# Inertia force of a reciprocating masses

1. Sep 21, 2005

### hanson

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.

2. Nov 1, 2010

### Gary C

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

3. Nov 1, 2010

### Ranger Mike

question- are you mixing rotating mass and reciprocating mass?
example only big end pf con rod is rotation
the piston end is reciprocating
will these not require different formulas to measure true inertia ?

4. Nov 1, 2010

### Gary C

There is a mix of the mass. The mass used in the equation should include the mass of all reciprocating components (piston, rings, and if employed, piston rod and cross-head) and a portion (estimated at 2/3) of the mass of the connecting rod. The inertia forces of the crankshaft should be evaluated separately as it is pure rotational and the inertia forces are dependent on the geometry of any counter weights. The most common use of the equation above is for calculating bearing loads and rod load reversal angles to ensure proper lubrication.