- Email: [email protected]
Galling initiation due to frictional heating
Wear 254 (2003) 1127–1133
Galling initiation due to frictional heating E. van der Heide a,∗ , D.J. Schipper b a
TNO Industrial Technology, P.O. Box 6235, 5600 HE, Eindhoven, The Netherlands b University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
Abstract The lifetime of sheet metal forming (SMF) tools is often limited by galling, a wear type that affects the surface quality of the products and the lifetime of SMF tools. Since SMF tools represent high economical value, it is clear that improvement and prediction of tool life is of high industrial importance. Therefore, models are required that can predict friction and wear related phenomena in SMF-processes, in particular galling. This paper demonstrates the application of a wear model, which is able to predict the initiation of galling in lubricated sheet metal forming processes, to laboratory results gained with the TNO slider-on-sheet tribometer. Experiments are conducted with different (coated) tool surfaces, in sliding contact with stainless steel sheet, using two lubricants. By comparing the critical temperature of the generated boundary layer with the flash temperature at the interface of the sheet and individual tool summits, it is possible to predict whether or not galling initiation will occur. It is shown that the laboratory results are in good agreement with the predicted results of the presented wear model. Galling initiation in lubricated sheet metal forming processes, can be avoided by the application of smooth tool surfaces with enhanced thermal conductivity and lubricants which form boundary layers with a high critical temperature. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Galling; Lubricants; Tribometer; Metal forming; Flash temperature; Coatings
1. Introduction Galling is a wear process associated with the tendency for lubricant film breakdown resulting in pick-up of sheet material by the tool surface and subsequent scoring (severe scratching) of the work piece surface [1]. This wear type eventually results in fracture of the formed products or, worse, jamming of the tooling. Since sheet metal forming (SMF) tools represent high economical value and because change of tooling causes standstill in production, it is clear that improvement and prediction of tool life is of high industrial importance. Therefore, models are required that can predict the initiation of galling. In lubricated sheet metal forming material transfer, even at the initiation stage, is controlled by (local) lubricant failure. Blok [2] postulated that seizure of lubricant films happens when the flash temperature Tf [3] reaches a critical, constant level. Experiments with model lubricant systems showed that the friction behaviour of a lubricant in a pin–plate system, operating at low sliding speed, changes abruptly as a function of temperature [4]. The critical temperature, Tcr , at which this change occurs depended on the concentration of the surfactant. Spikes and Cameron [5] proved that failure in ∗ Corresponding author. Tel.: +31-40-265-0421; fax: +31-40-265-0302. E-mail address: [email protected] (E. van der Heide).
lubricated systems at low or moderate sliding speeds is controlled by the degree of coverage of the surface by lubricant molecules. Since the coverage is controlled by the contact temperature, this confirms and refines the postulate of a constant scoring temperature. The concept of failure due to frictional heating is used in this work to predict galling initiation in lubricated sheet metal forming processes. As galling initiation is found at local tool surface defects like grinding marks or carbides [6], lubricant failure will be evaluated at asperity level of the contacting surfaces.
2. Wear model for the initiation of galling 2.1. Frictional heating for a single tool summit–sheet contact In SMF, a hard and relatively smooth tool surface is combined with a relative rough and soft sheet surface. Application of a plasticity index, e.g. [7], shows that plastic contact is likely to occur at the sheet asperity level. Application of a normal force Fn will force the sheet asperities to deform into plateau’s, a situation described in detail by [8]. A conceptual close-up of the contact in Fig. 1a shows the assumed role of the tool roughness. Hard summits, present at the tool surface, penetrate the sheet roughness plateau’s.
0043-1648/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0043-1648(03)00324-7
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q Tf = √ abKeff
(2)
The effective conductivity Keff has the dimension of thermal conductivity (W m−1 K−1 ), and depends on the (thermal) properties of the surfaces and on the applied operating variables [11]. As with the ‘macroscopic’ tribological contact, a semiellipsoidally shaped heat source has been adopted for the single summit case. The half circle with radius as , available for heat conduction, is therefore treated as if it were elliptically shaped with semi-axes as , perpendicular to the direction of sliding, and (1/2)as in the direction of sliding. This contact geometry does not affect the Péclet number, because the total contact length within the direction of sliding is equal for both situations, i.e. (as2 − y2 ). Furthermore, it does not affect the resulting normal force since the total contact area remains (1/2)πas2 . The relevant equation for effective thermal conductivity is now given by Eq. (3), see Appendix B, in which the subscripts s and t refer to, respectively, the sheet and the tool and κs to the thermal diffusivity of the sheet material. 1.158 0.432 av Keff = 2.746Kt + Ks 10.379 + 7.603 κs (3) Fig. 1. (a) Conceptual close-up of the action of tool summits, hs = −3σs ; (b) tool summit.
The amount of tool summits in contact and the depth of penetration of individual summits, will be a function of the height of the summits and of the separation between the mean plane of the summits and the sheet plateau, hs . Although galling initiation for SMF-contacts is determined by the combined action of the tool summits in contact, it is clear that the actual failure of lubricant boundary layers will occur at the scale of an individual summit. The contact of a rigid tool summit, spherically shaped with radius β, with ideally smooth, plastically deforming, sheet material, is shown in Fig. 1b. In [9], it is shown that there are three principal wear modes for this contact situation, i.e. ploughing, cutting or wedge formation. The amount of heat, q, generated in a single summit–sheet contact, can now be calculated for each wear mode, see Eq. (1), in which as is the radius of the contact and Hsheet the sheet’s hardness. The associated coefficient of friction f, is given in Appendix A. Curve fit solutions, describing the contact of two bodies with dissimilar conductivity, are presented in [10]. For a simple sliding contact, operating under boundary lubricated or dry conditions and assuming a semi-ellipsoidal, heat source, the basic equation for the flash temperature Tf is given by Eq. (2), in which a and b represent the semi-axes in and perpendicular to the direction of sliding. π q = fv as2 Hsheet 2
(1)
The influence of the material properties of the contacting surfaces on the resulting flash temperature follows from Eqs. (2) and (3). It shows that the flash temperature is proportional to the sheet hardness. Sheet materials with approximately the same diffusivity and used under the same contact conditions, which differ by a factor of two in sheet hardness will also differ by a factor two in flash temperature. Secondly, a modest increase in dimensionless tool conductivity causes a significant decrease in flash temperature. The influence of the dimensionless tool conductivity introduces the possibility to lower the maximum occurring flash temperature to acceptable values, e.g. by application of surface coatings with high thermal conductivity. 2.2. Galling initiation Initiation of galling is associated with lubricant failure, accompanied by material transfer from the sheet surface to the tool summits. The latter transfer of metal sheet to the tool summit is assumed to occur when the system operates in the wedge formation mode. By definition, the ploughing and cutting regime are free of transfer; in ploughing all material is displaced to the ridges at the wear track, in cutting material is removed from the surface in the form of long ribbon chips. The attack angles for which the transition to wedge formation occurs are estimated using the function fits Eq. (4) [12], which takes into account the attack angle θ, and, fHK , the dimensionless shear strength [9], defined as the quotient of the interfacial shear stress and the shear strength of the soft metal.
E. van der Heide, D.J. Schipper / Wear 254 (2003) 1127–1133
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θw,pl→c = 0.25(π − arccosfHK ), θpl→w = 0.5 arccos fHK
(4)
For dry sliding contacts, with characteristic values of 0.7–0.9 for fHK , the geometry of the asperities is of utmost importance. A small attack angle will allow the material of the soft surface to flow to the sides of the contact, preventing the formation of a wedge. With increasing dimensionless shear strength it becomes, however, impossible to prevent wedge formation, causing galling to occur. This observation is confirmed both by model experiments [12] and industrial experience with unfavourably matching surfaces like dry stainless steel sheet and uncoated tool steel. The introduction of (boundary) lubrication reduces fHK significantly, i.e. to values in between fHK = 0.4 and 0.7. Now, wedge formation can even be excluded from the diagram, leaving cutting and the preferred ploughing mode. In order to allow for initiation of transfer in a boundary lubricated sliding contact there must be a transition from the area of relatively low fHK values to the area of relatively high fHK values. Such a transition occurs if the lubricant film in the summit–sheet contact fails as a result of a local surface temperature rise to a value Tf that exceeds the critical temperature Tcr of the lubricant. Thus, the criterion for galling initiation for a lubricated tool summit–sheet contact is formulated as: Tf > Tcr and system operates in the wedge formation mode after removal of boundary layers. Assuming fHK = 0.9 for ‘dry’ sliding contact, yields: Tf > Tcr
and
0.226 < θ < 0.673
(5)
3. Experimental verification 3.1. Method Experimental validation of the lubricant failure model was done using the TNO slider-on-sheet test method [13], see Fig. 2. A slider is pushed against sheet material with a normal force Fn . Then the slider moves in the x-direction, with a sliding speed v. At the end of the track (track length l) the slider is lifted from the sheet and moved over a distance of 1 mm in the y-direction. The slider, still lifted from the sheet, returns to the starting line x = 0. The normal force is re-applied and the next track is made, assuring virgin sheet
Fig. 2. TNO slider-on-sheet test.
material in the contact. Experiments were performed with sliders of standard dimensions, i.e. ∅ 44 mm × 8 mm, radius 6 mm; using a normal force of 100 N, a sliding speed of 0.50 m s−1 and a track length of 1700 mm. Each track was set 1 mm next to the previous track; 400 tracks were made per test. Experiments were performed at 20 ◦ C room temperature and 70% relative humidity. The experimental results were compared with the predicted behaviour of the systems, based on calculations with the failure model. In order to estimate the amount of summits that initiate galling in a slider-on-sheet test it was necessary to correct for the size difference between the roughness measurement and the true area of contact in a the slider-on-sheet test. The nominal area of contact, An , for the slider-on-sheet configuration for Fn = 100 N, was calculated using finite element simulations; it amounted to 0.25 mm2 . The true area of contact followed from calculations based on [8], see [14] for more details, it was 0.188An = 0.047 mm2 . Now, the amount of summits that initiate galling was estimated, by multiplying the true area of contact with the density of the ‘galling initiating summits’, i.e. the amount of summits that initiate galling based on the roughness measurement divided by the measurement area. The presented numbers were rounded off to integer values. 3.2. Materials The sheet material used in the experiments was 0.8 mm cold rolled, austenitic stainless steel AISI 304, finish 2B. All sheets were taken from the same batch. The hardness of the sheet material was 181–187 HV1 kgf , measured at the surface
Table 1 Roughness data and thermal conductivity for the sliders K (W m−1 K−1 )
WN 1.2379, uncoated WN 1.2379 + TiN WN 1.2379 + TiN, mirror finish WN 1.2379 + DLC 80WC–20Co
20 44 44 448 112
Ra (2D-stylus) (m)
Parameters from interference microscopy
//
⊥
σ s (m)
η (m−2 )
0.04 0.09 0.02 0.03 0.02
0.08 0.09 0.02 0.06 0.03
0.35 0.63 0.069 0.44 0.051
2.43 2.68 1.43 2.20 1.60
× × × × ×
1010 1010 1010 1010 1010
βm (m) 3.6 2.7 103 4.0 111
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of the sheet material. The average roughness expressed in Ra was 0.09 m. The experiments were performed parallel to the rolling direction. As properties Ks = 16.2 W m−1 K−1 ; ρs = 8030 kg m−3 and cp,s = 420 J kg−1 K−1 are taken. Conventional tool steel WN 1.2379, was taken as reference tool material. A set of WN 1.2379 sliders were hardened and tempered three times at 520–540 ◦ C to a resulting hardness of 60–61 HRc, and polished with abrasive paper. The resulting Ra was about 0.04 m parallel (//) and about 0.08 m perpendicular (⊥) to the sliding direction (see Table 1). One of these sliders was used in its uncoated form. The other sliders were coated with TiN or DLC. Both, commercially available, layers were vapour deposited at a process temperature below 520 ◦ C. One of the TiN surfaces has been polished further. The other sliders were used without
any mechanical treatment after coating deposition. Furthermore, experiments were performed with a mirror finished 80WC–20Co slider, with a hardness of 1360 HV. The conductivity of the materials is given in Table 1. Interference microscopy was performed, in order to calculate roughness data suited for modelling. A full description of the interference microscope is given in [12]. The roughness measurements covered an area of 0.149 mm2 , using a pixel size of, respectively, 1.49 m in the x-direction and 1.45 m in y-direction. An tool asperity is regarded as a summit when all eight surrounding neighbours have lower height, thus preventing saddle-points to be assigned as summit. In Table 1, the often used roughness parameters σ s , η and βm of the surfaces are listed, in which σ s is the standard deviation in height, η the summit density and βm the mean radius, respectively.
Fig. 3. Summit data for (a) WN 1.2379; (b) WN 1.2379 + DLC; (c) WN 1.2379 + TiN (rough); (d) WN 1.2379 + TiN (smooth) and (e) 80WC–20Co.
E. van der Heide, D.J. Schipper / Wear 254 (2003) 1127–1133
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Fig. 4. Calculated flash temperature as a function of the summit’s attack angle.
The summit’s attack angle follows from Eq. (6) [15], assuming a separation hs = −3σs .
√ (s − hs )(2β + hs − s) arctan , if β + hs − s θ = π , if 2
s − hs < β (6) s − hs ≥ β
In Fig. 3 are presented the actual radius β and angle of attack θ in order to calculate Tf for each summit using Eq. (1)–(3) and as = β sin θ. The selected base lubricant, Shell Ondina 32, was a so called white oil: a highly refined, practically colourless, mineral oil. The density of this lubricant is 868 kg m−3 , its kinematic viscosity at 40 and 100 ◦ C is, respectively, 32 and 5 mm2 s−1 . Experiments were performed with this base oil, referred to as lubricant O, and with a solution of 0.5 wt.% FM in Ondina, referred to as lubricant O+. The additive friction modifier (FM) belongs to the group of long chained fatty amides. This group of additives is characterised by a polar ‘head’, that consists of an O=C–NH2 group, and a long non-polar hydrocarbon ‘tail’. The average carbon chain length for additive FM is 18. Boundary layers, based on the additive FM, are formed by adsorption [16]. The lubricants’ critical (failure) temperature Tcr were ≈65 ◦ C for lubricant O and ≈120 ◦ C for lubricant O+ [14], respectively.
4. Results An example of Tf as a function of the summit’s attack angle, for system (a) and (b) of Fig. 3 is presented in Fig. 4. The calculated amount of summits that is expected to initiate
galling for the different systems given in the row ‘wear model’ of Table 2. From these results it is clear that there is a distinct influence of the tool roughness and thermal conductivity, on the presence or absence of galling initiating summits. Experimental results in terms of the coefficient of friction as a function of the sliding distance are presented in Fig. 5a and b, respectively, for lubricant O and O+. Galling initiated directly from the start of the experiments for the uncoated and TiN (rough) coated slider. The type of lubricant, O or O+, did not seriously affected the results. The 80WC–20Co and DLC coated slider were found to be insensitive to material transfer. No lumps grew at the slider’s wear scar, no scratches were detected in the tracks on the sheet, neither at the start of the experiment nor at the end of the experiments. Galling is prevented by the application of these surfaces, as predicted by the model calculations. The smooth TiN surface prevented galling to occur for the Ondina lubricated case. No scratches were detected in the tracks on the sheet and no lumps built up at the slider’s wear scar. Consequently, friction remained at a rather constant level of about 0.075, as shown in Fig 4a. Yet, the experiment performed with the lubricant O+ produced a minor increase in friction beyond 400 m sliding distance. Scratches were developed within the wear track on the sheet although not at the start of the experiment but after a certain sliding distance. Since scratching is not initiated directly from the beginning of the experiment it is assumed that some changes in the topography of the slider caused failure at increased sliding distance. A possible explanation could be local wear of the coating, which in turn could generate wedge forming summits at a flash temperature level similar to that of the ‘rough’ TiN surface.
Table 2 Predicted and measured performance for the systems lubricated with Ondina 32 (O) and Ondina 32 + 0.5% FM (O+) WN 1.2379 Lubricant Wear model #summits Experimental result
O 193 Y
O+ 51 Y
WN 1.2379 + TiN (rough)
WN 1.2379 + TiN (smooth)
WN 1.2379 + DLC
80WC–20Co
O 139 Y
O 0 N
O 0 N
O 0 N
O+ 35 Y
O+ 0 Ya
#Summits: the amount of summits that is expected to initiate galling; Y: galling; N: no galling. a After a certain sliding distance.
O+ 0 N
O+ 0 N
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Fig. 5. Experimental results for (a) lubricant O and (b) lubricant O+, with: (A) WN 1.2379; (B) WN 1.2379 + TiN rough; (C) WN 1.2379 + DLC; (D) 80WC–20Co; (E) WN 1.2379 + TiN smooth.
5. Conclusions Experimental results with two lubricants and five (coated) tool surfaces are compared with calculated results, in order to validate the lubricant failure model. It is concluded that the model is able to predict galling initiation accurately in 9 out of 10 cases; see Table 2. One system cannot be described with the present failure model yet. Material transfer and scratching is avoided at the start of this experiment, as predicted by the model. With increased sliding distance, however, there appeared scratches in the tracks of the sheet and transfer was visible at the wear scar of the slider. Such a change in behaviour can be explained by assuming local wear of the coating which affects the summit geometry and distribution. This time dependent effect is not incorporated in the (present) model. From the results it is concluded that galling initiation in lubricated sheet metal forming processes, can be avoided by the application of smooth tool surfaces with enhanced
thermal conductivity and by the application of lubricants which form boundary layers with a high critical temperature.
Acknowledgements This work was sponsored by the Netherlands Ministry of Economic Affairs, within the framework of the Innovation Directed Research Programme (IOP Oppervlaktetechnologie).
Appendix A. Coefficient of friction Eqs. (A.1)–(A.3) represent the coefficient of friction f for the three wear modes cutting, ploughing and wedge formation [9], respectively: π 1 fc = tan θ − + arccos fHK (A.1) 4 2
E. van der Heide, D.J. Schipper / Wear 254 (2003) 1127–1133
ξ2 sin θ + cos(arccos fHK − θ) (A.2) ξ2 cos θ + sin(arccos fHK − θ) 2 1 − 2 sin ξ1 + 1 − fHK sin θ + fHK cos θ fw = 2 1 − 2 sin ξ1 + 1 − fHK cos θ − fHK sin θ
fpl =
(A.3) with ξ1 = θ −
π 1 sin θ − arccos fHK + arcsin √ (A.4) 4 2 1 − fHK
π sin θ ξ2 = 1 + + arccos fHK − 2 θ − 2 arcsin √ 2 1 − fHK (A.5) Appendix B. K eff for simple sliding contact The flash temperature for elliptical contact reads [10]: fFn v fFn v Ks −1 Kt =√ (B.1) + Tf = √ 0.375S θ ab abKeff s with
av θs = (0.375S) + 0.589 φ κs s∗
−0.5 s∗
1/s∗
(B.2)
In which κs represents the thermal diffusivity of the sheet material; a and b the semi-axes in and perpendicular to the direction of sliding; φ = b/a. The shape factors S and s∗ are defined according to Eqs. (B.3) and (B.4). s∗ (φ) = 0.5 exp(1 − φ) − 2.5 √ 2 φ 2 |1 − φ| S(φ) = K 1 + φπ π 1+φ
(B.3) (B.4)
K(n) represents the complete elliptic integral of the first kind with modulus n. For φ = 2, the shape factors S and s∗ are,
1133
respectively, 0.971 and −2.316. Substitution in Eqs. (B.2) and (B.1) results in an expression for Keff as given by Eq. (3). References [1] J.L. Andreasen, M. Eriksen, N. Bay, Major process parameters affecting limits of lubrication in deep drawing of stainless steel, in: K. Dohda, T. Nakamura, W.R.D. Wilson (Ed.), Proceedings of the 1st International Conference on Tribology in Manufacturing Processes’97, Gifu, Japan, 1997, pp. 122–127. [2] H. Blok, The postulate about the constancy of scoring temperature, in: P.M. Ku (Ed.), Interdisciplinary Approach to Friction and Wear, Symposium Troy, New York, NASA SP-237, 1969, pp. 153–248. [3] H. Blok, The flash temperature concept, Wear 6 (1963) 483–494. [4] J.J. Frewing, The heat of adsorption of long-chain compounds and their effect on boundary lubrication, Proc. R. Soc. Lond. A 182 (1943) 270–285. [5] H.A. Spikes, A. Cameron, Scuffing as a desorption process—an explanation of the Borsoff effect, ASLE Trans. 17 2 (1973) 92–96. [6] E. Schedin, B. Lehtinen, Galling mechanisms in lubricated systems: a study of sheet metal forming, Wear 170 (1993) 119–130. [7] J.A. Greenwood, J.B.P. Willamson, Contact of nominally flat surfaces, Proc. R. Soc. Lond. A 295 (1966) 300–319. [8] J. Pullen, J.B.P. Williamson, On the plastic contact of rough surfaces, Proc. R. Soc. Lond. A 327 (1972) 159–173. [9] K. Hokkirigawa, K. Kato, An experimental and theoretical investigation of ploughing, Tribol. Int. 21 (1) (1988) 51–57. [10] J. Bos, H. Moes, Frictional heating of tribological contacts, J. Tribol. 117 (1995) 171–177. [11] H.S.C. Metselaar, B. Kerwijk, E.J. Mulder, H. Verweij, D.J. Schipper, Wear of ceramics due to thermal stress: a thermal severity parameter, Wear 249 (2002) 962–970. [12] M.B. de Rooij, Tribological aspects of unlubricated deepdrawing processes, Ph.D. thesis, University of Twente, The Netherlands, 1998. [13] E. van der Heide, A.J. Huis in ’t Veld, D.J. Schipper, The effect of lubricant selection on galling in a model wear test, Wear 251 (1–12) (2001) 973–979. [14] E. van der Heide, Lubricant failure in sheet metal forming processes, Ph.D. thesis, University of Twente, The Netherlands, April 2002. [15] Y. Xie, J.A. Williams, The prediction of friction and wear when a soft surface slides against a harder rough surface, Wear 196 (1996) 21–34. [16] D. Kenbeek, T.F. Buenemann, H. Rieffe, Review of organic friction modifiers—contribution to fuel efficiency, SAE-paper 2000-01-1792, 1998.
Galling initiation due to frictional heating E. van der Heide a,∗ , D.J. Schipper b a
TNO Industrial Technology, P.O. Box 6235, 5600 HE, Eindhoven, The Netherlands b University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
Abstract The lifetime of sheet metal forming (SMF) tools is often limited by galling, a wear type that affects the surface quality of the products and the lifetime of SMF tools. Since SMF tools represent high economical value, it is clear that improvement and prediction of tool life is of high industrial importance. Therefore, models are required that can predict friction and wear related phenomena in SMF-processes, in particular galling. This paper demonstrates the application of a wear model, which is able to predict the initiation of galling in lubricated sheet metal forming processes, to laboratory results gained with the TNO slider-on-sheet tribometer. Experiments are conducted with different (coated) tool surfaces, in sliding contact with stainless steel sheet, using two lubricants. By comparing the critical temperature of the generated boundary layer with the flash temperature at the interface of the sheet and individual tool summits, it is possible to predict whether or not galling initiation will occur. It is shown that the laboratory results are in good agreement with the predicted results of the presented wear model. Galling initiation in lubricated sheet metal forming processes, can be avoided by the application of smooth tool surfaces with enhanced thermal conductivity and lubricants which form boundary layers with a high critical temperature. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Galling; Lubricants; Tribometer; Metal forming; Flash temperature; Coatings
1. Introduction Galling is a wear process associated with the tendency for lubricant film breakdown resulting in pick-up of sheet material by the tool surface and subsequent scoring (severe scratching) of the work piece surface [1]. This wear type eventually results in fracture of the formed products or, worse, jamming of the tooling. Since sheet metal forming (SMF) tools represent high economical value and because change of tooling causes standstill in production, it is clear that improvement and prediction of tool life is of high industrial importance. Therefore, models are required that can predict the initiation of galling. In lubricated sheet metal forming material transfer, even at the initiation stage, is controlled by (local) lubricant failure. Blok [2] postulated that seizure of lubricant films happens when the flash temperature Tf [3] reaches a critical, constant level. Experiments with model lubricant systems showed that the friction behaviour of a lubricant in a pin–plate system, operating at low sliding speed, changes abruptly as a function of temperature [4]. The critical temperature, Tcr , at which this change occurs depended on the concentration of the surfactant. Spikes and Cameron [5] proved that failure in ∗ Corresponding author. Tel.: +31-40-265-0421; fax: +31-40-265-0302. E-mail address: [email protected] (E. van der Heide).
lubricated systems at low or moderate sliding speeds is controlled by the degree of coverage of the surface by lubricant molecules. Since the coverage is controlled by the contact temperature, this confirms and refines the postulate of a constant scoring temperature. The concept of failure due to frictional heating is used in this work to predict galling initiation in lubricated sheet metal forming processes. As galling initiation is found at local tool surface defects like grinding marks or carbides [6], lubricant failure will be evaluated at asperity level of the contacting surfaces.
2. Wear model for the initiation of galling 2.1. Frictional heating for a single tool summit–sheet contact In SMF, a hard and relatively smooth tool surface is combined with a relative rough and soft sheet surface. Application of a plasticity index, e.g. [7], shows that plastic contact is likely to occur at the sheet asperity level. Application of a normal force Fn will force the sheet asperities to deform into plateau’s, a situation described in detail by [8]. A conceptual close-up of the contact in Fig. 1a shows the assumed role of the tool roughness. Hard summits, present at the tool surface, penetrate the sheet roughness plateau’s.
0043-1648/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0043-1648(03)00324-7
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q Tf = √ abKeff
(2)
The effective conductivity Keff has the dimension of thermal conductivity (W m−1 K−1 ), and depends on the (thermal) properties of the surfaces and on the applied operating variables [11]. As with the ‘macroscopic’ tribological contact, a semiellipsoidally shaped heat source has been adopted for the single summit case. The half circle with radius as , available for heat conduction, is therefore treated as if it were elliptically shaped with semi-axes as , perpendicular to the direction of sliding, and (1/2)as in the direction of sliding. This contact geometry does not affect the Péclet number, because the total contact length within the direction of sliding is equal for both situations, i.e. (as2 − y2 ). Furthermore, it does not affect the resulting normal force since the total contact area remains (1/2)πas2 . The relevant equation for effective thermal conductivity is now given by Eq. (3), see Appendix B, in which the subscripts s and t refer to, respectively, the sheet and the tool and κs to the thermal diffusivity of the sheet material. 1.158 0.432 av Keff = 2.746Kt + Ks 10.379 + 7.603 κs (3) Fig. 1. (a) Conceptual close-up of the action of tool summits, hs = −3σs ; (b) tool summit.
The amount of tool summits in contact and the depth of penetration of individual summits, will be a function of the height of the summits and of the separation between the mean plane of the summits and the sheet plateau, hs . Although galling initiation for SMF-contacts is determined by the combined action of the tool summits in contact, it is clear that the actual failure of lubricant boundary layers will occur at the scale of an individual summit. The contact of a rigid tool summit, spherically shaped with radius β, with ideally smooth, plastically deforming, sheet material, is shown in Fig. 1b. In [9], it is shown that there are three principal wear modes for this contact situation, i.e. ploughing, cutting or wedge formation. The amount of heat, q, generated in a single summit–sheet contact, can now be calculated for each wear mode, see Eq. (1), in which as is the radius of the contact and Hsheet the sheet’s hardness. The associated coefficient of friction f, is given in Appendix A. Curve fit solutions, describing the contact of two bodies with dissimilar conductivity, are presented in [10]. For a simple sliding contact, operating under boundary lubricated or dry conditions and assuming a semi-ellipsoidal, heat source, the basic equation for the flash temperature Tf is given by Eq. (2), in which a and b represent the semi-axes in and perpendicular to the direction of sliding. π q = fv as2 Hsheet 2
(1)
The influence of the material properties of the contacting surfaces on the resulting flash temperature follows from Eqs. (2) and (3). It shows that the flash temperature is proportional to the sheet hardness. Sheet materials with approximately the same diffusivity and used under the same contact conditions, which differ by a factor of two in sheet hardness will also differ by a factor two in flash temperature. Secondly, a modest increase in dimensionless tool conductivity causes a significant decrease in flash temperature. The influence of the dimensionless tool conductivity introduces the possibility to lower the maximum occurring flash temperature to acceptable values, e.g. by application of surface coatings with high thermal conductivity. 2.2. Galling initiation Initiation of galling is associated with lubricant failure, accompanied by material transfer from the sheet surface to the tool summits. The latter transfer of metal sheet to the tool summit is assumed to occur when the system operates in the wedge formation mode. By definition, the ploughing and cutting regime are free of transfer; in ploughing all material is displaced to the ridges at the wear track, in cutting material is removed from the surface in the form of long ribbon chips. The attack angles for which the transition to wedge formation occurs are estimated using the function fits Eq. (4) [12], which takes into account the attack angle θ, and, fHK , the dimensionless shear strength [9], defined as the quotient of the interfacial shear stress and the shear strength of the soft metal.
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θw,pl→c = 0.25(π − arccosfHK ), θpl→w = 0.5 arccos fHK
(4)
For dry sliding contacts, with characteristic values of 0.7–0.9 for fHK , the geometry of the asperities is of utmost importance. A small attack angle will allow the material of the soft surface to flow to the sides of the contact, preventing the formation of a wedge. With increasing dimensionless shear strength it becomes, however, impossible to prevent wedge formation, causing galling to occur. This observation is confirmed both by model experiments [12] and industrial experience with unfavourably matching surfaces like dry stainless steel sheet and uncoated tool steel. The introduction of (boundary) lubrication reduces fHK significantly, i.e. to values in between fHK = 0.4 and 0.7. Now, wedge formation can even be excluded from the diagram, leaving cutting and the preferred ploughing mode. In order to allow for initiation of transfer in a boundary lubricated sliding contact there must be a transition from the area of relatively low fHK values to the area of relatively high fHK values. Such a transition occurs if the lubricant film in the summit–sheet contact fails as a result of a local surface temperature rise to a value Tf that exceeds the critical temperature Tcr of the lubricant. Thus, the criterion for galling initiation for a lubricated tool summit–sheet contact is formulated as: Tf > Tcr and system operates in the wedge formation mode after removal of boundary layers. Assuming fHK = 0.9 for ‘dry’ sliding contact, yields: Tf > Tcr
and
0.226 < θ < 0.673
(5)
3. Experimental verification 3.1. Method Experimental validation of the lubricant failure model was done using the TNO slider-on-sheet test method [13], see Fig. 2. A slider is pushed against sheet material with a normal force Fn . Then the slider moves in the x-direction, with a sliding speed v. At the end of the track (track length l) the slider is lifted from the sheet and moved over a distance of 1 mm in the y-direction. The slider, still lifted from the sheet, returns to the starting line x = 0. The normal force is re-applied and the next track is made, assuring virgin sheet
Fig. 2. TNO slider-on-sheet test.
material in the contact. Experiments were performed with sliders of standard dimensions, i.e. ∅ 44 mm × 8 mm, radius 6 mm; using a normal force of 100 N, a sliding speed of 0.50 m s−1 and a track length of 1700 mm. Each track was set 1 mm next to the previous track; 400 tracks were made per test. Experiments were performed at 20 ◦ C room temperature and 70% relative humidity. The experimental results were compared with the predicted behaviour of the systems, based on calculations with the failure model. In order to estimate the amount of summits that initiate galling in a slider-on-sheet test it was necessary to correct for the size difference between the roughness measurement and the true area of contact in a the slider-on-sheet test. The nominal area of contact, An , for the slider-on-sheet configuration for Fn = 100 N, was calculated using finite element simulations; it amounted to 0.25 mm2 . The true area of contact followed from calculations based on [8], see [14] for more details, it was 0.188An = 0.047 mm2 . Now, the amount of summits that initiate galling was estimated, by multiplying the true area of contact with the density of the ‘galling initiating summits’, i.e. the amount of summits that initiate galling based on the roughness measurement divided by the measurement area. The presented numbers were rounded off to integer values. 3.2. Materials The sheet material used in the experiments was 0.8 mm cold rolled, austenitic stainless steel AISI 304, finish 2B. All sheets were taken from the same batch. The hardness of the sheet material was 181–187 HV1 kgf , measured at the surface
Table 1 Roughness data and thermal conductivity for the sliders K (W m−1 K−1 )
WN 1.2379, uncoated WN 1.2379 + TiN WN 1.2379 + TiN, mirror finish WN 1.2379 + DLC 80WC–20Co
20 44 44 448 112
Ra (2D-stylus) (m)
Parameters from interference microscopy
//
⊥
σ s (m)
η (m−2 )
0.04 0.09 0.02 0.03 0.02
0.08 0.09 0.02 0.06 0.03
0.35 0.63 0.069 0.44 0.051
2.43 2.68 1.43 2.20 1.60
× × × × ×
1010 1010 1010 1010 1010
βm (m) 3.6 2.7 103 4.0 111
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of the sheet material. The average roughness expressed in Ra was 0.09 m. The experiments were performed parallel to the rolling direction. As properties Ks = 16.2 W m−1 K−1 ; ρs = 8030 kg m−3 and cp,s = 420 J kg−1 K−1 are taken. Conventional tool steel WN 1.2379, was taken as reference tool material. A set of WN 1.2379 sliders were hardened and tempered three times at 520–540 ◦ C to a resulting hardness of 60–61 HRc, and polished with abrasive paper. The resulting Ra was about 0.04 m parallel (//) and about 0.08 m perpendicular (⊥) to the sliding direction (see Table 1). One of these sliders was used in its uncoated form. The other sliders were coated with TiN or DLC. Both, commercially available, layers were vapour deposited at a process temperature below 520 ◦ C. One of the TiN surfaces has been polished further. The other sliders were used without
any mechanical treatment after coating deposition. Furthermore, experiments were performed with a mirror finished 80WC–20Co slider, with a hardness of 1360 HV. The conductivity of the materials is given in Table 1. Interference microscopy was performed, in order to calculate roughness data suited for modelling. A full description of the interference microscope is given in [12]. The roughness measurements covered an area of 0.149 mm2 , using a pixel size of, respectively, 1.49 m in the x-direction and 1.45 m in y-direction. An tool asperity is regarded as a summit when all eight surrounding neighbours have lower height, thus preventing saddle-points to be assigned as summit. In Table 1, the often used roughness parameters σ s , η and βm of the surfaces are listed, in which σ s is the standard deviation in height, η the summit density and βm the mean radius, respectively.
Fig. 3. Summit data for (a) WN 1.2379; (b) WN 1.2379 + DLC; (c) WN 1.2379 + TiN (rough); (d) WN 1.2379 + TiN (smooth) and (e) 80WC–20Co.
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Fig. 4. Calculated flash temperature as a function of the summit’s attack angle.
The summit’s attack angle follows from Eq. (6) [15], assuming a separation hs = −3σs .
√ (s − hs )(2β + hs − s) arctan , if β + hs − s θ = π , if 2
s − hs < β (6) s − hs ≥ β
In Fig. 3 are presented the actual radius β and angle of attack θ in order to calculate Tf for each summit using Eq. (1)–(3) and as = β sin θ. The selected base lubricant, Shell Ondina 32, was a so called white oil: a highly refined, practically colourless, mineral oil. The density of this lubricant is 868 kg m−3 , its kinematic viscosity at 40 and 100 ◦ C is, respectively, 32 and 5 mm2 s−1 . Experiments were performed with this base oil, referred to as lubricant O, and with a solution of 0.5 wt.% FM in Ondina, referred to as lubricant O+. The additive friction modifier (FM) belongs to the group of long chained fatty amides. This group of additives is characterised by a polar ‘head’, that consists of an O=C–NH2 group, and a long non-polar hydrocarbon ‘tail’. The average carbon chain length for additive FM is 18. Boundary layers, based on the additive FM, are formed by adsorption [16]. The lubricants’ critical (failure) temperature Tcr were ≈65 ◦ C for lubricant O and ≈120 ◦ C for lubricant O+ [14], respectively.
4. Results An example of Tf as a function of the summit’s attack angle, for system (a) and (b) of Fig. 3 is presented in Fig. 4. The calculated amount of summits that is expected to initiate
galling for the different systems given in the row ‘wear model’ of Table 2. From these results it is clear that there is a distinct influence of the tool roughness and thermal conductivity, on the presence or absence of galling initiating summits. Experimental results in terms of the coefficient of friction as a function of the sliding distance are presented in Fig. 5a and b, respectively, for lubricant O and O+. Galling initiated directly from the start of the experiments for the uncoated and TiN (rough) coated slider. The type of lubricant, O or O+, did not seriously affected the results. The 80WC–20Co and DLC coated slider were found to be insensitive to material transfer. No lumps grew at the slider’s wear scar, no scratches were detected in the tracks on the sheet, neither at the start of the experiment nor at the end of the experiments. Galling is prevented by the application of these surfaces, as predicted by the model calculations. The smooth TiN surface prevented galling to occur for the Ondina lubricated case. No scratches were detected in the tracks on the sheet and no lumps built up at the slider’s wear scar. Consequently, friction remained at a rather constant level of about 0.075, as shown in Fig 4a. Yet, the experiment performed with the lubricant O+ produced a minor increase in friction beyond 400 m sliding distance. Scratches were developed within the wear track on the sheet although not at the start of the experiment but after a certain sliding distance. Since scratching is not initiated directly from the beginning of the experiment it is assumed that some changes in the topography of the slider caused failure at increased sliding distance. A possible explanation could be local wear of the coating, which in turn could generate wedge forming summits at a flash temperature level similar to that of the ‘rough’ TiN surface.
Table 2 Predicted and measured performance for the systems lubricated with Ondina 32 (O) and Ondina 32 + 0.5% FM (O+) WN 1.2379 Lubricant Wear model #summits Experimental result
O 193 Y
O+ 51 Y
WN 1.2379 + TiN (rough)
WN 1.2379 + TiN (smooth)
WN 1.2379 + DLC
80WC–20Co
O 139 Y
O 0 N
O 0 N
O 0 N
O+ 35 Y
O+ 0 Ya
#Summits: the amount of summits that is expected to initiate galling; Y: galling; N: no galling. a After a certain sliding distance.
O+ 0 N
O+ 0 N
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Fig. 5. Experimental results for (a) lubricant O and (b) lubricant O+, with: (A) WN 1.2379; (B) WN 1.2379 + TiN rough; (C) WN 1.2379 + DLC; (D) 80WC–20Co; (E) WN 1.2379 + TiN smooth.
5. Conclusions Experimental results with two lubricants and five (coated) tool surfaces are compared with calculated results, in order to validate the lubricant failure model. It is concluded that the model is able to predict galling initiation accurately in 9 out of 10 cases; see Table 2. One system cannot be described with the present failure model yet. Material transfer and scratching is avoided at the start of this experiment, as predicted by the model. With increased sliding distance, however, there appeared scratches in the tracks of the sheet and transfer was visible at the wear scar of the slider. Such a change in behaviour can be explained by assuming local wear of the coating which affects the summit geometry and distribution. This time dependent effect is not incorporated in the (present) model. From the results it is concluded that galling initiation in lubricated sheet metal forming processes, can be avoided by the application of smooth tool surfaces with enhanced
thermal conductivity and by the application of lubricants which form boundary layers with a high critical temperature.
Acknowledgements This work was sponsored by the Netherlands Ministry of Economic Affairs, within the framework of the Innovation Directed Research Programme (IOP Oppervlaktetechnologie).
Appendix A. Coefficient of friction Eqs. (A.1)–(A.3) represent the coefficient of friction f for the three wear modes cutting, ploughing and wedge formation [9], respectively: π 1 fc = tan θ − + arccos fHK (A.1) 4 2
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ξ2 sin θ + cos(arccos fHK − θ) (A.2) ξ2 cos θ + sin(arccos fHK − θ) 2 1 − 2 sin ξ1 + 1 − fHK sin θ + fHK cos θ fw = 2 1 − 2 sin ξ1 + 1 − fHK cos θ − fHK sin θ
fpl =
(A.3) with ξ1 = θ −
π 1 sin θ − arccos fHK + arcsin √ (A.4) 4 2 1 − fHK
π sin θ ξ2 = 1 + + arccos fHK − 2 θ − 2 arcsin √ 2 1 − fHK (A.5) Appendix B. K eff for simple sliding contact The flash temperature for elliptical contact reads [10]: fFn v fFn v Ks −1 Kt =√ (B.1) + Tf = √ 0.375S θ ab abKeff s with
av θs = (0.375S) + 0.589 φ κs s∗
−0.5 s∗
1/s∗
(B.2)
In which κs represents the thermal diffusivity of the sheet material; a and b the semi-axes in and perpendicular to the direction of sliding; φ = b/a. The shape factors S and s∗ are defined according to Eqs. (B.3) and (B.4). s∗ (φ) = 0.5 exp(1 − φ) − 2.5 √ 2 φ 2 |1 − φ| S(φ) = K 1 + φπ π 1+φ
(B.3) (B.4)
K(n) represents the complete elliptic integral of the first kind with modulus n. For φ = 2, the shape factors S and s∗ are,
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respectively, 0.971 and −2.316. Substitution in Eqs. (B.2) and (B.1) results in an expression for Keff as given by Eq. (3). References [1] J.L. Andreasen, M. Eriksen, N. Bay, Major process parameters affecting limits of lubrication in deep drawing of stainless steel, in: K. Dohda, T. Nakamura, W.R.D. Wilson (Ed.), Proceedings of the 1st International Conference on Tribology in Manufacturing Processes’97, Gifu, Japan, 1997, pp. 122–127. [2] H. Blok, The postulate about the constancy of scoring temperature, in: P.M. Ku (Ed.), Interdisciplinary Approach to Friction and Wear, Symposium Troy, New York, NASA SP-237, 1969, pp. 153–248. [3] H. Blok, The flash temperature concept, Wear 6 (1963) 483–494. [4] J.J. Frewing, The heat of adsorption of long-chain compounds and their effect on boundary lubrication, Proc. R. Soc. Lond. A 182 (1943) 270–285. [5] H.A. Spikes, A. Cameron, Scuffing as a desorption process—an explanation of the Borsoff effect, ASLE Trans. 17 2 (1973) 92–96. [6] E. Schedin, B. Lehtinen, Galling mechanisms in lubricated systems: a study of sheet metal forming, Wear 170 (1993) 119–130. [7] J.A. Greenwood, J.B.P. Willamson, Contact of nominally flat surfaces, Proc. R. Soc. Lond. A 295 (1966) 300–319. [8] J. Pullen, J.B.P. Williamson, On the plastic contact of rough surfaces, Proc. R. Soc. Lond. A 327 (1972) 159–173. [9] K. Hokkirigawa, K. Kato, An experimental and theoretical investigation of ploughing, Tribol. Int. 21 (1) (1988) 51–57. [10] J. Bos, H. Moes, Frictional heating of tribological contacts, J. Tribol. 117 (1995) 171–177. [11] H.S.C. Metselaar, B. Kerwijk, E.J. Mulder, H. Verweij, D.J. Schipper, Wear of ceramics due to thermal stress: a thermal severity parameter, Wear 249 (2002) 962–970. [12] M.B. de Rooij, Tribological aspects of unlubricated deepdrawing processes, Ph.D. thesis, University of Twente, The Netherlands, 1998. [13] E. van der Heide, A.J. Huis in ’t Veld, D.J. Schipper, The effect of lubricant selection on galling in a model wear test, Wear 251 (1–12) (2001) 973–979. [14] E. van der Heide, Lubricant failure in sheet metal forming processes, Ph.D. thesis, University of Twente, The Netherlands, April 2002. [15] Y. Xie, J.A. Williams, The prediction of friction and wear when a soft surface slides against a harder rough surface, Wear 196 (1996) 21–34. [16] D. Kenbeek, T.F. Buenemann, H. Rieffe, Review of organic friction modifiers—contribution to fuel efficiency, SAE-paper 2000-01-1792, 1998.