Appendix B
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 defined 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*D2, where
Inertia is in
D is the cylinder diameter in cm
Taking into account material density, the formula can be rewritten as:
Inertia = .098 *ρ *L *D4,
where
ρis the density in kg/cm3
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, first 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/cm3
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..
Part void:
D = 3 inches = 7.6 cm
L = 1 inch = 2.5 cm
The inertia would be calculated as follows:
Inertia, cylinder = .098* .0028* 6.4* (10.1)4 = 18.1
Dukane Manual Part No. | Page 105 |
