9/20/2016 comparison of torsional and simple two mass...

9/20/2016

1

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


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



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



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



Sudden Load Changes• Starting a Motor – Sudden Load Application

• Shutdown or Trip – Sudden Load Removal

• Soft Start Mechanisms Available



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



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



• 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”


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

9/20/2016 comparison of torsional and simple two mass...

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