Machinery Malfunction
Diagnosis and Correction
Vibration Analysis and Troubleshooting
for the Process Industries

Robert C. Eisenmann, Sr., P.E.
Global Machinery
Diagnostics
Services Manager
GE Energy
- Sugar Land, Texas
President
— MACHINERY
DIAGNOSTICS,
Inc. —- Minden,
Nevada
and

Robert C. Eisenmann, Jr.
Manager of Rotating Equipment — HAHN & CLAY — Houston, Texas
Rotating Equipment Technical Authority - BP Products North America - Houston, Texas

PTR
Cliffs,
New by:
Jersey
07632
The original
HardPrentice
Copy formatHall,
of this Englewood

book was previously
published
Pearson
Education, Inc.
Copyright Assigned to Robert C. Eisenmann, Sr. by Hewlett-Packard effective June 6, 2005.


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Original Library of Congress Cataloging in Publication Data
Eisenmann, Robert C. 1943Machinery malfunction diagnosis and correction: vibration analysis and troubleshooting for
the process industries / Robert C. Eisenmann, Sr., and Robert C. Eisenmann, Jr.
cm -- (Hewlett- Packard professional
books)
Acquisitionsp.
editor:
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Includes
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ISBN
Manufacturing

Manager:
Alexis
R.
Heydt
Illustrations
by: Robert
C. Eisenmann,Robert
Sr.
1. Machinery -- Monitoring. 2. Machinery
-- Vibration.
I. Eisenmann,
C., 1970Production
team:
Sophie
Papanikolaou,
Jane
Bonnell,
Lisa
Iarkowski,
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Morgan,
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Mosco,
II. Title. III. Series.
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.



To Mary Rawson Eisenmann,
Wife and Mother
Who Always Kept The Home Fires Burning
While The Boys Went Off To Play With Their Machines


Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1 - Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Machinery Categories 4
Chapter Descriptions 5
Bibliography 8

Chapter 2 - Dynamic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Malfunction Considerations and Classifications 9
Fundamental Concepts 10
Vector Manipulation 21
Undamped Free Vibration 28
Case History 1: Piping System Dynamic Absorber 31
Free Vibration with Damping 37
Forced Vibration 45
Case History 2: Steam Turbine End Cover Resonance 55
Torsional Vibration 58
Bibliography 66

Chapter 3 - Rotor Mode Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Mass and Support Distribution 67
Case History 3: Two Stage Compressor Rotor Weight Distribution 72
Inertia Considerations and Calculations 74

Damping Influence 96
Stiffness Influence 105
Critical Speed Transition 120
Mode Shape Measurement 130
Case History 4: Vertical Generator Mode Shape 137
Analytical Results 142
Case History 5: Eight Stage Compressor Mode Shape Change 143
Bibliography 148

Chapter 4 - Bearings and Supports . . . . . . . . . . . . . . . . . . . . . . . . 149
Fluid Film Radial Journal Bearings 150
Case History 6: Shaft Position In Gas Turbine Elliptical Bearings
Fluid Film Radial Bearing Clearance Measurements 165
Case History 7: Expander Journal Bearing Clearance 174

161

iv


v

Bearing Supports — Measurements and Calculations 179
Case History 8: Measured Steam Turbine Bearing Housing Stiffness 181
Case History 9: Measured Gas Turbine Bearing Housing Stiffness 185
Bearing Housing Damping 187
Fluid Film Thrust Bearings 188
Rolling Element Bearings 193
Before Considering Bearing Redesign 196
Bibliography 198


Chapter 5 - Analytical Rotor Modeling . . . . . . . . . . . . . . . . . . . . 199
Modeling Overview 199
Undamped Critical Speed 201
Case History 10: Mode Shapes for Turbine Generator Set 206
Case History 11: Torsional Analysis of Power Turbine and Pump 208
Stability and Damped Critical Speed Calculations 213
Case History 12: Complex Rotor Damped Analysis 217
Forced Response Calculations 222
Case History 13: Gas Turbine Response Correlation 226
Case History 14: Charge Gas Compressor with Internal Fouling 230
Case History 15: Hybrid Approach To A Vertical Mixer 236
Bibliography 242

Chapter 6 - Transducer Characteristics . . . . . . . . . . . . . . . . . . . 243
Basic Signal Attributes 244
Proximity Displacement Probes 253
Velocity Coils 272
Piezoelectric Accelerometers 278
Pressure Pulsation Transducers 285
Specialized Transducers 288
Aspects of Vibration Severity 294
Bibliography 302

Chapter 7 - Dynamic Signal Characteristics . . . . . . . . . . . . . . . 303
Electronic Filters 303
Time and Orbital Domain 316
Time and Frequency Domain 333
Case History 16: Steam Turbine Exhaust End Bearing Dilemma 343
Signal Summation 347

Case History 17: Opposed Induced Draft Fans 349
Amplitude Modulation 353
Case History 18: Loose and Unbalanced Compressor Wheel 356
Frequency Modulation 359
Case History 19: Gear Box with Excessive Backlash 362
Bibliography 364


vi

Chapter 8 - Data Acquisition and Processing . . . . . . . . . . . . . . . 365
Vibration Transducer Suite 365
Recording Instrumentation 369
Data Processing Instrumentation 379
Data Presentation Formats 383
Bibliography 394

Chapter 9 - Common Malfunctions . . . . . . . . . . . . . . . . . . . . . . . 395
Synchronous Response 395
Mass Unbalance 398
Bent or Bowed Shaft 400
Case History 20: Repetitive Steam Turbine Rotor Bow 402
Eccentricity 406
Case History 21: Seven Element Gear Box Coupling Bore 407
Shaft Preloads 410
Resonant Response 416
Case History 22: Re-Excitation of Compressor Resonance 419
Machinery Stability 422
Case History 23: Warehouse Induced Steam Turbine Instability 429
Case History 24: Pinion Whirl During Coastdown 432

Mechanical Looseness 435
Case History 25: Loose Steam Turbine Bearing 438
Rotor Rubs 440
Cracked Shaft Behavior 443
Case History 26: Syngas Compressor with Cracked Shaft 446
Foundation Considerations 449
Case History 27: Floating Induced Draft Fan 451
Case History 28: Structural Influence of Insufficient Grout 454
Bibliography 458

Chapter 10 - Unique Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
Parallel Shaft - Two Element Gear Boxes 459
Case History 29: Herringbone Gear Box Tooth Failure 466
Epicyclic Gear Boxes 470
Case History 30: Star Gear Box Subsynchronous Motion 477
Process Fluid Excitations 483
Case History 31: Boiler Feed Water Pump Splitter Vane Failures 496
Case History 32: Hydro Turbine Draft Tube Vortex 499
Electrical Excitations 507
Case History 33: Motor With Unsupported Stator Midspan 515
Case History 34: Torsional Excitation From Synchronous Motor 519
Reciprocating Machines 522
Case History 35: Hyper Compressor Plunger Failures 526
Bibliography 534


vii

Chapter 11 - Rotor Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Before Balancing 536

Standardized Measurements and Conventions 539
Combined Balancing Techniques 545
Linearity Requirements 547
Case History 36: Complex Rotor Non-Linearities 548
Single Plane Balance 552
Case History 37: Forced Draft Fan Field Balance 560
Two Plane Balance 564
Case History 38: Five Bearing, 120 MW Turbine Generator Set 575
Weight Sequence Variation 586
Case History 39: Three Bearing Turbine Generator at 3,600 RPM 588
Case History 40: Balancing A 36,330 RPM Pinion Assembly 597
Three Plane Balance 606
Static-Couple Corrections 616
Multiple Speed Calculations 618
Response Prediction 619
Trim Calculations 622
Balancing Force Calculations 623
Balance Weight Splitting 626
Weight Removal 628
Shop Balancing 629
Bibliography 636

Chapter 12 - Machinery Alignment . . . . . . . . . . . . . . . . . . . . . . . . 637
Pre-Alignment Considerations 638
Optical Position Alignment 649
Case History 41: Hyper Compressor Position Alignment 654
Laser Position Alignment 658
Optical and Laser Bore Alignment 660
Wire Bore Alignment 663
Case History 42: Hyper Compressor Bore Alignment 667

Shaft Alignment Concepts 669
Rim and Face Shaft Alignment 673
Reverse Indicator Shaft Alignment 681
Optics, Lasers, and Wires for Shaft Alignment 691
Hot Alignment Techniques 692
Case History 43: Motor to Hot Process Pump Alignment 697
Bibliography 702


viii

Chapter 13 - Applied Condition Monitoring . . . . . . . . . . . . . . . . 703
Maintenance Philosophies 703
Condition Monitoring 705
Machinery Performance 706
Vibration Response Data 708
Bearing Temperature Data 711
Data Trending 712
Case History 44: Four Pole Induction Motor Bearing Failure 714
Case History 45: Cracked Gas Compressor Intermittent Instability 718
Case History 46: High Stage Compressor Loose Thrust Collar 721
Pre-Startup Inspection and Testing 724
Startup Inspection and Testing 732
Case History 47: Turbine Solo Operation with Tapered Journal 735
Case History 48: Coupled Turbine Generator Startup 736
Case History 49: Heat Soak and Load Stabilization 739
Bibliography 742

Chapter 14 - Machinery Diagnostic Methodology . . . . . . . . . . . 743
Diagnostic Objectives 744

Mechanical Inspection 744
Test Plan Development 745
Data Acquisition and Processing 746
Data Interpretation 749
Conclusions and Recommendations 750
Corrective Action Plan 750
Case History 50: Steam Turbine Electrostatic Voltage Discharge
Case History 51: Barrel Compressor Fluidic Excitation 758
Case History 52: High Speed Pinion Instability 766
Conclusions on Diagnostic Methodology 770
Bibliography 770

751

Chapter 15 - Closing Thoughts and Comments . . . . . . . . . . . . . 771
Economic Reality 772
Corporate Considerations 773
Presentation of Results 778
Silver Bullets 780

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781
A — Machinery Diagnostic Glossary
B — Physical Properties 795
C — Conversion Factors 797
D — Index 801

781


Preface


W

hen my son graduated from Texas
A&M University, he was understandably eager to start working, and begin earning a livable salary. He accepted a maintenance engineering position at a large
chemical complex, and embarked upon learning about process machinery. In the
months and years that followed, he and his colleagues had many questions concerning a variety of machinery problems. From my perspective, most of these
problems had been solved twenty or thirty years ago. However, it was clear that
the new engineering graduates were devoting considerable effort attempting to
unravel mysteries that had already been solved.
The obvious question that arises might be stated as: How come the new
engineers cannot refer to the history files instead of reworking these issues? A partial answer to this question is that the equipment files often do not provide any
meaningful historical technical data. Major corporations are reluctant to spend
money for documentation of engineering events and achievements. Unless the
young engineers can find someone with previous experience with a specific malfunction, they are often destined to rework the entire scenario.
Although numerous volumes have been published on machinery malfunctions, there are very few technical references that address the reality of solving
field machinery problems. This general lack of usable and easily accessible information was a primary force in the development of this text. The other significant
driving force behind this book was the desire to coalesce over thirty-three years
of experience and numerous technical notes into some type of structured order
that my son, and others could use for solving machinery problems.
This is a book about the application of engineering principles towards the
diagnosis and correction of machinery malfunctions. The machinery under discussion operates within the heavy process industries such as oil refineries, chemxi


xii

ical plants, power plants, and paper mills. This machinery consists of steam, gas
and hydro turbines, motors, expanders, pumps, compressors, and generators,
plus various gear box configurations. This mechanical equipment covers a wide
variety of physical characteristics. The transmitted power varies from 50 horsepower, to units in excess of 150,000 horsepower. Rotational speeds range from

128 to more than 60,000 revolutions per minute. There is a corresponding wide
range of operating conditions. Fluid temperatures vary from cryogenic levels of
minus 150°F, to values in excess of plus 1,200°F. The operating pressures range
from nearly perfect vacuums to levels greater than 40,000 pounds per square
inch. Physically, the moving elements may be only a few feet long, and weigh less
than 100 pounds — or they may exceed 200,000 pounds, and cover the length of a
football field. In virtually all cases, these process machines are assembled with
precision fits and tolerances. It is meaningful to note that the vibration severity
criteria for many of these machines are less than the thickness of a human hair.
In some respects, it is amazing that this equipment can operate at all.
When the number of individual mechanical components are considered, and the
potential failure mechanisms are listed, the probabilities for failures are staggering. Considerable credit must be given to the designers, builders, and innovators
of this equipment. They have consistently produced machines that are constantly evolving towards units of improved efficiency, and extended reliability.
The majority of machinery problems that do occur fall into what I call the
ABC category. These common problems are generally related to Alignment, Balance, and incorrect Clearances (typically on bearings). Due to the continual
appearance of these malfunctions, an entire chapter within this text has been
devoted to each of these subjects. Machines also exhibit other types of failures,
and a sampling of common plus unique problems are described within this book.
Some people might view this document as a textbook. Others might consider this to be a reference manual, and still other individuals might use this
book for troubleshooting. It has also been suggested that this book be categorized
as a how to do it manual. Since 52 detailed case histories are combined with
numerous sample calculations and examples, each of these descriptions are accurate and applicable. In the overview, the contents of this book cover a variety of
machinery malfunctions, and it engages the multiple engineering disciplines
that are required to solve real world problems. Regardless of the perception, or
the final application, this is a book about the mechanics, measurements, calculations, and diagnosis of machinery malfunctions. I sincerely hope that this text
will provide some meaningful help for students, for new graduates entering this
field, as well as provide a usable reference for seasoned professionals.
Finally, I would like to extend my deepest personal thanks to John Jensen
of Hewlett Packard for the inspiration, encouragement, and opportunity to write
this book. I am further indebted to John for his detailed and thorough review of

much of the enclosed material. I would also like to thank Ron Bosmans, Dana
Salamone, and Pamela Puckett for their constructive comments and corrections.
Robert C. Eisenmann, Sr., P.E.
October 1997


C

H

A

P

T

Introduction

E

R

1

1

M

n


➜

e

ior

al
B
K ehav

ysi
c

tio

nta
me
tru e

x
➜ E

Ph

Ins

achinery development has been synonymous with technological progress. This growth has resulted in an evolutionary
trend in industrial equipment that moves towards increased complexity, higher
speeds, and greater sophistication. The water wheel has evolved into the hydroelectric plant, the rudimentary steam engine has grown into the gas turbine, and
coarse mechanical devices have been replaced by elegant electronic circuits.

Throughout this evolution in technology, new industries and vocations have
developed. In recent decades, the Machinery Diagnostician has appeared within
most maintenance engineering organizations. These individuals generally possess an extensive knowledge of the machinery construction. They understand
repair procedures, and they have a working knowledge of the peripheral equipment. This includes familiarity with the lube and seal oil system, the processing
scheme, and the machine controls. Diagnosticians are generally knowledgeable
of the machinery monitoring or surveillance instrumentation that covers everything from transducers to the data logging computers. Furthermore, when a
problem does appear on a piece of equipment, it generally falls under the jurisdiction of the machinery diagnostician to resolve the difficulty, and recommend
an appropriate course of corrective action. This requirement imposes another set
of demands. That is, these individuals must be familiar with problem solving
techniques and proven methodology for correcting the machinery malfunction.
Clearly, the diagnostician must be qualified in many technical disciplines.
As depicted in the adjacent diagram, the basic areas of expertise include knowledge of machinery, knowledge of physical behavior, plus knowledge of instrumentation. The machinery background must be
thorough, and it must allow the diagnostician to focus upon
realistic failure mechanisms rather than esoteric theories.
The category of physical behavior embraces technical fields
w l e dg
such as: statics, dynamics, kinematics, mechanics of
no
materials, fluid dynamics, heat transfer, mathematics,
and rotordynamics. Knowledge in these areas must be
fully integrated with the instrumentation aspects of
pe
c
ri e n
the electronic measurements required to document
Machinery
and understand the machinery motion.

1



2

Chapter-1

Competence in these three areas is only achieved by a combination of
knowledge and field experience. Acquiring knowledge often begins with specific
technical training. For instance, all academic institutions provide the mathematics and physics necessary to grasp many physical principles. A few universities
provide an introduction to the world of analytical rotordynamics. Unfortunately,
academia is often burdened by the necessity to obtain research grants, and generate complex general solutions for publication. Certainly the college level contributions to this field are significant, and the global solutions are impressive.
However, the working machinery diagnostician often cannot use generalized concepts for solving everyday problems. To state it another way, integral calculus is
absolutely necessary for success in the classroom, but it is reasonably useless for
most activities performed on the compressor deck.
Within the industrial community, a variety of training programs are available. Instrumentation vendors provide courses on the application and operation
of their particular devices. Similarly, machinery vendors and component suppliers have various courses for their clientele. Although these training courses are
oriented towards solutions of field problems, they typically display shortcomings
in three areas. First, the industrial courses are limited in scope to three or four
days of training. This time frame is acceptable for simple topics, but it is inadequate for addressing complex material. Second, industrial training courses are
restricted to the instruments or devices sold by the vendor providing the training. Although this approach is expected by the attendees, it does limit the depth
and effectiveness of the training. The third problem with vendor training resides
in the backgrounds of the training specialists. Although these people are usually
well qualified to represent the products of the vendor, they often lack an understanding of the realities within an operating plant. Clearly, the smooth presentation of fifty computer generated slides has no relationship to the crucial decisions
that have to be made at 2:00 AM regarding a shaking machine.
Another disturbing trend seems to permeate the specialized field of vibration analysis. Within this technical area, there have been long-term efforts by
some vendors to train people to solve problems based entirely on simplistic vibratory symptoms. This is extraordinarily dangerous, and the senior author has
encountered numerous instances of people reaching the wrong conclusions based
upon this approach. Many problems display similar vibratory symptoms, and
additional information is usually required to sort out the differences. In all cases,
the measurements must be supplemented with the logical application of physical
laws. In addition, the machinery construction and operation must be examined

and understood in order to develop an accurate assessment of the malfunction.
Very few professional organizations provide a comprehensive and integrated approach targeted to the topic of machinery diagnosis. The text contained
herein attempts to provide a pragmatic and objective overview of machinery malfunction analysis. The three fundamental areas of physical behavior, machinery,
and instrumentation knowledge are integrated throughout this book. The structure of this text is directed towards developing a basic understanding of fundamental principles. This includes the applicability of those principles towards
machinery, plus the necessary instrumentation and computational systems to


3

describe and understand the actual behavior of the mechanical equipment.
It should be recognized that acquiring basic knowledge does not guarantee
that the diagnostician will be qualified to engage and solve machinery problems.
As previously stated, experience is mandatory to become proficient in this field.
Although the preliminary knowledge may be difficult to obtain, the experience
portion may be even harder to acquire. This is particularly true for the individual that works in an operating complex that contains a limited assortment of
mechanical equipment. For this diagnostician, the ability to develop a wellrounded background may be hampered due to an absence of mixed machinery
types, and associated problems. References such as the excellent series of books
by Heinz Bloch1 provide detailed machinery descriptions, procedures, and guidelines. If the diagnostician is not familiar with a particular machine, this is the
one available source that will probably answer most mechanical questions.
In a further attempt to address the experience issue, this text was prepared
with 52 field case histories interspersed throughout the chapters. These case
studies are presented with substantial details and explanations. The logical
steps of working through each particular problem are reviewed, and the encountered errors as well as the final solutions are presented. It is the author’s hope
that these field examples on major process machinery will provide additional
insight, and enhance the experience level of the machinery diagnostician.
The equipment discussed in this text resides within process industries such
as oil refining, pipeline, chemical processing, power generation, plus pulp and
paper. The specific machines discussed include pumps, blowers, compressors, and
generators that vary from slow reciprocating units to high speed centrifugal
machines. The prime movers appear in various configurations from induction

motors, to cryogenic and hot gas expanders, hydro-turbines, multistage steam
turbines, and large industrial gas turbines. In some cases the driver is directly
coupled to the driven equipment, and in other trains an intermediate gear box is
included. Some of the discussed machinery was installed decades ago, and other
mechanical equipment was examined during initial field commissioning.
It is an objective of this text to assist in understanding, and to demonstrate
practical solutions to real world machinery problems. This book is not designed
to be mathematically rigorous, but the presented mathematics is considered to
be accurate. In all cases, the original sources of the mathematical derivations are
identified. This will allow the reader to reference back to the original technical
work for additional information. Significant equations in this text are numerically identified, and highlighted with an outline box such as equation (2-1).
Developmental and supportive equations are sequentially numbered in each
chapter. In addition, intermediate results plus numeric sample calculations are
also presented. These examples are not assigned equation numbers. In essence,
this book is structured to supplement a formal training presentation, and to provide an ongoing reference.

1 Heinz P. Bloch, Practical Machinery Management for Process Plants, Vol. 1 to 4 (Houston, TX:
Gulf Publishing Company, 1982-1989).


4

Chapter-1

MACHINERY CATEGORIES
It is organizationally advantageous to divide process machinery into three
categories. Typically, these individual machinery categories are administered
under a singular condition monitoring program since they share a common technology. However, the allocation of resources among the three segments varies in
direct proportion to the process criticality of the mechanical equipment.
The first segment covers the large machinery within an operating plant.

These main equipment trains are generally critical to the process. In most
instances the plant cannot function without these machines. For example, the
charge gas compressor in an ethylene plant, or a syngas compressor in an ammonia plant fall into this category. This equipment typically ranges between 5,000
and 50,000 horsepower. Operating speeds vary from 200 to 60,000 RPM, and
fluid film bearings are normally employed. Most of the machinery problems presented within this text reside within this critical category.
Machines of this class are typically equipped with permanently installed
proximity probe transducer systems for vibration and position measurements,
plus bearing temperature pickups, and specialized transducers such as torque
sensors. Historically, the field transducers are hard wired to continuous monitoring systems that incorporate automated trip features for machinery protection.
These monitoring systems are also connected to process and/or dedicated computer systems for acquisition of static and dynamic data at predetermined sample rates. These data acquisition computer systems provide detailed information
concerning the mechanical condition of the machinery.
The second major group of machines are categorized as essential units.
They are physically smaller than the critical units, they normally have lower
horsepower ratings, and they are usually installed with full backup or spare
units. Machines within this category include trains such as product pumps,
boiler feed water pumps, cooling water pumps, etc. Individual units in this category may not be critical to the process — but it is often necessary to keep one out
of two, or perhaps two out of three units running at all times. It should be recognized that a particular service may be considered as essential equipment when a
fully functional main and spare unit are in place. However, if one unit fails, plant
operation then depends upon the reliability of the remaining train. In this manner, an essential train may be rapidly upgraded to the status of a critical unit.
These essential machinery trains are usually instrumented in a manner
similar to the critical units previously discussed. Shaft sensing proximity probe
systems, and thermocouples are hard wired to monitoring systems. These monitoring systems may be integrated with computerized trending systems. Due to
the similarity of construction and installation of the critical and the essential
machines, the text contained herein is directly applicable to essential units.
The third group of machines are referred to as general purpose equipment. These units are physically smaller, and they generally contain rolling element bearings. These machines are often installed with full backups, or they are
single units that are non-critical to the process. Machines within this category
have minimal vibration or temperature measuring instrumentation perma-


Chapter Descriptions


5

nently installed. This equipment is often monitored with portable data loggers,
and the information tracked with dedicated personal computer systems. In many
instances, small machines are not subjected to detailed analytical or diagnostic
procedures. An in-depth analysis might cost more than the original purchase
price of the equipment. Although there are not many direct references to small
machinery within this book, the techniques and physical principles discussed for
large machines are fully appropriate for these smaller units.
The technology necessary to understand the behavior of process machinery
has been evolving for many years. For example, dedicated machinery monitoring
systems are being replaced by direct interfaces into Distributed Control Systems
(DCS) for trending of general information. Detailed dynamic data is simultaneously acquired in a separate diagnostic computer system. This improvement in
data trending and resolution allows a better assessment of machinery malfunctions. In addition, numerous developments in the areas of rotor dynamics, aerodynamics, blade design, cascade mechanics, metallurgy, fabrication, testing, plus
optimizing bearing and support designs have all combined to provide a wealth of
knowledge. Understanding these individual topics and the interrelationship
between design parameters, mechanical construction, vibratory behavior, position between elements, and the array of electronic measurements and data processing can be an intimidating endeavor.
In support of this complex requirement for knowledge plus experience, this
book has been prepared. To provide continuity through the chapters, various facets of several basic types of industrial machines are examined. It is understood
that one text cannot fully cover all of the material requested by all of the readers.
However, it is anticipated that the information presented within this text will
provide a strong foundation of technical information, plus a source for future reference. The specific topics covered in this book are summarized as follows.

CHAPTER DESCRIPTIONS
The following chapter 2 on dynamic motion begins with a general classification of machinery vibration problems. A review of the fundamental concepts
provides a foundation that extends into a description of a simple undamped
mechanical system. The addition of damping, plus the influence of forced vibration are discussed. Although the majority of the emphasis is placed upon lateral
motion, the parallel environment of torsional vibration is introduced. Finally, the
theoretical concepts are correlated with actual measured machinery vibratory

characteristics for lateral and torsional behavior.
Rotor mode shapes are discussed in chapter 3. This topic begins with a
review of static deflection, followed by the influence of rotor mass, and the distribution of mass and supports. Various aspects of inertia of mechanical systems
are discussed, and critical distinctions are identified. Next, system damping, and
effective support stiffness are discussed, and their influence upon the deflected
mode shapes are demonstrated. The physical transition of a rotor across a critical speed, or balance resonance region is thoroughly explained. These basic con-


6

Chapter-1

cepts are then extended into measured and calculated rotor mode shapes. In
addition, the construction of interference maps are introduced, and a variety of
illustrations are used to assist in a visualization of these important concepts.
Chapter 4 addresses machinery bearings and supports in rotating systems. This includes an introduction to oil film bearing characteristics, and some
computational techniques. This is followed by proven techniques for determination of radial fluid film bearing clearances, plus the measurement of bearing
housing coefficients. Fluid film thrust bearings are also discussed, and the characteristics of rolling element bearings are reviewed. Appropriate case histories
are included within this chapter to assist in explanation of the main concepts.
Analytical rotor modeling is introduced in chapter 5. This is a continuation of the machinery behavior concepts initiated in the previous chapters. These
concepts are applied to the development of an undamped critical speed analysis
for lateral and torsional behavior. This is followed by the inclusion of damping to
yield the damped response, plus a stability analysis of the rotating system. Further refinement of the machinery model allows the addition of dimensional forcing functions to yield a synchronous response analysis. This step provides
quantification and evaluation of the transient and steady state vibration
response characteristics of the machinery. Finally, the validity and applicability
of these analytical techniques are demonstrated by six detailed case histories
distributed throughout the chapter.
Chapter 6 provides a discussion of transducer characteristics for the
common measurement probes. A traditional industrial suite of displacement,
velocity, acceleration, and pressure pulsation probes are reviewed. The construction, calibration, and operating characteristics of each transducer type are subjected to a comprehensive discussion. In addition, the specific advantages and

disadvantages of each standard transducer are summarized. Specialized transducers are also identified, and their general applications are briefly discussed.
Finally, the topic of vibration severity and the establishment of realistic vibration limits is discussed.
Dynamic signal characteristics are presented in chapter 7. This section
addresses the manipulation and examination of dynamic vibration signals with a
full range of electronic filters. In addition, an explanation of combining time
domain signals into orbits, and the interrelationship between the time and frequency domain characteristics are examined. Finally, common signal combinations such as signal summation, amplitude modulation, and frequency
modulation are discussed. In all cases, appropriate examples are presented.
Chapter 8 covers data acquisition and processing in terms of the
instrumentation systems required for accurate field data acquisition, plus the
processing of the data into useful hard copy formats. Sample forms are included
to facilitate documentation of field measurements. In addition, the functions and
necessary compatibility issues between instruments and transducers are discussed, and operational guidelines are offered. This chapter concludes with an
overview of the most useful machinery data presentation formats.
Based upon the concepts discussed in the previous sections, chapter 9 discusses the origin of many of the common malfunctions experienced by process


Chapter Descriptions

7

machinery. The topics include synchronous (rotational speed) excitations such as
unbalance, bowed shafts, eccentricity, and resonant responses. The influence of
preloads, machinery stability, mechanical looseness, rubs, and cracked shafts are
discussed. In addition, foundation considerations are reviewed from several perspectives. These general problems are applicable to all rotating machines, and
several case histories are included to illustrate these fundamental mechanisms.
Chapter 10 addresses the unique behavior of different types of machinery. Excitations associated with gear boxes, electrical frequencies, and fluid excitations are included. In addition, the behavioral characteristics of traditional
reciprocating machines, plus hyper compressors are reviewed. Although this
group does not cover all of the potential sources of excitation, it does provide a
useful summary of problems that occur with regularity on many types of
machines. Again, a series of fully descriptive field case histories are distributed

throughout the chapter.
Rotational speed vibration is the dominant motion on most industrial
machines. Chapter 11 is devoted to an in-depth discussion of this synchronous
behavior, and the direct application of these concepts towards rotor balancing.
This chapter begins with the initial thought process prior to balancing, and the
standardized measurements and conventions. The concept of combined balancing techniques are presented, and the machinery linearity requirements are
identified. The development of balancing solutions are thoroughly discussed for
single plane, two plane, and three plane solutions. In addition, static-couple solutions using two plane calculations are presented, and multiple speed calculations
are discussed. The use of response prediction, and trim balance calculations are
reviewed, and several types of supportive calculations are included. Again, field
case histories are provided to demonstrate the applicability of the rotational
speed analysis, and rotor balancing techniques on process machines.
The last portion of chapter 11 deals with shop balancing machines, techniques, and procedures. Although the fundamental concepts are often similar to
field balancing, the shop balancing work is generally performed at low rotative
speeds. This shop balancing discussion includes additional considerations for the
various types of machinery rotors, and common balance specifications.
Machinery alignment persists as one of the leading problems on process
machinery, and this topic is covered in chapter 12. Alignment is discussed in
terms of the fundamental principles for casing position, casing bore, and shaft
alignment. Each type of machinery alignment is discussed, and combined with
explanations of several common types of measurements and calculations. This
includes dial indicator readings, optical alignment, wire alignment, plus laser
alignment, proximity probes, and tooling balls. The applicability of each technique is addressed, and suitable case histories are provided to demonstrate the
field use of various alignment techniques.
The concepts of applied condition monitoring within an operating plant
are discussed in chapter 13 of this text. This chapter was based upon a tutorial
by the senior author to the Texas A&M Turbomachinery Symposium in Dallas,
Texas. The first portion of this chapter describes the logic and evolution of condition monitoring, and the typical parameters involved. These concepts are illus-



8

Chapter-1

trated with machinery problems detected during normal operation. The second
part of this chapter reviews the turnaround checks and calibrations that should
be performed on the machinery control and protection systems. The third portion
of this chapter covers the application of condition monitoring during a post-overhaul startup of a machinery train. Again, case studies are used to illustrate the
main points of the transient vibratory characteristics.
Chapter 14 address a machinery diagnostic methodology that may be
used for diagnosis of complex mechanical problems. This chapter was based upon
a paper prepared by the senior author for an annual meeting of the Vibration
Institute in New Orleans, Louisiana. This topic discusses the fundamental tools,
successful techniques, and the seven-step process used for evaluation of machinery problems. Again, specific field case histories are included to illustrate some of
the germane points of this topic.
The final chapter 15 is entitled closing thoughts and comments, and it
addresses some of the other obstacles encountered when attempting to solve
machinery problems. This includes candid observations concerning the problems
of dealing with multiple corporate entities, plus the politics encountered within
most operating plants. In many instances, an acceptable solution is fully dependent upon a proper presentation of results that combine economic feasibility
with engineering credibility.
The appendix begins with a machinery diagnostic glossary for the specialized language and terminology associated with this business. For reference
purposes, a list of the physical properties of common metals and fluids, plus a
table of conversion factors are included. The technical papers and books cited
within this text are identified with footnotes, and summarized in a bibliography
at the end of each chapter. In addition, a detailed index is provided in the last
appendix section that includes technical topics, corporate references, and specific
authors referenced throughout this book.
It is the authors’ hope that the material included within this book will be
beneficial to the machinery diagnostician, and that this text will serve as an

ongoing technical reference. To paraphrase the words of Donald E. Bently (circa
1968), founder and owner of Bently Nevada Corporation …we just want to make
the machinery run better… To this objective, we have dedicated our professional
careers and this manuscript.

BIBLIOGRAPHY
1. Bloch, Heinz P., Practical Machinery Management for Process Plants, Vol. 1 to 4,
Houston, TX: Gulf Publishing Company, 1982-1989.


C

Dynamic Motion

H

A

P

T

E

R

2

2


M

any mechanical problems are initially
recognized by a change in machinery vibration amplitudes. In order to understand, and correctly diagnose the vibratory characteristics of rotating machinery,
it is essential for the machinery diagnostician to understand the physics of
dynamic motion. This includes the influence of stiffness and damping on the frequency of an oscillating mass — as well as the interrelationship between frequency, displacement, velocity, and acceleration of a body in motion.

MALFUNCTION CONSIDERATIONS AND CLASSIFICATIONS
Before examining the intricacies of dynamic motion, it must be recognized
that many facets of a mechanical problem must be considered to achieve a successful and acceptable diagnosis in a timely manner. For instance, the following
list identifies some of the related considerations for addressing and realistically
solving a machinery vibration problem:
❍
❍
❍
❍
❍
❍

Economic Impact
Machinery Type and Construction
Machinery History — Trends — Failures
Frequency Distribution
Vibratory Motion Distribution and Direction
Forced or Free Vibration

The economic impact is directly associated with the criticality of the
machinery. A problem on a main process compressor would receive immediate
attention, whereas a seal problem on a fully spared reflux pump would receive a
lower priority. Clearly, the types of machinery, the historical trends, and failure

histories are all important pieces of information. In addition, the frequency of
the vibration, plus the location and direction of the motion are indicators of the
problem type and severity. Traditionally, classifications of forced and free vibration are used to identify the origin of the excitation. This provides considerable
insight into potential corrective actions. For purposes of explanation, the following lists identify some common forced and free vibration mechanisms.
9


10

Chapter-2

Forced Vibration Mechanisms

Free Vibration Mechanisms

❍
❍
❍
❍
❍
❍
❍
❍

❑
❑
❑
❑
❑
❑

❑
❑

Mass Unbalance
Misalignment
Shaft Bow
Gyroscopic
Gear Contact
Rotor Rubs
Electrical Excitations
External Excitations

Oil Whirl
Oil or Steam Whip
Internal Friction
Rotor Resonance
Structural Resonances
Acoustic Resonances
Aerodynamic Excitations
Hydrodynamic Excitations

Forced vibration problems are generally solved by removing or reducing the
exciting or driving force. These problems are typically easier to identify and solve
than free vibration problems. Free vibration mechanisms are self-excited phenomena that are dependent upon the geometry, mass, stiffness, and damping of
the mechanical system. Corrections to free vibration problems may require physical modification of the machinery. As such, these types of problems are often difficult to correct. Success in treating self-excited problems are directly related to
the diagnostician’s ability to understand, and apply the appropriate physical
principles. To address these fundamental concepts of dynamic motion, including
free and forced vibration, the following chapter is presented for consideration.
It should be mentioned that much of the equation structure in this chapter
was summarized from the classical textbook by William T. Thomson1, entitled

Mechanical Vibrations. For more information, and detailed equation derivation,
the reader is encouraged to reference this source directly. The same basic equation structure is also described in his newer text entitled Theory of Vibration
with Applications2. Regardless of the vintage, at least one copy of Thomson
should be part of the reference library for every diagnostician.

FUNDAMENTAL CONCEPTS
Initially, consider a simple system consisting of a one mass pendulum as
shown in Fig. 2-1. Assume that the pendulum mass M is a concrete block suspended by a weightless and rigid cable of length L. Further assume that the system operates without frictional forces to dissipate system energy. Intuitively, if
the pendulum is displaced from the vertical equilibrium position, it will oscillate
back and forth under the influence of gravity. The mass will move in the same
path, and will require the same amount of time to return to any specified reference point. Due to the frictionless environment, the amplitude of the motion will
remain constant. The time required for one complete oscillation, or cycle, is
called the Period of the motion. The total number of cycles completed per unit of
1 William Tyrell Thomson, Mechanical Vibrations, 2nd Edition, 9th Printing, (Englewood
Cliffs, New Jersey: Prentice Hall, Inc., 1962), pp.1-75
2 William T. Thomson, Theory of Vibration with Applications, 4th Edition, (Englewood Cliffs,
New Jersey: Prentice Hall, 1993), pp. 1-91.


Fundamental Concepts

11

time is the Frequency of the oscillation. Hence, frequency is simply the reciprocal
of the period as shown in the following expression:
1
Frequency = ------------------Period

(2-1)


The box around this equation identifies this expression as a significant or
important concept. This same identification scheme will be used throughout this
text. Within equation (2-1), period is a time measurement with units of hours,
minutes or seconds. Frequency carries corresponding units such as Cycles per
Hour, Cycles per Minute (CPM), or Cycles per Second (CPS or Hz). Understandably, the oscillatory motion of the pendulum is repetitive, and periodic. As shown
in Marks’ Handbook3, Fourier proved that periodic functions can be expressed
with circular functions (i.e., a series of sines and cosines) — where the frequency
for each term in the equation is a multiple of the fundamental. It is common to
refer to periodic motion as harmonic motion. Although many types of vibratory
motions are harmonic, it should be recognized that harmonic motion must be
periodic, but periodic motion does not necessarily have to be harmonic.

Stationary I-Beam

W

φ

φ

cos

W=MG

W

Cable Length - L

φ


sin

φ

Mass
A

C
B

Negative

Fig. 2–1 Oscillating Pendulum Displaying Simple Harmonic Motion

Max. Neg. Displ.
Zero Velocity
Max. Pos. Accel.

Equilibrium
Zero Displacement
Maximum Velocity
Zero Acceleration

Positive
Max. Pos. Displ.
Zero Velocity
Max. Neg. Accel.

3 Eugene A. Avallone and Theodore Baumeister III, Marks’ Standard Handbook for Mechanical Engineers, Tenth Edition, (New York: McGraw-Hill, 1996), pp. 2-36.



12

Chapter-2

In a rotating system, such as a centrifugal machine, frequency is normally
expressed as a circular rotational frequency ω. Since one complete cycle consists
of one revolution, and one revolution is equal to 2π radians, the following conversion applies:
ω = 2π × Frequency = 2π × F

(2-2)

Combining (2-1) and (2-2), the rotational frequency ω may be expressed in
terms of the Period as follows:
2π
ω = ------------------Period

(2-3)

The frequency units for ω in equation (2-3) are Radians per Second, or Radians per Minute. Again, this is dependent upon the time units selected for the
period. Although these are simple concepts, they are continually used throughout this text. Hence, a clear and definitive understanding of period and frequency are mandatory for addressing virtually any vibration problem.
Returning to the pendulum of Fig. 2-1, a gravitational force is constantly
acting on the mass. This vertical force is the weight of the block. From physics it
is known that weight W is equal to the product of mass M, and the acceleration of
gravity G. As the pendulum oscillates through an angular displacement φ, this
force is resolved into two perpendicular components. The cosine term is equal
and opposite to the tension in the string, and the sine component is the Restoring
Force acting to bring the mass back to the vertical equilibrium position. For
small values of angular displacement, sinφ is closely approximated by the angle φ
expressed in radians. Hence, this restoring force may be represented as:

Restoring Force ≈W ×φ

(2-4)

Similarly, the maximum distance traveled by the mass may also be determined from plane geometry. As shown in Fig. 2-1, the cable length is known, and
the angular displacement is specified by φ. The actual change in lateral position
for the mass is the distance from A to B, or from B to C. In either case, this distance is equal to L sinφ. Once more, for small angles, sinφ ≈ φ in radians, and the
total deflection from the equilibrium position may be stated as:
Deflection ≈L ×φ

(2-5)

This repetitive restoring force acting over the same distance has a spring
like quality. In actuality, this characteristic may be defined as the horizontal
stiffness K of this simple mechanical system as follows:
Force
Stiffness = K = -----------------------------Deflection

(2-6)

If equations (2-4) and (2-5) are substituted into (2-6), and if the weight W is
replaced by the equivalent mass M times the acceleration of gravity G, the following expression is produced:


Fundamental Concepts

13

Force
W ×φ

W
M×G
K = ------------------------------ ≈ --------------- = ----- = ----------------Deflection L ×φ
L
L

(2-7)

Later in this chapter it will be shown that the natural frequency of oscillation for an undamped single degree of freedom system is determined by equation
(2-44) as a function of mass M and stiffness K. If equation (2-7) is used for the
stiffness term within equation (2-44), the following relationship results:
ω =

K
------ =
M

M×G 1
----------------- × ------ =
L
M

G
---L

(2-8)

Equation (2-8) is often presented within the literature for describing the
natural frequency of a simple pendulum. A direct example of this concept may be
illustrated by considering the motion of the pendulum in a grandfather’s clock.

Typically, the pendulum requires 1.0 second to travel one half of a stroke, or 2.0
seconds to transverse a complete stroke (i.e., one complete cycle). The length L of
the pendulum may be determined by combining equations (2-3) and (2-8):
2π
ω = ------------------- =
Period

G
---L

If the period is represented in terms of the pendulum length L, the above
expression may be stated as:
L
Period = 2π × ---G

(2-9)

Equation (2-9) is a common expression for characterizing a simple pendulum. The validity of this equation may be verified in technical references such as
Marks’ Handbook4. For the specific problem at hand, equation (2-9) may be
solved for the pendulum length. Performing this manipulation, and inserting the
gravitational constant G, plus the period of 2.0 seconds, the following is obtained:
2

2

2

( 386.1 Inches/Second ) × ( 2.0 Seconds )
G × Period
L = --------------------------------- = -------------------------------------------------------------------------------------------- = 39.12 Inches

2
2
4π
4π
Thus, the pendulum length in a grandfather’s clock should be 39.12 inches.
This value is accurate for a concentrated mass, and a weightless support arm. In
an actual clock, the pendulum is often ornate, and weight is distributed along
the length of the support arm. This makes it difficult to accurately determine the
location of the center of gravity of the pendulum mass. Nevertheless, even rough
measurements reveal that the pendulum length is in the vicinity of 40 inches. In
addition, clock makers normally provide a calibration screw at the bottom of the
pendulum to allow the owner to adjust the clock accuracy. By turning this adjustment screw, the effective length of the pendulum may be altered. From the previ4 Eugene A. Avallone and Theodore Baumeister III, Marks’ Standard Handbook for Mechanical Engineers, Tenth Edition, (New York: McGraw-Hill, 1996), p. 3-15.


14

Chapter-2

ous equations, it is clear that changing the pendulum length will alter the period
of the pendulum. By moving the weight upward, and decreasing the arm length,
the clock will run faster (i.e., higher frequency with a shorter period). Conversely,
by lowering the main pendulum mass, the length of the arm will be increased,
and the clock will run slower (i.e., a lower frequency with a longer period).
Although the grandfather clock is a simple application of periodic motion, it
does provide a realistic example of the fundamental concepts. Additional complexity will be incorporated later in this text when the behavior of a compound
pendulum is discussed. It should be noted that a compound pendulum is a
mechanical system that normally contains two degrees of freedom. This additional flexibility might be obtained by adding flexible members such as springs,
or additional masses to a simple system. In a two mass system, each mass might
be capable of moving independently of the other mass. For this type of arrangement, each mass must be tracked with an independent coordinate system, and
this would be considered as a two degree of freedom system.

The number of independent coordinates required to accurately define the
motion of a system is termed the Degree of Freedom of that system. Process
machinery displays many degrees of freedom, and accurate mathematical
description of these systems increases proportionally to the number of required
coordinates. However, in the case of the simple pendulum, only one coordinate is
required to describe the motion — and the pendulum is a single degree of freedom system exhibiting harmonic motion. More specifically, this is an example of
basic dynamic motion where the restoring force is proportional to the displacement. This is commonly referred to as Simple Harmonic Motion (SHM). Other
devices such as the undamped spring mass (Fig. 2-7), the torsional pendulum
(Fig. 2-25), the particle rotating in a circular path, and a floating cork bobbing up
and down in the water at a constant rate are all examples of SHM.
Before expanding the discussion to more complex systems, it is desirable to
conclude the discussion of the simple pendulum. Once again, the reader is
referred back to the example of the oscillating pendulum depicted in Fig. 2-1. On
this diagram, it is meaningful to mentally trace the position of the mass during
one complete cycle. Starting at the vertical equilibrium position B, the displacement is zero at time equal to zero. One quarter of a cycle later, the mass has
moved to the maximum positive position C. This is followed by a zero crossing at
point B as the mass approaches the maximum negative value at position A. The
last quarter cycle is completed as the mass returns from the A location back to
the original equilibrium, or center rest point B.
Intuitively, the mass achieves zero velocity as it swings back and forth to
the maximum displacement points A and C (i.e., the mass comes to a complete
stop). In addition, the maximum positive velocity occurs as the mass moves
through point B from left to right, combined with a maximum negative velocity
as the mass moves through B going from right to left. Finally, the mass must deaccelerate going from B to C, and accelerate from C back to point A. Then the
mass will de-accelerate as it moves from A back to the original equilibrium point
B that displays zero lateral acceleration.
Another way to compare and correlate the displacement, velocity, and accel-


Fundamental Concepts


15

eration characteristics of this pendulum would be a time domain examination.
Although a meaningful visualization of the changes in displacement, velocity,
and acceleration with respect to time may be difficult — a mathematical description simplifies this task. For instance, assume that the periodic displacement of
the mass may be described by the following fundamental equation relating displacement and time:
Displacement = D × sin ( 2π × F × t )
where: Displacement
D
F
t

=
=
=
=

(2-10)

Instantaneous Displacement
Maximum Displacement (equal to pendulum position A or C)
Frequency of Oscillation
Time

In a rotating system, such as a centrifugal machine, this expression can be
simplified somewhat by substituting the rotational frequency ω that was previously defined in equation (2-2) to yield:
Displacement = D × sin ( ωt )

(2-11)


The instantaneous velocity of this periodic motion is the time derivative of
displacement. Velocity may now be determined as follows:
Velocity =

d
Displacement = D × ω × cos ( ωt )
dt

By converting the cosine to a sine function, expression (2-12) is derived:
Velocity = D × ω × sin ( ωt + π ⁄ 2 )

(2-12)

Note that velocity leads displacement by π/2 or 90°. Another way to state
the same concept is that displacement lags behind velocity by 90° in the time
domain. The same procedure can now be repeated to examine the relationship
between velocity and acceleration. Since acceleration is the time rate of change
of velocity, the first time derivative of velocity will yield acceleration. The same
result may be obtained by taking the second derivative of displacement with
respect to time to obtain acceleration:
Acceleration =

d
dt

2
2

2


Displacement = – D ×ω × sin ( ωt )

By adding π to the sine term, the negative sign is removed, and the following expression is obtained:
2

Acceleration = D ×ω × sin ( ωt + π )

(2-13)

Acceleration leads displacement by π or 180°, and it leads velocity by 90°. It
may also be stated that displacement lags acceleration by 180° in time. The relationship between displacement, velocity, and acceleration may be viewed graphically in the polar coordinate format of Fig. 2-2. This diagram reveals that