Dynamic forces are associated with accelerating masses.
Inertia force, F_{1} = – m f_{g}
m = mass of body
f_{g} = acceleration of centre of mass of the body
I_{g} = moment of inertia about an axis passing through centre of mass G and perpendicular to plane of rotation of the body
a = angular acceleration of the body.
T_{g1}, T_{g2}, T_{g3} etc. = external torques on the body about centre of mass G
Thus a dynamic analysis problem is reduced to one requiring static analysis.
where k = radius of gyration
Velocity And Acceleration of Piston
If the crank OA rotates in the clockwise direction
l and r = lengths of connecting rod and crank
Let, × = displacement of piston from inner dead centre.
θ = angle turned by crank from inner dead centre.
n = l/r
then maximum value of sin2q can be unity, and (n^{2 }>>1), for large connecting rod.
So × = r (1 – cosθ)
This is the expression for a simple harmonic motion. Thus the Piston executes a simple harmonic motion when the connecting rod is large.
The negative sign indicates that the sense of angular acceleration of the rod is such that it tends to reduce the angle b.
Piston Effort (Effective Driving Force)
Let, A_{1} = area of Piston (cover end)
A_{2} = area of piston end
p_{1} = pressure on cover end
p_{2} = pressure on piston end
m_{1} = mass of reciprocating parts
Force on piston F_{p} = p_{1}A_{1} – p_{2}A_{2}
Inertia force; F_{b} = mf
Net force on piston F = F_{p} – F_{b}
Let, F_{t} = crank effort
F_{c} = force on connecting rod
F_{t }= F_{c} sin (θ + β)
T = F_{t} × r
The mass of connecting rod can be replaced by two point masses at two point, if it is ensured that the two masses together have the same dynamical properties as before.
FLYWHEEL
Function
Turning Moment Diagram
Turning Moment diagram for single cylinder four stroke engine
TM diagram for multicylinder engine
Fluctuation of Energy
From the two values of the energies of the flywheel corresponding to the position c, it is concluded that
a_{1} – a_{2} + a_{3} – a_{4} + a_{5} – a_{6} = 0
Fluctuation of Speed
Maximum fluctuation of speed
∴ Maximum fluctuation of energy
DE = Maximum energy – Minimum energy
We can also write
Here, I = Mass moment of inertia of the flywheel about its axis of
rotation
w_{max }= Maximum angular speed during cycle
w_{min} = Maximum angular speed during cycle
w_{mean} =
during cycle
Work done per cycle
Work done per cycle = T_{mean }× q
Work, T_{mean} is mean torque,
q is angle turned is one cycle
= 2p, in case of two stroke engine
= 4p, in case of 4 stroke engine
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Vibrations Doc  5 pages 
1. What is dynamics force analysis in mechanical engineering? 
2. How is flywheel used in mechanical engineering? 
3. What are the benefits of using flywheels in mechanical systems? 
4. How do engineers analyze the dynamics forces in mechanical systems? 
5. What are some practical applications of dynamics force analysis and flywheel in mechanical engineering? 
Vibrations Doc  5 pages 

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