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Surface Roughness - Standards and Uncertainty
R. Krüger-Sehm and L. Koenders
Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
Generation
- Grinding
- Honing
- Lapping
Function
- Gloss
- Paintability
- Wear
Characterisation
- Measurement
- Visualisation
- Quantification
Surfaces
Diamond turned Al surface different scales
Nomarski picture
3D picture of the AFM data obtained near the centre
Picture showing the grooves and some contamination
Diagram Wavelength vs. Amplitude - Instruments
100 nm
10 nm
1 nm
100 pm10 nm 100 nm
1 µm
1 µm 1 mm 10 mm
100 µm
10 µm
10 µm 100 µm
SEM
Light scattering (vis)
SPM
Confocal
microscope
Interference
microscope
Stylus
instrument
Wavelength
Ampl
itude
Instruments, Specimens and Procedures
Guidelines
SpecificationCalibrationEvaluationVerification
SurfaceMeasurement
Standards
SurfaceMeasurementInstruments
Standards
ISO 14 638 Geometrical product specifications(GPS) matrix model
ISO 5436-1 Standard specimen
ISO 5436-2 Software standards
ISO 4287 Definition of surface-parameters
ISO 4288 Surface properties – stylus instruments – rules and conditions
ISO 11562 Characteristics of Gauß filter
ISO 4291 Characteristics of 2RC filter
ISO 3274 Stylus instruments definitions
ISO 12179 Calibration of stylus instruments
ISO 13565-1 Filter-definition for Rk parameters
ISO 13565-2 Definition of Rk parameters
EN 10049 Measurement of Ra and RPc on metallic flat products with stochastic surface texture (skidded stylus)
EAL-G-20 Calibration of stylus instruments for measuring surface roughness
Standards for Roughness Measurement
Diagram Wavelength vs Amplitude - Standards
Dissemination of Units by Calibration Standards
Pt, D
Ra, Rz, Rsm,... Ra, Rz, Rq, ... Traceable Interference Microscope PTB
Stylus Instrument PTB
Interference Microscope
Stylus Instrument
Guidelines to support
traceability
MeasurementstandardsISO type
A
C D1, D2
established e.g. EAL G20, ISO12179
draft in VDI-committee PTB
Industry
Contact Stylus Instrument (ISO 3274), Specifications
Feature usual typical usual Lateral measuring range 20 mm 50 ...120 mm 300 mmVertical measuring range 0.3 µm 60 µm 1mm Vertical resolution 16 bit Straightness deviation @ 50 mm (Wt0) 20 nm 50 nm 100 nmNoise amplitude @ λc = 0,8 mm (Rz0) 1 nm 20 nm 30 nm Tip radius 0.1 µm 2 ... 5 µm 25 µm
x
zy
ze(x) traced profile
z0(x)instrument reference profile
feed unit
transducer
ampli-fier
A/D-conv.
para-meter
stylus tipsettingsparametersprofiletopography
zg(x) zc(x)zs(x)
l s-Filter
l c-Filter
Alternative setup
ISO 4288:
The waviness cutoff-wavelength depends on the surface specifications. In roundness and straightness measurement the separation wavelength is fixed to 0,8mm(rsp equivalent wave numbers). This must be observed in case of calculating the influence of the measured roughness in form measurement.
ISO 3274:
The primary profile contains the influence from the stylus. Further calculations do not describe the real surface, but a morphological changed one.
ISO 3274:
Applicable for stylus instruments with datum (plane). ISO 12179 allows secondary measuring systems. Practical result: standardisation of metal sheet measurement with skidded stylus systems in SEP 1940, rsp. prEN 10049.
Special Remarks
Periodic profiles
RSm in mm
Stochastic profiles
Ra in µm
Stochastic profiles
Rz in µm
Sampling length
l r in mm
evaluation length
l n in mm
Cutoff
λ c in mm
short wave-length
λ s in µm
Bandwidth
B
max. tip radius r tip
in μm
max. sampl interval
in µm
>0.013 ..0.04 >(0.006) .0.02 >(0.025) ..0.1 0.08 0.4 0.08 2.5 30 2 0.5
>0.04 ..0.13 >0.02 ..0.1 >0.1 ..0.5 0.25 1.25 0.25 2.5 100 2 0.5
>0.13 ..0.4 >0.1 ..2 >0.5 ..10 0.8 4 0.8 2.5 300 2 (5) 0.5
>0.4 ..1.3 >2 ..10 >10 ..50 2.5 12.5 2.5 8 300 5 1.5
>1.3 ..4 >10 ..80 >50 ..200 8 40 8 25 300 10 5
Excerpt of Standards:
•ISO 3274 (1996)
•ISO 4287 (1997)
•ISO 4288 (1996)
•ISO 11562 (1996)
Measurement Conditions
Calibration of Devices
Quality management: Calibration have to be done periodically
and have to be documented!
Aim, result Sample/Standard To do Noise of instrument Flat glass Determination of Rz0, Ra0, ... Straightness deviation of the datum
Flat glass Determination of Wt0
Control/correction of vertical axis/amplification
Certified depth setting standard
Determination of Ptn, Dn for position „c“; comparison with certified value
Repeatability of probing Certified depth setting standard
n repetitions of Pt at the same position
• Depth measurement standards „Type A“ according to ISO 5436 -1
• Nominal values of grooves from 20 nm to 10 µm
• Lateral width from 2 µm to 100 µm • Roughness on measurement areas
down to 1 nm • Uncertainty (k=2) between 3 nm and
25 nm
Depth Setting Standards (1)
dept
h of
pro
file
groo
ve d
epth
roug
hnes
s
width
1 2
3 4
5 6
DPt
roug
hnes
s dept
h
Depth Setting Standards (2)
Substrate: Ø ~ 50 mm, 10 mm thick
Ni-P on Ni , Hardness ~ 580 HV
Grooves ~ 0.24 µm to 75 µm
Width at groove ground 100 µm to 200 µm
• Depth measurement standards „Type A1“ according to ISO 5436 -1
• Nominal values of grooves between 1 µm and 5 mm
• Lateral sizes between 100 µm and 1mm
• Roughness on measurement areas about Rz = 20 nm
• Traceability to length unit by stylus instrument traced back by gauge block, traced back by interferometric calibration
• Uncertainty (k=2) between 25 nm and 60 nm
Depth Setting Standards (3)
Lateral calibration standard
For λc/mm 8 2,5 0,8 0,25 0,08
50 µ
m50
µm
4x
4x
4x
start on reference plane
20 µm (2x)
Feature Typical value Geom etric (type C) Depth(Rz1m ax ) 1, ..., 10 µm Period lateral (RSm ) 80, ..., 250 µm λc 250 µm ; 0.8 m m ; 2.5 m m Lateral standard (type C) Depth 5 µm Period lateral (RSm ) 25, 100, 250, 1000,
2500 µm for λc 80, 250, 800, 2500,
8000 µm
Design
Image:
Dark field
Measurement scheme
Roughness Standard Specimen
Geometrical Calibration Standard (Type C)
Feature Typical value
Geom etric (type C) Depth(Rz1m ax ) 1, ...,10 µm
Period lateral (RSm ) 80, ..., 250 µm λc 250 µm ; 0,8 m m ; 2.5 m m
Profil of geometrical standard
Roughness Calibration Standards, Specifications
Feature typical
Rz 1 ... 20 µm Ra 0.16 ... 3 µm λc 0.8 mm; 2.5 mm
Profile repetition 4 mm
starting points of the evaluation lengths in mm from the starting line
Meßstellenplan für PTB-Rauhnormale (gg), λc= 2,5 mm
Startpunkte der Meßstrecken in mm von Startlinie
richtung
Startlinie
starting line
PTB
Maßstab 5:1
Mess-
scale 5:1
Mittellinie
symmetry line
(1,2
5 m
m)
0,50 mm (11x)
0,20 mm (11x)
Roughness - Standards, Measurement Schemes
starting points of the evaluation lengths in mm from the starting line
Meßstellenplan für PTB-Rauhnormale (g, m, f), λc = 0,8 mm
0.55 4.6 8.65 12.7
Startpunkte der Meßstrecken in mm von Startlinie
richtung
Startlinie
starting line
PT
B
Maßstab 5:1
0.3
0
Mess-4.35
4.1
scale 5:1
8.4
8.15
12.5
12.2
Mittellinie
symmetry line
3 m
m3
mm
Same scale
0.0 1.0 2.0 3.0 4.0 5.0-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
Rauhnormal
μm
mm
• Roughness measurement standard „Type D2“ according to ISO 5436-1
• Nominal values of Rz = {150, 300, 450} nm, expressed in Ra between Ra = 25 nm and 80 nm
• Manufacturing by single diamond turning of digital generated profile amplitude and shape of profile predictable
• profile repetition length 1,25 mm,
• For λc = 0,25 mm
• Calibration with contact stylus instrument, traced back by depth measurement standard
• Uncertainty of calibration (k=2) ~ 6 % and 8 %,
• Approved in Round Robin of 11 DKD-laboratories
• Useable for calibration of interference microscopes, for calibration and verification
Super fine roughness standards
Nano-Roughness-Standards & Specifications
- 1-dim Profil
- Profile Repetition 5*40 µm
- Measuring length 40 µm for5 nm < Ra < 20 nm
- Scan range < 100 µm => λc
- x-y Scans => use of pictures
- Tip shape => λs
- data points < 4000 => λs
Roughness measurement
Aim, result Used standard To Do Noise of device Flat glass Determination of Rz0, Ra0, ... Control or correction of the vertical axis/amplification
Certified depth setting standard
Determination of Ptn, Dn for position „c“, Comparison with certified value
Selection of waviness filter
Roughness standard to be calibrated
Determination of Ra, Rz with λc=0,8 mm Using ISO 8288 (DIN 4768) to select λc
Determination of roughness
Roughness standard to be calibrated
Measurement plan; determination of roughness parameters and standard deviation
Estimation of measurement uncertainty
Calculation following the rules of GUM and related guides
Calibration Verification
Parameter calculation Puncertainty of roughness profil
λc-filter function Fcuncertainty of primary profil
λs-filter function Fsuncertainty of total profil
Model of Uncertainty of Roughness Parameter
Instrument function GSurface profile
uncertainty of parameter value u(K) K
=
P
{Fc
[Fs
(G
(ze (x)) ]}
x
zy
ze(x) traced profile
z0(x)instrument reference profile
feed unit
transducer
ampli-fier
A/D-conv.
para-meter
stylus tipsettingsparametersprofiletopography
zg(x) zc(x)zs(x)
l s-Filter
l c-Filter
Instrument-Function of Stylus Instrument
zg(x) = C ⋅ [ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)]
where
C Calibration factor z0 Noise of instrument
ze Contacted profile zpl Plastic deformation of surface
zg Total profile zsp Profile deviation by tip radius dev
zref Profile of reference plane
Uncertainty Budget (1)
zg(x) = C ⋅ [ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)] = C ⋅ zu(x)
where
C Calibration factor zu uncalibrated profile
Model for stylus instruments
Using the product rule
u2(zg) = u2(C) ⋅ z2u + C ⋅ u2(zu)
with with
C = Ptm/Ptn C = Dm/Dn
where where
Ptm value measured Dm value measured
Ptn value certified Dn value certified
Evaluation of Depth Setting Standardsde
pth
of p
rofile
groo
ve d
epth
roug
hnes
s
width
1 2
3 4
5 6DPt
roug
hnes
s dept
h
paraboladept
h of
pro
file
groo
ve d
epth
roug
hnes
s
width
1 2 5 6
3 4
dept
h
Pt D
roug
hnes
s
fitting
Evaluation of type A1 and type A2 depth setting standard, influence of roughness
A
A1: Reference line @ levelling 1A2: Reference line @ levelling 2A:Levelling deviationPt1: @ levelling 1Pt2: @ levelling 2
PtPt
Influence of levelling
Uncertainty Budget (2)Using the product rule u2(zg) = u2(C) ⋅ z2
u(x) + C ⋅ u2(zu) with C = Ptm/Ptn where Ptm value measured Ptn value certified
Each value is uncertain u2(Ptm), u2(Ptn) u2(C) = 1/Pt4m ⋅ [Ptn2 ⋅ u2(Ptm) + Ptm2 ⋅ u2(Ptn)]
With a calibrated instruments Ptn ≈ Ptm (C ~ 1) u2(C) = 1/Pt2m ⋅ [u2(Ptm) + u2(Ptn)]
u2(C) ⋅ zu2 = 1/Pt2m ⋅ [u2(Ptm) + u2(Ptn)]
If the depth of the standard is close to the value of the sample to be measured zu
2/Pt2m ~ 1 u2(C) ⋅ zu
2 = u2(Ptm) + u2(Ptn) u2(zg) = u2(Ptm) + u2(Ptn) + u2(zu)
Model for this valueCalibration certificate
Uncertainty Budget (3)
Model for Pt Ptm is not measured at the same position as the groove is calibrated.
Ptm = Ptn + ∆Pt + b
Track n
Track m- value of the standard at right track
- gradient of the standard ∆Pt/∆y
- repeatability of the instrument b
u2(Ptm ) = u2(Ptn ) + u2(∆Pt) + u2(b )
)(2nPts( )2
31 Gay ⋅⋅2
41
nU⋅
Uncertainty Budget (4)
Effect of λs
Measured profile has uncorrelated points. Due to filtering the points are correlated! The effect of filtering can be expressed by a factor fs [Krystek] u(zf) = fs ⋅ u(zunf) f2s = Δx/(α⋅ λs ⋅√2) where α = √log(2)/π
Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 2001 Meas. Sci. Technol. 12 63
Table for factor fs
λs in µm Δx in µm fs 2.5 0.5 0.55 8 1.5 0.53 8 0.5 0.31
Uncertainty Budget (5)Effect of λc
Similar to λs. The effect of filtering can be expressed by a factor fs [Krystek] u(w) = fc ⋅ u(zs) f2c = Δx/(α⋅ λc ⋅√2) Where α = √log(2)/π However, λc is much more larger than Δx since the uncertainty of the filtered is nearly similar to those of the unfiltered.
zc = zs – w
u2(zc) = u2(zs) + u2(w) u2(zc) = u2(zs) + f c u(zs)
Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 2001 Meas. Sci. Technol. 12 63
Table for factor fc
λc in µm Δx in µm fc 250 0.5 0.055 800 0.5 0.031 2500 1.5 0.017
Uncertainty Budget (6)
Effect of parameter function K The uncertainty of the parameter K depends on the algorithm. By the algorithm for K the uncertainty may be different to those of the single point. It is described as a “smoothing factor” S since the uncertainty is reduced in most cases. Example: usys(Rz) = S(Rz) * u(zg) Here S(Rz) is the smoothing factor!
using
Uncertainty Budget (7)
zu(x) = ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)
u2(zu) = u2(ze) + u2(zref) + u2(z0) + u2(zpl) + u2(zsp) where u2(ze) uncertainty of probed profile
⋅⋅
nRzs
S)(1 2
2
u2(zref) uncertainty of reference profile 12
20Wt
u2(z0) uncertainty due to noise of instrument ( )2
02 1211 Rz
S⋅⋅
u2(zpl) uncertainty due to plastic deformation 3
2pla
u2(zsp) uncertainty due to unknown tip shape
2
2 )(20131
⎟⎠
⎞⎜⎝
⎛⋅⋅⋅ spru
mnm
S μ
S is smoothing factor of parameter
Uncertainty of Points of Profile (1)
Ch.
Input quantity keyword
Determined by
Typical value
Sensitivity-coeff.
Method, distribution
Variance /nm2
3.1 Reference standard
2
41
nU⋅ Un = 15 nm (Cal.
certificate)
1 B Gauss
56
3.2 Deviation in localisation ( )2
31 Gay ⋅⋅ ay = 100 µm
G = 20 nm/mm
G B Rect.
1,3
3.3 Repeatability )(2nPts s = 3 nm 1 B
Gauss 9
3.4 Topography ⋅
⋅nRzs
S)(1 2
2 s(Rz) = 50
nm 1 A
Gauss 521
Chapters are given in relationship to DKD 4-2
Example for a roughness standard of type D with Rz ≈3 µm
Uncertainty of Points of Profile (2)
Ch. Input quantity keyword
Determined by Typical value
Sensitivity-coeff.
Method, distribution
Variance /nm2
3.5 Straightness datum 12
20Wt
Wt0 = 50 nm 1 B
Rect. 0
3.6 Residual noise ( )2
02 1211 Rz
S⋅⋅ nm200 =Rz 1 A
Rect. 83
3.7 Plastic deform. 3
2pla
apl = 5 nm 1 B
Rect. 8,3
3.8 Stylus tip 2
2 )(20131
⎟⎠
⎞⎜⎝
⎛⋅⋅⋅ spru
mnm
S μ
u(rsp ) = 0,5 µm
-20 nm/mm B Rect.
83
Point variance
Sum of variances )(2gzu 761,6
Point )( gzu 28 nm
Chapters are given in relationship to DKD 4-2
Uncertainty of Points of Profile (3)
Ch.
Input quantity keyword
Determined by
Typical value
Sensitivity-coeff.
Method, distribution
Variance /nm2
3.1 Reference standard
2
41
nU⋅ Un = 15 nm (Cal.
certificate)
1 B Gauss
56
3.2 Deviation in localisation ( )2
31 Gay ⋅⋅ ay = 100 µm
G = 20 nm/mm
G B Rect.
1,3
3.3 Repeatability )(2nPts s = 3 nm 1 B
Gauss 9
3.4 Topography 22
2)(1 fs
nRzs
S ⋅⋅
s(Rz) = 50 nm
1 A Gauss
130
Chapters are given in relationship to DKD 4-2
Example for a roughness standard of type D with Rz ≈3 µm
Using ls filtering!
Uncertainty of Points of Profile (4)
Ch. Input quantity
Determined by Typical value
Sensitivity-coeff.
Method, distribution
Variance /nm2
3.5 Straight-ness datum
220
12 sfWt Wt0 = 50
nm 1 B
Rect. 0
3.6 Residual noise ( ) 22
02 1211
sfRzS
⋅⋅⋅ nm200 =Rz 1 A Rect.
25
3.7 Plastic deform. 2
2
3 spl f
a⋅
apl = 5 nm 1 B Rect.
2.5
3.8 Stylus tip 22
2 )(20131
ssp frumnm
S⋅⎟
⎠
⎞⎜⎝
⎛ ⋅⋅⋅μ
u(rsp ) = 0,5 µm
-20 nm/mm B Rect.
2.5
Point variance
Sum of variances )(2szu 226,3
Point uncert.
)( szu 15 nm
Chapters are given in relationship to DKD 4-2
Using ls filtering!
u2sys(Rz) = S2 ⋅u2(zs) = (10/25)* u2(zs)
usys(Rz) = 0.6* u (zs) ~ 9 nm
Since S is smaller than 1 U(Rz) can be approximated with the coverage factor of k = 2 by
[2)( ⋅≈RzU 2
41
nU⋅ + nRzs )(2
+ 12
20Rz
+ 212 )](Rzuv
Abbreviation Uncertainty Source Determined by 2
41
nU⋅ calibration factor from calibration certificate
nRzs )(2
statistic on surface standard deviation of Rz,
n preferred 12
12
20Rz
noise flat glass roughness measurement, 12
by rectangular probability distribution
212 )](Rzuv unknown systematic
errors comparison
Comment: Approximation of starting model of uncertainty, containing the most important sources or those, which are subject to change
Uncertainty of Parameter
lamba-ctype in mm Ra Rz1max Rz Ra Rz1max RzGeometrical coarse 2,5 0,2 0,3 0,2 0,5 0,3 0,3standard coarse 0,8 0,2 0,3 0,4 0,4 0,3 0,3Type C3 medium 0,8 0,3 0,4 0,4 0,2 0,2 0,2
fine 0,8 0,4 0,3 0,4 0,5 0,3 0,5fine 0,25 0,6 0,6 0,5 0,5 0,5 0,5
number of labsRoughness very coarse 2,5 0,5 0,6 0,7 0,4 0,5 0,3standard coarse 0,8 0,5 0,6 0,5 0,5 0,5 0,4type D1 medium 0,8 0,4 0,3 0,5 0,5 0,5 0,1
fine 0,8 0,3 0,7 0,7 1,1 0,3 0,9number of labs 7 5Roughness coarse 0,25 0,3 1,3 0,5 0,6 1,5 0,6standard medium 0,25 0,3 1,2 0,8 0,4 0,8 0,7type D2 fine 0,25 0,9 2,1 1,9 1 2,4 1,9number of labs 6 4
Parameters with lamba-s Parameters without lamba-s
9 4
Comment:• Noticed are the standard deviations of the average values of parameters (excerpt)• Average over laboratories, numbers are mentioned• Labs far from average are excluded (En-criterion of EAL G7)• With λs no significant improvement of uncertainty component, even deterioration• better value in comparison with and without ls
Comparison of Roughness Parameters in DKD - Round Robin
Contribution to Uncertainty
0,5%
2,0%
0,5%
0,5%traceability
surface
noisecomparison
Expanded uncertainty of roughness parameters, e.g. Rz: ~ 3.5% of measurement value.
Contribution of Sources: