DYNAMICS OF MACHINESBy

Dr.K.SRINIVASAN,Professor,AU-FRG Inst. for CAD/CAM,Anna University

Topic : Balancing of Rotating masses

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

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

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

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 shaftscrank shaftsGrinding wheels

Steam & GasTurbine rotors

Unbalanced force on the bearing rotor systemBearing 1Bearing 2Shaft withrotors

Cut away section of centrifugal compressor

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

Benefits of balancingIncrease 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.

Rotating a rotor which has unbalancecauses 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

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.

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

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

. Types of Unbalance Static Unbalance Dynamic Unbalance

STATIC BALANCING(SINGLE PLANE BALANCING)

Single plane balancing

Adequate for rotors which are short in length, such as pulleys and fans

O2mrF = m r 2Magnitude of unbalanceVibration occursElasticity of the bearing

123m4r4 2m1r1 2m2r2 2m3r3 2Balancing of several masses revolving in the same plane using aSingle balancing massbearing m b

m2

m1

m4

m3

x

y

m1r1 2m2r2 2m3r3 2m4r4 2m b r b 2bGraphical method of determination magnitude and Angular position of the balancing massForce vector polygonO

m1r1 2 cos 1+ m2r2 2 cos 2 + m3r3 2cos 3+ m4r4 2 cos 4 = mb cos bm1r1 2 sin 1+ m2r2 2 sin 2 + m3r3 2sin 3+ m4r4 2 sin 4 = mb sin bmagnitude m b and position b can be determined by solving the above two equations.Determination of magnitude and Angular position of the balancing mass

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

m r 2m r 2lBrg ABrg B Statically balanced but dynamically unbalancedLoad on each support Brg due to unbalance = (m r 2 l)/ LrrDynamic or "Dual-Plane" balancing

On an arbitrary plane C

Several masses revolving in different planesApply dynamic couple on the rotating shaftDynamic unbalance

Balancing of several masses rotating in different planesF aF bF cF dABCDLMEnd view

PlaneMass 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)AMaraMara-la-Mara la

L(Ref.plane)MlrlMl rl00BMbrbMbrblbMbrb lbCMcrcMcrclcMcrc lcMMmrmMmrmdMmrmdDMdrdMdrdldMdrdld

lalblclddABCDL,Ref planeMFcFbFaFdFmF lEnd viewside view of the planes

FcFbFaFdFm =?F l =?Couple polygonforce polygonCaCcCdCbCm=Mmrmd FaFbFcFdFmFl=Ml rl

From couple polygon, by measurement, Cm = Mm X r m X dFrom force polygon, by measurement, Fl = Ml X rl

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 DExample :

ABCD10 cm20 cml d18 kg12.5 kgM a =190 o =100oEnd view

PlaneMass M kgRadius r cmForce / 2, M r , kg. cmDist. From ref plane l , cmCouple / 2 M r lkg cm 2AMa=? 8 8 Ma00B18 6108101080C12.5 6 75302250DMd=? 88 Mdld=?8 Md ld

ABCD10 cm20 cml d18 kg12.5 kgM a =190 o =100oO10802,2508 Md ld= 2312 kg cm 2

O108758 Md =63.5 kg. cm8 Ma = 78 kg .cmCouple polygonforce polygond= 203oM d

From the couple polygon, By measurement, 8 Md ld= 2,312 kg cm 2

Md ld = 2312 / 8 = 289 kg cm d= 203oFrom 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

Unbalanced force on the bearing rotor systemBearing 1Bearing 2Shaft withrotors

Cut away section of centrifugal compressor

Balancing machines:static balancing machinesdynamic balancing machinesHard knife edge railsChalk markThin discMeasurement static unbalance:

Static balancing machines:Universal level used in static balancing machine

A helicopter- rotor assembly balancer

Field balancing of thin rotors :Thin discSignal fromSine wave generator

Oscilloscope signalRequired 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

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

2A1A2A3

X (Mur)

1231230/n/n90o180o Mu r M [ {1- (/n)2}2 +{2(/n)}2]

X=Dynamic balancing machinesVibration amplitude versus rotating unbalanceAmplitude versus rotating speedPhase angle versus rotating speed

Pivoted carriage balancing machinePlane 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.

CRADLE TYPE BALANCING MACHINE

Pivoted-cradle balancing machine with specimen mountedrotor

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 planeGisholt type balancing machineStroboscopeflashes lightAngle marked end plateattached to the rotorstroboscopevoltmeter

View of Precision Balance Machine