1. BA 7764-11, 1 Rigid Balancing Improving the mass distribution of rigid rotors to reduce residual unbalance at service speed!

2. BA 7764-11, 2 Contents Definition Types of unbalance Unbalance effects Reasons for doing balancing Results of unbalance Causes of unbalance Balancing methods Single-plane, two-plane and multi-plane balancing Sensitivity matrix approach Evaluating the balance quality Balancing equipment Industries using balancing ISO standards

3. BA 7764-11, 3 Definition of Balancing ISO 1925: Mechanical Vibration - Balancing - Vocabulary Balancing:Procedure by which the mass distribution of a rotor is checked and, if necessary, adjusted to ensure that the residual unbalance or the vibration of the journals and/or forces on the bearings at a frequency corresponding to service speed are within specified limits. Unbalance:That condition which exists in a rotor when vibratory force or motion is imparted to its bearings as a result of centrifugal forces. or in more common terms Balancing: Procedure to improve the mass distribution of a rotating object so when it rotates, its bearings are not subjected to excessive periodic forces at the fundamental frequency. Unbalance:A rotor is not completely balanced when the center of gravity axis does not coincides with the rotational axis as prescribed by construction.

4. BA 7764-11, 4 Types of Unbalance - Static Unbalance DD E:Center of gravity displacement S:Center of gravity U:Unbalance mass D-D:Shaft axis T-T:Center of gravity axis TT E  Static Unbalance If an unbalance is added to a completely balanced rotor in the same radial plane as the center of gravity, this constitutes a static unbalance. This unbalance causes a parallel displacement of the center of gravity axis from the rotational axis. S FUFU U

5. BA 7764-11, 5 Types of Unbalance - Couple Unbalance Couple Unbalance If two equal unbalances are added to a completely balanced rotor at the same radius in two different planes exactly opposite one another, they constitute a couple unbalance. In this case the center of gravity axis is inclined to the rotational axis and intersects it at the center of gravity of the rotor. DD E:Center of gravity displacement S:Center of gravity U:Unbalance mass D-D:Shaft axis T-T:Center of gravity axis T T  S F U1 F U2 U1 U2 U1 = U2

6. BA 7764-11, 6 Types of Unbalance - Quasi-static Unbalance Quasi-static Unbalance A combination of static and couple unbalance existing in most rotors. In this case the center of gravity axis is inclined to the rotational axis and intersects it at a point other than the center of gravity of the rotor. DD E:Center of gravity displacement S:Center of gravity U:Unbalance mass D-D:Shaft axis T-T:Center of gravity axis T T  S F U1 F U2 U1 U2 U1 <> U2

7. BA 7764-11, 7 Types of Unbalance - Dynamic Unbalance Dynamic Unbalance A combination of static and couple unbalance existing in most rotors. In this case the center of gravity axis is inclined to the rotational axis but does not intersects it. DD E:Center of gravity displacement S:Center of gravity U:Unbalance mass D-D:Shaft axis T-T:Center of gravity axis T T  S F U1 F U2 U1 U2 U1 <> U2

8. BA 7764-11, 8 Unbalance Effects The effects of unbalance will be: Displacement of the center of gravity Centrifugal forces created during rotation Unbalance: Specific unbalance or center of gravity eccentricity: Centrifugal force: e:Center of gravity displacement r:Radius to unbalance mass S:Center of gravity u:Unbalance mass m:Rotor mass F:Centrifugal force  F u S e r m

9. BA 7764-11, 9 Reasons for doing Balancing Optimal design Better performance Cost-effective operation Longer service life Increased safety It is estimated that more than 50% of all vibration problems in machinery can be traced to one single cause: UNBALANCE Quality balancing leads to:

10. BA 7764-11, 10 Results of Unbalance (1) Fatigue fractures Increased mech- anical looseness Reduction of the utility value Impairment of operational safety Reduced perceived quality Rotor unbalance Centrifugal forces and moments High dynamic bearing loading

11. BA 7764-11, 11 Results of Unbalance (2) Higher dynamic bearing loading –Speeds up wear and shortens service life time –Makes use of lighter/cheaper constructions of bearing types impossible –Makes high service speeds impossible/undesirable Fatigue fracture –Fracture of housings, associated parts and foundations –Breaking of rotating shaft components –Makes service speeds near resonance frequencies dangerous Increased mechanical looseness –Screws, bolts and key couplings loosened by excessive shaking Reduction of the utility value –Diminution of the operational accuracy

12. BA 7764-11, 12 Results of Unbalance (3) Impairment of operational safety and comfort –Physical damage to operators and bystanders –Increased annoyance and human fatigue –Decreased human comfort Reduced perceived quality –Excessive noise and vibration indicate poor manufacturing quality and/or wear-down

13. BA 7764-11, 13 Causes of Unbalance (1) Material faults –Blow-holes in cast components –Non-homogeneous material density –Uneven material thickness etc. Construction and design errors –Components not symmetric –Unmachined surfaces on the rotor –Variations in roundness and construction due to coarse tolerances etc. Manufacturing and assembly errors –Misshaping from welding and casting faults –Shrinking after welding or soldering –Permanent deformation caused by relieved stress –Stress caused by uneven tightening of bolts and screws etc.

14. BA 7764-11, 14 Causes of Unbalance (2) Faults during operation –Erosion or corrosion of the rotor –Material build-up on impellers –Thermal deformation of hot gas exhaust fans –Blade fracturing on turbine rotors –Wear on grinding wheels –Displacement of rotor parts caused by centrifugal force –General wear etc. Errors and faults can be reduced, but they can never be eliminated to the extent that balancing becomes unnecessary. Faults which occur during operation over a long period of time are especially unavoidable.

15. BA 7764-11, 15 Balancing Methods - Overview Balancing Balancing MachineIn-situ Balancing RigidElastic Single-planeTwo-planeMulti-plane

16. BA 7764-11, 16 Balancing Methods Two methods are available for accurately balancing rotors: Balancing on a permanently installed balancing machine –Primarily used during the manufacturing stage on individual parts (fast and efficient) –Allows “direct” balancing (potentially higher accuracy) Balancing the rotors in their fully assembled, operational state (Field Balancing) –Provides a practical efficient method for test facilities and plant maintenance to balance completely assembled machines –In-situ balancing: No need for dismantling the machine and transporting the rotor to a balancing machine (time and cost savings) –Generally lower capital investment –Operationally induced changes can be measured and compensated (e.g. thermal influences, centrifugal forces, assembly-induced unbalance) –Higher flexibility regarding rotor weights and dimensions

17. BA 7764-11, 17 Rigid Balancing ISO 1925: Mechanical Vibration - Balancing - Vocabulary Rigid rotor:A rotor is considered to be rigid when its unbalance can be corrected in any two (arbitrarily selected) planes. After the correction, its residual unbalance does not change significantly (relative to the shaft axis) at any speed up to the maximum service speed and when running under conditions which approximate closely to those of the final supporting system. Note:A rotor which qualifies as a rigid rotor under one set of conditions, such as service speed and initial unbalance, may not qualify as rigid under other conditions. Definition:Balancing of rotors that can be considered to be rigid (ISO 1925)

18. BA 7764-11, 18 Elastic Balancing Definition:Balancing of rotor that cannot be considered to be rigid due to elastic deflection (ISO 1925). Such rotors are called elastic or flexible rotors. Flexible rotors will exhibit unbalance condition changes as a result of changes in centrifugal forces caused by changes in rotational speed Rotors with reversible unbalance are shaft-elastic rotors as opposed to plastic rotors that maintain a certain degree of deformation Shaft-elastic rotors are operated either close to or above one of their critical speeds At their critical speeds, shaft-elastic rotors will have their maximum deflections due to a summation of natural modes As a rule of thumb, 2 measuring planes and 2+n correction planes are sufficient for balancing a shaft-elastic rotor, where n is the number of significant critical speeds. Flexible rotors are often found in large power-generating and process machines such as turbines, pumps and generators

19. BA 7764-11, 19 Single-plane [Static] Balancing - Overview Definition:Procedure by which the mass distribution of a rigid rotor is adjusted to ensure that the residual static unbalance is within specified limits (ISO 1925). Static unbalance is corrected in a single radial correction plane of the rotor and as close as possible to the plane of the center of gravity. Therefore Static Balancing is also called Single-plane Balancing. Static unbalance can be corrected without measuring it during rotation using knife-edges or roller stands. However, far better accuracy is obtained by measuring the unbalance during rotation. Static balancing is often sufficient for narrow rotors like: –fans, ventilators, grinding disks, pulleys, flywheels, clutches, gears, impellers etc. A rotor being completely statically balanced is not necessarily dynamically balance

20. BA 7764-11, 20 Single-plane Balancing - Measurement Procedure Balance quality; Measurement geometry/plane/points/directions; Service speed; Machine data; Test/operator information; Analyzer setup etc. Measure initial vibration/unbalance. Is balancing required? Attach/remove a trial weight and measure the resulting vibration/unbalance. Skipped for trim balancing! Document and save results Measure residual vibration/unbalance. Is further balancing required? Calculate correction weight’s mass and position. Attach/remove correction weight. Trial Run Verification Run Reporting Project Setup Initial Run OK Y N N Y Trim Calculation

21. BA 7764-11, 21 Single-plane Balancing - Graphic Evaluation VRVR VCVC Notation: V O :Original unbalance V T :Trial weight effect V R :Resultant of V O and V T V C :Required result of correction weight M C :Correction mass M T :Trial weight mass  C :Correction angle relative to the trial weight  T :Trial weight angle  O :Original unbalance angle Correction formulas: VOVO OO VTVT VTVT Single Plane

22. BA 7764-11, 22 Single-plane Balancing - Limitations As a rule of thumb, single-plane balancing is sufficient for disc-shaped rotors, provided the disc is accurately mounted perpendicular to the shaft axis and any vibrations from the design and construction drawings are small. At high rotational speeds, disc-shaped rotors may require two-plane balancing. If significant amount of couple unbalance is present, two-plane balancing must be performed. The longer the rotor - compared to its diameter - the more likely there is significantly couple unbalance. Example requiring dynamic balancing: D D T T

23. BA 7764-11, 23 Two-plane [Dynamic] Balancing - Overview Definition:Procedure by which the mass distribution of a rigid rotor is adjusted to ensure that the residual dynamic unbalance is within specified limits (ISO 1925). Dynamic unbalance is corrected in at least two radial correction planes of the rotor. Therefore Dynamic Balancing is also called Two- plane Balancing. Dynamic unbalance only becomes apparent when the rotor is rotating and must consequently be corrected by measuring it during rotation. Dynamic balancing is normally required on wide rotors like: –paper machine rolls, centrifuge drums, electric motors and generators, compressors and turbines, crushing and cutting rotors, machine tool spindles, grinding rolls, fans and blowers with longer distances between ends etc. A rotor being completely dynamically balanced will also be in completely statically balance

24. BA 7764-11, 24 Two-plane Balancing - Measurement Procedure Balance quality; Measurement geometry/planes/points/directions; Service speed; Machine data; Test/operator information; Analyzer setup etc. Measure initial vibration/unbalance in both planes. Is balancing required? Attach/remove a trial weight in the other plane and measure the resulting vibration/unbalance in both planes. Skipped for trim balancing! Document and save results Measure residual vibration/unbalance. Is trim balancing required? Trial Run 1 Calculation Reporting Project Setup Initial Run OK Y N N Y Trim Trial Run 2 Verification Run Attach/remove a trial weight in one of the planes and measure the resulting vibration/unbalance in both planes. Skipped for trim balancing! Calculate the correction weights’ mass and position. Attach/remove correction weights.

25. BA 7764-11, 25 Two-plane Balancing - Graphic Evaluation V 0,2  O,2 Plane 1Plane 2  O,1 V O,1 Initial Unbalance V R,1 V T,1 V R,1 Trial Mass Plane 1 V R,2 V T,2 V R,2 Trial Mass Plane 2 V T,1 V T,2 V T,1 Resultant Vectors Correction: Add correction weights in plane 1 and 2 - based on the effects of the trial weights - in order to compensate out the initial unbalance vectors V O,1 and V O,2

26. BA 7764-11, 26 Two-plane Balancing - Limitations If a rotor has almost exclusively static unbalance, a two-plane balancing should not be performed: –In best case the balancing is not optimal: two correction masses must be used and they are significantly larger than for single-plane balancing –In worst case, the balancing procedure will also give quite erroneous results Single-plane balancing should be done, if a two-plane balancing shows: –The trial vector and the influence vector are in approximately the same direction in each measuring plane –The trial vector and the influence vector are of approximately the same length –The permissible balancing and vibration tolerances can be achieved at both measuring planes by attaching one correction mass in only one correction plane –The calculated correction masses are very large and approximately 180° apart indicating a very large couple unbalance

27. BA 7764-11, 27 Multi-plane Balancing - Overview Definition:As applied to the balancing of flexible rotors, any balancing procedure that requires unbalance correction in more than two correction planes (ISO 1925). Multi-plane balancing is required for e.g.: –Machine trains consisting of a number of rigid rotors each with two bearings –Flexible rotors, especially shaft-elastic rotors (power-generating and process machines) The sequence for performing multi-plane balancing of coupled rigid rotors is similar to that of single and two-plane balancing

28. BA 7764-11, 28 Sensitivity Matrix - Overview Unknown Unbalance Weights n Inputs U j Measured Vibration n Outputs V i {V} = [S] {U} Estimation of the sensitivity matrix S ij (f) from the inputs U j and outputs V i j = 1,...n; i = 1,...n; where n = number of planes S ij (f) is also known as the Influence Coefficient matrix Machine S ij (f)

29. BA 7764-11, 29 Sensitivity Matrix - Construction Input-output formulation: {V} = [S] {U} Correction mass formulation: {0} = [S] {U} + [S] {C} => - {V} = [S] {C} => {C} = - [S] -1 {V} Sensitivity matrix elements: {V T } = {V} + [S]{T} => [S] {T} = {V T - V} {V}:Initial vibration vector {V T }:Resultant vibration vector with trial masses {U}:Unbalance mass vector {C}:Correction mass vector {T}:Trial mass vector [S]:Sensitivity matrix Conclusion: The sensitivity matrix is constructed a column at a time by applying trial masses.

30. BA 7764-11, 30 Sensitivity Matrix – Trim Balancing Knowing the sensitivity matrix allows for later trim balancing using only a single run. Trim balancing requires that: The mass and mass distribution of the rotor are not significantly changed The speed at which the balancing is performed does not change The supports for the rotor are unchanged all the way to ”ground” The instrumentation is identically applied

31. BA 7764-11, 31 Evaluating the Balance Quality Two methods are available for assessing the balance quality: Evaluating the residual mechanical vibrations –Measure the vibrations at the machine surface as close to the bearing planes as possible –Compare the measured results to allowed limits for different categories of machines as described in standards Compliance with the balance quality grades –Measure the vibrations at the machine surface as close to the bearing planes as possible and calculate the residual unbalance –Determine the “Permissible residual unbalance” for the given classification of the rotor (grade) and the service speed (ISO 1940) –Compare the residual unbalance with the determined permissible residual unbalance as described in ISO 1940 –NB: Strictly speaking this requires a free-free rotor condition

32. BA 7764-11, 32 Permissible Residual Unbalance Permissible residual unbalance e per is a function of: –Balance Quality Grade (G) –Rotational Speed [RPM] (e per *  = constant) A permissible residual unbalance equal to the Balancing Grade is obtained at approx. 10.000 RPM (Red) Example: (Blue) For a balance quality grade of “G 6.3” (e.g. fans) and a speed of 2.000 RPM, the permissible residual unbalance is: e per  30  m. This has to be compared with the calculated residual unbalance, e.g. u res = 4,5 g; r = 400 mm and m = 350 kg => e res  5,1  m < 30  m. Speed [RPM] e per [  m]

33. BA 7764-11, 33 Field Balancing Equipment Handheld balancing instruments –Handy, easy-to-use, dedicated and inexpensive –Contains only basic functionality Portable analyzer systems –Integrated part of general S&V analyzer solution with growth path and scalability –Advanced functionality like data management, data comparison and data validation; geometry definition; advanced weight splitting; trim balancing etc. –Graphical evaluation of results –Powerful reporting facilities

34. BA 7764-11, 34 Balancing Machines Balancing machines can roughly be separated into two classes: Soft-bearing machines –Very soft rotor supports in the horizontal direction giving excellent sensitivity - especially for light rotors –The rigid rotor critical speeds are well below the balancing speed –Rotor calibration is required –Generally more difficult to operate than hard-bearing machine –Mainly used for high-precision, low-volume balancing requirements and for balancing of light rotors Hard-bearing machines –The rotor supports are structurally rigid and are each mounted on one or more (stiff) force gauges. –The rigid rotor critical speeds are far above the balancing speed –No rotor calibration is required –Generally easy to operate –Accepts a wide range of rotor sizes –Used more generally today than soft-bearing machines

35. BA 7764-11, 35 Industries using Balancing Examples include: Automotive, motorcycles, trains, ships –Crankshafts, flywheels, clutches, impellers, gearbox components, drive shafts, brakes, wheels, tires etc. Aerospace & Defense –Gas turbine rotors, propellers, wheels etc. Rotating Machinery and Heavy Industry –Turbines, compressors, electric motors, generators, pumps, fans etc. –Paper machinery rolls, centrifuges, stirring apparatus, winder spindles etc. –Cutting wheels, grinding discs, gears, drive assemblies etc. Consumer Products –Household appliances, white goods, office equipment, power tools etc. Balancing is used in a wide range of industries from balancing of small precision components in disc drives to crankshafts of slowly running ship diesel engines.

36. BA 7764-11, 36 ISO Standards A number of standards are available. The most important ones are: ISO 1925:2001 Mechanical vibration - Balancing - Vocabulary ISO 1940-1:2003 Mechanical vibration - Balance quality requirements for rotors in a constant (rigid) state - Part 1: Specification and verification of balance tolerances ISO 1940-2:1997 Mechanical vibration - Balance quality requirements of rigid rotors -- Part 2: Balance errors ISO 2953:1999 Mechanical vibration - Balancing machines - Description and evaluation ISO 19499:Committed Draft March 2003 Mechanical vibration - Balancing and to balancing standards - Introduction ISO 20806:Final Draft March 2004 Mechanical vibration - In-situ balancing of rotors - Guidance, safeguards and reporting