Balancing Rotating Parts Machinery's Handbook, 31st Edition
203
M B
CG
Workpiece
CG
CG
Fixture
M A
M W
Lathe Fixture
M B
M B
r B r W
l 1
l 2
r A
r A
θ
θ
M A
M A
M
M W
M
A
W
Schematic View
Fig. 6. Usually a single counterbalancing mass is placed in one plane selected to be 180 degrees directly opposite the combined center of gravity of the workpiece 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 Fig. 6, 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. (7) (8) 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. Example: In Fig. 6 the combined weight of the workpiece and the fixture is 18.5 lb. The following dimensions were determined from the layout of the fixture and by calculating the centers of gravity: r W = 2 in.; r A = 6.25 in.; r B = 6 in.; l 1 = 3 in.; l 2 = 5 in.; and θ = 30 ° . Calculate the weights of the counterbalancing masses. . . M 6 3 185 2 8 1644 B = + = ^ h M r l W W = M r l l B B 1 1 2 + ^ h sin M r A = M r M r 2 A B B W W i −
sin r M r M r r l M r l l B w w 1 1 2 2 A B B i −
. 2 625 30 1644 6 185 2 986 lb . . . sin # # # # # # = − = ° ^ ^ h h h
^
lb (each weight)
M
w w
=
=
A
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