Power Transmission
Machine Design Equations and Calculators

  Flywheel Mass, Size Design Equations and Calculator

Preview: Flywheel Mass, Size Design Calculator

The torque-angle relationship for an engine or machine depends on the the amount of work required. The large variation that is possible between different machine designs shows that dynamic measurement or kinematic analysis is necessary to determine the torque fluctuation. It is often necessary, however, to come up with a rough estimate for preliminary design purposes or for checking the reasonableness of calculated values. For these purposes, the energy variation for a machine or internal-combustion engine can be estimated by:

Energy equation variation flywheel

U = 0.5 J ( ω²_max - ω²_min )

Polar-mass moment of inertia Fly Wheel. This inertia includes the flywheel inertia and the inertia of all rotating parts, referred to the flywheel speed by multiplying by the square of the ratio of the shaft speeds.

J = U / ( ω²_avg C_s )

Coefficient of Speed Variation of a Flywheel

C_s = ( ω_max - ω_min ) / ω_avg

Suggested Design Values for the Coefficient of Speed Fluctuation C_s

Required speed uniformity	Cs
Very uniform	≤ 0.003
Moderately uniform	0.003-0.012
Some variation acceptable	0.012-0.05
Moderate variation	0.05-0.2
Large variation acceptable	≥ 0.2

The coefficient of energy variation C_u can be approximated for a two-stroke engine with from 1 to 8 cylinders using the equation:

C_u = 7.46 / ( N_c + 1 )³

Coefficient of energy variation for a four-stroke engine with from 1 to 16 cylinders using the two-branched equation:

C_u = 0.8 / ( N_c - 1.4 )^1.3 - 0.015

Flywheel Weight:

W = J g / r²_a

Cross Sectional Area of Flywheel:

A = J g / ( 2 π ρ r³_a )

Power required :

P = T ω

Where:

J = Polar-mass moment of inertia, Ib · s² · ft (N · s² · m)
U = Energy Variation, difference between the flywheel energy at maximum speed and at minimum speed, Ib · ft (J)
N_c = Number of cylinders
C_u = Coefficient of energy variation
C_s = Uniformity Speed Constant
K = 33 000 lb · ft · rpm/hp
ω = Rotational speed, rad/s
ω_avg = Average of ω_max and ω_min , rad/s
P = Power, hp (W)
g = Gravity 9.81 m/s²
D = Diameter m
r_a = radius m
W = Mass kN
A = Cross sectional Area m²
ρ = Material Density kg/m³
T = Torque J ( 1 ft-lb = 1.355817948 J)

Typical Machine Power Cycle