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2003 Course Dynamics of Machinery

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Total No. of Questions : 12] P1034 [Total No. of Pages : 5 [3864]-132 B.E. (Mech. and Mech./SW) DYNAMICS OF MACHINERY (2003 Course) (402042) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) 2) 3) 4) 5) 6) Answer three questions from section-I and three questions from section-II. Answers to the two sections should be written in separate books. Neat diagrams must be drawn wherever necessary. Figures to the right indicate full marks. Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. Assume suitable data, if necessary. SECTION - I Unit - I Q1) a) Explain the gyroscopic action in an air plane taking a vertical loop in the sky. Assume suitable directions and determine the effects of gyroscopic action. [6] b) Inertia of a pair of a locomotive driving wheels together with the shaft is 380 kgm2. The effect of diameter of each wheel is 2m and mean track width is 1.5m. The defect in the rail causes one wheel to fall and rise again 10mm in a total time of 0.1 sec., while the locomotive is traveling along a straight level track at 100 km/hr. If the fall and rise of the wheel is with simple harmonic motion, find the gyroscopic reaction couple on the locomotive. [10] OR Q2) a) Define following terms related to gyroscope, i) Axis of spin. ii) Axis of precision. iii) [3] Axis of couple. P.T.O. b) A motor cyclist travels round a curved track of 80m radius at 80km/hr. Determine the angle of heel, if : [13] Mass of the motorcycle with rider = 120kg Combined center of gravity from ground = 0.425m Mass of each wheel = 0.8kg Radius of gyration of each wheel = 0.220m Effective wheel diameter = 0.6m The mass of rotating parts is 1.4kg having a radius of gyration of 0.09m and it rotates at 3 times the speed of the wheel and in opposite direction. Unit - II Q3) a) Explain a suitable method to determine the unbalance in radial engines.[4] b) The cranks of a four cylinder marine oil engine are arranged at a angular interval of 90o. The engine speed is 700 rpm and the reciprocating mass per cylinder is 800kg. The inner cranks are 1m apart and 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 amongst the firing order 1-2-4-3 and 1-4-2-3 and also determine the magnitude of the unbalanced primary couple for that arrangement. [12] OR Q4) a) A five cylinder in line engine has distance between axes of neighboring cylinders equal to 700mm, crank lengths 325mm. Mass of reciprocating parts of 1st, 3rd and 4th cylinders are 155kg each. Angle between first and 3rd crank is 285o and that between 1st and 4th crank is 435o. Assuming crank no.1 at zero degrees, find reciprocating masses and crank angles of second and fifth cylinder so as to achieve complete primary balance. [12] b) Write a note on balancing of rotating masses. [4] Unit - III Q5) a) A horizontal circular disc of 400mm diameter and 20kg mass is supported by a vertical stepped shaft at the center. The shaft has two steps. First step is 20mm diameter and 200mm long whereas the second step is 15mm diameter and 250mm long, determine the frequency of torsional oscillations of the disc, if the modulus of rigidity of the shaft is 80000 [10] N/mm2. [3864]-132 2 b) What is the physical significance of the different values of damping factor. [8] OR Q6) a) Prove that for finding the natural frequency of a cantilever system loaded at its end, the mass of the cantilever is taken into account by adding 33/140 of its mass to the main mass. [10] b) The disc of torsional pendulum has a mass moment of inertia of 0.06 kgm2. The brass shaft attached to it is of 100mm diameter and 400mm long. When the pendulum is vibrating, the observed amplitudes on the same side of the rest position for successive cycles are 9o, 6o and 4o. Find, i) ii) iii) iv) Logarithmic decrement. Damping torque at unit velocity. Time period of vibration. What would the frequency be if the disc is removed from viscous fluid? Assume the modulus of rigidity as 4.4 1010 N/m2. [8] SECTION - II Q7) a) What are frequency response curves? [8] State 4 observations from these plots drawn for different damping conditions. b) A 75kg machine is mounted on springs of stiffness k = 11.76 105 N/m with an assumed damping factor = 0.20. A 2kg piston within the machine has a reciprocating motion with a stroke of 0.08m and a speed of 3000 cycles per minutes. Assuming the motion of the piston to be harmonic, determine the amplitude of vibration of the machine and the vibratory force transmitted to the foundation. [10] OR Q8) a) Draw vector representation diagram for force transmissibility showing all the forces and angles and hence derive the following expression for force transmissibility. [8] [3864]-132 3 b) A radio set of 20kg mass must be isolated from a machine vibrating with an amplitude of 0.05mm at 500 cpm. The set is mounted on four isolators, each having a spring scale of 31400 N/m and damping factor of 392 N-sec/m. i) What is the amplitude of vibration of the radio? ii) What is the dynamic load on each isolator due to vibration? [10] Q9) a) Explain Principal Modes of vibration with respect to 2 DOF translational system. [6] b) Derive a frequency equation for the two natural frequencies for small oscillations of a coupled pendulum shown in fig.1. Assume the rods as mass less and rigid. Also obtain two expressions for the angular amplitude ratios in the two Principal Modes. [10] OR Q10) a) Explain torsionally equivalent shaft and show that length of equivalent shaft is given by [6] [3864]-132 4 b) Two identical rotors are attached to the two ends of a stepped shaft. Each rotor weighs 450kg and has a radius of gyration of 0.38m. The diameter of the shaft is 0.75m for the first 0.25m length, 0.1m diameter for the next 0.1m length and 0.0875m diameter for the remaining length. The total length for the shaft is 0.6m. Assume Modulus of rigidity as 80 109 N/m2. Find : i) The frequency of torsional vibration. ii) Position of node. Draw amplitude and node plot. [10] Q11) a) What do you mean by critical speed of shaft? Derive the expression for a light shaft deflection having a single disc neglecting damping. Explain [8] the significance of 0o and 180o phase difference in critical speed. b) A disc of mass 4kg is mounted midway between bearings which may be assumed to be simply supported. The bearing span is 0.48m. The steel shaft which is horizontal, is 9mm in diameter. The CG of the disc is displaced 3mm from the geometric center. If the shaft rotates at 760 rpm, find the maximum stress in the shaft. Take E = 1.96 1011 N/m2. [8] OR Q12) a) Explain any two of the following with the help of neat diagrams. i) Vibrometer. ii) FFT Spectrum Analyzer. iii) Piezo electric Accelerometer. iv) [8] Frequency Measuring Instrument. b) A device used to measure torsional acceleration consist of a ring having a moment of inertia of 0.049kg-m2 connected to a shaft by a spiral spring having a scale of 0.98 N-m/rad and a viscous damper having a constant of 0.11 N-m-sec/ rad. When the shaft vibrates with a frequency of 15cpm, the relative amplitude between the ring and the shaft is found to be 2o. What is the maximum acceleration of the shaft? [8] xxxx [3864]-132 5

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