Machinery's Handbook, 31st Edition
202 Balancing Rotating Parts is selected to be 10 inches; calculate the magnitude of the counterbalancing mass and its position. In balancing plane B the counterbalancing mass is selected to be 10 lb; calculate its radius and position. Solution: For balancing plane A :
Balancing Plane A
M lb
r in.
b in.
θ deg.
Plane
Mrb cos θ
Mrb sin θ 240.0 − 339.4 − 1296.0 − 1395.4
Mrb 480 − 480 1296
1 2 3 A B
10 8 8 10 12 9
30
6
415.7 339.4
135 270
− 6 12
0.0
?
10
? ?
15 a
755.1
0
10
?
= ∑ Mrb cos θ
= ∑ Mrb sin θ
a 15 inches = distance c between planes A and B .
. 7551
. 13954
cos
sin
2
2
2
2
Mrb
Mrb
h
h
h
h
^
^
^
+ − ^
+
R
i
R
i
M M
= = =
=
10 15 ^
A
r c A
h
. 106
lb Mrb Mrb
A
. 7551 13954 h .
cos sin
x y
= − +
h
h
^
− − − ^ ^
− −
R R
i i
tan
=
i
A
h
^
118 25 ° ′
=
i
A
For balancing plane B :
Balancing Plane B
a in.
M lb
r in.
θ deg.
Plane
Mra cos θ
Mra sin θ
Mra
10 8 8 10 12 9
9
1 2 3
30
720
623.5
360.0 1187.9 − 324.0 1223.9
21
135 270
1680
− 1187.9
3 0
324
0.0
?
10
? ?
− 564.4
A B
10
?
15 a
= ∑ Mra cos θ
= ∑ Mra sin θ
a 15 inches = distance c between planes A and B .
. 10 15 5644 12239 . 2 + ^ ^ h h
cos
sin
2
Mra
Mra
2
2
h
h
h
^
^
^
+
−
R
i
R
i
r
=
=
M c B
B
. 8985
in.
= =
cos sin
. 5644 12239 .
x y
Mra Mra
= + −
h
h
^
− − − ^ ^
− −
i i
R R
tan
=
i
B
h
h
^
294 45
° ′
=
i
B
Balancing Lathe Fixtures.— Lathe fixtures rotating at a high speed require balancing. Often it is assumed that the center of gravity of the workpiece and fixture and of the coun terbalancing masses are in the same plane; however, this is not usually the case. Counter balancing masses are required in two separate planes to prevent excessive vibration or bearing loads at high speeds.
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