LMS Rotating Machinery 2013

Rotating Machinery

Rotating Machinery Agenda

3

Torsional Vibration 2

Order Fundamentals

4

Gears, Motors, Bearings, Pumps…

5

Resonances

1

Angle Domain

6

Balancing

LMS International, A Siemens Business copyright 2013 2


Gears, Motors, Bearings, Pumps

TransError, Sidebands. …

Order Fundamentals

RPM, 1st order, 2nd order

Angle Domain

Within one revolution…

RPM Fluctuation

Torsional Vibration

Balancing Resonances

13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1

.


http://rds.yahoo.com/_ylt=A0WTb_pyk4NKBUABN.KJzbkF;_ylu=X3oDMTByZW5nMjM4BHBvcwMyNwRzZWMDc3IEdnRpZANJMTE0XzEzNQ--/SIG=1ipfd757k/EXP=1250223346/**http:/images.search.yahoo.com/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fsearch%2Fimages%3Fp%3Drotor%2Bhelicopter%26b%3D21%26ni%3D20%26ei%3DUTF-8%26pstart%3D1%26fr%3Dyfp-t-501&w=500&h=377&imgurl=static.flickr.com%2F161%2F415318536_dc023a04d9.jpg&rurl=http%3A%2F%2Fwww.flickr.com%2Fphotos%2Fmundoo%2F415318536%2F&size=110k&name=Tail+rotor&p=rotor+helicopter&oid=55e6a36c394302f4&fr2=&fusr=Mundoo&lic=3&no=27&tt=42430&b=21&ni=20&sigr=11e8q5kis&sigi=11eradhun&sigb=139b99slh

Why is understanding Rotating Machinery important?

Warranty Costs

Often driven by perceived issues via vibration from customers

Example: JD Powers Ride Comfort

Competitive Advantage

Distinguish your product from competition

Example: Washing machine “walking”

Performance/Fuel Economy

Eliminate vibration that effects product performance

Examples: Torque Converter lockup. Knock sensors. Production Line

Durability

Reduce Vibration Levels. Torsional Inputs. Dynamic Loading

Noise

Eliminate unwanted noise

Example: Piston slap in engine, screaming pumps


Product Development Process C

os

t o

f C

han

ge

Concept Detail

Drawing

Prototype Production Field

Failure

Troubleshoot

Rotating Part

Engineer

Rotating Part

Validate

Rotating Part

Concept

Modeling


http://www.lmsintl.com/testing/rotating-machinery/options

http://www.lmsintl.com/simulation/powertrain-motion

http://www.lmsintl.com/testing/rotating-machinery/options

Electric Motor

Noise ▪ Objective

Sound Pressure Level

Tones/Narrow-Band

▪ Subjective No „Disturbing“ Noise

Vibration ▪ Unbalance

▪ Mode-Free Bands

Price Module ~$6-11 per

Features and Volume

Kinematics

Dynamics

Stress ▪ Rotation and Torque

▪ Unbalance

▪ Mechanical Commutation

Durability ▪ Motor Flange (PP plastic)

▪ Durability to >7000 h

▪ „Shake ‚n„ Bake“

Sine/Random -22–75ºC LMS International, A Siemens Business copyright 2013 6

Engine

Piston Noise

Valve Impact Noise

Combustion profile

Gear rattle

Torsional vibrations

Engine surface vibration

Engine knock

Engine ancillaries

Unbalanced inertia forces

Cylinder to cylinder

variation of combustion

Bending of crankshaft

Valve train dynamics

Bearing forces

Camshaft bending


Vehicle Chassis

Driveline Boom

Wheel Imbalance

Tire Uniformity

Driveline Endurance


Washing Machine


Wind Turbine

GEARBOX

LOW SPEED

SHAFT

ROTOR

BLADES

HUB

NACELLE

HIGH SPEED SHAFT

with MECHANICAL

BRAKE

ELECTRICAL

GENERATOR

ELECTRONIC

CONTROLLER

COOLING

UNIT

TOWER


Production Equipment

Increase production/speed -> Increase Vibration/Decrease Life


Pain: Set Register deviations from 20 µm may become

visible up of a modern sheetfed press


Dental Equipment


Green Revolution brings new challenges!

Turbo Whine - Tones

Cylinder deactivation - Vibration

Battery cooling fans - Whine

Direct injection engines – Ticking Sounds

Hybrid engine shutoff – No powertrain masking

Electric Motors – Spin backwards and forwards!


Order Fundamentals




TransError. Sidebands. …

Order Fundamentals

RPM. 1st order. 2nd order

Angle Domain


RPM Fluctuation

Torsional Vibration


Brackets. Accessories

13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



Fourier Transform

“Any real world signal can be expressed by adding up a unique set of sine waves”

Complicated signals become easier to understand

No information is lost when converting

Frequency (Hz) Time

(seconds)

Amplitude

Amplitude

Amplitude

Fourier Transform


Basics of Sine Waves

Amp

time

1 second


Basics of Sine Waves: Frequency

Amp

time

1 second

Amp

time

1 second


Basics of Sine Waves: Amplitude

Amp

time

1 second

Amp

time

1 second


Basics of Sine Waves: Amplitude

Amp

time

5 Peak

0

-5

5

3.5 RMS (.707 of Peak)

10 Peak-to-Peak (2xPeak)


What is an Order?

An order is a vibration and/or acoustic

response of a structure due to a

rotating component of a physical

structure.


Order Fundamentals

Shaft spins at 600 rpm

What is Frequency?


Order Fundamentals


What is Frequency?

600 Rev

Minute x 1 Minute

60 Second = 10 Rev

Second


Order Fundamentals

Am

plit

ud

e

Frequency

Hz

0 100 50

Spectrum of Shaft

Spinning at 600 rpm


Order Fundamentals


What is Frequency?


Order Fundamentals


What is Frequency?

6000 Rev

Minute x 1 Minute

60 Second = 100 Rev

Second


Order Fundamentals

Am

plit

ud

e

Frequency

Hz

0 100 50

Spectrum of Shaft

Spinning at 6000 rpm


Order Fundamentals


What is Frequency?


Order Fundamentals


What is Frequency?

3300 Rev

Minute x 1 Minute

60 Second = 55 Rev

Second


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Sweep from 600

to 6000 rpm

10 Hz


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Sweep from 600

to 6000 rpm

100 Hz


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Sweep from 600

to 6000 rpm


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Sweep from 600

to 6000 rpm

600 rpm 6000

1st Order


Order Fundamentals

Shaft 1 at 600 RPM

Pulley on Shaft 1 is 3x

pulley diameter on Shaft 2

What is rpm for Shaft 2?

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Order Fundamentals

Shaft 1 at 600 RPM



What is rpm for Shaft 2?

Answer: 1800 rpm

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Order Fundamentals

Shaft 1 at 600 RPM



What is frequency for

Shaft 2?

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Order Fundamentals

Shaft 1 at 600 RPM



What is frequency for

Shaft 2?

Answer: 30 Hz Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Order Fundamentals

Am

plit

ud

e

Frequency

Hz

0 100 50

Spectrum of Shaft 1

spinning at 600 rpm. Shaft

2 spinning at 1800 rpm

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Order Fundamentals

Am

plit

ud

e

Frequency

Hz

0 100 200

Spectrum of Shaft 1

spinning at 6000 rpm. Shaft

2 spinning at 18000 rpm

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1

300 400 500


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1

30 Hz


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1

300 Hz


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1


Sweep

Am

plit

ud

e

Frequency

Hz

0 100 50 200 150 250 300

Shaft 2

Shaft 1

Pulley

Ratio:

3 to 1

What if all speeds are

relative to Shaft 2?


How to Measure?

Remote Optical Probe:

• Reflective Tape needed on shaft


Zebra Tape Example


TL RUNUP

DEMONSTRATION Project: Orders.lms


Colormap (ie, Campbell Diagram)

0.00 2000.00Hz

Point1 (CH1)

900.00

3500.00

rpm

Tach

o1 (T

1)

-20.00

80.00

dB Pa

AutoPow er Point1 WF 251 [984.96-3482.9 rpm]

Frequency

RP

M


Campbell Map Sweep vs 2D Steady State

0.00 6400.00Hz

Point1 (CH1)

0.00

4.50e-3

Amplit

udePa

0.00

1.00

Amplit

ude

F AutoPow er Point1 1084 rpm

Am

plit

ud

e

Frequency

Resonance or Forcing Frequency?


Colormap (ie, Campbell Diagram)

0.00 2000.00Hz

Point1 (CH1)

900.00

3500.00

rpm

Tach

o1 (T

1)

-20.00

80.00

dB Pa


Frequency

RP

M

Resonance is apparent


Order vs Frequency

900.00 3500.002000 30001200 1400 1600 1800 2200 2400 2600 2800 3200

rpm

Tacho1 (T1)

20.00

70.00

30.00

40.00

50.00

60.00

dBPa

F Order 6.00 Point1

RPM

What frequency?

2700 RPM, 6th Order:

2700 RPM/60 RPM = 45 Hz

45 Hz * 6 order = 270 Hz


Frequency and Orders

Amp

time

1 second

Amp

1 revolution

2nd Order 2 Hertz

Event per Second Event per Revolution

Frequency Order


Order Example #1:

Fan spins at 6000

rpm.

What is frequency

of main shaft?


Order Example #1:

100 Hz (6000 rpm/60)

Fan spins at 6000

rpm.

What is frequency

of main shaft?


Order Example #1:

100 Hz (6000 rpm/60)

Fan spins at 6000

rpm.

What is frequency

of main shaft?

0 200 400 600

Am

plit

ud

e


Order Example #1:

Fan spins at 6000

rpm.

What is frequency

of blade pass?


Order Example #1:

Fan spins at 6000

rpm.

What is frequency

of blade pass?

600 Hz 100 Hz x 6 blades

1 2

3

4

5

6


600 Hz 100 Hz x 6 blades

Order Example #1:

Fan spins at 6000

rpm.

What is frequency

of blade pass?

1 2

3

4

5

6

0 200 400 600

Am

plit

ud

e


Order Example #1:

Fan spins at 6000

rpm.

What is order of

blade pass?

1 2

3

4

5

6


Order Example #1:

Fan spins at 6000

rpm.

What is order of

blade pass?

6th order

1 2

3

4

5

6


Order Example #1:

Fan spins at 6000

rpm.

What is order of

blade pass?

6th order

1 2

3

4

5

6

Independent of rpm


Imbalance

1st ORDER is due to

Imbalance of spinning shaft


VL ENGINE

DEMONSTRATION


Order Example - 2 stroke

2 Stroke, 2 Cylinder

Engine at 600 rpm.

What is combustion

frequency?




Engine at 600 rpm.

What is combustion

frequency?

10 Hz x 2 cylinders

=

20 Hz




Engine at 600 rpm.

What is combustion

order?



2 Stroke. 2 Cylinder

Engine at 600 rpm.

What is combustion

order?

2nd order



4 stroke. 6 cylinder

engine.

What is combustion

order?



4 stroke. 6 cylinder

engine.

What is combustion

order?

3rd Order


Combustion occurs over 2 revs

1 cycle

1st revolution 2nd revolution

Intake Compression Power Exhaust


Torsional Vibration





Order Fundamentals


Angle Domain


RPM Fluctuation

Torsional Vibration



13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



What is Torsional Vibration?

0.00 19.00 s

200.00

2200.00 A

mplit

ude

rpm

F 1:Tacho1

What is unusual

about this RPM-

time curve?


Torsional Vibration

0.00 19.00 s

200.00

2200.00

Am

plit

ude

rpm

F 1:Tacho1

13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1

RPM is not

steadily

increasing.

Small fluctuations

up/down occur.


What is Torsional Vibration?

Torsional vibration is a fluctuation

(reversal) in the speed of a rotating

component.


Torsional Vibration: Causes

Non-constant RPM generated by motion of

crankshaft. connecting rod and piston:

• Piston motion is not constant during

combustion cycle (combustion versus

compression)

• Piston has inertia properties to overcome

• Entire mechanism does not output smooth

torque (example: top dead center change of

direction)


Problems caused by Torsional Vibration

Durability Problems

Flexible Coupling wear

Worn Gear teeth/failed gears

Vibration Comfort

Vibration of the steering wheel. seats. pedals

Noise problems

Engine start/stop noise

Resonance of long drive shafts. causing interior noise

Meshing and rattle noise problems from gearboxes

Resonance in auxiliary drives (generators. compressors.

and steering pumps)

Synchronization Problems

Reduced performance

Reduced fuel economy


TORSIONAL VIBRATION

HOW TO MEASURE?


Measuring Torsional Vibration: Order Cut Example

Pulses converted to RPM

Perform multiple FFTs

on rpm vs time trace

V

time

time

Time or rpm

De

lta

rp

m

Order Cut

from

Waterfall 15.00 500.00Hz

1000

3500

rpm

0

61

rpm

0.00 19.00 s

200.00

2200.00

Am

plit

ude

rpm

F 1:Tacho1

rpm


AC vs DC

RPM

time

+

RPM

RPM

Overall RPM (DC)

Torsional Vibration (AC)

Net RPM (AC and DC)

frequency


Pulses per Rev: Maximum Torsional Order

Amp

For a 50 Hz Sine

Wave. what

should sampling

rate be? time



time

Amp

For a 50 Hz Sine

Wave. what

should sampling

rate be?

100 Hz Twice the frequency of

interest



rev

Amp

For a 50th Order

torsional

vibration. What

should pulse per

revolution be?



rev

Amp

For a 50th Order

torsional

vibration. What

should pulse per

revolution be?

100 ppr Twice the order of interest


1 Pulse/Rev versus Multi Pulse/Rev

Same shaft

Blue – 120 ppr

Green - 1 ppr

0.00 8.50s

800.00

3600.00

Ampl

itude

rpm

F 3333:Torsion

F 1:Tacho1


Maximum Torsional Order

0.00 7000.00Hz

Torsion (V1)

1000.00

3500.00

rpm

Tach

o1 (T

1)

-20.00

80.00

dB rpm

74.74

AutoPow er Torsion WF 251 [1013.4-3497.3 rpm]

Nothing Shows Here

because of pulse/rev

limit


Units and Display Tip


Virtual channels: Torsional Vibration


TL TORSIONAL

DEMO Project: Torsion2.lms


How to Measure? Magnetic Pickup

Magnetic Pickups:

• Works on Gears

• No external power

required


aerodyneng.com


How to Measure? FEAD example


How to Measure? Shafts



!

Overlap on Ends

causes

discontinuity


Offline Overlap: Uncorrected

Big dips in RPM

Overview

Top –Even Spacing

Bottom – Uneven spacing

due to overlap

}

Zoomed in

for detail }


Offline Overlap: Corrected

ZEBRA_MOMENTS_TO_ANGLE ZEBRA_MOMENTS_TO_RPM

Corrected

LMS

Test.Lab

10 SL1


Zebra Tape Example


31.26 57.71s

4379.83

5019.96

Am

plit

ude

rpm

0.72

0.86

Am

plit

ude

F 6:Ring_Gear

Torsional Vibration Resonance

Torsional Vibration can be

amplified by resonance:

Crankshaft in Engine

Drive Shaft


Virtual Channels :Torsional Vibration difference


VL FLEXIBLE TORSIONAL DEMO

Database: Shaft with U-Joints


Problems caused by Torsional Vibration

Durability Problems

Flexible Coupling wear

Vibration Comfort

Vibration of the steering wheel. seats. pedals

Noise problems

Engine start/stop noise

Resonance of long drive shafts. causing interior noise

Meshing and rattle noise problems from gearboxes

Resonance in auxiliary drives (generators. compressors.

and steering pumps)

Synchronization Problems

Reduced performance

Reduced fuel economy


Driveline Torsional Vibration



Ever-tightening fuel economy requirements are driving lower torque converter locking limits

Cylinder deactivation technology

Diesel engines

1000.00 3500.00rpm

Tacho1 (T1)

0.00

1.40

Am

plit

ude

°

0.00

1.00

Am

plit

ude

F Order 2.00 TorsionAngle



Different types of dampers: friction. spring. etc

Trans Diff'l

Wheel/Brake

Wheel/Brake

Engine

Damper

Torsional Spring



4-8

20-50

50-90

90

130

750

1350

300

750

60

120

1350

1950

Eliminated with

Turbine Damper

Driveline Torsional Modes are a function of the rotational inertia and stiffness

of the driveline elements.


AMESIM

DEMO Database: Boom and Clunk.ame


Gears, Motors, Pumps,

Bearings, ...





Order Fundamentals


Angle Domain


RPM Fluctuation

Torsional Vibration



13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



Gears


Gears and Bearings

Gear Issues:

Transmission Error

Sidebands

Gear Whine

Gear Rattle


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is shaft

frequency?


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is shaft

frequency?

10 Hz 600rpm/60


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is shaft

frequency?

10 Hz 600rpm/60

0 20 40 60

Am

plit

ud

e


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is frequency

of gear mesh?


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is frequency

of gear mesh?

10 Hz x 48 teeth =

480 Hz


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is frequency

of gear mesh?

10 Hz x 48 teeth =

480 Hz

0 20 40 60


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is gear mesh

order?


Order Example #2:

48 Tooth Gear

spins at 600 rpm.

What is gear mesh

order?

48th order


Transmission Error

50 tooth gear

25 tooth gear

50 tooth gear

spins at 100 rpm.

What is rpm of 25

tooth gear?


Transmission Error

50 tooth gear

25 tooth gear

50 tooth gear

spins at 100 rpm.

What is rpm of 25

tooth gear?

200 rpm


Transmission Error

50 tooth gear

25 tooth gear

50 tooth gear

spins at 100 rpm.

What is rpm of 25

tooth gear?

200 rpm

Transmission Error means it

is not 200 rpm


Transmission Error

Transmission Error of 0

means no loss, perfect

transmission

50 tooth gear

25 tooth gear

Transmission Error = Actual RPM Gear2 – Theoretical RPM Gear2

Where Theoretical RPM at Gear2 = Actual RPM Gear1 x Gear Ratio


Gears: Transmission Error

Can Gear rotation

speeds effect

Transmission Error?


TL GEAR

TRANSMISSION

ERROR DEMO Project: gear_trans_error.lms


Transmission Error Calculation Procedure

Gear1

rpm

Gear2

Theory

rpm time

1. Measure RPM of driving and

driven gear vs time

2. Calculate theoretical rpm of driven

gear

3. Subtract difference of theoretical

gear speed and actual driven gear

speed vs time

4. Perform FFT on rpm difference

(overall or versus time)

Difference

rpm time

time

Gear 2

Actual

rpm time

0.00 5.00order

Derived Order (rpm)

0.00

0.03

Am

plit

ude

°

1.0024

Curve 1.0024 order

0.0192 °

Multiple Gear1 rpm by Gear Ratio

Subtract Gear2Actual-Gear2Theory

2

3

4


Transmission Error Causes

Perfectly Meshed

Gear 1 Gear 2



Eccentric Not Perfect Circle

Manufacturing

defect can cause

Gear to be

oblong/eccentric

Gear 1 Gear 2 Gear 2



Eccentric - Not Perfect Circle

Manufacturing

defect can cause

Gear to be

oblong/eccentric

Gear 1 Gear 2 Gear 2



Eccentric Not Perfect Circle

Manufacturing

defect can cause

Gear 2 to be

oblong/eccentric

rev

Gear 2

vs

Gear1

Gear 2 Gear 2


0.00 1.00s

-1.10

1.10

Real

g

0.00 1.00s

-1.00

1.00

Real

gModulation

100th Order – “Gear Mesh”

2nd Order Ampitude Modulation

due to Eccentric Gear


Modulation -> Sideband

0.00 1.00s

-1.00

1.00

Real

g

0.00 1.00s

-1.10

1.10

Real

g

90.00 110.00Hz

0.00

1.00

Am

plit

ude

g

100th Order






0.00 1.00s

-1.00

1.00

Real

g

0.00 1.00s

-1.10

1.10

Real

g

90.00 110.00Hz

0.00

1.00

Am

plit

ude

g

100th Order




90.00 110.00Hz

0.00

0.64

Am

plit

ude

g

Spectrum 2_per_rev_mod

+/- 2 order



Off Center Rotation

Gear 1

Gear 2

Shaft mis-

alignment and/or

resonance causes

gear 2 to spin off

center

Center of Rotation shift



Off Center Rotation

Gear 1

Gear 2

Shaft mis-

alignment and/or

resonance causes

gear 2 to spin off

center



0.00 1.00s

-1.00

1.00

Real

g

0.00 1.00s

-1.10

1.10

Real

gModulation


1st Order Amplitude Modulation

due to Off Center Shaft Rotation



0.00 1.00s

-1.00

1.00

Real

g

0.00 1.00s

-1.10

1.10

Real

g


1st Order Amplitude Modulation


90 11010095 105

Hz

0.00

1.00

Am

plit

ude

g

100th Order

90 11010095 105

Hz

0.00

0.64

Am

plit

ude

g

Spectrum 1_per_rev_mod

+/- 1 order


Gear Sidebands

90 11010095 110

Hz

0.00

1.00

Am

plit

ude

g

Offset RotationEccentric GearGear Mesh Only

Sideband Order

(+/-)

Problem

0 None

1 Offcenter Shaft

Rotation

-Shaft Resonance

-Imbalanced Shaft

-Improper install

2 Eccentric Gear

- Manufacturing Issue


Sidebands

0.00 5000.00Hz

VIBR:2:+Z (CH2)

899.96

2909.99

rpm

TA

CH

:9999:+

RX

(T

1)

-50.00

50.00

dB

m/s

2

AutoPow er VIBR:2:+Z WF 202 [899.96-2910 rpm]

Sidebands vary

by rpm/load in

real life


Gear whine: Noise generated by the loading and unloading of the individual teeth around the point of engagement

Gear rattle: Noise induced by teeth impacting each other at non-powered gears fluctuating with lash clearance

Gearbox Major Noise Types

FREQUENCY

RP

M

RP

M

FREQUENCY

Whine

Gearbox Rattle vs Whine


Example: Gear Rattle/Backlash


Gear Simulation Approaches

Definition

Analytical method (reference: Cai / ISO / …)

Accounts for varying stiffness of the contact

• Width of the tooth varies

• Number of teeth that are in contact varies

(e.g. helical gear)

Applies the force to a single point at the tooth

center

Gear types supported

Spur and helical

Advantages

High solving speed

High level of detail

Limitation

Heavy manual modeling work (geometry,

kinematics, dynamics)

Solution is … GTSE! (see next slide)

p b

h

k

Meshing

path

Pitch point

Force

Applied


Gear Train Super Element (GTSE)

Definition

One interface for creating a complete (multi-stage) gear train

Uses the same analytical algorithm as the Gear Contact Force (Cai, ISO)

Includes the definition and creation of bodies, joints, contacts and geometry of the whole train

Advantages

Fast and easy modeling

Fast solving speed (analytical contact)

Automatic detailed geometry creation and possible import of existing geometry

The gear contact force element can be

used in a standalone mode but the

feature is included in the GTSE as well


AMESIM GEAR

RATTLE DEMO


Bearings


Bearings

Various types

Ball bearings

Roller bearings

Needle bearings

Tapered roller bearings

Spherical roller bearings

Thrust bearings

Widely used: from bicycles to aerospace. control systems. axles. …


http://rds.yahoo.com/_ylt=A0WTefftmstL0WUARICjzbkF/SIG=134e35bgi/EXP=1271721069/**http:/img.wdimporters.com/773/20090827/2f2c86d0-f3ef-4e1d-88cc-fc9d3f78a540.jpg

http://rds.yahoo.com/_ylt=A0WTefdLm8tLBWUAibejzbkF/SIG=11v6m6edg/EXP=1271721163/**http:/www.jota-bearing.com.tw/about/62.jpg

http://rds.yahoo.com/_ylt=A0WTefTCm8tLL2YA42.jzbkF/SIG=12msnpfkk/EXP=1271721282/**http:/img.alibaba.com/photo/222119041/tapered_roller_bearings.jpg

http://rds.yahoo.com/_ylt=A0WTefgfnMtLy0cAT3OjzbkF/SIG=133rfmcqs/EXP=1271721375/**http:/www.atcomaart.com/Upload%20Image/Bearings/spherical-roller-bearing.jpg

Bearing Parts

Outer Race

Inner Race

Rolling Elements


http://upload.wikimedia.org/wikipedia/commons/3/30/BallBearing.gif

Bearings

Inner shaft spins at

600 rpm.

What is bearing ball

pass frequency?


Bearings

Inner shaft spins at

600 rpm.

What is bearing ball

pass frequency?

600 rpm/60 x 8 =

80 Hz


Bearing Parts



Bearing Frequencies

Bearing Defects and their frequencies

• FTF: Fundamental Train Frequency: Defect in

the cage

• BSF: Ball Spin Frequency: Defect in the ball =

2 Ball defect Frequency

• Ball Defect Frequency: Defect in the ball

when it tends to roll rather than spin

• BPFO: Ball Pass Frequency Outer race: Defect

on the outer race

• BPFI: Ball Pass Frequency Inner race: Defect

on the inner race

• Combinations of the above

cos1

2

1

dp

drRPMFTF


Bearing frequencies

cos1

2

1

dp

drRPMFTF

cos1

2

12

2

dp

drz

dr

dpRPMBSF

cos1

2

1

dp

drzRPMBPFO

cos1

2

1

dp

drzRPMBPFO

Rolling element irregularities and defects

FTF: Fundamental Train Frequency: Defect in the cage

α is contact angle between load and rolling plain

BSF: Ball Spin Frequency: Defect in the ball = 2 Ball defect

Frequency

• Ball Defect Frequency: Defect in the ball when it tends to

roll rather than spin

BPFO: Ball Pass Frequency Outer race: Defect on the outer race

BPFI: Ball Pass Frequency Inner race: Defect on the inner race

Combinations of the above


Example Defect Frequencies for a Bearing

RPM BSF

Ball Spin

FTF Fundamental Train

BPFO Outer Race

BPFI Inner Race

100 3.979451 0.675251 6.077258 8.922742

500 19.89726 3.376254 30.38629 44.61371

1000 39.79451 6.752509 60.77258 89.22742

1500 59.69177 10.12876 91.15887 133.8411

2000 79.58902 13.50502 121.5452 178.4548

2500 99.48628 16.88127 151.9315 223.0685

3000 119.3835 20.25753 182.3177 267.6823

3500 139.2808 23.63378 212.704 312.296

4000 159.178 27.01004 243.0903 356.9097

Pitch Diameter = 1.548 inches

Ball Diameter = 0.3125 inches

Number balls = 9


Example Defect Frequencies for a Bearing

RPM BSF

Ball Spin

FTF Fundamental Train

BPFO Outer Race

BPFI Inner Race

100 3.979451 0.675251 6.077258 8.922742

500 19.89726 3.376254 30.38629 44.61371

1000 39.79451 6.752509 60.77258 89.22742

1500 59.69177 10.12876 91.15887 133.8411

2000 79.58902 13.50502 121.5452 178.4548

2500 99.48628 16.88127 151.9315 223.0685

3000 119.3835 20.25753 182.3177 267.6823

3500 139.2808 23.63378 212.704 312.296

4000 159.178 27.01004 243.0903 356.9097

Pitch Diameter = 1.548 inches

Ball Diameter = 0.3125 inches

Number balls = 9

2.387

Order

.405

Order

3.646

Order

5.354

Order


Bearing Defects

Good Bearing

Bad Bearing

Bearing defect can become failure due to:

Bearing defect starts as surface erosion (of bearing

or race). possibly due to hard contaminants

scraping bearing material



FFT on Impact Event

time frequency

FFT

Bearing Defect Impact


Impact Event Frequency Analysis (Simplfied)

0.00 3.00s

Time

0.00

4000.00

Hz

Hig

hP

ass500 (

CH

2)

0.00

0.01

Am

plit

ude

V

0.00 3.00s

-0.01

0.34

Real

V

Impacts are 0.6

seconds apart.

What is frequency?


Impact Event Frequency Analysis (Simplfied)

0.00 3.00s

-0.01

0.34

Real

V

0.00 3.00s

Time

0.00

4000.00

Hz

Hig

hP

ass500 (

CH

2)

0.00

0.01

Am

plit

ude

V

Impacts are 0.6

seconds apart.

What is frequency?

1.66 Hz 1/time interval or

1/0.6

0.00 2000.00Hz

0.00

300e-6

Am

plit

ude

V

0.00

1.00

Am

plit

ude

1.57


Real Life Bearing Data

8.20 11.80s

-40.00

30.00

Real

g

0.00

1.00

Am

plit

ude

F 4:Outer Race Faulted Bearing 2000 RPM:None

F 5:Outer Race Good Bearing 2000 RPM:None

Difficult to see

impacts associated

with defect.

Bandpass filtering

required.


Envelope

0.61 0.65s

-0.10

0.12

Real

V

4:HighPass500:None

5:Envelope_of_HighPass:None

ENVELOPES

• Envelope done by Hilbert

Transform

• Hilbert Transform separates slowly

varying envelope from rapidly

varying signal


Step by Step Envelope

t

t

t

Bandpass Filter (based on accel resonance)

Envelope

FFT

Hz

Amp

frequency

FFT

1

2

3


Identification of bearing defects

Frequency analysis

FFT of Time signal

Peaks in the spectrum

– Compare VS known defect frequencies

– Compare VS spectrum of good bearing

Use of location

Maximum amplitude along axis of static load

Use of calculated or derived variables

Cepstrum

Envelope analysis

• In case machinery faults have a modulating effect

Gearboxes (cracks. broken teeth). bearings (defects on inner/outer race). Turbine-

blades (cracks. distorted)


Identification of bearing defects

Cepstrum

Step 1 FFT of signal to identify bandwidth of interest

Step 2 Band Pass Filtering according to step 1

Step 3 Calculate Real or Complex Cepstrum

Step 4 Identify the 1/frequencies and compare with defect frequencies

Envelope detection

Step 1 FFT of signal to identify bandwidth of interest

Step 2 Band Pass Filtering according to step 1

Step 3 Calculate Hilbert transform

Step 4 Calculate Envelope

Step 5 FFT of envelope


Step by Step Envelope

t

t

t

Bandpass Filter (based on accel resonance)

Envelope

FFT

Hz

Amp

frequency

FFT

1

2

3


Bearing Simulation

Many levels of detail possible:

Simple Lumped Model

First is simple lumped stiffness and damping

Using ideal or measured stiffness and

damping for the bearing

Used as component in larger system

Discrete Detailed Model

Rigid Body

More detailed and accounts for local loads in

the bearing

Capture transient dynamic behavior

Discrete Detailed Model with Flexible Body

mesh geometry and solve for modes of

deformation

Get more accurate loads for the bearing and

the supporting structure than the rigid body

model

Flexible contact captures local deformation

and is the most accurate method


Sample Discrete Bearing Model

Primary components:

Inner Race

Outer Race (not shown)

Cage

Rollers

Skeleton sketch for layout

Skeleton is only a Part document, not a body, it controls the size and position of all bodies in the model

Use of a sketch skeleton in this manner only works if bodies are coupled with force elements

Design Table controls all major geometry and dynamic parameters

One approach to how a bearing “could” be designed. The various radius values control the cutting of the Cage

Results are contact forces and displacement, velocity, and acceleration of the rollers, cage, and rotating race


VL Bearing Demo


Bearing Simulation


Electric Motors


Basics of Electric Motors

Motors

AC Motor

DC Motor

Basic Parts: Brush, Stator, Rotor, Commutator

Controllers

DC Motor Controller

Wave Rectifiers - Voltage = Speed, Current = Torque

Pulse Width Modulation – Voltage (via Pulse width) = Speed, Current = Torque

AC Motor Controller

Pulse Width Modulation - Switching Frequency = Speed, Pulse Width = Torque(ie

current)


http://electronics.howstuffworks.com/electronics-parts-pictures.htm

AC Motor


DC Motor


Order Example – Motor Speed

DC Brushless

Motor with 12

copper windings.

What is

commutation

order?


Order Example – Motor Speed

DC Brushless

Motor with 12

copper windings.

What is

commutation

order?

12th Order


Electric Motors: AC/DC Power Transformation

Amp

AC Power

Amp

DC Power

Motor

Controller

Regulate Torque

and Speed via

Voltage and

Current


Example: AC to DC (and vice versa) Power Conversion

Examples:

Alternator charging battery in car

• Alternator: Full Wave, 3 phase rectifier

• Battery: DC power

• AC to DC power

Electric Drive

• 750 V DC Battery

• AC Drive Motor

• DC to AC Power


Control via Pulses: Changing Frequency

FFT

FFT

1 3 7

1 3 7

Frequency Different


Control via Pulses: Changing Width

Note: Original Frequency

of Signal 1 and 2 is same,

only Pulse Width Different

Blue – Original Frequency

Red – Half Pulse Width

Green – Long Pulse Width

Signal 1

Signal 2


Pulse Width Modulated

Pulse Wave

Unmodulated

Pulse

Wave

Modulate

d

(PWM)

Sine Wave

Sine Wave


Motor Inertia “Smooths” Pulse Wave Signal

Pulse Wave

Modulated

(PWM)

Sine Wave


Pulse Width Modulated Drive (Switching Frequency)

sideband switching orders that don't track with the wheel.

Electric Motor and

Combustion Engine Orders

Electric Motor

Control Switching

Frequencies

Hybrid Electric Drive


Pulse Width Modulated Drive


AC to DC Motor Controller

Single Phase AC Power

110 V, 60 Hz (USA)

220 V, 50 Hz (Europe)

degrees

240 120

Amplitude

V

Volts

Amplitude

360

DC Voltage Level =0


DC Motor Controller


110 V, 60 Hz (USA)


240 120

Amplitude

V

Volts

Amplitude

360

degrees Half Wave Rectified

DC Voltage Level =

Vpeak/Pi


DC Motor Controller


110 V, 60 Hz (USA)


Amplitude

V

Volts

Amplitude

degrees

DC Voltage Level

2*(Vpeak/Pi)

240 120 360

Full Wave Rectified


DC Motor Controller

3 Phase AC Power

60 Hz (USA)

50 Hz (Europe)

Carried on 3 wires

degrees

240 120

Amplitude

V

Volts

Amplitude

360

DC Voltage Level =0


DC Motor Controller

degrees

Amplitude

V

Volts

Amplitude

240 120 360

Half wave rectified – 3 x Line Frequency – Normal Operation

3 Phase AC Power

Line Frequency:

60 Hz (USA)

50 Hz (Europe)

DC Voltage Level

Hz

Am

p


DC Motor Controller

Full wave rectified – 6 x Line Frequency – Normal Operation

Volts

Amplitude

degrees

240 120 360

3 Phase AC Power

Line Frequency:

60 Hz (USA)

50 Hz (Europe)

DC Voltage Level

Hz

Am

p


DC Motor Controller with Problem

Full wave rectified – 5th order – Controller problem

Volts

Amplitude

degrees

240 120 360

3 Phase AC Power

Line Frequency:

60 Hz (USA)

50 Hz (Europe)

Hz

Am

p

Problem

Frequencies

High 2nd, 3rd, 4th and

5th order on Full

Rectified 3 Phase

power indicates

problem


Summary of Motor Controller Frequencies

Electrical Expected Frequencies

Single Phase, Half Rectified Wave 1 x Line Frequency

Single Phase, Full Rectified Wave 2 x Line Frequency

Three Phase, Half Rectified Wave 3 x Line Frequency

Three Phase, Full Rectified Wave

6 x Line Frequency


Electric Motors: AC/DC Power Transformation

Amp

AC Power

Amp

DC Power

Motor

Controller

Regulate Torque

and Speed via

Voltage and

Current


Hydraulic Pump


Hydraulic Pumps

Various types

Vane

Piston

Gerotor

Screw

Gear

Controls pressure in hydraulic lines


Hydraulic Vane Pumps

Hydraulic Vane

Pump with 8 vanes.

What is pressure

pulsation order? low

high


Hydraulic Vane Pumps

Hydraulic Vane

Pump with 8 vanes.

What is pressure

pulsation

frequency?

8x rotation

speed

low

high


Pulse amplitude versus freq

Higher number of compartments = smaller fluctuations

Odd number of vanes smaller fluctuations rather than even – guaranteed overlap

Shape of compartment and bleed back valves


AC vs DC Pressure

Pressure

time

+

Pressure

Pressure Average Pressure (DC)

Pressure Pulsation (AC)

Net Pressure (AC and DC)


If AC Fluctuation > DC Pressure

Pressure

time

+

Pressure

Pressure Average Pressure (DC)

Pressure Pulsation (DC)

Net Pressure (DC)


Cavitation Formation of vapor bubbles in hydraulic line or pump

Cavitation is when vapor bubble collapses (instantaneous when bubble reaches high pressure line)

Can be violent event, damage hydraulic lines and pumps

Many possible causes:

Line resonance

Pump intake creates vacuum

Valve-Pump interaction

High frequency actuators

Phase diagram

temperature

pre

ssure

boilingliquid

solid

gas

cavitation


http://en.wikipedia.org/wiki/File:Cavitation.jpg

AMESIM HYDRAULIC

CIRCUIT DEMO WITH

CAVITATION


Cavitation Observations

Hydraulic system can be sized to perform function,

but dynamic performance can be easily overlooked

Dynamic interaction of complete system: valves,

pumps, lines, etc


Balancing





Order Fundamentals


Angle Domain


RPM Fluctuation

Torsional Vibration



13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



Balancing

Two shafts spinning.

Which one vibrates more? Front View – Shaft 1

Front View – Shaft 2

Mass Added


Balancing


Which one vibrates more?

Answer:

Shaft 2!



Mass Added


Balancing



600 rpm

6000 rpm

Mass Added

Mass Added


Balancing



6000 rpm

600 rpm

6000 rpm

Mass Added


Imbalance

Imbalance:

is the product of mass and

distance (radius)

customary unit of measure is g-

cm or oz.-in.

Complex quantity

Force due to imbalance (where

has unit's rad/sec2):

22 ImRF

Imbalance force

increases

exponentially with

speed

0

25

50

75

100

125

150

0 1000 2000 3000 4000 5000 6000

Shaft Speed, RPM

Ce

ntr

ifu

ga

l F

orc

e, N

40 g-cm

20 g-cm

Imbalance force

increases

exponentially with

speed


Balance Example

Fan and Shaft are each 99.5% balanced.

Is fan/shaft assembly 99.5% balanced?

Fan Shaft


Balance Example



Fan Shaft

NO


Balancing

How to fix?


Mass Added


Balancing

How to fix?

Mass on each side


Mass Added


Balancing

How to fix?

Eliminate Mass


Mass Added


Types of Imbalance

Static Imbalance Where (Principal Inertia Axis) PIA is displaced parallel to

geometric centerline.

Couple Unbalance Where (Principal Inertia Axis) PIA intersects the geometric

centerline at center of gravity (CG).

Dynamic Unbalance Where (Principal Inertia Axis) PIA and geometric centerline do

no coincide (run parallel) or touch.

Static

PIA

Geometric

Centerline

Center of Gravity

Static

PIA

Geometric

Centerline

Center of Gravity


Causes of Imbalance

Shaft Bending Resonance If shaft is above 70% of it‟s natural frequency (critical speed) it

is considered to be a flexible rotor. and the PIA and geometric

centerline do not correspond.

Bearing Clearance/Radial Endplay

Improper Installation Shaft offset from center of rotation

Static

Geometric

Centerline


Imbalance Example: Power Generator


Imbalance Example: Power Generator

During periods of in-

use, large rotors/shafts

will droop.

Upon startup,

generators must be run

a low speeds for long

time, to allow the main

shaft to straighten

When the generator is

run at high speed, the

imbalance forces

prevent the shaft from

straightening, causing

high vibration.

Generator


VL

IMBALANCE

DEMO Database: Shaft with U-Joints

and Added Mass


Drive Shaft Durability due to Imbalance


Drive Shaft Durability due to Imbalance

Imbalance

weights

induce

jump-rope

mode

Prop shaft

must

survive

maximum

expected

imbalance

Virtual strain

gauges

must be

below

certain

target LMS International, A Siemens Business copyright 2013 254


Production Line Equipment Story:

• Line Speed Increased

• Large Roller (with Gears) goes from 100 rpm to 300 rpm

• Production equipment vibrates at unacceptable levels

• Gear Mesh frequency is much higher

Changing Gears does not reduce the vibration. Why Not?



Production Line Equipment Story:

• 1st Order Imbalance is problem – Very sensitive to speed

• Imbalance on shaft holding gears causes mesh

frequency amplitude increase

Solution: Balance roller reduced gear mesh by factor of 6


Faster



Baseline

Frequency

Vib

ratio

n A

mp

litu

de

1st order

imbalance

Gear Mesh


How to Measure Imbalance?

1 tach. 1 response of system

Find a speed

Measure 1st order

Baseline

With Known Mass added at specific angle

Determine Influence Coefficent

Amplitude and phase at speed of response (usually acceleration in g‟s)

Trial Mass (kg and location in angle)

This effectively „calibrates‟ the vibration plane to the mass plane

Influence Coefficient

relates Vibration Plane to

Imbalance


Influence Coefficient (IC)

Influence Coefficent (IC) – Relates vibration at response to imbalance

IC = Change in Response/Change in Imbalance

•Change in Response = Baseline vs TrialMass

•Change in Imbalance known due to weight and angular placement and radius

Assumptions:

All response due to imbalance

Linear IC between response and imbalance

Influence Coefficient

relates Vibration Plane to

Imbalance


Find a Speed for Balancing

Optimal Speed

Just Imbalance

Imbalance + Resonance

g g

rpm rpm


Shaft Centerline Measurement


Proximity probe X

Proximity probe Y

t

t

seconds

X

Y

-0.24 0.24Real

mm

-0.24

0.24

Real

mm

0.00

1.00

Real

14.61 14.74s

14.61 14.74

1:1

X

Y


Shaft Centerline Plot

-0.24 0.24Real

mm

-0.24

0.24

Real

mm

0.00

1.00

Real

14.61 14.63s

14.61 14.63

1:1

Indicates how

well shaft rotates

around center


TL SHAFT

CENTERLINE

DEMO


Angle Domain





Order Fundamentals


Angle Domain


RPM Fluctuation

Torsional Vibration



13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



Angle Domain Introduction

Engine

Front

Crankshaft

Optical Probe

0 10

Engine runup from 600 to 6000 rpm with 1 pulse/rev in 10 seconds

Why does time between

pulses change?

Time

seconds

0 10

V

rpm


Angle Domain Introduction

Engine

Front

Crankshaft

Optical Probe

0 10

Why does time between

pulses change?

Answer: Engine gets faster!

Time

seconds

0 10

V

rpm

Engine runup from 600 to 6000 rpm with 1 pulse/rev in 10 seconds


Transform Time to Angle

Time Data V

Time

seconds

V

Revolutions

Angle

1 rev 1 rev 1 rev 1 rev 1 rev

Angle Data

View data in angle domain

Angle

domain

makes

revolutions

uniform

distance

apart


Insights revolution/degree domain

Cylinder #5 Pressure

Vibration on Block

1 revolution


How to go from time to angle?

0 10

Time

seconds

0 10

V

rpm

Integrate RPM

Time

seconds

0 10

RPM is Speed. Angle is Distance Traveled

degrees

Now we can relate

each time

instance with a

particular angle!


Transform Data vs Time to Data vs Angle

Vibration/sound

amplitude

degrees

Vibration/sound

amplitude

time

Now we can relate

each time

instance with a

particular angle!


Resampling

Vibration/sound

amplitude

degrees

Resampling and angle domain resolution:

• 360 points/rev = 1.0 degree




High Resolution

required


How to Measure?

Incremental Encoder Features:

• High Pulse per Revolution: 360. 720.

1800. etc (A and B)

• Single Pulse Revolution (INDEX)

• Distinguish Forward and Backward

Incremental Encoder


How to Measure?


INCREMENTAL

ENCODER DEMO


Engine Analysis

Question: Is it useful to look

at data over 1 revolution

for a 4 stroke engine?


Engine Analysis




NO


Engine Analysis




NO -

1 combustion cycle occurs

over 2 revs


Combustion occurs over 2 revs

1 cycle

1st revolution 2nd revolution

Intake Compression Power Exhaust


Angle Maps

0.00 719.00°

0.00

72000.00

°

1.30

13161069.00

Am

plitu

de

Pa

22.61

0.00 719.00°

0.00

72000.00

°

-7.73

6.88

Real

g

22.61

0.00 719.00°

block:+Z (CH18)

-7.00

6.00

Real

g

0.00

1.00

Am

plit

ude

F Angle block:+Z 3009.8 rpm

Averaged 0.00 719.00°

PCYL1 (CH1)

-1000000.00

13000000.00

Real

Pa

0.00

1.00

Am

plit

ude

F Angle PCYL1 3009.8 rpm

Averaged


Maximums from 2 conditions

0.00 719.00°

0.00

72000.00

°

-7.73

6.88

Real

g

22.61

0.00 100.00#

26.00

102.00

Am

plitu

de

g

F Maximum block:+Z Cyl5Accel


Cycles


Maximum Acceleration versus Angle

0.00 720.00Real

°

26.00

102.00R

eal

g

0.00

1.00

Real

0.00 73000.00°

X X value at Maximum block:+Z Cyl5Accel




TL ANGLE DOMAIN

DEMONSTRATION Project: angle_data.lms


Problems where angle domain helps…

Piston Slap

Combustion Noise

False Knock detection

Injector Noise

Valve Timing


Example: Piston Slap



Pis

ton

Sla

p

Pis

ton

Sla

p

Pis

ton

Sla

p



Solution:

Offset Piston Rod


Example: Pilot Injection P

ressu

re

angle

Normal Cylinder Pressure

Pre

ssu

re

angle

Pilot Ignition Cylinder Pressure


Example: Pilot Injection P

ressu

re

angle

Pilot Ignition Cylinder Pressure

Pilot Ignition:

1.Reduces Noise

2.More gradual pressure

buildup in cylinder

(pressure rise rate)

3.More fuel combusted


PLAY PILOT

IGNITION DATA Project: angle_data.lms


Example: Pilot Ignition P

ressure

angle

How to analyze:

1.Derived channels: Differentiate

Cylinder Pressure

2. Frame Statistics AD: Take Maximum

of Differentiated data

Pre

ssure

/s

angle

Take Max


Example: Pilot Ignition


Example: Spark Timing d

B(A

) O

ve

rall

Le

ve

l

Spark Timing

degrees

0 -2 -4 -6 -8 -10 2

To

rqu

e N

/m

80

78

76

74

* Note: This is generalized graph

200

190

180

170


AMESIM ENGINE

DEMO


Resonances





Order Fundamentals


Angle Domain


RPM Fluctuation

Torsional Vibration



13.98 14.44 s

1635.46

1764.56

Am

plit

ude

rpm

F 1:Tacho1



What causes

Vertical

Lines?

1.

0.00 2000.00Hz

Point1 (CH1)

900.00

3500.00

rpm

Tacho1 (

T1)

-20.00

80.00

dB Pa


Colormap of Runup


Natural Frequency

(rad/sec)frequency naturalm

kn

Natural frequency is the frequency at which a system naturally vibrates once it

has been forced into motion

ground

m

c k

x(t)

f(t)

Single Degree of Freedom System


Resonant Frequency

Resonance is the buildup of a large amplitude that occurs when a structure is

excited at its natural frequency

ω f = 0.4 ω f = 1.01 ω f =1.6 Frequency

Am

pli

tud

e

ω n = 1.0

3 Single Degree of Freedom Systems with

same mass, stiffness and damping LMS International, A Siemens Business copyright 2013 303

Aircraft Flutter


Natural Frequency

k = 1 N/m k = 4 N/m k = 9 N/m

What will happen to the natural frequency as the beam stiffness is increased?

Assume the mass of the beam is 1 kg and the excitation frequency is constant

ωn

k

m

ωn = 1 rad/s ωn = 2 rad/s ωn = 3 rad/s

Am

pli

tud

e

Frequency


31.26 57.71s

4379.83

5019.96

Am

plit

ude

rpm

0.72

0.86

Am

plit

ude

F 6:Ring_Gear

Torsional Vibration Resonance

Torsional Vibration can be

amplified by resonance:

Crankshaft in Engine

Drive Shaft


More Resonances

Accessory brackets

Mount Brackets

Rigid Body Modes


CAE-Test Correlation


LMS Rotating Machinery 2013

Documents

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