9/20/2016 comparison of torsional and simple two mass...
TRANSCRIPT
9/20/2016
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Comparison of Torsional and
Translational System
M
K, Lb/in
Force, F (Lb)Travel, x (inch)
Inertia, I
Kt , In-Lb/radian
Torque, ф
Simple Two Mass System
I2I1
Kt
Torsional Resonance Failure Torsional Vibration
• What is Torsional Vibration?
• How to Calculate Torsional Natural Frequencies
• What is Inertia
• What is Torsional Stiffness
• Torsional Mode Shapes
• Torsional Forced Response
Torsional Vibration
Lateral vibration Torsional vibration
What is Torsional Vibration?
• Torsional vibration occurs when inertias
oscillate (rotate) relative to each other
• Normally cannot be detected with
accelerometers or proximity probes
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Paper Overview – Field Measurement
• Testing Methods
• Procedures for Torsional Testing
• Demodulation
• Use of Strain Gages
• Indirect Methods
• Calibration Techniques
• Case Histories
Torsional Vibration and Analysis
• Easy to Analyze compared to Lateral Rotordynamics
• Difficult to Measure compared to Radial Vibration
• Shaft Stress and Fatigue lead to Failures
• Many Machine Trains are Susceptible
Frontispiece from
Ref. 4, Vol. 1
X-Shaped Cracks Develop
At Radius between Shaft Steps
Gear Teeth Breakage
From Torque Oscillations
Pictures from “Understanding How Components Fail” by D.J. Wulpi
Torsional Failures
Types of Torsional Analyses
Steady State – Undamped Analysis
• Frequencies
• Mode Shapes
Transient – Damping Included
• Forced Response vs. Time or Speed
• Runup Time Analysis
• Static and Dynamic Shaft Stresses
Key Elements of Torsional Systems
1. Inertias, connected by
2. Torsional springs
• A “Lumped Spring-Mass” Model is created
• Simplification of Model
• Improper Modeling Difficult to Detect
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Polar Inertia of a Disk Trifilar Pendulum – Measure J
WT = Total Weight
f = CPS
Oscillation Frequency
Total Rotor Inertia Test Calculating Torsional Stiffness
IP = P (Do4- Di
4)/32 IN4 G = 11.5 X 106 PSI
Shaft Penetration Effect Lumped Parameter Train Modeling
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Adding Stiffnesses Example 2-Mass System
Simple 2-Mass System Example 2-Mass System
KE = 5.16 X 106 IN-LB/RAD
J1 = 27,654 LB-IN2 = 71.63 LB-IN-SEC2
J2 = 40,008 LB-IN2 = 103.62 LB-IN-SEC2
3-Mass System Typical Geared System
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Reducing Geared System to
Equivalent SystemHow Gear Forces Can Excite
Torsional Resonances
Gear mesh force
Reaction forces
2-Mass 2D Animated Mode Shape 2-Mass 3D Animated Mode Shape
Typical Interference Diagram Torsional Forced Response
Excitation Mechanisms
Synchronous Motors
• Transient Condition only During Startup
• All Torsional Resonances Excited from Twice Line Frequency to Zero
• Very High Transient Torques
• Stress and Cumulative Fatigue Analysis Required
• Source of Many Spectacular Failures
• Possible to Design System for Acceptable Number of Starts
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Torsional Forced Response
Excitation Mechanisms
Reciprocating Machinery
• Torque Pulsations Always Exist
• B.I.C.E.R.A. Handbook (ref. 1)
• Magnitude of Pulsations must be known
• Number of Cylinders and Firing Order Changes Pulsations
• Source of Many Spectacular Failures
• Possible to Design System for Acceptable Life
Torsional Forced Response
Excitation Mechanisms
Variable Frequency Motor Drives
• Original - 6-Step Synthesized Current Waveform
• Modern Drives Much Better (e.g. PWM Drives)
• Harmonic Torque Pulsations at 6X, 12X, 18X, etc.
• Drive Manufacturer will Usually Supply Information
Torsional Forced Response
Excitation Mechanisms
Gears
• Gear Mesh - unusual
• Radial and Tangential Forces Created (1X and 2X)
• Torsional Vibration shows up as Radial Vibration
• Tooth Spacing Errors
• Pitch-Line Runout
• Low Quality or Worn Gears
• Gear Teeth Act as Additional Torsional Spring
KT = 1.6 X 106 (Face Width) (Larger Gear Radius)2 IN-LB/RAD
Torsional Forced Response
Excitation Mechanisms
Sudden Load Changes• Starting a Motor – Sudden Load Application
• Shutdown or Trip – Sudden Load Removal
• Soft Start Mechanisms Available
Torsional Forced Response
Excitation Mechanisms
Electrical System Interaction
• Very Important on Large T-G Sets
• Ref. 2 Discusses in Detail
• Equivalent Stiffness-Inertia-Damping of Grid Added to Model
• Electrical Faults
• Line Frequency and Twice Line Frequency – Large TG sets
Blade Failures and when Electrical System Fluctuations Occur
Torsional Forced Response
Excitation Mechanisms
Other• Vane Pass (Fans, Pumps, Turbines)
• Lobe-Pass (Screw Compressors)
• Magnitude of Pulsations Usually must be Measured
• Off-Design Operation can Magnify Pulsations
• Generally 2-3 Percent of Full Load Torque
•Couplings
• Hooke’s Joints (Universal Joints) – Offset – Primarily 2X
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Torsional Damping
Discrete Damping
• Electrical System
• Fluid Film Bearings (geared systems)
• Friction Dampers
• Viscous Dampers
• Rubber “Damper” Couplings
• Grid-Type Couplings
• Heat Generation Considerations
Source:
Ref. 12
P. 233-4
Resilient “Damper” Coupling
Resilient “Damper” Coupling Torsional Damping
Modal Damping
• Material Properties - Hysteresis
• Usually 1 to 3 percent of Critical Damping
• As Low as 0.2 percent
• As High as 7 percent
• Fluid Interaction with Rotating Parts
Shaft Stress and Fatigue
Shaft Stress =16 Tp D3 PSI
Endurance Limit• Infinite Life Stress Limit – In Theory
•About 30,000 PSI for Steel Alloys
• Stress Concentration Factors
• Application may be > 20,000 PSI in Aircraft
• <15,000 PSI in Rotating Machinery
• <10,000 PSI with Corrosion or Critical Duty
Typical Fatigue Stress Cycle Plot
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Good Torsional Design Practice
• Select High Quality Shaft Material
• Minimize Stress Risers
• Realistic Estimates of Torque Pulsations
• High Quality Gears
• Adequate Margin for Increased Production
1. Avoid Keys – No Sharp Corners in Keyways
2. Generous Polished Radii in Shaft Steps
3. Shot-Peening can help
4. Avoid Snap-Ring Grooves
5. Avoid Shaft Damage and Tool Marks
Example 1
1,775 RPM Motor - 3 Vane Pump Impeller – Pulsations at 5,325 CPM
High Vibrations at Vane-Pass Frequency – Balancing and Alignment?
Many attempts at Optimizing Pump – No Effect
Torsional Analysis indicated Resonance at 5,300 CPM
Coupling Change Ineffective
New 4-Vane Impeller Installed – Vibrations Eliminated
Example 2
Severe Gear Wear – Replaced Gears twice
High Vibrations at 1X and 2X
Components Carefully Balanced
Train Carefully Hot Aligned
Failures Continued
Example 2No Torsional Analysis ever performed by Designer
Turbine Speed Range 4,480 to 4,600 RPM
Gear Ratio 5.97:1 - Fan Speed 750 to 770 RPM
Torsional Analysis Completed – Softer Couplings Required
Stiffer Couplings would not have Solved the Problem
Example 3Synchronous Motor – Speed Increaser – Axial Compressor
New Train – Torsional Design Integral Part of Package
No Keys in any Shaft – Integral Flanges and Hydraulic Fits
Increased Gear DP to Withstand Torsional Forces
Example 3 – Motor Torque Curves
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Example 3 – Runup Time Analysis
2nd Torsional
Resonance
1st Torsional
Resonance
Example 3 – Pinion Vibration During Startup
2nd Torsional
Resonance
1st Torsional
Resonance
Example 3 – Mode Shapes Example 3 – Startup Simulation
Synchronous Motor
Low Speed Shaft Stress
During Startup
Example 3 – Startup Simulation
Synchronous Motor Train
High Speed Shaft Stress
During Startup
Example 3
• Startup Stress Plots are Used to Count High Stress Cycles
• Accounting for Stress Concentrations and Environment,
the Number of Startups Before Failure Can be Calculated
• Infinite Life is Preferred
• 2000 Startups were Projected for Example 3
• 15 Years of Uneventful Operation
• Even though the 1st Torsional Resonance was Less Than
7 Percent away from Running Speed, no Problems were
ever encountered
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Example 4Engine Driven Triplex Pump
Example 4Engine Driven Triplex Pump
Example 4Engine Driven Triplex Pump
• Speed Range 500 to 850 RPM
• “Normal” Speed 680 RPM
• Field Operated by Truck Driver
• Pump Full Tank of Nitrogen into the Earth in 10 Minutes
• High Vibration
• Many Component Failures
• Universal Joints – 2X
• Triplex Design – 3X
• Train Resonance at 1,640 CPM – 2 Degrees Peak Oscillations
• Severe Limits on Applied “Fix”
Example 4Engine Driven Triplex Pump
Added Inertia by Replacing Adaptor Plate with Larger One
Added 30,000 LB-IN2
New Torsional Resonance at 1,080 CPM
Moved 2X and 3X Interference Below Operating Speed Range
Significant Drop in Vibration and Failures
Example Summary
These Four Examples Show Some
of the Ways a System can be Modified
to Avoid Torsional Problems:
1. Change the Excitation Frequency – 3 Vanes to 4 Vanes
2. Change the Torsional Stiffness – Coupling Modifications
3. Design the Components to Withstand Forces
4. Add Inertia to System – Larger Flywheel
Review of Test Methods
1. Direct Measurement of Torsional
Vibration of the Shaft
2. Direct Measurement of Torsional Shear
Stress (Strain)
3. Indirect Measurement of Torsional
Vibration
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Review of Torsional ResponseTorsional Modal Response Review
• Torsional resonances will normally have
relatively low damping (<<5% critical)
• With low modal damping, mode shapes are
very near “undamped” modes calculated
• Measurement of torsional stress or vibration
at one location can normally be used to
evaluate response throughout the train
Selection of Type of Measurement
Torsional
Stress Here Torsional
Vibration
Here
Torsional Vibration Measurement
• Torsiograph method
• Demodulation
–Gear Teeth
–Chain Links
–Optical Encoders
Torsiograph Mounting Torsiograph Limits
• A 3 Deg oscillation
• Angular acceleration can make the inner
disk hit the stop, preventing measurement
• The low pass nature of the instrument
would prevent accurate AC measurement
below about 5 Hz
• Instrument is no longer available (HBM?)
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Demodulation Principle
Demonstration of Torsional Modulation
for 1xRPM Response
0 360 720
Shaft Angle, Degrees
En
co
der
Ou
tpu
t
"Without Torsional Vibration" "With Torsional Vibration
Input Signals for Demodulation
• Gear Teeth or Chain
– Must have very accurate gear teeth and creative
signal processing
– Proximity probe or velocity pickup used to
sense pulses
• Optical Encoders
– Very accurate pulse separation and ease of
mounting
Encoder Location
• Can be installed at any free shaft end (same
as a torsiograph)
• Using a measuring wheel, any shaft section
with about 4” axial length exposed can be
sampled
Example Encoder
Encoder Mounting
Equipment Shafting
Encoder
Adjust Height with
All Thread
Floor/Grating Under Equipment
Heavy Plate to Hold in Place(Clamp as Required)
Encoder Mounting
Equipment Shafting
Encoder
Hinge near base
Floor/Grating Under Equipment
(Clamp as Required)
PreLoad Wheel with BungieCord or Spring
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Trailer Mounted Reciprocating Pump
Example
Encoder
Setup
Test Equipment SetupTorsional Vibration Calibrator
Torsional Stress Measurement
• Using Strain Gages the Shaft Shear Strain is
Measured on the Surface of the Shaft
• Shear Strain is Related to Shear Stress
Using the Modulus of Rigidity
– (stress) (strain) x G
Gage Layout
• For the most accurate measurement of shear strain, two rosettes are mounted on opposite sides of the shaft
– Excludes and strain due to bending by self compensation with gages on opposite sides of shaft
• Measurement of high shaft strain amplitudes may required a ½ bridge test
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Gage Layout Gage Layout
Power GroundS+
S-
FM Telemetry
• The signals from the shaft must be
transmitted to the test equipment
• A radio transmitter is mounted on the shaft
– Battery powered
– Induction powered
• A receiving unit produces an analog or
digital signal for analysis
Torsional Shear Test
Reasons to TestQuill Shaft Coupling Prior to
Mounting Gages
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Coupling with Gages Installed Calibration of Strain Gages
• Strain gages are calibrated using a shunt
calibration
• Typical calibration shunt is a precision
resistor that is equivalent to 1000µ
compressive strain
• Each gage application is shunt calibrated
prior to testing
Reciprocating Pump Reciprocating Pump Example, 2X
Reciprocating Pump Example, 3XReciprocating Compressor Torsional
Resonance Excited by Multiple
Harmonics
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Cooling Tower Fan Fan Vibration Readings
Fan Torsional Vibration Synchronous Motor Startup
Motor RPM and Relative Torsional Vibration
vs. Time During Start
0
200
400
600
800
1000
1200
1400
0 1 2 3 4 5 6 7 8
Time, Seconds
Mo
tor
Sh
aft
Sp
ee
d,
RP
M
-10
-5
0
5
10
15
To
rsio
na
l T
wis
t, D
eg
RPM Torsional Response
Peak Torsional
Vibration at 1093
RPM shaft speed
Synchronized at
~1146 RPM Shaft
Speed
#1 Probe Wiped
Here
Rigid Body Torsional With
Coupling To Electrical Grid
Synchronous Motor Startup
Shaft Torque During Motor Start
Motor Full Load Torque = 15,312.5 Ft-Lb
-30000
-20000
-10000
0
10000
20000
30000
40000
50000
60000
70000
0 2 4 6 8 10 12 14
Time, Sec
To
rqu
e, F
t-L
b
Synchronous Motor Startup
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Locomotive
Load Test of ALCO16
0
0.1
0.2
0.3
400 500 600 700 800 900 1000 1100
Shaft Speed, RPM
To
rsio
na
l
Vib
rati
on
, D
eg
Pk
0.5x 1x 1.5x 2x 2.5x 3x 3.5x 4x 4.5x
5x 5.5x 6x
Load Test of ALCO16
0
0.02
0.04
0.06
0.08
0.1
400 500 600 700 800 900 1000 1100
Shaft Speed, RPM
Am
pli
tud
e,
De
g P
k
6.5x 7x 7.5x 8x 8.5x 9x
Locomotive
Locomotive Assessment
Stress-Time History Using Phase Relationship
per BICERA Fig. 3, Page 264 and Measured
Response
-6000
-4000
-2000
0
2000
4000
6000
0 0.05 0.1 0.15 0.2
Time, Sec
Str
es
s A
mp
litu
de
, P
SI
5710 psi Maximum
5910 psi Minimum
Tractor Fan Torsional Response
Tractor Sensor Mounting Sensor Mounting
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Optical Speed Pickup Mounting Test Equipment
Tractor Test ResultsTorsional Response at Load / 2025 RPM
0
0.05
0.1
0.15
0.2
0.25
0.3
0 2000 4000 6000 8000 10000 12000 14000
Frequency, CPM
To
rsio
na
l R
esp
on
se
, D
eg
P-P
Crank Response Fan Response
0.5xEngine
1.0xEngine 1.5xEngine 3.5xEngine 4.5xEngine