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Assignment on Power Transmission and Vibrations

Module Learning Outcomes

1) Use calculations to determine forces and torques in friction and positive drive systems, Including epicyclics, in power transmission systems and to balance rotating shafts.

2) Conduct free and forced vibrations of single degree of freedom systems

1a) Why toothed gears are preferred over Rope, Belt, and chain drive? Also specify the application for each drive system. (06 Marks)

b) State law of gearing? What do you understand by the term ‘interference’ as applied to gears? (04 Marks)

c) Two gear wheels with 50 and 30 teeth respectively, mesh externally, the speed of the smaller being 1800 r.p.m. Determine the velocity of sliding between the gear teeth faces at the point of engagement, at the pitch point, and at the point of disengagement if the smaller gear is the driver. Assume that the gear teeth are 18° involute form, addendum length is 8 mm and the module is 5 mm. Also find the angle through which the pinion turns while any pairs of teeth are in contact. (15 Marks)

d) An indexing mechanism of the milling machine uses a gear train shown in figure task 1d. The drive is from gear wheels A and B to the bevel gear wheel D. The following table shows the tooth number on each gear, solve using tabular method.

How many revolutions does D makes for one revolution of A under the following situations:

 Gear A B C D E F Number of teeth 65 65 50 25 24 20 Diametral pitch in mm 06 06 10 10 06 06

Tabular column (05 Marks)

(i) If A and B are having the same speed and same direction (04 Marks)
(ii) If A and B are having the same speed and opposite direction (02 Marks)
(iii) If A is making 80 rpm and B is at rest (03 Marks)
(iv) If A is making 80 rpm and B 40 rpm in the same direction. (04 Marks)
(v) Also define the term Speed ratio and train value (02 Marks)

Figure Task 1d (20 Marks)

e) A rotor has the following properties.

 Sl.No Mass (Kg) Radius(m) Angle Distance from first mass 1 12 0.1 θ1=00 0 2 8 0.12 θ2=600 0.16 3 6 0.14 θ3=1350 0.32 4 5 0.12 θ4=2700 0.56

If the shaft is balanced by two counter masses located at 100 mm radii and revolving in Planes midway of planes 1 and 2, and midway of 3 and 4, determine the magnitude of the masses and their respective angular positions. (15 Marks)

2. (a) With application point of view explain the difference between
(i)free and forced vibration (03 Marks)
(ii)Damped and Undamped Vibration (03 Marks)
(iii)Under damped, over damped and critically damped system (04 Marks)

(b) Consider the spring mass system shown in Figure Task 2b. It has a mass, m of 4 kg and the spring constants k1 = 5 N/m and k2 = 8 N/m. Determine the natural frequency of vibration of spring mass system inclined at an angle of 30?. (20 Marks)

(c) A damping machine with vibratory system is to be designed with following parameters K= 100N/m, C=2 N-sec/m, M=1kg

Find
(i) Decrease of amplitude from its starting value after complete oscillations (08 Marks)
(ii) The frequency of oscillation (02 Marks)