Tuesday, December 2, 2014



To give an overall idea about the balancing of Rotating Equipment components to the Maintenance and Operations personnel.
 The scope of the manual is to explain the purpose of balancing the rotating equipment components and to give a brief information about the balancing procedures, balancing machines and the prevalent balancing standards.

1.1        Balance Quality Grade: G Xxx
1.2        Center Of Gravity
1.3        Principal Inertia Axis
1.4   Correction Plane (For Balancing)
1.5   Static Unbalance                                                                       
1.6        Couple Unbalance
1.7        Critical Speed
1.8        Dynamic Unbalance
1.9        Rotor
1.10      Rigid Rotor
1.11      Flexible Rotor
1.12      Specific Unbalance
1.13      Residual  Unbalance
1.14      Permissible Residual Unbalance  (U per  )
1.15      Units Of Unbalance Introduction                                                 
2.1        Reasons For Balancing
2.2        Causes Of Unbalance
3     Safety & Environmental Precautions                                                           
3.1        Safety Of The Balancing Machines
3.2        Safety While Balancing The Rotors
3.3        Safety  During The  Field Balancing Of The Rotating Equipment :
4    BALANCING  MACHINES:                                           
4.1        Gravity Balancing Machines:
4.2        Centrifugal Balancing Machines:                                
4.2.1     SOFT BEARING BALANCING MACHINES                   
5     BALANCING METHODS                                              
5.1        Preparation For Balancing                                          
5.2        Shop  Balancing                                                                     
5.2.1     SYMMETRICAL ROTOR                                            
5.2.3     OVERHUNG AND NARROW ROTORS                        
5.3        High Speed Balancing –
5.4        Field Balancing-                                 
6     BALANCING STANDARDS.                                                                                      

1       Terminology

1.1      Balance Quality Grade: G Xxx 

For rigid rotors, G , is the product of specific unbalance , e, and rotor maximum service angular velocity. Service angular velocity is nothing but the service RPM expressed in radians per second.( w )
G = e *  w 

1.2      Center Of Gravity –

The point in a body of a rotor through which the resultant of the weights of its component particles passes for all orientations of the body with respect to a gravitational field is called the center of gravity - C.G.
This can also be described as the point about which the rotor’s weight is equally distributed.

1.3      Principal Inertia Axis –

A line about which the rotor weight is equally distributed is known as Principle Inertia Axis ( PIA in short ) . It is obvious that the Center of Gravity  ( CG ) is always on the Principal Inertia Axis ( PIA )

1.4   Correction Plane (For Balancing)-

The plane perpendicular to the shaft axis of a rotor in which correction for unbalance is made. The correction can be in the form of material addition, or material removal, or any change in the weight distribution in this plane.

1.5      Static Unbalance

It is that condition of unbalance for which the central principal axis is displaced only parallel to the shaft axis.

1.6      Couple Unbalance

It is that condition of the unbalance for which the central principal axis intersects the shaft axis at the center of gravity.

1.7      Critical Speed

It is that speed at which a system resonance is excited. The resonance may be of journal supports ( rigid mode ) or flexure of the rotor ( flexural mode ). There are many critical speeds for a rotor and they are denoted like first, second, third in lateral and torsional modes.

1.8      Dynamic Unbalance

It is that condition of unbalance for which the central principal axis ( PIA )  is not parallel to and does not intersect the shaft axis. Obviously the CG is not on the shaft axis as well .It is usually a combination of the static and couple unbalance. This is the type of unbalance, which is usually found in practice in the unbalanced rotor.

The Dynamic unbalance is equivalent to two unbalance vectors in two specified planes, which completely represent the total unbalance of the rotor.
Dynamic unbalance may also be resolved into a static and couple unbalance vectors whose vector sum is also equal to the total unbalance of the rotor.

1.9      Rotor 

A body capable of rotation, which generally has journals supported by the bearings.


1.10   Rigid Rotor 

A rotor is considered rigid if its unbalance can corrected in any two correction planes. After the correction, the residual unbalance does not change significantly at any speed up to the maximum service speed. In other words it also means that the rotor service speed is much lower than its first lateral critical speed.

1.11   Flexible Rotor

A rotor that does not satisfy the definition of the rigid rotor is known as a flexible rotor. It also means that the rotor needs to be balanced in such a way that it remains reasonably balanced while it attains the maximum service speed. The rotor of this class runs at least above the first lateral critical speed. While passing through the critical speeds there is some amount of elastic deflection depending on the mode shapes. The correction planes are so selected that, the elastic deflection has no severe impact on the balance of the rotor, at that speed range.

1.12   Specific Unbalance

The static unbalance U divided by the rotor mass M. This will also yield the value for mass eccentricity, which is denoted by  e

1.13   Residual  Unbalance 

The unbalance of any kind that remains after the balancing of the rotor is known as residual unbalance. This must be less than the permissible value, as per the balancing standers adopted for that class of rotor.

1.14   Permissible Residual Unbalance  (U per   

The maximum residual unbalance permitted for a rotor or for a correction plane for the rotor is termed as permissible residual unbalance. This is expressed as
U per  = e per  x  m  ,  Where m is the mass of the rotor.

1.15   Units Of Unbalance

Unbalance is measured in gram-millimeters or ounce inches. It simply means the quantity of unbalance mass (m) , multiplied by the distance  ( R ) from shaft axis.
As an example, an unbalance of 15 gm at  100 mm radius will introduce an unbalance of  ( 15 x 100 ) = 1500 gm-mm , in that plane.
This is independent of speed of rotation. However the same unbalance will produce higher centrifugal force if the speed of rotation increases. In fact the centrifugal force generated due to unbalance is proportional to the “ square “ of RPM.  ( F =  m x R x W x W)

2       Introduction

One of the basic problems in the rotating machinery is the unwanted vibration. Since the rotor rotates, if it is out of balance, vibration will be present primarily because of the unbalance. This can corrected by balancing the rotor. There are many other reasons for balancing the rotors.

2.1      Reasons For Balancing

An unbalanced rotor will cause vibrations, and may result into premature bearing failures, seal failures, noisy operation, shaft & coupling damage, structural vibrations and failures. This depends on the degree of unbalance and also the tolerance of the various components to theses forces produced due to unbalance.  Therefore balancing of the rotor is required for the following reasons-
Ø  Reduce stresses on the rotor shaft, bearings, coupling, gears, frame, foundations, adjoining structure and machinery, etc.

2.2       Causes Of Unbalance

Ideally speaking, a fully machined (from outside and inside) and absolutely symmetrical rotor should be inherently balanced in the “ as machined ” condition, even if it is not “ balanced “ after manufacturing. However this is rarely achieved. The reasons are as follows-
Ø  Anisotropy of the material due to voids in casting, inclusions and blowholes in the welding, metallurgical differences, and so on.
Ø  Geometrical differences resulting in non- symmetry
Ø  Distortion during operation because of mechanical forces, thermal distortion, looseness at higher speeds due to centrifugal forces
Ø  Corrosion, erosion and the deposits on the rotating parts in service

3       Safety & Environmental Precautions

3.1      Safety Of The Balancing Machines :

The balancing machines handle rotating components like rotors of pumps, turbines and compressors. The lifting and shifting of these parts should be done by qualified trained personnel and by using the load tested lifting equipment like cranes, slings, eyebolts and shackles.
When the rotors are balanced, they are rotated at a certain speed. The area around the machine should be well cordoned and should be kept safe for the personnel working nearby. The rotor should be thoroughly checked for any loose part or the damage so as to exclude any possibility of loose part on the rotating component.
Please see the photograph of the Balancing Machine equipped with the safety barriers and the enclosure, for the safety.
The rotor has to be coupled very carefully with the balancing machine coupling. The error at this point results in a faulty balancing and a chance of rotor getting uncoupled while being rotated in the balancing machine.
Every balancing machine has a safe working limit as far as the maximum speed and the maximum weight of the rotor it can safely handle. The balancing machine should be strictly used within this limit. Exceeding the limit may result in damage to the machine, rotor and the personnel operating the machine, etc.

3.2      Safety While Balancing The Rotors :

The unbalance correction usually carried out by adding or removing the mass on the rotor. The addition of the mass can be achieved by welding, bolting, riveting etc. This operation should be performed using all the PPEs (personal protective equipment) like hand gloves, welder’s glasses and face shields, etc.
The mass can be removed by grinding, machining etc. The appropriate PPEs life, face shields, hand gloves, etc must be used. Secondly, if the correction is done, while the rotor is still on the rollers of the balancing machine, it should be positively ensured that the machine does not start spinning the job accidentally.
A care must be taken to remove the mass gradually as per the recommended practices and keep the strength and integrity of the rotor in mind while doing any such operations. The addition of mass or removal of mass should not result in weak spot or should not cause a major disturbance to the flow in the equipment.

3.3      Safety  During The  Field Balancing Of The Rotating Equipment :

Some of the large and slow speed rotors like boiler fans, conveying blowers, and Cooling tower fans, etc are balanced at site for convenience. The equipment is run for a short time to take the vibration and phase readings. The correction is made in steps by adding the mass at a specific radius and angle. Extreme care is necessary while adding the masses and also while taking the readings. Usually three or even more trials are necessary in the field balancing. After every trial followed by correction on the rotor the equipment is started for taking the readings. Under no circumstances the equipment should accidentally start when the job is being carried out on the rotor.
The addition of the mass can be achieved by welding, bolting, riveting etc. This operation should be performed using all the PPEs (personal protective equipment) like hand gloves, welder’s glasses and face shields, etc. Proper work permits, hot work permits and positive isolation of the equipment while the weights are being added on the rotor must be strictly followed. All the concerned personnel should be informed before starting the job and also after completing the balancing job.


The purpose of the balancing machine is to determine the magnitude and angular position of the unbalance in the plane of reference called the balancing plane.

4.1      Gravity Balancing Machines:

This type of machine includes the Horizontal ways, knife-edges and the roller stand. The rotor to be balanced is placed on it and rolled slowly so that the heavy side rolls down due to gravity. This machine is good enough only to detect the static unbalance and useful for narrow rotors only. This is a useful step for the subsequent dynamic balancing, because the statically balanced rotor with a reduced residual unbalance is easy to balance on the dynamic balancing machines.

4.2      Centrifugal Balancing Machines:

The rotor is supported by the balancing machine bearings and rotated around a horizontal or vertical axis. The centrifugal balancing machine is capable of measuring the static unbalance (single plane) and static or couple unbalance (in two-plane machine). It should be noted that only a two plane rotating balancing machine can detect a couple and hence a dynamic unbalance. In these types of machines, the amplitude and phase of motions or reaction forces of rotating centrifugal force vector is sensed and measured and also indicated to the operator for the balance correction.
Two types of the centrifugal balancing machines are commonly used. They are called soft bearing machines and the hard bearing machines.


The name “ soft bearing balancing machine “ is derived from the fact that these machine support the rotor to be balanced on the bearings which are very flexible. This allows the rotor and bearing pedestals to vibrate freely and generously in the direction perpendicular to the rotor axis. The resonance of the rotor system occurs at a speed much lower than the speed at which the actual balancing is carried out. Please refer the ”Phase angle and displacement amplitude versus rotational speed in the SOFT BEARING balancing machines” given below.

Phase angle and displacement amplitude versus rotational speed in the SOFT BEARING balancing machines





Hard bearing balancing machines are similar to the soft bearing balancing machines in construction. The only difference being their bearing supports are much stiffer in comparison. This results in a resonance of the rotating system occurring much above the balancing speed. The hard bearing balancing machine is therefore specially designed to be operated well below the resonance .

Phase angle and displacement amplitude versus rotational speed in the HARD BEARING balancing machine

Basically there are three types of balancing jobs encountered and the methods involved used for those types may be categorized as
 Shop balancing
High Speed balancing
Field balancing 




5.1      Preparation For Balancing

Before starting the balancing of a rotor few things are important to remember. The list is very long but some of the important points are highlighted below-

If the rotor to balanced is the one which was used in service, clean the rotor thoroughly and inspect for any damage, cracks, wear etc. A thorough degreasing followed by ash blasting or ceramic bead blasting is an ideal way to clean the rotor.
In case of a doubt, magnetic particle inspection or Dye Penetration test is helpful in determining the surface & subsurface flaws and cracks etc.
It is always a good idea to remove all the deposits, especially polymer deposits and the deposits on fan rotors, turbine blades, before balancing.
The straightness of the rotor shaft must be checked and the ovality, taper and  wear on the journals must be measured. If the shaft is bent and the journals are not within the specified accuracy, there is no use of balancing in this case. These faults must be corrected first to achieve the accurate balancing.
The rotor assembly and fitment of the impellers and discs on the shaft must be checked for proper  shrink fits, perpendicularity and axial location. No rotating part should be loosely installed on the shaft.
It is also important to measure the radial and axial runouts on the impeller discs and shrouds. This has to be within the limits specified. Any correction or machining required has to be done before the balancing. After balancing no corrections are possible .
The rotor is balanced by supporting the journals on the balancing machine rollers. Hence both the journals of the rotor as well as the rollers of the balancing machine have to be inspected and should be free of inaccuracy.
The compressor, fan and pump rotors must be balanced on the balancing machine by rotating them in their usual direction of rotation. Where as the turbine rotor is reverse rotated while balancing.
The rotor to be balanced must be a full assembly including the keys, the coupling half , any subassemblies like overspeed mechanism, lube oil pump driving gear and so on. This ensures that the full rotating assembly is precisely balanced as one single unit in the final balancing step.

5.2      Shop Balancing

Most of the rotors are balanced in the shop where they are manufactured. The Original Equipment Manufacturers who manufacture pumps , turbines and compressors , carry out the balancing of their rotors by this method. Depending on the size, weight and the speed of the equipment, different types of the balancing machines are used. In most of the cases the speed used to rotate the rotor is much less than the actual speed of the rotor. Depending on the shape of the rotor different methods are employed. Some of the shop balancing machines have direct drives and the rotor to be balanced is connected by a suitable end drive adapter, which connects the rotor to the driver by a universal joint. In some of the balancing machines, the drive is by a belt for spinning the rotor, as shown on the Universal Balancing machine on the previous page.
For balancing the rotor the important dimensions like the bearing span ( D), distance between CG and the correction planes ( BL & BR ), distance between bearing and the correction plane ( A ) must be measured and noted carefully.


The type of rotor that falls under this category must satisfy the following conditions
·         Correction planes are within the bearings
·         The distance “B” is greater than 1/3 of  “ D”
·         The correction planes are equidistant from the center of gravity CG and when the correction planes are not equidistant from the CG, the permissible unbalance calculated per plane should be in that proportion.
U per Left =   U per ( BR / B )
U per Right  = U per ( BL / B )
This type of rotors are  typically seen in double entry boiler fans etc. Please see the following figure.


These type of rotors are also popularly known as “ Dumb-bell” rotors. 

      The correction planes are equidistant from the center of gravity CG and when the correction planes are not equidistant from the CG, the permissible unbalance calculated per plane should be in that proportion.
U per Left =   U per ( BR / B )
U per Right  = U per ( BL / B )
This type of rotors is typically seen in turbo-expanders, integral gear air compressor rotors and so on.


These are very common for the overhung fans and overhung pump impellers. These types of rotors are supported by two bearings and as compared to the impeller diameter the width of the impeller is very small making it a narrow  rotor.

The following rules and conditions apply to the overhung and narrow rotors.
The distance between the correction planes is less than 1/3 the distance between the bearings. ( B < 1/3 D.)
The permissible dynamic bearing loads are assumed to be equal.
Couple corrections are made 180 degrees apart in their respective planes.
The plane for static corrections may be a third plane or either of the planes used for couple corrections.
Allocate  per as static and couple residual unbalance as follows :
U per  Static = U per / 2  *   D / 2*C
U per  Couple  = U per / 2 *  3*D / 4*C
Permissible unbalance allocation for overhang and narrow impellers require that two-plane unbalance correction divided into static and couple unbalance equivalents.

5.3      High Speed Balancing

The high speed balancing or “ at  speed balancing “ is done for high speed critical centrifugal compressors and turbines etc. It requires a very sophisticated set up and a balancing machine. These types of facilities are limited in number worldwide and they are very expensive as well.
The installation consists of a chamber capable of holding the rotor along with the bearing pedestals, and also a place for the balancing personnel to move inside for weight correction on the same rotor by machining, grinding, etc. The complete set up is in a bunker and the in an airtight chamber or enclosure. The chamber is connected to the vacuum pumps. The vacuum is maintained to avoid the airflow through the impeller. At very high speed the windage and friction will be very disturbing, and dangerous as well. Secondly it will require a prime mover of very high horsepower to spin the rotor at that speed. One more problem will be the heating up of the air inside the chamber. Rotating the rotor in a vacuum chamber solves all these problems. There are protection devices to safeguard against the vacuum failure.
Normally a variable speed drive or motor and gearbox combination is used. The balancing equipment are also very sophisticated and they include computerised system which calculates the unbalance and the angular position etc. It records the initial unbalance and also records all the stepwise corrections. It is worth noting that for balance correction, say by grinding, the rotor must be stopped and vacuum must be relieved. Again after the correction, the rotor must be tested in re-evacuated chamber. This makes the High Speed balancing a very time consuming, labour intensive and expensive operation.
It must be noted that all the rotors do not deserve such a stringent testing. The multistage, critical rotors, falling in the category of  “ Flexible Rotors”, meaning operating above their first lateral (bending) critical speed, must be tested this way. This testing revels characteristics of the dynamic rotor response. 
Please refer to the following pictures showing a complete set-up for high speed balancing. Note the enclosure, the bearings with pickups and the vacuum seals, etc. On these types of machines the critical multi-impeller rotors are also tested for what is popularly known as  “ Over Speed Testing “.

5.4      Field Balancing

This is one more practical way of balancing the rotating equipment and the name of this method is due to the fact that it is done in the field. This is also suitable for big rotors rotating at lower speeds for example air blowers, fans, etc. Generally this method is used for small finer corrections and not the major adjusting. This is usually done when the machine vibrations show an increase and the cause is the imbalance. The rotors such as ID fans show “ out of balance “ after some use due to thermal distortion, corrosion, erosion, wear and tear and deposits etc. If the imbalance resulting due to such a problem is not very high, it can be corrected easily by “ field balancing”. It is much easier to do a field balancing than, de-coupling, opening the equipment, and taking out the complete rotor assembly, transporting from site to balancing facility and then fixing back the same way after the shop balancing.
Secondly, many of the equipment are so designed that a “ field balancing” provision is made on the rotor. Electric motors, air fan rotors, and sometimes even the steam turbines have a provision for adding the balance correction weights without removing the rotor from the casing. The end covers have widows to get access to the balance correction ring or slots in which the balance weights are added and fixed permanently so that they do not move in service.
In the field balancing, single plane, two-plane and multi plane balancing is possible. It depends on the shape of the rotor and the running speed. Very narrow overhung type rotors are balanced in the single plane. Relatively broad rotor life ID fan rotors and electric motor rotors are balanced in two planes.

Example of a single plane field balancing, showing measurement points

As a preparation for the field balancing of the rotor it is essential to verify that the cause of the vibration is unbalance. After this is confirmed, it is a god idea to inspect the rotor for any major damage. If the rotor is coated with dirt and dust or some polymer deposits, it is essential to clean the rotor. High-pressure hot water cleaning is one of methods to clean at site. Then some field dimensions like bearing span (D), correction plane and CG ( BL & BR ) , correction radius (R), correction planes and bearings ( A ) etc are required, to calculate correction weights.

Example of a two - plane field balancing, showing measurement points 

The field balancing is done by using  many different equipment. There are some portable field balancing equipment available. They have portable vibration pickups and strobe light. The vibration measure provides an indication of the unbalance mass and the reading is in proportion of the unbalance. 

The vibration magnitude indicated by the equipment may be displacement, velocity or acceleration depending on the type of transducer and the selected unit of display.

As indicated in the two previous examples, the pickup is mounted on the bearing housing to measure the vibrations. The angle of unbalance can be found out if there is a  shaft  “ key “  which is used to trigger the strobe. Other wise optical pickup is also used to determine the angle.

Second possible way is to use the “three trial runs “ method. The first run is take in the rotor in “ as it is “ condition. The vibration amplitude and the phase are measured. In the second trial a “ suitable trial weight” is attached to the rotor and the rotor is brought to the operating speed again. 

This time the vibration amplitude and the angle is noted. Then based on these two readings, the exact balance correction weight is found out and attached. The third run is usually is a final run and it is expected that the rotor is balanced at this stage. The vibration levels are within the permissible level. Occasionally a last “ trim balancing “ is carried out if necessary.


There are many standards available today, which give guidelines for balancing. One can easily determine the allowable limits from these standards.  One of the most commonly used standard is ISO-1940.  This gives the values of Balance Quality Requirements of the Rigid Rotors.
To use this standard one must know what type of rotor is to be balanced. See the Table 1 for determination of the type of rotor. From this table the second thing to note is the grade. For example centrifugal pump impellers, and flywheels fall under  G 6.3 grade. The steam and gas turbine rotors and turbo compressor impellers are under grade G 2.5. After selecting the grade from table 1, next step is to go to Figure 1-A or Figure 1 – B, to find the maximum permissible residual unbalance e per .
As an example, we have a centrifugal compressor rotor of weight 2200 lb. weight. The maximum operating speed is 5000 RPM.  The grade as per table 1 is G2.5. Then the formula become
U per =  ( G * e per * weight of rotor / 2 ) Max cont. RPM
                        =  ( 2.5 * 6.0 * 2200 / 2 ) / 5000
                        =   3.3  oz-inch
If we use the formula given in API - 617, the formula is
U per = 4 W / N , where W = total rotor weight in lbs. and  N = Max Continuous operation  RPM.  Applying this formula to the previous example, we get
U per = 4 W / N = 4 * 2200 / 5000 = 1.76   oz – inch.
Obviously API - 617 standard is more stringent, as it allows a smaller permissible unbalance of 1.76 oz-inch compared to the 3.3 oz-inch allowed by ISO -1940.

The other API standards also specify the similar things as far as dynamic balancing of the rotors is concerned. The allowable residual unbalance per plane as specified by different API standards is tabulated as follows-

API 611
Gen. Purpose Steam Turbines
U max = 4 W / N
API 616
Gas Turbines For Refineries
U max = 4 W / N
API 6 17
 Centrifugal Compressors
U max = 4 W / N
API 610
Centrifugal Pumps for Petroleum , gas etc
U max = 4 W / N
Where       Umax = residual unbalance in ounce-inches ( gram-millimetres in SI )
                        W = Journal static weight load in pounds ( kilograms in SI )
                        N  =  maximum continuous speed in revolutions per minute RPM.
The above formula for SI units is expressed as ,  U max = 6350 W / N
Balance Quality Grade
Product of
 E per * W

G 4000
Crankshafts/ drives of rigidly mounted slow ( where the piston speed is less than 9 m/s ) marine diesels with uneven number of cylinders.
G 1600
Crankshafts/ drives of  rigidly mounted two-cycle engines.
G 630
Crankshafts/ drives of rigidly mounted large four-cycle engines and Crankshafts/ drives of elastically mounted marine diesel engines.
G 250
Crankshafts/ drives of  rigidly mounted fast( where the piston speed is more than 9 m/s ) four cycle diesel engines
G 100
Crankshafts/ drives of fast diesel engines with six or more cylinders. And complete engines for cars, trucks, etc
G 40
Car wheels, wheel rims, wheel sets, drive shafts,
Crankshafts/ drives of elastically mounted fast four-cycle engines with six or more cylinders.
Crankshafts/ drives of engines of cars, trucks, etc
G 16
Drive shafts ( propeller shafts, cordon shafts with special requirements ) ,
Parts of crushing machines, agricultural machinery, individual components of engines for cars, trucks, etc.
G 6.3
Parts of the process plant machines Centrifuge drums, paper machinery rolls, print rolls, fans, flywheels,  assembled aircraft gas turbine rotors, , pump impellers, machine tool and general machinery parts, medium and large electric armatures, small electric armatures
G 2.5
Gas and steam turbines, rigid turbo generator rotors, turbo compressors, machine tool drives, medium and large electric armatures with special requirements, turbine driven pumps
G 1
Tape recorder and phonograph drives, grinding machine drives
Small electric armatures with special requirements
G 0.4
Spindles, discs and armatures of precision grinders,
Note : W = 2 p N / 60   rad / sec.

API 617 For Centrifugal Compressors specifies the following guidelines.
Ref.  Para - Major parts of the rotating element, such as shaft, balancing drum, and impellers shall be dynamically balanced. When a bare shaft with a single keyway is dynamically balanced, the keyway shall be filled with a fully crowned half-key. The initial balance correction to the shaft shall be recorded. A shaft with keys 180 degrees apart but not in the same transverse plane shall also be treated as described above.
Ref. para - The rotating element shall be multiplane dynamically balanced during the assembly. His shall be accomplished after adding no more than two major components. Balancing correction shall be applied only to the elements that are added. Other components may require minor corrections during the final trim balancing of the completely assembled element. On rotors that have single keyways, the keyway shall be filled with fully crowned half-key. When specified, the weight of all half keys used during the final balancing of the assembled element shall be recorded on the residual unbalance worksheet. The maximum allowable residual unbalance per plane ( journal ) shall be calculated as follows; -
U max  =  4 * W / N       ( and  in SI units U max = 6350 W / N )
Where Umax = residual unbalance in ounce-inches ( gram-millimetres in SI )
                        W = Journal static weight load in pounds ( kilograms in SI )
                        N = maximum continuous speed in revolutions per minute RPM.
When spare rotors are supplied they shall be dynamically balanced to the same tolerance as main rotor.
Ref. Para – High speed balancing ( balancing in  the high speed balancing machine at the operating sped ) shall be done only with the purchaser’s specific approval. The acceptance criteria for this balancing shall be mutually agreed upon by the purchaser and the vendor.   
The other standards like API : 610-for pumps, API :611 – for steam turbines,  API : 672 – packaged integrally geared compressors, etc also provide similar guidelines.

7       References

ISO 1940 – Balance Quality Of Rotating Rigid Bodies – classifies all rigid rotors and recommends balance tolerances for them.
API  STANDARD 610 -  Centrifugal Pumps For Petroleum , Heavy Duty Chemical, And Gas Industry.
API  STANDARD 611- General Purpose Steam Turbines For Refinery Services.
API  STANDARD 616 – Gas Turbines for Refinery Services.
API  STANDARD 617 -  Centrifugal Compressors  For Petroleum , Chemical, and Gas Service Industry.
Machinery Component Maintenance and Repair by Heinz P Bloach & Fried K. Geitner – Gulf Publishing.
Compressors Selection & Sizing –By Royce N. Brown – Gulf Publishing Company.
Hard – Bearing Balancing Machines – SHENCK RoTec GmbH.
PGW- Turbo Compressors for the Process Industry – Pumpen- und Geblasewerk Leipzig GmbH.
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