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Velocity and acceleration

Unit 1<br>Dynamics of Machines

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Velocity and acceleration

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  1. DOM

  2. Velocity and Acceleration of the Reciprocating Parts in Engines

  3. Velocity and Acceleration of the Reciprocating Parts in Engines • The velocity and acceleration of the reciprocating parts of the steam engine or internal combustion engine (briefly called as I.C. engine) may be determined by graphical method or analytical method. • The velocity and acceleration, by graphical method, may be determined by one of the following constructions: • 1. Klien’s construction, • 2. Ritterhaus’s construction, • 3. Bennett’s construction. • We shall now discuss these constructions, in detail, in the following pages.

  4. Approximate analytical method for velocity and acceleration of the piston • Consider the motion of a crank and connecting rod of a reciprocating steam engine as shown in Figure Let OC be the crank and PC the connecting rod. Let the crank rotates with angular velocity of ω rad/s and the crank turns through an angle θ from the inner dead centre (briefly written as I.D.C). Let x be the displacement of a reciprocating body P from I.D.C. after timetseconds, during which the crank has turned through an angle θ.

  5. Approximate analytical method for velocity and acceleration of the piston • https://www.youtube.com/watch?v=RsuGFDcoB2Y&list=PLdLe0dTcWW-t1rz5BDBzZVv-wHy2MabGK&index=3

  6. Approximate analytical method for velocity and acceleration of the piston • Motion of a crank and connecting rod of a reciprocating steam engine. Let l = Length of connecting rod between the centres, r = Radius of crank or crank pin circle, φ = Inclination of connecting rod to the line of stroke PO, and n = Ratio of length of connecting rod to the radius of crank = l/r.

  7. Approximate analytical method for velocity and acceleration of the piston

  8. Velocity of the piston

  9. Velocity of the piston

  10. Acceleration of the piston

  11. Angular velocity and acceleration of the connecting rod • Consider the motion of a connecting rod and a crank as shown in Fig. 15.7.From the geometry of the figure, we find that CQ = l sinφ=r sinθ

  12. Angular velocity and acceleration of the connecting rod

  13. Angular velocity and acceleration of the connecting rod

  14. Angular velocity and acceleration of the connecting rod

  15. DYNAMIC FORCEANALYSISVelocity and Acceleration of Reciprocating Part • https://www.youtube.com/watch?v=RsuGFDcoB2Y&list=PLdLe0dTcWW-t1rz5BDBzZVv-wHy2MabGK&index=3

  16. DYNAMIC FORCEANALYSIS • Displacement of piston (x) = r[(1-cos θ)+sin2θ /2n] • Velocity of Piston (Vp) = • Acceleration of Piston (Ap) = • Angular velocity of connecting Rod (ωc ) = • Angular acceleration of connecting Rod (Ac) = - ω2 Sinθ/n

  17. DYNAMIC FORCEANALYSIS

  18. Session objectives • Motion analysis of slider Crank mechanism • How to calculate the displacement, velocity and acceleration. • Forces acting in a slider Crank mechanism • Torque in an engine

  19. Slider Crank mechanism- Analysis • Displacement of piston,x = • Velocity of piston, v = • Acceleration of piston, a =

  20. Motion Analysis Problem • The crank and connecting rod of a steam engine are 0.3 m and 1.5 m in length. The crank rotates at 180 r.p.m. Clockwise. Determine the velocity and acceleration of the piston when the crank is at 40 degrees from the inner dead centre position. Also determine the Position of the crank for zero acceleration of the piston. Given r=0.3 m, l = 1.5 m N = 180 rpm q = 40 Deg.

  21. To find • v • a • q = ? When a=0 • Solution • r=0.3 m, l = 1.5 m, N = 180 rpm, q = 40 Deg. • ω= π* N / 60 = π* 180/60 = 18.85 rad/s • Velocity of piston:

  22. Solution R=0.3 m, l = 1.5 m, N = 180 rpm, q = 40 Deg. • = π* N / 60 = π* 180/60 = 18.85 rad/s Acceleration of piston:

  23. Formulae • Angular displacement:

  24. Problems on Approximate analytical method for velocity and acceleration of the piston • .In a slider crank mechanism, the length of the crank and connecting rod are 150 mm and 600 mm respectively. The crank position is 60° from inner dead centre. The crank shaft speed is 450 r.p.m. (clockwise). Using analytical method, determine: 1. Velocity and acceleration of the slider, and 2. Angular velocity and angular acceleration of the connecting rod.

  25. Given : r = 150 mm = 0.15 m ; l = 600 mm = 0.6 m ; θ = 60°; N = 400 r.p.m or ω=π× 450/60 = 47.13 rad/sTo Find: Velocity and acceleration of the slider and Angular Velocity and Angular Acceleration of the connecting rod Solution: Using Formula: • Velocity of Piston (Vp) = • Acceleration of Piston (Ap) =

  26. Solution for Velocity and acceleration of the slider We know that ratio of the length of connecting rod and crank, n= l/r= 0.6 / 0.15 = 4

  27. Solution for Angular Velocity and Angular Acceleration of the connecting rod

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