CARL’S BALANCING SCHOOL

SYNOPSIS

This webpage presents and explains the simplest empirical, trial and error, do-it-yourself

balancing method suitable for dynamic single or two plane balancing of rotating

machinery. This method is suitable for onsite/in-place or job shop balancing. No

mathematics is required or used.

All empirical balancing methods require some method of measuring the amount of

unbalance in a rotor. Measurements may be taken of the displacement, velocity or

acceleration of its vibration. The first part of this article makes two assumptions: that

you have some means of measuring unbalance or vibration and that there is no display

of the location of the unbalance, that is, there is no strobe flash illuminating a location

on the rotor.

The second part of this article is a detailed explanation of the process of setting up a

balancing amplifier which has a strobe output to display the location of the unbalance,

either the heavy or light side. The explanation is at the balancing technician level with

no mathematics. Simple vector diagrams are used to explain what the operator will see

during the setup process but are not used in the process itself. Phase angle shift in the

amplifier and cross-effect of the unbalances in the rotor and how to correct for them are

explained in detail. This process calibrates the amplifier to display the location of the

unbalance. This speeds up the balancing job particularly for production applications.

INTRODUCTION

A few years ago (this is now 2017) I set out to design and build a professional level

dynamic balancing machine. The immediate need was to balance the rotor of the

spindle drive motor for one of my cam grinders. The back story is that I had previously

(about 1985) empirically balanced two rotors for small tool and cutter grinders and that

effort left a remnant interest in both static and dynamic balancing.

In the intervening years I collected information on balancing – most of it was at the

engineering level and used vector algebra to develop complex equations for balancing

but nothing on how to do it. The balancing technician at the Westinghouse Marine

Division loaned me the manuals for his IRD Mechanalysis balancing machines which

uses vector diagrams to balance rotors. Victor Wowk’s book Machinery Vibration:

Balancing1 has the best explanation of unbalance and presents several methods for its

1 ISBN 0-07-071938-1 It is at this time (2017) available on print-on-demand.

correction. I recommend this book as the best source of further information for the

balancing technician.

I intended to use the four run without phase response method2 to balance the motor

rotor. Quite by chance at this time I gained the acquaintance of George Cox, proprietor

of Cox and Sprague Machinists, the local balancing professional. He took one look at

my balancing machine and amplifier and said “I like it.” He showed me around the

shop, and demonstrated balancing a rotor.

The most interesting thing was that he did not use any math, no vector diagrams, just a

weight scale and a ball of modeling clay with his balancing machine and its amplifier. I

have a stack of paper on balancing methods about 4” thick but had never encountered

this method.

It is the method of dynamic balancing developed by the Gisholt Machine Company

during the 1930’s. It is based upon the simple empirical balancing procedure and

extends this by adding null and calibration circuits to the amplifier. These circuits

eliminate cross-effect and calibrate the amplifier to read correction weight directly in the

operator’s choice of units. The location of the correction is indicated by a strobe flash.

No calculations or vector diagrams are used at any time during the balancing process.

This method is suitable for dynamic one or two plane balancing of rotors.

The process of setting up the amplifier is at the heart of the Gisholt method.

Instructions for this are in the manual for the RetroTek Model 135 Balancing Amplifier

which may be found here. This adjustment may be done without a detailed

understanding of the underlying principles and was therefore not included with the

amplifier manual. I placed this information in this separate article for those who are

interested a better understanding of the method. The setup of the amplifier begins by

balancing a rotor with the empirical method and this method may be used with any

method of measuring unbalance.

This article contains a full explanation of how to balance a rotor with or without a strobe

flash to indicate the location of the unbalance. It also explains some interesting – and

confusing – phenomena that the balancing machine operator will observe during the

process. No math is required, just a method of measuring the unbalance, and a stick of

modeling clay. A weight scale is used only after completing the empirical balance

procedure to measure a trial weight for setup of the amplifier if that is required.

2 Wowk p. 117 ff

The method of making the measurement and the design of any required fixture is up to

you. I will explain how to use your choice of measuring method and how to interpret

what you see in the process. The method for making corrections of unbalance depend

upon the design and construction of the rotor and this is also your responsibility.

A final word on safety: I had a small rotor come out of its bearings. It was briefly

exciting but not particularly dangerous. The rotor was scratched and I learned a lesson.

A larger rotor could have been a different story. Static balancing is relatively safe, all

that is required is the ability to safely place the rotor on a balancing stand with sufficient

weight capacity. Dynamic balancing of a rotor in a balancing machine is a very much

different matter and the danger increases with rotor weight and the square of the

operating speed. If you do not know the danger and how to handle it, do not attempt to

make a balancing machine and balance a rotor or to balance a rotor in place. There are

other dangers such as catching a finger or piece of clothing in the exposed belts of a

belt-driven machine or on a key or in a keyway or fan blades. Your safety is your

responsibility.

EMPIRICAL – TRIAL AND ERROR – BALANCING METHODS

Dynamic balancing is the art and science of finding and correcting unbalance in a

rotating device. Unbalance in a rotor causes rotating forces in its bearing supports and

these forces in turn cause vibration in the associated device – shaking it up and down,

round and round.

If this vibration is unwanted the unbalance may be corrected by a balancing operation.

The rotor is installed in a balancing machine and run at some speed. Pickups (vibration

sensors) sense the vibration and generate an electrical signal which is sent to an

amplifier or an equivalent readout /measuring device. The amount is relatively easy to

measure. The signal generated by the pickups is directly proportional to the amount of

vibration which is in turn directly proportional to the amount of unbalance.3

The location is harder to find: it may be at one spot or distributed throughout the rotor.

The unbalance may be an excess mass, possibly a set screw, a key or a casting defect.

Or the unbalance may be a mass deficiency such as a void in a casting or a keyway. It

may be eccentricity (runout) developed during machining. Even though the unbalance

may be distributed through the rotor, its effects add or subtract to a single effect at each

end and it is convenient to speak of heavy and light spots at each end located at 180°

from each other.

3 The amount of vibration is not directly proportional to the RPM of the rotor. The rotor must run at the

same RPM during the entire balancing operation.

Prior to installation in the balancing machine the rotor will be marked by numbers in a

circumferential plane. The operator should be able to see two or three numbers in his

sight line. The strobe flash will illuminate one of these numbers. The marks on the

rotor will occupy an angular distance, for example 12 marks would be 30° apart, and if

the operator estimates to half a division there remains a 15° uncertainty. The correction

must be applied closer to the unbalance location than that.

Finding both the amount and location is made more complex by cross-effect: any

unbalance at one end of the rotor will also cause an effective unbalance at the other

end. Cross-effect will add or subtract from the direct effect depending on the phase

angle between them. Corrections for unbalance at one end will change the cross-effect

and thus the unbalance readings at the other end.

Another problem is that the unbalance is measured by the pickups in the rotor bearing

planes – that is, at the pickups mounted on the rotor carriage. Corrections of the

unbalance are not made at the bearings but at correction planes somewhere else on the

rotor.

Dynamic balancing is not inherently simple, but a simple method, empirical balancing,

can do a very good job. This may be done with a variety of ways, one of which will be

explained below. All empirical methods measure the initial unbalance, then place a trial

weight somewhere on the rotor. This introduces a new mass which combines with the

initial unbalance to form a new total unbalance and a reading of this unbalance is taken.

Multiple runs with a trial weight placed at different locations around the rotor provide

sufficient information to accurately balance it.

This empirical balancing method does not require vector diagrams or calculations4. To

understand the method I will use vector diagrams for illustrations. They provide a

means of visualizing the process, in particular how the addition of a trial weight changes

the resulting unbalance.

VECTOR DIAGRAM

Unbalance in a rotor has two dimensions: its amount and its location. Quantities with

two dimensions are vectors and are depicted in a vector diagram. An unbalance vector

is a line whose length is proportional to the amount of unbalance. The tail of a vector is

at the center of the diagram and its tip points toward the location of the unbalance.

4 There are other balancing methods which do rely upon vector diagrams or calculations.

Unbalance vectors are written as its name followed by an amount of weight at a

location: U = 0.6 gm @ 1.

The effect of the unbalance is measured by the balancing amplifier. An effect vector

also has two dimensions: the amount shown on the amplifier meter and the location on

the rotor illuminated by the strobe flash. The length of an effect vector is proportional to

the meter reading and the tip of the vector points to the location of the flash on the rotor.

Effect vectors are written as it name followed by the meter reading and the flash

location: EU = 3.2 @ 18.

The conventions for labeling the vectors are:

1. U: initial unbalance

2. TW: trial weight

3. R: the sum (resultant) of the initial unbalance U and a trial weight TW

4. EU: the measured effect of an initial unbalance

5. ER: the measured effect of R the sum of U and TW

6. Subscript letters L or R indicate the end of the rotor where necessary

Similar vectors are used for two different parameters: an unbalance and its measured

effect. The unbalance vector will have the name U, TW or R and the amount will

include the unit of the unbalance weight U = 0.6 gm @ 1. The effect or measurement

vector will prefix the name with E (the effect of) and the amount will be the meter

reading only with no unit: EU = 3.2 @ 18.

FIGURE 1

Figure 1is the left end view of the rotor used in these demonstrations. The numbering

begins at the top of the rotor. The direction of rotation is counter-clockwise and the

numbers increase in this direction. There is no zero location – the numbers begin at 1

and the rotor has been divided into 24 locations. Number 25 will be used in some of the

tables – it is the same location as #1.

The unbalance vector is the vertical line beginning at the center and pointing toward the

location of the unbalance – the black dot at #1. It is read as: the initial unbalance vector

U is 0.6 gm at #1.

The effect vector is the line beginning at the center of the diagram and pointing toward

#18. The two parameters of this vector are the meter reading and the location number

illuminated by the strobe flash. Effect vectors are read as: the effect of the unbalance U

is 3.2 at #18. The effect vector EU shows a phase shift of 105° counter-clockwise from

the location of the unbalance. Because the direction of rotation is also CCW, this would

imply that the flash occurs ahead of the unbalance. This is, of course, impossible and

the flash has to occur after the unbalance so the phase shift is 360° - 105° = 255°.5

These notes assume that the reader knows that vectors may be added by one of two

ways: the parallelogram or the head to tail method. This balancing school will use the

head to tail method extensively. If you are not familiar with vectors and how they are

added and subtracted, please take time to do a little bit of homework. This knowledge

is essential for any balancing technician. Your reward for obtaining this information will

be a better understanding of the problems inherent in balancing and how they are

overcome.

THE BALANCING PROBLEM

The rotor has been unbalanced with a 0.6 gm weight at location #1 in the left end and

installed in the balancing machine. The first run yields a measurement of the initial

unbalance EUL = 3.2 @ 18. There are immediately two problems. The meter reading

has no meaning and the flash is indicating the wrong location. The true effect of an

unbalance is always at the same location as the unbalance. The effect vector EU in

Figure 1 is at a 105° angle from the true location of the unbalance. The heavy spot on

the rotor is at #1; the flash is at #18: the strobe is indicating the wrong location. The

amplifier has a phase shift.

5 The amplifier has been setup to read the light side so the phase shift from the heavy side is 180° away

and the phase shift is 255° - 180° = 75° after the light side.

It gets worse. No unbalance has been installed in the right plane but it now has a

reading UR = 0.5 @ 13. The unbalance in the left end has generated an apparent

unbalance in the right end. This is cross-effect. During the balancing procedure a

change in the amount of unbalance will affect the amount and location of the unbalance

in the other end.

The dynamic balancing problem is that the meter reading is only a number, the strobe

flash may be at the wrong location, and any correction at one end may change the

unbalance at the other end. Despite this, a technician using the Empirical balancing

method will be able to quickly balance any rotor. The process is able identify the heavy

and light spot(s), correct for phase shift, and cancel any cross-effect.

These notes assume that the basic setup procedure of the balancing amplifier has been

completed: all switches and potentiometers have been set to their initial settings, the

filter has been tuned to the operating speed of the balancing machine, and the operator

has selected the appropriate scale for the amount meter.

THE BASIC PRINCIPLE OF EMPIRICAL BALANCING

Note on professional with phase response and empirical w/o phase – the basic principle

does not need or use phase

The empirical “amount only” procedure begins with by running the rotor in the balancing

machine in its as received condition and the amount of unbalance is recorded at the top

of a table as the initial readings. For Table 1 they are: the initial unbalance U is 0.6 gm

@ #1. The effect EU is 3.2 @ 1. The amplifier has been adjusted for no phase shift

and reading the heavy side. Therefore the effect vector lies on the unbalance vector,

that is, they point to the same location.

A trial weight is applied at successive locations around the rotor beginning at location

#1(Columns 1 & 3). The meter readings and strobe flash location are recorded for each

trial weight location (Columns 2 & 4). Table 1 is the complete data set for most of the

experiments in the balancing school. It includes both the amount and location of EU,

although the first empirical balancing method will use only the amount.

U = 0.6 gm @ 1 EU = 3.2 @ 1 EU = 3.2 @ 1

TW @ Location Effect ER TW @ Location Effect ER

0.3 gm @ 1 4.6 @ 1 0.3 gm @ 13 1.5 @ 1

0.3 gm @ 2 4.4 @ 1½ 0.3 gm @ 14 1.7 @ 24

0.3 gm @ 3 4.3 @ 2 0.3 gm @ 15 2.0 @ 23½

0.3 gm @ 4 4.2 @ 2 0.3 gm @ 16 2.4 @ 23

0.3 gm @ 5 4.0 @ 2½ 0.3 gm @ 17 2.7 @ 23

0.3 gm @ 6 3.7 @ 2½ 0.3 gm @ 18 3.0 @ 23

0.3 gm @ 7 3.5 @ 2½ 0.3 gm @ 19 3.4 @ 23½

0.3 gm @ 8 3.0 @ 3 0.3 gm @ 20 3.6 @ 23½

0.3 gm @ 9 2.7 @ 3 0.3 gm @ 21 4.0 @ 24

0.3 gm @ 10 2.4 @ 3 0.3 gm @ 22 4.2 @ 24

0.3 gm @ 11 2.0 @ 2½ 0.3 gm @ 23 4.3 @ 24

0.3 gm @ 12 1.7 @ 2 0.3 gm @ 24 4.4 @ 24

0.3 gm @ 25 / 1 4.6 @ 1

Table 1

The amount readings in Columns 2 & 4 are then plotted on the vertical axis of a graph

(Figure 2) against the locations of TW (Columns 1 & 3) on the horizontal axis. The

heavy spot is clearly at #1 and the light spot is at #13.

Figure 2

The simple method of placing a trial weight at successive locations around the rotor has

revealed the heavy and light spots. No location information was used or needed. The

amount meter has solved the problem of locating the unbalance.6

EMPIRICAL, TRIAL AND ERROR, BALANCING

The data in Table 1 and Figure 2 were developed by placing a trial weight in each of the

tapped holes in the proving rotor and recording the measurements. This works well but 6 There are slight measurement errors in this data set. The amounts for the trial weight placed at #1 (and

#25 which is the same location) are slightly high due to the placement of the trial weight at this location.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30

U

N

B

A

L

A

N

C

E

LOCATION

takes some time. We can use the data to learn how to simplify the process. Our

starting point is the amount of the initial unbalance effect: EU = 3.2. A trial weight at

most but not all locations on the rotor will change that amount. There are two locations

for the trial weight at which the meter reading will be the same as the initial unbalance.

Figure 3 will show us how this works.

Figure 3

If the trial weight is added at the heavy spot their weights add; if the trial weight is added

at the light spot their weights subtract. Somewhere between these two limits there has

to be two locations at which the effect of the trial weight makes no change in the

measured amount of combined unbalance. A horizontal line in Figure 3 has been

drawn at the amount of the effect of the initial unbalance: EU = 3.2. This divides the

graph into two regions: above the line the measured amounts are greater than the initial

unbalance effect and below the line the amounts are less.

Somewhere between #7/8 and # 18/19 the measured amount will be the same as the

effect of the initial unbalance. A trial weight placed at locations #1 to #7 and 19 to # 24

will increase the meter reading and a trial weight placed at locations #8 to #18 will

decrease the meter reading. The amount of the first trial weight run will almost always

indicate whether the weight is closer to the heavy or to the light spot. For the second

run move the trial weight one side or the other of the first run. If the amount increases

the weight has been moved toward the heavy side. If the amount decreases the weight

has been moved toward the light spot. At this time you will know which side the trial

weight is on and in which direction the heavy or light spot – the unbalance – will be

found.

You may chose to move in either direction. In general it is preferable to move toward

the light spot particularly if the rotor has significant unbalance. If the initial unbalance of

the rotor is small it may be advantageous to move the trial weight toward the heavy

spot. Continue moving the weight until the minimum or maximum reading has been

found.

The size of the trial is not critical. It should be large enough to make a change in the

measurements but not so large that the vibration becomes excessive. That sentence

did not say much other than that it is a judgment call. George says that after years of

experience he can estimate a beginning weight while damping the initial vibration with

his fingers on the rotor carriage. George does job shop balancing using soft bearing

balancing machines. The rotor is supported in bearings that are free to move in the

horizontal plane. When the balancing machine accelerates the rotor to the operating

speed, the angular acceleration causes the rotor and its bearing carriages to vibrate at

their natural frequency. He damps this vibration with a finger on each carriage and the

force that he feels gives him an estimate of the unbalance. He can then pick a trial

weight. If you are using a hard bearing machine this short cut is not available to you.

A trial weight that is larger than the initial unbalance will generate a data table and curve

like those shown above. The only difference is that the high and low amounts will have

a greater difference and the cross-over point between the high and low side will be at a

different location. The location of the cross-over is dependent upon the amount of the

trial weight.

Let’s balance this rotor using the empirical “amount only” method. We will do a thought

experiment using the data in Table 1 as an example.

1. First run: the effect of the initial unbalance is EU = 3.2

2. Select a trial weight and install at some location on the rotor and make another

run.

3. TW = 0.3 gm

4. The location is #15 and the meter reading is R = 2.0: #15 is on the light side of

the rotor

5. Move the trial weight to one side or another of #15

6. The location is #16 and the amount is 2.4: the heavy side is toward the higher

numbers

7. We want to find the light side so move the trial weight to a lower number

8. The location is #14 and the amount is 1.7 We are going the right way.

9. The next location is #13 and the amount is 1.5.

10. The next location is #12 and the amount is 1.7. We have gone one division too

far.

11. The final location is #13. The light is at or near #13 and the amount is 1.5.

The rotor is not yet completely balanced. Adding more weight at #13 will complete the

balancing procedure:

TW @ Location Residual Unbalance

0.3 gm @ 13 1.5

0.4 gm @ 13 1.0

0.5 gm @ 13 0.5

0.6 gm @ 13 0.02

0.7 gm @ 13 0.5

Table 2

A trial weight of 0.7 gm @ 13 is clearly too much correction. The final correction would

be 0.6 gm at #13. Any residual unbalance may be checked and possibly improved by

adding or subtracting very small amounts to the trial weight and slightly shifting its

location. We have balanced the rotor using only the amount reading from the amplifier

meter.

Dynamic balancing is the art and science of finding and correcting the hidden unbalance

which may be anywhere in the rotor. The amplifier provides hints by measuring the

effect of the initial unbalance and the effects of a trial weight placed at several locations

on the rotor.7 You must interpret these hints and manipulate the trial weight to reveal

the hidden unbalance.

This empirical, trial and error, method is the simplest method but it may not be the

fastest. It is suitable for one-off improvised balancing where the sophisticated

equipment of the professional is not available. The next step up is an amplifier which

has both a meter to read the amount and a strobe to indicate the location. Indicating

the location is more difficult because a phase shift in the system may cause the flash to

indicate a wrong location. These amplifiers are setup to correct the location information

and to directly measure the amount of correction. This greatly reduces the amount of

time required to balance the remaining batch of identical rotors.

The next three sections are a detailed discussion of the problem of indicating the correct

location of the unbalance. Some interesting things happen when location information is

provided by the flash of the strobe. The graph of the amounts is a nice cosine curve.

7 Add a note here about the power point on balancing for more information. Add info to pp on

displacement, velocity, and acceleration.

The location information is more complex and this reveals more about the effect of

adding a trial weight to an initial unbalance.

HOW THE INITIAL UNBALANCE AND TRIAL WEIGHTS COMBINE

The initial unbalance and the additional unbalance generated by the trial weight will add

vectorially. Eight of the entries from the complete data set in Table 1 and Figure 2 were

selected for this exercise.

Table 3 Figure 2

Column 1of Table 3 contains the locations of the trial weight for this example. Column 2

reports the measurements (Effect) taken at each location of TW. Figure 2 is repeated

here for a visual graphical presentation of the data at all 24 locations. At location #1 the

trial weight is at the same location as the initial unbalance U and the amount of the total

effect the greatest. At the succeeding locations, the amount of the effect decreases

because TW is moving away from the heavy spot and toward the light spot. At location

13 TW is 180° from U, that is, TW is at the light spot, so the amount of the trial weight

vector subtracts from the amount of the unbalance vector and the total effect is the

least. As TW continues to move to higher numbered locations it is moving away from

the light spot toward the heavy spot and the amount of the effect increases. So far so

good.

Now look at the flash angle for each location of TW. The amplifier is reading the heavy

side so at location 1 the flash is at 1. As TW is stepped around the rotor, away from the

heavy side and toward the light side, the total unbalance (U + TW) will also move away

from the heavy side and toward the light side, that is for the first 4 locations (#1 to #10).

The change in the flash angle is slow: while U + TW moves 10 locations, the flash angle

moves only 2 divisions. Then suddenly at the next location of TW, #13, the flash angle

returns to #1. A the next location, 16, the flash angle jumps in the other direction to #

22 and then moves slowly back to 1. This is unexpected. Let’s expand the segment of

Table 2 from #10 to #16 to see this in more detail.

U = 0.6 gm @ 1 EU = 3.2 @ 1

TW @ Location Effect

.3 gm @ 10 2.4 @ 3

.3 gm @ 11 2.0 @ 2½

.3 gm @ 12 1.7 @ 2

.3 gm @ 13 1.5 @ 1

.3 gm @ 14 1.7 @ 24

.3 gm @ 15 2.0 @ 23½

.3 gm @ 16 2.4 @ 23

Table 4

Table 4 shows that the phase angle does not jump between #10 & #13 and between

#13 & #16 it moves smoothly. It moves faster than between locations #1 & 10 and

between #16 & 1.

In Figure 2 the amount decreases smoothly from TW @ #1 to TW @ # 13 then

increases smoothly from TW @ # 13 to TW @ #1. The location begins at #1, the effect

is in phase with the unbalance, and then moves from #1 to #3 as the trial weight is

stepped from #1 to # 9. Then the location reverses direction and moves back to #1 as

the trial weight is stepped from #9 to #13. A similar change is seen at the trial weight is

moved from #13 to #1.

Figure 4

All of the data in Table 3 is graphed as vectors in Figure 4. The initial unbalance weight

is the black dot at location #1. The tail of its unbalance vector U is at the center of the

rotor and its head points to #1. The trial weight unbalance vectors are also drawn from

the center of the rotor. These vectors have the same amount = 0.3 gm and their tips will

be at the same radius from the center and therefore lie on a circle.

To add the trial weight vectors TW to the initial unbalance vector, the tails of all the TW

vectors and the center of the trial weight circle are moved to the tip of U (Figure 5).

Figure 5

Figures 4 & 5 are a bit complex and do not show the sum of U and TW. The sums of all

eight locations of TW are shown individually in Figures 6 & 7. At each location of TW

the sum of the initial unbalance U (which is stationary) and the trial weight TW is the

resultant R. The vector sum of U and TW combine the amounts of unbalance and the

angle between them: they add vectorially.

A B C D E

Figure 6

A. The trial weight is at the same location as the unbalance: the phase angle = 0°.

The amounts of unbalance add and the resultant R lies on the same line as U.

(U and TW are shown offset to right and between dimension extension lines for

clarity).

B. TW has moved to location #4 and its vector is at 45° from U. R has rotated in the

same direction as TW and the heavy spot is now located at #2 (rounded to the

nearest ½ division to match the reading of the strobe flash). The amount of

unbalance has decreased because TW has moved from the heavy spot and

toward the light spot.

C. TW has moved to location #7 and its vector is at 90° from U. The amount

continues to decrease and R is now located at 2½.

D. TW is at location # 10 and its vector is at 135° from U. The amount of R

continues to decrease and R is now located at #3.

E. TW is at location #13 and its vector is at 180° from U. The amount of R is as low

as it will go. But R has moved in the opposite direction and is now pointing back

at its origin at #1. The location of R – the heavy spot – will be at #1 when TW

lies on a common line with U, either at an angle of 0° or 180°.

Reminder: it appears that the location of R has jumped counter-clockwise from #3 to #1

but Table 4 shows that it has moved very rapidly as TW rotates clockwise from #10 to

#13.

Figure 7 continues the rotation of TW clockwise from #13 to #1:

F G H I

Figure 7

F. As TW rotates from #13 to #16 the amount of unbalance R increases. In this

interval the location of the unbalance moves rapidly from #1 to # 23 moving in the

opposite direction from the direction of TW.

G. TW rotates to #19 and is now at a right angle to U. The amount of unbalance

continues to increase and the location is moving in the same direction as TW and

is at 23½.

H. TW is at 22 and the amount of R is increasing. The location of the heavy spot is

at 24.

I. The trial weight has returned to location #1. The amount of unbalance is at its

maximum and the heavy spot is once again at #1. (U and TW are shown offset

to right and between dimension extension lines for clarity).

The process of stepping a trial weight around the rotor has revealed the location but not

the amount of the initial unbalance. When the trial weight is at the heavy spot the

amount is at a maximum and the flash will illuminate the same location as it did for the

initial unbalance. When the trial weight is at the light spot - 180° from the heavy spot –

the amount will be at its minimum and again the flash will be at the same location as the

initial unbalance. This is the fundamental principle of empirical, trial and error, dynamic

balancing.

SELECTION OF THE TRIAL WEIGHT

The next question is the effect of different trial weight amounts. Two more sets of runs

were made with larger trial weights than the previous examples (Table 5). The first row

of the table is the ratio of the trial weight to the initial unbalance. All of the data for the

illustrations in the previous sections were for a trial weight one-half of the initial

unbalance (Columns 1 & 2). The two new runs are for a TW that is 0.8 times U (TW =

0.5 gm, Columns 3 & 4) and for a TW that is 1.25 times U (TW = 0.8 gm, Columns 5 &

6).

U=0.6 gm @1 EU = 3.2@ 1

TW ÷ U 0.5 0.8 1.25

TW & Loc Effect ER TW & Loc Effect ER TW & Loc Effect ER

.3 @ 1 4.6 @ 1 .5 @ 1 5.4 @ 1 .8 @ 1 6.5 @ 1

.3 @ 4 4.3 @ 2 .5 @ 4 4.9 @ 2½ .8 @ 4 6.1 @ 2½

.3 @ 7 3.5 @ 2½ .5 @ 7 4.0 @ 4 .8 @ 7 4.9 @ 4½

.3 @ 10 2.4 @ 3 .5 @ 10 2.4 @ 4½ .8 @ 10 3.0 @ 6

.3 @ 13 1.5 @ 1 .5 @ 13 0.9 @ 1 .8 @ 13 0.9 @ 13

3 @ 16 2.4 @ 23 .5 @ 16 2.3 @ 21½ .8 @ 16 2.9 @ 19

.3 @ 19 3.5 @ 23½ .5 @ 19 3.9 @ 22 .8 @ 19 4.9 @ 21

.3 @ 22 4.3 @ 24 .5 @ 22 4.9 @ 23½ .8 @ 22 6.0 @ 23

.3 @ 1 4.6 @ 1 .5 @ 1 5.3 @ 1 .8 @ 1 6.5 @ 1

Δ Amount 2.8 4.5 5.6

Δ Location +/- 2½ Div +/- 3½ Div +/- 12 Div

Table 5

The bottom two rows summarize the effects of different trial weights. A larger trial

weight asserts a greater influence on the total unbalance. The change in both the

amounts and the range of the indicated locations increase with larger trial weights.

There is an interesting and important difference in the indicated location when TW is

greater than U. The location of the total R for the three different trial weights at #13 are

highlighted in bold in the center of the table. If TW is less than U the location of the

resultant is at #1, the initial heavy spot. If TW is greater than R then TW has formed a

new heavy spot which is now located at #13.

The last row of Table 5 lists the range of the indicated location for the three trial weights.

This may be illustrated in a vector diagram. A trial weight circle, which represents the

tips of all the possible trial weight vectors of the same weight is drawn from the tip of U

(Figure 8).

.

Figure 8

Next two vectors R, the sums of U and TW, are drawn tangent to the TW circle and

extended to the location circle. These vectors and their extensions define the maximum

change in the location. Figure 8 shows that when the ratio of TW to U (TW ÷ U) is 0.3,

the maximum excursion of the location flash is ± 1 division. For the next three

examples the vector diagram has been further simplified by removing the unused part of

the location circle.

Figures 9A, 9B & 9C illustrate how the range of the location increases with a larger trial

weight. If TW is less than U (Figures 9A, B) the location oscillates back and forth

between these two extremes of R as TW rotates around the trial weight circle. The

location is at #1 when the trial weight is at #1 or #13. Figure 9C shows that when TW is

greater than U the strobe flash will occur at any of the locations on the weight circle as

TW rotates around the trial weight circle.

FIGURE 9A Figure 9B

Figure 9C

Summary: there are no hard rules for the selection of the weight of the trial weight. It is

difficult to measure the effects of a small trial weight. A weight that is too large could

cause excessive vibration. If the measured effects of the trial weight are too small,

increase the weight. If the vibration of the rotor and carriage becomes too large

decrease the weight. This is a matter of the operator’s judgment.

PHASE ANGLE OR LOCATION

Balancing a rotor requires two pieces of information. The first is the amount of the

unbalance. This is relatively easy to acquire. The output of the pickups and the meter

reading are proportional to the amount of unbalance. The meter reading will decrease

as the rotor balance is improved, that is, as the amount of unbalance decreases.

The second piece of information that is required to balance a rotor is where to put the

correction. This is harder to acquire. The placement of a correction should be at the

correct location within small limits. The strobe flash will illuminate one number on the

divisions marked on the rotor. The number of divisions and the accuracy of their

placement will vary. An inherent problem of balancing under these conditions is that the

operator can see that the flash strikes at, for example, #5 on an 10 division scale but the

numbers on this scale span 36°. Where in this span does the correction go?

The second problem is that there are phase shifts throughout the system. There is no

fixed or positive correlation between the location of the unbalance and the strobe flash.

It is influenced by the RPM of the rotor, the setting of the filter and the phase shift

potentiometers, and the switches on the front panel. The strobe flash may be at a

completely different spot than the .

Figure 10

Figure 10: the rotor is unbalanced by 0.6 gm at #1 in the left end. The rotation of the

rotor is counter-clockwise. The flash occurs at #18, 7 divisions ahead of the heavy spot,

from a larger to smaller division number. A better way of expressing this phase shift is

that it is 255° after the high spot has passed the operator’s view at top dead center.

This phase shift is caused by several factors. First, the arrows outside the location

circle at numbers 7 & 19 show the direction of the motion of the carriage. The pickups

sense the oscillation of the carriage and trigger the flash when the carriage stops

moving in one direction and reverses to the other direction. Detection of the movement

of the carriage occurs in the horizontal plane and, for the balancing machine used in this

balancing school, the operator views the rotor from the top. This accounts for 90° of the

105° phase shift. This ‘zero point’ is difficult to find accurately and the circuitry used in

the amplifier for this detection is inherently less stable than the amount meter circuit.

There may be some errors in this circuit.

The filter circuit generates a phase shift in its output signal as it is tuned. There may an

unknown phase change in this circuit. Last, there is a phase shift circuit in the amplifier

to correct for these errors. The flash angle may be adjusted by a potentiometer but this

control may not be adjusted correctly.

Determining the location of the unbalance is inherently more difficult than measuring the

amount. The empirical balancing method is able to find the location of both the light and

heavy spots by stepping a trial weight around the rotor, even in the presence of a phase

shift.

EMPIRICAL BALANCING WITH PHASE SHIFT

You have a rotor mounted in the balancing machine. You do not know whether the

unbalance is an excess weight or a deficiency of weight. You do not where it is. The

meter readings are only a number and the strobe flash is probably illuminating the

wrong location. And you don’t know if that wrong location is on the heavy or light side.

That’s a quite a litany of bad news. What do you do? You run the basic empirical

balancing method using both the amount and location readings. What follows is a

variety of this method and the explanation is more detailed.

Let’s think about this a bit. How does the amount change as the trial weight is stepped

around the rotor when there is no phase shift? First, the amount is at its maximum

when the trial weight is at the heavy spot: TW will add to U. The amount is at its

minimum when the trial weight is at 180° from the heavy spot – the light spot: TW will

subtract from U. The meter will locate the . The strobe will illuminate either the heavy

or light spot depending upon the setup of the amplifier and the geometry of the rotor.8

8 All of the discussion of balancing so far has used a symmetrical rotor mounted between its bearings and

there has been no mention of the setup of the amplifier – whether it is reading the heavy or light spot. An overhung rotor may have reversed location readings, hence the note “depending upon … the geometry of the rotor.” Most amplifiers will have a switch for the operator to change which side is read.

Second, how does the location change as the trial weight is stepped around the rotor?

We know from Figures 6 & 7 that the resultant of adding a trial weight at the either the

light or heavy spot lies on the initial unbalance vector. That is, at these two locations

there is no change of the indicated location – which may be in error due to phase shift.

The effect of TW at any other location is to move the indicated location – the strobe

flash – away from the initial indicated unbalance location, oscillating through some

angle if TW is less than U or going around the circle if TW is greater than U.

A phase shift in the amplifier simply moves all the indicated locations some fixed

amount in one direction. The relative locations remain the same. The light and heavy

spot will be mis-identified but they will be 180° apart. The intermediate readings will

change as shown in Figures 6 & 7 above.

Let’s go looking for the unbalance using the data for the previous experiments (Table 1)

to balance the rotor. At each step in the process a table will list the previous and

current meter reading and strobe flash location and explain their significance. Those

measurements by themselves have little or no meaning. The change of the

measurements is the key: which way are they moving. Is the meter reading larger or

smaller; is the indicated location at a smaller or larger number?

This process will begin at some meter reading and at some indicated location which will

be the location of the initial unbalance plus or minus some phase angle. The addition of

a trial weight will change the meter reading and, if the trial weight is not placed at the

unbalance, the indicated location will change, that is there will be an additional phase

shift caused by the trial weight.

Our goal is to place the trial weight at the unbalance. The meter reading will be at either

its maximum or minimum. The strobe flash will occur at the same location as that of the

initial unbalance – that is, there will be no additional phase shift caused by the trial

weight. This process will use both measurements together to locate the unbalance.

Step 1: run the rotor and record the effect EU of the initial unbalance U:

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

What does this tell us? The amount is just a number and without another number to

compare it with, it has little meaning. The location number is the true location of the

unbalance plus an unknown phase shift.

Step 2: this gives us a starting point. Let’s put the trial weight at the indicated location

#18, run the rotor and record the effect of the first trial weight location:

EU = 3.2 @ 18

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

What do we know now? The effect of adding the trial weight is to decrease the amount

of unbalance by a small value, from 3.2 to 3.0, and move the indicated location by two

divisions to a smaller number. In comparison to the small change of the amount, this is

a large change. The amount went down so the trial weight has been moved away from

the heavy spot and toward the light spot. The change in location is, as we will soon see,

is ambiguous. For this step #18 appears to be closer to the heavy spot than #16 and

conversely, #16 to closer to the light spot, but it may not be.

Step 3: To resolve this ambiguity we will next move the trial weight to the new indicated

location #16.

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

0.3 gm @ 16 2.4 @ 16

The new reading is 2.4 @ 16. The amount changed by a lot and we are now certain

that the light spot is at a lower number but the location did not change at all. Should it

have changed? Why didn’t it change? Figures 6 & 7 provide the answer but let’s use

what we have learned about empirical balancing and continue moving the trial weight in

the same direction. Remember that the amount meter tells the truth – the location

information is more complex .

Step 4: move the trial weight to #14:

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

0.3 gm @ 16 2.4 @ 16

0.3 gm @ 14 1.7 @ 17

The new reading is 1.7 @ 17. We are definitely moving the trial weight toward the light

spot and the location is almost back to the initial unbalance at #18. This implies that the

trial weight is less than the weight of the initial unbalance and the location of the trial

weight is approaching the light spot. Both measurements are telling us the same thing.

Step 5: So far we have moved the trial weight 2 divisions each time. We will continue

this:

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

0.3 gm @ 16 2.4 @ 16

0.3 gm @ 14 1.7 @ 17

0.3 gm @ 12 1.7 @ 19

The new reading is 1.7 @ 19. The amount went up from 1.5 to 1.7 and the location

moved two divisions from #17 to #19. The trial weight has been moved too far and is on

the other side of the light spot. We now know that the correct location is #13.

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

0.3 gm @ 16 2.4 @ 16

0.3 gm @ 14 1.7 @ 17

0.3 gm @ 12 1.7 @ 19

0.3 gm @ 13 1.5 @ 18

Step 6: the final location of the trial weight is at #13. The amount is 1.5, the lowest

possible effect with this trial weight. The location is the same as the initial unbalance

effect reading. The conclusion is that the trial weight is at the light spot. That’s it.

When you know how to read the change in the indicated location it will tell the same

story as the amount.

The amount meter says that the rotor is not yet balanced so the trial weight is too small.

I measured the trial weight at the beginning – it is 0.3 gm. It has reduced the initial

unbalance from 3.2 to 1.5, about half. I have a 0.3 gm set screw in place at 13 so I’ll

add a 0.3 gm clay trial weight at 13 and see what happens. The clay weight will go on

the outside diameter of the rotor so the radius of its effect will increase, but 0.3 gm will

be a good start. A problem with clay weights is that it is applied as a lump so its radius

and location are uncertain.

EU = 3.2 @ 18.

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.0 @ 16

0.3 gm @ 16 2.4 @ 16

0.3 gm @ 14 1.7 @ 17

0.3 gm @ 12 1.7 @ 19

0.3 gm @13 1.5 @ 18

0.6 gm @ 13 0.4 @ ≈ 1

The residual unbalance is 0.4 at an indistinct location somewhere around #24 to #3.

The amount is excellent, could be improved, but the location continues to move away.

It moved from #18 to #1, a large change. The trial weight is too heavy for its increased

radius. This is where claying the rotor9 has an advantage: cut off a tiny bit of clay and

run the rotor again. You may push the clay lump a small amount one way or the other

and find some improvement.

The final runs are truly trial and error. We are looking for very small improvements in

both the amount. The amplifier is no longer able to sense the location of the residual

unbalance – the flash will appear to be at different locations. Take your time. George

was taught by his father and uncle to make haste slowly. Add and subtract small

pieces of clay, push the clay lump a tiny distance one way and then the other always

watching the effect. At some point using the most sensitive scale on your amplifier you

will have balanced the rotor as well as you can. There is no such thing as perfect

balance. There is only a point at which you can not reduce it with your balancing

machine and amplifier, and the time you wish to spend. The best I could do after

numerous runs was R = 0.04 ≈ 1. The unbalance was improved from 3.2 to 0.04, a

factor of 80.

Let’s put in some real unbalance numbers. The initial unbalance U was 0.6 gm at a

radius of 0.875” = 0.525 gm-in. The reduction in unbalance was a factor of 80 so the

residual unbalance is 0.525 gm-in ÷ 80 = 0.0066 gm-in. The residual unbalance weight

is the residual unbalance divided by its radius from the center of the rotor = 0.0066 ÷

0.875 = 0.0075 gm. This may not be gyroscope balance but it is very good.

This set of runs began with the trial weight at 18 and moved to smaller location numbers

to find the light spot. We could have balanced the rotor by moving the trial weight the

other way. The indicated location of the initial unbalance was #18, the addition of the

trial weight at #18 moved the resultant location to #16. The direction of movement was

from a larger to smaller number.

Some balancing manuals instruct the operator to next move the weight in the opposite

direction. Instead of moving the trial weight to the new indicated location #16, go the

opposite way from #18 to say #20. Table 6 shows the results:

9 George, my mentor, uses modeling clay almost exclusively for trial weights.

EU = 3.2 @ 18

TW @ Location Effect (U + TW)

0.3 gm @ 18 3.2 @ 16

0.3 gm @ 20 3.7 @ 16½

0.3 gm @ 22 4.2 @ 17

0.3 gm @ 24 4.4 @ 17½

0.3 gm @ 1 4.6 @ 18

0.3 gm @ 2 4.5 @ 18½

Table 6

Once again the amount of the effect of adding a trial weight at successive locations has

located the unbalance, this time the heavy spot. Those balancing manuals do caution

the operator that the unbalance may increase during this process. It is your choice, go

either way. If you go toward the heavy spot monitor the unbalance to insure that the the

rotor cannot lift out of the balancing machine.

The location information has been erroneous through this process. The last step to

adjust the amplifier to read the . Leave the trial weight(s) in place and add another

small trial weight at a spot away from the balancing trial weights. You want to create a

new unbalance, a new pair of heavy and light spots, at a known location on the rotor.

Because there is a phase shift the strobe will not illuminate the new unbalance. Adjust

the amplifier phase shift potentiometer as needed to bring the clay weight to the top of

the rotor.

Just one problem remains. If you cannot adjust the phase shift to illuminate the heavy

spot – the amplifier is set to read the light spot. This one is easy. Simply flip the two

A/B switches for the side of the rotor with the unbalance and the strobe will show the

heavy side. Now the phase shift can be adjusted. Some of the RetroTek amplifiers

have an’ invert heavy to light’ switch included with the phase adjust potentiometer.

Push or pull the knob to change which spot is illuminated. The last resort is to adjust

the filter. It creates a phase shift which changes as it is tuned – it is very good at that.

The problem with using the filter to tune the phase shift is that as the filter goes out of

tune the amount reading on the meter will decrease – the amplifier becomes less

sensitive.

In general, once the phase shift has been set for an amplifier in a specific balancing

machine it should not be necessary to repeat this setup process. The setting of the

phase shift will be checked during the plane separation and calibration setup and will be

fine tuned then if necessary.

One more bit of advice, if during any run things appear to be going haywire, check to

see if a clay weight has departed into the unknown.

Summary of the empirical balancing procedure:

1. Run the rotor in its original as received condition. Record or remember the

readings as the vector EU, the effect of the initial unbalance.

2. Install a trial weight at the location of EU and take the new reading.

3. The change in amount will indicate which direction to go. If the amount declines

the location of the trial weight is on the light side of the rotor. Continue to go in

that direction – that is if the location has gone from a higher to lower number

continue to a lower number.

4. If the amount increases move the trial weight in the opposite direction of change

of the location from the initial to the first trial run.

5. When the amount is at its minimum, and the strobe flash is at the location of the

initial unbalance effect, the trial weight is at the light spot. Or, when the amount

is at its maximum and the strobe flash is at the location of the initial unbalance

effect, the trial weight is at the heavy spot.

6. Once the unbalance has been located the trial weight may be adjusted to

balance the rotor as much as possible.

CROSS-EFFECT

So far the balancing school has looked at an unbalance in only the left end of the rotor

and at a known location. That was for simplicity and to demonstrate the basic principles

of the empirical balancing system. The balancing problem gets a bit more complex

when an additional unbalance is introduced into the right end of the rotor, and to make it

even more complex, this new weight will be in a different location than our initial left

unbalance. To study this effect the amplifier will be set to read the heavy spot directly –

no phase shift.

The unbalance weight in the left end of the rotor also unbalances the right end. This is

cross-effect: any unbalance or change in unbalance in one end affects the state of

balance in the other end.

To demonstrate cross-effect the rotor was first unbalanced with an unbalance weight U

= 0.6 gm in the left plane. Readings for the left plane direct effect and for the cross-

effect in the right plane were taken (Table 7).

U = 0.6 gm @ 1 in the left plane

Left Direct Reading Right C-E Reading

3 @ 1 0.6 @ 13

Table 7

That weight was removed and a smaller unbalance weight = 0.4 gm was placed in the

right plane and again readings for both planes were taken (Table 8).

U = 0.4 gm @ 15 in the right plane

Left C-E Reading Right Direct Reading

0.5 @ 5 1.4 @ 17

Table 8

These readings are the direct and cross-effects for each of the initial unbalances. The

left unbalance weight was re-installed and the readings for the combined unbalance are

shown in Table 9.

UL = 0.6 gm @ 1 in the left plane

UR = 0.4 gm @ 15 in the right plane

Total Left Reading Total Right Reading

3.2 @ 1½ 1.7 @ 16

Table 9

When all of the readings are combined into one table it is easier to see how the direct

and cross-effect combine (Table 10):

Left Plane Right Plane

Direct effect 3 @ 1 Direct effect 1.4 @ 17

Cross-effect 0.5 @ 5 Cross-effect 0.6 @ 13

Total effect 3.2 @ 1 Total effect 1.7 @ 16

Table 10

The cross-effect in the left plane (0.5) from the right plane unbalance is a small

percentage of the left plane direct effect (3.1) and does not make much change in the

total effect. The amount increases from 3.1 to 3.2 and the location does not change.

The cross-effect in the right plane (0.5) from the left plane unbalance is a larger

percentage of the right plane direct effect (1.7) and has a larger effect. The amount

increases from 1.7 to 2.2 and the location moves one division toward the cross-effect –

from 17 to 16.

Figure 11

A vector diagram (Figure 11) illustrates the addition of the amounts and locations of the

direct and cross effects for both the left and right planes. The legend for this diagram is:

EUL = Effect of unbalance in left end

CER/L = Cross-effect from right unbalance to left end

EUL + CER/L = Sum of direct and cross-effects at left end

EUR = Effect of unbalance in right end

CEL/R = Cross-effect from left unbalance to right end

EUR + CEL/R = Sum of direct and cross-effects at right end

Figure 11 shows the cross-effects adding to the initial unbalances. It is possible for the

cross-effect to reduce rather than increase the apparent unbalance at the other end. I’ll

leave drawing that vector diagram as an exercise for the reader. Cross-effect can be a

serious problem with overhung rotors. Those are a more advanced balancing problem

but the Gisholt method amplifiers cope with this easily using the techniques we have

learned so far. See the section on overhung rotors in the RetroTek Balancing Amplifier

Instructions for the details.

It is easy to correct for cross-effect. Simply work on the end of the rotor with the

greatest amount reading. After moving a trial weight, check each end of the rotor. The

next move of the trial weight will be at the end with the greatest reading. Go back and

forth as necessary until both ends are as well balanced as desired or possible.

At this point there are two possibilities: you may proceed directly to making corrections

on the rotor or you can calibrate the amplifier. If you are using a simple vibration

measuring system you can proceed directly to making the permanent correction. This

requires more time because each correction effectively begins a new balancing problem

and the succeeding correction must be determined by the empirical method.

If you are using a RetroTek, West Coast Balancing or other Gisholt type amplifier with

provision for adjusting phase shift, plane separation, and amount calibration the you can

setup the amplifier. The instructions for this are detailed here. The advantage of a

calibrated amplifier is that the amount and location of each successive correction is

calculated and displayed by the amplifier. Successive rotors of a batch may be

balanced directly without further adjustments of the amplifier.

Empirical balancing a rotor with clay trial weights on amount only is straightforward.

The amount meter tells no lies. The resultant unbalance of the trial weights when

stepped around the rotor follows a sine or cosine curve10. Once two or three data points

are obtained the operator will be able to locate the area of the curve in which the trial

weight is installed.

The addition of a strobe to indicate location of the unbalance introduces a complication:

as the trial weight is stepped around the rotor, the change in the indicated location does

not always match the change in the amount. The change in location is also a sine or

cosine curve but displaced at 90° to the amount curve. With this knowledge the

operator is able to use location in addition to amount information to balance the rotor.

CORRECTIONS: MAKE HASTE SLOWLY

The rotor is now temporarily balanced with trial weights. In George’s shop (and mine)

there will be a lump of modeling clay at the light spot on each temporary balancing

plane of the rotor.11 Permanent corrections will replace the clay by adding weight in the

permanent balancing plane (which may be the same as the temporary plane or in a

different location) or by removing weight at 180°. That choice will be determined by the

design and manufacture of the rotor and/or specified by the customer. The following

discussion will be based upon the removal of weight by drilling holes but that logic may

be extended to adding weight. It also assumes that the rotor will be balanced to the

least residual unbalance possible. The reason for this is to illustrate and explain the

10

Which curve is displayed is determined by the location of the first data point. 11

The temporary balancing planes may not be the same as the permanent correction planes.

problems that the operator might see when working to fine residual unbalance

tolerances.

The rotor is unbalanced by a 0.6 gm weight located at #1 and its vector is U. The

correction is made at a 7.5° error, either drilling a hole at 24 ½ or adding a weight at 12

½. In either case its vector C is opposite in direction to U.

A small correction (25% of U): C = 0.25 x 0.6 gm = 0.15gm (Figure 12A) is not sufficient

to make a large change in either the amount or location of the residual unbalance. R is

reduced by about 25% and the location error is closer to the unbalance location than is

the correction.

.

Figure 12 A Figure 12 B

A larger correction of 50% of U: C = 0.5 x 0.6 gm = 0.3 gm (Figure 12B) will reduce R by

nearly 50% but with a location error almost equal to the correction error. This would

work well if you are drilling holes because if further corrections are no larger than 50%

of the residual unbalance, the final corrections could be made with either 2 or 3 closely

spaced holes. This is considered to be the best looking and most professional pattern

of drilled holes.

A correction larger than 50% of U = 0.45 gm at our error of ½ division = 7.5° continues

to reduce the residual unbalance but at the cost of forcing the succeeding correction to

be made at a greater angle and outside the ideal closely spaced three holes (Figure

13A).

Figure 13 A Figure 13 B

This pattern continues with a correction of 100% of U (Figure 13B) at the same error

generates the greatest reduction in the residual unbalance but the location of the

succeeding correction will be at a bit more than 90° from the first correction.

Figure 14

A correction C that is greater (125 %) than the unbalance U will create a new heavy

spot at 180° from the correction (Figure 14). The subsequent correction R would be

about 150° from the first correction. That the location of a subsequent correction is at a

location greater than about 90° from the first indicates that the prior correction is greater

than the initial unbalance.

When balancing my test/demonstration rotor I found it very easy to remove too much

material when the residual unbalance was very low. The first result is that successive

corrections were made at greater angles and there were holes all the way around the

rotor. I was effectively chasing my tail trying to compensate for previous mistakes.

CONCLUSION

This Dynamic Balancing School was the result of my problems with empirical balancing.

I could successfully balance a rotor but I did not understand what I was doing. I was

always getting confused when the location did not go in a consistent direction. I

expected the change in location to be parallel to or consistent with the change in

amount. It isn’t. As the amount decreases the direction of change of the location can

reverse its direction and its change is at a different rate.

The biggest aids in understanding were the graph of the amount of unbalance against

the location of the trial weight in Figure 2. Then the vector diagrams in Figures 4 – 7

showed how the trial weight added to the initial unbalance. Once I tied the tail of the trial

weight vector to the head of the initial unbalance vector I could see the head of TW

rotating around the head of U in Figure. Then I could see the location oscillating back

and forth through an angle. And then I figured out that the angle of oscillation was

related to the ratio of the trial weight to the initial unbalance and I was almost there.

The last piece was that when the trial weight was at either the initial heavy or light spot

the strobe flash was at the location indicated for the initial unbalance. The strobe flash

does tell the truth, just in the presence of a phase shift it tells the truth only occasionally.

The amount meter always tells the truth and with those two pieces of information plus

the technique of managing cross-effect you too can empirically balance a rotor.

ACKNOWLEDGMENTS

Dennis for the first design of the amplifier. From it I learned that opamps were the

electronic device to use and I used two circuit modules from his design.

Scott for refusing to design the amplifier for me.

Steve for loaning me two books on operational amplifier circuit design.

Dick for introducing me to George Cox of Cox and Sprague Machinists, a professional

balancing technician with 50 years of experience.

George for loaning me a RetroTek balancing amplifier from which I reverse engineered

the amplifier front panel with its plane separation and calibration circuits which

implement the Gisholt balancing method. He also loaned me a rotor carriage from a

Gisholt balancing machine which I copied for my machine.