ASSIGNMENT 1

1. Two gear wheels mesh externally to give a velocity ratio of 3 to 1. The involute teeth has 6 mm module and 20° pressure angle. Addendum is equal to one module. The pinion rotates at 90 rpm. Determine Number of teeth on pinion to avoid interference and the corresponding number on the wheel; (4) The length of path and are of contact .Contact ratio and .The maximum velocity of sliding. 2. (i) Derive an expression to determine the length of path of contact between two spur gears of different size. Briefly explain the sub—classification of compound gear trains with neat sketches. 3. (i) Explain the various pitches of helical gears with sketch. ii) Two 15 mm module 20° pressure angle spur gears have addendum equal to one module. The pinion has 25teeth and the gear 50 teeth. Determine whether interference will occur or not. If it occurs, to what valve should the pressure angle be changed to eliminate interference? (6) 4. An epicyclic gear train consists of three gears 1, 2 and 3 .the internal gear 1 has 72 teeth and gear 3 has 32 teeth. The gear 2 meshes with both gear .1 and gear 3 and is carried on an arm A. which rotates about the centre 02 at 20 rpm. If the gear 1 is fixed, determine the speed of gears 2 and 3 (ii) Write short notes on speed ratio of a planetary gear train. (4) 5. With the help of a neatly drawn sketch of a spur gear, explain elaborately the nomenclature of gears. 6. An epicyclic gear train is shown in Fig. 14(b). The input S has 24 teeth. Gears P and C constitute a compound planet having 30 and 18 teeth respectively. If all the gears are of the same pitch, find the speed ratio of the gear train assuming A to be fixed. 7. (i) State and prove the law of gearing. (10) (ii) Show that the involute curves as the profiles of mating gears satisfy the law of gearing. (6) 8. A compound gear train using spur gears is required to give a total reduction ratio of 250 to 1 in four steps. The modules of the gears are 5 mm for the first step, 7 mm for the second, 10 mm for the third and 16 mm for the fourth. Arrive at the individual speed ratios, if a tolerance of ±0.2% is allowed in the total reduction ratio. (4) Find the numbers of teeth of all gears, if the minimum number of teeth for any pinion is 20. (4) Find the pitch circle diameters of all gears and the centre distances. (4) Sketch a line diagram showing the gear train. (4)

ASSIGNMENT 2

1.A single cylinder vertical petrol engine of total mass 300 kg is mounted upon a steel chassis frame and causes a vertical static deflection of 2 mm. The reciprocating parts of the engine has a mass of 20 kg and move through a vertical stroke of 150 mm with simple harmonic motion. A dashpot is provided whose damping resistance is directly proportional to the velocity and amounts to 1.5 kN per metre per second. Considering that the steady state of vibration is reached ; determine : 1. the amplitude of forced vibrations, when the driving shaft of the engine rotates at 480 r.p.m., and 2. the speed of the driving shaft at which resonance will occur. 2.A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine: 1. the resistance of the dashpot at unit velocity; 2. the ratio of the frequency of the damped vibration to the frequency of the undamped vibration; and 3. the periodic time of the damped vibration. 3.The arms of a Porter governor are each 250 mm long and pivoted on the governor axis. The mass of each ball is 5 kg and the mass of the central sleeve is 30 kg. The radius of rotation of the balls is 150 mm when the sleeve begins to rise and reaches a value of 200 mm for maximum speed. Determine the speed range of the governor. If the friction at the sleeve is equivalent of 20 N of load at the sleeve, determine how the speed range is modified. 4.The turbine rotor of a ship has a mass of 3500 kg. It has a radius of gyration of 0.45 m and a speed of 3000 r.p.m. clockwise when looking from stern. Determine the gyroscopic couple and its effect upon the ship: 1. when the ship is steering to the left on a curve of 100 m radius at a speed of 36 km/h. 2. when the ship is pitching in a simple harmonic motion, the bow falling with its maximum velocity. The period of pitching is 40 seconds and the total angular displacement between the two extreme positions of pitching is 12 degrees 5.A coil of spring stiffness 4 N/mm supports vertically a mass of 20 kg at the free end. The motion is resisted by the oil dashpot. It is found that the amplitude at the beginning of the fourth cycle is 0.8 times the amplitude of the previous vibration. Determine the damping force per unit velocity. Also find the ratio of the frequency of damped and undamped vibrations. 6.A pair of locomotive driving wheels with the axle, have a moment of inertia of 180 kg-m2. The diameter of the wheel treads is 1.8 m and the distance between wheel centres is 1.5 m. When the locomotive is travelling on a level track at 95 km/h, defective ballasting causes one wheel to fall 6 mm and to rise again in a total time of 0.1 s. If the displacement of the wheel takes place with simple harmonic motion, find : 1. The gyroscopic couple set up, and 2. The reaction between the wheel and rail due to this couple.