CALCULATION OF 3-D ROUGHNESS MEASUREMENT UNCERTAINTY WITH VIRTUAL SURFACES Michel Morel and Han Haitjema Eindhoven University of Technology Precision Engineering section P.O. Box 513 – W-hoog 2.107 5600 MB Eindhoven KEYWORDS: 1
Surface, Roughness, Uncertainty.
INTRODUCTION
Where it is generally agreed that 3-D roughness measurements is the most proper way of evaluating surface characteristics, the use of this technique is not yet wide-spread. This is due to the lack of instrumentation in industry, due to the lack of standardization in this field, due to the lengthy measurement time which is usually needed and due to a lack of insight in the uncertainty of 3-D roughness parameters. Where it is generally agreed that a measurement of a quantity is useless when there is no uncertainty attributed to it, the ISO standard 14253 [1] makes this an explicit requirement for any geometrical measurement in industry. In this paper it is described how an already used method for on-line evaluation of conventional 2 -D roughness uncertainty [2] has been extended to include 3-D roughness measurements as well.
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METHOD
General method The principle of the uncertainty evaluation method is that, based upon the measured profile and upon calibration results of the measured surface, an on-line uncertainty budget is made based on simulated (so-called virtual) measurements (i.e. surfaces). For each influencing factor, the difference in parameters P between the original and the virtual surface gives the standard uncertainty per parameter per influence (see figure 1). The standard uncertainty u for each influencing factor is calculated with formula 1:
P ± u=
(P
nominal
− Pnominal-u + Pnominal − Pnominal+ u 2
)
(1)
Extended Method In order to calculate the influence of flatness and noise, virtual ‘noise’ surfaces are needed. If an optical flat is measured both influences e.g. flatness and noise, are incorporated in the measurement. This surface can be used to create new virtual surfaces. New surfaces can be generated by Fourier transforming the surface, randomizing the phase and inverse transformation. However, because of edge effects, the autocorrelation in its non- periodic definition does not remain the same. This is illustrated in figure 2. E.g. when the period of a sine is not a multiple of the measurement length or the step size is not a multiple of the period, Fourier analyses spreads the power of the edge discontinuity sine over higher frequencies. Another manner to obtain ‘randomly’ different noise surfaces is by changing the sign and the orientation of the three axis. This keeps the autocorrelation constant. Each of these surface can be added. Counting the original surface, eight different surfaces can be used. The uncertainty for flatness and noise can now be calculated for each generated surface. The standard uncertainty is calculated with the squared mean taken from each uncertainty (the difference between nominal and recalculated parameters) of each surface.
Correction to nominal
Surface
Correction surface if needed
Correction to nominal + uncertainty Correction to nominal uncertainty
Calculate Parameters
Calculate Parameters
Calculate standard uncertainty with formula 1
Calculate Parameters
Figure 1. Calculation of the standard uncertainty.
Figure 2a. Generated sine, period = 220, Amplitude = 1, step = 0.1, data points = 10000.
Figure 2b. Generated sine with randomized phase, based on sine in figure 2a.
Total uncertainty Following the GUM [3], the squared sum of the different standard uncertainty gives the total standard uncertainty in the calculated parameter. This implementation of a virtual instrument differs basically from a Monte-Carlo type implementation [4] as it generates directly an uncertainty budget which gives an overview of the influences of the different uncertainties, and it requires only two simulations per influencing factor instead of some hundreds. Just the reference/ noise evaluation method requires eight simulati ons. These methods require still considerable less calculation time then the Mont-Carlo implementation.
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IMPLEMENTATION
Our concept is implemented for a Mitutoyo type SVC-624-3D roughness measuring instrument. The roughness parameters according to Sto ut [5] are calculated by own-developed software. In the simulations, the following uncertainties are considered:
•
calibration of z -axis (ordinate)
The z-a xis can be calibrated with groove and step standards. The uncertainty in the calibration factor directly influences any amplitude parameter, but not spacing parameters or dimensionless parameters.
•
calibration of x and y-axis (abcissa)
Both axis can be calibrated with an calibrated sine standard. The uncertainty in the calibration factor directly influences any spacing parameter, but hardly amplitude parameters or dimensionless parameters (only via the filtering).
•
squareness x and y-axis
The squareness can be measured with a laser interferometer or with a calibrated grid. The squareness uncertainty may unfluence any parameter as a different grid is calculated.
•
cut-off long wavelength λ c in x and y direction
To determine the actual cut-off wavelength and the actual filtering characteristics a 'moving -table' like apparatus can be used. An alternative is that a profile which contains sharp peaks is measured both filtered and unfiltered and that the amplitude spectra are compared. The filter used is the standard Gaussian filter. Both filters may influence any parameter.
•
cut-off short wavelength λ s in x and y direction
The influence of this condition depends strongly on the fine -roughness of the sample and on the used stylus-tip radius. It can be determined in basically the same way as λc.
•
stylus tip geometry
The stylus tip radius can be measured using a microscope or by measuring an uncoated razor blade. Obviously, measurements can not be re-calculated with a smaller stylus tip radius, so for this case the profile is only recalculated for a larger stylus tip. The top angle can be measured with the same method. The tip radius may influence any parameter, although the top angle’s influence depends on the fine-roughness of the sample.
•
measuring force
The measuring force can be calibrated using a balance. A proper tip and a proper measuring force should give a small regular trace in aluminum and certainly no scratch in a steel surface. Usually with steel samples, the influence of the measurement force is very small. As the plastic deformation with one trace is in the order of nm.
•
step size in X and Y direction
•
absolute flatness and noise
The step-size (or sampling rate) is taken as 1 µm here, in order to measure an equa lly spaced X and Y grid. The variation in data points is can also be used as a sort of check, to see if the used sampling rate is correct.
The absolute flatness and noise is measured with an optical flat, which is assumed perfe ctly flat when compared to the guidance.
•
software
Improper calculation and rounding errors may cause deviations. A useful method to check roughness software is to generate data -files containing signals of which the parameters can be determined analytically, such as sinusoidal, triangular and block-type surfaces. The filter-function can be checked
by Fourier analysis on both the raw and filtered surface, or by considering a peak-response in x and y direction.
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CALIBRATION AND TRACEABILLITY
All incorporated uncertainties can be calibrated and are traceable to the proper standard. It is necessary to calibrate the roughness tester ones every year in order to input the proper calibration data. Normally, only the z-axis is calibrated. Step, groove and sine sta ndards which are used to calibrate the z-axis, are not sufficient to calibrate all incorporated machine influences. In the future new calibration standards must be developed to calibrate all these influences fast and traceable.
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RESULTS
The measurements are carried out on a Mitutoyo type SVC-624-3D roughness measuring instrument. The surface measured is a PTB 015 halle standard as depicted in figure 3. As this standard is particularly developed for 1D roughness, the profile in the y-direction does no t differ. In x-direction the sample repeats each 5 cut-off wavelengths of 0.8 mm. According to 1D standards this profile would be measured with a measurement length of 6.4 mm (eight times the cut-off wavelength in order to obtain good entry and exit lengths) with a step size of 0.5 µm and processed with five cut-offs of 0.8 mm. In 2D a measurement of the same dimensions would require over 160 million data points. Instead the surface is measured with a step size in x and y direction of 1 µm and the measurement length is 1 mm. In this manner still one cut-off of 0.8 mm can be the sampling length in both directions of the 2D measurement.
Figure 3a. Processed measurement of PTB - 015 Halle standard. Sampling length and λ c are 0.8mm, λs is 2.5 mm.
Figure 3b. Autocorrelation of PTB- 015 Halle standard. nominal uncertainty u x-axis y-axis z-axis squareness x-y λc x-axis λc y-axis λs x-axis λs y-axis Radius top angle Force step size x-axis step size y-axis Flatness & noise Total
1 1 1 0° 0.80 mm 0.80 mm 2,5 µm 2,5 µm 2 µm 60 ° 0.75 mN 1 µm 1 µm 1 (1s)
1% 1% 1% 0.1 ° 2% 2% 20% 20% 50% 50% 50% 100% 100% 100%
Uncertainty Sa 0.11821 µm 0.0 nm 0.0 nm 1.18 nm 0.89 nm 0.20 nm 0.07 nm 0.44 nm 0.2 nm 0.07 nm 0.0 nm 0.1 nm 0.06 nm 0.42 nm 2.71 nm 3.16 nm
Uncertainty Sz 1.072 µm 0.0 nm 0.0 nm 10.73 nm 15.18 nm 0.23 nm 1.17 nm 6.39 nm 6.30 nm 0.21 nm 0.0 nm 0.3 nm 14.33 nm 8.42 nm 54.68 nm 60.77 nm
uncertainty Sdq 0.00269 0.00004 0.00001 0.00005 0.00019 0.0 0.0 0.0001 0.00022 0.00002 0.0 0.00001 0.00022 0.00026 0.00038 0.00059
uncertainty Ssk 0.11035 0.0 0.0 0.0 0.009 0.004 0.006 0.003 0.00001 0.00002 0.0 0.00004 0.002 0.0032 0.01 0.0125
Table 1. uncertainty budget of a PTB-015 Halle roughness standard. The results for this sample, with the uncertainty expressed as two standard deviations are: Sa Sz Sdq Ssk
= 0.11821 µm ± 6.4 nm = 1.072 µm ± 122 nm = 0.003 ± 0.0012 = 0.110 ± 0.0250
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CONCLUSION
Where this method calculates an accurate machine -surface specific uncertainty budget it opens a way for further standardization and harmonization in the measurement of 3 -D surface roughness.
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ACKNOWLEDGEMENT
This research is supported by Mitutoyo Nederland B.V.
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REFERENCES
[1] ISO 14253 -1:1998. Decision Rules for proving conformance or non-conformance with specifications. ISO, Geneva, 1998 [2] Han Haitjema and Michel Morel, ‘The concept of a virtual roughness tester’, in: M. Dietzch and H. Trumpold (ed) Proceedings X. International Colloquium on Surfaces, 31 jan-2 feb 2000, pp 239 – 244. Shaker Verlag, Aachen, 2000. [3] Guide to the Expression of Uncertainty in Measurement (GUM), ISO, Geneva, 1995 [4] H. Schwenke et al, Assessment of Uncertainties in Dimensional Metrology by Monte Carlo Simulation: Proposal of a Modular and Visual Software, Annals of the CIRP 49/1/2000, pp 395-398 [5] K.J.Stout et al, ‘The Development Methods for the Characterisation of Roughness in 3 Dimensions, Volume 1 and 2’, EC Contract No. 3374/1/0/170/90/2, March 1993. AUTHORS Ir. Michel Morel. Dr. Han Haitjema, Precision Engineering section, Faculty of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Fax +31 402473715, e-mail
[email protected] or
[email protected]
