Review and summary

REVIEW AND SUMMARY

• The property of matter offering a resistance to any change of its state of rest or of uniform motion in a straight line is known as inertia.

• Inertia force is a fictitious force, which when acts upon a rigid body, brings it in equilibrium.

Inertia force = - Accelerating force = - m a

• Inertia torque is a fictitious torque, which when applied upon the rigid body, brings it in equilibrium position.

Inertia torque = - Externally applied torque = -Iα

• D'Alembert's principle states that the inertia forces and torques, and the external forces and torques acting on a body together result in statical equilibrium.

i.e., EF = 0 and EM = 0

The D'Alembert's principle is used to reduce a dynamic analysis problem into an equivalent problem of static equilibrium.

• Velocity and acceleration of the reciprocating parts in engines:

• Klien's construction for determining velocity and acceleration of the reciprocating parts in engines is also discussed in this chapter. 

• Forces on the reciprocating parts of an engine: 

1. Piston effort (FP):

(a) For horizontal reciprocating engines:

(b) For vertical reciprocating engines: 

(i) To find net load on the piston (F1):

where p1A1 = Pressure and cross-sectional area on the back end side of the piston.

P2A2 = Pressure and cross-sectional area on the crank end side of the piston, and

a = Cross-sectional area of the piston rod.

(ii) To find the inertia force of the reciprocating parts (FP):

2. Force acting along the connecting rod (FQ):

3. Thrust on the sides of cylinder walls (FN):

4. Crank-pin effort (FT):

5. Thrust on crankshaft bearing (FB):

6. Crank effort on the crankshaft (T):

• Simple pendulum:

where l = Length of the pendulum

• Compound pendulum:

where h = Distance of point of suspension from the C.G

• Equivalent length of a simple pendulum, which gives the same frequency as compound pendulum, is

• Equivalent dynamical system:

where m = Mass to be replaced by m, and m2,

l1 and l2 = Distance from C.G of mass m1 and m2 respectively, and

L = Total distance between the masses m1 and m2

• Correction couple (TC) is given by (Refer Fig. Error! Reference source not found.),

• Inertia force analysis in a reciprocating engine, considering the weight of connecting rod, can be determined both graphically and analytically.

• Inertia torque by analytical method:

Total torque exerted on the crankshaft, T = T1 + T2 + T3