SCANNING VOL. 32, 244–249 (2010) & Wiley Periodicals, Inc.
On Discovering Relevant Scales in Surface Roughness Measurement— An Evaluation of a Band-Pass Method J. BERGLUND1, C. AGUNWAMBA2, B. POWERS3, C. A. BROWN3
Sandvik Tooling, R & D Center Olofstro¨m, Olofstro¨m, Sweden Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, Massachusetts 3 Surface Metrology Lab, Worcester Polytechnic Institute, Worcester, Massachusetts 4 Functional Surfaces Research Group, Halmstad University, Halmstad, Sweden 2
Summary: When characterizing surfaces and searching for correlations to functional properties, such as friction, ﬁnding the right scale of roughness for evaluation can improve correlations. However, in traditional roughness parameter analysis, a wide range of scales, or all scales of topography in the surface roughness measurements are evaluated together. In this study a multi-scale method using a series of band-pass ﬁlters is employed for ﬁnding scales of topography with strong correlations to friction. SCANNING 32: 244–249, 2010. r 2010 Wiley Periodicals, Inc.
Key words: metrology, surface roughness, multiscale analysis, band-pass ﬁlter, friction
Introduction There are several methods available to characterize surfaces using roughness measurements. The general objective of the characterization is to measure and analyze the surface topography to get an understanding of how the topography has been inﬂuenced by previous events; for example, manufacture or wear and how the surface topography inﬂuences its function (Williams 2005). Topographical data in a surface measurement contains information on wide range of scales, from the smallest features detectable by the instrument to larger features, the size of which is limited by the Address for reprints: J. Berglund, Va¨llaregatan 30, 29338 Olofstro¨m, Sweden E-mail: [email protected]
measurement area. A major difﬁculty, in general, when characterizing surfaces is the lack of information on the scale of surface topography responsible for different functions or effects (Thomas 1999). In a stamping tool, friction is an important process parameter which controls the ﬂow of material in the tool and the ﬁnal quality of produced parts. The friction in the stamping tool is affected by the surface roughness (Wiklund et al. 2008). However, because of the complexity of the stamping process with regard to the multitude of tribological conditions in the tool during operation, it is not obvious which scales of surface roughness are important for a well functioning process. Surfaces are commonly characterized using some roughness parameter, such as Ra (average roughness), after the data has been ﬁltered using some ﬁlter with a standard cutoff. This calculated parameter is then correlated with some function or process parameter. Following this procedure, all scales of topography in the surface roughness measurements are evaluated together. The relevant scales are evaluated together with the irrelevant scales, which may lead to weaker correlations. Multi-scale methods have been used to improve such functional correlations by employing; for example, scale-sensitive fractal analysis (Berglund and Rose´n 2009, ASME B46 2002). In this study, the objective was to evaluate a method employing a band-pass ﬁlter with varying bandwidth and center wavelength for ﬁnding correlations between a functional property of interest and surface roughness data at the most appropriate scale or range of scales.
Received 28 November 2009; Accepted with revision 12 January 2010
Materials and Methods
DOI 10.1002/sca.20168 Published online 2 February 2010 in Wiley Online Library (wiley onlinelibrary.com)
The method used to ﬁnd correlations between surface roughness data and the functional property was a series of band-pass ﬁlters together with surface
J. Berglund et al.: An evaluation of a band-pass method roughness parameters. As reference, a traditional surface roughness parameter analysis was conducted. The software MountainsMap (version 22.214.171.12474) from Digital Surf was used to calculate all surface roughness parameters. All parameters available in the software from the new standard (ISO/DIS 25178-2) were used. Some of the parameters have conﬁgurable options and are presented with the settings used, the default settings in the software, see Table I. For the band-pass ﬁlters, combinations of lowpass and high-pass gaussian ﬁlters were used
(Muralikrishnan and Raja 2009). A low-pass ﬁlter is ﬁrst applied using the upper wavelength cutoff, luc. Then, that result is ﬁltered with a high-pass ﬁlter at the lower wavelength cutoff, llc, as shown in Figure 1. The cutoffs refer to the wavelength where the ﬁlter has approximately 50% transmission. The resulting overall 50% cutoff for the new ﬁlter is slightly different from the original speciﬁcations. This is caused by the resulting multiplication of the previous two ﬁlters in the frequency domain. Thus, it is difﬁcult to specify the overall cutoff for this method.
TABLE I Surface roughness parameters (ISO/DIS 25178-2) Parameter Sdr Sdq Vvv (p 5 80%) Smr (c 5 1 mm under the highest peak) Sxp (p 5 50%, q 5 97.5%) Sa Smc (p 5 10%) Sq Vmc (p 5 10%, q 5 80%) Vv (p 5 10%)
Vvc (p 5 10%, q 5 80%) Spc (pruning 5 5%) Ssk Spd (pruning 5 5%) Sv Str (s 5 0.2) Sz Sp Sda (pruning 5 5%) Sal (s 5 0.2)
S5v (pruning 5 5%) Sku S10z (pruning 5 5%) S5p (pruning 5 5%) Sdv (pruning 5 5%) Vm (p 5 10%) Vmp (p 5 10%) Std Shv (pruning 5 5%) Sha (pruning 5 5%)
Fig 1. A low-pass ﬁlter (A) is combined with a high-pass ﬁlter (B) to create a band-pass ﬁlter (C).
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In this study, three different bandwidths were used: 20, 50 and 100 mm. These band-pass ﬁlters were used with a range of center wavelengths from 10 to 180 mm in increments of 10 mm. In the example shown in Figure 1, the band-pass ﬁlter with bandwidth 20 mm and center wavelength 100 mm was constructed using a low-pass ﬁlter with cutoff 90 mm and a high-pass ﬁlter with cutoff 110 mm. Surface roughness measurements were made using a white light interferometer. The instrument used was a Wyko RST Plus from Veeco Instruments at magniﬁcation 10 , giving a measurement area of 577 mm (x) 428 mm (y) as well as a lateral sampling of 0.785 mm (x and y). To reduce the statistical uncertainty, three measurements were made on each surface. The functional property in this study is friction from tribotesting of sample surfaces using the Bending Under Tension (BUT) test method. The BUT test represents mild tribological conditions with medium normal pressure, low sliding length and no surface expansion (Bay et al. 2008). In this test method, the metal sheet strip is bent around a nonrotating tool pin (the sample surface of this study) while it is clamped in two claws. Pulling the strip with the front claw while breaking the back claw with a controlled force ensures sliding of the strip around the pin under controlled back tension. The torque on the tool pin is measured and the friction coefﬁcient can be calculated (Bay et al. 2008). The sheet metal used in the testing was DP600 with surface roughness Ra 1 mm and thickness 1 mm. The amount of lubrication was checked on every sheet strip to be approximately 1 g/m2. Three workpiece materials were used for the tool pins in this study:
TABLE II Summary of the tool pin combinations Tool pin
1 2 3 4 5 6
GGG70L GGG70L Carmo Carmo Sleipner Sleipner
Low High Low High Low High
TABLE III Results from BUT tests, mean coefﬁcient of friction (m) and standard deviation (s) Tool pin 1 2 3 4 5 6
0.140 0.150 0.133 0.141 0.137 0.161
0.001 0.005 0.002 0.002 0.001 0.003
Examples of surface roughness measurements are presented in Figures 2 and 3, the cylindrical form has been removed.
Surface Roughness Parameters
Surface roughness parameters were calculated for all surfaces. However, ﬁrst the cylindrical form was removed and the roughness data was levelled. No other ﬁltering was done. The roughness parameters were correlated with the friction data using linear regression. The correlation coefﬁcients, R2, are presented in Table IV below. As can be seen, two fairly strong correlations were found with the parameters Sdr (R2 5 0.72) and Sdq (R2 5 0.70).
GGG70L (EN-JS-2070), cast nodular iron Carmo, tool steel from Uddeholm Tooling Sleipner, tool steel from Uddeholm Tooling
Machine tool used for machining the sample surfaces for the experiments was a Hermle C40U Dynamic, a 5 axis machining center with a Capto C5 spindle interface and a spindle capable of 24000 RPM. A variation of the cutting data was used to produce surfaces with different levels of roughness. A summary of the tool pin combinations is given in Table II.
The surfaces were ﬁltered using all combinations of ﬁlter parameters (bandwidth and center wavelength). After that, surface roughness parameters were calculated and correlations were calculated using linear regression. The strongest correlation (R2 5 0.94) was reached with the parameter Sa using two ﬁlters:
Bandwidth 50 mm with center wavelength 20 mm Bandwidth 100 mm with center wavelength 10 mm
The frictional data obtained in the BUT test is presented in Table III. Three tests were performed with each tool pin. The results are presented as mean values with respective standard deviation.
The four roughness parameters with the strongest correlations are shown in Figure 4 (A)–(D). Also, relatively strong correlations (R240.75) were found with the parameters Sdr, Sdq, Vv, Vmc, Vvc and
J. Berglund et al.: An evaluation of a band-pass method
Fig 2. Example surface roughness measurement (tool pin 2) with cylindrical form removed.
Fig 3. Example surface roughness measurement (tool pin 3) with cylindrical form removed.
Vvv, with similar patterns in the plots as the ones presented in Figure 4. In each plot, the results from ﬁlters with the three different bandwidths (20, 50 and 100 mm) are presented as functions of the ﬁlter center wavelengths. Examples of the same surfaces as in Figures 2 and 3 ﬁltered using the band-pass ﬁlter with bandwidth 50 mm and center wavelength 20 mm are presented in Figures 5 and 6.
Discussion In the traditional parameter analysis, all scales of topography in the surface roughness measurements
TABLE IV Correlation coefﬁcients, R2, for correlations between some surface roughness parameters and friction Parameter Sdr Sdq Vvv Smr Sxp Sa Smc Sq Vmc Vv
R2 0.72 0.70 0.31 0.29 0.29 0.19 0.17 0.17 0.16 0.16
Parameter Vvc Spc Ssk Spd Sv Str Sz Sp Sda Sal
R2 0.15 0.12 0.11 0.09 0.06 0.04 0.04 0.02 0.02 0.01
Parameter S5v Sku S10z S5p Sdv Vm Vmp Std Shv Sha
R2 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00
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Fig 4. (A–D) Correlation coefﬁcients, R2, for the four roughness parameters with the strongest correlation to friction. In each plot, the results from ﬁlters with three different bandwidths (20, 50 and 100 mm) are presented as functions of the ﬁlter center wavelengths.
Fig 5. Surface of Figure 2 (tool pin 2) ﬁltered using the band-pass ﬁlter with bandwidth 50 mm and center wavelength 20 mm.
are evaluated together. With the band-pass ﬁlters, ranges of scales of the topography in the measurements are evaluated separately. A comparison between the correlations found using the traditional parameter analysis (two parameters with R240.7) with the correlations found using band-pass ﬁlters (10 parameters with R240.75, of which 6 parameters with R240.9) shows that stronger correlations were found employing the band-pass ﬁlters. This demonstrates that the correlations that can be
found between the functional parameter of interest and the surface topography are dependent on the scale of observation. In the present work, there will be no effort made to explain the tribological phenomena responsible for the correlations found between coefﬁcient of friction and the surface topography of the tool pins. However, one can note that other works have shown that the surface topography, together with the lubricant, creates hydrodynamic effects which
J. Berglund et al.: An evaluation of a band-pass method
Fig 6. Surface of Figure 3 (tool pin 3) ﬁltered using the band-pass ﬁlter with bandwidth 50 mm and center wavelength 20 mm.
inﬂuence the friction greatly (Wiklund et al. 2008). What is shown in this study is that it is likely that these effects are more present at a certain scale of topography of the tool surface. Scales with a center wavelength near 30 mm appear to have these highest correlations at all tested bandwidths. A traditional high-pass ﬁlter with a cutoff of 80 mm would probably produce similar results. However, with such method one would not know of the correlations which could possibly be found at other scales.
Conclusions Using surface roughness parameters, such as the ones available in the new ISO standard, for characterization of surfaces can give good results and, in some cases, strong correlation between a particular parameter and some functional property of interest. However, together with an appropriate ﬁlter, producing roughness data limited in scale, more parameters can be used for characterization and stronger correlations can be found.
Additionally, scales of interests can be identiﬁed for each parameter and conclusions can be drawn about scales of relevance.
References ASME B46. US National Standard ASME B46.1 Surface Texture (Surface Roughness, Waviness, and Lay). The American Society of Mechanical Engineers, New York (2002). Bay N, Olsson DD, Andreasen JL: Lubricant test methods for sheet metal forming. Tribol Int 41, 844–853 (2008). Berglund J, Rose´n B-G: A method development for correlation of surface ﬁnish appearance of die surfaces and roughness measurement data. Tribology Lett 36, 157–164 (2009). ISO/DIS 25178-2. Geometrical product speciﬁcations (GPS)—Surface texture: Areal - Part 2: Terms, deﬁnitions and surface texture parameters. http://www.iso.org Muralikrishnan B, Raja J: Computational Surface and Roundness Metrology, Springer, London (2009). Thomas TR: Rough Surfaces 2nd ed., Imperial College Press, London (1999). Wiklund D, Rose´n B-G, Gunnarsson L: Frictional mechanisms in mixed lubricated regime in steel sheet metal forming. Wear 264, 474–479 (2008). Williams J: Engineering Tribology, Cambridge University Press, Cambridge (2005).