dynamics of machines by dr.k.srinivasan, professor, au-frg inst. for cad/cam, anna university topic...
TRANSCRIPT
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DYNAMICS OF MACHINESBy
Dr.K.SRINIVASAN,Professor,
AU-FRG Inst. for CAD/CAM,Anna University
Topic : Balancing of Rotating masses
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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
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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”
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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
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• 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
Rotating components for balancing
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Unbalanced force on the bearing –rotor system
Bearing 1 Bearing 2
Shaft withrotors
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Cut away section of centrifugal compressor
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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
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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.
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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.
NEED FOR BALANCING
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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.
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● 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
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Unbalance due to unequal distribution of masses
Unbalance due to unequal distance of masses
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. Types of Unbalance
Static Unbalance
Dynamic
Unbalance
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STATIC BALANCING(SINGLE PLANE BALANCING)
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Single plane balancing
Adequate for rotors which are short in length, such as pulleys and fans
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O2
m
r
F = m r 2
Magnitude of unbalance
Vibration occurs
Elasticity of the bearing
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m2
m1
m4
m3
x
y
1
2
3
m4r4 2
m1r1 2
m2r2 2
m3r3 2
Balancing of several masses revolving in the same plane using aSingle balancing mass
bearing
m b
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m1r1 2m2r2 2
m3r3 2
m4r4 2
m b r b 2
b
Graphical method of determination magnitude and Angular position of the balancing mass
Force vector polygon
O
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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.
Determination of magnitude and Angular position of the balancing mass
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Dynamic or "Dual-Plane" balancing
Dynamic balancing is required for components such as shafts and multi-rotor assemblies.
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m r 2
m r 2l
Brg A Brg B
Statically balanced but dynamically unbalanced
Load on each support Brg due to unbalance = (m r 2 l)/ L
r
r
Dynamic or "Dual-Plane" balancing
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On an arbitrary plane C
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Several masses revolving in different planesApply dynamic couple on the rotating shaft
Dynamic unbalance
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Balancing of several masses rotating in different planes
F a
F b
F c
F d
A B C D
L M
End view
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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 0 0
B Mb rb Mbrb lb Mbrb lb
C Mc rc Mcrc lc Mcrc lc
M Mm rm Mmrm d Mmrmd
D Md rd Mdrd ld Mdrdld
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la
lb
lc
ld
d
A B C D
L,Ref plane
M
Fc
Fb
Fa
Fd
Fm
F l
End viewside view of the planes
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Fc
Fb
Fa
Fd
Fm =?
F l =?
Couple polygon force polygon
Ca
Cc
Cd
Cb
Cm=Mmrmd
Fa
Fb
Fc
Fd
Fm
Fl=Ml rl
From couple polygon, by measurement, Cm = Mm X r m X dFrom force polygon, by measurement, Fl = Ml X rl
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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
Example :
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Plane Mass M kg
Radius r
cm
Force / 2, M r , kg. cm
Dist. From ref plane l , cm
Couple / 2 M r lkg cm 2
A Ma=? 8 8 Ma 0 0
B 18 6 108 10 1080
C 12.5 6 75 30 2250
D Md=? 8 8 Md ld=? 8 Md ld
A B C D10 cm
20 cm
l d
18 kg
12.5 kg
M a
=190 o =100o
End view
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A B C D
10 cm
20 cm
l d
18 kg
12.5 kg
M a
=190 o =100o
O
1080
2,250
8 Md ld= 2312 kg cm 2
O
108
75
8 Md =63.5 kg. cm
8 Ma = 78 kg .cm
Couple polygon force polygon
d= 203o
M d
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From the couple polygon, By measurement, 8 Md ld= 2,312 kg cm 2
Md ld = 2312 / 8 = 289 kg cm
d= 203o
From force polygon,
By measurement, 8 Md = 63.5 kg cm
8 Ma = 78.0 kg cm
Md = 7.94 kg
Ma = 9.75 kg
ld = 289 /7.94 = 36.4 cm
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Unbalanced force on the bearing –rotor system
Bearing 1 Bearing 2
Shaft withrotors
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Cut away section of centrifugal compressor
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Balancing machines:static balancing machinesdynamic balancing machines
Hard knife edge rails
Chalk mark
Thin disc
Measurement static unbalance:
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Static balancing machines:
Universal level used in static balancing machine
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A helicopter- rotor assembly balancer
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Field balancing of thin rotors :
Th
in
disc
Signal fromSine wave generator
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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
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Field balancing with 3-mass locations (without sine wave generator)
Required balancing mass , mb = mt [ad/dc]
2A1
A2A 3
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X (Mur)
1 2 3 1 2 30/n
/n
90o
180o
Mu r
M [ {1- (/n)2}2 +{2(/n)}2] ½ X=
Dynamic balancing machinesVibration amplitude versus rotating unbalance
Amplitude versus rotating speed Phase angle versus rotating speed
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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.
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CRADLE TYPE BALANCING MACHINE
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Pivoted-cradle balancing machine with specimen mounted
rotor
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•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
Gisholt – type balancing machine
Stroboscopeflashes light
Angle marked end plateattached to the rotor
stroboscope
voltmeter
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View of Precision Balance Machine