R09 Set No. 2 - Padhle · PDF fileCode No: 09A50303 R09 Set No. 2 ... DYNAMICS OF MACHINERY ... Determine the angular velocity of precession of the ywheel. The spin speed of

Code No: 09A50303 R09 Set No. 2

III B.Tech I Semester Examinations,May/June 2012DYNAMICS OF MACHINERY

Common to Mechanical Engineering, Mechatronics, ProductionEngineering, Automobile Engineering

Time: 3 hours Max Marks: 75Answer any FIVE Questions

All Questions carry equal marks? ? ? ? ?

1. (a) Describe the function of a simple Watt governor. What are its limitations?

(b) Each arm of a Porter governor is 300 mm long and is pivoted on the axis ofrotation. Each ball has a mass of 6 kg, and the sleeve weighs 18 kg. The radiusof rotation of the ball is 200 mm when the governor begins to lift, and 250mm when the speed is maximum.Determine the maximum and the minimumspeeds and the range of speed of the governor. [5+10]

2. Describe, in detail, the dynamic analysis of the slider crank mechanism to de-termine the velocity and acceleration of the piston, and the angular velocity andangular acceleration of the connecting rod. [15]

3. (a) What are the important types of free vibrations? What type of stresses areproduced in case of free vibration of different types?

(b) A simply supported shaft of length 1.6 m carries a mass of 120 kg placed 500mm from one end. If E = 200 GN/m2 and diameter of shaft is 50 mm, thenfind the natural frequency of transverse vibrations. [7+8]

4. (a) An engine has 3 single acting cylinders whose cranks are spaced at 1200 toeach other. The turning moment diagram for each cylinder consists of a tri-angle having the following values.

Angle 00 600 1800 1800 − 3600

Torque (N-m) 0 200 0 0

Find the mean torque and the moment of the inertia of the flywheel to keepthe speed with in 180 ± 3 rpm.

(b) Draw the turning moment diagram for a single cylinder double-acting steamengine. [10+5]

5. Layout a four bar mechanism such that ϕ12 = 500 and Ψ12 = 600. The input crankand the output link should both rotate in the counter clockwise direction. [15]

6. (a) Discuss how a single revolving mass is balanced by two masses revolving indifferent planes.

(b) A shaft carries four masses as shown in Figure 1 and figure 2. The balancingmasses are to be placed in planes L and M. If the balancing masses revolve ata radius of 100 mm, find their magnitudes and angular positions. [7+8]

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Figure 1:

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Figure 2:

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7. The layout and dimensions of a double shoe brake is shown in Figure 3. Thediameter of the brake drum is 300 mm, and the contact angle for each shoe is 900.If the coefficient of friction for the brake lining and the drum is 0.4, find the springforce necessary to transmit a torque of 30 N-m. Also determine the width of thebrake shoes, if the bearing pressure on the lining material is not to exceed 0.28N/mm2. [15]

Figure 3:

8. Each road wheel of a motor cycle is of 600 mm diameter and has a moment ofinertiaof 1.1 kg-m 2. The motor cycle and the rider together weight 220 kg, and thecombined centre of mass is 620mm above the ground level when the motor cycle isupright. The moment of inertia of the rotating parts of the engine is 0.18 kg-m2.The engine rotates at 4.5times the speed of road wheels in the same sense. Findthe angle of wheel necessary when the motor cycle is taking a turn of 35 m radius ata speed of 72 kg/h. [15]

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1. (a) Differentiate between:

i. Band brake and band-and- block brake.

ii. Absorption dynamometer and transmission dynamo meter.

(b) The brake drum of a single block brake of diameter 600 mm is rotating at 400r.p.m. as shown in Figure 4. The force required at the end of the lever toapply the brake is 300 N. If the angle of contact is 900, and the coefficient offriction between the drum and the brake block is 0.3, find the braking torque.Take b = 60 mm; a = 375 mm and L = 825 mm. [7+8]

Figure 4:

2. Explain the concepts of Function Generation, Path Generation, and Rigid BodyGuidance with suitable examples. [15]

3. (a) Define the terms : ‘coefficient of fluctuation energy’ and ‘coefficient of fluctu-ation of speed’.

(b) Find a relation for the coefficient of fluctuation of speed in terms of the max-imum fluctuation of energy and the kinetic energy of the flywheel at meanspeed. [6+9]

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4. (a) Explain what do you understand by gyroscopic stabilization. Illustrate withthe help of a sketch how this is carried out in ships.

(b) Obtain a relation between the gyroscopic torque and the couple applied bythe waves for complete stabilization, if the waves be sinusoidal. [7+8]

5. The guns are designed so that, on firing, the barrel recoils against a spring. Adashpot is engaged that allows the barrel to return to its position at the end ofeach recoil. A gun barrel has a mass of 500 kg and a recoil spring constant of 300N/mm. The barrel recoils 1 m on firing. Determine:

(a) The initial recoil velocity of the gun barrel, and

(b) The critical damping co-efficient of the dashpot engaged at the end of therecoil stroke. [15]

6. A Porter governor carries a central load of 30 kg, and each ball weighs 4.5 kg. Theupper links are 200 mm long while the lower links are 300 mm long. The pointsof suspension of the upper and lower links are 50 mm from the axis of the spindle.Working from first principles, calculate the speed of the governor in rpm, if theradius of rotation of governor balls is 125 mm. [15]

7. The cranks of a two cylinder uncoupled outside cylinder locomotive are at rightangles, and are 300 mm long. The distance between the centre lines of the cylindersis 1.75 m. The wheel centre lines are 1.45 m apart. The rotating mass per cylinderis 360 Kg, and the mass of the reciprocating parts of cylinder is 300 Kg. Thewhole of the rotating and two-thirds of the reciprocating masses are to be balancedin the plane of the driving wheels at a radius of 750 mm. Find:

(a) The magnitude and angular positions of the balance masses

(b) The maximum speed of the locomotive in km/hr without lifting the wheelsfrom the rails, if the dead weight on each driving wheel is 30 kN and diameterofthe driving wheel is 1.8 m, and

(c) The Swaying couple at the maximum speed. [15]

8. For the mechanism shown in Figure 5, find the required input torque for the staticequilibrium. The lengths OA and AB are 250 mm and 650 mm respectively. F =500 N. [15]

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Figure 5

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Figure 5:





1. Explain clearly the difference in the nature of unbalance caused by primary andsecondary disturbing forces in the case of a reciprocating mass. What is the essentialdifference between the unbalance caused by a reciprocating mass and that causedby a revolving mass? How will you achieve the complete balance in the case ofmulti - cylinder in - line engine? [15]

2. (a) Describe in detail the Klein’s construction for obtaining the velocity and ac-celeration of the reciprocating parts of a steam engine.

(b) Define and explain the terms: Inertia force and Inertia torque. [7+8]

3. (a) A flywheel of mass 10 kg and radius of gyration 200 mm is spinning about itsaxis, which is horizontal and is suspended at a point distant 150mm from theplane of rotation of the flywheel. Determine the angular velocity of precessionof the flywheel. The spin speed of flywheel is 900rpm.

(b) Whatwill be the effect of the gyroscopic couple on a disc fixed at certain angleto a rotating shaft? [7+8]

4. (a) Define the term: “Magnification factor”.

(b) A mass of 2.5 kg is hung from a string of stiffness 3 KN/m. The vibration iscontrolled by a dashpot, and it is found that the amplitude of vibration di-

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minishes to one-fourth of its initial value in 5 complete oscillations. Assuminglinear damping, find the damping co-efficient of the dashpot. [4+11]

5. (a) Explain the working of a multi-plate clutch with the help of a neat sketch.

(b) A multi-plate clutch has three pairs of contact surfaces. The outer and innerradii of the contact surfaces are 150 mm and 80 mm respectively. The max-imum axial spring force is limited to 0.9 kN, and the coefficient of friction is0.3. Assuming uniform wear, find the power transmitted by the clutch at 1500rpm. [7+8]

6. (a) What are free-body diagrams of a mechanism? How are they helpful in findingthe various forces acting on the various members of the mechanism?

(b) Find the torque required to be applied to the link AB of the mechanism shownin Figure 6 to maintain the static equilibrium. [5+10]

Figure 6:

7. Determine the three precision positions of input and output angles for a mechanismto generate a function y = x1.8 , where x varies from 1 to 5, using Chebyshev’sspacing. Assume that the initial values for the input and output crank are 30degrees and 90 degrees respectively, and the difference between the final and initialvalues for the input and output cranks are each equal to 90 degrees. [15]

8. A spring controlled governor of the Hartnell type has two rotating balls of mass1.35 kg each. The ball arm is 75 mm and the sleeve arm is 62.5 mm. In the mid

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position of the sleeve, the sleeve arm is horizontal and the balls rotate in a circle of100 mm radius. The total sleeve movement is 30 mm. Due to maladjustment of thespring, it is found that the equilibrium speed at the topmost position of the sleeveis 420 rpm and that corresponding to the lowest position is 435 rpm. Determine:

(a) The stiffness and initial compression of the spring;

(b) The required initial compression of the spring to give an equilibrium speed atthe topmost position which is 12 rpm more than that at the lowest position.Neglect the moment due to the mass of the balls. [15]

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1. (a) Prove that the maximum fluctuation of energy 4E is given by:4E = E . 2Cs ,where E = Mean kinetic energy of the flywheel, and Cs = Coefficient of fluc-tuation of speed.

(b) An engine flywheel has mass of 6.5 tonnes, and the radius of gyration is 2 m.If the maximum and minimum speeds are 120 rpm and 118 rpm respectively,find the maximum fluctuation of energy. [7+8]

2. (a) A multiple clutch has three pairs of contact surfaces. The outer and inner radiiof the contact surfaces are 100 mm and 50 mm respectively. The maximumaxial spring force is limited to 1 kN. If the coefficient of fiction is 0.35, assuminguniform wear, find the power transmitted by the clutch at 1500 rpm.

(b) A single plate clutch having both sides effective is required to transmit 30 kWat 1500 rpm. The outer diameter of the plate is limited to 300 mm, and theintensity of pressure between the plates is not to exceed 0.07 MPa. Assuminguniform wear and a coefficient of friction 0.35, determine the inside diameterof the plate. [7+8]

3. (a) What is the principle of a gyroscope? Discuss the factors that affect thestability of an automobile while negotiating a curve.

(b) A thin circular disc is fitted to a shaft as shown in Figure 7. Weight of thedisc is 500N and diameter is 1.2m. Shaft rotates at 300 rpm in anticlockwisedirection when seen from the right side. Find the effect of the gyroscopiccouple on the shaft, and the bearing reactions at A and B taking the effect ofthe weight of the disc. [7+8]

4. Synthesize a 4 - bar mechanism to generate a function y = log x for 1 ≤ x ≤ 2. Therange of the output crank may be chosen as 900 while that of input crank be 600.Assume three precision points which are to be obtained from Chebyshev spacings.

[15]

5. For the static equilibrium of the quick return mechanism shown in Figure 8, findthe maximum input torque T2 required for a force of 250 N on the slider D. Angleθ is 1050, and the Coefficient of friction is 0.15 for each sliding pair. [15]

6. (a) Explain the terms: sensitiveness, isochronism and hunting in connection withgovernors.

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Figure 7:

Figure 8:

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(b) Determine the:

i. Maximum speed

ii. Minimum speed

iii. Range of speed of a Watt governor of open arm type shown in Figure 9 inwhich the length of arm AE = 400 mm, and length EF = 50 mm, whenthe angle θ changes from 350 to 300. [7+8]

Figure 9:

7. A shaftcarries 3 pulleys A,B and C at distances 60 cm, and 120 cm apart . Thepulleys are out of balance to the extent of 19.6 N , 17.2 N, and 24.5 N respectively ata radius of 2.5 cm in each case. The angular positions of the out-of-balance massesin the pulleys B and C with respect to pulley A are 900 and 2100 respectively.Determine in position and magnitude, the balance weights required in planes Land M mid-way between planes A, B, and C respectively. The radius of rotationof balance weights is 12.5 cm. [15]

8. Three rotors A, B, and C having moments of inertia of 2000, 6000, and 3000 kg-m2

respectively are carried on a uniform shaft of 0.35 m diameter. The length of theshaft between the rotors A and B is 6 m, and that between D and C is 32 m. Findthe natural frequency of torsional vibration. The modulus of rigidity for the shaftmaterial is 80 GN/m2 . [15]

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R09 Set No. 2 - Padhle · PDF fileCode No: 09A50303 R09 Set No. 2 ... DYNAMICS OF MACHINERY ... Determine the angular velocity of precession of the ywheel. The spin speed of