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Frictional mechanisms in mixed lubricated regime in steel sheet metal forming
Available online at www.sciencedirect.com
Wear 264 (2008) 474–479
Frictional mechanisms in mixed lubricated regime in steel sheet metal forming Daniel Wiklund a,∗ , Bengt-G¨oran Ros´en b , Lars Gunnarsson c a
Chalmers University of Technology and Halmstad University, S-412 96 G¨oteborg, Sweden b Halmstad University, Box 823, S-301 18 Halmstad, Sweden c KIMAB, Corrosion and Metals Research Institute AB, S-114 28 Stockholm, Sweden Accepted 28 August 2006 Available online 21 February 2007
Abstract The friction is of critical importance to sheet metal forming operations. It affects the flow of material in the tool and thereby the scrap rate and final quality of products. In the experimental work the frictional response was measured in a bending under tension (BUT) test under mixed lubricated conditions. The study includes stainless steel, but previous research on carbon steels, coated and uncoated, are discussed also. The experimental results could be explained by the theory of pad bearings. The frictional response showed a correlation to the surface topography, e.g. the amplitude parameter (Sq ) and texture aspect ratio parameter (Str ). When predicting the frictional response of surfaces with multi-component distributions, the standard deviation of the distribution above the mean line could be used. © 2007 Published by Elsevier B.V. Keywords: Surface roughness; Steel sheets; Bending under tension; Mixed lubrication; Pad bearings; WC-index
1. Introduction The Swedish government has identified forming and simulation of manufacturing processes as prioritised R&D activities to support the Swedish industry. This emphasises the importance of research activities in sheet metal forming with the focus on the influence of friction. The friction in a stamping tool is an important process parameter to control the flow of material in a tool and thereby the scrap rate and final quality of a product. Consequently it is also an important parameter in numerical simulations of forming operations. However, friction models in commercial software are still based on the Coulomb’s friction model which is insufficient in sheet metal forming. A better understanding of the frictional mechanism would potentially improve the forming operation process and the precision of simulation. Furthermore, the disadvantage of almost all environmentally-
friendly lubrication alternatives is their mediocre performance. Application of advanced surface topographies could support a successful implementation of environmentally-friendly lubricants. In general, the friction mechanisms in mixed lubricated regimes are explained either by hydrodynamic and/or hydrostatic effects generated by surface asperities or void volumes in the surface. In the first approach asperities are acting as sliding bearings generating lift effects. In the second approach, cavities, pits, or holes which exist on the rough surface generate lift effects and/or act as reservoirs of lubricant which will leak out to the surrounding areas. The two approaches are not mutually exclusive, even if they are often treated that way. The objective of this study is to increase the understanding of the frictional mechanisms in mixed lubricated regime. 2. Theoretical approach
∗
Corresponding author. E-mail addresses: [email protected] (D. Wiklund), [email protected] (B.-G. Ros´en), [email protected] (L. Gunnarsson). 0043-1648/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.wear.2006.08.032
In this section, a theoretical approach to the frictional mechanism will be presented based on the theory of pad bearings, followed by micro-oil pockets.
D. Wiklund et al. / Wear 264 (2008) 474–479
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Fig. 1. The geometry of a linear pad bearing.
2.1. Pad bearings It has been shown that the friction coefficient in a mixed lubricated regime (μmix ) can be related to the friction coefficient in a boundary lubrication regime (μb ) [1,2]. Pa − Ph (1) μmix = μb Pa Pa is the apparent pressure and Ph is the pressure in the lubricant. In other words, the more load carried by the lubricant, the less is the friction coefficient. Load capacity per unit length of an infinite linear pad bearing (see Fig. 1) can be expressed as [3]: 2K W 6UηB2 = 2 2 − ln(K + 1) + (2) L K+2 h0 K where η is dynamic viscosity and K = (h1 − h0 )/h0 . In terms of non-dimensional load (W* ), Eq. (2) can be expressed as: 2K 1 ∗ W = 2 − ln(K + 1) + (3) K K+2 h20 W 6UηB2 L
(4)
In Fig. 2, load capacity, the so-called load coefficient (6W* ), is plotted versus K. The figure shows how the load capacity varies with the inclination of the bearing. The load capacity of a finite bearing is smaller and may be approximated by a correction factor ηw [4]. The correction factor is a function of ratios L/B and h1 /h0 . Some values of the factor are presented in Table 1. Table 1 The correction factor ηw [4] h1 /h0
1.5 2 5
When asperities are regarded as pad bearings in the discussion section, there are two assumptions made. Firstly, it implies cavitation in the oil. Otherwise the lubricant pressure would increases upstream of an asperity and decreases downstream. In accordance with full Sommerfeld solution, the changes of pressure would then cancel each other out. In Section 4 the Half-Sommerfeld boundary condition is assumed, i.e. the negative pressure is cancelled out by cavitation. Secondly, the hydrostatic action in the oil is assumed to be negligible in accordance with the justification of Vermeulen and Scheers [5]: - The metallic rim of a void is more likely to sustain the load than is the oil, because the compressibility is much larger for the oil than for the metal. - The pressures in sheet metal forming are quite low, restricting the possibilities for effective sealing. - The flow rate is proportional to the gap-size to power 3 which easily generates outwards flow even at low pressures. 2.2. Micro-oil pockets
where: W∗ =
Fig. 2. Variation of load capacity with convergence ratio in the linear pad bearing.
Some years ago important studies were made on cavities imprinted on sheet surfaces. These pockets, size of 1 mm × 1 mm, were filled with oil and underwent an ironing process [6–8]. The studies did show that the lubricant could be squeezed out and lubricate their boundaries to minimise direct metallic contact in the surrounding region. Based on such studies, an index was created to describe the frictional behaviour in a contact between sheet and tool [9]. The WCindex is defined as the number of isolated oil pockets (NIOPt ) multiplied by the border length of the lubricant area at the area fraction of contact (BLalfa ) and divided by the area fraction of contact (α): WCindex =
L/B 1/4
1/2
1
2
4
∞
0.055 0.06 0.085
0.17 0.18 0.23
0.42 0.44 0.48
0.69 0.69 0.72
0.835 0.84 0.87
1 1 1
NIOPt × BLalfa α
(5)
The number of isolated oil pockets are calculated only in the part of the surface which is supposed to be in contact with the tool. The index indicates the surface capacity to lubricate the contact zone. There are five steps to determine the index:
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D. Wiklund et al. / Wear 264 (2008) 474–479
Table 2 The mechanical properties and thickness of the stainless steel sheet materials Grade
Surface
t0 (mm)
316 L 304 304 304 304 304 304 304 304
2F Ground 280 2D 2B BA DB EDT rough EDT smooth EBT
0.78 0.70 0.70 0.70 0.71 0.71 0.30 0.80 0.95
Rp0.2 (MPa)
Rm (MPa)
347 307 280 307 299 284 272 279 463
A60 (%)
618 669 646 661 634 615 597 601 729
53 – – – 55 53 43 49 41
n(10–15%)
HV0.025
– – – – 0.37 0.35 0.40 0.39 0.24
219.2 410.6 202.0 221.4 233.6 237.4 206.4 211.6 270.4
Table 3 The surface topography data of the stainless steels sheets and the friction coefficient measured in the bending under tension test Surface
Sq (m)
±(95%)
Sq
±(95%)
Str (%)
c.o.f.
±(90%)
2F Ground 280 2D 2B BA DB EDT rough EDT smooth EBT
0.9916 0.3830 0.1036 0.1932 0.0352 0.1934 1.4626 0.6104 2.4142
0.0367 0.0228 0.0143 0.0068 0.0014 0.0031 0.2360 0.0425 0.0781
0.1278 0.0743 0.0257 0.0433 0.0064 0.0369 0.1770 0.0977 0.1908
0.0070 0.0076 0.0020 0.0013 0.0001 0.0004 0.0051 0.0054 0.0085
82.52 0.73 49.83 74.74 42.62 10.76 78.52 79.66 55.82
0.0697 p(0.0229)/a(0.0961) 0.0496 0.0546 0.0323 p(0.0393)/a(0.0574) 0.1081 0.0686 0.1222
0.0042 p(0.0013)/a(0.0011) 0.0039 0.0086 0.0017 p(0.0025)/a(0.0021) 0.0032 0.0051 0.0020
The denotation (p) means sliding perpendicular to surface furrows and (a) along them. A subsequent column to a parameter with the denotation ±(90%) or ±(95%) represents the confidence interval.
(1) The surface is plastically deformed in a surface indentation test (SIT). SIT is performed similarly in a traditional hardness indentation test, but the indentation tool is a flattened Brinell ball. (2) The deformed surface is topographically measured. (3) The surface is filtered with an envelope filter. (4) The area fraction of contact is calculated from the bearing area curve plotted on a normal probability paper. (5) The index is calculated, based on the 3D surfacemeasurement of the deformed surface, in Matlab.
In this study two lubricants were mixed, Castrol CR 502 (45%) and Castrol SW 4015 (55%). The sliding velocity was 100 mm/s with a back tension force set at a level which resulted in a tension in the strip of approximately 80% of the yield strength. The tool material was a quenched and tempered tool steel Calmax, radius of 5 mm, ground perpendicular to the sliding direction with a 600 # grit paper which results in a surface roughness of Ra ≈ 0.1 m.
3. Experiments
The material properties in this experimental study are shown in Table 2.
In this paper three experimental studies are discussed. The experimental procedure with data on the material properties and the surface topographies on stainless steels are shown in this paper because this is a new study. For detail information about the other two studies there are references in Section 4. 3.1. Measuring the friction coefficient The bending under tension (BUT) test was used to measure the friction coefficient. The test simulates the die profile radius conditions in a stamping tool. A steel sheet strip is bent and drawn over a cylindrical tool bar under tension. Varying tribological conditions can be controlled by varying sliding speed, contact pressure, choice and quantity of lubricant. The lubricant was applied in excess in order to reduce the influence of lubricant amount.
3.2. Material properties
3.3. Surface measurement technique and data The steel sheet surface topographies were measured with an interference microscope, WYKO RST Plus, from Veeco Instruments Inc., USA. A 2.5× objective, producing a 2.5 mm × 1.9 mm field of view with x- and y-sampling of 3.9 and 3.4 mm, respectively, was used. The surfaces were filtered with a Gaussian (robust) filter 0.25 mm × 0.25 mm. The surface topography data and the frictional response in the bending under tension test are shown in Table 3. 4. Results and discussion The objective of this study is to increase the understanding of the frictional mechanisms in mixed lubricated regime. In the first section the results of the experimental work with stainless
D. Wiklund et al. / Wear 264 (2008) 474–479
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steel are discussed on the basis of the pad-bearing theory. Then, in the next section, the WC-index is discussed and how it is related to the pad-bearing theory. 4.1. Interpretation of the frictional response with the theory of pad bearings Let us first consider the surface topography as elementary convergent and divergent planes. Then it is possible to predict a mean value of the load capacity for all elementary planes by Eq. (2). It is obvious that the model is insufficient, but it is useful as a basis for discussion. A more proper way would be to use finite element methods. The problem is that such an approach has to consider micro-EHL effects and cavitation of oil which is still not possible in this case. There is interesting research going on in that area [10]. However, the sliding velocity (U) and the dynamic viscosity (η) are held constant in the BUT tests for stainless steel. The mean exit oil-film thickness (h0 ) of the elementary planes will be proportional to the roughness of the surface. Let us use Sq (or Ra) to represent this film thickness because it is a rather stable parameter. A regression analysis of the three-dimensional RMS slope (Sq) and surface roughness (Sq ) shows a positive linear correlation of R2 = 0.89 (see Table 3). The expression of (h1 − h0 ) can be represented by the RMS slope. This implies that the K-value, which is the ratio of (h1 − h0 )/(h0 ), will show only marginal variations and, as a consequence, the load coefficient (Eq. (3)). Furthermore, if we consider the surface as a number of profiles, then the total width of elementary planes (B) will be the same since the measuring length of profiles is constant. However, the length (L) of planes will not be the same when the profiles are not identical. Then the correction factor ηw is unknown also, since the ratio L/B cannot be calculated. Consequently, there are two dominating parts in Eq. (2): the exit oil film thickness and the leakage effect but only the first one can be calculated. Two surfaces have visible furrows which means that these surfaces will definitely have longer length of the planes when the sliding direction is perpendicular to the furrows and thereby less leakage. Table 1 shows that the length of planes, the ratio of L/B, considerably influences the load capacity. In the experimental work these surfaces have been tested when sliding along as well as perpendicular to the furrows. A way to evaluate the results could be to calculate the mean of the frictional response in the two directions. If the leakage effect of the other surfaces is about the same, then a correlation to the roughness parameter would be expected. The regression plot is shown in Fig. 3. The correlation to Sq is R2 = 0.93 and is also the best. However, according to the model a correlation to the square of Sq would be expected, but then the correlation is less (R2 = 0.79) yet significant. The strong directionality shown by the anisotropic surface “Ground 280” confirms the model. The surface shows a low friction when sliding perpendicular to the furrows and high friction when sliding along (see Table 3). The surface “DB” also shows directionality, but not that strong. The texture aspect ratio parameter (Str ), a parameter based on the autocorrelation function, could be useful to predict the directionality behaviour (see
Fig. 3. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) for the stainless steel sheets.
Table 3). When the texture aspect ratio is low, about 10% in this experiment, there is an obvious directionality behaviour. This means that the texture aspect ratio parameter could be very useful to approximate the ratio of L/B and the correction factor ηw , but then a larger experimental study needs to be made. A remark about the results with surface “BA” which has a sheet roughness less than that of the tool: this means it could well be the roughness of the tool that is controlling the frictional response when testing BA. In that case there are two scenarios. Either the frictional response would be lower for BA if the tool roughness is decreased, or it could be much higher if it is too low to generate hydrodynamic effects. 4.2. The WC-index How could the results be interpreted from the perspective of the WC-index? The area fraction of contact, α, in Eq. (5), is the dominant parameter since the other two are not independent parameters. The number of oil pockets (NIOPt ) is counted in areas which are supposed to have contact with the tool. Thereby an increased contact area increases the probability of finding pockets. In addition, the probability for a longer border length of lubricant area (BLalfa ) will increase with α. The strong dependence can be seen in Fig. 4 when the index is plotted versus the α value [11].
Fig. 4. The area fraction of contact vs. the WC-index.
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Fig. 5. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) in carbon steel sheets [11]. Only one measurement of each surface, e.g. the raw data of the surface topography, has been saved from the originally study and data of three surfaces are missing altogether.
Fig. 6. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) above mean line for carbon steel sheets [11].
4.3. General comments and conclusions Consequently only the real contact area α has to be calculated to find a correlation to the friction coefficient. In fact, if the α value is plotted versus the friction coefficient, the correlation is significant at 1% level (R2 = 0.78), even if there is a mix of different textures and coatings. The surface topographies were shot blasted, electron beam-textured and electro-chromium deposition, and the materials were electrogalvanized, hot-dipped, or uncoated. The methodology to determine the area fraction of contact could also be interpreted as a way of predicting the number of elements with small enough film thickness to generate significant hydrodynamic effects. The procedure to calculate the fraction of contact means that there is a relation to the standard deviation of the distribution above the mean line. A high area fraction of contact implies that there is a low Sq -value above mean line and vice versa. In Eq. (2), the load capacity of an elementary plane is decreasing with the square of the exit oil film thickness (h0 ). For instance, if a surface has low summit slopes and deep valleys, e.g. multi-component distribution, the roughness parameter would be misleading when predicting the friction coefficient (see Fig. 5). Then, the most important parts to analyse are the summits. In fact, that is the procedure when determining the fraction of contact in the WC-index, where the valleys are excluded. That implies that the standard deviation of the distribution above the mean line could be a more suitable way to predict the friction coefficient (see Fig. 6). The measurements in Fig. 6 are from the original sheets, e.g. sheets which have not been plastically deformed in the SIT. Evidently there is a transformation of the surface topography when it is subjected to load, but the basic features are still present. Therefore the original surfaces can be evaluated relative to each other. There would be additional advantages of measuring deformed surfaces, but the elastic relaxation after the SIT test detracts from its value. Finally the result from the AUTOsurf project are presented in Fig. 7 [12]. One surface is excluded since the aspect ratio parameter (Str ) is only 25%. The surface could show directionality behaviour and the surface has only been tested in one direction. The correlation is much lower but significant at 1% level.
The experimental results could be explained by the theory of pad bearings. The frictional response showed a correlation to the surface topography, e.g. the amplitude parameter (Sq ) and texture aspect ratio parameter (Str ). When predicting the frictional response of surfaces with multi-component distributions, the standard deviation of the distribution above the mean line was more suitable. The frictional response in mixed lubricated regime is controlled by a large number of factors. However, the original surface topography is a dominating one besides oil viscosity, sliding velocity, and pressure, which were held constant in these experiments. In the study there was a mix of different materials with different hardness and coatings as well, yet a correlation to surface parameters could be found. In the experiment with the material from AUTOsurf, the correlation was lower. A plausible explanation is that the aspect ratio parameter is not enough to predict the leakage phenomena. Even isotropic surfaces can have different amounts of leakage. Large peaks, isotropic geometry in this case, will probably show less leakage than small peaks. These surfaces have shown a decreasing coefficient with increasing peaks area in a former study [12]. To improve the precision, more research is needed to predict the leakage effect of surfaces.
Fig. 7. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) above mean line for carbon steel sheets from the AUTOsurf project.
D. Wiklund et al. / Wear 264 (2008) 474–479
It was also shown that the WC-index could be interpreted with the theory of pad bearings. Furthermore, the strong directionality of anisotropical surfaces shown in the experiment with stainless steel are difficult to explain with micro-oil pockets. The contact conditions are probably not very dependent on the sliding direction. Thereby the numbers of active oil pockets in the contact zone would be of the same order. A quite constant frictional response would be expected if the leakage effects from these oil pockets would be dominating. However the basis of data are too limited in this study for definite conclusions about this. Acknowledgements The authors wish to thank all the partners in VAMP 28-project for funding and support in this work. Vinnova, Outokumpu Stainless AB, Volvo Cars, Finnveden Metal Structures AB, Linde Maskiner AB, Arcelor (Ocas), Alfa Laval Lund AB, SSAB Tunnpl˚at AB, ESS-K˚a Metall AB, Scania CV. References [1] W.C. Emmens, Tribology of Flat Contacts and Its Application in Deep Drawing, University of Twente, Twente, 1997.
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[2] G. Monfort, J. Defourny, Tribological factors in the stamping of coated and uncoated steel sheets, in: 16th IDDRG Congress, Borl¨ange, Sweden, 1990. [3] G. Stachowiak, A. Batchelor, Engineering Tribology, second ed., Butterworth-Heinmann, 2001. [4] J. Frene, Hydrodynamic Lubrication; Bearings and Thrust Bearings, Elsevier, Amsterdam\New York, 1997, p. 470. [5] M. Vermeulen, J. Scheers, Micro-hydrodynamic effects in EBT textured steel sheet, Int. J. Mach. Tools Manuf. 41 (13–14) (2001) 1941– 1951. [6] A. Azushima, M. Uda, Interpretation of the speed dependence of the friction coefficient under the micro-PHL condition in sheet drawing, in: CIRP Annals, Int. Inst. for Production Engineering Research, Palo Alto CA Berne, 1991. [7] J. Bech, N. Bay, M. Eriksen, Study of mechanisms of liquid lubrication in metal forming, CIRP Ann. Manuf. Technol. 47 (1) (1998) 221– 226. [8] J. Bech, N. Bay, M. Eriksen, Entrapment and escape of liquid lubricant in metal forming, Wear 232 (2) (1999) 134–139. [9] A. Wihlborg, L. Gunnarsson, Frictional study of uncoated EBT steel sheets in a bending under tension friction test, Wear 237 (1) (2000) 129– 136. [10] B. Nilsson, Adaptive Finite Element Methods for the Reynolds Thin Film Model with Cavitation, in Department of Applied Mechanics, Chalmers University of Technology, G¨oteborg, 2005. [11] A. Wihlborg, et al., Surface indentation test (SIT) for sheet metal, in: Proceedings of the 26th Leeds-Lyon Symposium on Tribology, 1999. [12] D. Wiklund, A. Wihlborg, B.-G. Rosen, Evaluation of surface topography parameters for friction prediction in stamping, Wear 257 (12 SPECISS) (2004) 1296–1300.
Wear 264 (2008) 474–479
Frictional mechanisms in mixed lubricated regime in steel sheet metal forming Daniel Wiklund a,∗ , Bengt-G¨oran Ros´en b , Lars Gunnarsson c a
Chalmers University of Technology and Halmstad University, S-412 96 G¨oteborg, Sweden b Halmstad University, Box 823, S-301 18 Halmstad, Sweden c KIMAB, Corrosion and Metals Research Institute AB, S-114 28 Stockholm, Sweden Accepted 28 August 2006 Available online 21 February 2007
Abstract The friction is of critical importance to sheet metal forming operations. It affects the flow of material in the tool and thereby the scrap rate and final quality of products. In the experimental work the frictional response was measured in a bending under tension (BUT) test under mixed lubricated conditions. The study includes stainless steel, but previous research on carbon steels, coated and uncoated, are discussed also. The experimental results could be explained by the theory of pad bearings. The frictional response showed a correlation to the surface topography, e.g. the amplitude parameter (Sq ) and texture aspect ratio parameter (Str ). When predicting the frictional response of surfaces with multi-component distributions, the standard deviation of the distribution above the mean line could be used. © 2007 Published by Elsevier B.V. Keywords: Surface roughness; Steel sheets; Bending under tension; Mixed lubrication; Pad bearings; WC-index
1. Introduction The Swedish government has identified forming and simulation of manufacturing processes as prioritised R&D activities to support the Swedish industry. This emphasises the importance of research activities in sheet metal forming with the focus on the influence of friction. The friction in a stamping tool is an important process parameter to control the flow of material in a tool and thereby the scrap rate and final quality of a product. Consequently it is also an important parameter in numerical simulations of forming operations. However, friction models in commercial software are still based on the Coulomb’s friction model which is insufficient in sheet metal forming. A better understanding of the frictional mechanism would potentially improve the forming operation process and the precision of simulation. Furthermore, the disadvantage of almost all environmentally-
friendly lubrication alternatives is their mediocre performance. Application of advanced surface topographies could support a successful implementation of environmentally-friendly lubricants. In general, the friction mechanisms in mixed lubricated regimes are explained either by hydrodynamic and/or hydrostatic effects generated by surface asperities or void volumes in the surface. In the first approach asperities are acting as sliding bearings generating lift effects. In the second approach, cavities, pits, or holes which exist on the rough surface generate lift effects and/or act as reservoirs of lubricant which will leak out to the surrounding areas. The two approaches are not mutually exclusive, even if they are often treated that way. The objective of this study is to increase the understanding of the frictional mechanisms in mixed lubricated regime. 2. Theoretical approach
∗
Corresponding author. E-mail addresses: [email protected] (D. Wiklund), [email protected] (B.-G. Ros´en), [email protected] (L. Gunnarsson). 0043-1648/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.wear.2006.08.032
In this section, a theoretical approach to the frictional mechanism will be presented based on the theory of pad bearings, followed by micro-oil pockets.
D. Wiklund et al. / Wear 264 (2008) 474–479
475
Fig. 1. The geometry of a linear pad bearing.
2.1. Pad bearings It has been shown that the friction coefficient in a mixed lubricated regime (μmix ) can be related to the friction coefficient in a boundary lubrication regime (μb ) [1,2]. Pa − Ph (1) μmix = μb Pa Pa is the apparent pressure and Ph is the pressure in the lubricant. In other words, the more load carried by the lubricant, the less is the friction coefficient. Load capacity per unit length of an infinite linear pad bearing (see Fig. 1) can be expressed as [3]: 2K W 6UηB2 = 2 2 − ln(K + 1) + (2) L K+2 h0 K where η is dynamic viscosity and K = (h1 − h0 )/h0 . In terms of non-dimensional load (W* ), Eq. (2) can be expressed as: 2K 1 ∗ W = 2 − ln(K + 1) + (3) K K+2 h20 W 6UηB2 L
(4)
In Fig. 2, load capacity, the so-called load coefficient (6W* ), is plotted versus K. The figure shows how the load capacity varies with the inclination of the bearing. The load capacity of a finite bearing is smaller and may be approximated by a correction factor ηw [4]. The correction factor is a function of ratios L/B and h1 /h0 . Some values of the factor are presented in Table 1. Table 1 The correction factor ηw [4] h1 /h0
1.5 2 5
When asperities are regarded as pad bearings in the discussion section, there are two assumptions made. Firstly, it implies cavitation in the oil. Otherwise the lubricant pressure would increases upstream of an asperity and decreases downstream. In accordance with full Sommerfeld solution, the changes of pressure would then cancel each other out. In Section 4 the Half-Sommerfeld boundary condition is assumed, i.e. the negative pressure is cancelled out by cavitation. Secondly, the hydrostatic action in the oil is assumed to be negligible in accordance with the justification of Vermeulen and Scheers [5]: - The metallic rim of a void is more likely to sustain the load than is the oil, because the compressibility is much larger for the oil than for the metal. - The pressures in sheet metal forming are quite low, restricting the possibilities for effective sealing. - The flow rate is proportional to the gap-size to power 3 which easily generates outwards flow even at low pressures. 2.2. Micro-oil pockets
where: W∗ =
Fig. 2. Variation of load capacity with convergence ratio in the linear pad bearing.
Some years ago important studies were made on cavities imprinted on sheet surfaces. These pockets, size of 1 mm × 1 mm, were filled with oil and underwent an ironing process [6–8]. The studies did show that the lubricant could be squeezed out and lubricate their boundaries to minimise direct metallic contact in the surrounding region. Based on such studies, an index was created to describe the frictional behaviour in a contact between sheet and tool [9]. The WCindex is defined as the number of isolated oil pockets (NIOPt ) multiplied by the border length of the lubricant area at the area fraction of contact (BLalfa ) and divided by the area fraction of contact (α): WCindex =
L/B 1/4
1/2
1
2
4
∞
0.055 0.06 0.085
0.17 0.18 0.23
0.42 0.44 0.48
0.69 0.69 0.72
0.835 0.84 0.87
1 1 1
NIOPt × BLalfa α
(5)
The number of isolated oil pockets are calculated only in the part of the surface which is supposed to be in contact with the tool. The index indicates the surface capacity to lubricate the contact zone. There are five steps to determine the index:
476
D. Wiklund et al. / Wear 264 (2008) 474–479
Table 2 The mechanical properties and thickness of the stainless steel sheet materials Grade
Surface
t0 (mm)
316 L 304 304 304 304 304 304 304 304
2F Ground 280 2D 2B BA DB EDT rough EDT smooth EBT
0.78 0.70 0.70 0.70 0.71 0.71 0.30 0.80 0.95
Rp0.2 (MPa)
Rm (MPa)
347 307 280 307 299 284 272 279 463
A60 (%)
618 669 646 661 634 615 597 601 729
53 – – – 55 53 43 49 41
n(10–15%)
HV0.025
– – – – 0.37 0.35 0.40 0.39 0.24
219.2 410.6 202.0 221.4 233.6 237.4 206.4 211.6 270.4
Table 3 The surface topography data of the stainless steels sheets and the friction coefficient measured in the bending under tension test Surface
Sq (m)
±(95%)
Sq
±(95%)
Str (%)
c.o.f.
±(90%)
2F Ground 280 2D 2B BA DB EDT rough EDT smooth EBT
0.9916 0.3830 0.1036 0.1932 0.0352 0.1934 1.4626 0.6104 2.4142
0.0367 0.0228 0.0143 0.0068 0.0014 0.0031 0.2360 0.0425 0.0781
0.1278 0.0743 0.0257 0.0433 0.0064 0.0369 0.1770 0.0977 0.1908
0.0070 0.0076 0.0020 0.0013 0.0001 0.0004 0.0051 0.0054 0.0085
82.52 0.73 49.83 74.74 42.62 10.76 78.52 79.66 55.82
0.0697 p(0.0229)/a(0.0961) 0.0496 0.0546 0.0323 p(0.0393)/a(0.0574) 0.1081 0.0686 0.1222
0.0042 p(0.0013)/a(0.0011) 0.0039 0.0086 0.0017 p(0.0025)/a(0.0021) 0.0032 0.0051 0.0020
The denotation (p) means sliding perpendicular to surface furrows and (a) along them. A subsequent column to a parameter with the denotation ±(90%) or ±(95%) represents the confidence interval.
(1) The surface is plastically deformed in a surface indentation test (SIT). SIT is performed similarly in a traditional hardness indentation test, but the indentation tool is a flattened Brinell ball. (2) The deformed surface is topographically measured. (3) The surface is filtered with an envelope filter. (4) The area fraction of contact is calculated from the bearing area curve plotted on a normal probability paper. (5) The index is calculated, based on the 3D surfacemeasurement of the deformed surface, in Matlab.
In this study two lubricants were mixed, Castrol CR 502 (45%) and Castrol SW 4015 (55%). The sliding velocity was 100 mm/s with a back tension force set at a level which resulted in a tension in the strip of approximately 80% of the yield strength. The tool material was a quenched and tempered tool steel Calmax, radius of 5 mm, ground perpendicular to the sliding direction with a 600 # grit paper which results in a surface roughness of Ra ≈ 0.1 m.
3. Experiments
The material properties in this experimental study are shown in Table 2.
In this paper three experimental studies are discussed. The experimental procedure with data on the material properties and the surface topographies on stainless steels are shown in this paper because this is a new study. For detail information about the other two studies there are references in Section 4. 3.1. Measuring the friction coefficient The bending under tension (BUT) test was used to measure the friction coefficient. The test simulates the die profile radius conditions in a stamping tool. A steel sheet strip is bent and drawn over a cylindrical tool bar under tension. Varying tribological conditions can be controlled by varying sliding speed, contact pressure, choice and quantity of lubricant. The lubricant was applied in excess in order to reduce the influence of lubricant amount.
3.2. Material properties
3.3. Surface measurement technique and data The steel sheet surface topographies were measured with an interference microscope, WYKO RST Plus, from Veeco Instruments Inc., USA. A 2.5× objective, producing a 2.5 mm × 1.9 mm field of view with x- and y-sampling of 3.9 and 3.4 mm, respectively, was used. The surfaces were filtered with a Gaussian (robust) filter 0.25 mm × 0.25 mm. The surface topography data and the frictional response in the bending under tension test are shown in Table 3. 4. Results and discussion The objective of this study is to increase the understanding of the frictional mechanisms in mixed lubricated regime. In the first section the results of the experimental work with stainless
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steel are discussed on the basis of the pad-bearing theory. Then, in the next section, the WC-index is discussed and how it is related to the pad-bearing theory. 4.1. Interpretation of the frictional response with the theory of pad bearings Let us first consider the surface topography as elementary convergent and divergent planes. Then it is possible to predict a mean value of the load capacity for all elementary planes by Eq. (2). It is obvious that the model is insufficient, but it is useful as a basis for discussion. A more proper way would be to use finite element methods. The problem is that such an approach has to consider micro-EHL effects and cavitation of oil which is still not possible in this case. There is interesting research going on in that area [10]. However, the sliding velocity (U) and the dynamic viscosity (η) are held constant in the BUT tests for stainless steel. The mean exit oil-film thickness (h0 ) of the elementary planes will be proportional to the roughness of the surface. Let us use Sq (or Ra) to represent this film thickness because it is a rather stable parameter. A regression analysis of the three-dimensional RMS slope (Sq) and surface roughness (Sq ) shows a positive linear correlation of R2 = 0.89 (see Table 3). The expression of (h1 − h0 ) can be represented by the RMS slope. This implies that the K-value, which is the ratio of (h1 − h0 )/(h0 ), will show only marginal variations and, as a consequence, the load coefficient (Eq. (3)). Furthermore, if we consider the surface as a number of profiles, then the total width of elementary planes (B) will be the same since the measuring length of profiles is constant. However, the length (L) of planes will not be the same when the profiles are not identical. Then the correction factor ηw is unknown also, since the ratio L/B cannot be calculated. Consequently, there are two dominating parts in Eq. (2): the exit oil film thickness and the leakage effect but only the first one can be calculated. Two surfaces have visible furrows which means that these surfaces will definitely have longer length of the planes when the sliding direction is perpendicular to the furrows and thereby less leakage. Table 1 shows that the length of planes, the ratio of L/B, considerably influences the load capacity. In the experimental work these surfaces have been tested when sliding along as well as perpendicular to the furrows. A way to evaluate the results could be to calculate the mean of the frictional response in the two directions. If the leakage effect of the other surfaces is about the same, then a correlation to the roughness parameter would be expected. The regression plot is shown in Fig. 3. The correlation to Sq is R2 = 0.93 and is also the best. However, according to the model a correlation to the square of Sq would be expected, but then the correlation is less (R2 = 0.79) yet significant. The strong directionality shown by the anisotropic surface “Ground 280” confirms the model. The surface shows a low friction when sliding perpendicular to the furrows and high friction when sliding along (see Table 3). The surface “DB” also shows directionality, but not that strong. The texture aspect ratio parameter (Str ), a parameter based on the autocorrelation function, could be useful to predict the directionality behaviour (see
Fig. 3. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) for the stainless steel sheets.
Table 3). When the texture aspect ratio is low, about 10% in this experiment, there is an obvious directionality behaviour. This means that the texture aspect ratio parameter could be very useful to approximate the ratio of L/B and the correction factor ηw , but then a larger experimental study needs to be made. A remark about the results with surface “BA” which has a sheet roughness less than that of the tool: this means it could well be the roughness of the tool that is controlling the frictional response when testing BA. In that case there are two scenarios. Either the frictional response would be lower for BA if the tool roughness is decreased, or it could be much higher if it is too low to generate hydrodynamic effects. 4.2. The WC-index How could the results be interpreted from the perspective of the WC-index? The area fraction of contact, α, in Eq. (5), is the dominant parameter since the other two are not independent parameters. The number of oil pockets (NIOPt ) is counted in areas which are supposed to have contact with the tool. Thereby an increased contact area increases the probability of finding pockets. In addition, the probability for a longer border length of lubricant area (BLalfa ) will increase with α. The strong dependence can be seen in Fig. 4 when the index is plotted versus the α value [11].
Fig. 4. The area fraction of contact vs. the WC-index.
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Fig. 5. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) in carbon steel sheets [11]. Only one measurement of each surface, e.g. the raw data of the surface topography, has been saved from the originally study and data of three surfaces are missing altogether.
Fig. 6. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) above mean line for carbon steel sheets [11].
4.3. General comments and conclusions Consequently only the real contact area α has to be calculated to find a correlation to the friction coefficient. In fact, if the α value is plotted versus the friction coefficient, the correlation is significant at 1% level (R2 = 0.78), even if there is a mix of different textures and coatings. The surface topographies were shot blasted, electron beam-textured and electro-chromium deposition, and the materials were electrogalvanized, hot-dipped, or uncoated. The methodology to determine the area fraction of contact could also be interpreted as a way of predicting the number of elements with small enough film thickness to generate significant hydrodynamic effects. The procedure to calculate the fraction of contact means that there is a relation to the standard deviation of the distribution above the mean line. A high area fraction of contact implies that there is a low Sq -value above mean line and vice versa. In Eq. (2), the load capacity of an elementary plane is decreasing with the square of the exit oil film thickness (h0 ). For instance, if a surface has low summit slopes and deep valleys, e.g. multi-component distribution, the roughness parameter would be misleading when predicting the friction coefficient (see Fig. 5). Then, the most important parts to analyse are the summits. In fact, that is the procedure when determining the fraction of contact in the WC-index, where the valleys are excluded. That implies that the standard deviation of the distribution above the mean line could be a more suitable way to predict the friction coefficient (see Fig. 6). The measurements in Fig. 6 are from the original sheets, e.g. sheets which have not been plastically deformed in the SIT. Evidently there is a transformation of the surface topography when it is subjected to load, but the basic features are still present. Therefore the original surfaces can be evaluated relative to each other. There would be additional advantages of measuring deformed surfaces, but the elastic relaxation after the SIT test detracts from its value. Finally the result from the AUTOsurf project are presented in Fig. 7 [12]. One surface is excluded since the aspect ratio parameter (Str ) is only 25%. The surface could show directionality behaviour and the surface has only been tested in one direction. The correlation is much lower but significant at 1% level.
The experimental results could be explained by the theory of pad bearings. The frictional response showed a correlation to the surface topography, e.g. the amplitude parameter (Sq ) and texture aspect ratio parameter (Str ). When predicting the frictional response of surfaces with multi-component distributions, the standard deviation of the distribution above the mean line was more suitable. The frictional response in mixed lubricated regime is controlled by a large number of factors. However, the original surface topography is a dominating one besides oil viscosity, sliding velocity, and pressure, which were held constant in these experiments. In the study there was a mix of different materials with different hardness and coatings as well, yet a correlation to surface parameters could be found. In the experiment with the material from AUTOsurf, the correlation was lower. A plausible explanation is that the aspect ratio parameter is not enough to predict the leakage phenomena. Even isotropic surfaces can have different amounts of leakage. Large peaks, isotropic geometry in this case, will probably show less leakage than small peaks. These surfaces have shown a decreasing coefficient with increasing peaks area in a former study [12]. To improve the precision, more research is needed to predict the leakage effect of surfaces.
Fig. 7. The friction coefficient vs. the amplitude parameter RMS deviation (Sq ) above mean line for carbon steel sheets from the AUTOsurf project.
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It was also shown that the WC-index could be interpreted with the theory of pad bearings. Furthermore, the strong directionality of anisotropical surfaces shown in the experiment with stainless steel are difficult to explain with micro-oil pockets. The contact conditions are probably not very dependent on the sliding direction. Thereby the numbers of active oil pockets in the contact zone would be of the same order. A quite constant frictional response would be expected if the leakage effects from these oil pockets would be dominating. However the basis of data are too limited in this study for definite conclusions about this. Acknowledgements The authors wish to thank all the partners in VAMP 28-project for funding and support in this work. Vinnova, Outokumpu Stainless AB, Volvo Cars, Finnveden Metal Structures AB, Linde Maskiner AB, Arcelor (Ocas), Alfa Laval Lund AB, SSAB Tunnpl˚at AB, ESS-K˚a Metall AB, Scania CV. References [1] W.C. Emmens, Tribology of Flat Contacts and Its Application in Deep Drawing, University of Twente, Twente, 1997.
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[2] G. Monfort, J. Defourny, Tribological factors in the stamping of coated and uncoated steel sheets, in: 16th IDDRG Congress, Borl¨ange, Sweden, 1990. [3] G. Stachowiak, A. Batchelor, Engineering Tribology, second ed., Butterworth-Heinmann, 2001. [4] J. Frene, Hydrodynamic Lubrication; Bearings and Thrust Bearings, Elsevier, Amsterdam\New York, 1997, p. 470. [5] M. Vermeulen, J. Scheers, Micro-hydrodynamic effects in EBT textured steel sheet, Int. J. Mach. Tools Manuf. 41 (13–14) (2001) 1941– 1951. [6] A. Azushima, M. Uda, Interpretation of the speed dependence of the friction coefficient under the micro-PHL condition in sheet drawing, in: CIRP Annals, Int. Inst. for Production Engineering Research, Palo Alto CA Berne, 1991. [7] J. Bech, N. Bay, M. Eriksen, Study of mechanisms of liquid lubrication in metal forming, CIRP Ann. Manuf. Technol. 47 (1) (1998) 221– 226. [8] J. Bech, N. Bay, M. Eriksen, Entrapment and escape of liquid lubricant in metal forming, Wear 232 (2) (1999) 134–139. [9] A. Wihlborg, L. Gunnarsson, Frictional study of uncoated EBT steel sheets in a bending under tension friction test, Wear 237 (1) (2000) 129– 136. [10] B. Nilsson, Adaptive Finite Element Methods for the Reynolds Thin Film Model with Cavitation, in Department of Applied Mechanics, Chalmers University of Technology, G¨oteborg, 2005. [11] A. Wihlborg, et al., Surface indentation test (SIT) for sheet metal, in: Proceedings of the 26th Leeds-Lyon Symposium on Tribology, 1999. [12] D. Wiklund, A. Wihlborg, B.-G. Rosen, Evaluation of surface topography parameters for friction prediction in stamping, Wear 257 (12 SPECISS) (2004) 1296–1300.