Rotor Balancing: Fundamentals for Systematic Processes

Preface
Preface to the 9th (German) Edition
Contents
1 Introduction
1.1 Preliminary Note
1.2 Importance and Quality of Balancing
1.3 Development of Balancing Technology and Balancing Machines
1.3.1 Unbalance Types
1.3.2 Balancing Machines
1.4 Standards and Guidelines
1.4.1 Historical Course
1.4.2 Current Situation
1.5 List of Current Standards
2 Physical Basics
2.1 Preliminary Note
2.2 Physical Quantities
2.3 Scalar and Vector
2.3.1 Addition
2.3.2 Multiplication
2.4 System of Units
2.4.1 Basic Quantities
2.4.2 Derived Quantities
2.5 Physical Laws
2.5.1 Newton’s 2nd Law
2.5.2 Mass Attraction
2.6 Circular Motion
2.6.1 Plane Angle
2.6.2 Angular Frequency
2.6.3 Circular Speed
2.6.4 Angular Acceleration
2.6.5 Circular Acceleration
2.6.6 Torque
2.6.7 Moment of Inertia
2.6.8 Radial Acceleration
2.6.9 Centrifugal Force
2.7 Vibration
2.7.1 Single Mass Oscillator with Centrifugal Excitation
2.7.1.1 Subcritical Area
2.7.1.2 Resonance Area
2.7.1.3 Supercritical Area
2.7.2 Degrees of Freedom
2.7.3 Dynamic Stiffness
3 Terms and Explanations
3.1 Preliminary Note
3.2 Rotor Balancing
3.3 Balancing Task
3.4 Rotor
3.5 Unbalance
3.6 Unbalance Condition
3.7 Unbalance Behaviour
3.8 Unbalance Tolerances
3.9 Correction
3.10 Correction Plane
3.11 Shaft Axis
3.12 Rotor Behaviour
3.12.1 Rotors with Rigid Behaviour
3.12.2 Rotors with Flexible Behaviour
3.12.2.1 Rotors with Shaft Elastic Behaviour
3.12.2.2 Rotors with Component-Elastic Behaviour
3.12.2.3 Rotors with Settling Behaviour
3.13 Rotor Concept
4 Theory of Balancing
4.1 Preliminary Note
4.2 General
4.2.1 Unbalance State
4.2.2 Rotor Concept
4.2.3 Rotor Behaviour
4.2.3.1 General
4.2.3.2 Effects of Rotor Behaviour
4.2.3.3 Principle of Order
4.2.4 Unbalance Tolerances
4.2.5 Balancing Task
4.3 Unbalances and Correction
4.4 Unbalance of the Disc-Shaped Rotor
4.5 Unbalance of a General Rotor
4.5.1 Resultant Unbalance
4.5.2 Moment Unbalance
4.5.3 Couple Unbalance
4.5.4 Modal Unbalance
4.5.5 Equivalent Modal Unbalance
4.6 Overview of the Balancing Tasks
4.6.1 General
4.6.2 The Balanced Rotor
4.6.3 Single-Plane Balancing
4.6.4 Two-Plane Balancing
4.6.5 Multi-Plane Balancing
4.6.5.1 Example 1
4.6.5.2 Example 2
4.6.5.3 Example 3
4.6.5.4 Example 4
4.7 Conclusion of the New Perspective
4.7.1 Significance of Resonances
4.7.2 Significance of Flexural Resonances above the Service Speed
4.7.3 Treatment of Flexural Resonances above Service Speed
4.8 Handling Unbalance Tolerances
4.8.1 Concept
4.8.2 Procedure
4.8.2.1 Example 1
4.8.2.2 Example 2
4.8.2.3 Example 3
4.8.2.4 Example 4
5 Theory of the Rotor with Rigid Behaviour
5.1 Preliminary Remark
5.2 Rotor Behaviour
5.3 Unbalanced Condition
5.3.1 Static Unbalance
5.3.1.1 Example 1
5.3.1.2 Example 2
5.3.1.3 Example 3
5.3.1.4 Example 4
5.3.2 Resulting Unbalance
5.3.2.1 Example 1
5.3.2.2 Example 2
5.3.3 Moment Unbalance
5.3.3.1 Example
5.3.4 Dynamic Unbalance
5.4 Display of the Unbalance Condition
5.4.1 Unbalances
5.4.2 Position of the Axis of Inertia
5.4.3 Overview
6 Theory of the Rotor with Flexible Behaviour
6.1 Preliminary Note
6.2 Settling Behaviour
6.3 Component-Elastic Rotor Behaviour
6.4 Shaft Elastic Rotor Behaviour
6.4.1 Idealised Rotor with Shaft-Elastic Behaviour
6.4.2 Influence of Bearing Stiffness
6.4.3 Flexural Resonance Speeds at Standstill
6.4.4 General Rotor with Shaft-Elastic Behaviour
6.4.5 Unbalance Effects on the Rotor with Shaft-Elastic Behaviour
6.4.5.1 Modal Unbalances
6.4.5.2 Equivalent Modal Unbalances
6.4.6 Balancing a Rotor with Shaft-Elastic Behaviour
6.4.6.1 First Flexural Mode
6.4.6.2 Second Flexural Mode
6.4.6.3 Third Flexural Mode
6.4.7 Choice of Correction Planes
6.4.7.1 Variety of Rotors
6.4.7.2 Example 1
6.4.7.3 Example 2
6.4.7.4 Example 3
6.4.7.5 Example 4
6.4.7.6 Example 5
6.4.7.7 Example 6
6.4.7.8 Example 7
7 Tolerances for Rotors with Rigid Behaviour
7.1 Preliminary Note
7.2 Basics
7.2.1 Tolerance Planes
7.2.2 Correction Planes
7.2.3 Limitation of the Permissible Residual Unbalance
7.3 Similarity Considerations
7.3.1 Rotor Mass and Permissible Residual Unbalance
7.3.2 Service Speed and Permissible Residual Unbalance
7.3.2.1 Special Cases
7.4 Determining the Permissible Residual Unbalance
7.4.1 General
7.4.2 Balancing Grades G
7.4.2.1 Classification
7.4.2.2 Special Cases
7.4.2.3 Permissible Residual Unbalance
7.4.3 Experimental Determination
7.4.4 Limits from Specific Targets
7.4.4.1 Limitation by Bearing Forces
7.4.4.2 Limitation Through Vibrations
7.4.5 Proven Experience
7.4.5.1 Almost Identical Rotor Size
7.4.5.2 Similar Rotor Size
7.5 Allocation to Tolerance Planes
7.5.1 Rotors with a Single Tolerance Plane
7.5.1.1 Practical Review
7.5.1.2 Acceptance
7.5.2 Rotors with Two Tolerance Planes
7.5.2.1 Restrictions on Inboard Rotors
7.5.2.2 Restrictions on Outboard Rotors
7.6 Assignment of the Unbalance Tolerance to the Correction Planes
7.6.1 Single-Plane Case
7.6.2 Two-Plane Case
7.7 Assembled Rotors
7.8 Unbalance Readings for the Balancing Process
7.8.1 Example
7.9 Checking the Residual Unbalance
7.9.1 Acceptance Criteria
7.9.2 Unbalance Readings in Tolerance
7.9.3 Unbalance Readings Outside Tolerance
7.9.4 Region of Uncertainty
7.9.5 Particularities when Measuring Unbalances
7.9.6 Checking on a Balancing Machine
7.9.7 Checking Without a Balancing Machine
8 Tolerances for Rotors with Flexible Behaviour
8.1 Preliminary Note
8.2 General
8.2.1 Balancing Target
8.2.2 Balancing Procedures
8.3 Tolerance Criteria
8.3.1 Vibrations
8.3.1.1 Vibrations According to ISO 21940-12
8.3.1.2 Problems with Vibrations
8.3.1.3 Conclusion
8.3.2 Unbalances
8.3.2.1 Total Permissible Unbalance
8.3.2.2 Tolerance Planes
8.3.2.3 Distribution of the Total Permissible Unbalance
8.3.2.4 Modal Influence on the Permissible Unbalances
8.4 Unbalance Tolerances for Procedures A to I
8.4.1 Tolerances of Low-Speed Balancing Procedures
8.4.1.1 Procedure A: Single-Plane Balancing
8.4.1.2 Procedure B: Two-Plane Balancing
8.4.1.3 Procedure C: Balancing Individual Components Before Assembly
8.4.1.4 Procedure D: Balancing After Limiting the Starting Unbalance
8.4.1.5 Procedure E: Sequential Balancing During Assembly
8.4.1.6 Procedure F: Balancing in Optimal Planes
8.4.2 Tolerances of High-Speed Balancing Procedures
8.4.2.1 Procedure G: Multiple-Speed Balancing
8.4.2.2 Procedure H: Balancing at Service Speed
8.4.2.3 Procedure I: Balancing at a Fixed Speed
8.5 Unbalance Tolerances for Procedure G
8.5.1 Unbalance Tolerances According to ISO 21940-12
8.5.2 Unbalance Tolerances According to DIN ISO 21940-12, Beiblatt 1
8.5.2.1 Distribution to Several Unbalances
8.5.2.1.1 Even Distribution
8.5.2.1.2 Weighted Distribution
8.6 Tolerances for the Balancing Process
8.7 Assessment of the Unbalance State Achieved
8.7.1 Assessment by Vibrations
8.7.1.1 Assessment in a High-Speed Balancing Machine
8.7.1.2 Assessment in the Test Field
8.7.1.3 Assessment in Service Condition
8.7.2 Assessment by Unbalances
8.7.2.1 Assessment in a Low-Speed Balancing Machine
8.7.2.2 Assessment in a High-Speed Balancing System
8.7.2.3 Assessment in the Test Field
8.7.2.4 Assessment in Service
8.8 Susceptibility and Sensitivity of Machines to Unbalance
8.8.1 Classification of the Susceptibility of Machines
8.8.2 Modal Sensitivity Ranges
8.8.3 Limit Curves
8.8.3.1 Example 1
8.8.3.2 Example 2
8.8.3.3 Special Case Acceleration
8.8.3.4 Example
8.8.4 Experimental Determination of the Modal Sensitivity
8.8.4.1 Example 1
8.8.4.2 Example 2
9 Procedures for Balancing Rotors with Rigid Behaviour
9.1 Preliminary Note
9.2 Bodies Without Own Bearing Journals
9.2.1 General
9.2.2 Unbalances Due to Assembly
9.2.3 Index Balancing
9.2.3.1 Single Plane with Unbalances
9.2.3.2 Single Plane with Fit-Related Errors
9.2.3.3 Generalisation
9.2.4 Further Use of the Index Balancing Method
9.2.5 Auxiliary Shafts, Adapters
9.3 Assemblies
9.3.1 General
9.3.2 Procedure
9.3.2.1 Example 1
9.3.2.2 Example 2
9.3.3 Interchangeability of Parts
9.3.4 Correction of the Assembly Error
9.3.5 Dummies (Substitute Masses)
9.4 Rotors with Parallel Keys
9.4.1 General
9.4.2 Shaft with Complete Key
9.4.3 Shaft with Half Key
9.4.4 Influence on the Unbalance Condition
9.4.5 Bias for a Parallel Key
9.4.6 Constructive Measures
10 Procedures for Balancing Rotors with Flexible Behaviour
10.1 Preliminary Note
10.2 General
10.3 Rotor Configurations
10.3.1 Basic Elements Of Shaft-Elastic Rotors
10.3.2 Balancing Principles
10.3.3 Rotor with Discs
10.3.3.1 A Single Disc
10.3.3.2 Two Discs
10.3.3.3 More than Two Discs
10.3.4 Rigid Sections
10.3.5 Rolls
10.3.6 Integral Rotor
10.3.7 Combinations
10.3.8 Repairs
10.4 Balancing Procedures
10.4.1 Procedure A: Single-Plane Balancing
10.4.2 Procedure B: Two-Plane Balancing
10.4.3 Procedure C: Balancing Individual Components Before Assembly
10.4.4 Procedure D: Balancing After Limiting The Initial Unbalance
10.4.5 Procedure E: Sequential Balancing During Assembly
10.4.5.1 Problem with Transfer Unbalances
10.4.5.2 Solution
10.4.5.3 Problem Assembly
10.4.6 Procedure F: Balancing in Optimal Planes
10.4.7 Procedure G: Balancing at Multiple Speeds
10.4.7.1 2  +  N procedure and N + 2 Procedure
10.4.7.2 Correction Ratio
10.4.7.3 Recommendation
10.4.7.4 Computer Support
10.4.7.5 Beiblatt 1 to DIN ISO 21940-12
10.4.8 Procedure H: Balancing at Service Speed
10.4.9 Procedure I: Balancing at a Fixed Speed
10.4.10 Settling Behaviour Procedure
11 Description of the Balancing Task
11.1 Preliminary Note
11.2 Balancing Rotors with Rigid Behaviour
11.2.1 Rotor with Journals
11.2.1.1 Tabular Description of a Rotor Type
11.2.1.2 More Tables
11.2.1.3 Maximum Data
11.2.1.4 Additional Information on the Rotors
11.2.2 Rotors Without Journals
11.3 Balancing Rotors with Flexible Behaviour
11.3.1 Low-Speed Balancing
11.3.2 High-Speed Balancing
11.3.2.1 General
11.3.2.2 Tabular Overview
12 Balancing Machines
12.1 Preliminary Note
12.2 Quotation and Technical Documentation
12.2.1 Horizontal Balancing Machines
12.2.1.1 Limits for Rotor Mass and Unbalance
12.2.1.2 Efficiency of the Measuring Run
12.2.1.3 Unbalance Reduction Ratio RUR
12.2.1.4 Rotor Dimensions
12.2.1.5 Bearing Journal
12.2.1.6 Setting Range of the Correction Planes
12.2.1.7 Drive
12.2.1.8 Brake
12.2.1.9 Additional Information
12.2.2 Vertical Balancing Machines
12.2.2.1 Limits for Rotor Mass and Unbalance
12.2.2.2 Rotor Dimensions
12.2.2.3 Influence of the Moment Unbalance
12.2.3 Non-Rotating Balancing Machines
12.2.4 High-Speed Balancing Machines
12.2.4.1 Drive
12.2.4.2 Bearing Pedestals
12.2.4.3 Measuring Device
12.3 Technical Details and their Assessment
12.3.1 Drive
12.3.1.1 Squirrel-Cage Motor
12.3.1.2 Slip Ring Motor
12.3.1.3 DC Motor
12.3.1.4 Drive Power
12.3.1.5 Cardan Shaft Drive
12.3.1.6 Belt Drive
12.3.1.7 Induction Field Drive
12.3.1.8 Self-Drive
12.3.1.9 Compressed Air Drive
12.3.2 Display Systems
12.3.3 Functional Principle of the Balancing Machine
12.3.4 Brake
12.3.5 Speed
12.3.6 Calibration and Setting of the Measuring Device
12.3.6.1 Soft-Bearing Balancing Machine
12.3.6.2 Hard-Bearing Balancing Machine
12.3.7 Foundation
12.3.8 Minimum Achievable Residual Unbalance Umar
12.3.9 Bearing Support
12.3.9.1 Twin-Roller Bearing
12.3.9.2 V-Block Bearing
12.3.9.3 Sleeve-Bearing
12.3.9.4 Spindle Bearing
12.3.9.5 Service Bearings
12.3.9.6 Special Bearing Systems
12.3.10 Mass Moment of Inertia, Number of Cycles
12.3.11 Measuring Principle
12.3.12 Test Rotors, Test Masses
12.3.12.1 Test Rotors
12.3.12.2 Test Masses
12.3.13 Overload
12.3.14 Environmental Influences
12.3.15 Unbalance Reduction Ratio RUR
12.3.16 Economic Efficiency
12.4 Boundary Conditions
13 Tests on Balancing Machines
13.1 Preliminary Note
13.2 Statistics with Unbalances
13.2.1 Circular Scatter Field
13.2.2 Ring-Shaped Scatter Field
13.2.2.1 Example 1
13.2.2.2 Example 2
13.2.3 Characteristics of One- and Two-Dimensional Normal Distributions
13.2.4 Further Special Features
13.2.5 Spot Checks or a Hundred Percent Check
13.2.6 Key Figures
13.2.7 Rejects
13.3 Test Rotors and Test Masses
13.3.1 General
13.3.2 Test Rotors Overview
13.3.2.1 Individual Test Rotors
13.3.3 Test Masses
13.3.4 Test Rotors in Detail
13.3.4.1 Type A Test Rotors
13.3.4.2 Test Rotors Type B
13.3.4.3 Test Rotors Type C
13.3.5 Test Conditions
13.4 Test of the Minimum Achievable Residual Unbalance Umar
13.4.1 Start Condition
13.4.2 Correction
13.4.3 Test Runs with Test Masses
13.4.4 Evaluation of the Umar Test
13.4.5 Abbreviated Umar Test
13.5 Unbalance Reduction Ratio Test RUR
13.5.1 Start Condition
13.5.2 Test Runs with Test Masses
13.5.3 Evaluation of the RUR Test
13.5.4 Abbreviated RUR Test
13.6 Test of the Moment Unbalance Influence Ratio IMU
13.6.1 Starting Conditions
13.6.2 Test Runs with Test Masses
13.6.3 Evaluation of the IMU Test
13.7 Compensation Test for the Index Process
13.7.1 Start Condition
13.7.2 Test Runs with Test Masses
13.7.3 Evaluation of the Compensation Test
14 Unbalance Correction
14.1 Preliminary Note
14.2 Types of Correction
14.2.1 Material Removal
14.2.2 Relocating Material
14.2.3 Adding Material
14.3 Correction Time
14.3.1 Organisation of the Correction
14.3.2 Automation of the Correction
14.4 Correction Errors
14.4.1 Correction Masses
14.4.2 Correction Planes
14.4.3 Correction Radii
14.4.3.1 Radial Correction
14.4.3.2 Correction on the Circumference
14.4.3.3 Correction by Spreading Two Correction Masses
14.4.4 Correction Angle
14.4.5 Permissible Correction Errors
14.5 Unbalance Reduction Ratio
14.5.1 General
14.5.2 Small Correction Step
14.5.3 Large Correction Step
14.5.4 Series
15 Preparation and Execution of Rotor Balancing
15.1 Preliminary Note
15.2 Causes for Unbalances
15.3 Design Guidelines and Drawing Specifications
15.4 Layout of the Correction
15.5 Work Planning
15.5.1 Rotor Condition During Balancing
15.5.2 Permissible Unbalance Readings for the Balancing Process
15.5.2.1 Commonly Practiced Approach
15.5.2.2 Current Approach of the Standards
15.6 Automation
15.7 Loading and Unloading
15.8 Preparations on the Rotor
15.9 Production Cycle Rotor Balancing
16 Errors in the Balancing Process
16.1 Preliminary Note
16.2 Causes for Errors
16.2.1 General
16.2.2 Missing Parts
16.2.3 Additional Parts or Effects
16.2.4 Changed Rotor State
16.2.5 Rotor Behaviour is Not Reproducible
16.2.6 Unbalance Measurement
16.3 Handling of Errors
16.3.1 Error Types
16.3.1.1 Systematic Errors
16.3.1.2 Random Errors
16.3.1.3 Scalar Error
16.3.2 Determination of Errors
16.3.2.1 Estimation of Errors
16.3.2.2 Measuring Errors
16.3.2.3 Errors During Measurement
16.3.3 Treatment of Errors
16.3.3.1 Calculation of Systematic Errors
16.3.3.2 Calculation of Random Errors
16.3.3.3 Calculation of Scalar Errors
16.3.4 Determination of the Combined Error
16.4 Permissible Indications for the Residual Unbalance
16.5 Acceptance Criteria
16.5.1 General
16.5.2 Unbalance Readings in Tolerance
16.5.3 Unbalance Readings Outside the Tolerance
16.5.4 Region of Uncertainty
16.6 Special Methods for Measuring Errors
16.6.1 General
16.6.2 Measuring Systematic Errors
16.6.3 Measuring Random Errors
16.6.4 Measuring Scalar Errors
16.7 Examples of Errors and Their Handling
16.7.1 General
16.7.2 Examples
16.7.2.1 Movable Parts
16.7.2.2 Liquids or Solids in Cavities
16.7.2.3 Thermal Influences and Effects due to Gravity
16.7.2.4 Windage Effects
16.7.2.5 Magnetized Rotor
16.7.2.6 Tilted Service Ball Bearings
16.7.2.7 Incomplete Assembly
16.7.2.8 Coupling Face on Rotor
16.7.2.9 Fitting Errors
16.7.2.10 Relative Rotation of Mounted Parts
16.7.2.11 Adapter Unbalance
16.7.2.12 Unbalance of the Drive Shaft
16.7.2.13 Adapter Run-out
16.7.2.14 Eccentricity of Balancing Bearings
16.7.2.15 Systematic and Random Errors of the Measurement Chain
16.7.3 Specialties When Measuring Unbalances
16.7.3.1 Errors When Measuring on a Balancing Machine
16.7.3.2 Errors when Measuring Without a Balancing Machine
17 Protective Measures for Balancing
17.1 Preliminary Note
17.2 General
17.3 Dangers Due to the Rotor
17.4 Protection Classes
17.4.1 Protection Against Contact
17.4.2 Protection Against Particles or Parts
17.4.2.1 Area-specific Energy
17.4.2.2 Absolute energy
17.4.2.3 Impulse
17.5 Choice of Enclusures
17.6 Examples of Protection Classes
17.6.1 Class 0
17.6.2 Class A
17.6.3 Class B
17.6.4 Class C
17.6.5 Class D
17.7 Protection Class C for Universal Balancing Machines
17.7.1 Design of the Protection
17.7.2 Marking of the Protection
17.8 Hazards and Safety Requirements
18 In-Situ Balancing
18.1 Preliminary Note
18.2 Vibration Limits
18.3 Task
18.4 Theory of In-situ Balancing
18.4.1 Causes for Unbalances
18.4.2 Difficulties
18.4.3 Methodology
18.4.3.1 Correction in a Single Plane
18.4.3.2 Correction in Two Planes
18.4.3.3 Correction in More Than Two Planes
18.5 Practice of In-situ Balancing
18.5.1 Measuring Techniques
18.5.2 Measuring Planes
18.5.3 Boundary Conditions
18.6 ISO 21940-13
19 Symbols, Vocabulary and Definitions
19.1 Preliminary Note
19.2 Symbols
19.3 Vocabulary and Definitions
19.3.1 Mechanics—Mechanik—Mécaniques
19.3.2 Rotors—Rotoren—Rotors
19.3.3 Unbalance—Unwucht—Balourd
19.3.4 Balancing—Auswuchten—Équilibrage
19.3.5 Balancing Machines—Auswuchtmaschinen—Machines à équilibrer
19.3.6 Flexible Rotors—Nachgiebige Rotoren—Rotors flexibles
19.3.7 Rotating Rigid Free-Bodies—Rotierende starre freie Körper—Corps-libres rigides en rotation
19.3.8 Balancing Machine Tooling—Zubehör zu Auswuchtmaschinen—Outillage de machine à équilibrer
20 Documents for Calculations
20.1 Preliminary Note
20.2 Decimal Multiples and Decimal Parts
20.3 Conversion Factors for SI Units and Inch/Pound Units
20.4 Nomogramms, Diagramms
20.4.1 Nomogramms
20.4.2 Diagrams
Image Sources
References
Index