surf roughnes parameters & calibration

8/13/2019 Surf Roughnes Parameters & Calibration

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Surface Texture Parameters

Average Parameters

Height Parameters

Spacing Parameters

Hybrid Parameters

Functions


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Amplitude Parameters

R a ..Roughness Average (also AA and CLA)R q...Root mean square roughness (also RMS)

R ti

RtRoughness Total

R ymax (Ry) (Rmax)

R tm..Roughness Peak

R p...Roughness Peak

R pi

P pm.Roughness Peak Mean

R pymax (R pmax ) (R py)

R v..Roughness Valley

R vi.

R vm..Roughness Valley Mean

R vymax (R vmax ) (R vy)

R 3z..

R 3y (R 3ymax ) (R 3max )

R 3i.

R z..Ten Point Height Mean

RHR..Roughness Height RangeR sk Skew

R kuKurtosis


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HtpHeight between Bearing Ratios

H..Swedish Height

R & W consisting of 4 mean values:

R

Ar

W...

Aw.

4 maximum values:

Pt.

W tWmax.

Aw..

Two different surfaces with the same R a


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Surface Finish Definitions


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Mean Line

The mean line is defined as the line which bisects the profile such thatthe area above and below the line equal and a minimum.

Terminology

Typical for an analog filter


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Typical for an digital filter:

Sampling length = Cut-off = Filter Cut-Off

For unfiltered measurement.

Sampling Length = Assessment Length

R q

R q...Root Mean Square Roughness Average

Older terms: RMS ...Root Mean Square, Still widely used in some industries (i.e. optical)

R q is the Root Mean Square of the distance of the filtered or

unfiltered Roughness Profile from its mean line.

Rq is the standard Deviation of the Amplitude Density Distribution.

Because this Parameter squares Amplitudes it is more sensitive to peaks and valleys.


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Analog Systems

Digital Systems

Continuous:

Discrete:

Advantage: Statistically very stable.

Disadvantage: Only available in middle to higher priced instruments.

WARNING: R q. is not 11.1% higher than R a

=

==

N i

ii y

1

2q

N1

R

Where L is the assessment length and N is the number of Data points

R q

=L

0

2 )(L1

Rq dx x y

R a

R a: Roughness Average

Older terms: AAArithmetrc Average

R a is the Arithmetic Average of the distance of the filtered or unfiltered Roughness profile from its Mean Line


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dx x y = L0a |)(|L1

R

=

==

N i

i

y1

ia || N1

R

Analog Systems

Digital Systems

Continuous:

Discrete:

Where L is the assessment length and N is the number of Data points

Advantages: Statistically very stable parameter.Easy and cheap to implement into instrumentation.Good for random type surfaces (Processes like grinding)

Disadvantages: Not a good discriminator for different types of surfacesLooses its usefulness when skew (Rsk) exceeds 1.5

WARNING: Ra is not the same as RMS (Rq).

Adding 11.1% to the Ra reading, or calibrating the instrument11.1% higher is incorrect except for sinusoidal surfaces

R a

Rt, Rp, Rv

Rt: Total Roughness Rp: Roughness Peak Rv: Roughness Valley

Rt is the highest Peak to the lowest Valley in the assessment length

Rp is the highest Peak in the assessment length Rv is the lowest Valley in theassessment length

All three Parameters can be used Filtered or Unfiltered In Filtered Mode Rp andRv do not have to be in the same sampling length

R t = R p + R v


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Rt, Rp, Rv

These Parameters are essentially divergent as there is no guarantee that theMeasurement Line crosses the extremes of the surface.

For this reason these Parameters tend to vary considerably on multiple measurements.

Large errors of measurement can also be introduced when using a Skidded Instrumentin the presence of significant or isolated Peaks or dirt.

Peaks are important in the study of Friction and Wear as the interaction betweensurfaces concentrates around them.

Presence of Peaks can make dimensional measurements on Parts subjected to Wearunreliable, as the Wear removes the Peaks, which were originally included in themeasurement.

Valleys are significant for Lubrication properties.

Propagation of Fractures and Corrosion start in valleys.

R ti, R tm, R ymax , R pm, R vi, R vm, R vmax

The averaging used for these Parameters makes them more stable than pure extreme values .

R ti: is the maximum peak-to-valley height in the sampling length i.

R tm: is the mean of all the R ti values obtained within the assessment length.


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R ymax : is the largest R ti value within the assessment length.

R ymax (ISO) = R max (DIN) = R y (RTH)

R ti, R tm, R ymax , R pm, R vi, R vm, R vmax

=

==+++==

ni

inn 1ti

tnt3t2t1Ztm R

1.....R ..........R R R (DIN)R R

Where n is the number of sampling length or cut-offs.

R pi: is the maximum peak height in the sampling length i.

R pm : is the mean of all the R pi values obtained within the assessment length.

=

==

ni

in

1 pi

1 pm R R

R ti, R tm, R ymax , R pm , R vi, R vm, R vmax

R pmax = R p is the largest R pi value within the assessment length.

R vi: is the maximum valley depth in the sampling length i.

R vm: is the mean of all the Rvi values obtained within the assessment length.

=

==

ni

in

1 pi

1 pm R R

R vmax = R v Is the largest Rvi value within the assessment length.


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R 3z, R 3y, R 3i, R 3ymax , R 3max .R 3z was originally developed in Germany, with the intent to reduce the instability of

the Peak Parameters by ignoring Profile extremes.

R 3yi The deviation from the third highest peak to the third lowest valley in thesample length I, where vertical and horizontal thresholds have to be exceeded.

R 3ymax Is the highest R 3yi within the assessment length .

In order to streamline the parameter description with the R ymax Paramater oneshould assume that :

R 3ymax (ISO) = R 3max (DIN) = R 3y (RTH)R 3z Is the mean of all the R3yi values obtained within the assessment of length.

n

R .....R R R

n1

R 323231

33 yn y y

ni

i yi z

+++==

=

=

R ku Kurtosis

Can detect if Profile "Spikes" are evenly distributed above and below the Mean Line.

It provides a measure of the sharpness of the Surface Profile or ADF.

Spiky surfaces have a high Kurtosis value R ku>3, bumpy surfaces have a low

kurtosis value R ku


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R sk

R sk ..Skew R sk - Skew - is the measure of the symmetry of the Profile about the Mean Line.

It will distinguish between asymmetrical Profiles of the same R a, R q, R tm, R ymax , R t.

Negative Skew indicates a predominance of valleys, while positive Skew will be seen on"peaky" surfaces.

Typically:

Plateau Honing R sk negativeGrinding ..R sk zeroTurning, Bead Blasting R sk positive

dx y x y L 3

03q

sk ])([LR 1R

=

3

13q

sk )(R 1

R =

== y y

n

ni

ii

Continuous:

Digital:

Analog Systems

Digital Systems

Negative Skew Positive Skew

R sk

If R sk exceeds 1.5, R a should not be used as the only control Parameter.

This condition also indicates that Phase Corrected Filter should be used.

Surfaces with positive R sk can give large measurement errors if Instruments with Skidsare used.

R sk is a non-dimensional parameter


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R zi, R zy, R z, R zm

The original intent in creating the R z Parameter was to allow the measurement of veryshort surfaces, where by choosing a cut-off length to suit the available surface, theinformation lost due to the filtering makes this prohibitive.

R z is also known as the ISO 10 point height parameter.

It is measured on the unfiltered profile only

It is numerically the average height difference between the five highest peaks and thefive lowest valleys within the assessment length, where vertical and horizontalthresholds have to be exceeded.

Presently there is an ongoing heated discussion whether the Rz parameter shouldactually be filtered or unfiltered.

This led to the Rzm parameter, which now logically has to extend to R zi and R zymax(or R zmax or R zy).

5

)YYYY(Y)YYYYY((ISO)R v5v4v3v2v1 p5 p4 p3 p2 p1z

++++++++=


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Spacing Parameters

S Mean Local Peak Spacing

Sm..Mean Peak Spacing

HSCHigh Spot Count

PC...Peak Count

K-Factor.Randomness

SS...... is the mean spacing between adjacent local peaks, measured over theassessment length. (A local peak is the highest part of the profile measured between twoadjacent minima, and is only included if the distance between the peak and its precedingminima is at least 1% of the R t of the profile.

Where n is the number of peak spacings.


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SmSm....... is the mean spacing between profile peaks at the mean line, measured overthe assessment length. (A profile peak is the highest point of the profile between anupwards and a downwards crossing of the profile of the mean line.)

Where n is the number of peak spacings.

HSC

HSC...... The high spot count is the number of complete profile peaks (withinthe assessment length) projecting above the mean line, or a line parallel with themean line. This line can be set at a selected depth below the highest peak or aselected distance above or below the mean line.

HSC is always expressed in number of counts per assessment length.

This parameter has been found useful in applications where the penetrat ion of asperities through athreshold can be critical. A typical example would be peaks exceeding a flight height level for memorydisks. Peaks that are to high can cause a crash of the reading head.


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PcPc...... The peak count is the number of local peaks which project through aselectable band centered about the mean line. The count is determined onlyover the assessment length though the results are given in peaks per cm (or perinch). The peak count obtained from assessment lengths of less than one cm(or 1 inch) is obtained by using a multiplication factor. The parameter shouldtherefore be measured over the greatest assessment length possible.

This parameter is mostly used in the USA. It has been found extremely

useful for painting, forming and plating applications.

HYBRID PARAMETERSt p % Bearing Ratio, Material Ratio

Mr .DIN Symbol for t p %

R k For describing the Material Portion in the roughness Profile divides into the followingParameters:\

R k Core Roughness DepthR pk ..Reduced Peak HeightR vk .Reduced Valley DepthM r1 Material Component relative to PeaksM r2.Material Component relative to ValleysA1...Mater ial filled Profile Peak Area

A2Lubricant filled Profile Valley Area

aAverage Wavelengthq.RMS Average Wavelength

a..Average Slope

q.RMS Average Slope


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Material Ratio CurveThe Material rat io curve, formerly called Abbot-Firestone curve or Bearing ratio curve, is a graphicalrepresentation of the tp parameter in relation to the profile level. This curve contains all theamplitude information of a profile. It is a close relative to t he amplitude density function (Integrat ionof the ADF yields the material ratio curve.As the shape of t his function varies significantly relative to different processes the description of it'sshape can provide very detailed information about a surface profile. See Rsk, Rku and RK

parameters.

The abscissa can be displayed in two ways:

As a linear axis (see above picture).As a cumulative Gaussian probability axis.

This is particularly useful for random surfaces as the plot beco mes a straightline. For the assessment of multiple processed parts, with the individual

processes being Gaussian each process is shown as a straight line.


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a q Average wavelength, is a measure of the spacings between local peaks andvalleys,

taking into account their relative amplitudes and individual spacialfrequencies.

Being a hybrid parameter, determined from both amplitude and spacinginformation,it is,, for some applications, more useful than a parameter based solely on

amplitude or spacing.

For a profile that is not sinusoidal this parameter must not be confused withtrue spacing parameters like S or Sn.

Average wavelength takes every point of the profile into account.

a q (contd)Average wavelength can be particularly useful in applications where the presence of certain harmonics on parts changes with time of usage.

Closely spaced irregularities of a surface are normally of a relatively smallamplitude, but wear rapidly with the part being used like in roller or ball

bearings or rotational or reciprocational friction applications.

This leaves the lower frequency components of the surface more dominant.

In process control average wavelength is useful to monitor the condition of grindingwheels, as it relates to the average grit size.

In turning the condition of the tool edge and machine feeds can be monitored.

Average wavelength is related to the power spectrum and represents an estimate ofthe weighted mean of the Fourier spectrum.


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a qAverage slope is the mean (arithmetic or rms) of the slopes at all the po ints of a profile within

the assessment length.

The slope of a profile is the angle (expressed as a gradient) between that profile and the meanline.

Being the slope of the profile at a given point.

These parameters have been found useful in assessing contact, optical and frictional propert iesas there is a relation to hardness, elasticity, electrical and thermal conductivity, plastic andelastic deformation, reflectivity, friction, adhesion and others.

Average slope is also used to compute t rue profile length (See appropriate sheet).

These parameters are sensitive to t he numerical model used in computing slopes. Large

differences in computed values can show between different instruments .

n: The shaded area is computed (Area3)

o: R vk is calculated as the height of the triangle with an area equal to the shaded Area3.

The base of this triangle is DF.... which is 100 - M r2.

o: Shows R vk exceeding below the lowest valley of the profile.

This is correct, it can, but it does not happen all the time.

It is also possible that R pk goes higher than the highest profile peak.

Adding up R pk + R K + R vk does NOT equal R t.


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Now we can finally put it all together into one single picture:

This parameter att empts to numerically evaluate the material ratio curve of surfaces manufacturedwith a process resulting in a negative skew.

The processes that this parameter relates to in particular are Plateau Honing, Lapping and all kinds ofmultiple machining operations which intend to remove peaks but leave larger valleys from a previous process.

The parameter originated in Germany and has been implemented in the Automotive Industry.

A strong argument as to the validity of RK and it's associated parameters is continuing, but if theIndustry asks for it - We got it.

The way R k is derived is essentially twofold:

1 ... A special filtering technique is applied which is intended to minimize the residual distort ions ofthe filtered profile still existing after phase corrected filters have been applied.

2...From this roughness profile the Material Ratio curve (former Abbott-Firestone or Bearing Ratiocurve) is computed and the R K parameters are extracted from this.


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Gaussian Plotting of Material Ratio Graph

The process t ransition point helps in putting a numerical surface finish value to different functional

parts of the surface. The profile height between say 0.05% material ratio (to ignore stray extremes) andthe process transition point is approximately four times R q.

Reference:Whitehouse D.J. Assessment of surface finish profiles produced by multi -process manufacture.Proc Instn Mech Engrs 1985 Vol 199 No B4 p.263-270


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Surface Texture Symbols

0.030

0.015

cut-off

Lay

Max RoughnessSpacing

0.002.-263

32

Max Waviness WidthMax Waviness Height

Max R a

Min R a

Surface may be produced by any method

Material removal by machining is required;Material must be provided for that purpose.

Material removal allowance in inches(or millimeters)

Material removal prohibited

0.001


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Calibration with the aid of Roughness Standards

Carry out 12 measurements on each roughness standard, distributed over the measurementsurface as shown in the measuring points pattern (Figure 2).

Calculate the arithmetical mean for each roughness parameter.

Give the deviations from the mean values stated in the PTB calibration certificate in percent andmicrons.


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NIST Calibration Procedure

4000 Data points

2RC Filter

Measured at 9 locations

Each measurement repeated twice

PTB Calibration ProcedureStylus instrument - Complete instrument combination (2)

Measuring Rz in 5 profile sections on a flat glass and stating the arithmetical mean(5.1).

Measuring with depth setting standard (5.2)

Probing each groove of the depth setting standard 5 times, as per measurementlocation pattern (figure 1)

Finding the mean value from 5 measurements each grove.

Determining the deviation of t he arithmetical mean from the Pi value for the groovespecified in t he PTB calibration certificate, in percent and microns.

Measuring with roughness standard (5.3)

Each roughness standard is probed 12 times, as per measurement location pattern(figure 2)

Determining the mean value from 12 measurements per roughness standard for Ra,Rz, Rmax.

Determining the deviation of the arithmetical mean from the Ra, Rz, Rmax valuesspecified in the appropriate PTB calibration certificates for the roughness standard,in percent and microns, and the respective uncertainties of the measurement.

The instrument can be calibrated if the deviations do not exceed three times theuncertainty of the measurement of the standard stated.

Preparing the calibration certificate as per sample certificate.


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Measurement Practice

Parameter Variation

Vibration

Gage R & R


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Repeatability and within-sample variation

22

ve EV +=

surf roughnes parameters & calibration

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