Dynamics of machinery Questions.docx

7/28/2019 Dynamics of machinery Questions.docx

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VELTECH MULTITECH DR.R.RANGARAJAN DR.SAKUNTHALA

ENGINEERING COLLEGE

Department of Mechanical Engineering

ME 2302 DYNAMICS OF MACHINERYFifth Semester

CYCLE TESTI

Set- I

Time: 2 hours Total Marks=50

Date :

Answer all the Question

Part-A (5 x 2 = 10 marks)1. State the principle of superposition.

2. State D Alemberts Principle.

3. What is cam dynamics?

4. Write different types of balancing?5. What are the effects of hammer blow and swaying couple?

PARTB

(1 x8 + 2 x 16 = 40 MARKS)

6.a) In a slider crank mechanism, the length of the crank and connecting rod are 100mm and

400mm respectively. The crank rotates uniformly at 600 rpm clockwise when the crank

has turned through 45 from the inner dead centre. Find, by analytical method: 1.

Velocity and acceleration of the slider, and 2. Angular velocity and angular acceleration

of the connecting rod. (8)

OR

6.b) What do you mean by balancing of linkages? List the various methods used for it.(8)

7.a) A horizontal steam engine running at 210rpm has a bore of 190mm and stroke of

350mm. The piston rod is 20mm in diameter and connecting rod length is 950mm. The

mass of the reciprocating parts is 8kg and the frictional resistance is equivalent to a

force of 350N.

Determine the following when the crank is at 115 from the inner dead centre, the

mean pressure being 4500N/m2 on the cover side and 100 N/m2 on the crank side.

1. Thrust on the connecting rod, 2. Thrust on the cylinder walls

3. load on the bearings, and 4. Turning moment on the crankshaft.

OR

7.b) The torque delivered by a two-stroke engine is represented by T= (1000 + 300 sin -

500 cos ) N-m, where is the angle turned by the crank from the innerdead centre.

The engine speed is 250rpm. The mass of the flywheel is 400 kg and radius of gyration

400mm. Determine:

(i) the power developed

(ii) the total percentage fluctuation of speed,

(iii) the angular acceleration of flywheel when the crank has rotated

through an angle of 60 from the inner dead center, and

(iv) the maximum angular acceleration and retardation of the flywheel.


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8.a) A shaft carries four masses in parallel planes A,B,C and D in this order along its length.

The masses at A and C are 20 kg and 15kg respectively, and each has an eccentricity of

60mm. The masses at A and D have an eccentricity of 80mm. The angle between the

masses at B and C is 100 and that between the masses at B and A is 190, both being

measured in the same direction. The axial distance between the planes A and B is

100mm and that between B and C is 200mm. If the shaft is in complete dynamic balance,determine:

1. the magnitude of the masses at A and D,

2. the distance between planes A and D, and

3. the angular position of the mass at D.

OR

8.b) A four cylinder vertical engine has cranks 150mm long. The planes of rotation of the

first, second and fourth cranks are 400mm, 200mm and 200mm respectively. From the

third crank and their reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Findthe mass of the reciprocating parts for the third cylinder and the relative angular positions

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


3/11


ENGINEERING COLLEGE


ME 2302 DYNAMICS OF MACHINERYFifth Semester

CYCLE TESTI

Set- II


Date :


Part-A (5 x 2 = 10 marks)1.What is a free body diagram?

2.What are the forces involved in cam analysis.

3.What do you mean by equivalent offset inertia force?4.Write importance of balancing?5. What are the forces acting on the connecting rod?

PARTB

(1 x8 + 2 x 16 = 40 MARKS)6.a) The radius of gyration of a flywheel is 1 meter and the fluctuation of speed is not to

exceed 1% of the mean speed of the flywheel. If the mass of the flywheel is 3340 kg and

the steam engine develops 150 kW at 135rpm, then find

(i) Maximum fluctuation of energy and

(ii) Co-efficient of fluctuation of energy. (8)

6.b) Prove that the resultant unbalanced force is minimum when half of the reciprocating

masses are balanced by rotating masses, i.e., when c= 1/2 (8)

7.a) A single cylinder vertical engine has bore of 300 mm and a stroke of 400 mm. the

connecting rod is 1000 mm long. The mass of the reciprocating parts is 140 kg. On the

expansion stroke with the crank at 30 from the top dead centre, the gas pressure is

0.7 Mpa. If the engine runs at 250 r.p.m, determine:

(i) net force acting on the piston (ii) resultant load on the gudgeon pin

(iii) thrust on the cylinder walls, and(iv) the speed above which other things remaining same, the gudgeon pin loads would

be reversed in direction.

7.b)The turning moment diagram for a multi cylinder engine has been drawn to a scale of

1mm = 4500 N-m vertically and 1= 2.4 horizontally. The intercepted areas between

output torque curve and mean resistance line taken in order from one end are

342,23,245,303,115,232,227 and 164 mm2, when the engine is running at 150 r.p.m. If

the mass of the flywheel is 1000 kg and the total fluctuation of speed does not exceed

3% of mean speed, find the minimum value of the radius of gyration.


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8.a) The camshaft of high speed pump consists of a parallel shaft 25mm diameter and 480mm

long. It carries three eccentrics, each of diameter 60 mm and a uniform thickness of

18mm. The assembly is symmetrical as shown in figure given below and bearing are at A

and B. The angle between the eccentrics is 120 and the eccentricity of each is 12.5 mm.

The material density is 7000kg/m3, and the speed of rotation is 1430 r.p.m. Find the

dynamic load on each bearing due to the out of balance couple.

OR

8.b) The cranks of a three cylinder locomotive are set at 120. The reciprocating masses

are 450 kg for the inside cylinder and 390 kg for each outside cylinder. The pitch of the

cylinder is 1.2m and the stroke of each piston 500mm. The planes of rotation of the

balance masses are 960mm from the inside cylinder.

If 40% of the reciprocating masses are to be balanced , determine:

(i) the magnitude and the position of the balancing masses required at a radialdistance of 500mm: and

(ii) The hammer blow per wheel when the axle rotates at 350 r.p.m.


5/11


ENGINEERING COLLEGE


ME 2302 DYNAMICS OF MACHINERY

Fifth Semester

CYCLE TEST II

Set- I


Date :


Part-A (5 x 2 = 10 marks)

1. What are the different types of vibrations?

2. Define critical speed of the shaft?

3. Differentiate between transverse and torsional vibration.

4. What is meant by harmonic forcing?

5. Define transmissibility.

PARTB

(1 x8 + 2 x 16 = 40 MARKS)

6.a) Find the equivalent stiffness of vibration of the system shown in figure . If S1= 5000N/m , S2 = S3 = 8000 N/m and m= 25 kg. find the natural frequency of vibration of the

system.

6.b) A body having a mass of 15 kg is suspended from a spring which deflects 12mm under

the weight of the mass. Determine the frequency of the free vibrations. What is the

viscous damping force needed to make the motion aperiodic at a speed of 1mm/s

If , when damped to this extent, a disturbing force having a maximum value of 100N

and vibrating at 6 Hz is made to act an the body, determine the amplitude of the ultimate

motion.

7.a) A shaft 30mm diameter and 1.5 long has a mass of 16 kg per meter length. It is simply

supported at the ends and carries three isolated loads 1kN, 1.5kN and 2kN at 0.4 m, 0.6m


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and 0.8m respectively from the left support. Find the frequency of the transverse

vibrations: 1. Neglecting the mass of the shaft and 2. Considering the mass of shaft. Take

E = 200 Gpa.

OR

7.b) The flywheel of an engine driving a dynamo has mass of 200kg and has a radius of

gyration of 30 cm. The shaft at the flywheel end has an effective length of 25cm and is5cm diameter. The armature mass is 225 kg and has a radius of gyration of 25.5 cm. The

dynamo shaft has a diameter of 4.375 cm and an equivalent length of 20cm. Neglecting

the inertia of the shaft and coupling, calculate the frequency of the torsional vibrations

and position of node. The modulus of rigidity for the shaft material is 80 GN/m2.

8.a) A vehicle has a mass of 490 kg and the total spring constant of its suspension system is

58800 N/m. The profile of the road may be approximated to a sine wave of amplitude

40mm and wave length 4.0 meters. Determine:

(i) the critical speed of the vehicle,

(ii) the amplitude of the steady state motion of the mass when the vehicle is driven atcritical speed and damping factor is 0.5 and

(iii) the amplitude of steady state motion of the when the vehicle is driven at 57km/hr

and the damping factor is 0.5

OR

8.b) An industrial machine weighing 445 kg is supported on a spring with a statical deflection

of 0.5cm. If the machine has rotating imbalance of 25 kg-cm, determine the force

transmitted at 1200 rpm and the dynamic amplitude at the speed.


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ENGINEERING COLLEGE



Fifth Semester

CYCLE TESTII

Set- II


Date :



1. What are the causes and effects of vibration?2.What do you mean by damping and damped vibration?

3. What are the cause of critical speed?

4. What are the conditions to be satisfied for an equivalent system to that of geared system in

torsional vibrations?

5. Define damping ratio.

PARTB

(1 x8 + 2 x 16 = 40 MARKS)

6.a) A shaft supported freely at the ends has a mass of 140 kg placed 325 mm from one end.

Determine the frequency of the natural transverse vibrations if the length of the shaft is750mm, E= 200GN/m2 and shaft diameter is 40mm.

OR

6.b) Find the stiffness of each spring when a refrigerator unit having a mass of 30 kg is to be

supported by three spring. The force transmitted to the supporting structure is only 10%

of the impressed force. The refrigerator unit operates at 420 r.p.m.

7.a) A vertical shaft 30mm diameter and 1m long is mounted in long bearing and carries a

pulley of mass 10 kg midway between the bearings. The centre of pulley is 0.5 mm from

the axis of the shaft. Find (i) the whirling speed, and (ii) the bending stress in the shaft,

when it is rotating at 2000 r.p.m. Neglect the mass of the shaft and take Youngs

modulus of the material of the shaft as 200 GN/m2.OR

7.b) A steel shaft ABCD 1.5 m long has flywheels at its ends A and D. Flywheel A is of mass

500 kg and has a radius of gyration of 600 mm and flywheel D is of mass 700 kg and has

a radius gyration of 900mm. The connecting shaft has a diameter of 50mm for the

portion AB which is 400 mm long; and has a diameter of 60 mm for the portion BC

which is 500 mm long and has a diameter d mm of the portion CD so that the node of

the torsional vibration of the system will be at the centre of the length BC, and (ii) the

natural frequency of the torsional vibrations, given that the modulus of rigidity for steel =

8 x 10 10 N/m2.


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8.a) A body having a mass of 15 kg is suspended from a spring which deflects 12 mm under

the weight of the mass. Determine the frequency of the free vibrations. What is the

viscous damping force needed to make motion aperiodic at vibration. What of the

viscous damping force needed to make the motion aperiodic at a speed of 1 mm/s?

If , when damped to this extent, a disturbing force having a maximum value of100N and vibrating at 6 Hz is made to act on the body, determine the amplitude of the

ultimate motion.

OR

8.b) A machine of mass 75 kg is mounted on spring of stiffness 12 x 105 N/m and with an

assumed damping factor of 0.2. A piston within the machine of mass 2 kg has a

reciprocating motion with a stroke of 80mm and a speed of 3000 cycles/min.

Assuming the motion to be simple harmonic, find

(i) the amplitude of motion of the machine

(ii) its phase angle with respect to the exciting force,

(iii) the force transmitted to the foundation,

(iv) the phase angle of transmitted force with respect to the exciting force, and(v) the phase lag of the transmitted force with respect to the applied force.


9/11


ENGINEERING COLLEGE



Fifth Semester

MODEL EXAMINATION

Set- I


Date : Answer all the Question


1. What is meant by unbalance in cam dynamics and state its causes?

2. Write the condition for zero and non occurrence of jump.3. Define correction couple and state its use.4. State the function of a flywheel in a punching machine.

5. What is meant by rocking with reference to the balancing of masses?

6. State the conditions for static and dynamic balancing.

7. What is meant by hammer blow and state the expression to determine the maximum

speed above which the wheels will lift off the rails?

8. Define axis of precession.

9. State the effect and reason of gyroscopic couple on ship while rolling.

10.Can Porter governor be an isochronous governor? Explain

PART B (5x16=80)

11. (a). The length of crank and connecting rod of a horizontal engine are 200mm and 1m

respectively. The crank is rotating at 400rpm. When the crank has turned through 30

from the inner dead centre, the difference of pressure between cover and piston rod is

0.4N/mm2. If the mass of the reciprocating parts is 100 kg and cylinder bore is

0.4m.then calculate:

(i) inertia force (ii) force on piston

(ii) piston effort (iv) thrust on the sides of the cylinder walls.

(Or)

(b). A 3 cylinder single acting engine has its cranks at 120o . The turning moment

diagram for each cycle is a triangle for the power stroke with a maximum torque of

60 Nm at 60o the dead centre of the corresponding crank. There is no torque on the .

return stroke. The engine runs at 400 rpm.

Determine

i) The power developed,

ii) The coefficient of fluctuation of speed if the mass of the flywheel

is 10kg and its radius of Gyration is 88 mm,

iii) The coefficient of fluctuation of energy and

iv) The maximum angular acceleration of flywheel.


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12.(a). ).i) Four masses A,B,C and D are completely balanced. Masses C and D make angles

of 90o and 2100 respectively with B in the same sense. The planes containing B

and C are 300mm apart. Masses A,B,C and D can be assumed to be

concentrated at radii of 360, 480, 240 and 300 mm respectively. The masses B,C

and D are 15kg,25kg and 20kg respectively. Determine the mass of A and its

angular position & the positions of planes A and D.ii) Derive the expression for variation in tractive force due to unbalance in reciprocating

engines.

(Or)(b). The crank and connecting rod of a vertical petrol engine, running at 1800rpm are 60mm

and 270mm respectively. The diameter of the piston is 100mm 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 650KN/m2.

Determine i)The net force of the piston,ii) The net load on the gudgeon pin,

iii)The thrust of the cylinder walls and

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

13.(a). The following relate to the connecting rod of a reciprocating engine:

Mass = 50kg

Distance between bearing centers=900mm

Diameter of big end bearing = 100mm

Diameter of small end bearing -= 80mm

Time of oscillation when the connecting rod is suspended from

Big end = 1.7 s

Small end = 1.85 s

Determine:

i) The radius of gyration kof the rod about an axis through centre of mass

perpendicular to the plane of oscillation.

ii) The moment of inertia of the rod about the same axis, and

iii)The dynamically equivalent system of the connecting rod comprising

two masses, one at the small end bearing centre.

(Or)

(b

14.(a). A five cylinder in-line engine running at 750 rpm has successive cranks 144 o apart,

the distance between the cylinder centre lines being 375mm. The piston stroke is

225mm and the ratio of the connecting rod to the crank is 4.Examine the engine for

balance of primary and secondary forces and couples. Find the maximum values ofthese and position of the central crank at which these maximum values occur. The

reciprocating mass for each cylinder is 15kg.


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(Or)

(b).In a hartnell governor, the lengths of ball and sleeve arms of a ball crank lever are

120mm and 100mm respectively. The distance of the fulcrum of the bell crank lever

from the governor axis is 140mm each governor ball has a mass of 4 kg. The governor

runs at a mean speed of 300 rpm with the ball arms vertical sleeve arms horizontal. Foran increase of speed of 4 percent, the sleeve moves 10mm upwards.

Neglecting friction, find:

i) The minimum equilibrium speed if the total sleeve movement is limited to 20mm.

ii) The spring stiffness,

iii) The sensitiveness of the governor, and

iv) The spring stiffness if the governor is to be isochronous at 300 rpm.

15.(a).The upper arms of a porter governor are 350mm long and are pivoted on the other side

at a radial distance of 40mm from the axis of rotation. The lower arms are 250mm

long and pivoted at a radial distance of 30mm from the axis of rotation. The mass ofeach ball is 5kg and the mass of the central load is 40kg. If the limiting inclinations of

upper arms to the vertical are 30o and 40o , find the speed range of the governor.

(Or)

(b). A 2.3 tonne racing car has a wheel base of 2.5m and a track of 1.4m. The centre of

mass of the car lies at 0.6 m above the ground and 1.5m from the rear axle. Equivalent

mass of engine parts is 150kg with k 160mm. The back axle ratio is 5. The engine

shaft and flywheel rotate clockwise when viewed from front. Each wheel has a

diameter of 0.7 m and a moment of inertia of 0.7kg.m2. Determine the load

distribution on the wheels when the car is rounding a curve 100 m radius at a speed

of 74km/hr to the left..

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Dynamics of machinery Questions.docx