Chapter 38
Balancing of
machines
. 2)
3
Balancing of Rotating masses
attached
3 maner to
shaft AB
rotating with w
Fi =
-Mia i =
Mir ; wa
{
radid acceleration of particle i
ai--r ; WC Eads the
lacting shaft
[F =
[mr wh) =
Sum
of faces produced
al
by mosses
~
y
Reaction introduced ot
bearings A and B--RA and RB
A RA RB
·M
=> 도 FE +
m3
⑧
裴 で “品 ℃ _ 昌
M1
%
ใ 、
=
n
= ƩF =
VI ƩFG は + (EFY
* Also
bending moments distance ding zo
[M =
zmr zw2/vector Summotion (
w2 imo
[[Mx
2 Fx xz 2mrt
Anolythical
~ = =
[My = [Fy xz = 2mrz we Go
= Ʃµ = V / EM 1 +
R
IEMy
+
-For er
,
bearing
A considered or
reference plane ,
Reaction of
Bearing
B /RB) :
RX( = [Mt =
R = distance between A and B
* Stotic balonce ([F 0) =
~
If all maner in some
plans [M =
LxEF =
0
~
If masses in
planes , additional
dynamic
balance required ?
*
Dynamuc Bolance (IM = o)
Complete Static
Balance
only if Dynamic
balance
satified!
=>
-
+ or
ช้
, An example
DATA
>
0
_
Z z
-
Plans mr mr
^ 0,03 -0
,
2 -
, 006
0 ㆁ
W = Goo sys 048 260
°
α 0 .
04 1 ,
2 0
,
20 rad/S
reference Plans
=
3
°
0
, 043 6 6 .
,104
0
120
* Forces
2 = Emruflo = whe mr coso = (or [0 ·
,
03 -
1 + 0
.
04 (1260 % + 00656(120 % ]
= [Fx =
2 187N
,
2 Fy = Wh z mr eino = (20NK T0 03 .
,
.
0 + 0. 04-sin1260) + 0, 045 sin 1120
°
1)
Ʃ }= - 1, 663 N
= ƩF = 2 FSN,
* Moment
ZMAx = w2z mrz iin0 = - .. = [ Max = 213 ,
4 Nm
2 zmrz we whimrego Kor
&
E-0 006 1+ 048 un 1260) + 117 en 120
May co
= = = .
0 , 0
. ,
287 34 Nm
EMay
= -
= ,
=> En =
358 ,
of Nm
Reation ot RA ? EF RA RB
bearing
② B *
= +
EMN 3
m=
in OB
-
88, 92 v
4 di -
:
RB =
µ 3 ZFA= RAGOOA T RB COG OB
{
between A, B
length f, RACa0a = [Fx- RisCes OB
Q2 N
Em-119
=
81N
x-dir RBCO
,
and R OABB
I Fy
=
=
= 2 RB = V=
1 1 hg , α N =
Ra ein 0t = -
90 , 581
= RA = 151, 95N
Balancing of
machines
. 2)
3
Balancing of Rotating masses
attached
3 maner to
shaft AB
rotating with w
Fi =
-Mia i =
Mir ; wa
{
radid acceleration of particle i
ai--r ; WC Eads the
lacting shaft
[F =
[mr wh) =
Sum
of faces produced
al
by mosses
~
y
Reaction introduced ot
bearings A and B--RA and RB
A RA RB
·M
=> 도 FE +
m3
⑧
裴 で “品 ℃ _ 昌
M1
%
ใ 、
=
n
= ƩF =
VI ƩFG は + (EFY
* Also
bending moments distance ding zo
[M =
zmr zw2/vector Summotion (
w2 imo
[[Mx
2 Fx xz 2mrt
Anolythical
~ = =
[My = [Fy xz = 2mrz we Go
= Ʃµ = V / EM 1 +
R
IEMy
+
-For er
,
bearing
A considered or
reference plane ,
Reaction of
Bearing
B /RB) :
RX( = [Mt =
R = distance between A and B
* Stotic balonce ([F 0) =
~
If all maner in some
plans [M =
LxEF =
0
~
If masses in
planes , additional
dynamic
balance required ?
*
Dynamuc Bolance (IM = o)
Complete Static
Balance
only if Dynamic
balance
satified!
=>
-
+ or
ช้
, An example
DATA
>
0
_
Z z
-
Plans mr mr
^ 0,03 -0
,
2 -
, 006
0 ㆁ
W = Goo sys 048 260
°
α 0 .
04 1 ,
2 0
,
20 rad/S
reference Plans
=
3
°
0
, 043 6 6 .
,104
0
120
* Forces
2 = Emruflo = whe mr coso = (or [0 ·
,
03 -
1 + 0
.
04 (1260 % + 00656(120 % ]
= [Fx =
2 187N
,
2 Fy = Wh z mr eino = (20NK T0 03 .
,
.
0 + 0. 04-sin1260) + 0, 045 sin 1120
°
1)
Ʃ }= - 1, 663 N
= ƩF = 2 FSN,
* Moment
ZMAx = w2z mrz iin0 = - .. = [ Max = 213 ,
4 Nm
2 zmrz we whimrego Kor
&
E-0 006 1+ 048 un 1260) + 117 en 120
May co
= = = .
0 , 0
. ,
287 34 Nm
EMay
= -
= ,
=> En =
358 ,
of Nm
Reation ot RA ? EF RA RB
bearing
② B *
= +
EMN 3
m=
in OB
-
88, 92 v
4 di -
:
RB =
µ 3 ZFA= RAGOOA T RB COG OB
{
between A, B
length f, RACa0a = [Fx- RisCes OB
Q2 N
Em-119
=
81N
x-dir RBCO
,
and R OABB
I Fy
=
=
= 2 RB = V=
1 1 hg , α N =
Ra ein 0t = -
90 , 581
= RA = 151, 95N
