filters and harmonics

5/28/2018 Filters and Harmonics

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Filters andHarmonics


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Undulations Per Revolution

(UPR)

Filters and Harmonics

Undulations Produced by Manufacturing Process


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Undulations Per Revolution

(UPR)


UPR = Harmonics

A profile Showing a Dominant 8th

and 60th Harmonic


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What is an Harmonic?


1st Harmonic (Eccentricity)

2nd Harmonic (Ovality)

5th Harmonic

0

0

0

360

360

360

Harmonic Amplitude

1

1 2

1 2 3 4 5


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Harmonics


A Roundness profile

Showing a 3rd Harmonic

The 3rd Harmonic Shown as

a Waveform

Harmonic Amplitude

Harmonic Amplitude


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Harmonics


90

0180

270

Component

centre

Datum

Axis

1st Harmonic (Eccentricity)


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Harmonics


2nd Harmonic (Ovality)

90

0180

270


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Harmonics


3rd Harmonic (Tri-Lobed)

90

0180

270


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Harmonics


3rd Harmonic (Tri-Lobed)

0

90

180

270

Wheel

Wheel

Centreless Grinding


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Harmonics


4th Harmonic

Distortion on a Cylinder bore


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Harmonics


Higher Order Harmonics

Produced by Machine Tool Chatter


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Filters


Filters are Used to Separate Different Harmonics


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Filters


Unfiltered Profile

A profile Showing a Dominant 8th

and 60th Harmonic


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Filters


Standard Filter Values

1-15 UPR

1-50 UPR

1-150 UPR

1-500 UPR


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Filters


1-15 UPR Filter

60th Harmonic Has Been Removed


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Filters


15-500 UPR Filter

8th Harmonic Has Been Removed


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2CR Filter


Reduces the Amplitude of the Harmonic at the

selected UPR Value by 25%

Fil d H i


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Characteristics of a 2CR Filter


1-50 UPR Filter

Filt d H i


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Characteristics of a 2CR Filter


15-500 UPR Filter

Filt d H i


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Effects of a 2CR Filter


An Unfiltered Profile

Filt d H i


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1-500 UPR

Filt d H i


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1-150 UPR

Filt d H i


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1-50 UPR

Filt d H i


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1-15 UPR



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Gaussian Filter


Profile

Filter

Weighting Function

Mean line

Unfiltered profile

Harmonic Value

X

Z

Reduces the Amplitude of the Harmonic at the

selected UPR Value by 50%



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Characteristics of a Gaussian

Filter


1-50 UPR Filter



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Characteristics of a Gaussian

Filter


15-500 UPR Filter



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Filters Continued


The Gaussian Filter

Unfiltered Profile



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Filters Continued


The Gaussian Filter

1-500 UPR



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Filters Continued


The Gaussian Filter

1-150 UPR



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Filters Continued


The Gaussian Filter

1-50 UPR



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Filters Continued


The Gaussian Filter

1-15 UPR



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Filters Continued


Comparison of the Gaussian Filter and 2CR Filter

1-15 UPR 2CR Filter 1-15 UPR Gaussian Filter



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Filters - Stylus Tip Diameter


Tip Diameter Must Be

Considered When

Selecting Filters



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Tip Diameter Selection / Filter

Selection


Part Diameter (mm)Circumferential Filter Cut-off

(UPR)

D < 8 1-15

D < 8 < 25 1-5025 < D < 80 1-150

80 < D < 250 1-500

250 < D 1-1500

The above table shows the recommended filter to use according to component size

(ISO 12180-2)



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Filter Selection


The formula shows the recommended filter to use according to component size

(ISO 12181-2)

UPR = d0.8Where: d = Part Diameter



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Tip Diameter Selection


See ISO 12180-2 for further information

R= d24

Where: R = Stylus Tip Radius

d = Part Diameter



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Harmonic Analysis


6000 RPM

x100 RPM

Component

Wheel Eccentricity

Grinding Wheel



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Harmonic Analysis


x

60:1 Speed Ratio

Induces a 60th

Harmonic



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Harmonic Analysis


1st Harmonic - Function of MeasurementMeasurementSet-up Erro r2nd Harmonic - Function of Measurement or Manufacture

MeasurementSet-up Error or Machin ed ou t of Square3rd to 7th Harmonic - Function of Manufacture

Workpiece Hold ing Method

7th to 15th Harmonic - Function of Manufacture

Instabi l i tyof the Machin ing Process15th Harmonic Upwards - Function of Material & Manufacture

Reactio n o f Materials, Machine Chatter



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Harmonic Analysis


Roller Bearing Assembly

Race containing

16 Rollers

Surface with 16th

Harmonic



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Harmonics Amplitude Display


RONt 1.54m, Ecc 0.43m, Conc 0.85m



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Harmonics Histogram Display

RONt 1.54m, Ecc 0.43m, Conc 0.85m



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Harmonic Analysis

Different Profiles - Identical Roundness

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