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### Balancing Rotating Fixtures Turning Operations on a Lathe Formulas and Calculator

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**Balancing Rotating Fixtures For Turning Operations on a Lathe Formulas and Calculator **

Manufacturing fixtures rotating at a high speed require balancing. Often it is assumed that the center of gravity of the work piece and fixture and of the counterbalancing masses are in the same plane; however, this is not usually the case. Counterbalancing masses are required in two separate planes to prevent excessive vibration or bearing loads at high speeds.

Usually a single counterbalancing mass is placed in one plane selected to be 180 degrees directly opposite the combined center of gravity of the work piece and the fixture. Two equal counterbalancing masses are then placed in the second counterbalancing plane, equally spaced on each side of the fixture.

Turning Lathe Fixture

Schematic View

Usually a single counterbalancing mass is placed in one plane selected to be 180 degrees directly opposite the combined center of gravity of the work piece and the fixture. Two equal counterbalancing masses are then placed in the second counterbalancing plane, equally spaced on each side of the fixture.

Referring to the illustration above, the two counterbalancing
masses M_{A} and the two angles θ are equal. For the design in this illustration, the following
formulas can be used to calculate the magnitude of the counterbalancing masses. Since
their angular positions are fixed by the design, they are not calculated.

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**Balancing Rotating Fixtures For Turning Operations on a Lathe Formulas**

Eq :

M_{B} = [ M_{W }r_{W} ( *l*_{1} + *l*_{2} ) ] / ( r_{B}* l*_{1} )

M_{A} = [(M_{B} r_{B} - M_{W} r_{W} ) / ( 2 r_{A} sin θ )

In these formulas M_{W} and r_{W} denote the mass or weight and the radius of the combined
center of gravity of the workpiece and the fixture.

Where:

M_{W} = Combined weight/Mass (lb, kg),

r_{W} = Radius (in, mm),

M_{A} = Mass (lb, kg),

r_{A} = Radius (in, mm),

M_{B} = Mass (lb, kg),

r_{B} = Radius (in, mm),

Reference:

Machinery's Handbook 30th edition

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