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Dynamics of Machinery (October 2009)

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Total No. of Questions : 12] P968 [Total No. of Pages : 4 [3664]-123 B.E. (Mechanical) DYNAMICS OF MACHINERY (2003 Course) (402042) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) Answer 3 questions from Section I and 3 questions from Section II. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. Q1) a) b) Q2) a) b) Q3) a) b) c) SECTION - I Unit - I Define the following terms related to gyroscope with neat sketch: (i) Axis of spin, (ii) Axis of couple, (iii) Axis of precession, (iv) Active and Reactive gyro. couple. [8] A disc of mass 5 kg and of radius of gyration of 90mm is mounted centrally on a horizontal shaft of 120mm length between the bearings. The disc is spinning about the axis of the shaft at 620 rpm anticlockwise, when viewed from the right-hand side bearing. The shaft precesses about a vertical axis at 35rpm in the clockwise direction when observed from the top. Determine the resultant reaction at each bearing due to the mass and the gyroscopic effect. [8] OR Explain the terms - steering, pitching and rolling in a ship. Discuss their gyroscopic effects. [8] A pair of flanged wheels 1.2m in diameter are mounted on axle rolls along rails spaced at 1.3m apart. The axle negotiates a curve of 150 m mean radius at a speed of 60 km/hr. Determine the reactions at the rails. The wheels are thin discs of 270 kg mass each. The rails are at the same level. Neglect the mass of the axle. [8] Unit - II What do you understand by (i) static unbalance and (ii) Dynamic unbalance. [4] With the help of a neat sketch, explain in brief the working of static and Dynamic balancing machines. [4] A shaft rotates in two bearings A and B, 1.8m apart and projects 0.45m P.T.O. Q4) a) b) c) Q5) a) b) c) Q6) a) b) c) beyond A and B. At the extreme ends of the shaft are attached two pulleys of masses 20kg and 48 kg; their centre of gravity being 12.5mm and 15.5mm respectively, from the axis of the shaft. In the middle of the bearings is attached a third pulley of mass 50kg with centre of gravity out by 15.5mm. If the three pulleys have been arranged so as to obtain static balance; Determine the dynamic force produced on the bearings when the shaft speed is 300 rpm. [8] OR What are V-engines? How do they differ from the rest of the reciprocating [4] engines. Explain the direct and reverse Crank method for determining unbalanced forces in radial engines. [4] The cranks of a four cylinder marine oil engine are arranged at angular intervals of 90 . The engine speed is 70rpm and the reciprocating mass per cylinder is 800 kg. The inner cranks are 1m apart and are symmetrically arranged between the outer cranks which are 2.6m apart. Each crank is 400mm long. Determine the firing order of the cylinders for best balance of reciprocating masses and also magnitude of the unbalanced primary couple for that arrangement. [8] Unit - III Describe the following method to find natural frequency of vibratory system. (i) Equilibrium method, (ii) Energy method, (iii) Rayleigh method. [6] A cylindrical disc of mass 'm' and radius 'r' is suspended from apoint on its circumference. Determine its natural frequency of oscillation. [6] A homogeneous solid cylinder of length "L", cross - sectional area 'A' and specific gravity 'S' (S < 1.0) is floating in water with its vertical. Neglecting any accompanying motion of water, determine the differential equation of motion and the period of oscillation of the cylinder if it depressed slightly and then released. [6] OR Derive an expression for the motion of spring-mass-dashpot system in case of - (i) over damped system, (ii) critically damped system, (iii) under damped system. [6] A horizontal spring mass system with coulomb damping has a mass of 5.0 kg attached to a spring of stiffness 980 N/m. If the c.o.f. is 0.025; calculate. i) the frequency of free oscillations. ii) the number of cycles corresponding to 50% reduction in amplitude if the initial amplitude is 50 mm and. iii) the time taken to achieve this reduction. [6] An underdamped shock absorber is to be designed for a motor cycle of [3664] - 123 2 Q7) a) b) Q8) a) b) Q9) a) b) mass 200 kg such that during road bump, the damped period of vibration is limited to 2 sec and the amplitude of vibration should reduce to onesixteenth in one cycle. Find the necessary (i) stiffness; (ii) Damping coefficient of the shock absorber. [6] SECTION - II Unit - IV Define motion and force transmissibility and derive expression for it, incase of spring-mass-dashpot vibratory system. [8] A body of mass 75 kg is suspended from a spring which deflects 18 mm under the load. It is subjected to a damping effect adjusted to a value 0.25 times that required for critical damping. Find the natural frequency of undamped and damped vibrations and ratio of successive amplitude for damped vibrations. If the body is subjected to a periodic disturbing force of 625N and of frequency equal to 0.63 times the natural undamped frequency, find the amplitude of forced vibrations and phase difference with respect to the disturbing force. [8] OR Draw and explain transmissibility versus frequency response curves and phase angle versus frequency response curves. [4] A mass of 250 N is supported by a spring and dashpot. The spring is stretched by 150 mm due to weight and the dashpot has coefficient of damping 1000N per metre per see. If the support is oscillation in S.H.M. with amplitude 25 mm and frequency 6 rad / sec. Find. [12] i) The amplitude of load; ii) The relative amplitude between load and support. iii) The amplitude of the load when the frequency of disturbing force is equal to the natural frequency. iv) The amplitude of the load when the dash pot has been grounded and the frequency of support is (a) 6 rad / sec; (b) equal to natural frequency of load. Unit - V What do you understand by torsionally equivalent shaft? Derive an expression for the equivalent length of a shaft which have several steps.[4] A periodic torque having a maximum value of 0.65 N-m, at a frequency corresponding to 5 rad / sec is impressed upon a flywheel suspended from a wire. The wheel has a moment of inertia of 0.15 kg-m2 and the wire is having diameter of 6 mm and length of 1.2 m. The modulus of rigidity of the material of wire is equal to 0.8 x 1011 N/m2. A viscous dashpot applies damping couple of 0.693 N-m at an angular velocity of 1.5 rad / sec. Calculate : (i) The maximum angular displacement from the rest position, (ii) The maximum couple applied to dashpot, and (iii) The angle by which the angular displacement lags the torque. [12] [3664] - 123 3 Q10)a) b) OR Derive an expression for natural frequency of torsional vibrations of a two and three rotor system. [4] An electric motor running at 2250 rpm drives a centrifugal pump running at 650 rpm through a single stage gear reduction. The motor armature has a moment of inertia of 32 kg m2 and the pump impeller of 84 kg m2. The shaft from the pump to gears is 90 mm diameter and 3600 mm long and that from motor to the gears is 600 mm long. What should be the diameter of the shaft from the motor to the gears to ensure the node for natural torsional vibrations is at the gears? Determine the frequency of these vibrations and the amplitude of the impeller vibrations for an amplitude of one degree of the motor. [12] Unit - VI Q11)a) b) Q12)a) b) c) How will you determine the critical speed of a rotor shaft? State its significance in the design of a shaft of a rotating machine? Explain the method of determining whirling of shafts carrying single rotor. [9] A vertical shaft 12.5 mm in diameter rotates in sleeve bearings and disc of mass 15 kg is attached to the shaft at mid span. The span of the shaft between bearings is 0.5 m. The mass centre of the axis is 0.5 mm from the axis of the shaft. Determine the critical speed of rotation of the shaft. What is the speed range in which the bending stress in the shaft will exceed 125 N/mm2? Assume E = 2 x 105 N/mm2. [9] OR Explain the basic principle of Seismic pick-up used for measurement of displacement and acceleration. [6] What is FFT? With the help of block diagram, explain the working of FFT analyzer. State the applications of FFT analyzer with reference to vibrations and noise. [6] A vibration measuring device is used to find the displacement, velocity and acceleration of a machine running at 150 rpm. If the natural frequency of the instrument is 4 Hz and it shows 5 m what are the three readings? Assume no damping. [6] Y [3664] - 123 4

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