Solution for Theory of Machines 2 - · PDF fileis neglected.The lengths of the balss and...

Mumbai University Mechanical (Semester -V)

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Solution for Theory of Machines 2

December 2015

Index

Q.1)

a) …………………………………………………………………………. 2-3

b) ………………………………………………………………………….4-5

c) ………………………………………………………………………….5

d) ………………………………………………………………………….6-7

e) ………………………………………………………………………… 8-10

Q.2)

a) …………………………………………………………………………. 10-11

b) ………………………………………………………………………….11-12

Q.3)

a) …………………………………………………………………………. N.A

b) …………………………………………………………………………. 13-16

Q.4)

a) …………………………………………………………………………. 17-18

b) ………………………………………………………………………….19

Q.5)

a) …………………………………………………………………………. 20-21

b) …………………………………………………………………………. N.A

Q.6)

a) …………………………………………………………………………. 22-23

b) …………………………………………………………………………. 24-26



Q1)

(a) What do you understand by dry clutch and wet clutch?

Ans: Dry clutch



Wet clutch:

A multiple clutch is shown in fig.It consist of two sets of plates the

driving plates and driven plates arranged alternately,driving shaft,splined

driven shaft etc.It consist of more than one driving as well as driven

plates.So the number of pair of contacting surfaces is more than two.

As shown in fig.friction paltes are splined on their outer circumference

and engage with coressponding splines on the casing .Friction plates

having ring of friction lining on both sides except the first plate which is

adjacent to casing .This plate is having friction lining on one side.

The pressure plates as shown in fig are splined on their inner

circumference and engage with the corresponding splines on the driven

shaft.Both friction plates and pressure plates are free to sides axially.



(b) Define dynamically equivalent systems .State the condition is

necessary to make two systems dynamically equivalent.

Ans:

It can be replaced by an equivalent system of two rigidly concentrated

masses m1 and m2 situated respectively at a distance l1 and l2 from its

C.G as shown in fig.

* A two mass dynamically equivalent system must satisfy the following

three condition.

(1)The sum of the two masses muct be equal to the mass of the rigid body.

m1 + m2= m

(2)The centre of gravity of the two masses must coincide with that of the

rigid body

m1 l1 = m2 l2



(c) Explain the necessity of gear box in automobile.

Ans:



(d) Explain the following term with reference to governor.

(i) Sensitiveness (ii) Stability

(ii) Isocronism (iv) Coefficient of insensitiveness

Ans Sensitiveness

ii) Stability:

A governor is said to be stable when for each speed within the working

range there is only one radius of rotation of governor balls at which the

governor is in equilibrium.

For stable governor when equilibrium speed increases ,radius of flyball

increases .

For unstable governor when equilibrium speed increases ,radius of

flywall decreases.



iii) Isocronism:

vi) cofficient of insentiveness:



(e) What do yoy understand by gyroscopic couple? Derive a formula for

its magnitude.

Ans:



vi) Gyroscopic couple on Disc:

Q2)

(a) A cone clutch with a semi-cone angle of 150 transmits 10kW at 600

rpm. The normal pressure intensity between the surface in contacts is

not to exceed 100 kN-m2 .The width of the friction surfaces is half of

the mean diameter .Assume µ=0.25 .Determine (i) the outer and inner

diameter of the plate .(ii) width of the come face.(iii) the axial force to

engage the clutch

Ans: Note : similar sum



(b)In the epicyclic gear train shown in the figure .The compound wheels

A and B as well as internal wheels C and D route independently about the

axis O.The wheels E and F rotate on the pins fixed to the arm ‘a’. All the

wheels are of the same module .The number of teeths on the wheels are :

TA =52 ,TB = 56 ,TE = TF = 36

Determine the speed of C ,if (i) the wheel D fixed and arm ‘a’ rotates at

200rpm clockwise (ii)the wheel D rotates at 20 rpm counter clockwise

and arm ‘a’ rotates at 200 rpm clockwise.



Ans:

Given :

TA =52 ,TB = 56 ,TE = TF = 36

NA = 200 rpm ND = -20 rpm

Since the diameteral pitch is same for all the wheels,From fig.

The required speed can be worked out from the following table



Q3)

(a) A horizontal gas engine running at 210 rpm has a bore of 220 mm and

a stroke of 440 mm.The connecting rod is 924 mm long and the

reciprocating parts weigh 20 kg when the crank has turned through an

angle of 300 from the inner dead center ,the gas pressures on the cover

and the crank sides are 500 kN/m2 .and 60 kN/m2 respectively

.Diameter of the piston is 40 mm.Determine : (i) turning moment on

the crank shaft (ii) thrust on the bearings (iii) acceleration of the

flywheel which has a mass of 8 kg and radius of gyration of 600 mm

while the power of engine is 22 kW

Ans: N.A

(b) In a spring loaded hartnell type of governor ,the mass of each ball is

4kg and lif of the sleeve is 40 mm.The governor begins to float at 200

rpm when the radiud of the ball path is 90 mm.The mean working

speed of the governor is 16 times the range of the speed when friction

is neglected.The lengths of the balss and roller arms of the bell crank

lever are 100mm and 80 mm respectively .The pivot centre and axis of

the governor are 115 mm apart.Determine the initial compression of

the spring ,taking into account the obliquity of arsm.Assume the

friction at the sleeve to be equivalent to a force of 15N,determine the

total alteration in speed before the sleeve begins to move from the

mid-position.

Ans: Note similar sum

Mass of each ball,m = 5kg

Lift of sleeve ,x= 5cm =0.05 m

Initial speed ,N1 =240rpm



v



Q4)

(a) Each wheel of a motorcycle is of 600 mm diameter and has a moment

of inertia of 1.2 kg- m2 .The total mass of the motorcycle and the rider

is 180 kg and combined centre of mass in 580 mm above the ground

level when the motor cycle is upright .The moment of inertia of the

rotating parts of the engine is 0.2 kg-m2 .the engine speed id 5 times

the speed of the wheels and is in the same sense .Determine the angle

of wheel necessary when the motor cycle takes a turn of 35 m radius

at a speed of 54 km/h.

Ans: note : similar sum



(b) Single plate clutch transmits 25 kW at 900 rpm.The maximum

pressure intensity between the plates is 85 kN/m2 .The outer diameter

of the plate is 360 mm.Both the sides of the palte are effective and the

coefficient of friction is 0.25 .Determine (i) inner diameter of the plate

,and (ii) axial force to engage the clutch.

Ans:



Q5)

(a) A differentail band brake ,as shown in fig.2 has an angle of contact of

2250 .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 drum is

0.30.Find (a) The necessary force(F) for the clockwise and the

anticlockwise rotation of the drum and (b) The value of ‘OA’ for the

brake to be self locking ,when the drum rotates clockwise

Ans:



Limitng ratio of tension is,

Tsking moment about fulcrum O,

Breaking the torque is ,

(b) A cast iron flywheel is requires to absorb 25000 N-m of energy as

speed is increased from 120 to 125 rpm.If the wheel is to be solid disc

having a diameter 8 times its thickness .Determine its diameter

.Density of C.I. = 7200 kg/m3.

Ans: N.A

Q6)

(a) A loaded porter governor has 4 links each 25 cm long, 2 revolving

masses each weighing 30 N and a central dead weight weighing 200

N.All the links are attatched to repective sleeves at radial distances of

4 cm from the axis of rotation .The masses revolve at a radius of 15

cm at minumum speed and at a radius of 20 cm at maximum speed

.Determine the range of speed



Ans: note : similar sum



(b)

The turbine rotor of ship has a mass of 900 kg and radius of gyration

600 mm.It rotates at 1800 rpm.Clockwise looking from the

stern.Determine gyroscopic couple and its effect when (i) the ship is

travelling at 40 km/hr and steers to left in a curve of 300 m radius (ii)

the ship is pitching and the bow is descending with maximum

velocity.The pitching is simple harmonic ,the periodic time being 30

seconds and total angular moment between the extreme positions is

120

Ans:note : similar sum

Solution for Theory of Machines 2 - · PDF fileis neglected.The lengths of the balss and...

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