1. AU-FRG Inst. for CAD/CAM,
DYNAMICS OF MACHINES By
Dr.K.SRINIVASAN,
Professor,
AU-FRG Inst. for CAD/CAM,
Anna University
Topic : Balancing of Rotating masses

2. What is balancing of rotating members?
Balancing means a process of restoring a rotor which has unbalance to a balanced state by adjusting the mass distribution of the rotor about its axis of rotation

3. "is the process of attempting to improve the mass distribution
Balancing
"is the process of attempting to improve the mass distribution
of a body so that it rotates in its bearings without unbalanced centrifugal forces”

4. Mass balancing is routine for rotating machines,some reciprocating machines,
and vehicles
Mass balancing is necessary for quiet operation, high speeds , long bearing life, operator comfort, controls free of malfunctioning, or a "quality" feel

5. Rotating components for balancing
• Pulley & gear shaft assemblies
• Starter armatures
• Airspace
components
• High speed machine
tool spindles
• flywheels
• Impellers
• Centrifuge rotors
• Electric motor rotors
• Fan and blowers
• Compressor rotors
• Turbochargers
• Precision shafts
 crank shafts
 Grinding wheels
• Steam & GasTurbine
rotors

6. Shaft with
rotors
Bearing 1
Bearing 2
Unbalanced force on the bearing –rotor system

7. Cut away section of centrifugal compressor

11. Unbalance is caused by the displacement of the mass centerline from the axis of rotation.
Centrifugal force of "heavy" point of a rotor exceeds the centrifugal force exerted by the light side of the rotor and pulls the entire rotor in the direction of the heavy point.
Balancing is the correction of this phenomena by the removal or addition of mass

12. Benefits of balancing Increase quality of operation.
Minimize vibration.
Minimize audible and signal noises.
Minimize structural fatigue stresses.
Minimize operator annoyance and fatigue.
Increase bearing life.
Minimize power loss.

13. NEED FOR BALANCING Noise occurs due to vibration of the whole machine.
Rotating a rotor which has unbalance
causes the following problems.
The whole machine vibrates.
Noise occurs due to vibration of
the whole machine.
Abrasion of bearings may shorten
the life of the machine.

14. Rotating Unbalance occurs due to the following reasons.
● The shape of the rotor is unsymmetrical. ● Un symmetrical exists due to a
machining error. ● The material is not uniform, especially in
Castings.
● A deformation exists due to a distortion.

15. ● An eccentricity exists due to a gap of fitting
● An eccentricity exists due to a gap of fitting. ● An eccentricity exists in the inner ring of
rolling bearing.
● Non-uniformity exists in either keys or key
seats.
● Non-uniformity exists in the mass of flange

16. Unbalance due to
unequal distribution
of masses
unequal distance of masses

17. . Types of Unbalance Static Unbalance Dynamic Unbalance

18. (SINGLE PLANE BALANCING)
STATIC BALANCING
(SINGLE PLANE BALANCING)

19. Single plane balancing
Adequate for rotors which are short in length,
such as pulleys and fans

20.  Magnitude of unbalance F = m r 2 Vibration occurs m O2 r
Elasticity of the bearing

21. m3r3 2 m2r2 2 2 1 3 m1r1 2 m b m4r4 2 bearing
Balancing of several masses
revolving in the same plane using a
Single balancing mass
m3r3 2
m2r2 2 2 1 3
bearing
m1r1 2
m b
m4r4 2

22. Force vector polygon m4r4 2 m3r3 2 b m b r b 2 m2r2 2 m1r1 2
Graphical method of determination
magnitude and
Angular position of the balancing mass
m4r4 2
m3r3 2 b
m b r b 2
m2r2 2 O
m1r1 2
Force vector polygon

23. Determination of magnitude and Angular position of the balancing mass
m1r1 2 cos 1+ m2r2 2 cos  2
+ m3r3 2cos  3+ m4r4 2 cos  4
= mb cos b
m1r1 2 sin 1+ m2r2 2 sin  2
+ m3r3 2sin  3+ m4r4 2 sin  4
= mb sin b
magnitude ‘m b’ and position ‘b’ can be determined
by solving the above two equations.

24. Dynamic or "Dual-Plane" balancing
Dynamic balancing is required for components such as shafts and multi-rotor assemblies.

25. Load on each support Brg due to unbalance = (m r 2 l)/ L
Dynamic or "Dual-Plane" balancing
Statically balanced
but dynamically unbalanced
m r 2 r r
Brg A
Brg B l
m r 2
Load on each support Brg
due to unbalance = (m r 2 l)/ L

26. On an arbitrary plane C

27. Dynamic unbalance Several masses revolving in different planes
Apply dynamic couple on the rotating shaft 
Dynamic unbalance

28. A B C D L M Balancing of several masses rotating in different planes
F c
End view
F b 
F d
F a L M

29. A Ma ra Mara -la -Mara la L Ml rl Ml rl B Mb rb Mbrb lb Mbrb lb C Mc
Plane
Mass M
( kg)
Radius r
(cm)
Force / 2,
M r =F ,
(kg. cm)
Dist. From ref plane
l , (cm)
Couple / 2
M r l = C
(kg cm 2) A Ma ra
Mara
-la
-Mara la L
(Ref.plane) Ml rl
Ml rl B Mb rb
Mbrb lb
Mbrb lb C Mc rc
Mcrc lc
Mcrc lc Mm rm
Mmrm d
Mmrmd D Md rd
Mdrd ld
Mdrdld

30. A C B D M L, Fm la Fc lb lc Fb ld Fa d F l Fd End view Ref plane
side view of the planes

31. Fc Fm =? Fb Fa F l =? Fd Fd Fc Fm Fb Fl=Ml rl Fa force polygonCc Fd Fb Fc Fa Cb Fm Ca Cd Fb
Fl=Ml rl
Cm=Mmrmd Fa
F l =? Fd
Couple polygon
force polygon
From couple polygon, by measurement, Cm = Mm X r m X d
From force polygon, by measurement, Fl = Ml X rl

32. Example :
A shaft carries four masses in parallel planes A,B,C,&D in this order. The masses at B & C are 18 kg & 12.5 kg respectively and each has an eccentricity of 6 cm. The masses at A & D have an eccentricity of 8 cm. The angle between the masses at B & C is 100 o and that between B & A is 190o both angles measured in the same sense. The axial dist. between planes A & B is 10cm and that between B & C is 20 cm. If the shaft is complete dynamic balance,
Determine,
1 masses at A & D
2. Distance between plane C &D
3. The angular position of the mass at D

33. B C A D 18 kg  =100o  =190 o 12.5 kg End view M a Plane Mass M kg
10 cm
 =100o
 =190 o
20 cm
12.5 kg
l d
End view
M a
Plane
Mass M kg
Radius r cm
Force / 2,
M r ,
kg. cm
Dist. From ref plane
l , cm
Couple / 2
M r l
kg cm 2 A
Ma=? 8
8 Ma B 18 6
108 10
1080 C
12.5 75 30
2250 D
Md=?
8 Md
ld=?
8 Md ld

34. B C A D 18 kg  =100o  =190 o 12.5 kg M d M a force polygon
10 cm
 =100o
 =190 o
20 cm
12.5 kg
M d
l d
M a
force polygon
Couple polygon 75
2,250
108
8 Md =63.5 kg. cm
1080
d= 203o
8 Ma = 78 kg .cm O
8 Md ld= 2312 kg cm 2 O

35. From the couple polygon,
By measurement, Md ld= 2,312 kg cm 2
 Md ld = / 8 = 289 kg cm
d= 203o
From force polygon,
By measurement, 8 Md = 63.5 kg cm
8 Ma = 78.0 kg cm
Md = kg
Ma = kg
ld = 289 /7.94 = cm

36. Shaft with
rotors
Bearing 1
Bearing 2
Unbalanced force on the bearing –rotor system

37. Cut away section of centrifugal compressor

41. Balancing machines: Measurement static unbalance:
static balancing machines
dynamic balancing machines
Measurement static unbalance:
Hard knife edge rails
Thin disc
Chalk mark

42. Static balancing machines:
Universal level used in static balancing machine

43. A helicopter- rotor assembly balancer

44. Field balancing of thin rotors :
Thin disc
Signal from
Sine wave generator

45. Required balancing mass , mb = mt [oa/ab]
Oscilloscope signal
Required balancing mass , mb = mt [oa/ab]
angular position of the mass = 
During field balancing of thin disc using sine wave generator, the measured amplitude of vibration without trial mass is 0.6 mm and its phase angle is 30o from the reference signal. With trail mass attached, the amplitude is 1.0mm and its phase angle is 83o from the reference signal. Determine the magnitude and position of the required balancing mass

46. Field balancing with 3-mass locations (without sine wave generator)
Required balancing mass , mb = mt [ad/dc]

47. M [ {1- (/n)2}2 +{2(/n)}2] ½ X=
Dynamic balancing machines
Vibration amplitude versus rotating unbalance
Mu r
M [ {1- (/n)2}2 +{2(/n)}2] ½ X=
180o X
(Mur) 
90o 1 2 3 1
/n 2 3
/n
Amplitude versus rotating speed
Phase angle versus rotating speed

48. Pivoted – carriage balancing machine
Plane 1 coincides with pivot plane.
Vibration levels as functions of angular position plotted.
Minimum vibration level angle noted.
Magnitude of trial mass varied by trial and error to reduce vibration.
Repeated with plane 2 coinciding with the pivot plane.

49. CRADLE TYPE BALANCING MACHINE

50. Pivoted-cradle balancing machine with specimen mounted
rotor
Pivoted-cradle balancing machine with specimen mounted

51. Gisholt – type balancing machine
stroboscope
Stroboscope
flashes light
Angle marked end plate
attached to the rotor
voltmeter
Rotor mounted in spring supported half bearings.
Vibration of bearing in particular direction used as direct measure of amount of unbalance in the rotor.
Effect of unbalances in two planes separated by two electrical circuits one for each reference plane

52. View of Precision Balance Machine