pryor - single plane balancing made simple

8/12/2019 Pryor - Single Plane Balancing Made Simple

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Single Plane Balance Made Simple(An Introduction to Balancing)

William T. Pryor III

Technical DirectorPdM Solutions, Inc.

530 G. Southlake Blvd.

Richmond, VA [email protected]

Abstract: An introduction to rotor balancing will be presented. This paper is intended asan aid to entry level balancing technicians who want a solid basis of understanding for

performing corrective action balancing. The focus will be on single plane balance

solutions; however the methodology discussed can be expanded to multi-plane situations.

Transducer and rotor setup will be discussed to help minimize common pitfalls. Trialweight selection calculations and placement considerations will be reviewed. Two

graphical methods for solving the single plane balance solution will be presented.

Examples of splitting and consolidating weight will be shown.

Key Words: 1/Revolution (Keyphasor) timing mark, tracking filter, 1X filteredvibration response, 1X Phase, high spot, heavy spot, balance setup, single plane balance,

weight split, and weight consolidation

Introduction: The physical process of balancing a rotor is not difficult. It simplyinvolves getting the proper tools together and following a short procedure. More and

more, the entire balance process is taught as a color by numbers process which is totallycontained within our vibration data collector. If the steps are followed, the user needs to

know absolutely nothing about rotor vibration response to reduce 1X vibration levels.

Many vibration training programs spend only a few hours on balance, teaching the

student to setup their vibration transducer and tachometer, measure the initial vibration,put the weight at a zero of their choosing, and follow what the box indicates. What could

be easier? So if the fault is balance and the person performing the balance only wants to

follow what the black box tells them to do, there is no need to read further.

However, if the desire is to understand not only the balancing process but also gain abetter understanding of rotor behavior, then the following information will be helpful as

an initial introduction. We will learn that balance is both a corrective action as well as adiagnostic tool. How else can we make a controlled change to a machine and measure

the change in behavior. We shall see that even for the beginning analyst taking the time

to evaluate the balance results will improve their understanding of machinery and makethem a better analyst.
mailto:[email protected]:[email protected]:[email protected]


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For this paper we will concentrate on the tools and the setup required to complete a

successful balance. We will then perform a single plane balance using both vector and

influence coefficient methods. Both of these methods rely on the placement of a trialweight of a known magnitude and angle in order to calculate the sensitivity of a rotor to

unbalance. This is sometimes referred to as the calibration method of balancing. We

shall see that if we follow a good setup and balance procedure that this process will behighly successful in performing rotor balancing. The following are the basic stepsrequired to perform a balance.

1. Setup for Successa. Required Equipment

b. Machinery Convention

c. Instrumentation and Rotor Setup

2. Trial Weight Selection3. Trial Weight Placement

4. Single Plane Calculation

5. Trim Balance6. Weight Splitting/Combining

Always remember that having all the correct tools assembled and then performing a good

setup will go a long way toward completing a successful balance. Always follow theprocess.

Required Equipment: The following equipment is necessary to complete a balance.

Having all the tools together and in place before the balance process begins helps to

ensure a successful balance evolution. Having to run back and forth to the office for

forgotten items takes focus away for performing the balance and can easily lead tomaking a mental mistake. It also makes other people associated with the balance

uncomfortable because we look disorganized. Since most of the people we are working

with do not understand vibration analysis or balancing, having everything readilyavailable helps keep the focus on the task and not the individual performing the task.

1. Vibration transducers and cables2. Once-per-revolution sensor and cable

3. Reflective tape (if required)

4. Vibration meter capable of measuring speed, 1X amplitude, and 1X phase

5. Marker or paint stick6. Polar graph paper with triangles/parallels

7. Calculator

8. Balance weights and scale

9. Tools required to access rotor/install weights

While instrumentation and how the actual measurements are made are not a specific part

of this paper, knowing the capabilities/limitations of the transducers and vibration meteris important. The balance technician needs to know that that the expected machine speed


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fits within the capabilities of the instrumentation and that the filter bandwidth of balance

analyzer is capable of precisely filtering to the machine running speed without allowing

unwanted components to be within the filter window. This is especially important forbelt driven units where there is the potential for 1 or more frequency components to be

trapped within the measurement filter resulting in measurement error.

Machinery Convention: It is important to use proper machinery convention when

balancing and performing machinery condition assessment. If we use a few simple steps

to document machinery layout and transducer orientation we can make the data collectionand analysis process much easier. Initially we need to establish a view direction. View

direction is always from the outboard of the driver looking toward the driven equipment.

Making a sketch is always helpful especially if the information collected may be shared

with another analyst. Figure 1 shows a machine drawing with the correct view directionindicated on the drawing.

Figure 1: View Direction

Once view direction is established, the 2nd

item we need to document is the direction of

rotation for each of the shafts. Knowing the shaft rotation is very important inperforming phase evaluation of a rotor. In our industry the default standard is to

measure lagging (against rotation) angles. Since balancing requires evaluation of phase

and the accurate placement of corrective weights, properly determining rotationaldirection is important.

The 3rd

item required is the orientation of the measurement transducers (Figure 2) withrespect to a machine reference. A sketch is very helpful. For a horizontal machine the

orientation of the transducers should be shown relative to the true vertical (UP) position

or to the right hand side horizontal joint. For vertical equipment the transducerorientation should be shown in relation to discharge piping or other fixed reference. The

reference point should be shown on the equipment sketch and the angle of the transducerrelative to the reference should also be indicated.

After sketching the orientation relative to the machine reference position each of the

transducers should be labeled with an X or Y. For some reason this has always been an

area where there is a lot of confusion and many mistakes are made. The most commonmistakes are 1) thinking that X and Y orientations change depending on rotational

View Direction

Driver to Driven


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direction and 2) confusing the X and Y transducer position with true horizontal and

vertical directions. They are not related to either of these.

Figure 2: Transducer Orientations

Very simply, designating a transducer as either X or Y isbased on establishing the positive X and Y axis of theCartesian coordinate system. These axes are mutually

perpendicular to one another and can exist anywhere over

3600, independent of rotational direction and geometric

orientation. The easiest way to avoid mistakes is to draw the

positive X and Y axis on a sheet of paper and then rotate it

until it lines up with the transducers.

Using the transducer placements documented in Figure 2 the following would be the X

and Y axis for each example.

Figure 3: Establishing X and Y axis

Instrumentation and Rotor Setup: It is assumed that a complete vibration analysis has

been performed prior to attempting a balance. Ensure that measurements have been taken

and evaluated in the horizontal, vertical, and axial direction prior to attempting a rotor

750L

150R

00

900R

450L

1350L

450L 450R

00

900R 750L

450R

450L

1350L

150R

450L

X

X

X

X

Y

Y

Y

Y


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balance. Ensure that the measurement results indicate that the most likely cause of the

elevated 1X level is due to unbalance. Remember that there are many malfunctions

which can cause a 1X response. Here are a few of the more common occurrences:

1. Misalignment

2. Bowed, bent, or eccentric shaft3. Rubs4. Internal wearbearing or seals

5. Loose rotor componentsBuilt-up shafts

6. Operating close to natural frequency7. Product build-up on rotor

8. Rotor damage

9. Weak mounting supportLoose or damaged components

The list goes on, so during the entire balance process remain skeptical. Always

remember that the rotor did not go out of balance by itself. Something changed in order

for the levels to increase. Rely on your measurements and observations during thebalance. There are many times that the rotor does not behave as expected and the balance

becomes a diagnostic tool for identification of the root cause.

The instrument setup phase of the balance offers a good opportunity to perform a visualinspection of the machine. Look for loose or damaged components, indications of

rubbing, product/dirt buildup, or make a rotor runout measurement. This gives additional

confidence that balancing the rotor is the right thing to do. Many of the malfunctionslisted above will respond favorably for some period of time to balancing however you

may not have left the machine in a better condition even though the amplitudes have

decreased. Always maintain a questioning attitude.

Instrumentation/Rotor Setup consideration:

1. Ensure that the machine is properly Locked Out/Tagged Out.

2. Find a good place to setup your balance analyzer away from the machine. Ensure that

power is available and that area is protected from the environment.

3. Locate and verify the weight addition location.

4. Ensure that the proper trial weight is present and that balance weight installation toolsare available at the unit.

5. Determine the direction of rotor rotation.

6. As a good practice rotate the rotor until a fixed shaft reference such as a key or

keyway is in line with the weight access location. While not required, performing this

step will make it easy to re-establish the setup condition for future diagnostics. (If a


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permanently installed 1/rev reference is available, rotate the shaft until the rotor reference

mark is in line with the transducer and use this as the fixed rotor reference.)

7. If no permanent 1/rev sensor is installed; install sensor and rotor reference mark such

as reflective tape. While not required for success, installing shaft reference (tape) in line

with a visible reference such as a key or keyway is a good practice. This makes it easy tore-establish the test setup conditions in the future.

8. Install vibration transducers at each bearing and run cables back to the balance

analyzer. Previous vibration data should be reviewed and transducers installed on theplane of maximum motion. In most instances this will be in the horizontal plane.

NOTE: A single plane balance only requires a single measurement and balance plane to

perform the calculation/correction. However, vibration readings should be taken at bothbearing locations during the balance. This is necessary to verify that rotor balance is the

problem and that the balance condition can be solved using only 1 plane. Remember, if

rotor balance is the fault condition, balancing should reduce levels at both bearings andlevels should be reduced in the perpendicular radial plane as well as the axial direction.

An increase in level in other planes/locations can indicate a malfunction is present other

than unbalance or that the balance solution requires more than 1 plane to correct.

9. When the shaft reference mark is in line with the 1/rev sensor, the rotor 0 degree is set

in line with the vibration transducer. Place a 0 mark on the rotor when the rotor is in this

position.

10. Rotate the rotor in the direction of rotation and mark each subsequent hole/blade with

an increasing number as the rotor is turned 360 degrees. Note: Location 0 will also be

marked with the highest blade/hole number to indicate both 0 degrees and 360 degrees.

In the following example a rotor with 8 blades is to be balanced. The rotor turns in acounter clockwise direction as viewed from the motor to the fan. The vibration

measurement transducer is placed in the horizontal position at the right hand side

horizontal joint (90 degrees right from true vertical). When fan blade 0 (also blade 8) isin line with the measurement transducer the reflective tape is lined up with the 1/rev

transducer which is located at 25 degrees right of true vertical. (See Example 1)


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Example 1Setup Diagram


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Trial Weight Selection: Rotor trial weights are selected based on either user experience

with the same/similar machinery or by calculating a weight which will yield

approximately 10% of the rotor weight based on centrifugal force. In the end, our goal isto select a trial weight and then place it on the rotor to yield a change in rotor response ofat least 15 degrees or cause an amplitude change of 10%. Changes less than these

recommended values can be used, however the resulting weight and placement angle can

be either over or under stated.

To use the centrifugal force calculation we need to get a good estimate of the rotor

weight, know the speed of the machine, and determine the radius of weight placement.

When we have this information we can use 1 of the following calculations to determinethe trial weight amount.

Centrifugal Force: Cf = m r

2

Cf= Centrifugal Force Lbf

m = Mass of the rotor =otor eight

ravity=

Note: 1 G = 32.2 Ft/Sec2

= 386.4 in/sec2

r = Weight add radius (inches)

= Rotor speed in radians =

Or for English units this can be simplified to the following equation:

()

WT = trial weight, oz.

r = radius of trial weight, in.

W = static weight of rotor, lb.

N = speed of rotor, RPM


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Trial weight calculation example:

Calculate the size of the trial weight needed for an electric AC motor operating at 1780RPM. The rotor weighs 1800 pounds. Weight can be added to the rotor at a radius of 6

inches.

Using the centrifugal force calculation (Cf = m r2) the simplest way to solve this

equation is to break it down into its individual parts.

1stwe want to generate a force which is equal to 10% of the rotor weight

1)

2) Weight add radius = 6

3) Mass = Unknown

4) Calculate rotor speed in radians

2= 34775

Solving for Mass:

This result needs to be converted into weight units by multiplying it by gravity

Trial Weight =M(386.4 in/sec2) = ( )() .3334 lb

Oz. = (.3334 Lb) (16 oz/Lb) = 5.33 Oz.

As an alternative the following equation can be used for calculation of a trial weight for

English units only. Input values must be in inch, pounds, and RPM.

()

=

()

()=

= 5.33 Oz.

WT = trial weight, oz.

r = 6 radius

W = 1800 lb.N = 1780 RPM


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Trial weight placement:Once the trial weight amount has been determined we have to

determine where on the rotor it will be placed. For the person who is just beginning in

the field of vibration analysis and balancing the decision on where to place the trialweight can seem very confusing. Hopefully, we have heard the discussion about the

relationship of the rotor heavy (angular location of mass unbalance) spot to the rotor high

(angular location of positive peak of 1X sine wave) spot. Initially this may not make a lotof sense, but if we understand that the physical location of the mass unbalance (heavyspot) and the angular location defined by the measured phase angle (high spot) are almost

never in the same location then we have made a start in the right direction. It is also

correct to say that the rotor high spot will lag the heavy spot by a fixed lag angle. As wegain experience we will come to understand that this phase lag relationship is result of

rotor operation relative to a natural frequency. However, for a given rotor the

relationship of the heavy spot to the high spot will remain constant over the life of the

unit. The relationship between heavy and high spots can be shown by the followingdiagram where the high spot will always lag the heavy spot between 0 and 180 degrees.

While this concept is at first hard to understand, what does make sense is that our end

goal is to place a weight on the rotor which is 180 degrees opposite the rotor heavy spot.

When we start to balance a rotor, we usually have no idea of what the high spot - heavyspot relationship actually is. As a result, when we initially place a trial weight on a rotor

it is based on our observation, measurement, and over time experience. It is a best guess

based on available information and experience with similar machinery.

In some instances we can help ourselves in determining trial weight placement by

observing a shutdown of the rotor and watching the phase (change in high spot) changeduring shutdown. In this way we can make an estimation (best guess) of the rotor phase

lag. Since we are typically using our data collector to perform a balance, the ability toobserve (track) amplitude and phase during a shutdown can be difficult due to the

instruments inability to quickly update during a transient condition. The following plotwas developed from a series of amplitude and phase measurements made on a machine

with a VFD drive. 1X amplitude and phase were acquired at various speeds and then

plotted in Excel. This plot is referred to as a Bod which is a plot of phase and amplitude

vs. speed. Notice that as the rotor speed is increased there is a peak in amplitudeaccompanied by approximately a 180 degree change in phase. This is a plot of a rotor


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passing through a critical speed. Remember that the phase is defining the lag angle from

the rotor heavy spot, which cannot change position, to the measured high spot. As a

result, we see that the Heavy Spot-High Spot relationship changes by 180 degrees as arotor passes though a resonance. Superimposed on the plot is a vector representation of

the lag angle at various speeds.

While a plot like this is not required, anything we can do to observe the phase change canbe helpful in selecting trail weight placement. So based on observation the following

rules can be applied:

1Well below resonance add 180 degrees to measured angle2Close to the resonance peak add 90 degrees to measured angle

3Well above resonance place weight at measured angle

Remember trial weight placement it is only a best guess based on available information.

If the user is unsure, it is usually a safe guess to add 90 degrees to the high spot angle for

weight placement.


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Single Plane Balance Data collection steps:The steps required to perform a single

plane balance are the same for both the Vector and Influence Coefficient solution

methods. In the end both methods will yield the same information. Our data collectorsand balance programs use the Influence Coefficient method so this may be the method

which the user should get the most familiar with. Now that we are setup and are prepared

to install a trial weight we are ready to complete the remaining steps. For a single planebalance the following steps are required to collect the necessary data to perform the rotorbalance.

1. Acquire initial set of 1X amplitude and phase data.Note: as a good practice log 1X data in vertical, horizontal, and axial directions at

both bearings.

2. Shut down machine and observe 1X amplitude and phase during shutdown toassist in trial weight placement

3.

Draw initial 1X vector on Polar graph paper

4. Determine trial weight angular placement. Show trial weight magnitude andplacement on polar graph.

5. Attach trial weight to rotor.6. Run machine and log 1X amplitude and phase at all locations. (Trial Run).7. Shutdown machine8. REMOVE TRIAL WEIGHT9. Draw Trial Weight vector on polar graph.10.Perform balance calculations - determine magnitude and angle of corrective

weight.

11.Attach weight to machine.12.Run equipment and log 1X amplitude and phase at all locations. Perform an

evaluation of the data. Ask the following questions:1. Did 1X amplitudes decrease at all locations? If not balance may not be the

only fault.

2. Is a trim run required to further reduce levels?16.For trim run use Sensitivity/Response Vector to calculate trim balance correction.

Repeat steps 13-15. Note: If amplitudes do not decrease following trim balance

other factors may be affecting the rotor. Perform a full analysis and performnecessary inspection before adding additional weight.


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Single Plane Balance - Vector Method - Plot and calculations - Example

Step 1: A = Initial Vibration Response (Mil @ Angle)Step 2: TW = Trial Weight Placement (Weight @ Angle)

Step 3: B = Trial Weight Vector = A + Effect of Trial Weight (Mil @ Angle)

Following step 3 the single plane balance solution can be calculated.

Step 4: C = Trial Weight Effect = B - A (Draw a line from the head of the A to the head

of the B vector. Measure the magnitude of C

Vector MethodSteps 1-4

Step 5: Calculate the Rotor Sensitivity to weight:

S =

=

= 22.06

Step 6: Calculate the Correction Weight = (Sensitivity) (Initial Response)

= (S

) (A mil) = (22.06

) (5 Mil) = 110.3 Gr.

110 Grams is the weight required to balance the rotor.


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Step 7: Measure the angle between C and A. This angle represents the number of

degrees that the final correction weight must be rotated from Trial Weight

location.

Vector MethodWeight Placement Steps 7-10

Step 8: Draw arrow from C to A. This is the direction to move final balance weight fromtrial weight location

For our example the final weight needs to be placed at an angle 360CCW from where the

trial weight was installed.

Step 9: Show the final correction (CW) balance weight location on the polar graph.For our example the corrective weight is 110 Grams at 354

0

Step 10: Show location of rotor heavy spot on the graph.The rotor heavy spot is located180 degrees from where the corrective weight is installed. In our example theheavy spot (U) is located at 174

0.


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Vector MethodDocument Steps 11-13

Step 11: Measure the angle (Lagging) from the Initial Vector (A) to the location of theinstalled Corrective Weight (CW). This is the angle of the Sensitivity Vector.

The Corrective Weight is at the rotor Light Spot.

Step 12: Combine this measured angle with the calculated rotor sensitivity to weight.

(Weight/mil @ Angle). This vector is the Rotor Sensitivity Vector.

From our example the Rotor Sensitivity vector is 22

@ 164

0

Step 13: Save the Sensitivity (S) Vector and use it for Trim and future balance jobs on

this or like machines. For trim balance use the formula CW = S * A1 where A1represents a newly measured unbalance vector.

Proof: CW = (22

@ 164

0) (5mil @ 190

0) = 110 Gram @ 354

0

Note: To multiply a vectorMultiply the magnitude - (22

) (5 ml) = 110 Gram

Add the angles - 1640+ 190

0= 354

0


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Single Plane Balance - Influence Coefficient - Plot and calculations - Example

Step 1: A = Initial Vibration Response (Mil @ Angle)

Step 2: TW = Trial Weight Placement (Weight @ Angle)

Step 3: B = Trial Weight Vector = A + Effect of Trial Weight (Mil @ Angle)

Step 4: C = Trial Weight Effect = B - A (Draw a line from the head of the A to the head

of the B vector. Move C to the center by drawing a parallel vector usingtriangles or parallels. Record the magnitude and angle.

Our example shows C to = 3.4 mil @ 460

Influence CoefficientSteps 1-4

Step 5: Calculate the Influence Coefficient

Response at plane 1 to weight at plane 1

Dividing VectorsDivide the magnitudes and subtract the angles.


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Using our example

= 0.0453

@ 160

This is the rotor influence coefficient. Note that the influence coefficient is the reciprocal

of the rotor sensitivity vector calculated in the previous example.

Step 6: Calculate the location of the Heavy Spot (Unbalance)

( )

This is the location of the rotor Heavy Spot

From our example:

= 110.4 gram @ 1740

Step 7: Weight Add location = U11+ 1800(Light Spot)

Wt add location = 110.4 gram @ 1740+ 1800 = 110.4 Gram @ 3540

Step 8: Show location of Heavy Spot and Light Spot on graph

Influence CoefficientFinal Documentation

Step 9: Save Influence Coefficient for future balance work on this equipment


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Rotor Trim Balance: If we have done a good job documenting our balance results,

performing a new or trim balance on this machine will should be a simple task. Using

our previously measured Sensitivity or Influence Coefficient for a rotor it is possible tocalculate a balance solution based on a single measurement run.

If in the future the rotor is found to be out of balance we simply have to measure thecurrent amplitude and phase and use our Sensitivity/Influence Coefficient to calculate asolution. As an example if we continue to use our balance example lets calculate a trim

balance for the rotor if in the future 1X levels increased to 6.4 mils at an angle of 1400.

Using the rotor Sensitivity vector calculated during the vector method the current

corrective solution is as follows:

Wt add = (22

@ 164

0) ( 6.4 mil @ 140

0) = 141 gram @ 304

0

The weight add solution using the Influence Coefficient is as follows:

Wt add=

= 141 gram @ 3040

From this we can see that by using previous balance data we should be able to reduce

levels in 1 run of the rotor. Good balance practice is to keep a record of previous balancework for the future.


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Splitting weight between 2 locationsGraphical solution

Step 1: Show magnitude and angle of weight on a polar graph

Example - Wt add = 141 grams @ 3040

Step 2: Show locations of adjacent balance location on graph

Example - Holes are spaced at 450intervals. Available holes located at 270

0and 315

0

Step 3: Using triangles or parallels construct a parallelogram. Use the location of the

balance weight as a starting point. From this location draw a line which is parallel to the

1sthole until it intersects the angle of the 2

ndhole. Repeat the process by drawing a line

which is parallel to the 2nd

hole until it intersects the angle of the 1sthole. The point at

which the lines intersect is the magnitude of the weight which needs to be installed in that

hole. See drawing below.

From our example, the balance weight of 141 grams @ 3040can be split into 2 weights of

40 grams @ 2700and 110 grams @ 315

0


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Resolving 2 weights into a single solutionweight addition

Step 1: Show the magnitude and location of the 2 weights on a polar plot

B5 = 65 grams B6 = 100 Grams

Step 2: Using triangles or parallels construct a parallelogram. Use the location of thebalance weight at the 1

sthole and draw a line which is parallel to hole #2. Next use the

location of the balance weight at the 2nd

hole and draw a line parallel to hole #1. Where

the lines intersect is the magnitude and direction of the combined weights. See drawingbelow.

Summary: Successful rotor balance is achieved by following a few simple steps.

Evaluation of the data and paying attention during the balance process is key to being agood balance technician. With experience, the analyst will find that the balance process

is as much a diagnostic tool as it is corrective. Hopefully the analyst who is just

beginning to balance or the one who is looking to improve their skills will find thisinformation helpful. The information presented is only a beginning and there is still a lot

to learn.


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A couple of closing items: The first is to always remember that there are many

machinery faults which occur at 1X running speed. If we begin the balance process and

the results are not as expected, stop and review. It is very likely that balance is not thefault and that continuing the balance will not result in a favorable outcome. In these

circumstances balance has been a valuable diagnostic tool. Not everything will balance.

Secondly we have shown that Influence Coefficients are a powerful tool. Withexperience they can provide powerful insights into a rotors behavior characteristics. The

Influence Coefficient for a given rotor should not change over the life of the equipment.

Changes in magnitude or angle of the coefficient can indicate changes in rotor or supportconditions or may be the result of external forces such as misalignment. There is a lot to

learn just by adding a weight to a rotor.

pryor - single plane balancing made simple

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