# Inertia force of a reciprocating masses

hi all!
I am learning the derivation of the formula of the inertia force of reciprocating masses, which is a typical formula that I am sure all of you must know.
F=mrw^2{cosB+(cos2B)/n}
I know that the cosB term is called the 1st harmonic, and the cos2B term is the 2nd harmonic.
Also, I know that this is not an exact formula, since a approximation was made in the derivation. That, n>>l, right?
But I cannot see if without the assumption, what will be the relation?
I am told that there should be some higher order terms after mw^2{cosB+(cos2B)/n}. But I don't see what they are and how they are produced. Is that something like Taylor series is used in order to produce the higher order terms??
I am confused.

hi all!
I am learning the derivation of the formula of the inertia force of reciprocating masses, which is a typical formula that I am sure all of you must know.
F=mrw^2{cosB+(cos2B)/n}
I know that the cosB term is called the 1st harmonic, and the cos2B term is the 2nd harmonic.
Also, I know that this is not an exact formula, since a approximation was made in the derivation. That, n>>l, right?
But I cannot see if without the assumption, what will be the relation?
I am told that there should be some higher order terms after mw^2{cosB+(cos2B)/n}. But I don't see what they are and how they are produced. Is that something like Taylor series is used in order to produce the higher order terms??
I am confused.

According to "Internal Combustion Engines Applied Thermosciences" the equation you reference includes a series expansion approxmation [(1 - E) ^(1/2) is approxmately (1 - E/e)] to simplify the estimation of piston displacement as a function of crank angle.

The equation I have for force is:

F=maω^2 (cos⁡(β) + a/l cos(2β))

Where:
F is the instantaneous inertia force
m is the effecting rotating mass of the piston and connecting rod
a is the radius of the crankshaft
ω is the rotational velocity of the crankshaft in radians per unit time
β is the instantaneous crank angle
l is the length of the connecting rod

Ranger Mike