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This application note presents formulas for calculating
reflected load parameters.
The mechanical systems used in motion control applications can be divided into four basic
categories: direct, gear, belt-pulley and leadscrew. Reflecting parameters back to the motor shaft
eases the calculations necessary for sizing and selecting.
Cylinder Inertia
The first formula is for calculating the inertia of a cylinder. This is important since many mechani-
cal components can be calculated using this formula.
The inertia of a solid cylinder can be calculated if either the weight and radius, or the density and
radius and length are known.
The inertia of a hollow cylinder can be calculated if the weight and radius are known, or the densi-
ty and radius and length are known.
Application Notes
Mechanics
For known weight and radius: J
For known density, radius and length: J
Where:
J
=
inertia (lb-in-s
L
W =
weight (lb)
r
=
radius (in)
l
=
length (in)
p =
density of material (lb/in
g =
gravitational constant (386 in/s
For known weight and radius: J
For known density, radius and length: J
Where:
J
=
inertia (lb-in-s
L
W =
weight (lb)
r
=
outside radius (in)
o
r
=
inside radius (in)
i
l
=
length (in)
p =
density of material (lb/in
g =
gravitational constant (386 in/s
Page 7
= 1 W r
L
2
2 g
4
= 1 πlpr
L
2
g
)
2
)
3
)
2
= 1 W ( r
+ r
L
2
2
)
o
i
2 g
= π lp ( r
L
4
o
2 g
)
2
)
3
)
2
- r
4
)
i
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