Chapter 1 Gyroscope · 2019-11-19 · 6. What is Gyroscopic couple? 03 7. Explain the gyroscopic effect on steering of ship. 04 03 8. What is gyroscopic effect in aeroplane? How it

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Theory of Machines(2151902) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Chapter 1 – Gyroscope

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Theory

1. 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

2. Illustrate the effect of Gyroscopic couple on a car. 06

3. Explain basic terms used for gyroscopic with proper diagram. 04

4. Discuss the gyroscopic effect and stability of a four wheel vehicle moving along a curved path. 07

5. How stability of four wheels automobile is affected due Gyroscopic couple and centrifugal force. Explain with necessary expression.

04

6. What is Gyroscopic couple? 03

7. Explain the gyroscopic effect on steering of ship. 04 03

8. What is gyroscopic effect in aeroplane? How it can be reduced? 03

9. Explain the gyroscopic effect with suitable example. 03

10. Derive an equation for an Aeroplane taking turn with usual notations. 07

11. Derive an equation for stability of four wheeler taking turn. 07

Examples

1.

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

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pitches 50 above and 50 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.

2.

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

07

3.

The turbine rotor of a ship having a mass of 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

4.

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 kg.m2. 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 kg.m2 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

5. 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

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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.

6.

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

7.

An automobile car of weight of 20 kN is taking right turn along a curved path of 25m mean radius at 30

km/h. the width of track of vehicle is 1.3m and the wheel base is 2m. The effective wheel radius is

0.3m. The moment of inertia of the rotating parts is 10kgm2 and moment of inertia of each wheel is 10

kg.m2. The C.G. of the car is 0.75m above the road level. The engine flywheel rotates at 3000 rpm

clockwise when viewed from front. Find out the reactions between the wheels and the ground.

07

8.

An aeroplane flying at 240 km/hr turns towards the left and completes a quarter circle of radius 60 m.

The mass of the rotary engine and its propeller is 500 kg and radius of gyration is 0.35m. The engine

speed is 2200 rpm clockwise looking from tail end. Find the gyroscopic couple on the aeroplane and

state its effect.

07

9.

An aeroplane makes a complete half circle of 50 meters radius, towards left, when flying at 200 km per

hr. The rotary engine and the propeller of the plane has a mass of 400 kg and a radius of gyration of 0.3

m. The engine rotates at 2400 r.p.m. clockwise when viewed from the rear. Find the gyroscopic couple

on the aircraft and state its effect on it.

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Theory of Machines (2151902) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Chapter 2 – Friction Devices: Clutches, Brakes and Dynamometers

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Theory

1. Derive expression for frictional torque for single plate clutch considering uniform wear and

uniform pressure condition. 06

07

2. Establish formula for the fractional torque transmitted by single disc clutch. 07

3. What is the function of a clutch? Classify clutches. 04

4. What are the characteristics of good friction materials? State different friction materials used in friction clutches.

04 04

5. What are characteristics of friction lining material used for clutch? 03

6. Explain the working of cone clutch with neat sketch. 04

7. Derive expression for frictional torque for centrifugal clutch 06 04

8. List advantages and applications of centrifugal clutch. 03

9. With a neat sketch, explain construction, operation and application of a centrifugal clutch. 07

10. Give differences between brake and clutch. 04

11. Give classification of brakes. 04

12. Enlist the factors on which capacity of a break depends. 03 03

13. What is meant by a self locking and a self energized brake ? 04

14. Explain the working of band brake. 04

15. Give advantages of differential band brake over simple band brake. 03

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16. Describe the working of band and block brake with the help of neat sketch and derive the equation for ratio of tight and slack side tensions.

07

17. 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

18. Describe with the help of a neat sketch the principles of operation of an internal expanding shoe brake.

04

19. Draw the construction of Internal expanding shoe brake. 03

20. 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

21. Determine the retardation of a four wheel car when the brakes are applied to the rear wheel. 04

22. Determine the retardation of a four wheel car when the brakes are applied to the front wheel. 04

23. What is dynamometer? How it differs from brake? 04 04

24. Give only two differences and one similarity between Brake and Dynamometer. 03

25. What is the function of a dynamometer? List various types of dynamometers. Explain any one with neat sketch.

07

26. 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

27. Explain construction and working of torsion dynamometer. 07

28. Give advantages and disadvantages of hydraulic dynamometer. 04

29. Explain working of epicyclic train dynamometer. 03 03

30. Explain working of Bevis Gibson flash light torsion dynamometer. 03

31. What is the advantage of a transmission type dynamometer over an absorption type dynamometer? 03 04

32. Describe construction and operation of Prony brake absorption dynamometer. 03

33. Explain any one type of dynamometer with neat sketch. 04

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Examples

1.

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

2.

100 kW is transmitted at 3000 rpm by a multi plate 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

3.

A multiple disc clutch, steel on bronze is to transmit 4.5kW at 750 rpm. The inner radius of the

contact is 40mm and outer radius of the contact is 70mm. The clutch operates in oil with an

expected coefficient of 0.1. The average allowable pressure is 0.35N/mm2.

Find : 1. the total number of steel and bronze discs

2. the actual axial force required

3. the actual average pressure and

4. the actual maximum pressure.

07

4.

A centrifugal clutch is to be design to transmit 15kW at 900 rpm. The shoes are four in number. The

speed at which the engagement begins is 3/4th of the running speed. The inside radius of the pulley

rim is 150mm. the shoes are lined with the material of coefficient of friction of 0.25.

Determine 1. Mass of the shoes 2. Size of the shoes.

07

5.

A simple band brake is applied on a drum of 560 mm diameter which is rotating at 240 rpm. The

band having an angle of contact on the drum of 2700. One end of the band is fitted to a fixed pin

while the other end is fitted to the lever 140mm from the fixed pin. The lever is 800 mm long and is

perpendicular to the diameter that bisects the angle of contact. If the coefficient of friction is 0.3,

what will be the necessary pull at the end of the lever to stop the drum when the power absorbed is

40 kW. Also calculate the width of the band if its thickness is 3mm and maximum tensile stress is

limited to 40 N/mm2.

07 07

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6.

A band brake acts on the ¾ th of circumference of a drum of 450 mm diameter which is keyed to the

shaft. The band brake provides a braking torque of 225 N-m. One end of the band is attached to a

fulcrum pin of the lever and the other end to a pin 100 mm from the fulcrum.

If the operating force is applied at 500 mm from the fulcrum and the coefficient of friction is 0.25,

find the operating force when the drum rotates in the (a) anticlockwise direction, and (b) clockwise

direction.

07

7.

A differential band brake shown in Figure, has an angle of contact of 2250. 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

8.

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.

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9.

A differential band brake has a drum with a diameter of 400 mm. The two ends of the band are fixed

to the pins on the opposite sides of the fulcrum of the lever at distances of 20 mm and 100 mm from

the fulcrum. The angle of contact is 2700 and the coefficient of friction is 0.2. Determine the brake

torque when a force of 600 N is applied to the lever at a distance of 400 mm from fulcrum

07

10.

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

11.

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.

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12.

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

13.

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

14.

A torsion dynamometer is fitted to a propeller shaft of a marine engine. It is found that the shaft

twists 2° in a length of 20 metres at 120 r.p.m. If the shaft is hollow with 400 mm external diameter

and 300 mm internal diameter, find the power of the engine. Take modulus of rigidity for the shaft

material as 80 GPa.

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Chapter 3 – Flywheels

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Theory

1.

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

2. Short note on Flywheel material. 03

3. Explain various applications of flywheel. 04 03

4. Derive the expression of maximum fluctuation of energy for multi-cylinder engine and coefficient of fluctuation of energy.

06 07

5. Derive an expression of fluctuation of energy for flywheel used in punching press.

06

6. What are the turning moment diagrams? Why are they drawn? 03

7. Define (i) Coefficient of fluctuation of energy and (ii) Coefficient of fluctuation of speed

03 04

8. Compare between flywheel and governor 04 03 03

9. Prove that the maximum fluctuation of energy, ΔEmax = 2.E.Cs with usual notations.

04

Examples

1.

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 = 4.50. 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

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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.

2.

Turning moment area for the revolution of a multi-cylinder engine with reference to the mean turning moment in sq. cm are :

- 0.32, 4.08, - 2.67, 3.33, - 3.1, 2.26, - 3.74, 2.74, - 2.58

The scale for the ordinate and abscissa are 1cm = 140 , 1cm= 6000 N-m

The mean speed is 200 rpm with 1.5% fluctuation. if hoop stress in the rim material is not to exceed 56bar, calculate the diameter and X-section of rim of the flywheel. Neglect the effect of bars and arms. Density of material = 0.0672 kg/cm3 (Assume Value of K and G=1)

07

3.

The T-θ 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.

(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.

07

4.

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

5. 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

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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.

6.

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

7.

A punching press is required to punch 40 mm diameter holes in a plate of 15 mm thickness at a rate of 30 holes/min. It requires 6 N-m of energy per mm2 of sheared area. If the punching takes 1/10 of a second and r.p.m. of the flywheel varies from 160 to 140. Then determine the mass flywheel having radius of gyration of 1 m.

07

8.

A machine is coupled to a two-stroke engine which produces a torque of (800 + 180 Sin 3θ) N-m, where θ is the crank angle. The mean engine speed is 400 rpm. The flywheel and the other rotating parts attached to the engine have a mass of 350 kg at a radius of gyration of 220 mm. Calculate;

1. Power of the engine, and

2. Total fluctuation of the speed of the flywheel in percentage when

(i) the resisting torque is constant, and

(ii) the resisting torque is (800 + 80 Sin θ) N-m.

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Chapter 4 – Governors

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Theory

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

isochronous. 03

2. Explain the terms: Hunting, Effort of a governor 04

3.

Elaborate following terms in context of Governor.

1. Sensitiveness of Governors

2. Stability of Governors

3. Isochronous Governor

06

4. Derive the expression for Effort and Power of a Porter Governor. 06

5. Explain working principle of centrifugal governor with suitable diagram. 04

6. 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

7. Explain following 1. Sensitiveness of Governors 2. Isochronous Governors

04 04

8. Explain following 1. Sensitiveness of Governors 2. Hunting and stability of governors.

04

9. What is isochronism in governors? 03

10. What is the importance of governor? 03

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11. Explain about isochronism and hunting of governor. 04

12. Explain hunting phenomena in governors. 03

13. Explain the concept of controlling force with controlling force diagram for spring controlled governors.

07

Examples

1.

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

2.

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

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Chapter 5 – Introduction to Dynamics

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Theory

1. Explain shaking forces and shaking moments. Derive their expressions for a four bar linkage.

07

2. 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

3. Explain impulse and momentum. 07 04 04

4. How is the effect of friction forces considered in the static force analysis of a mechanism having turning pairs?

07

5. Discuss the dynamic force effect on reciprocating engine using Klein’s construction.

05

6. Discuss the effect of inertia force on connecting rod. 05 04

7. Define Centroid and centre of gravity. Give difference between two. 03

8. State and explain parallel axis theorem. 03 03

9. State Newton’s three laws of motion. 03 03

10. Explain the concept of Free body diagram with proper example. 04 04

11. State Lami’s theorem and give suitable example. 03 04

12. Derive an expression of radius of gyration for connecting road. 05

13. Discuss the effect of friction on the forces acting at joints of mechanism. 05

14. List experimental methods used for finding out the radius of gyration of 07

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components having complicated geometry? Explain any one method in detail, with neat sketch.

15. Explain D’alembert’s Principle 03 03 03 04

16. Derive the expression for total torque on crank shaft of IC engine by considering dynamic force.

07

17. Differentiate between static and dynamic force analysis. 04

18. What is free body diagram? Give its importance for finding static force analysis of any system using proper illustration.

07 04

19. Differentiate between applied and constraint force. 03 03

20. For all objects Center of Mass and Centroid must be on same point or not. Discuss it using suitable example.

04

21. Give difference between Center of Mass and centroid. 03

22. Explain about equilibrium of a component acted upon by four coplanar and non-concurrent forces.

04

23. Explain velocity analysis of a link by complex algebra approach. 07

24. Explain the principle of virtual work. 03

25. Define and explain the superposition theorem as applicable to a system of forces acting on a mechanism.

03

Examples

1. 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

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2.

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 300 from the inner dead centre.

09

3.

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

09

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4.

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

5.

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

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6.

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 07

7.

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

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8.

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

9.

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

10.

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

11. In I.C. Engine, the crank radius is 300mm and length of connecting rod is 750mm. The mass of the piston is 1.25kg and diameter of the piston is 100mm. The speed is 900 rpm and net gas pressure is 750kN/m2.

07

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Find: 1. Piston Effort, 2. Thrust in connecting rod, 3. Piston side thrust, 4. crank pin effort, 5. Torque acting on crankshaft and 6. Radial force or load on main bearings when crank has made 450 from TDC.

12.

Two equal weights of 1000 N each are lying on two inclined planes connected by a string passing over a frictionless pulley as shown in fig. Using D’Alembert’s principle, find the acceleration of weights and tension in the string. The coefficient of friction between the plane and weights is 0.2

07

13.

Determine the range of values of force P for which the block of 500 N weight will be in equilibrium on an inclined plane shown in Fig. Take μ=0.35.

07

14. Find the inertia force for the following data of an I.C. engine: Bore = 175 mm, stroke = 200 mm, engine speed = 500 r.p.m., length of connecting rod = 400 mm, crank angle = 60° from T.D.C and mass of reciprocating parts = 180 kg.

04

15.

A rectangular RCC column is centrally cast over a concrete bed. RCC (as shown in Fig. 1) column is of section 30 x 45 cm and height 4 m. The concrete bed is of size 3 x 4.5 m and thickness 30 cm. Find the mass moment of inertia of the column and bed combination about its vertical centroidal axis. Mass density of concrete =

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GTU Paper Analysis


2500 kg/m3.

16.

For the static equilibrium of the quick-return mechanism shown in Fig.1, determine the input torque T2 to be applied on the link AB for a force of 300 N on slider D. The dimensions of the various links are; OA = 400 mm, AB = 200 mm, OC = 800 mm and CD = 300 mm.

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GTU Paper Analysis


17.

The crank and connecting rod of a vertical petrol engine, running at 1800 rpm are 60 mm and 270 mm respectively. The diameter of piston is 100 mm and the mass of the reciprocating parts is 1.2 kg. During expansion stroke when the crank has turned 20 from T.D.C., the gas pressure is 650 kN/m2. Determine the find;

(i) Net force on piston

(ii) Net load on gudgeon pin

(iii) Thrust on the cylinder walls

(iv) Speed at which the gudgeon pin load is reversed in direction.

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