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 kg-cm2M 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 *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 kg-cm2Inertia, void = .098* .0028* 2.5* (7.6)4 = 2.3 kg-cm2Inertia, tool = Inertia, cylinder – Inertia, void = 16 kg-cm2

Dukane Manual Part No. 403-570-01

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Dukane 403570-01 user manual Moment of Inertia, Explanation of Inertia

403570-01 specifications

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