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TURNING MOMENT DIAGRAM

Unit 1<br>DYNAMICS OF MACHINES

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TURNING MOMENT DIAGRAM

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  1. Turning moment diagram

  2. Session-06

  3. 4 stroke engine – Turning moment diagram

  4. 4 stroke engine – Turning moment diagram

  5. Purpose • Turning moment diagram is a graphical representation of turning moment or torque(along Y-axis) versus crank angle (X-axis) forvarious positions of crank. • The area under the TMD gives the work donper cycle. • The work done per cycle when divided by thecrank angle per cycle gives the mean torque Tm. • The mean torque Tm multiplied by the angularvelocity of the crank gives the power consumed by the machine or developed by an engine.

  6. Fly wheels • The Fly wheel stores the excessive mechanical energy from the engine. • It stores the energy during power stroke and releases it during the other strokes. • Two types • Disk type • Rim type

  7. Types of flywheels • Rim type • I = mD2/4 • Disc type • I = mD2/8

  8. Important Terms • Maximum fluctuation of speed • It is the difference between the maximum & minimum speeds in a cycle. N1 – N2 • Coefficient of fluctuation of speed • It is the ratio of maximum fluctuation of speed to the mean speed • It is expressed as percentage of mean speed

  9. Energy stored in flywheel Or Iw2Cs E = mk2w2Cs Where, m = mass (kg) k = radius of gyration (m) [ k2 = D/4 for rim type k2 = D/8 for disc type] w = angular velocity of flywheel (rad/s) Cs = coefficient of fluctuation of speed (no unit) E = excessive energy (J) I = mass Moment of inertia (kg-m2)

  10. Session-07

  11. Energy in fly wheels problems Formulae • Excess energy, stored in flywheel, E = mk2w2Cs or Iw2Cs • Work done /cycle = area under the curve • Work done /cycle = Tmean x (angle for one cycle) • i.e. Net Area = Tmean x 4p (for 4 stroke engine)

  12. Coefficient of Fluctuation of Speed

  13. Energy Stored in a Flywheel

  14. A single cylinder 4 stroke gas engine develops20 KW at 300 rpm with work done by the gases during the expansion being 3 times thework done on the gases during compression.The work done during the suction & exhauststrokes is negligible. The total fluctuation ofspeed is 2% of the mean. The TMD may be assumed to be triangular in shape. Find themass moment of inertia of the flywheel.

  15. Given: Power = 20 kw N = 300rpm WE= 3xWC Cs = 0.04 4 stroke engine i.eq = 4p (2revs) I = ?

  16. Since the area above the mean turning moment line represents the maximum fluctuation of energy, therefore maximum fluctuation of energy,

  17. Energy in multi cylinder engine

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