the road may be

taken as 0.6.

08

OR

(b) A band and block brake, having 14 blocks each of which subtends an angle of 15°

at the centre, is applied to a drum of 1 m effective diameter. The drum and

flywheel mounted on the same shaft has a mass of 2000 kg and a combined radius

of gyration of 500 mm. The two ends of the band are attached to pins on opposite

sides of the brake lever at distances of 30 mm and 120 mm from the fulcrum. If a

force of 200 N is applied at a distance of 750 mm from the fulcrum, find: 1.

maximum braking torque, 2. angular retardation of the drum, and 3. time taken by

the system to come to rest from the rated speed of 360 r.p.m. The coefficient of

friction between blocks and drum may be taken as 0.25.

08

Q.3 (a) Elaborate following terms in context of Governor.

1. Sensitiveness of Governors

2. Stability of Governors

3. Isochronous Governor

06

(b) A Porter governor has equal arms each 250 mm long and pivoted on the axis of

rotation. Each ball has a mass of 5 kg and the mass of the central load on the sleeve

is 25 kg. The radius of rotation of the ball is 150 mm when the governor begins to

lift and 200 mm when the governor is at maximum speed. Find the range of speed,

sleeve lift, governor effort and power of the governor when the friction at the

sleeve is neglected.

08

OR

Q.3 (a) Derive the expression for Effort and Power of a Porter Governor 06

2

(b) A Hartnell governor with central sleeve, spring and two right angled bell cranked

levers rotates between 288 and 320 rpm, for sleeve lift of 3 cm. the sleeve arm and

the ball arm are 10 and 14 cm respectively. The levers are pivoted at 12 cm from

the governor axis and the mass of each ball is 3 kg. The space restriction imposes

the condition that maximum radius of rotation of the fly ball not to exceed 15 cm.

calculate 1. Load on the spring at the lowest and the highest equilibrium speed and

2. Stiffness of spring

08

Q.4 (a) Derive expression for frictional torque for centrifugal clutch. 06

(b) The equation of the turning moment curve of a three crank engine is (5000 + 1500

sin 3θ) N-m, where θ is the crank angle in radians. The moment of inertia of the

flywheel is 1000 kg-m2 and the mean speed is 300 rpm. Calculate : 1. power of the

engine, and 2. the maximum fluctuation of the speed of the flywheel in percentage

when (i) the resisting torque is constant, and (ii) the resisting torque is (5000 + 600

sinθ) N-m.

08

OR

Q.4 (a) Derive expression for frictional torque for single plate clutch considering uniform

wear and uniform pressure condition. 06

(b) A machine punching 38 mm holes in 32 mm thick plate requires 7 N-m of energy

per sq. mm of sheared area, and punches one hole in every 10 seconds. Calculate

the power of the motor required. The mean speed of the flywheel is 25 metres per

second. The punch has a stroke of 100 mm. Find the mass of the flywheel required,

if the total fluctuation of speed is not to exceed 3% of the mean speed. Assume that

the motor supplies energy to the machine at uniform rate.

08

Q.5 (a) Discuss the dynamic force effect on reciprocating engine using Klein’s

construction. 05

(b) The following data relate to a horizontal reciprocating engine:

Mass of reciprocating parts = 120 kg, Crank length = 90 mm, Engine speed = 600

rpm, Connecting rod: Mass = 90 kg, Length between centres = 450 mm, Distance

of center of mass from big end centre = 180 mm, Radius of gyration about an axis

through centre of mass = 150 mm. Find the magnitude and the direction of inertia

torque on the crankshaft when the crank has turned 30o from the inner dead centre.

09

OR

Q.5 (a) Discuss the effect of inertia force on connecting rod. 05

(b) Neglecting the friction determine the magnitude and direction of the couple which

must be applied to link 2 to drive the linkage against the forces shown in Fig.1.

Draw a free body diagram of each link and show forces acting. O2A = 4 cm,

AB=14 cm, AC=18 cm, BC=8 cm, O4D=7 cm, O4C=10 cm, O2O4=14 cm

Fig.1

09

1

Seat No.: ________ Enrolment

No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY BE – SEMESTER – V (NEW) EXAMINATION – WINTER 2015

Subject Code: 2151902 Date:05/12/ 2015

Subject Name: Theory of Machines

Time: 10:30am to 1:00pm Total Marks: 70 Instructions:




Q.1 (a) What is isochronism in governors? Prove that a Porter governor cannot be

isochronous.

03

(b) Explain the terms: Hunting, Effort of a governor 04

(c) In figure-1, a four bar mechanism is shown. Calculate the required value of

torque T2 and various forces on links for equilibrium of the system.

07

Q.2 (a) How do the effects of gyroscopic couple and of centrifugal force make the rider

of a two-wheeler tilt on one side? Derive an expression for its stability.

07

(b) The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of

0.75 m. It rotates at 1800 rpm clockwise when viewed from stern. Determine

the gyroscopic couple and its effect in the following cases:

(i) If the ship travelling at 100 km/hr steers to the left along a curve of 80 m

radius. (ii) If the ship pitches 5 above and 5 below the normal position and the

bow is descending with maximum velocity. The pitching motion is simple

harmonic motion with a periodic time of 20 s. (iii) If the ship is rolling with an

angular velocity of 0.03 rad/s clockwise when looking from stern.

Also find the maximum angular acceleration during pitching.

07

OR

(b) A four wheeled trolley car has a total mass of 3000 kg. Each axle with its two

wheels and gears has a total moment of inertia of 32 kgm2. Each wheel is of 450

mm radius. The centre distance between two wheels on an axle is 1.4 m. Each

axle is driven by a motor with a speed ratio of 1:3. Each motor along with its

gear has a moment of inertia of 16 kgm2 and rotates in the opposite direction to

that of the axle. The centre of mass of the car is 1 m above the rails. Calculate

the limiting speed of the car when it has to travel around a curve of 250 m

radius without the wheels leaving the rails.

07

Q.3 (a) Define Coefficient of fluctuation of energy and Coefficient of fluctuation of

speed for flywheel. Find a relation for the coefficient of speed in terms of

maximum fluctuation of energy.

07

(b) The turning moment diagram for a multi-cylinder engine has been drawn to a

vertical scale of 1 mm = 650 Nm and a horizontal scale of 1mm = 4.5. The

areas above and below the mean torque line are -28, +380, -260, +310, -300,

+242, -380, +265 and -229 mm2. The fluctuation of speed is limited to 1.8% of

the mean speed which is 400 rpm. The density of the rim material is 7000 kg/m3

and width of the rim is 4.5 times its thickness. The centrifugal stress in the rim

material is limited to 6 N/mm2. Neglecting the effect of the boss and arms,

determine the diameter and cross section of the flywheel rim.

07

OR

2

Q.3 (a) With a neat sketch, explain construction, operation and application of a

centrifugal clutch.

07

(b) A punching machine carries out 6 holes per minute. Each hole of 40 mm

diameter in 35 mm thick plate requires 8 Nm of energy/mm2 of the sheared area.

The punch has a stroke of 95 mm. Find the power of the motor required if the

mean speed of the flywheel is 20 m/s. If total fluctuation of speed is not to

exceed 3% of the mean speed, determine the mass of the flywheel.

07

Q.4 (a) Derive an expression of retardation for a vehicle moving up an inclined plane

when (i) brakes are applied to front wheels only (ii) brakes are applied to all four

wheels.

07

(b) A differential band brake shown in Figure-2, has an angle of contact of 225.

The band has a lining whose coefficient of friction is 0.3 and the drum diameter

is 400mm. The brake is to sustain a torque of 375 Nm. Find (i) the necessary

force for the clockwise and counter-clockwise rotation of the drum and (ii) the

value of OA for the brake to be self-locking, when the drum rotates clockwise.

07

OR

Q.4 (a) What is the advantage of a transmission type dynamometer over an absorption

type dynamometer? Explain the construction and working of any one

transmission type dynamometer.

07

(b) A single plate clutch is required to transmit 8 kW at 1000 rpm. The axial

pressure is limited to 70 kN/m2. The mean radius of the plate is 4.5 times the

radial width of the friction surface. If both the sides of the plate are effective and

the coefficient of friction is 0.25, find the (i) inner and outer radii of the plate

and the mean radius (ii) width of the friction lining (iii) axial force to engage the

clutch.

07

Q.5 (a) Explain shaking forces and shaking moments. Derive their expressions for a four

bar linkage.

07

(b) List experimental methods used for finding out the radius of gyration of

components having complicated geometry? Explain any one method in detail,

with neat sketch.

07

OR

Q.5 (a) Explain impulse and momentum. 07

(b) How is the effect of friction forces considered in the static force analysis of a

mechanism having turning pairs?

07

Figure-1 [Q.1 (C)] Figure-2 [Q.4 (b)]

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V (OLD) - EXAMINATION – SUMMER 2017



Q.1 (a) What is a function of a governor? How does it differ from that of a flywheel?

Also explain the terms sensitiveness, hunting and stability relating to

governors.

07

(b) Describe the working of a band and block brake with the help of a neat sketch.

Deduce the relation for ratio of tight and slack side tensions.

07

Q.2 (a) Explain gyroscopic couple and discuss its effect on an aero plane taking turns

when viewed from rear.

07

(b) In a Hartnell governor, the extreme radii of rotation of the balls are 40 mm and

60 mm, and the corresponding speeds are 210 rpm and 230 rpm. The mass of

each ball is 3 kg. The lengths of the ball and the sleeve arms are equal.

Determine the initial compression and the constant of the central spring.

07

OR

(b) Derive the equation for the height of Watt governor. 07

Q.3 (a) Explain the term ‘turning moment diagram’, ’Coefficient of fluctuation of

speed and ‘’Coefficient of fluctuation of energy’. 07

(b) Each arm of a Porter governor is 200 mm long and is pivoted on the axis of the

governor. The radii of rotation of the balls at the minimum and the maximum

speeds are 120 mm and 160 mm respectively. The mass of the sleeve is 24 kg

and each ball is 4 kg. Find the range of speed if the friction at the sleeve is

18N.

07

OR

Q.3 (a) What is a flywheel? What is its use? Derive a relationship for the coefficient

of fluctuation of speed in terms of maximum fluctuation of energy and the

kinetic energy of the flywheel at mean speed.

07

(b) The turbine of rotor of a ship has mass of 2.2 tonnes and radius of gyration of

320 mm, rotates at speed of 1800 r.p.m. clockwise when looking from aft.

Determine gyroscopic couple and its effect when the

(i) ship turns right at a radius of 250 m with a speed of 25 km/hr

(ii) ship pitches with the bow rising at an angular velocity of 0.8 rad/sec

(iii) ship rolls at an angular velocity of 0.1 rad/sec

07

Q.4 (a) What do you understand by type synthesis, number synthesis and dimensional

synthesis? Describe the classification of the synthesis problem with suitable

examples.

07

2

(b) The crank and connecting rod of a petrol engine, running at 1800 r.p.m. are

50 mm and 200 mm respectively. The diameter of the piston is 80 mm and the

mass of the reciprocating parts is 1 kg. At a point during the power stroke, the

pressure on the piston is 0.7 N/mm2, when it has moved 10 mm from the inner

dead centre. Determine: 1. Net load on the gudgeon pin, 2. Thrust in the

connecting rod, 3. Reaction between the piston and cylinder, and 4. The engine

speed at which the above values become zero.

07

OR

Q.4 (a) Explain dynamically equivalent two mass systems. 07

(b) A single cylinder double acting steam engine develops 150 kW at a mean

speed of 80 r.p.m. The coefficient of fluctuation of energy is 0.1 and the

fluctuation of speed is ± 2% of mean speed. If the mean diameter of the

flywheel rim is 2 metre and the hub and spokes provide 5% of the rotational

inertia of the flywheel, find the mass and cross-sectional area of the flywheel

rim. Assume the density of the flywheel material (which is cast iron) as 7200

kg/m3.

07

Q.5 (a) Prove the Freudenstein’s equation for Four Link Mechanism. 07

(b) Explain three position synthesis of Slider Crank mechanism. 07

OR

Q.5 (a) Explain the Chebychev spacing and structural error in brief. 07

(b) Explain three position synthesis for Four Bar Mechanism. 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER– V • EXAMINATION – WINTER 2016

Subject Code: 151902 Date: 30/11/2016


Time: 02:30PM – 05:00PM Total Marks: 70 Instructions:




Q.1 (a) Explain following terms associated with a governor.

1. Sensitivity 2. Controlling Force

3. Height of the Governor 4. Isochronism

08

(b) Derive the equation relating speed of the governor with the height of the

governor for a Watt governor.

06

Q.2 (a) Derive the equation of the stability of a four wheeler negotiating a turn. 07

(b) Derive the equation of displacement, velocity and acceleration of a piston in

terms of crank rotation.

07

OR

(b) 1. Define and explain D’Alembert’s principle with a suitable example.

2. State application of the flywheel and differentiate between a flywheel and

governor.

02

05

Q.3 (a) The crank and connecting rod of a vertical petrol engine, running at 1800 rpm

are 60 mm and 270 mm respectively. The diameter of the piston is 100 mm and

the mass of the reciprocating parts is 1.2 kg. During the expansion stroke when

the crank has turned 20o from the TDC, the gas pressure is 650 kN/m2.

Determine: (i) net force on the piston (ii) net load on the gudgeon pin (iii) thrust

on the cylinder.

07

(b) Explain the term “self locking” in brakes and derive the equation for the same

for a band brake.

07

OR

Q.3 (a) Enlist types of dynamometer and with the help of neat sketch explain working

of rope brake dynamometer.

07

(b) For an internal expanding shoe brake, derive the equation of braking torque. 07

Q.4 (a) A double block brake as shown in Fig. 1, is set by a spring that produces a force

of 3.5 kN. The brake drum diameter is 400 mm and the angle of contact for

each block is 110o. If the coefficient of friction between block and the drum is

0.45, determine the maximum torque that can be absorbed. If the bearing

pressure is not to exceed 0.4 MPa, determine the maximum width of the block.

07

(b) Describe a step by step procedure to draw Klein’s construction for determining

acceleration.

07

OR

Q.4 (a) A punching machine is required to punch 30 mm diameter hole in a 20 mm

thick plate at a rate of 20 holes per minute. It requires 6 Nm of energy / mm2 of

area sheared. If punching takes places in 1/10 of a second and rpm of flywheel

varies from 160 to 140, determine the mass of the flywheel with radius of

gyration 1 m.

07

2

(b) Illustrate the procedure to determine lengths of links of four bar mechanism

using Freudnestein’s equation.

07

Q.5 (a) Enlist graphical methods for synthesis of four bar mechanism and illustrated

any one of them.

07

(b) The turbine rotor of a ship having a mass of 200 kg rotates at 2000 rpm. Its

radius of gyration is 0.3 m. If the rotation of the rotor is clockwise looking from

the aft, determine the gyroscopic couple set by the rotor when (1) ship takes a

left turn at a radius of 300 m at a speed of 30 kmph (2) ship pitches with bow

rising at a n angular velocity of 1 rad/s and (3) ship rolls at an angular velocity

of 0.1 rad/s.

07

OR

Q.5 (a) With the required equation, describe step by step procedure of Bloch’s method

for synthesis.

07

(b) The upper arms of a porter governor are pivoted on the axis of rotation and the

lower arms are attached to the sleeve at a distance of 37.6 mm from the axis.

The lengths of the arm and suspension links are 300 mm. The weight of each

ball is 60 N and the load on the sleeve is 480 N. If the extreme radii of rotation

of balls are 200 mm and 250 mm, find the corresponding equilibrium of speeds.

07

*************

Fig 1.

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V- EXAMINATION – SUMMER 2016



Q.1 (a) What is Brake? What is meant by a self locking and a self energized brake? 07

(b) A simple band brake is operated by a lever of length 550 mm. The brake drum has a diameter of 550 mm and the brake band embraced 5/8 of the circumference. One end of a band is attached to the fulcrum of the lever while the other end is attached to a pin on the lever 100 mm from the fulcrum. If the effort applied to the end of the lever is 2.5 KN and the co-efficient of friction is 0.25. Find the maximum braking torque on the drum. Show the diagram of brake.

07

Q.2 (a) Explain Frudennstein’s method of three point synthesis of mechanism. 07 (b) Define Synthesis. Explain in brief the classification of synthesis. 07

OR (b) Explain Bloch’s Synthesis Method for synthesizing a 4 bar mechanism 07 Q.3 (a) Explain the term height of governor. Derive an expression for height in case of Watt

governor. What are the limitations of Watt governor? 07

(b) A Porter governor of an engine has a central mass of 18 kg. The lower and

upper arms are pivoted on the axis of rotation and of 300 mm and 250 mm long respectively. The frictional force acting between spindle and sleeve is 25 N. if the limiting inclinations of the upper arms to the vertical are 30° and 40° for the minimum and maximum radius of rotation of the ball respectively. Determine the range of speed of the Porter governor with considering friction, if the mass of each ball is 2.5 kg.

07

OR Q.3 (a) What is the main function of a governor? How does it differ from flywheel?

Differentiate between inertia and centrifugal governor. 07

(b) In a Wislon-Hartnell governor, each radial spring has a stiffness of 0.8 N/mm and their free length is 130 mm. The mass of each ball is 5 kg. The length of the ball arm of each bell crank lever is 90 mm and that of the sleeve arm is 80 mm. The auxiliary spring lever is pivoted at its mid point. When the radius of rotation of the ball is 110 mm, the equilibrium speed is 320 rpm. When the speed of sleeve increases by 5% then the sleeve is lift by 10 mm. find the required stiffness of auxiliary spring.

07

Q.4 (a) Derive an equation for gyro-couple with usual notations. 07 (b) What is meant by dynamically equivalent system? State and prove conditions

for it. 07

OR Q.4 (a) Discuss the effect of the gyroscopic couple on a disc fixed at a certain angle to a

rotating shaft. 07

(b) Draw and explain Klein’s construction for determining the velocity and acceleration of the piston of a reciprocating I.C.Engine.

07

Q.5 (a) Derive an expression of turning moment on crankshaft of a horizontal 07

2

reciprocating engine neglecting the effect of the mass of the connecting rod. (b) A flywheel fitted to a punching press runs at 250 rpm and has radius of gyration

is 1m. The press punches 700 holes per hour. The energy required for each punching operation is 20KN.m and 2 second for each operation, determine the power of the motor and mass of the flywheel if speed of the flywheel is not fall below 220 rpm.

07

OR Q.5 (a) Explain the turning moment diagram for 4 cylinder four stroke cycle internal

combustion engine. 07

(b) What is the function of dynamometer? Classify the dynamometers. Explain with neat sketch any one dynamometer.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V EXAMINATION – WINTER 2015

Subject Code: 151902 Date:15/12/2015


Time: 10:30am to 1:00pm Total Marks: 70 Instructions:




Q.1 (a) With the help of a neat sketch explain the working of a single block or shoe brake. 07

(b) The arms of a porter governor are each 25 cm long and pivoted on the governor

axis. Mass of each ball is 5 kg and mass of the central sleeve is 30 kg. The radius of

rotation of the balls is 15 cm when the sleeve begins to rise and reaches a value of 20

cm for maximum speed. Determine the range of the governor.

07

Q.2 (a) Describe the construction and operation of a brake rope dynamometer. 07

(b) In a spring loaded Hartnell type governor, the extreme radii of rotation of the balls

are 80 mm and 120 mm. The ball arm and the sleeve arm of the bell crank lever are

equal in length. Mass of each ball is 2 Kg. If the speeds at the two extreme positions

are 400 and 420 rpm, find (i) the initial compression of the central spring and (ii) the

spring constant.

07

OR

(b) A porter governor has equal arms each 200 mm in length and pivoted on the axis of

rotation. The mass of each ball is 5 kg and the mass of sleeve is 25 kg. The radius

of governor is 100 mm when governor begins to lift. If the frictional increase

of speed is 1%, then determine the governor effort and power.

07

Q.3 (a) Explain the operation of flywheel in a punching machine 07

(b) The turbine rotor of a ship has a mass of 2.2 tones and rotates at 1800 r.p.m.

clockwise when viewed from the left. The radius of gyration of the rotor is 320mm.

Determine the gyroscopic couple and its effect when (1) Ship turns right at a radius

of 250m. with a speed of 25 km/hr.(2) Ship pitches with the bow rising at an angular

velocity of 0.8 rad/sec. (3)Ship rolls at an angular velocity of 0.1 rad/sec.

07

OR

Q.3 (a) Define the flywheel and state its importance. Explain the types of flywheels. 07

(b) The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of 0.45

m and a speed of 3000 rpm clockwise when looking from stern. Determine the

gyroscopic couple and its effect upon the ship:

1. When the ship is steering to left on a curve of 100 m radius at a speed of 36 km/h

2. When the ship is pitching in a simple harmonic motion, the bow falling with

its maximum velocity. The period of pitching is 40 seconds and the total angular

displacement between the two extreme positions of pitching is 12 degrees.

07

Q.4 (a) Draw and explain Klein’s construction for determining the velocity of the

piston of a Reciprocating engine

07

(b) A connecting rod is suspended from the point 25 mm above the small end centre and

650 mm above its C.G. it takes 35 seconds for 20 oscillations. Find dynamically

equivalent system of two masses when the mass is located at small end centre.

Mass of the connecting rod is 40 Kg.

07

OR

2

Q.4 (a) What is meant by dynamically equivalent system? State and prove conditions

for it.

07

(b) In I.C .Engine Mechanism the Crank radius is 400mm and Connecting rod is 950

mm long. The diameter of piston is 100mm and net gas pressure acting on the

piston is 15 MPa. Find (1) Thrust in connecting road (2) Piston side exhaust (3)

Torque acting on Crankshaft (4) Radial force or load on main bearings when crank

has made 45° from TDC. Mass is 200kg and rpm is 400

07

Q.5 (a) Explain Freudenstein’s method for a four bar mechanism 07

(b) Explain Bloch’s synthesis method. 07

OR

Q.5 (a) Explain Chebyshev Method to find precession points for the function. 07

(b) Explain three position synthesis of slider crank mechanism 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V • EXAMINATION – SUMMER • 2015

Subject Code: 151902 Date: 05/05/2015


Time: 02.30pm-05.00pm Total Marks: 70 Instructions:




Q.1 (a) For a vehicle with brakes applied on front wheels, derive the equation of

retardation for following conditions: (a) Vehicle moves up on an inclined road

(b) Vehicle moves on a level ground (c) Vehicle moves down the road

07

(b) With the help of a neat sketch, explain functioning of a hydraulic dynamometer. 07

Q.2 (a) Derive the equation of natural frequency of a compound pendulum. 07

(b) A rear engine automobile travelling along a track of 100 m mean radius has 4

wheels each of 2 kg.m2 and 0.6 m radius. Rotating parts of engine have moment

of inertia of 1 kg.m2. The engine axis is parallel to the rear axle and the crank

shaft rotates in the same sense as the road wheels. The gear ratio, engine to back

axle, is 3:1. The vehicle weighs 14.17 kN and has its CG 0.5 m above the

ground level. Determine speed of the vehicle around the curve for all four

wheels to maintain contact with the road surface if wheel track is 1.5 m.

07

OR

(b) Derive the expression of stability of a two wheeled vehicle.

07

Q.3 (a) Synthesize a four-bar linkage to give the following values for the angular

velocities and accelerations: ω2 = 200 rad / sec, ω3 = 85 rad / sec, ω4 = 130 rad

/ sec, α2 = 0 rad / sec2, α3 = -1000 rad / sec2, α4 = -1600 rad / sec2.

07

(b) The controlling force in a spring controlled governor is 1500 N when the radius

of rotation of the balls is 200 mm and 887.5 N when it is 130 mm. The mass of

each ball is 8 kg. If the controlling force curve is a straight line, determine the

controlling force and the speed of rotation when the radius of rotation is 150

mm. Also find the increase in the initial tension so that the governor is

isochronous. What will be the isochronous speed?

07

OR

Q.3 (a) Differentiate between flywheel and governor and explain following terms related

to governor:

(a) Sensitivity

(b) Power of the governor

07

(b) Derive the expression of effort of a Porter governor. 07

Q.4 (a) Define: ‘Co-efficient of fluctuation of Energy’ and ‘Co-efficient of fluctuation of

Speed’. Also prove that the maximum fluctuation of energy, ΔE = 2.E.Cs

Where, E = Mean kinetic energy of flywheel, and Cs = Coefficient of fluctuation

of speed.

07

2

(b) The effective steam pressure on the piston of a vertical steam engine is 200

kN/m2 when the crank is at 40o from the IDC on the down stroke. The crank

length is 300 mm and the connecting rod length is 1200 mm. The diameter of the

cylinder is 800 mm. What will be the torque on the crankshaft if the engine

speed is 300 rpm and the mass of the reciprocating parts 250 kg?

07

OR

Q.4 (a) A turbine rotor weighing 9.8 kN rotates at 2000 rpm clockwise when viewed

from stern. The vessel pitches with an angular velocity of 0.5 rad/s. Calculate the

gyroscopic couple during the rise of the bow if rotor has radius of gyration as

0.254 m.

07

(b) A vertical cylinder petrol engine has a bore of 100 mm and stroke of 120 mm.

The length of the connecting rod between centres is 250 mm. The mass of the

piston is 1.1 kg. Speed of the engine is 1500 rpm. In the expansion stroke with a

crank at 30o from TDC, the gas pressure is 700 kN/m2. Determine

a. Net force on the piston

b. Force on the connecting rod

c. Thrust on the cylinder wall

d. Crank effort

e. Speed above which the gudgen pin force would reverse in

direction.

07

Q.5 (a) Synthesise a 4-bar linkage using Freudenstein’s equation to generate the function

y = x1.5 for the interval 1 ≤ x ≤ 4. The input crank is to start from 30o and have a

range of 90o. The output follower is to start from 0o and have range of 90o. Take

three accuracy points. Assume length of the fixed link to be 50 mm.

07

(b) Turning moment diagram for an engine consists of a curve defined by equation:

T = (19614 + 9316.7 sin (2θ) – 5590 cos (2θ)) N.m, θ: crank angle from IDC.

If resisting torque is constant, determine (a) Power developed by the engine

(b)Moment of inertia of flywheel in kg.m2, to limit the fluctuation of speed to

1% of mean speed which is 180 rpm (c) Angular acceleration of flywheel when

the crank has turned through 45o from IDC.

07

OR

Q.5 (a) With the help of a neat sketch explain relative pole method for motion

generation using 4-bar mechanism.

07

(b) Derive the expression of displacement, velocity and acceleration of piston with

respect to the crank rotation.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V • EXAMINATION – WINTER • 2014

Subject Code: 151902 Date: 28-11-2014 Subject Name: Theory of Machines Time: 10.30 am - 01.00 pm Total Marks: 70 Instructions:


Q.1 (a) What is the main function of a governor? How does it differ from flywheel?

Differentiate between inertia and centrifugal governor. 07

(b) In a spring controlled governor, the controlling force curve is a straight line. The balls are 400 mm apart when the controlling force is 1500 N and 240 mm when it is 800 N. The mass of each ball is 10 kg. Determine the speed at which the governor runs when the balls are 300 mm apart. By how much should the initial tension be increased to make the governor isochronous? Also find the isochronous speed.

07

Q.2 (a) “Rope brake type dynamometer is an absorption type dynamometer.” Justify this statement. Also explain principle and working of belt transmission dynamometer with neat sketch.

07

(b) A band and block brake having 12 blocks, each of which subtends an angle of 160 at the center, is applied to a rotating drum of diameter 600 mm. The blocks are 75 mm thick. The drum and the flywheel mounted on the same shaft have a mass of 1800 kg and have a combined radius of gyration of 600 mm. The two ends of the band are attached to pins on the opposite sides of the brake fulcrum at distances of 40 mm and 150 mm from the fulcrum. If a force of 250 N is applied at a distance of 900 mm from the fulcrum, find:

1. The maximum braking torque 2. The angular retardation of the drum 3. The time taken by the system to be stationary from the rated speed of

300 rpm. Take coefficient of friction between the blocks and the drum as 0.3.

07

OR (b) Design a slider-crank mechanism so that displacement of the slider is

proportional to the crank rotation in the interval 300≤ θ ≤1000. Assume initial distance of the slider equal to 15 cm and final distance to be 10 cm.

07

Q.3 (a) In an I.C. engine mechanism, the crank radius is 400 mm and connecting rod is 950 mm long. The diameter of piston is 100 mm and net gas pressure acting on the piston is 15 MPa. Mass of connecting Rod is 100 Kg and engine speed is 1000 RPM. Find : 1) Thrust in connecting rod, 2) Piston side thrust, 3) Torque acting on crank shaft and 4) Radial force or load on main bearings when crank has made 45o from TDC.

07

(b) Draw and explain Klein’s construction for determining the velocity and acceleration of the piston in slider crank mechanism.

07

OR Q.3 (a) Explain dynamically equivalent two mass system with neat sketch using

analytical method and prove the same using graphical method. 07

2

(b) A vertical double acting steam engine runs at 220 rpm and having cylinder diameter of 320 mm and the stroke of 460 mm. The mass of the reciprocating parts is 230 kg and the diameter of piston rod is 50 mm. The connecting rod length is 1.22 m. When the crank has turned through 130o from the TDC, the steam pressure above the piston is 32000 N/mm2 and below the piston is 16000 N/mm2. Determine the effective turning moment on the crank shaft.

07

Q.4 (a) A machine has to carry out punching operations at the rate of 10 holes per minute. It does 6 kN-m of work per mm2 of the sheared area in cutting 25 mm diameter holes in 20 mm thick plates. A flywheel is fitted to the machine shaft, which is driven by constant torque. The fluctuation of speed us between 180 and 200 rpm. The actual punching operation takes 2 second. The frictional losses are equivalent to 1/6th of the work done during punching. Find: 1) power required to drive the punching machine, and 2) mass of flywheel, if the radius of gyration of the wheel is 0.5 m.

07

(b) Draw and explain turning moment diagram for: 1) 4-Stroke single cylinder engine and, 2) Punching press.

07

OR Q.4 (a) Explain Bloch’s Synthesis Method for synthesizing a 4- bar mechanism. 07

(b) The length of the arms of a Porter governor is 300 mm long. The upper and lower arms are pivoted to links at 50 mm and 60 mm, respectively, from the axis of rotation. The mass of each ball is 5 kg and the sleeve is of mass 60 kg. The frictional force on sleeve is 35 N. Determine the range of speed for extreme radii of rotation of 120 mm and 150 mm.

07

Q.5 (a) The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of 0.75 m. It rotates at 1800 rpm clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases:

1. If the ship travelling at 100 km/h steers to the left along a curve of 80 m radius.

2. If the ship is pitching and the bow is descending with maximum velocity. The pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between extreme positions is 10o.

3. If the ship is rolling with an angular velocity of 0.03 rad/s clockwise when looking from stern.

In each case, determine the direction in which the ship tends to move.

07

(b) Explain concept of synthesis of mechanism with example. Also explain the following terms : 1) Function generation 2) Path generation 3) Type synthesis 4) Number synthesis

07

OR Q.5 (a) A racing car of mass 3000 kg has a wheel base of 2.5 m and track of 1.5 m. The

C.G is located 0.6 m above the ground level and 1.5 m from the rear axle. Each wheel is of 1 m diameter and 0.8 kg.m2 moment of inertia. The back axle ratio is 4.5. The drive shaft engine flywheel and transmission are rotating clockwise when viewed from the front with equivalent mass of 150 kg with radius of gyration 0.2 m. Determine the load distribution on the wheels if the car is rounding a curve of 80 m radius at 120 km/h when: 1) taking a right turn, and 2) taking a left turn.

07

(b) Define: ‘Co-efficient of fluctuation of Energy’ and ‘Co-efficient of fluctuation of Speed’. Also prove that the maximum fluctuation of energy, ΔE = 2.E.Cs Where, E = Mean kinetic energy of flywheel, and Cs = Coefficient of fluctuation of speed.

07

*************

1

Seat No.: ________ Enrolment No._____

GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V • EXAMINATION – SUMMER • 2014

Subject Code: 151902 Date: 13-06-2014


Time: 10:30 am - 01:00 pm Total Marks: 70 Instructions:




Q.1 (a) Describe the working of a band and block brake with the help of a neat sketch. Deduce

the relation for ratio of tight and slack side tensions.

07

(b) A Porter governor has all the arms of 300 mm long. The upper and lower arms are pivoted

to the links of 50 mm and 60 mm respectively from the axis of rotation. Each ball has a

mass of 6 kg and the sleeve mass is 55 kg. The force of friction on the sleeve of the

mechanism is 40 N. Determine the range of speed of the governor if the extreme radii of

rotation of the balls are 150 mm and 200 mm.

07

Q.2 (a) How do the effects of gyroscopic couple and of centrifugal force make the rider of a

two-wheeler tilt on one side? Derive a relation for the angle of heel.

07

(b) In a single acting four stroke engine, the work done by the gases during the expansion

stroke is three times the work done during the compression stroke. The work done

during the suction and exhaust strokes is negligible. The engine develops 15 kW at 300

rpm. The fluctuation of speed is limited to 2% of the mean speed. The turning-

moment diagram during the compression and the expansion strokes may be assumed to

be triangular in shape. Determine the inertia of the flywheel.

07

OR

(b) The crank and the connecting rod of a vertical single cylinder gas engine running at

1500 rpm are 50 mm and 225 mm respectively. The diameter of the piston is 80 mm

and the mass of the reciprocating parts is 1.25 kg. At a point during the expansion

stroke when the piston has moved 20 mm from the TDC, the pressure on the piston is

750 kN/m2. Determine the (i) net force on the piston, (ii) thrust in the connecting rod,

(iii) thrust on the sides of the cylinder walls and (iv) engine speed at which the above

values are zero.

07

Q.3 (a) Describe the procedure to design a four-bar mechanism by relative pole method when

three positions of the input link (1, 2, 3) and the out put link (1, 2, 3) are known.

07

(b) A double block brake shown in Figure 1, is applied on a drum of diameter 500 mm.

The angle of contact is 90o and the coefficient of friction is 0.35. The force applied on

end of each lever arm is 4000 N. Determine the brake torque on the drum.

Figure 1

07

OR

2

Q.3 (a) Define the following terms in context of governor:

(i) Sensitiveness, (ii) Hunting, (iii) Isochronism, (iv) Stability (v) Effort,

(vi) Power and (vii) Coefficient of insensitiveness.

07

(b) The rotor of a marine turbine has a moment of inertia of 750 kg.m2 and rotates at 3000

rpm clockwise when observed from aft. If the ship pitches with angular SHM having a

periodic time of 16 s and amplitude of 0.1 rad, find (i) maximum angular velocity of the

rotor axis, (ii) maximum value of the gyroscopic couple and (iii) the gyroscopic effect

as the bow dips.

07

Q.4 (a) 1) What are the turning moment diagrams? Why are they drawn?

2) Find a relation for the coefficient of fluctuation of speed in terms of maximum

fluctuation of energy and the kinetic energy of the fly wheel at mean speed.

07

(b) When, why and how is the correction couple applied by considering the inertia of the

connecting rod of a reciprocating engine?

07

OR

Q.4 (a) What is Freudenstein’s equation? How is it helpful in designing the four-bar mechanism

when three positions of the input (1, 2, 3) and the out put link (1, 2, 3) are

known?

07

(b) 1) What is a function of dynamometer? List out the different types of dynamometers.

2) The rope brake dynamometer consisting of a pulley of 1 m diameter. The rope of

diameter of 10 mm is wrapped over the rim of the pulley. The dead weight on the

brake is of 50 kg while the spring balance shows a reading of 120 N when the speed

of the engine is 180 rpm. Find the power of the engine.

07

Q.5 (a) Each arm of a Proell governor is 250 mm long and each ball has a mass of 4.5 kg. The

central load acting on the sleeve is 30 kg. The pivots of all the arms are 40 mm from the

axis of rotation. The vertical height of the governor is 190 mm. the extension links of

the lower arms are vertical and the governor speed is 200 rpm when the sleeve is in the

mid position. Determine the length of the extension links and the tension in the upper arms.

07

(b) A rear engine automobile is traveling along curved track of 120 m radius. Each of the

four wheels has a moment of inertia of 2.2 kg.m2 and an effective diameter of 600 mm.

The rotating parts of the engine have a moment of inertia of 1.25 kg.m2. The gear ratio

of the engine to the rear wheel is 3.2. The engine axis is parallel to the rear axle and the

crank shaft rotates in the same sense as the road wheels. The mass of the vehicle is

2050 kg and the centre of mass is 520 mm above the road level. The width of the track

is 1.6 m. What will be the limiting speed of the vehicle to maintain the stability during

turning?

07

OR

Q.5 (a) A riveting machine is driven by an electric motor of 2.5 kW. The actual time to

complete one riveting operation is 1.2 s and it absorbs 10 kN.m of energy. The moving

parts including the flywheel are equivalent to 200 kg and 0.5 m radius of gyration.

Determine the speed of the flywheel immediately after riveting if it is 360 rpm before

riveting. Also, find the number of rivets closed per minute.

07

(b) The piston diameter of an IC engine is 120 mm and the stroke is 200 mm. The

connecting road is 4.2 times the crank length and has a mass of 50 kg. The mass of the

reciprocating parts is 25 kg. The centre of gravity of the connecting rod is at a distance

of 170 mm from the crank pin centre and the radius of gyration about an axis through

the centre of mass is 140 mm. The engine runs at 300 rpm. Find the magnitude and the

direction of the inertia force and the corresponding torque on the crank shaft when the

angle turned by the crank is 60o from the IDC.

07

******************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V • EXAMINATION – WINTER 2013

Subject Code: 151902 Date: 29-11-2013


Time: 10.30 am - 01.00 pm Total Marks: 70 Instructions:




Q.1 (a) Differentiate between Governor and Flywheel. 07

(b) Explain stability of a two-wheeled vehicle.

07

Q.2 (a) Explain the term height of governor. Derive an expression for height in case

of Watt governor. What are the limitations of Watt governor?

07

(b) Synthesis a 4-bar mechanism to generate a function y = log10 x in the interval

of 1≤ x ≤ 10. The input crank length is to be 50 mm. The input crank is to be

rotate from 450 to 105

0 while output crank moves from 135

0 to 225

0. Use 3

precession points with Chebyshev spacing’s.

07

OR

(b) Explain Bloch’s Synthesis Method for synthesizing a 4 bar mechanism. 07

Q.3 (a) An open belt drive connects two pulleys 120 cm and 50 cm diameter, on

parallel shafts 4 meters apart. The mass of the belt is 0.9 Kg per meter length

and the maximum tension is not to exceed 2000 N. The coefficient of friction

is 0.3. The 120 cm diameter pulley, which is driver, runs at 200 rpm. Due to

belt slip on one of the pulleys, the velocity of the driven shaft is only 450 rpm.

Calculate the torque on each of the shafts, the power transmitted and power

lost in friction. What is the efficiency of the drive?

07

(b) Explain inertia force analysis of a reciprocating engine using Klen’s

construction. 07

OR

Q.3 (a) The crank-pin circle radius of a horizontal engine is 300 mm. The mass

of the reciprocating parts is 250 Kg. When the crank has travelled 600

from I.D.C., the difference between the driving and the back pressure is

0.35 N/mm2. The connecting rod length between centers is 1.2 m and

the cylinder bore is 500 mm. If the engine runs at 250 rpm and if the

effect of piston rod diameter is neglected, calculate; (1) pressure on

slide bars, (2) thrust in the connecting rod, (3) turning moment on the

crank shaft.

07

(b) Prove that the ratio of the driving tensions on the two sides of a pulley

is T1/T2 = e μθ

Where, T1 = Tension in the tight side of the belt,

T2 = Tension in the slack side of the belt

θ = Angle of contact in radians

μ = coefficient of friction between the belt and pulley

07

2

Q.4 (a) Explain the effect of gyroscopic couple on four wheel drive. 07

(b) In a spring loaded Hartnell type governor, the extreme radii of rotation

of the balls are 80 mm and 120 mm. The ball arm and the sleeve arm of

the bell crank lever are equal in length. Mass of each ball is 2 Kg. If the

speeds at the two extreme positions are 400 and 420 rpm, find (i) the

initial compression of the central spring and (ii) the spring constant.

07

OR

Q.4 (a) A horizontal cross compound steam engine develops 294240 Watts at

90 rpm. The coefficient of fluctuation of energy, found from turning

moment diagram is 0.1 and speed is to be within 0.5 % of the mean

speed. Find the weight of the flywheel required if radius of gyration is

2 meters.

07

Q.4 (b) What is the function of dynamometer? Classify the dynamometers.

Explain with neat sketch any one dynamometer. 07

Q.5 (a) Explain with neat sketch Pickering governor. List the applications of

Pickering governor. 07

(b) The torque exerted on the crank shaft of a two stroke engine is given by

T = 15000 + 2000 Sin2θ - 1800 Cos2θ N-m. Assuming the resistance

torque to be constant, determine

(i) The power of the engine when running at 150 rpm

(ii) The moment of inertia of flywheel if the speed variation from

the mean speed of 150 rpm is not to exceed ± 0.5%

07

OR

Q.5 (a) What is turning moment diagrams? What information can be avail from

them? 07

(b) The turbine rotor of a ship is of mass 3500 Kg. It has a radius of

gyration of 0.45 meters and speed of 3000 rpm clockwise when looking

from stern. Determine the gyroscopic couple and its effect upon the

ship;

(i) When the ship is steering to the left on a curve of 100 meter

radius at a speed of 36 km/hrs.

(ii) When the ship is pitching in a SHM, the bow falling with its

maximum velocity. The period of pitching is 40 seconds and the

total angular displacement between the two extreme positions of

pitching is 12 degrees.

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–V • EXAMINATION – SUMMER 2013

Subject Code: 151902 Date: 16-05-2013 Subject Name: Theory of Machines Time: 10.30 am - 01.00 pm Total Marks: 70 Instructions:


Q.1 (a) (i) What is the function of a governor? How does it differ from a flywheel? (ii) Explain the terms relating to governor. Sensitiveness, Hunting and Stability

07

(b) Explain gyroscopic effect in case of naval ships with a diagram. Show the terminologies used to indicate sides, front and back of ship. Explain effect of steering, pitching and rolling, assuming ship moves left and right direction sequentially.

07

Q.2 (a) (i) What is gyroscopic couple? Derive a relation for its magnitude.

(ii) The moment of inertia of an aero plane air screw is 20 kg.m2 and the speed of rotation is 1250 rpm clockwise when viewed from the front. The speed of the flight is 200 km/hr. Calculate the gyroscopic reaction of the air screw on the aero plane when it makes a left hand turn on a path of 150 m radius.

07

(b) A Porter governor has arms of 380 mm long. The upper arms are pivoted at the axis of the sleeve and lower arms are attached to the sleeve at a distance of 40 mm from the axis. Each fly ball has a mass of 5 kg. and weight on sleeve is 45 kg. Find the range of speed of the governor if the extreme radii of rotation of the balls are 250 mm and 300 mm. The force of friction on sleeve of mechanism is 30 N.

07

OR (b) The following data refers to a Hartnell governor.

Length of horizontal arms of bell crank lever = 40 mm and Length of vertical arms of bell crank lever = 80 mm Mass of each flying ball 1.2 kg. , The maximum radius of rotation = 100 mm, The minimum radius of rotation = 70 mm, The distance of fulcrum to axis of rotation = 75 mm, Minimum equilibrium speed = 400 rpm, Maximum equilibrium speed 5 % higher than minimum equilibrium speed. Neglecting obliquity of arms determine: (i) spring stiffness (ii) initial compression

07

Q.3 (a) (i) What is a flywheel? What is its function in reciprocating engine?

(ii) What are turning moment diagrams? What information can be avail from them?

07

(b) Determine the maximum torque for a shoe brake shown in figure 1. The diameter of the brake drum is 400 mm and the angle of contact is 96. The applied force is 3 kN on each arm and the coefficient of friction between the drum and the lining is 0.35.

07

OR Q.3 (a) (i) What is a brake? What is the difference between a brake and a clutch?

(ii) What is meant by a self locking and self energized brake? 07

2

(b) The turning moment diagram for a petrol engine is drawn to a vertical scale of 1

mm = 5 N.m and a horizontal scale of 1 mm = 10. The turning moment repeats itself after every half revolution of engine. The areas above and below the mean torque line are 305, 710, 50, 350, 980 and 275 mm2. The rotating parts amount to a mass of 40 kg at a radius of gyration of 140 mm. Calculate the coefficient of fluctuation of speed if the speed of the engine is 1400 rpm.

07

Q.4 (a) (i) Define these terms: Coefficient of fluctuation of speed and coefficient of

fluctuation of energy. (ii) Derive a relation for the coefficient of fluctuation of speed in terms of maximum fluctuation of energy and the kinetic energy at mean speed.

07

(b) A horizontal gas engine running at 200 rpm has a bore of 200 mm and stroke of 400 mm. The connecting rod is 920 mm long and the reciprocating parts weigh 20 kg. When the crank has turned through an angle of 300 from inner dead center, the gas pressure on the cover and the crank sides are 460 kN/m2 and 70 kN/m2 respectively. Diameter of piston rod is 50mm. Determine

(i) turning moment on the crank shaft, and (ii) thrust on the bearings.

07

OR Q.4 (a) (i) State: D’Alembert’s principle.

(ii) Explain: Dynamically equivalent system. 07

Q.4 (b) The crank and connecting rod of a vertical petrol engine running at 1800 rpm are 60 mm and 260 mm respectively. The diameter of piston is 100 mm and the mass of the reciprocating parts is 1.2 kg. During the expansion stroke when the crank has turned 200 from the top dead center, the gas pressure is 600 kN/m2. Determine (i) net force on the piston, (ii) net load on gudgeon pin, (iii) Thrust on the cylinder walls.

07

Q.5 (a) (i) Explain the terms: Function generation, path generation and motion

generation (ii) What is Chebychev spacing? What is its significance?

07

(b) Design and draw a four bar mechanism to coordinate three positions of input and output links as given below using Relative Pole method. Take L1 = 60 mm (fixed) and L2 = 40 mm (crank). Find the length L3 and L4 graphically. θ 1 =380, θ 2 =900, θ 3 =1420 and φ 1 = 450, φ 2 = 800, φ 3 = 1150.

07

OR Q.5 (a) What is Frudenstein’s equation? How it is helpful in designing a four link

mechanism when three positions of the input (θ1, θ2, θ3) and the output link (φ1, φ2, φ3) are known.

07

(b) Design and draw a four bar mechanism to coordinate three positions of input and output links as given below using Inversion method. Take L1 = 50 mm (fixed) and L2 = 40 mm (crank). Find the length L3 and L4 graphically. θ 1 =380, θ 2 =900, θ 3 =1420 and φ 1 = 450, φ 2 = 800, φ 3 = 1150.

07

Figure 1, Que. 3 (b)

3

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GUJARAT TECHNOLOGICAL UNIVERSITY - mytoolbag.inmytoolbag.in/media/GTUPAPERS/1/2/MECHANICAL/S5/TOM.pdf · 4. R L Norton, Kinematics and Dynamics of Machinery, McGraw -Hill. 5. Kenneth