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Dukane Manual Part No. 403-570-01
Page 105
Appendix B
USEFUL UNIT CONVERSIONS
1 in. = 2.54 cm = .025 m
1 lb. = 0.45 kg
1 cm = 0.39 in.
1 m = 39.4 in.
1 kg = 2.20 lb.
Moment of Inertia
Explanation of Inertia
The moment of inertia is a measure of the mass and the
mass distribution of the tool. It is dened mathemati-
cally as the product of the mass times the distance of
that mass from the axis of rotation squared. For a cyl-
inder spinning around its axis, the formula for the mo-
ment of inertia is:
Inertia = 1/8 *M*D
2
,
where
Inertia is in kg-cm
2
M is the mass in kg
D is the cylinder diameter in cm
Taking into account material density, the formula can
be rewritten as:
Inertia=.098*ρ *L *D
4
,
where
ρ is the density in kg/cm
3
L is the cylinder length in cm
Calculating the Moment
of Inertia
For spin welder applications, most tools will have a
geometry close to a cylinder with internal cutouts for the
parts. To estimate the inertia of such a tool, rst calculate
the inertia of a solid cylinder, then the inertia of the void
created for the part using the density of the tool material,
and then subtract the two values.
Example:
Aluminum tool with outside dimensions:
D = 4 in. = 10.1 cm
L = 2.5 in. = 6.4 cm
P = 0.1 lb/in.
3
(density of
Aluminum) = .0028 kg/cm
3
The inertia would be calculated as follows:
Inertia,
cylinder
= .098* .0028* 6.4* (10.1)
4
= 18.1 kg-cm
2
Inertia,
void
= .098* .0028* 2.5* (7.6)
4
= 2.3 kg-cm
2
Inertia,
tool
= Inertia,
cylinder
– Inertia,
void
= 16 kg-cm
2
Part void:
D = 3 inches = 7.6 cm
L = 1 inch = 2.5 cm