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Modified 2D stylus profilometry and its application to frictional analyses in sheet metal forming operations
Tribology International 32 (1999) 553–558 www.elsevier.com/locate/triboint
Modified 2D stylus profilometry and its application to frictional analyses in sheet metal forming operations K.R. Gilmour *, S.J. Paul, M.R. Boyd, M.T.J. Ashbridge, A.G. Leacock School of Electrical and Mechanical Engineering, University of Ulster, Shore Road, Newtownabbey BT37 0QB, UK Received 11 October 1999; accepted 28 October 1999
Abstract Frictional conditions at contact interfaces can have a large influence on the success of some sheet metal forming operations. Topographic surface characterisation is a useful tool for obtaining data necessary for some tribological analyses, and it is proposed that a standard two-dimensional (2D) profilometer can be modified to provide inexpensive three-dimensional (3D) data without any significant loss of performance. A scanning white light interferometer is used to verify this hypothesis, and the results show that while the new profilometry technique is less accurate at low contact areas, it is sufficiently accurate for some purposes. Surface maps are created and the results used to calculate the real contact areas, bearing area curves and hydrodynamic lift pressures for a drawing-quality steel. 2000 Published by Elsevier Science Ltd. All rights reserved. Keywords: Topography; Forming; Hydrodynamic
1. Introduction Sheet metal forming operations typically involve the transfer of high forces through the tool/blank interface to deform the workpiece plastically to the required shape. Some forming operations, for example deep drawing, are particularly sensitive to frictional conditions at the various contact interfaces. Accurate numerical modelling and simulation of such a process requires an intimate knowledge of these conditions, which means having adequate means to predict the coefficients of friction at the interfaces during the operation. In a process such as deep drawing, modelling even only one contact interface — for example, the blankholder/blank interface — becomes very complex [1]. Many examples of work in this area can be found in recent literature. Studies on the effects of surface hardness [2] and roughness [3] have been attempted, along with research on lubrication and surface finish [4]. The effects of the real area of contact have also been examined [5,6]. The coefficient of kinetic friction at some point on an
* Corresponding author. Fax: +44-1232-366804. E-mail address: [email protected] (K.R. Gilmour).
interface, at an arbitrary time during the process, is a complex function of process variables, lubrication conditions and material characteristics. Material characteristics itself covers several variables, such as hardness and surface roughness. This paper covers the use of surface roughness data in the study of friction in the deep drawing process. Several techniques have been developed over the years to quantify the topography of metallic surfaces. These can be split broadly into two categories: contact (profilometry) and non-contact (interferometry) methods. Generally, non-contact methods are seen as faster and more accurate than profilometry techniques, and this is certainly true when both are used within their design limits. Obviously, it is of interest to both the academic and the industrialist to obtain sufficiently representative surface data at minimum cost. Interferometry systems are, however, prohibitively expensive compared with the cost of buying a two-dimensional (2D) profilometer and modifying the techniques in using it to obtain threedimensional (3D) surface data. It was hypothesised that a modified 2D profilometry technique would be sufficiently accurate for the purposes of assessing the surface characteristics of a drawingquality steel, and using these data to calculate quantities relevant to frictional analyses in deep drawing, such as
0301-679X/99/$ - see front matter 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 1 - 6 7 9 X ( 9 9 ) 0 0 0 8 5 - 7
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K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
real contact area, resistance to viscous flow and hydrodynamic lift pressure. To verify this, a non-contact scanning white light interferometer was used to check the data.
2. 3D surface topography characterisation using modified 2D stylus profilometry and scanning white light interferometry The idea of modifying the 2D profilometry technique to allow 3D surface mapping is not new, and has been used previously [7]. It is now generally accepted that the use of multiple parallel traces is a useful method of surface characterisation [8], and in the analysis of surfaces loaded with low contact pressures (in the region of 3 MPa) the large population of data decreases the probability of not sampling over low contact areas and asperity peaks. This is important because the typical pressures under the blankholder of a deep drawing press are relatively low. The modification is made by providing a conventional 2D profilometer with an indexing table, giving the extra planar direction and three degrees of freedom. A schematic view of the new system can be seen in Fig. 1. The stylus has a tip radius of 10 µm, and the voltage output is sent through an analogue-to-digital converter and thence to a data acquisition set-up on a personal computer. Displacement velocities and sampling rates can be defined by the user within the software, and the output is in the form of ASCII data. The main drawback with this system is that the current design forces the raising and lowering of the stylus between each parallel trace, and because all displacement values are taken from a datum on the lowest point on each individual trace, there is an inherent variation in the raw data. Although this introduces inaccuracies, an attempt can be made to compensate by first using a least-squares technique to normalise the sets of traces
and then expressing all height values relative to a common centre line. For validation of the experimental accuracy of this technique, the measured areas were scanned and characterised by a Zygo New-View 100, a non-contact interferometer. Combining the techniques of scanning white light interferometry (SWLI) with a conventional phaseshifting interferometer, this machine allows analysis down to a resolution of 0.1 nm.
3. Experimental and analytical procedures The material used in the tests was a 1.5 mm thick drawing-grade mild steel (BS 1449 part 1: Type CR4GP). Prior to scanning, the specimens were cleaned with a trichloroethane solution and then with a pressurised nitrogen gas stream. To avoid the possibility of any damage caused by surface wear of the profilometer’s stylus, the specimen surface was scanned first with the non-contact system. The scanned area, for both methods, was 2.8 mm×2.1 mm, and four different areas were scanned with each technique to minimise experimental error. The sample spacing for the interferometer was 8.8 µm, giving 75 930 data points on the specimen, and the profilometer allowed a sample spacing of 10 µm, providing 58 800 data points. After the scans had been completed the normalisation and compensating techniques described earlier were applied. As a visualisation aid, these surface data were extracted to a commercial software package and the surfaces shown in Figs. 2 and 3 were created. Fig. 2(a) and (b) show, respectively, the filled contour plots for the profilometry and interferometry techniques. Fig. 3(a) and (b) displays the same data, but in the form of a 3D surface plot. Only one area plot is shown as the others were very similar. While these provide excellent visual data, and illustrate the close similarity of the two techniques, they do not permit quantitative comparison. For this, the data must be analysed in other ways.
4. Bearing area curves
Fig. 1.
The modified 2D stylus profilometer.
First used in 1933 [9], the bearing area curve allows an assessment of the distribution of height values about the centre line of the surface. The curve is created by truncating the surface data for each plot at the centre line, and expressing the number of points truncated as a percentage of the total number of sampled points. The bearing area curves for each of the four sampled areas are presented in Fig. 4. The percentage bearing area, plotted against the height above the centre line, is shown for both techniques. These plots reveal a consistently small difference in the values obtained. Assuming that
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
555
Fig. 2. Filled contour plots: (a) contact result; (b) non-contact result.
Fig. 3. 3D surface plots: (a) contact result; (b) non-contact result.
the non-contact technique is the more accurate, the profilometry method slightly overestimates the height values near high bearing areas and underestimates them near low bearing areas. The explanation for this difference is most likely a combination of two reasons:
5. Resistance to viscous flow and hydrodynamic lift pressure
In the deep drawing operation, lubrication regimes at the contact interfaces vary from boundary lubrication to partial hydrodynamic, or mixed, lubrication. Crucial to an understanding of these is the knowledge of how the lubricant flows from the interface between the blank and the blankholder. The ‘Flow Factor Method’ [10,11] presents a useful model, and two main mechanisms of flow are developed to describe the process. Poiseuille flow is the pressure flow factor; a measure of the influence of surface roughness on lubricant flow. Couette flow is the shear flow factor; the velocity-driven component which is also influenced by the surface topography. Given the loading conditions and material properties we can use the topographical data to predict the real area of contact, and with this information it is then possible to calculate the distribution of the load between the asperities and the lubricant pockets. The authors used the finite difference method to create a program that solved the Reynolds equation for isoviscous conditions:
Surface mapping has a practical use for tribological analyses in its application to the study of lubricant flow.
∂ ∂p ∂ 3 ∂p h · ⫹ h3 ⫽0, ∂x ∂x ∂y ∂y
1. residual dirt particles missed in the cleaning process will have the effect of creating artificially high asperity peaks as scanned by the interferometry technique; and 2. the necessary method of trace alignment to allow 3D profilometry scanning will act as a smoothing filter for the data, causing a slight reduction in some of the height values measured.
冉 冊 冉 冊
(1)
556
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
Fig. 4.
Bearing area curves for sampled areas.
where h is the clearance height and p is the contact pressure. An initial grid spacing of 20 µm was employed, the calculated solution was equated to that through a flat parallel clearance space and an effective clearance height was found. To validate this technique a simple test rig, shown in Fig. 5, was designed to allow measurement of the resistance to viscous flow to be made. The oil in the cylinder is pressurised with the aid of an accumulator to keep
the pressure constant throughout the test. The lubricant leaked from the simulated blank/blankholder interface is collected over a period of time and the calculation of flow rate for a given pressure can be made. Hydrodynamic lift pressure arises from the draginduced flow of lubricant into the clearance space, and because cavitation prevents the creation of a negative pressure in the diverging parts of the clearance space, a net positive pressure results. A finite difference solution to the Reynolds equation:
冉 冊 冉 冊
∂ 3 ∂p ∂p ∂ ∂h h · ⫹ h3 ⫽6h·V , ∂x ∂x ∂y ∂y ∂x
(2)
provides a map of the pressure distribution over the surface. The numerical solution must also account for ‘carry-over flow’ in the regions of cavitation. Integration of the pressure distribution provides the total lift force. 6. Results
Fig. 5. Leakage test rig.
Fig. 6 shows the application of the finite difference solutions introduced earlier. Again, it is seen that the profilometry technique slightly underestimates the
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
557
7. Conclusions
Fig. 6.
Finite difference solution.
height, although the difference is within acceptable limits. It is also evident that, apart from the low contact areas, the difference in the two methods is constant; evidence of the slight filtering effect of the modified profilometry technique. The results shown in Fig. 6 are representative of those for all four samples. The difference observed can be accounted for with the resolution scales of the two techniques. The profilometry method is limited by the radius of the stylus tip, whereas the interferometer is limited by the wavelength of the light — orders of magnitude less. Fig. 7 shows a comparison of the experimentally determined effective clearance height and that obtained with the solutions to Eq. (1) — note that the graph does not show the 0,0 origin. The model shows good agreement with experiment; it is accurate throughout the measured range and within the small amount of experimental scatter. Using the same techniques, Eq. (2) was solved to measure the effect of the hydrodynamic lift pressure. Assuming process conditions in the region of 3 MPa blankholder pressure and 5–50 mm/s drawing velocity, the lift pressure was found to be extremely small — typically around 1% of the blankholder contact pressure. This is not significant for normal drawing velocities and lubricants, but it is possible that it may have an effect under a higher speed and viscosity.
Fig. 7.
Comparison of experimental data and calculated results.
A standard two-dimensional surface profilometer was modified to allow three-dimensional analyses. To validate this technique, a scanning white light interferometer was employed to verify the data, and these techniques were used in surface characterisation for frictional analyses. The following conclusions can be made. There is good general agreement between the two techniques and the measured results are consistently close to each other. The modified profilometry technique proves to be less accurate at extremely low contact areas, but this discrepancy is an inherent feature in the system. The discrepancies can be explained as a combination of hardware limitations and the effect of having to establish a common centre line in the use of multiple parallel traces. The use of analytical techniques in predicting real contact areas from the measured surface topography data has been validated experimentally. The measured data agree well with the predicted values and are all within experimental scatter. These analytical techniques were used to calculate the hydrodynamic lift pressure at the contact interfaces, but the results showed the effect to be negligible. Typical values were found to be around 1% of the blankholder pressure. To conclude, modified 2D profilometry has shown, as was expected, that it falls short of the accuracy of techniques like interferometry. What has been shown, however, is that the inaccuracies are within acceptable limits for some applications and it can provide useful data for a fraction of the cost of other methods. Used for the collection of data for use in frictional analyses in sheet metal forming operations, modified 2D profilometry is a useful, and comparatively inexpensive, solution to both industrial and academic laboratory needs.
References [1] Schey JA. Friction laws in metal forming tribology. In: Tribology in metalworking: friction, lubrication and wear. Ohio, USA: ASM International, 1983. [2] Reid JV. The effect of surface hardness on friction. Wear 1987;118:113–25. [3] Emmens WC. The influence of surface roughness on friction. Proceedings of IDDRG Workgroup Meeting 1998. General, Benelux. [4] Bello DO, Walton S. Surface topography and lubrication in sheet metal forming. Tribol Int 1987;20(2):59–65. [5] Wilson WRD. Real area of contact and boundary friction in sheet metal forming. J Mech Eng Sci 1988;30(7):475–89. [6] Klimczak T. Analysis of real contact area and change of surface texture on deep drawn steel sheets. Wear 1994;179:129–45. [7] Thomas TR. Rough surfaces. London: Longman Group, 1982. [8] Contet PH, Ville JF. Surfascan 3D — an industrial 3D surface characterisation instrument. Int J Mach Tools Manuf 1992;3(1/2):157–69.
558
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
[9] Abbot EJ, Firestone FA. Specifying surface quality: a method based on accurate measurement and comparison. Mech Eng 1933;55:569–73. [10] Patir MR, Cheng HS. An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication. ASME J Lubric Technol 1978;100:12–7.
[11] Tripp JH. Surface roughness effects in hydrodynamic lubrication — the flow factor method. ASME J Lubric Technol 1983;105:458–65.
Modified 2D stylus profilometry and its application to frictional analyses in sheet metal forming operations K.R. Gilmour *, S.J. Paul, M.R. Boyd, M.T.J. Ashbridge, A.G. Leacock School of Electrical and Mechanical Engineering, University of Ulster, Shore Road, Newtownabbey BT37 0QB, UK Received 11 October 1999; accepted 28 October 1999
Abstract Frictional conditions at contact interfaces can have a large influence on the success of some sheet metal forming operations. Topographic surface characterisation is a useful tool for obtaining data necessary for some tribological analyses, and it is proposed that a standard two-dimensional (2D) profilometer can be modified to provide inexpensive three-dimensional (3D) data without any significant loss of performance. A scanning white light interferometer is used to verify this hypothesis, and the results show that while the new profilometry technique is less accurate at low contact areas, it is sufficiently accurate for some purposes. Surface maps are created and the results used to calculate the real contact areas, bearing area curves and hydrodynamic lift pressures for a drawing-quality steel. 2000 Published by Elsevier Science Ltd. All rights reserved. Keywords: Topography; Forming; Hydrodynamic
1. Introduction Sheet metal forming operations typically involve the transfer of high forces through the tool/blank interface to deform the workpiece plastically to the required shape. Some forming operations, for example deep drawing, are particularly sensitive to frictional conditions at the various contact interfaces. Accurate numerical modelling and simulation of such a process requires an intimate knowledge of these conditions, which means having adequate means to predict the coefficients of friction at the interfaces during the operation. In a process such as deep drawing, modelling even only one contact interface — for example, the blankholder/blank interface — becomes very complex [1]. Many examples of work in this area can be found in recent literature. Studies on the effects of surface hardness [2] and roughness [3] have been attempted, along with research on lubrication and surface finish [4]. The effects of the real area of contact have also been examined [5,6]. The coefficient of kinetic friction at some point on an
* Corresponding author. Fax: +44-1232-366804. E-mail address: [email protected] (K.R. Gilmour).
interface, at an arbitrary time during the process, is a complex function of process variables, lubrication conditions and material characteristics. Material characteristics itself covers several variables, such as hardness and surface roughness. This paper covers the use of surface roughness data in the study of friction in the deep drawing process. Several techniques have been developed over the years to quantify the topography of metallic surfaces. These can be split broadly into two categories: contact (profilometry) and non-contact (interferometry) methods. Generally, non-contact methods are seen as faster and more accurate than profilometry techniques, and this is certainly true when both are used within their design limits. Obviously, it is of interest to both the academic and the industrialist to obtain sufficiently representative surface data at minimum cost. Interferometry systems are, however, prohibitively expensive compared with the cost of buying a two-dimensional (2D) profilometer and modifying the techniques in using it to obtain threedimensional (3D) surface data. It was hypothesised that a modified 2D profilometry technique would be sufficiently accurate for the purposes of assessing the surface characteristics of a drawingquality steel, and using these data to calculate quantities relevant to frictional analyses in deep drawing, such as
0301-679X/99/$ - see front matter 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 1 - 6 7 9 X ( 9 9 ) 0 0 0 8 5 - 7
554
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
real contact area, resistance to viscous flow and hydrodynamic lift pressure. To verify this, a non-contact scanning white light interferometer was used to check the data.
2. 3D surface topography characterisation using modified 2D stylus profilometry and scanning white light interferometry The idea of modifying the 2D profilometry technique to allow 3D surface mapping is not new, and has been used previously [7]. It is now generally accepted that the use of multiple parallel traces is a useful method of surface characterisation [8], and in the analysis of surfaces loaded with low contact pressures (in the region of 3 MPa) the large population of data decreases the probability of not sampling over low contact areas and asperity peaks. This is important because the typical pressures under the blankholder of a deep drawing press are relatively low. The modification is made by providing a conventional 2D profilometer with an indexing table, giving the extra planar direction and three degrees of freedom. A schematic view of the new system can be seen in Fig. 1. The stylus has a tip radius of 10 µm, and the voltage output is sent through an analogue-to-digital converter and thence to a data acquisition set-up on a personal computer. Displacement velocities and sampling rates can be defined by the user within the software, and the output is in the form of ASCII data. The main drawback with this system is that the current design forces the raising and lowering of the stylus between each parallel trace, and because all displacement values are taken from a datum on the lowest point on each individual trace, there is an inherent variation in the raw data. Although this introduces inaccuracies, an attempt can be made to compensate by first using a least-squares technique to normalise the sets of traces
and then expressing all height values relative to a common centre line. For validation of the experimental accuracy of this technique, the measured areas were scanned and characterised by a Zygo New-View 100, a non-contact interferometer. Combining the techniques of scanning white light interferometry (SWLI) with a conventional phaseshifting interferometer, this machine allows analysis down to a resolution of 0.1 nm.
3. Experimental and analytical procedures The material used in the tests was a 1.5 mm thick drawing-grade mild steel (BS 1449 part 1: Type CR4GP). Prior to scanning, the specimens were cleaned with a trichloroethane solution and then with a pressurised nitrogen gas stream. To avoid the possibility of any damage caused by surface wear of the profilometer’s stylus, the specimen surface was scanned first with the non-contact system. The scanned area, for both methods, was 2.8 mm×2.1 mm, and four different areas were scanned with each technique to minimise experimental error. The sample spacing for the interferometer was 8.8 µm, giving 75 930 data points on the specimen, and the profilometer allowed a sample spacing of 10 µm, providing 58 800 data points. After the scans had been completed the normalisation and compensating techniques described earlier were applied. As a visualisation aid, these surface data were extracted to a commercial software package and the surfaces shown in Figs. 2 and 3 were created. Fig. 2(a) and (b) show, respectively, the filled contour plots for the profilometry and interferometry techniques. Fig. 3(a) and (b) displays the same data, but in the form of a 3D surface plot. Only one area plot is shown as the others were very similar. While these provide excellent visual data, and illustrate the close similarity of the two techniques, they do not permit quantitative comparison. For this, the data must be analysed in other ways.
4. Bearing area curves
Fig. 1.
The modified 2D stylus profilometer.
First used in 1933 [9], the bearing area curve allows an assessment of the distribution of height values about the centre line of the surface. The curve is created by truncating the surface data for each plot at the centre line, and expressing the number of points truncated as a percentage of the total number of sampled points. The bearing area curves for each of the four sampled areas are presented in Fig. 4. The percentage bearing area, plotted against the height above the centre line, is shown for both techniques. These plots reveal a consistently small difference in the values obtained. Assuming that
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
555
Fig. 2. Filled contour plots: (a) contact result; (b) non-contact result.
Fig. 3. 3D surface plots: (a) contact result; (b) non-contact result.
the non-contact technique is the more accurate, the profilometry method slightly overestimates the height values near high bearing areas and underestimates them near low bearing areas. The explanation for this difference is most likely a combination of two reasons:
5. Resistance to viscous flow and hydrodynamic lift pressure
In the deep drawing operation, lubrication regimes at the contact interfaces vary from boundary lubrication to partial hydrodynamic, or mixed, lubrication. Crucial to an understanding of these is the knowledge of how the lubricant flows from the interface between the blank and the blankholder. The ‘Flow Factor Method’ [10,11] presents a useful model, and two main mechanisms of flow are developed to describe the process. Poiseuille flow is the pressure flow factor; a measure of the influence of surface roughness on lubricant flow. Couette flow is the shear flow factor; the velocity-driven component which is also influenced by the surface topography. Given the loading conditions and material properties we can use the topographical data to predict the real area of contact, and with this information it is then possible to calculate the distribution of the load between the asperities and the lubricant pockets. The authors used the finite difference method to create a program that solved the Reynolds equation for isoviscous conditions:
Surface mapping has a practical use for tribological analyses in its application to the study of lubricant flow.
∂ ∂p ∂ 3 ∂p h · ⫹ h3 ⫽0, ∂x ∂x ∂y ∂y
1. residual dirt particles missed in the cleaning process will have the effect of creating artificially high asperity peaks as scanned by the interferometry technique; and 2. the necessary method of trace alignment to allow 3D profilometry scanning will act as a smoothing filter for the data, causing a slight reduction in some of the height values measured.
冉 冊 冉 冊
(1)
556
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
Fig. 4.
Bearing area curves for sampled areas.
where h is the clearance height and p is the contact pressure. An initial grid spacing of 20 µm was employed, the calculated solution was equated to that through a flat parallel clearance space and an effective clearance height was found. To validate this technique a simple test rig, shown in Fig. 5, was designed to allow measurement of the resistance to viscous flow to be made. The oil in the cylinder is pressurised with the aid of an accumulator to keep
the pressure constant throughout the test. The lubricant leaked from the simulated blank/blankholder interface is collected over a period of time and the calculation of flow rate for a given pressure can be made. Hydrodynamic lift pressure arises from the draginduced flow of lubricant into the clearance space, and because cavitation prevents the creation of a negative pressure in the diverging parts of the clearance space, a net positive pressure results. A finite difference solution to the Reynolds equation:
冉 冊 冉 冊
∂ 3 ∂p ∂p ∂ ∂h h · ⫹ h3 ⫽6h·V , ∂x ∂x ∂y ∂y ∂x
(2)
provides a map of the pressure distribution over the surface. The numerical solution must also account for ‘carry-over flow’ in the regions of cavitation. Integration of the pressure distribution provides the total lift force. 6. Results
Fig. 5. Leakage test rig.
Fig. 6 shows the application of the finite difference solutions introduced earlier. Again, it is seen that the profilometry technique slightly underestimates the
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
557
7. Conclusions
Fig. 6.
Finite difference solution.
height, although the difference is within acceptable limits. It is also evident that, apart from the low contact areas, the difference in the two methods is constant; evidence of the slight filtering effect of the modified profilometry technique. The results shown in Fig. 6 are representative of those for all four samples. The difference observed can be accounted for with the resolution scales of the two techniques. The profilometry method is limited by the radius of the stylus tip, whereas the interferometer is limited by the wavelength of the light — orders of magnitude less. Fig. 7 shows a comparison of the experimentally determined effective clearance height and that obtained with the solutions to Eq. (1) — note that the graph does not show the 0,0 origin. The model shows good agreement with experiment; it is accurate throughout the measured range and within the small amount of experimental scatter. Using the same techniques, Eq. (2) was solved to measure the effect of the hydrodynamic lift pressure. Assuming process conditions in the region of 3 MPa blankholder pressure and 5–50 mm/s drawing velocity, the lift pressure was found to be extremely small — typically around 1% of the blankholder contact pressure. This is not significant for normal drawing velocities and lubricants, but it is possible that it may have an effect under a higher speed and viscosity.
Fig. 7.
Comparison of experimental data and calculated results.
A standard two-dimensional surface profilometer was modified to allow three-dimensional analyses. To validate this technique, a scanning white light interferometer was employed to verify the data, and these techniques were used in surface characterisation for frictional analyses. The following conclusions can be made. There is good general agreement between the two techniques and the measured results are consistently close to each other. The modified profilometry technique proves to be less accurate at extremely low contact areas, but this discrepancy is an inherent feature in the system. The discrepancies can be explained as a combination of hardware limitations and the effect of having to establish a common centre line in the use of multiple parallel traces. The use of analytical techniques in predicting real contact areas from the measured surface topography data has been validated experimentally. The measured data agree well with the predicted values and are all within experimental scatter. These analytical techniques were used to calculate the hydrodynamic lift pressure at the contact interfaces, but the results showed the effect to be negligible. Typical values were found to be around 1% of the blankholder pressure. To conclude, modified 2D profilometry has shown, as was expected, that it falls short of the accuracy of techniques like interferometry. What has been shown, however, is that the inaccuracies are within acceptable limits for some applications and it can provide useful data for a fraction of the cost of other methods. Used for the collection of data for use in frictional analyses in sheet metal forming operations, modified 2D profilometry is a useful, and comparatively inexpensive, solution to both industrial and academic laboratory needs.
References [1] Schey JA. Friction laws in metal forming tribology. In: Tribology in metalworking: friction, lubrication and wear. Ohio, USA: ASM International, 1983. [2] Reid JV. The effect of surface hardness on friction. Wear 1987;118:113–25. [3] Emmens WC. The influence of surface roughness on friction. Proceedings of IDDRG Workgroup Meeting 1998. General, Benelux. [4] Bello DO, Walton S. Surface topography and lubrication in sheet metal forming. Tribol Int 1987;20(2):59–65. [5] Wilson WRD. Real area of contact and boundary friction in sheet metal forming. J Mech Eng Sci 1988;30(7):475–89. [6] Klimczak T. Analysis of real contact area and change of surface texture on deep drawn steel sheets. Wear 1994;179:129–45. [7] Thomas TR. Rough surfaces. London: Longman Group, 1982. [8] Contet PH, Ville JF. Surfascan 3D — an industrial 3D surface characterisation instrument. Int J Mach Tools Manuf 1992;3(1/2):157–69.
558
K.R. Gilmour et al. / Tribology International 32 (1999) 553–558
[9] Abbot EJ, Firestone FA. Specifying surface quality: a method based on accurate measurement and comparison. Mech Eng 1933;55:569–73. [10] Patir MR, Cheng HS. An average flow model for determining effects of three dimensional roughness on partial hydrodynamic lubrication. ASME J Lubric Technol 1978;100:12–7.
[11] Tripp JH. Surface roughness effects in hydrodynamic lubrication — the flow factor method. ASME J Lubric Technol 1983;105:458–65.