at 6302 mechanics of machines learning material ii year auto regulation 2013

Mr.P.M.Subramanian, Asst Professor, Department of Automobile Engineering

12. What is higher pair?

When the two elements of a pair have a line or point contact when relative motion takes place

and the motion between the two elements is partly turning and partly sliding. The pair formed is

known as higher pair. Pair of friction discs, toothed gearing, belt and rope drives, ball and roller

bearings, cam and follower.

13. Differentiate between mechanism and kinematic chain.

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to

transmit definite motion it is called kinematic chain.

When one of the links of a kinematic chain is fixed, the chain is known as mechanism.It may be

used for transmitting or transforming motion eg Engine Indicators, Type Writer

14. Define Rubbing velocity at a pin joint?

The links in a mechanism are mostly connected by means of pin joints. The rubbing velocity is

defined as the algebraic sum between the angular velocities of the two links which are connected

by pin joints, multiplied by the radius of the pin

15. State Grashof’s law for a four bar mechanism.

According this law, the sum of the shortest and longest link length should not be greater

than the sum of the remaining two link length if there is to be continuous relative motion

between the two links.

16. Differentiate between kinematics and kinetics.

Kinematics deals with the relative motion between the various parts of the machine. Kinetics

deals with inertia forces which arise from the combined effect of the mass and motion of the

machine parts.

17. What is meant by completely constrained motion.

The motion between a pair is limited to a definite direction irrespective of the direction of the

force applied.eg: Motion of a square bar in a square hole

18. What is meant by incompletely constrained motion.

The motion between a pair can take place in more than one direction.ex; circular shaft in a

circular hole both sliding and rotating.


9. Define interference

The phenomenon when the tip of a tooth under cuts the root of its mating gear is known as

interference.

10. Define gear train

The combination of gear wheels by mean of which motion is transmitted from one shaft to

another shaft is called a gear train.

11. What are the types of gear train? (UQ)

Simple gear train ,Compound gear train ,Reverted Gear Train, Epicyclic gear train

12. What is simple gear train?

A simple gear train is one in which each shaft carries one wheel only. Simple gear trains are

employed where a small velocity ratio is required.

13. Define train value

It is the reciprocal of velocity ratio =(Speed of the driven )/(Speed of the driver) = (No.of teeth

on driver)/(No.of teeth on driven)

14. What is a compound train?

A compound gear train is one in which each shaft carries two wheels one of which acts as a

follower and other acts as a driver to the shaft. It is used for high velocity ratio.

15. What are the uses of epicyclic gear train?

Transmitting high velocity ratio, with gears of moderate size in a comparatively lesser space.

16. Define the following terms (a) Pressure angle (b) Module(UQ)

Pressure Angle: ϕ Angle between the common normal to two gear teeth at the point of contact

and the common tangent at the pitch point.

Module: Ratio of pitch circle diameter in mm to the no of teeth. Denoted by m.

17.What is law of gearing? (UQ)

The fundamental law of gearing states that the angular velocity ratio between the gears of a gear

set must remain constant throughout the mesh.


22. List the gear tooth systems used in industrial applications. (UQ)

Spur gears- clocks, household gadgets, motor cycles, automobiles, and railways to aircrafts

Helical gears- automotive gearboxes

Double helical or Herringbone gears - high capacity reduction drives like that of cement mills

and crushers

Internal gears- planetary gear drives of automobile automatic transmissions

Lathe carriage drive mechanism - rack and pinion arrangement.

straight bevel gear- automotive differentials, right angle drives of blenders and conveyors


�� = �� + ∅ = ��∅ �� + ∅

5. Define D-Alembert's principle for rotation.

The vector sum of all external moments and inertia torques acting upon a system of

rigid bodies is also zero.The inertia torque is a imaginary torque opposes the external

torque which when applied upon the rigid body brings it in equilibrium position. It is

equal to the accelerating torque in magnitude but opposite in direction.

6. What is the velocity of the piston in a horizontal reciprocating steam engine for the

position of the crank at inner dead center?

The velocity of the piston in a horizontal reciprocating steam engine is expressed as

ɷ�� +�� ɷ = Angular velocity of crank, r- crank radius, n= l/r, l= length of connecting rod, θ -

crank angle

At IDC θ = 0, Velocity =0

7. Write the expression for force acting along connecting rod of single slider crank

mechanism.

The force acting along connecting rod of single slider crank mechanism is given as

�� = ��∅ = ��

�� −��

PF - Piston Effort, � = Crank Angle, ∅ = �� !"# $%&'�� &()��*'#, , r- crank

radius, n= l/r, l= length of connecting rod

8. What is meant by static force analysis?

When the inertia effects due to the mass of the machine components are neglected, then

the analysis of mechanism is called as static force analysis.

9. What are the necessary conditions for static equilibrium of a body?

The vector sum of all the external forces acting upon the body is zero.∑ , = 0, known as

force law of equilibrium. The vector sum of the moments of all forces acting about an

arbitrary axis is zero.∑/ = 0, known as momentum law of equilibrium.

10. What is meant by two force member and state its conditions of equilibrium?

The member under the action of two forces will be equilibrium when

• The forces are of the same magnitude

• The forces act along the same line


• The forces are in opposite direction

11. Define free body diagram.

A free body diagram is a sketch or drawing of the body, isolated from the rest of the

machine and its surroundings upon which the forces and moments act on it.

12. State the principle of superposition.

The principle of superposition states that for linear systems, the individual responses to

several disturbances or driving functions can be superposed on each other to obtain the

total response of the system.

13. What is meant by dynamic force analysis?

When the inertia effects due to the mass of the machine components is also considered, in

addition to the externally applied loads then the analysis of mechanism is called as

dynamic force analysis.

14. What is meant by applied force?

The external forces acting on a system of body from outside the system are called

applied forces. The forces applied externally to a body with or without physical contact.

15. Define Active Force.

The force exerted by one body on another is called active force.

16. Define Reactive Force.

When one body exerts force on another body then the opposite force exerted by the

second body on the first is called reactive force.

17. Define Constraint Force.

When two or more bodies are connected together to form a group or system, the pair of

action and reaction forces between any two of the connected bodies are called constraint

forces. They exist internally within the body.

18. Write the expression for thrust acting on the crank shaft bearings.

The thrust acting on the crank shaft bearings is denoted by FB , PF - Piston Effort, � =

Crank Angle, ∅ = �� !"# $%&'�� &()��*'#,FQ - force acting along connecting

rod


�0 =�� ∗ �� + ∅ = ��∅ �� + ∅

19. What is meant by crank effort ( Turning Moment or Torque on the crank shaft) and give

its expression.

The product of the crank pin effort ( FT) and the crank pin radius (r) is known as crank

effort.

� = �� ∗ �� +��

PF - Piston Effort, � = Crank Angle, ∅ = �� !"# $%&'�� &()��*'#, , r- crank

radius, n= l/r, l= length of connecting rod

20. Enumerate the three methods used for static force analysis of a mechanism.

• Principle of Superposition

• Principle of Virtual Work

• Methods of normal and radial components.


13. What is magnification factor?

The ratio of maximum displacement of the forced vibration to the static deflection under

static force is known as magnification factor.

14. What is frequency response curve?

A curve between magnification factor and frequency ratio ids known as is

frequency response curve.

15. What is transmissibility?

It is defined as the ratio of the force transmitted to the force applied on the system.

16. What is torsionally equivalent shaft?

It is the shaft which has the same torsional stiffness as that of the stepped shaft so that it

twists to the same extent under a given torque as the stepped shaft would.

17. What is single rotor system?

A shaft fixed at one end carrying a rotor at the free end, is known as single rotor system.

18. What is node?

The point is section at which the amplitude of vibration is zero, is known as node.

19. What is two node frequencies?

One set of values given by the quadratic equation gives the position of two node and the

frequency thus obtained is known as two node frequency.

20. What is balancing?

Balancing is the process of designing or modifying machinery so that the

unbalance is reduced to an acceptable level and if possible is eliminated entirely.

21. What is mass moment?

The product of B.b or m.r is called as the mass moment.

22. What is reference plane?

Transfer the centrifugal force acting in each plane to a single parallel plane which is

termed as reference plane.


23. What is static balance?

A system is rotating masses is said to be in static balance if the combined mass centre of

the system lied on the axis of rotation.

24. What are conditions for complete balancing?

The resultant centrifugal forces must be zero The resultant couple must be zero.

25. What is dynamic balance?

A system of rotating masses is in dynamic balance when there does not exist any

resultant centrifugal force as well as resultant couple.

26. What are the types of locomotive?

Coupled locomotive ,Uncoupled locomotive.

27. Define tractive force

The resultant unbalance force due to the two cylinders along the line of stroke is known

as tractive force.

28. What is swaying couple?

The unbalance forces acting at a distance between the line of stroke of the two cylinders

constitute a couple in the horizontal direction. This couple is known as swaying couple. This

couple has swaying effect about a vertical axis and tends to sway the engine alternately in

clockwise and anticlockwise direction.

29. Define hammer blow

The maximum magnitude of the unbalance forces along the perpendicular to the line of

stroke is known as hammer blow. It causes the variation in the pressure between wheel

and rail.


UNIT I TUTORIAL PROBLEMS ( PART B)

1. A cam, with a minimum radius of 50 mm, rotating clockwise at a uniform speed, is

required to give a knife edge follower the motion as described below : (i) To move

outwards through 40 mm.during 100o rotation of the cam; (ii) To dwell for next 80"; (iii)

To return to its starting position during next 90", and (iv) To dwell for the rest period of a

revolution i.e. 90". Draw the profile of the cam when the line of .stroke of the follower is

off-set by 15 mm. The displacement of the follower is to take place with uniform

acceleration and uniform retardation. Determine the maximum velocity and acceleration

of the follower when the cam shaft rotates at 900 r.p.m.

2. Design a cam for operating the exhaust valve of an oil engine' It is required. to give equal

uniform acceleration and retardation during opening and closing of the valve each of

which corresponds to 60o of cam rotation. The valve must remain in the fully open

position for 200 of cam rotation.The lift of the valve is 37.5 mm and the least radius of the

cam is 40 mm.The follower is provided with a ro}ler of radius 20 mm and its line of

stroke passes through the axis of the cam.

3. Sketch and describe the working of two different types of quick return mechanisms. Give

examples of their applications. Derive an expression for the ratio of time taken in forward

and return stroke for one of these mechanisms.

4. A cam, with a minimum radius of 25mm, rotating clockwise at a uniform speed is to be

designed to give a roller follower, at the end of a valve rod, motion described as follows:

To raise the valve through 50 mm during 120o rotation of the cam; to keep the valve fully

raised through next 30o; to lower the valve during next 60o; and to keep the valve closed

during rest of the revolution. i.e. 150o. Draw the profile of the cam when (a) the line of

stroke of the valve rod passes through the axis of the cam shaft, and (b) the line of stroke

is offset 15 mm from the axis of the cam shaft. The displacement of the valve, while

being raised and lowered, is to take place with simple harmonic motion. Determine the

maximum acceleration of the valve rod when the cam shaft rotates at 100 r.p.m.

5. A cam rotating clockwise at a uniform speed of 1000 rpm is required to give a roller

follower the motion defined below: Follower to move outward through 50 mm during

120o of cam rotation, follower to dwell for the next 60oof cam rotation, follower to

return to its starting position during next 90o of cam rotation, follower to dwell for the

rest of the cam rotation. The minimum radius of the cam is 50 mm and diameter of roller

is 10 mm. The line of stroke of the follower is off-set by 20 mm from the axis of the cam

shaft. If the displacement of the follower takes place with uniform and equal acceleration

and retardation on both the outward and return strokes, draw the profile of the cam and

find the maximum velocity and acceleration during outstroke and return stroke.

6. Construct the profile of a cam to suit the following specifications : Cam shaft diameter =

40 mm ; Least radius of cam = 25 mm ; Diameter of roller = 25 mm; Angle of lift = 120°

; Angle of fall = 150° ; Lift of the follower = 40 mm ; Number of pauses are two of equal

interval between motions. During the lift, the motion is S.H.M. During the fall the motion

is uniform acceleration and deceleration. The speed of the cam shaft is uniform. The line

of stroke of the follower is off-set 12.5 mm from the centre of the cam.


7. The following data relate to a cam profile in which the follower moves with uniform

acceleration and retardation during ascent and descent. Minimum radius of cam = 25

mm, Roller diameter = 7.5 mm, Lift = 28 mm, offset of follower axis = 12 mm towards

right, angle of ascent = 90o, angle of descent = 90

o, angle of dwell between ascent and

descent = 45o, speed of the cam = 200 rpm. Draw the profile of the cam and determine

the maximum velocity and the uniform acceleration of the follower during the outstroke

and the return stroke.

8. It is required to set out the profile of a cam to give motion to the follower in such a way

that it rises through 31.4 mm during 180o of cam rotation with cycloidal motion and

returns with cycloidal motion during 180o of cam rotation. Determine the maximum

velocity and acceleration of the follower during the outstroke when the cam rotates at

1800 rpm clockwise. The base circle diameter of the cam is 25 mm and the roller

diameter of the follower is 10 mm. The axis of the follower passed through the cam

center.

9. Sketch and explain any four inversions of single slider crank chain mechanism.

10. Sketch and describe the inversions of a four bar chain mechanism.

11. The crank and connecting rod of a theoretical steam engine are 0.5 m and 2 m long

respectively. The crank makes 180 r.p.m. in the clockwise direction. When it has turned

45o

from the inner dead centre position, determine : (i) velocity of piston, (ii) angular

velocity of connecting rod, (iii) position and linear velocity of any point on the

connecting rod which has the least velocity relative to crank shaft.

12. The crank of a slider crank mechanism rotates clockwise at a constant speed of 300 rpm.

The crank is 150 mm and the connecting rod is 600 mm long. Determine 1. linear

velocity and acceleration of the midpoint of the connecting rod 2. Angular Velocity and

angular acceleration of the connecting rod at a crank angle of 450 from inner dead center

position.

13. A cam, with a minimum radius of 50 mm, rotating clockwise at a uniform speed, is

required to give a knife edge follower the motion as described below : (i) To move

outwards through 40 mm. during 100o rotation of the cam; (ii) To dwell for next 800;

(iii) To return to its starting position during next 900, and (iv) To dwell for the rest period

of a revolution i.e.900. Draw the profile of the cam when the line of .stroke of the

follower is off-set by 15 mm. The displacement of the follower is to take place with

uniform acceleration and uniform retardation. Determine the maximum velocity and

acceleration of the follower when the cam shaft rotates at 900 r.p.m.

14. Classify the kinematic pairs according to relative motion between them ,contact between

them and constraint between them with examples.


UNIT II TUTORIAL PROBLEMS ( PART B)

1. State and prove the law of gearing. Show that involute profile satisfies the conditions for

correct gearing.

2. A pair of gears, having 40 and 20 teeth respectively, is rotating in mesh, the speed of the

smaller being 200 rpm. Determine the velocity of sliding between the gear teeth faces at the

point of engagement, at the pitch point, and at the point of disengagement if the smaller gear is

the driver. Assume the gear teeth are 20o involute form, addendum length is 5 mm and the

module is 5 mm. also find the angle through which the pinion turns while any pairs of teeth are

in contact.

3. The following data relate to a pair of 20o involute gears in mesh: Module = 6 mm,

number of teeth on pinion = 17, Number of teeth on gear = 49; Addenda on pinion and gear

wheel = 1 module. Find: the number of pairs of teeth in contact; the angle turned through by the

pinion and the gear wheel when one pair of teeth is in contact; the ratio of sliding to rolling

motion when the tip of a tooth on the larger wheel (i) is just making contact, (ii) is just leaving

contact with its mating tooth, and (iii) is at the pitch point.

4. The pressure angle of two gears in mesh is 14.50 and has a module of 12 mm. The

number of teeth on pinion are 24 and on gear 60.The addendum of pinion and gear is same and

equal to one module. Determine (i) The number of pairs of teeth in contact,(ii) The Angle of

action of pinion and gear(iii)The ratio of sliding to rolling velocity at the beginning of contact, at

pitch point and at the end of contact.

5. Two gears of module 4 mm have 24 and 33 teeth. The pressure angle is 200 and each

gear has a standard addendum of one module. Find the length of arc of contact and the maximum

velocity of sliding if the pinion rotates at 120 r.p.m

6. A pair of spur gears with involute teeth is to give a gear ratio of 4:1. The arc of approach

is not to be less than the circular pitch and smaller is the driver. The angle of pressure is 14.5o.

Find: 1. The least number of that can be used on each wheel, and 2. The addendum of the wheel

in terms of the circular pitch.

7. Two 20o involute spur gears have a module of 10 mm. The addendum is one module. The

larger gear has 50 teeth and the pinion has 13 teeth. Does interference occur? If it occurs, to what

value should the pressure angle be changed to eliminate interference?

8. In an epicyclic gear train of the `sun and planet’ type shown in the figure below, the pitch

circle diameter of the internally toothed rings is to be 224 mm and the module 4 mm. when the

ring D is stationary, the spider A, which carries three planet wheels C of equal size, is to make

one revolution in the same sense as the sun wheel B for every five revolutions of the driving

spindle carrying the sun wheel B. Determine suitable numbers of teeth for all the wheels.


UNIT III TUTORIAL PROBLEMS ( PART B)

1. A vertical screw with single start square threads 50 mm mean diameter and 10 mm pitch is

raised against a load of 5500 N by means of a hand wheel, the boss of which is threaded to

act as a nut. The axial load is taken up by a thrust collar which supports the wheel boss and

has a mean diameter of 65 mm. if the co-efficient of friction is 0.15, for the screw and 0.18

for the collar and tangential force applied by each hand of the wheel is 140 N, find the

suitable diameter of the hand wheel.

2. A load of 10kN is raised by means of a screw jack, having a square threaded screw jack of 12

mm pitch and of mean diameter 50 mm. if a force of 100 N is applied at the end of a lever to

raise the load, what should be the length of the lever used? Co-efficient of friction = 0.15.

What is the mechanical advantage obtained? State whether the screw is self-locking or not.

3. A screw jack raises a load of 16 kN through a distance of 150 mm. The mean diameter and

the pitch of the screw are 56 mm and 10 mm respectively. Determine the work done and the

efficiency of the screw jack when the (i) load rotates with the screw. (ii) Loose head on

which the load rests does not rotate with the screw and the outside and the inside diameters

of the bearing surface of the lose head are 50 mm and 10 mm respectively. Take coefficient

of friction for the screw and the bearing surface as 0.11.

4. Outside diameter of a square threaded spindle of a screw jack is 44 mm.The screw pitch is 12

mm. If the coefficient of friction between the screw and the nut is 0.15,Friction between the

nut and the collar is 0.08.Determine (i) Force to be applied at the screw to raise a load of 3

KN.(ii)Efficiency of the screw Jack.(iii) Force to be applied at the pitch radius to lower the

same load of 3 KN.(iv) Efficiency while lowering the load.

5. The lead screw of a lathe has acme threads of 50 mm outside diameter and 10 mm pitch. The

included angle of the thread is 290. It drives a tool carriage and exerts an axial pressure of

2500 N. A collar bearing with outside diameter 100 mm and inside diameter 50 mm is

provided to take up the thrust. If the lead screw rotates at 30 rpm find the efficiency and the

power required to drive the screw. The coefficient of friction for screw threads is 0.15 and for

the collar is 0.12.

6. A shaft which rotates at a constant speed of 160 rpm is connected by belting to a parallel

shaft 720 mm apart, which has to run at 60, 80 and 100 rpm. The smallest pulley on the

driving shaft is 40 mm in radius. Determine the remaining radii of the two stepped pulleys

for 1. Crossed belts drive 2. An open belt. Neglect the thickness and slip.

7. A pulley is driven by a flat belt running at a speed of 600 m/min. The coefficient of friction

between the pulley and the belt is 0.3 and the angle of lap is 1600. If the maximum tension in

the belt is 700 N find the power transmitted by a belt.

8. A shaft rotating at 200 rpm drives another shaft at 300 rpm and transmits 6 kW through a

belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4 m. the

smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is 1. An open belt

drive, and 2. Cross belt drive. Take µ = 0.3


9. A pulley is driven by a flat belt, the angle of lap being 160o. The belt drive is 14 cm wide by

10cm and weighs 1.5 gm/m3. If the coefficient of friction is 0.3 and the maximum stress in

the belt is not to exceed 2.5MPa, find the greatest HP which the belt can transmit and the

corresponding speed of the belt.

10. 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 µ=0.12. The

density of the belt material is 1.2Mg/m3 and the maximum safe stress in the material is &

MPa. Calculate the power that can be transmitted between pulleys 300 mm diameter rotating

at 1500 rpm. Find also the shaft speed in rpm at which the power transmitted would be

maximum

11. The following data is given for a rope pulley transmitting 24 kW: Diameter of the pulley =

400 mm; Speed = 110 rpm; angle of groove = 45 deg.; angle of lap on smaller pulley = 160

deg.; Coefficient of friction = 0.28; number of ropes = 10; Mass in kg/m length of ropes = 53

C2; and working tension is limited to 122 C2 kN, where C is the girth of rope in meters. Find

the initial tension and diameter of the rope.

12. Determine the maximum power transmitted by a V-belt drive having the included V-groove

angle of 35o. The belt used is 18 mm deep with 18 mm maximum width and weighs 300 g

per meter length. The angle of lap is 145o and the maximum permissible stress is 1.5

N/mm2. Take co-efficient of friction to be 0.2.

13. The grooves on the pulleys of a multiple-rope drive have an angle of 50o and accommodate

ropes of 22 mm diameter having a mass 0f 0.8 kg per meter length for which safe operating

tension of 1200 N has been laid down. The two pulleys are of equal size. The drive is

designed for maximum power conditions. Speed of both the pulleys is 180 rpm. Assuming

coefficient of friction as 0.25, determine the diameters of the pulleys and the number of ropes

when the power transmitted is 150 kW.

14. A single plate clutch, effective both sides, is required to transmit 25 kW at 3200 rpm.

Determine the outer and inner radii of frictional surface, if the coefficient of friction is 0.3,

the ratio of radii is 1.25 and the maximum pressure is not to exceed 0.1 MPa. Also determine

the axial thrust to be provided by the springs. Assume the theory of uniform wear.

15. A 10kW engine develops a maximum torque of 100 N-m and is driving a car having a single

plate clutch of two active surfaces. Axial pressure is not to exceed 0.85 bar. External

diameter of friction plate is 1.25 times the internal diameter. Assume uniform wear and co-

efficient of friction = 0.3. Determine the dimensions of friction plate and axial force exerted

by the springs.

16. Two pulleys, one 450 mm diameter and the other 200 mm diameter are on parallel shafts

1.95 m apart and are connected by a crossed belt. Find the length of the belt required and the

angle of contact between the belt and each pulley. What power can be transmitted by the belt

when the larger pulley rotates at 200 rev/min, if the maximum permissible tension in the belt

is 1 kN, and the coefficient of friction between the belt and pulley is 0.25?


17. The pitch of 50 mm mean diameter threaded screw of a screw jack is 12.5 mm. The

coefficient of friction between the screw and the nut is 0.13. Determine the torque required

on the screw to raise a load of 25 kN, assuming the load to rotate with the screw. Determine

the ratio of the torque to raise the load to the torque required to lower the load and also the

efficiency of the machine.

18. A Screw jack has a square thread of mean diameter 6 cm and pitch 0.8 cm. The co-efficient

of friction at the screw thread is 0.09. A load of 3KN is to be lifted through 12 cm. Determine

the torque required and the work done in lifting the load through 12 cm. Find the efficiency

of the jack also.

19. Two parallel shafts 6 m apart are to be connected by a belt running over pulleys of diameters

60 cm and 40 cm respectively. Determine the exact and approximate lengths of the belt

required (i) If the belt is open (ii) If the belt is crossed.

20. An open belt drive connects two pu1leys 1.2 m and 0.5 m diameter on parallel shafts 3.6m

apart The belt has a mass of 1 kg/m length and the maximum tension in it is not to exceed 2

kN. The 1.2 m pulley which is the driver, runs at 200 r.p.m. Due to the belt slip on one of the

pulleys, the velocity of the driven shaft is only 450 r.p.m. If the coefficient of friction

between the belt and the pulley is 0.3,find : (i) Torque on each of the two shafts.(ii) Power

transmitted,(iii) Power lost in friction, and (iv Efficiency of the drive

21. A plate clutch has, three discs on the driving shaft and two discs on the driven shaft,

providing four pairs of contact surfaces. The outside diameter of the contact surfaces is 240

mm and inside diameter is 120 mm, Assuming uniform pressure and coefficient of friction as

0.3; find the total spring load pressing the plates together to transmit 25 kW at 1575 r.p.m. If

there are 6 springs each of stiffness 13 kN/m and each of the contact surfaces has worn away

by 1.25 mm, find the maximum power that can be transmitted, assuming uniform wear.

22. A car engine develops maximum torque at 15 kW and 2400 rpm. The data provided for the

clutch design are the following:

Intensity of pressure on the friction surface not to exceed 0.7 bar.

Provision is to be made for the loss of torque to wear as 30% of the engine torque.Coefficient

of friction for the mating lining riveted on both sides of the plate is 0.35.

Inside diameter of the friction plate is 0.6 times the outside diameter. Determine the suitable

dimensions of the clutch plate.


5. 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 travellbd 60o from I.D.C., the

difference between the driving and the back pressures is 0.35 N/mm2. The connecting rod

length between centers is 1.2 m and the cylinder bore is 0.5 m. If the engine runs at 250

r.p.m. and if the effect of piston rod diameter is neglected, calculate : (i)'pressure on slide

bars, (ii) thrust in the connecting rod, (iii) tangential force on the crank-pin,and (iv)

turning moment on the crank shaft.

6. A petrol engine has a stroke of 120 mm and connecting rod is 3 times the crank

length.The crank rotates at 1500 r.p.m.in clockwise direction.Determine : (i) Velocity

and. acceleration of the piston, and (ii) Angular velocity and angular acceleration of the

connecting rod, when the piston had travelled one-fourth of its stroke from I.D C.

7. A horizontal steam engine running at 240 rpm has a bore of 300 mm and stroke 600 mm.

The connecting rod is 1.05 m long and the mass of reciprocating parts is 60 kg. When the

crank is 600past its inner dead cen[re, the steam pressure on the cover side of the piston is

1 125 Mpa while that on the crank side is 0.125 MPa. Neglecting the area of the piston

rod, determine (i) the force in the piston rod; and (ii) the turning moment on the

crankshaft.

8. The following data refer to a steam engine test:

Net effective steam pressure = 0.8 MPa.The position of the crank from IDC = 30 0

Acceleration of the piston = 22m/s2.Diameter of the cylinder =25 cm.Crank Radius =24

cm.Length of the connecting rod = 96 cm.Mass of the recriprocating parts =200 Kg.

Determine:

(i) Normal reaction on the cross head guides

(ii) The resultant load on the gudgeon pin

(iii) Torque on the crank shaft.

9. An Internal combustion engine runs at 1500 rpm.The length of connecting rod is 48 cm

and crank radius is 12 cm.Determine at 30% of the outstroke

(i) The angular position of the crank.

(ii) The angular velocity of the connecting rod.

(iii) The linear acceleration of the piston.

(iv) The angular acceleration of the connecting rod.

10. If the crank and the connecting rod are 300 mm and 1 m long respectively and the crank

rotates at constant speed of 200 rpm.Determine

(i) the crank angle at which the maximum velocity occurs and (10)

(ii) maximum velocity of piston. (6)


UNIT V TUTORIAL PROBLEMS ( PART B)

1. A four-cylinder vertical engine has cranks 300 mm long. The planes of rotation of th'e

first, third and fourth cranks are 750 mm, 1050 mm and1650 mm respectively from that of the

second crank and their reciprocating masses are 150 kg, 400 kg and 250 kg respectively. Find:(i)

the mass of the reciprocating parts for the second cylinder and(ii) the relative angular positions

of the cranks in order that the engine may be in complete primary balance. (16)

2. Find. the frequency of the transverse vibrations of a shaft which is simply supported at its

ends and is of 40 mm in diameter and 2.5 m in length.The shaft carries three point load.s of

masses 30 kg, 70 kg and 45 kg at 0.5 m, 1 m and 1.7 m respectively from the left support. The

Young's modulus for the material of the shaft is 200 GPa. Neglect the weight of the shaft. (16)

3. A shaft carries four masses A,B,C and D of magnitude 400 Kg, 300 kg, 500 Kg and 200

kg respectively and all the masses revolving at the same radius of 100 mm in the planes

measured from A at 300 mm, 400 mm and 700 mm. The angle between the cranks measured

anticlockwise are A to B 450,B to C 70

0 and C to D 120

0.The balancing masses are to be placed

in planes P and Q. The distance between planes A and P is 100 mm, between P and Q is 400 mm

and between Q and D is 200 mm.If the balancing masses revolve at a radius of 70 mm, find their

magnitudes and angular positions.

4. The measurements on a mechanical vibrating system show that it has a mass of 20 Kg

and that the springs can be combined to give an equivalent spring of stiffness 10 N/mm. If the

vibrating system have a dashpot attached which exerts a force of 60 N when the mass has a

velocity of 1.5 m/s,find:(i) Critical Damping Coefficeient (ii) Damping Factor (iii) Logarithmic

Decrement (iv) Ratio of two consecutive amplitudes.

5. A single cylinder horizontal engine runs at 120 rpm The length of stroke is 400 mm. The

mass of the revolving parts assumed concentrated at the crank pin is 100 kg and mass of the

reciprocating parts is 150 kg. Determine the magnitude of the balancing mass required to be

placed opposite to the crank at a radius of 150 mm which is equivalent to all the revolving and

2/3rd of the reciprocating masses. If the crank turns 300 from the inner dead centre, find the

magnitude of the unbalanced force due to the balancing mass.

6. A shaft of 100 mm diameter and 1 metre long is fixed at one end and other end carries a

flywheel of mass 1 tonne. Taking Young's modlus for the shaft material as 200 GN/m2, find the

natural frequency of longitudinal and transverse vibrations.

7. A mass of 500 kg is mounted on supports having a total stiffness. of 100 kN/m and which

provides viscous damping, the damping ratio being 0.4. The mass is constrained to move

vertically and is subjected to a vertical disturbing force of the type Fcosɷt. Determine the

frequency at which resonance will occur and the maximum allowable value of F if the amplitude

at resonance is to be restricted to 5 mm.


8. A, B, C and D are four masses carried by a rotating shaft at radii 100mm, 150 mm, 150

mm and 200 mm respectively. The planes. in which the masses rotate are spaced at 500 mm

apart and the magnitude of the masses B, C and D are 9 kg, 5 kg and 4 kg respectively. Find the

required mass A and the relative angular settings of the four masses so that the shaft shall be in

cornplete balance.

9. The measurements on a mechanical vibrating system show that it has a mass of 8 kg and

that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the

vibrating system have a dashpot attached which exerts a force of 40 N when the mass has a

velocity of 1 m/s. find : (i) critical damping coefficient, (ii) damping factor, (iii) Logarithmic

decrement, and (iv) ratio of two consecutive amplitudes.

10. Derive the equations of motions and hence the natural frequency of longitudinal free

vibrations of spring-mass system by

(i) Equilibrium method (ii) Energy method (iii) Rayleigh'sMethod.

11. Four masses m1, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The

corresponding radii of rotation are 0.2 rn, 0.15 m, 0.25 m and 0.3 m respectively and the angles

between successive masses are 450, 75

0 and 135

0. Find the position and magnitude of the balance

mass required, if its radius of rotation is 0.2 m.

Additional Problems

12. A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes

which are equidistant from one another. The magnitude of A, C, D are 50 kg, 40 kg and 80 kg

respectively. The angle between A and C is 90o and that between C and D is 135

o. Determine

the magnitude of the planes B and E and their positions to put the shaft in complete rotating

balance.

13. A rotating shaft carries four masses A, B, C and D which are radially attached to it. The

mass centers are 30 mm, 38 mm, 40 mm and 35 mm respectively from the axis of rotation. The

masses A, C and D are 7.5 kg, 5 kg and 4 kg respectively. The axial distances between the

planes of rotation of A and B is 400 mm and between B and C is 500 mm. The masses A and C

are at right angles to each other. Find for a complete balance: i) the angle between the masses B

and D from mass A, ii) the axial distance between the planes of rotation of C and D, and the

magnitude of mass B.


14. The following data refers to a two cylinder locomotive: Rotating mass per cylinder = 300

kg; Reciprocating mass per cylinder = 330 kg; Distance between the wheels = 1500 mm;

Distance between cylinder centers = 600 mm; Diameter of tread of driving wheels = 1800 mm;

Crank radius = 325 mm; Radius of center of balance mass = 650 mm; Locomotive speed = 60

km/hr; angle between cylinder cranks = 90o; Dead load on each wheel = 40 kN. Determine: (i)

the balancing mass required in the planes of driving wheels if whole of the revolving and two-

third of the reciprocating mass are to be balanced, (ii) the swaying couple, (iii) the variation in

the tractive force, (iv) the maximum and minimum pressure on the rails and (v) the maximum

speed of locomotive without lifting the wheels from the rails.

15. A two cylinder uncoupled locomotive with cranks at 90o has a crank radius of 325 mm.

the distance between the centers of driving wheels is 1.5 m. the pitch of cylinders is 0.6 m. the

diameter of treads of the driving wheels is 1.8 m. the radius of center of gravity of balance

masses is 0.65 m. the pressure due to dead load on each wheel is 40 kN. The masses of

reciprocating and rotating parts per cylinder are 330 kg and 300 kg respectively. The speed of

the locomotive is 60 kmph. Find: (i) the balancing masses both in position and magnitude

required to be placed in the p0lanes of driving wheels to balance whole of the revolving and

two-third of reciprocating masses; (ii) the swaying couple; (iii) the variation in tractive force;

(iv) the maximum and minimum pressure on rails; and 5. The maximum speed at which it is

possible to run the locomotive, in order that the wheels are not lifted from the rails.

16. A shaft 1.5 m long, supported in flexible bearings at the ends carries two wheels each of

50 kg mass. One wheel is situated at the center of the shaft and the other at a distance of 375

mm from the center towards left. The shaft is hollow of external diameter 75 mm and internal

diameter 40 mm. the density of the shaft material is 7700 kg/m3 and its modulus of elasticity is

200 GN/m2. Find the lowest whirling speed of the shaft, taking into account the mass of the

shaft.

17. A vertical shaft of 5 mm diameter is 200 mm long and is supported in long bearings at tis

ends. A disc of mass 50 kg is attached to the center of the shaft. Neglecting any increase in

stiffness due to the attachment of the disc of the shaft, find the critical speed of rotation and the

maximum bending stress when the shaft is rotating at 75% of the critical speed. The center of

the disc is 0.25 mm from the geometric axis of the shaft. E = 200 GN/m2

18. An instrument vibrates with a frequency of 1 Hz when there is no damping. When a damping

is provided, the frequency of damped vibrations was observed to be 0.9 Hz. Find (i) the damping

factor and (ii) Logarithmic decrement

19. A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out

vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude

of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that

the damping force varies as the velocity, determine: (i) the resistance of the dashpot at unit

velocity; (ii) the ratio of the frequency of the damped vibrations to the frequency of the damped

at 6302 mechanics of machines learning material ii year auto regulation 2013

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