Section Subject Page
1. INTRODUCTION TO DYNAMIC BALANCING ... 1-1 2. TYPES OF UNBALANCE ... 2-1
A. Static Unbalance ... 2-2 B. Couple Unbalance ... 2-3 C. Quasi-Static Unbalance ... 2-4 D. Dynamic Unbalance ... 2-5
3. TYPES OF BALANCE PROBLEMS ... 3-1
A. Rigid Vs Flexible Rotors……… ... 3-1 B. Critical Speeds………... 3-4
4. HOW TO ENSURE THE DOMINANT PROBLEM IS UNBALANCE………. ... 4-1 A. Review of Typical Spectra and Phase Behaviors for Common
Machinery Problems ... 4-1 1. Mass Unbalance ... 4-1 2. Eccentric Rotor ... 4-1 3. Bent Shaft ... 4-3 4. Misalignment ... 4-3 5. Resonance... 4-3 6. Mechanical Looseness/Weakness ... 4-4
B. Summary of Phase Relationships for Various Machinery... 4-4
1. Force (or Static) Unbalance... 4-4 2. Couple Unbalance ... 4-4 3. Dynamic Unbalance ... 4-4 4. Angular Misalignment... 4-6 5. Parallel Misalignment ... 4-6 6. Bent Shaft ... 4-6 7. Resonance... 4-6 8. Rotor Rub... 4-6 9. Mechanical Looseness/Weakness Due to Base/Frame
Problems or Loose Hold Down Bolts ... 4-6 10. Mechanical Looseness Due to a Cracked Frame... 4-6
C. Summary of Normal Unbalance Symptoms ... 4-6
1. Special Characteristics ... 4-6 2. Centrifugal Force Due to Unbalance ... 4-6 3. Unbalance Force Directivity ... 4-7 4. Radial/Axial Vibration Comparison ... 4-7 5. Overhung Rotor Unbalance Directivity ... 4-7 6. Steadiness & Repeatability of Phase Due To Unbalance ... 4-8 7. Resonant Amplitude Magnification ... 4-8 8. Phase Behavior For Dominant Static,Couple & Dynamic Unbalance ... 4-8
TABLE OF CONTENTS AND SEMINAR AGENDA
Field Dynamic Balancing
Section Subject Page
5. CAUSES OF UNBALANCE ... 5-1
A. Assembly Errors ... 5-1 B. Casting Blow Holes ... 5-1 C. Fabrication Tolerance Problems ... 5-1 D. Key Length Problems ... 5-1 E. Rotational Distortion ... 5-3 F. Deposit Buildup or Erosion ... 5-3 G. Unsymmetrical Design ... 5-3
6. WHY DYNAMIC BALANCING IS IMPORTANT ... 6-1 7. UNITS OF EXPRESSING UNBALANCE ... 7-1 8. VECTORS ... 8-1
9. DYNAMIC FIELD BALANCING TECHNIQUES ...
A. Recommended Trial Weight Size ...
B. How a Strobe-Lit Mark On a Rotor Moves When a Trial Weight is Added ...
C. Single-Plane Balancing Using a Strobe Light And a Swept-Filter Analyzer ....
D. Single-Plane Method of Balancing ...
E. Balancing in One Run ...
F. Two-Plane Balancing Techniques ...
G. Cross-Effects ...
H. Single-Plane Method For Two-Plane Balancing ...
I. Vector Calculations For Two-Plane Balancing ...
J. Rotor Balancing By Static Couple Derivation ...
K. Single-Plane Balancing With Remote Phase And A Data Collector ...
L. Taking Phase Readings With A Data Collector...
M. Single-Plane Balancing Using A Data Collector ...
N. Two-Plane Balancing Using A Data Collector...
O. Overhung Rotors ...
P. Multi-Plane Balancing ...
Q. Splitting Balance Correction Weights ...
R. Combining Balance Correction Weights Using Vectors ...
S. Effect of Angular Measurement Errors of Potential Unbalance Reduction ...
1. Effect of Phase Angle Measurement Errors By Instruments ...
9-2. Effect of Angular Measurement Errors When Attaching Balance Correction Weights ...
9-TABLE OF CONTENTS AND SEMINAR AGENDA
Field Dynamic Balancing
Section Subject Page
10. Balancing Machines - Soft-Bearing Vs Hard-Bearing Machines ...
A. Soft-Bearing Machine ...
B. Hard-Bearing Machine ...
10-11. Recommended Vibration And Balance Tolerances ...
A. Vibration Tolerances ...
1. Recommended Overall Vibration Specifications ...
2. Synopsis Of Spectral Alarm Band Specifications ...
B. Balance Tolerances On Allowable Residual Unbalance ...
1. ISO 1940 Balance Quality Grades ...
a. Application of Tolerances to Single-Plane Problems ...
b. Application of Tolerances to Two-Plane Problems...
c. Application of Tolerances to Special Rotor Geometries ...
11-C. How to Determine Residual Unbalance Remaining in a Rotor After Balancing ...
D. Comparison of ISO 1940 With API and Navy Balance Specifications ...
11-APPENDIX A Balancing Terminology
APPENDIX B Weight Removal Charts
APPENDIX C Conversion Chart for Converting Inches of Flat Stock # 1020 Steel to Ounces of Weight
APPENDIX D Three-Point Method of Balancing
TABLE OF CONTENTS AND SEMINAR AGENDA
Field Dynamic Balancing
RECOMMENDED PERIODICALS FOR THOSE INTERESTED IN
PREDICTIVE MAINTENANCE
1. Sound and Vibration Magazine
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Mr. Jack Mowry, Editor and Publisher Phone: 216-835-0101
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Comments: This is a monthly publication that normally will include approximately 4-6 issues per year devoted to Predictive Maintenance. Their Predictive Maintenance articles
are usually practical and in good depth; normally contain real “meat” for the PPM vibration analyst. Sound and Vibration has been published for over 25 years.
2. Vibrations Magazine
The Vibration Institute
6262 South Kingery Hwy, Suite 212 Willowbrook, IL 60514
Institute Director - Dr. Ronald Eshleman Phone: 630-654-2254
Fax : 630-654-2271
Terms: Vibrations Magazine is sent to Vibration Institute members as part of their annual fee, (approx. $45 per year). It is available for subscription to non-members at $55/per year; $60/foreign.
This is a quarterly publication of the Vibration Institute. Always contains very practical and useful Predictive Maintenance Articles and Case Histories. Well worth the small investment.
Comments: Yearly Vibration Institute fee includes reduced proceedings for that year if desired for the National Conference normally held in June. They normally meet once per year at a fee of about $675/per person, ($600/person for Institute members) including conference proceedings notes and mini-seminar papers. All of the papers presented, as well as mini-courses, at the meeting are filled with “meat” for the Predictive Maintenance Vibration Analyst. Vibrations Magazine was first
published in 1985 although the Institute has been in existence since approximately 1972, with their first annual meeting in 1977. The Vibration Institute has several chapters located around the United States which normally meet on a quarterly basis. The Carolinas' Vibration Institute Chapter normally meets in Greenville, SC; Charleston, SC; Columbia, SC; Charlotte, NC; Raleigh, NC; and in the Winston Salem, NC areas. For Institute membership information, please contact: Dr. Ron Eshleman at 630-654-2254. When doing so, be sure to ask what regional chapter is located to your area. Membership fees for the “Annual Meeting Proceedings” are $30/per year (normal cost is approx. $60/per year for proceedings if annual
meeting is not attended). Please tell Ron that we recommended you joining the Vibration Institute when you call or write to him.
3. P/PM Technology Magazine
P.O. Box 1706
Minden, NV 89423-1706 (Pacific Coast Time) Phone: 702-267-3970; 800-848-8324
Fax : 702-267-3941
Publisher- Mr. Ronald James; Assistant Publisher: Susan Estes
Terms: $42/per year for qualified USA subscribers, (individuals and establishments involved with industrial plant and facilities maintenance; subscribers must be associated in engineering, maintenance, purchasing or management capacity). $60/year for unqualified subscribers. Comments: This is a bi-monthly magazine with articles about all facets of PPM Technologies,
including Vibration Analysis, Oil Analysis, Infrared Thermography, Ultrasonics, Steam Trap Monitoring, Motor Current Signature Analysis, etc. These are normally good practical articles. Also includes some cost savings information, although does not necessarily include how these cost savings were truly determined. P/PM Technology also hosts at least one major conference per year in various parts of the United States. Intensive training courses in a variety of condition monitoring technologies will also be offered in vibration analysis, root cause failure analysis, oil analysis, thermographic analysis, ultrasonic analysis, etc..)
4. Maintenance Technology Magazine
1209 Dundee Ave., Suite 8 Elgin, IL 60120
Phone: 800-554-7470 Fax : 804-304-8603 Publisher: Arthur L. Rice
Terms: $95/per year for non-qualified people This is a monthly magazine that usually has at least one article relating to Predictive Maintenance using vibration analysis within each issue. In addition to vibration, it likewise always offers other articles covering the many other
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5. Reliability Magazine
PO Box 856
Monteagle, TN 37356 Phone: 423-592-4848 Fax : 423-592-4849 Editor: Mr. Joseph L. Petersen
Terms: $49 per year in USA; $73 per year outside USA.
Comments: This bi-monthly magazine covers a wide variety of Condition Monitoring Technologies including Vibration Analysis, Training, Alignment, Infrared Thermography, Balancing, Lubrication Testing, CMMS and a unique category they entitle "Management Focus".
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CHAPTER
1
INTRODUCTION TO DYNAMIC BALANCING
INTRODUCTION TO DYNAMIC BALANCING
Unbalance has been found to be one of the most common causes of machinery vibration, present to some degree on nearly all rotating machines. Vibration due to an unbalance while the rotor is rotating is the result of a heavy spot located at a radius from the mass centerline producing a centrifugal force. The amount of centrifugal force will be the result of the weight of the heavy spot, the radius of such heavy spot and the speed the rotor is rotating. Thus, unbalance can be described as centrifugal forces that displace the rotors mass center from the rotors rotating center. Another way to state this in general is unbalance is a condition, which exists when vibratory forces or motion is applied to the bearings of a rotor as a result of centrifugal forces, particularly with respect to a rigid rotor. How far and in what manner this displacement takes place will be discussed later in this text.
In order to reduce the amount of forces generated by this imbalance there are several factors that we will have to understand. Before a part can be balanced certain
conditions must be met.
1. The vibration must be due to unbalance. A complete vibration analysis needs to be performed to make sure that unbalance is the primary cause of the vibration forces.
2. We must be able to start and stop the rotor. 3. We must be able to add or remove weight.
In most instances, weight corrections can be made with the rotor mounted in its normal installation, operating as it normally does. This process of balancing a part without taking it out of the machine is called IN-PLACE BALANCING. Balancing in-place
eliminates costly disassembly and eliminates the possibility of damage during the transportation of the rotor. Rotors that are totally enclosed such as some motors, pumps and compressors, can be removed and transported to a balancing machine. The principles of balancing are similar either way. Before we discuss balancing, we should first understand unbalance, where it comes from and what must be done to correct it.
TYPES OF UNBALANCE
Figure 1 helps illustrate unbalance. Here, assuming a perfectly balanced rotor, a 5 ounce (141.75 gram) weight is placed on the rotor at a 10-inch (254 mm) radius. This produces an unbalance of 50 oz-in (36000 gram-mm). Note that the same 5 ounce (141.75 gram) weight placed at 5 inches (127 mm) from the center would produce only a 25 oz-in (18000 gram-mm) unbalance. Figure 2 illustrates the same rotor as that in Figure 1 but with a correction made such that the rotor is balanced by countering the 50 oz-in (36000 gram-mm) original
unbalance by placing a correction of 50 oz-in (36000 gram-mm) (by placing an identical weight at a 10 inch (254 mm) radius directly opposite the original weight).
FIGURE 1. ILLUSTRATING UNBALACING
FIGURE 2. BALANCE CORRECTION
CHAPTER
2
Static unbalance is sometimes known as “force unbalance” or “kinetic unbalance”. Static
unbalance is a condition where the mass centerline is displaced from and parallel to the shaft centerline as shown in Figure 4. This is the simplest type of unbalance, which has classically been corrected for many years by placing a fan rotor on knife-edges and allowing it to “roll to the bottom”. That is, when the fan wheel is released, if the heavy spot is angularly displaced from the bottom (or 6:00 position), it will tend to roll to the bottom hopefully ending up in the 6:00 position if the rotor was sufficiently free to rotate. So-called correction of this unbalance was then
accomplished by placing a weight opposite this location (or at about 12:00).
Referring to Figure 3, in a “perfectly balanced rotor”, both the shaft and mass centerlines would coincide with one another with equal mass distribution throughout the rotor.
As mentioned before, unbalance occurs when the mass centerline does not coincide with the shaft centerline as shown in Figure 3. The mass centerline can be thought of as an axis about which the weight of the rotor is equally distributed. The mass centerline is also the axis about which the part would like to rotate if free to do so. However, if the rotor itself is restricted in it’s bearing, vibration will occur if the shaft and mass centerlines do not coincide. Following below will be a discussion on each of the four major types of unbalance, which include - STATIC, COUPLE, QUASI-STATIC and DYNAMIC UNBALANCE. Each of these types of unbalance
will be defined by the relationship between the shaft and mass centerlines of the rotor.
A. Static Unbalance
FIGURE 4. STATIC UNBALANCE
Actually, there are two types of static unbalance as shown in Figure 4A and Figure 4B. In Figure 4A, the unbalance is centered directly above the rotor center of gravity (CG). Figure 4B likewise shows static unbalance, but with equal masses placed at identical distances from the mass centerline and rotor CG on each end. Whether the static unbalance occurs as in either Figures 4A or 4B, each can be corrected by placement of a correction weight in only one plane at the CG, or by attaching two weights with one half the total weight at either end assuming the CG is equidistant from each bearing.
NOTE: This text is being written with the assumption that we would be able to attach a weight
of suitable size at the appropriate radius. If this cannot be accomplished, then the appropriate amount of weight can be removed from the heavy spot.
B. Couple Unbalance
Couple unbalance is a condition where the mass centerline intersects the shaft centerline at the rotor center of gravity as shown in Figure 5. Here, a couple is created by placement of equal weights 180° opposite each other and equidistant from the CG in opposite directions. A “couple” is simply two equal and parallel forces acting opposite one another, but not in the same plane. Instead, they are offset from one another, which would tend to rotate the rotor. Significant couple unbalance can introduce severe instability to the rotor causing it to wobble back and forth (like a “seesaw”) with the fulcrum at the rotor CG.
Unlike static unbalance, couple unbalance only becomes apparent when the shaft rotates. In other words, if the rotor is placed on knife-edges, it would not tend to rotate no matter what position it is placed since it would be statically balanced. Like static unbalance, couple unbalance likewise causes high vibration at 1X RPM. Unlike static unbalance, couple
unbalance will bring about a very different phase behavior, which will be discussed in Section IV. Unlike static unbalance, couple unbalance must be corrected in two planes with corrections 180° opposite each other.
The axial location of the correction couple will not matter as long as it is equal in magnitude, but opposite in direction to the unbalance couple. For example, looking at Figure 6, placement of the two 5 oz (141.75 gram) weights at an axial distance with 10 inches (254 mm) to the left and right of the CG as shown will create a clockwise couple unbalance. This can be
counteracted either by placing identical 5 oz (141.75 gram) weights at a 10-inch (254 mm) distance directly opposite the original weights or by placing 10 oz (283.5 gram) weights at an axial distance only 5 inches (127 mm) from the CG.
Only a very few cases will a rotor have true static or true couple unbalance. Normally, an unbalanced rotor will have some of each type. Combination of static and couple unbalance is further classified as “quasi-static” and “dynamic” unbalance.
FIGURE 6. CORRECTION OF COUPLE UNBALANCE C. Quasi-Static Unbalance
Quasi-static unbalance represents a specific combination of static and couple unbalance where the static unbalance is directly in line with one of the couple moments as shown in Figure 7. Quasi-static unbalance is that condition where the mass centerline intersects with the shaft, but at a point other than the rotor center of gravity (CG). In Figure 7, the Figures 7A and 7B illustrate quasi-static unbalance. In Figure 7A, the unbalance mass is placed at a location other than the CG which introduces both static and couple unbalance. In reality, Figure 7B represents the same unbalance as that in Figure 7A. The two unbalance masses acting
opposite one another close to the CG counteract one another statically, but do not compensate for the unbalance introduced by the unbalance mass on the top left-hand side of the rotor.
FIGURE 7A FIGURE 7B
Figure 8 illustrates another type of quasi-static unbalance often not even considered by analysts. In this case, assuming you had a perfectly balanced rotor, when this is connected to an unbalanced coupling, a quasi-static unbalance is created. This is a very common type of unbalance since most couplings are not balanced unless they are of great size or speed. Similarly, quasi-static unbalance can be introduced by inserting the wrong size key into the shaft or pump impeller, which again will create both a static and a couple unbalance. In each case, the required correction in addition to a static correction at the same location as the couple component nearest the coupling, key, etc.
FIGURE 8. UNBALANCED COUPLING CAUSING QUASI-STATIC UNBALANCE D. Dynamic Unbalance
Dynamic unbalance is the most common type of unbalance and can only be corrected by mass correction in at least two planes. Figure 9 illustrates dynamic unbalance which again is a combination of both static and couple unbalance, but with unbalance masses at different angular positions from one another as shown in Figure 9. Because the unbalance masses are at different angular positions, dynamic unbalance is that condition where the shaft centerline and mass centerline do not intersect with one another, nor are they parallel with one another. As will be pointed out in Section III, dynamic unbalance causes phase differences between the horizontal on one bearing versus the horizontal on the other bearing to be far different from either 0 or 180°. That is, the horizontal phase difference may be 60° or 180°, or most anything. However, if the horizontal phase difference is 60°, the vertical phase difference should be the same as the horizontal within one clock position (+/- 30°).
TYPES OF BALANCE PROBLEMS
CHAPTER
3
In order to achieve a satisfactory balance with the minimum number of start-stop operations it not only is important that we recognize the type of balance problem we have (static, couple, quasi-static or dynamic), it should now be obvious that not all balancing can be achieved by balancing in a single correction plane. A guide to determining whether single plane, two plane or multi-plane will be required will be determined by the ratio of the length to diameter of the rotor along with the speed of the rotor. It is also very important to recognize whether the rotor is flexible (one that bows)or rigid (one that maintains it geometric shape.) The L/D ratio is calculated using the dimensions of the rotor exclusive of the supporting shaft. See Table 1. The selection of single plane versus two-plane balancing based on the L/D ratio and rotor speed is offered only as a guide and may not hold true in all cases. Experience reveals that single plane balancing is normally acceptable for rotors such as grinding wheels, single-sheave pulleys, and similar parts even through their operating speed may be greater than 1000 RPM.
TABLE 1 A. Rigid Vs Flexible Rotors
Only a few rotors are made of a single disc, but instead they are made of several discs on a common shaft, often times in complex shapes and sizes. This makes it practically
impossible to know which disc(s) the heavy spot is located. The unbalance could be in any plane or planes located along the length of a rotor, and it would be most difficult and time consuming to determine where. In addition, it is not always possible to make weight
corrections in just any plane. Therefore, the usual practice is to compromise by making weight corrections in the two most convenient planes available. This is possible because any
condition of unbalance can be compensated for by weight corrections in any two balancing planes. This is true only if the rotor and shaft are rigid and do not bend or deflect due to the forces caused by unbalance.
Whether or not a rotor is classified as rigid or flexible depends on the relationship between the rotating speed (RPM) of the rotor and its natural frequency. You will recall that every object including the rotor and shaft of a machine has a natural frequency, or a frequency at which it likes to vibrate. When the natural frequency of some part of a machine is also equal to the rotating or some other exciting frequency of vibration, there is a condition of resonance. A flexible rotor balanced at one operating speed may not be balanced when operating at another speed. If a rotor were first balanced below 70% of the its first critical speed with the correction weights added in the two end planes, the two correction weights added would compensate for all sources of unbalance distributed throughout the rotor. If the rotor were increased to above 70% of the critical speed, the rotor would deflect due to the centrifugal force of the unbalance located at the center of the rotor as shown in Figure 10. As the rotor bends or deflects, the weight of the rotor is moved out away from the rotating centerline creating a new unbalance condition. It would then be necessary to rebalance the two end planes at this new operating speed, and then the rotor would be out of balance at the slower operating speed. The only solution to insure smooth operation at all speeds is to make the balance correction in the actual planes of unbalance, thus a multi-plane balance.
This subject will be discussed in greater detail later in the course.
FIGURE 10. ROTOR DEFLECTION DUE TO UNBALANCE ABOVE CRITICAL SPEED
FIGURE 11. ROTOR FLEXURAL MODES
Fig. 10A
Rotor with dynamic unbalance, balanced in two planes below
critical speed
Fig. 10B
Operating above critical speed the rotor deflects due
The rotor in Figure 10 represents the more simple type of flexible rotor. A Rotor can deflect in several ways depending on its operating speed and the distribution of unbalance through out the rotor. Figure 11 illustrates the first, second and third flexural modes a rotor could take while going through the first, second and third criticals. These rotors may require that balance
corrections be made in several planes to insure smooth operation through all speed ranges. Whether a flexible rotor requires multi-plane balancing depends on the normal operating speeds of the rotor and the significance of rotor deflection on the functional requirements of the machine. Flexible rotors generally fall into one of the following categories:
1. If the rotor operates at only one speed and a slight amount of deflection will
not accelerate wear or hamper the productivity of the machine, then balancing in any two correction planes to minimize bearing vibration may be all that is required.
2. If a flexible rotor operates at only one speed, but it is essential that rotor
deflection be minimized, then multi-plane balancing may be required.
3. If it is essential that a rotor operate smoothly over a broad range of speeds
where the rotor is rigid at lower speeds and flexible at higher speed, then multi-plane balancing is required.
B. Critical Speeds
The rotating speed at which the rotor itself goes into bending resonance is called a critical speed. Depending on how many bending modes the rotor goes through is dependant upon the number of operating speeds coincide with the rotors natural frequency. In general, rotors operating below 70% of their natural frequency are considered to be rigid rotors and above 70% of their natural frequency are considered to be flexible rotors.
When a rotor bends or deflects due to operating through its critical speed, the weight of the rotor is moved out away from the rotating centerline creating a new unbalanced condition. This rotor could be corrected by rebalancing in the two end planes; however, the rotor would then be out of balance at slower speeds where there is no deflection. The only solution to insure smooth operation at each speed is to make the corrections in the planes of unbalance, thus
multi-plane balancing. Remember, any unbalance can be corrected by making corrections in any two balance planes, but only if the rotor is a non-flexible rotor.
HOW TO ENSURE THE DOMINANT PROBLEM IS
UNBALANCE
CHAPTER
4
Before analysts begin balancing a machine, they should always ensure that the dominant problem is in fact unbalance before they begin. Vibration consultants commonly report that on over one-half the jobs on which they are requested to balance machinery, they do not in fact perform any
balancing, but find other problems requiring different corrective measures instead. An analyst should always employ both spectral and phase behaviors for some of the more common
machinery problems, each of which can cause high vibration at 1X RPM, including eccentric rotor, bent shaft, misalignment, resonance and even certain types of mechanical looseness/weakness. While there are still other problems that generate 1X RPM vibration, a review of Table II will help the analyst distinguish which problem is at hand.
It should be pointed out that the column entitled “TYPICAL SPECTRUM” in Table II means just that - that is, these spectra are not intended to be all-inclusive. For example, it is quite possible for misalignment to generate only high 1X RPM vibration in certain cases, however, they most often generate a noticeable 2X RPM peak. Therefore, such a spectrum is shown under the “TYPICAL SPECTRUM” column. Following below will be a quick review of Table II pointing out the more common spectral and phase behaviors of the problems shown. Later, a more detailed look will be taken specifically on unbalance symptoms.
A. REVIEW OF TYPICAL SPECTRA AND PHASE BEHAVIORS FOR COMMON MACHINERY PROBLEMS
1. Mass Unbalance: Table II shows that mass unbalance always generates high
vibration at 1X RPM. The centrifugal forces caused by unbalance always act in the radial direction, but can sometimes generate high axial vibration in the case of overhung rotors like in Unbalance Case C of Table II. Pure force, or static unbalance, is evidenced by identical phase in the radial direction on both the outboard and inboard bearings supporting the rotor. On the other hand, pure couple unbalance is evidenced by a 180° phase difference in the radial direction between the outboard and inboard bearings (the horizontals will be 180° out of phase with one another as well as the outboard and inboard verticals with one another in pure couple unbalance). Overhung rotors represent a special case of unbalance on which high axial vibration can be generated which is in phase between the inboard and outboard bearings supporting the overhung rotor as shown in Table II.
2. Eccentric Rotor: Like unbalance, an eccentric rotor will generate high vibration at
1X RPM of the eccentric rotor itself with the highest vibration normally being in a direction through the centers of the two rotors as shown in Table II under “ECCENTRIC ROTOR”. However, the main difference between an eccentric rotor and an unbalanced one is with respect to phase behavior-pure unbalance will normally cause the phase difference in the
horizontal and vertical directions to be about 90° while in the case of an eccentric rotor, the horizontal and vertical phase difference will normally be either approximately 0° or 180° (each of which indicate straight-line motion). One of the problems with an eccentric rotor occurs if one attempts to balance the eccentric rotor. What will often result is that the balance exercise may in fact reduce vibration in one radial direction, but increase it in the other, depending on the amount of eccentricity.
3. Bent Shaft: A bent shaft will most always generate high axial vibration with the greatest component being 1X RPM if bent near the shaft center, but can create a high 2X RPM component if bent near the coupling. One of the things that sets apart bent shaft symptoms from those of unbalance is with respect to phase behavior - a bent shaft will cause axial vibration on the outboard bearing of a rotor to approximately 180° out of phase with respect to that of the inboard rotor bearing, while unbalance will normally cause axial outboard and inboard phase to be about the same.
4. Misalignment: Although misalignment normally generates a 2X RPM component greater than or equal to 30% of the amplitude at 1X RPM, it can sometimes cause only a high 1X RPM component, particularly in the axial direction. However, one of the things that again differentiate it from unbalance is its phase behavior - misaligned shafts will cause phase across the coupling to be approximately 180° different, whereas unbalance will normally cause almost equal phase on either side of the coupling. As Table II shows, angular
misalignment is evidenced by a 180° phase change across the coupling in the axial direction whereas parallel, (or offset misalignment), causes a 180° difference in the radial direction across the coupling. Finally, a misaligned bearing cocked on the shaft generates spectra very similar to that of shaft misalignment. However, it can be detected by measuring at each of 4 points in the axial direction on each bearing as shown in Table II. This measurement should show that the phase is almost the same at each of the 4 points around the clock if the bearing is properly oriented. If there is a 180° phase difference across either points 1 and 3, or
between 2 and 4 as shown in Table II, a cocked bearing is indicated.
5. Resonance: Resonance occurs when a forcing frequency coincides with a
system natural frequency and can cause excessive vibration amplitudes. Even a small amount of unbalance, for example, can be greatly amplified if the rotor is operating at or near a natural frequency. Such a resonant problem is evidenced if the phase changes dramatically for only a small change in speed (Figure 12 shows that a rotor will experience almost a full 180° phase change when its speed passes completely through a natural frequency). At the same time, the amplitude first increases dramatically and then decreases as the rotor passes through the natural frequency (as shown in Table II).
6. Mechanical Looseness/Weakness: Table II shows three different types of
mechanical looseness, one of which is lesser known, but causes high radial vibration predominantly at 1X RPM which again causes a spectrum almost identical to an unbalance vibration spectrum as shown under mechanical looseness “Type A”. Type A looseness is caused by a looseness or weakness of machine feet, base plate, foundation, loose hold-down bolts at the base, distortion at the frame or base, etc. Again, the thing which sets it apart from unbalance is its phase behavior. Referring to “MECHANICAL LOOSNESS Type A” in Table I note that a problem is evidenced between the base plate and its base by a 180° phase change between these two sections. In other words, when a phase measurement is taken, if everything is moving together as it should, the phase should be almost identical as one moves his probe in the vertical direction from the foot to the baseplate, and then down to the base. One of the most important points about this type of looseness/weakness problem is that even if one is able to temporarily correct the problem by balancing and alignment procedures, the vibration will likely reoccur when even the least bit of unbalance or misalignment
symptoms return. They must first correct the looseness/weakness problem, then balance or align if any further correction measures are still required.
B. SUMMARY OF PHASE RELATIONSHIPS FOR VARIOUS MACHINERY
Section A above summarized the typical spectral and phase relationships for some of the more common machinery problems. One of the most important points that this section
hopefully made was that the key parameter that helped differentiate one problem from another was phase. Therefore, because of the importance of phase, following below will be a
summary showing how phase generally behave for each particular problem scenario (see Table II):
1. Force (or “static”) unbalance is evidenced by nearly identical phase in the
radial direction on each bearing of a machine.
2. Couple unbalance shows approximately a 180° out-of-phase relationship when
comparing the outboard and inboard horizontal, or the outboard and inboard vertical direction on the same machine.
3. Dynamic Unbalance is indicated when the phase difference is well removed
from either 0° or 180° but importantly is nearly the same in the horizontal and vertical directions. That is, the horizontal phase difference could be almost anything ranging from 0° to 180° between the outboard and inboard bearings; but the key point is that the vertical phase difference should be almost identical to the horizontal phase difference (+/- 30°). For example, if the horizontal phase difference between the outboard and inboard bearings is 60°, and dominant problem is dynamic unbalance, then the vertical phase difference between these two bearings should also be about 60° (+/- 30°). If the horizontal phase
difference varies greatly from the vertical phase difference when high 1X RPM vibration is present, this strongly suggests the dominant problem is not
unbalance.
4. Angular misalignment is indicated by approximately a 180° phase difference
FIGURE 12
CHANGE OF VIBRA TION DISPLACEMNT AND PHASE LAG WITH RPM AB
O VE , BEL OW AND A T ROTOR RESONANCE
5. Parallel misalignment causes radial phase differences across the coupling to
be approximately 180° out of phase with respect to one another.
6. Bent shaft causes axial phase on the same shaft of a machine to approach a
180° difference when comparing axial measurements on the outboard with those on the inboard bearing of the same rotor.
7. Resonance is shown by exactly a 90° phase change at the point when the
forcing frequency coincides with a natural frequency, and approaches a full 180° phase change when the machine passes through the natural frequency
(depending on the amount of damping present).
8. Rotor rub causes significant, instantaneous changes in phase.
9. Mechanical looseness/weakness due to base/frame problems or loose hold-down bolts is indicated by nearly a 180° phase change when one moves
the probe from the machine foot down to its baseplate and support base.
10. Mechanical looseness due to a cracked frame, loose bearing or loose rotor causes phase to be unsteady with widely differing phase measurements
from one measurement to the next. The phase measurement may noticeably differ every time you speed up the machine.
C. Summary of Normal Unbalance Symptoms
Sections A and B above summarized how the analyst can ensure that the dominant problem is unbalance. Following below will be a more detailed look at the symptoms normally present when some type of unbalance is the major problem:
1. Special Characteristics - unbalance is always indicated by high vibration at 1X RPM
of the unbalanced part. Normally, this 1X RPM vibration will dominate the spectrum. In fact, the amplitude at 1X RPM will normally be greater than or equal to 80% of the overall amplitude when the problem is limited to unbalance (may be only 50% to 80% of the overall if other problems exist in addition to unbalance).
2. Centrifugal Force Due to Unbalance - Mass unbalance produces centrifugal
For example, assuming a sample rotor with a 1 oz (28.35 grams) unbalance at an 18 inch (457.2 mm) radius (U= 18 oz-in) (12,962 gram-mm) turning 6000 RPM.
FC = (.000001775)(18 oz-in)(6000 RPM)2 F
C = 1150 lbs (from centrifugal force due to unbalance alone)
That is, only a 1 oz (28.35 gram) unbalance on a 3 foot (914.4 mm) diameter wheel turning 6000 RPM would introduce a centrifugal force of 1150 lbs (521.6 kg) that would have to be supported by the bearings in addition to the static rotor weight they must support. Importantly, note that the centrifugal force varies with the square of RPM (that is, tripling the speed will result in an increase in unbalance vibration by a factor of 9 times).
3. Unbalance Force Directivity - Mass unbalance generates a uniform rotating force
that is continually changing direction, but is evenly applied in all radial directions. As a result, the shaft and supporting bearings tend to move in somewhat a circular orbit. However, due to the fact that vertical bearing stiffness is normally higher than that in the horizontal direction, the normal response is a slightly elliptical orbit. Subsequently, horizontal vibration is normally somewhat higher than that in the vertical, commonly ranging between 1.5 and 2 times higher. When the ratio of horizontal to vertical is higher than about 5 to 1, it normally indicates problems other than unbalance, particularly resonance.
4. Radial/Axial Vibration Comparison - When unbalance is dominant, radial vibration
(horizontal and vertical) will normally be quite higher than that in the axial direction (except for overhung rotors).
5. Overhung Rotor Unbalance Directivity - Generally causes high 1X RPM vibration in
both the axial and radial directions. Overhung rotors most often have both static and couple FC = mrω2 g C F C = .000001775 Un 2 = .00002841 Wrn2 where: Fc = Centrifugal Force (lb)
u = Unbalance of Rotating Part (oz-in) w = Weight of Rotating Part (lb)
r = eccentricity of the rotor (in) n = Rotating Speed (RPM) (EQUATION 1) = Wr (386)(16) 2πn 60 2
6. Steadiness & Repeatability of Phase Due to Unbalance - Unbalanced rotors
normally exhibit steady and repeatable phase in radial directions. When the rotor is trim balanced, phase can begin to “dwell” back and forth under a strobe light as you
achieve a better and better balance, particularly if problems other than unbalance are present.
7. Resonant Amplitude Magnification - The effects of unbalance may sometimes be
amplified by resonance. Only a slight unbalance vibration can increase by a factor of 10 up to as much as 50 times if the rotor is operated at or near resonance with a system natural frequency.
8. Phase Behavior for Dominant Static, Couple and Dynamic Unbalance - Figure
13 illustrates typical phase measurements for a machine which has either static (Table A), couple (Table B) or dynamic (Table C) unbalance.
Static Unbalance Phase - Table A shows a machine having dominant static unbalance. Note that the horizontal phase difference between the #1 and #2 bearings is about 5° (30° minus 25°) compared to a vertical phase difference of about 10° (120° - 110°). Similarly, over on the pump, the horizontal phase difference at positions 3 and 4 is about 10° and the vertical phase difference is about 15°.
Couple Unbalance Phase - Table B illustrates typical couple unbalance phase readings. Note the 180° phase difference between positions 1 and 2 horizontal (210° - 30°), and the 175° phase difference between positions 1 and 2 vertical (295° - 120°).
Dynamic Unbalance - Table C illustrates typical behavior for dynamic unbalance. Note that the horizontal phase difference between outboard and inboard bearings can be anything from 0° to 180°. However, whatever the phase difference in horizontal, the phase difference in the vertical should then be almost identical (within one clock position or +/- 30°). In the Figure 13 example in Table C, note the 60° phase difference between positions 1 and 2 in both the horizontal and vertical directions; while over on the pump at positions 3 and 4, the 10°
difference in the pump horizontal readings compared to the 5° difference in the vertical (170° -165°).
Key Point About Unbalance Phase Behavior - Whatever the phase difference between the
outboard and inboard horizontal phase measurements on a rotor, the vertical phase difference between outboard and inboard bearings must be about the same (within +/- 30°), or the dominant problem is not unbalance. If, for example, the horizontal phase difference on a motor between its outboard and inboard bearings were 30°, while the outboard and inboard vertical phase difference was approximately 150°, an analyst would likely waste much time and effort if he attempted to balance the rotor.
FIGURE 13
TYPICAL PHASE MEASUREMENTS WHICH WOULD INDICATE EITHER STATIC, COUPLE OR DYNAMIC UNBALANCE
TABLE A
TABLE B
CAUSES OF UNBALANCE
CHAPTER
5
There are a variety of causes of unbalance. These can be summarized as follows:
A. Assembly Errors - Sometimes occur after assembly when the mass center of rotation of
one part does not line up with the mass center of rotation of the part to which it was
assembled. For example, even if both a pump impeller and the pump shaft were separately precision balanced and then assembled, this can happen if the pump impeller had been balanced on a balancing shaft that fit its bore within 1 mil, but then was mounted on the shaft which itself allows a clearance of over 3 mils. This would shift the mass of the impeller/shaft rotor away from the shaft center which would throw the assembly out of balance, or at least cause it to have noticeably more unbalance than that when each part was separately balanced.
B. Casting Blow Holes - Cast parts occasionally will be left with blow holes within them that
might not be detectable by visual inspection means. Depending on the diameter of the rotor as well as its speed, this can throw it considerably out of balance.
C. Fabrication Tolerance Problems - A common problem with parts such as a sheave deals
with stack up of clearance tolerance. In this case, since the bore of the sheave is necessarily larger than that for the shaft diameter, when a key or setscrews is employed, the take-up in clearance shifts the rotating centerline of the sheave away from that of the shaft on which it is mounted.
D. Key Length Problems - Use of no key or the wrong size of key can cause noticeable
unbalance problems. Mr. Ralph Buscarello of Update International points out the great importance of employing a half-key (full key length, but half-key depth) when balancing couplings, impellers, sheaves, etc. Figure 14 helps explain why this is important. Mr.
Buscarello recommends that a tag like the one shown in the figure should be attached to the finish balanced rotor any time a machine part is to be balanced and then mounted on a shaft. For example, if the coupling shown in Figure 14 had a “B” dimension of about 4 inches (101.6 mm) and an “A” dimension of 8 inches (203.2 mm), Mr. Buscarello recommends a final key length of about 6 inches [1/2 X (8 + 4) inches] or 152.4 mm [1/2 X (203.2 + 101.6) mm]. To further illustrate, assume a machine is to be outfitted with a 1/4" X 1/4" X 6"
(6.4 mm X 6.4 mm X 152.4 mm) key, then both the coupling and the shaft should be outfitted with1/4" X 1/8" X 6" (6.4 mm X 6.4 mm X 152.4 mm) keys when balancing. Also assume this coupling is perfectly balanced, weighs 5 lbs (2.3 kg), will operate at 1800 RPM and will be mounted on a 4" (101.6 mm) shaft diameter. The following will illustrate the effect of not using the proper half-key:
(b) Weight of 4" long key = (1.698)(4) = 1.132 oz (4" key)
6
(c) Unused key weight if used only 4" half-key
= 1.698 - 1.132 = .283 oz (unused half-key weight) 2
(d) Distance of Key CG from shaft center = 2" radius + (1/2 x 1/8") = 2.0625"
(e) So, if 6" half-key rather than a 4" half-key used, unbalance introduced when you insert 6" full key will be: 2.0625" x .283 lb. = .584 oz-in
(unbalance introduced by wrong half-key length used to balance the coupling).
Then, referring to the ISO balance tolerance table shown in Figure 54 (on page 11-16), let us see how this would affect an otherwise perfectly balanced coupling installed on a rotor turning 1800 RPM. Assuming the coupling weight of 5 lbs and the unbalance of .584 oz-in introduced by the key, this corresponds to a residual unbalance of .1168 oz-in/lb which equals .0073 lb-in/lb. Referring to Figure 54 at 1800 RPM, this would degrade the perfectly balanced coupling down to an ISO Balance Quality G 40, or one with a poor balance quality grade.
Of course, if no half-key were used at all when balancing the coupling, this would introduce even more unbalance to the system. And, one of the real problems with this being a coupling is that the weight would be overhung from the motor bearing meaning that it could introduce considerable couple unbalance. This fact is often overlooked, particularly when dealing with couplings, most of which are not even factory balanced unless specifically requested by the end user.
Figure 14 SUGGESTED TAG THAT SHOULD ACCOMPANY FINISH BALANCED KEYED ROTOR
Coupling outfitted with a 1/4" x 1/8" x 4" key
(a) Final key weight = (1/4" x 1/4" x 6" ) x .238 lb/in3 x 16 oz/lb = 1.698 oz (6” key)
E. Rotational Distortion - Sometimes, a part might be well balanced, but might distort when
rotating due to stress relieving or thermal distortion. Parts fabricated by welding process or shaped by pressing, drawing, bending and so forth will sometimes have high internal
residual stresses. If not relieved during the fabrication, they may begin doing so over a period of time when operating, distorting slightly and taking on a new shape. This can throw the rotor out of balance. In addition, some machines have problems with thermal distortion caused by such problems as uneven thermal expansion of parts when brought up to operating
temperatures. This sometimes mandates that the rotor be balanced at its normal elevated operating temperature.
F. Deposit Buildup or Erosion - Fan or impeller wheels are often thrown well out of balance
due to buildup of deposits of dirt or other foreign matter brought into them by the pumping fluid or air. When small pieces of these deposits break away, it can sometimes introduce serious unbalance. On the other hand, some high-speed centrifugal compressor rotors are susceptible to erosion from small droplets of water traveling at very high speeds which impact the impeller rotors. This can cause uneven erosion of impeller surfaces and eventually can introduce considerable
unbalance.
G. Unsymmetrical Design - Unbalance can be introduced if good symmetry is not
maintained in all parts. For example, rotor windings on electric motors are sometimes difficult to keep symmetrical; the thickness in sheaves sometimes vary from on side to the other; the density of coating finishes sometimes varies around the rotor periphery. Other problems can affect rotor symmetry, each of which can detrimentally affect rotor balance.
In summary, all of the above causes of unbalance can exist to some degree in a rotor. However, the vector summation of all unbalance can be considered as a concentration at a point termed the “heavy spot”. Balancing, then, is the technique for determining the amount
and location of this heavy spot so that an equal amount of weight can be removed at this location or an equal amount of weight added directly opposite.
CHAPTER
6
WHY DYNAMIC BALANCING IS IMPORTANT
The forces created by unbalance can be among the most destructive forces in rotating machinery if left uncorrected. Not only will these forces damage the bearing but they have been know to crack foundations, break welds, etc. In addition, the vibration displacement due to unbalance can be detrimental to product quality in many applications. The amount of force created by unbalance depends on the speed of rotation and the weight of the heavy spot. Figure 15 represents a rotor with a heavy spot (W) located at some radius (R) from the rotating centerline.
If the unbalance weight, radius and machine RPM are known, the force (F) generated can be found using the following formula:
F = 1.77 x (RPM/1000)2 x ounce-inches (EQUATION 2)
In this formula the unbalance is expressed in oz-inches and (F) is the force in pounds. The constant 1.77 is required to make the formula dimensionally correct. When the unbalance is expressed in terms of gram-inches, the force (F) in pounds can be found by using the following formula:
F = 1/16 x (RPM/1000)2 x gram-inches (EQUATION 3) For unbalance expressed in gram-mm, the force (F) in kg can be calculated using the following formula:
F = 0.001 x (RPM/1000)2 x gram-mm (EQUATION 4) From these formulas it can be seen that the centrifugal force due to unbalance actually increases by the square of the rotor RPM. For example, from Figure 16 we see that the force created by a 3 ounce weight attached at a radius of 30 inches (90 oz-in unbalance) and rotating at 3600 RPM is over 2000 lbs (907 kg). By doubling the speed to 7200 RPM, the unbalance force is increased to over 8000 pounds (3630 kg). From this we can see, especially on high-speed machines, a small amount of unbalance can create a tremendous amount of force.
CHAPTER
7
UNITS OF EXPRESSING UNBALANCE
Units of unbalance in a rotating work piece is normally expressed as the product of the unbalance weight (lbs., oz., grams, etc.) and its distance from the rotating centerline (inches, mm, etc.), see Figure 15. The units for expressing unbalance are generally oz-inches, gram-inches, gram-mm, etc. For example, a 1 oz (28.35 gram) weight located at 10" (254 mm) from the rotating centerline would be 10 oz-inches, (7200 gram-mm) and a 2 oz (56.7 gram) weight located 6" (152.4 mm) from the rotating centerline would be 12 oz-in (8641 gram-mm). Figure 16 represents other examples of unbalance expressed as the product of weight and distance.
FIGURE 15. THE FORCE DUE TO UNBALANCE CAN BE FOUND IF THE UNBALANCE WEIGHT (W), RADIUS (R) AND ROTATING SPEED ARE KNOWN
FIGURE 16. CENTRIFUGAL FORCE EXERTED BY UNBALANCE (OZ-IN) AT VARIOUS SPEEDS
FIGURE 17. UNITS OF UNBALANCE ARE EXPRESSED AS THE PRODUCT OF THE UNBALANCE WEIGHT AND ITS DISTANCE FROM THE ROTATIONAL CENTER
CHAPTER
8
Scalar quantities such as mass, time, volume, or force may be represented by a length of a single line in any arbitrarily chosen direction. A quantity, which has both magnitude and direction, is called a vector quantity. Describing a vector is giving it magnitude (length) and direction.
Unbalance forces generate a magnitude equivalent to a certain number of ounces of weight or ounce-inches and an angular direction with respect to a reference point on the rotor, can be represented by a vector. It should be apparent that unbalance forces that tend to move the rotor away from its axis of rotation cause a certain magnitude. These forces and their exact location on the rotor cannot be measured directly. However, their effects on the rotor and/or bearing supports can be measured.
An unbalance vector, then, can be described as a straight line whose length is proportional to the amount of unbalance and the angular direction measured from a reference point.
The combined effect of several unbalances or balance weights can be determined by vector calculations. Examples of several vectors are shown in Figures 18. In Figure 18A, vectors are drawn to represent the radial location of weights. The length of the vector represents the radius in inches. Figure 18B vectors are shown to represent the weight in ounces. In Figure 18C, the
vectors represent the amount of unbalance in ounce-inches.
Balancing vectors are used to represent the amount and angular location of unbalance, as well as to measure the effect of trial weight when solving balancing problems.
FIGURE 18B. VECTOR WEIGHT FIGURE 18A. VECTOR RADIUS (LENGTH)
FIGURE 18C. VECTOR UNBALANCE (RADIUS X WEIGHT) FIGURE 18
CHAPTER
9
DYNAMIC FIELD BALANCING TECHNIQUES
Generally, it is best to balance a good majority of rotating machines in place since it can be done under the actual operating conditions and speed which exist during operation, in its own bearings and on its own foundation. In addition, balancing in-place eliminates the possible damage to the rotor during disassembly and transportation to a balancing machine. Following will be information on what techniques should be mastered in order to best accomplish field balancing using portable balancing equipment.
Information on recommended techniques on performing field balancing including single-plane, two-single-plane, multi-plane and over-hung rotors will be discussed. In addition, instructions will be provided on directly related topics such as how to properly size trial weights, how to split balance correction weights when is not possible to place a single weight at the angular location specified by the solution, and how to vectorially combine the effects of several weights into one correction weight of just the right size and at just the right location. To begin with we will be discussing balancing using the vector method of balancing.
Although there are many instruments with balancing programs in them on the market today, the mastering of the vector solution will give us a very good understanding of the effects that we should get and how to read the vector to determine if we made an error in our weight selection and location. We will later discuss the use of instruments with built in balancing programs.
Although it is possible to balance any object with amplitude alone, we will begin our
discussion of balancing using conventional vectors, both amplitude and phase. At the end of this chapter you will find the instructions for balancing using just the amplitude, called the Four Point Method of Balancing.
A. Recommended Trial Weight Size
It is important that the size of the trial weight be carefully chosen as well as the location at which the trial weight will be placed. If the trial weight is too large, damage may be done to the machine if the trial weight happens to be installed at or close to the rotor heavy spot producing even more vibration, particularly if the rotor is operating above critical speed. On the other hand, if the trial weight is too small, it may bring about no significant change in amplitude or phase that can cause significant error when calculations for the proper correction weight and location are made.
As a general rule, a trial weight should produce either/or both a 30% change in amplitude or a 30° phase change. In order to provide a sufficiently large trial weight effect, but without risking damage to the rotor, it is recommended that a trial weight which will produce an equivalent unbalance force at each bearing of about 10% of the rotor weight supported by each bearing should be installed. Therefore, referring to Equation (1), a similar equation can be derived to help the analyst choose a proper trial weight:
FC =.000001775 Un2 = .00002841 Wrn2 (EQUATION 1 Repeated) Solving for U:
U = 563,380 FC (EQUATION 5)
Now, assuming the trial weight should cause a 10% effect (.10 X U),
TW = .10 X U = .10 (563,380) W = 56,338 W (with W=Bearing Load at this point) n2 n2
In order to make the equation easier for the analyst to use, double the constant (56,338) so that W can be considered the full rotor weight.
Therefore,
TW= 112,676W (EQUATION 6)
Where:
TW =Recommended Trial Weight Effect (oz-in) W =Weight of Rotating Part (lb)
n =Rotating Speed (RPM) n2
Now, if the radius at which the trial weight will be placed is known, the trial weight size that should be employed can be calculated as per the following:
TW = U = mr Therefore:
m = TW (EQUATION 7)
Where: m = Trial Weight Size (oz or grams)
r = Radius at which Trial Weight will be placed (in) TW = Trial Weight Effect (oz-in or gram-in)
r
An example will serve to illustrate the use of these equations:
Example - The rotor shown in Figure 19 is to be balanced. It has a weight of 453.6 kg.,
operates at 1800 RPM and has a 24" (609.6 mm) diameter wheel. To determine the recommended trial weight size (oz),
TW = 112,676 W = (112,676)(1000) = 34.78 oz-in n2 (1800)2 (at 12" radius) Then,
m = TW = 34.78 = 2.90 oz (Record trial weight size) r 12
The centrifugal force that would be developed by this 2.90 oz (82.2 gram) trial weight is: Centrifugal Force = (.000001775)(34.78 oz-in)(1800)2 = 200.0 lb.
is operated. In addition, the machine casings and inspection doors should be closed before operation in case the trial weights do accidentally come off the rotor. If it is not possible to close the casing or inspection door, a shield should be placed between the machine and the analyst for protection. The analyst and all others should place themselves to the side of the machine away from direction of rotation when the machine is operated. When attaching temporary clips or set-screwed trial weights, attempt to fasten these so that the centrifugal force is working for you to hold the weights (for example, if an analyst desires to attach a balance clip to fan blades, fasten them on the inside of the blades so that the throat rests against the blades inside surface).
Finally, it is a good idea to identify the location of the trial weights by marking them in case they do happen to come off.
B. How A Strobe-Lit Mark on a Rotor Moves When a Trial Weight Is Moved
Figure 20 shows an important concept about how a phase reference mark moves relative to the movement of a trial weight. This often confuses analysts, but really is a simple concept if one takes a close look. In Figure 20A, a rotor is shown with the key weight at the top (or 0°). Most analysts will put their phase reference mark in line with the key weight or some other convenient reference point, but it really does not matter exactly where the reference mark is applied. If the pickup is located at point A, the 90° position, and has a zero response time (no electronic lag), the strobe light will flash when the heavy spot is at the 90° position, and the phase mark will be seen at the top or 0° position. Now please refer to Figure 20B where the weight has been moved 90° clockwise to point B at the 180° position. Again, note that the phase mark is still at the 0° location, or 180° away from point B where the trial weight is now located. If the strobe light now flashes when B is at the pickup (90° position), this means that point A written on the rotor is at the 0° position while the phase mark is over at the 270° position (180° away from the heavy spot). Note what happened. The weight was moved 90° clockwise, but the phase mark moved 90° counterclockwise. The direction of rotation does not matter. You get the same results. The point is this: If you want to move a phase
reference mark clockwise, move the trail weight counterclockwise and vise versa. The reference mark always will shift in a direction opposite a shift of the heavy spot; and the angle that the reference mark shifts is equal to the angle that the heavy spot has shifted.
Instruments used to measure phase may or may not have an electronic lag, however, the effects will still be the same as discussed above. The fact that the phase shift is predictable can be used and the lag figured once the trial weight effect has been calculated. This will be discussed in more detail under “Balancing in One Run” later in this text.
FIGURE 20.
HOW A STROBE-LIT REFERENCE MARK MOVES WHEN A TRIAL WEIGHT IS MOVED FIGURE 20A.
TRIAL WEIGHT AT LOCATION A (90° CLOCKWISE FROM PHASE
REFERENCE MARK)
FIGURE 20A.
TRIAL WEIGHT MOVED TO LOCATION B (180° CLOCKWISE FROM PHASE
REFERENCE MARK)
C. Single-Plane Balancing Using A Strobe Light And A Swept-Filter Analyzer
At the start of a balancing problem we have no idea how large the heavy spot is, nor do
we know where on the part it is located. The unbalance in the part at the start of our problem is called the ORIGINAL UNBALANCE, and the vibration amplitude and phase readings that
represent the unbalance are called our ORIGINAL READINGS.
In the beginning we must tune our analyzer to a frequency of 1X RPM at which time our
strobe light will flash at a rate equal to 1X RPM. When in the filtered mode on the analyzer, this flashing strobe will appear to “freeze” the rotor and our reference mark will appear to be stopped.
For example, the part in Figure 21 has an original unbalance of 5.0 mils (127 microns)
at 120°. Once the original unbalance has been noted and recorded, the next step is to change the original unbalance by adding a TRIAL WEIGHT to the part. The resultant unbalance in the
part will be represented by a new amplitude and phase of vibration. The change caused by the trial weight can be used to learn the size and location of the original unbalance, or where the trial weight must be placed to be opposite the original unbalance heavy spot, and how large the trial weight must be to be equal to the original heavy spot.
FIGURE 21.
THIS ROTOR HAS AN ORIGINAL UNBALANCE OF 5.0 MILS (127 microns) AND 120° PHASE
By adding a trial weight to the unbalanced part, one of three things might happen:
1) First, if we are lucky, we might add the trial weight right on the heavy spot. If we do, the
vibration will increase, but the reference mark will appear in the same position it did on the original run. To balance the part, all we have to do is move the trail weight directly opposite its first position, and adjust the amount of the weight until we achieve a satisfactory balance.
2) The second thing that could happen is that we could add the trial weight in exactly the right
location opposite the heavy spot. If the trial weight were smaller than the unbalance, we would see a decrease in vibration, and the reference mark would appear in the same position as seen on the original run. To balance the part, all we would have to do is increase the weight until we reached a satisfactory vibration level.
If the trial weight were larger than the unbalance, then its position would now be the heavy spot, and the reference mark would shift 180°, or directly opposite where it was originally. In this case, all we would have to do to balance the part is reduce the amount of the trial weight until we achieved a satisfactory level.
3) The third thing that can happen by adding a trial weight is the usual one where the trial
weight is added neither at the heavy spot, nor opposite it. When this happens, the
reference mark shifts to a new position, and the vibration amplitude may change to a new amount. In this case, the angle and direction the trial weight must be moved, and how much the weight must be increased or decreased to be equal and opposite the original unbalance heavy spot, is determined by making a VECTOR DIAGRAM.
D. Single-Plane Vector Method Of Balancing
A vector is simply a line whose length represents the amount of unbalance and whose direction represents the angle of the unbalance. For example, if the vibration amplitude is 5.0 mils (127 microns) and the phase reference mark position is 120°, the unbalance can be represented by a line with an arrowhead (a vector) 5.0 divisions long pointed at 120° as illustrated in Figure 22. To simplify drawing vectors, polar coordinate graph paper like that shown is normally used. The radial lines, which radiate from the center, or origin, represent the angular position of the vector and are scaled in degrees increasing in the clockwise direction. The concentric circles with a common center at the origin are spaced equally for plotting the length of vectors.
When a trail weight is added to a part, we actually add to the original unbalance. The resultant unbalance will be at some new position between the trail weight and original unbalance. We see this resultant unbalance as a new vibration amplitude and phase reading. In Figure 22, our ORIGINAL unbalance was represented by 5.0 mils (127 microns) and a phase of 120°.
After adding a trial weight, Figure 23A, the unbalance due to both the ORIGINAL PLUS THE TRIAL WEIGHT is represented by 8 mils (203 microns) and a phase of 30°. These two
readings can be represented by vectors. Using polar graph paper, the ORIGINAL unbalance
vector is plotted by drawing a line from the origin at the same angle as the reference mark, or 120°, as shown in Figure 22. A convenient scale is selected for the length of the vector. In this example, each major division equals 1.0 mil (25.4 microns). Thus, the ORIGINAL unbalance
vector is drawn 5 major divisions in length to represent 5 mils (127 microns). The vector for the
ORIGINAL unbalance is labeled “O”.
Next, the vector representing the ORIGINAL PLUS THE TRIAL WEIGHT unbalance is drawn
to the same scale at the new phase angle observed. For our example, this vector will be drawn 8 major divisions in length to represent 8.0 mils (203 microns) at an angular position of 30° that was the new phase angle. The ORIGINIAL PLUS THE TRIAL WEIGHT vector is
labeled “O + T” in Figure 23A. These two vectors, together with the known amount of trial
weight, are all that’s needed to determine the required balance correction - both weight amount and location.
FIGURE 22
AN UNBALANCE OF 5 MILS (127 Microns) AT 120° CAN BE REPRESENTED BY A VECTOR DRAWN 5 DIVISIONS LONG AND POINTING AT 120°
To solve the balancing problem, the next step is to draw a vector connecting the end of the
“O” vector to the end of the “O + T” vector as illustrated in Figure 23 B. This connecting
vector is labeled “T” and represents the difference between vectors “O” and “ “O + T”
(O + T) - (O) = T. Thus, vector “T” represents the effect of the trial weight alone. By measuring
the length of the “T” vector using the same scale used for “O” and “O + T”, the effect of the
trial weight in terms of vibration amplitude is determined. For example, vector “T” in Figure 3B is 9.4 mils (239 microns) in length. This means that the trial weight added to the rotor
produced an effect equal to 9.4 mils (239 microns) of vibration. This relationship can now be used to determine how much weight is required to be equivalent to the original unbalance,
“O”. The correct balance weight is found following the formula:
Correction weight = Trial weight x O (EQUATION 8)
For our example, assume that the amount of trial weight added to the rotor in Figure 21 is 10 grams. From the vector diagram, Figure 23B, we know that “O” = 5.0 mils (127 microns) and
“T” = 9.4 mils (239 microns). Therefore:
Correction weight = 10 grams x 5 mils = 5.3 grams 9.4 mils
or
Correction weight = 10 grams x 127 microns = 5.3 grams 239 microns
To balance a part, our objective is to adjust vector “T” to make it equal in length and pointing
directly opposite the original unbalance vector “O”. In this way, the effect of the correction
weight will serve to cancel out the original unbalance, resulting in a balanced rotor. Adjusting the amount of weight according to the correct formula will make vector “T” equal in length to
the “O” vector. The next step is to determine the correct angular position of the weight.
The direction in which the trial weight acts with respect to the original unbalance is
represented by the direction of vector “T”. See Figure 23B. Vector “T” can always be thought
of as pointing away from the end of the “O” vector. Therefore, vector “T” must be shifted by the
included angle (O) between vector “O” and vector “T” in order to be opposite vector “O”. Of
course, in order to shift vector “T” the required angle, it will be necessary to move the trial
weight by the same angle. From the vector diagram, Figure 23B, the measured angle (O)
A B
FIGURE 23. THE SINGLE-PLANE VECTOR SOLUTION