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Surface asperity flattening in sheet metal forming — A 3-D relocation stylus profilometric study
Pergamon
Int. J. Mach. Tools Manufact. Vol. 35, No.2. pp. 169-175, 1995 Elsevier Science Ltd. Printed in Great Britain 0890-6955/9557.00 + .00
S U R F A C E A S P E R I T Y F L A q T E N I N G I N S H E E T M E T A L F O R M I N G - A 3-D R E L O C A T I O N STYLUS PROFILOMETRIC STUDY
X. ROIZARDf AND J. VON STEBUT~ tLM.I.T., I.U.T. D~T. GflNIE MI~,CANIQUEEl" PRODUCTIQUE B. P. 1559, F-25009 BESAN(~ONCEDEX, FRANCE. *L.S.G.S., I~XZOLEDES MINES, F-54042 NANCY, CEDEX, FRANCE.
SUMMARY Among the laser textured steel sheets retained for difficult stamping situations those with isolated, non communicating valleys are shown to be especially interesting. Such isolated valleys act simultaneously as traps for wear debris and as practically frictionless, high pressure oil pockets, participating in overall load carrying. These results are substantiated by 3D profilometry before and after friction to analyse specific residual roughness and friction-induced surface damage on the load carrying plateaux. difference consists in a different average plateau length 1", INTRODUCTION while plateau spacing Lss is similar. In addition, there is a significant difference in skewness : negative for T1 and Sheet surface roughness is known to be important positive for T2. for friction and galling in the press shop. From first principles in contact mechanics it is clear t) that the Friction experiments die/sheet surface asperity contact angle will dominate the amount of sheet surface shearing. Thus both roughness Strip drawing was done by means of a test rig (height) parameters 2) and horizontal spacing 3) must be (fig.2) described in detail in 7). A 50 mm wide and 0.7 mm considered for sheet surface topography optimisition in thick boundary lubricated (1) mild steel sheet was stamping. Montfort and al. have introduced the compound squeezed in between two non rotating O 20 ram, 60 mm parameter 4) which allows for clear empirical selection of long high speed steel dies (Ra _< 0.I iam) leading to a sheets correlating well with stamping behaviour. In perfectly symmetrie, extended ( = 0.3 mm wide at 4 kN) addition, negatively skewed surfaces (cf. abrasively worn double "line" contact. Normal loads of 4 kN were applied surfaces) also decrease the tool/sheet contact angle. by means of a pneumatic actuator. Friction experiments Another functional approach has been chosen by were run in the unidirectional multipass mode. This Rault and Entringer s). Their antigalling roughness profile implies return to the starting position with the dies "liffed is based on the valleys' capacity of trapping wear debris. off" in between two consecutive passes. Contact When embedded on the roughness plateaux these debris temperature was varied by means of heating elements lead to galling. This work showed in particular that there powered by a P!D controller. is a critical plateau length beyond which such debris embedding becomes important. Laser textured sheets, with RESULTS AND DISCUSSION a regular array of load carrying plateaux have brought about an economic solution in the same line as proposed Asperity truncation : debris generation and by Rault, with the additional advantage of being trapping practically isotropic and allowing for tailored plateau and valley lateral spacing. Fig. 3 shows how friction is successively modified In the present work we address both the wear in multipass operation. While there is only a slight debris trapping and the lubrication aspect. While the advantage of sheet T1 at room temperature this difference amount of lubricant stored in the sheet surface can be is patent at 100 °C where static friction increase after the quantified by the empty volume identical with the average 4 th pass indicates the onset of galling phenomena s). Some peak height Rpm 6) particular attention will be paid to the insight into the associated micromechanical modifications fact whether the roughness valleys communicate or not. can be gained from fig. 4, where surface topography of the virgin sheets is compared with that observed after 5 I~XPERIMENTAI,, DETAILS consecutive strip drawing passes. When looking at the beginning of the 50 mm Sheet surface morphology sliding distance it is clear that T1 resists much better to friction-induced surface truncation. This conclusion is The specimens retained for this study were two backed up by 2D relocation profilometry (fig. 5). types of uncoated, laser textured mild steel sheets Tl and Quantitative, statistical analysis (fig. 6-a) T2. For the first set the surface morphology consisted in substantiates these findings. an array of isolated valleys within essentially During the first pass the rate of surface truncation communicating plateaux, while the second set had of sheet T2 is twice that of Tl (60 % as compared to 30 isolated, flat continuous plateaux separated by a network %). Even though this rate decreases with pass number, the of communicating valleys (fig. 1). 3D topographic plots residual security margin in empty volume, likely to feed in were assessed by means of standard PC driven tactile lubricant and to trap wear particles is reduced to 20 % for profilometry 2,3) with a Talysurf l0 as pick-up. T2 (as compared to 40 % for TI). Corresponding quantitative data are compiled in table 1. (I) Our standatt sheet oiling procedure for boundat), lubrication From inspection of this table it is patent that the corresqxmdsto 4g of oil per m2 sheet surface. This amountsto roughness parameters are practically identical. The major approximately half of the empty surface volume Rpm 169
170
X. ROlZnRD and J. von STEBUT
(a)
(b) Depth distribution 0
,
---.___
-5
Sheet TI
~m ~
Total depth Mean depth
: 16.32 ~m : 5.92 ~m
Depth distribution 0 15
-5 I0
Sheet T2
-10
5
-
-15 ~m.,
o
Total depth Mean depth
: 11.64 ~m : 6.05 ~tm
Fig. 1 ." steel sheet surface morphology ," a - bearing (white) areas ; b - corresponding height distributions. ,,
be concluded for T2 that this is due to the joint effect of a higher rate of debris generation and to an insufficient residual empty volume for debris trapping. Asperity truncation : lubrication aspects
-.,d--
sheet /
I
Fig. 2 ." synoptic o f the friction test rig
Fig. 7 gives more morphological information on the modifications resulting from the first pass. For T2 secondary asperities have emerged giving rise to a net decrease in average peak spacing and, above all, leading to high contact angle asperity shearing, likely to generate more wear debris than for T1 where surface morphology changes are negligible. Wear particles contin ously generated will accumulate preferentially ahead of the advancing dies. At the end of a 50 mm friction pass when lifting the dies off the surface before going back to the beginning of the track, only those debris sticking to the dies will be recycled. Thus the abrasive action of debris will be much less effective in the beginning of a pass. The severely scratched surface at the end of pass # 5 for sheet T2 is therefore a consequence of wear part.cle ploughing. It can
Clearly the rates of asperity truncation and debris generation are fundamental aspects of tool/workpiece interaction in metal forming operations. However, if this is so why don't we find more debris entrapping on the largely continous plateaux of sheet # 1 with an array of isolated valleys ? This is what should be expected from Rault's results 5) concerning a critical sliding length for wear particle embedding. The reason of this could be related to a fundamental difference in morphology-specific lubrication efficiency. Therefore the remainder of this study is dedicated to potential microhydrodynamic mechanisms as conjectured in the literature 9,10.11). For reasons of simplicity we shall only retain the "unfavourable" T2 morphology with isolated plateaux and communicating valleys. As shown 9.ma2) high pressure lubricant pockets may form on the plateaux and participate in load carrying. Fig. 8 illustrates such entrapped oil pockets on a T2 type plateau. If this mechanism applies there should be a residual, persisting plateau roughness intimately related to the basic lubrication parameters like contact pressure, sliding speed, and temperature of the lubricant : In fig. 9 an fig. 10 the effect of one single 50 mm pass on the surface height distributions and associated "Abbott bearing plots" is shown as a function of contact temperature and sliding speed. As discussed in 13) the upper part left of the bend-over in the Abbott bearing plot corresponds to surface areas having been modified during strip drawing. The corresponding height difference 6Rz is the persistent, residual plateau roughness. Clearly 5Rz decreases with increasing contact temperature (fig. 9-c) implying that contact becomes more severe. On the
Surface asperity flattening in sheet metal forming
T1
T2
J
J
171
T2
T2
J
J
Ill,
T1
0,2
T2 T2
> ,;2
J
2
TI
0,2
1
2
3
4
5
passnumb~
Fig. 3 : Friction response during 5 consecutive muhipass S.D. routines for T1 and 7"2..
contrary, an increase in sliding speed and thus the fraction of hydrodynamic lubrication decreases contact severity and enhances persistent plateau roughness. Naturally these modifications in sliding contact conditions should be accompanied by modifications in friction. The friction values corresponding to the 6 situations studies in fig. 9 and fig. 10 are plotted out in fig. 11 as a function of 8Rz. It is striking that all friction data points both for varying contact temperature and sliding speed fit on to apractically linear empirical master plot : la = la0 - k ARz (k being a constant) (1) With these results and Amontons' second law of friction in mind a simple law of mixture model can be set up : overall friction is supposed to result from the junction shearing o f dry metal/metal contacts while the isolated pressurised lubricant pockets are assumed to share load carrying without substantial contribution to friction. The tangential friction F t f o r c e is w r i t t e n as :
Ft = 5". ard • "td + ~ arl • ql (2) with the overall load carrying,_.real bearing area : Ar = Y. ard + 2 . arl = Ard + Arl The weight coefficients ard and arl in (2) correspond to the load carrying areas of dry contact and lubricant pockets, 't d and ql being the respective shear strengths of the sheet metal and the lubricant (cf fig. 12). With ql << 'td we get from (2) : Ft = Ard. "td As generally admitted we shall suppose for the sheet hardness H = Fn / Ar, Fn being the overall contact load. Thus we get for the overall friction coefficient : Ft ( A t - Arl ) "t:d la = F--'-n Ar H (3) Xd is a sheet metal material constant describing pure H adhesive, dry friction : lad = ~_.d_. H
172
X. RoIzAm~and J. ,,on SlEiat i
@ a-1
®
Jl
a-2
y b-1
b-2
c-I
c-2
o e-
e~.
E !
~" 500 ~m
Fig. 4 ." 3-D projections o f sheets surface topology. a - 1, 2 ." "virgin" state (as received). b - 1, 2 : beginning of the 5 th pass. c - 1, 2 ." end of the 5t h pass.
T1
(a) Beginning of pass I(X),. ARz/Rz0 (%)
T2
:'~'~
-,_ f.~.'. . . . . LL '
' i'
Virgin
80 i 6O
/
(b)
End of pass
~
'
4O 20 ~
Pass #5 ~",j
1
',."
,
"'. ~"....
~
/ -
I
-
/ ]
-
I
~
1
-
I
!~
!:
!
:
!
:
!
0 1 2 3 4 5
pass # Fig. 5 .' two dimensional relocation profilometry f o r both sheets. Fig. 6 ." zSRz/RzO vs. sliding distance after 5 consecutive S.D. passes (50 turn each). Rz 0 ." total peak to valley roughness amplitude af the virgin sheet.
Surfaceasperityflatteningin sheetmetalforming
173
8.02 [am
I 82.68% ~-~
Residualpersisting 10t.tm plateaurougbn~'~
Vnlley
17.32%
4.97
300)am
Ilrn
1"
Fig. 8 ."plateat~ morphology of sheet T2
44.08%
~]
55.92%
Fig. 7 : major and secondary peaks on T2 surface sheet.
@
1[
((afterfriction))
(heightdistribution functions)
@
curves)(C°rresp°nding Abbottbearing ]
~ 8R~ i
~1
~
60°C 8R ml,
i
A h (tam)
l h
o
(~.m) ~ ' ~
5
T 8Rz
I
I
i
0
50
100 (%)
0
(
8 R z = f(T) )
1
50
100
Ar m(%) Aa
Fig. 9 : residual plateau roughness g)Rz derived from the corresponding Abbott curves as a function of tool temperature. Strip drawing with cylindrical tools ; sliding speed ." 10 rnm/min.
174
X. ROIZARDand J. von STEBUT
II
Q
rfrci°n' aI
(height distribution functions)
F
l
mm/min
(corresponding Abbott bearing curves)
8R z 10 ram/rain
I
,
J ~
5R
I(X) ram/rain
l
h (pro)
I h (~m)
[_looo ~m/m~. I !
F
iI
~
I
0
1(hgt) ram/rain
i
50
~oo (%)
50
lOO Ar --(%) Aa
8R z =f(V) ) II Fig. 10 : residual plateau roughness 6Rz derived from the corresponding Abbott curves as a function of sliding speed. Strip drawing with cylindrical tools ," tool temperature • 20 °C
0,3C
O O •
(Variation of sliding temperature)
20 °C 60 °C 100°C
[] [] []
(Variation of 20 mm/min sliding 200 mm/min speed) 2000 mm/min
0,25
0,213
~),15
I
I
0,5
1
t= 1,5
5Rz
Fig. 11 : friction coefficient during the first pass of strip drawing sliding friction as a function of the resulting persistent plateau roughness 6Rz in turn induced by different contact conditions.
A_, Expression (3) finally becomes It = ltd - 2 - ~ gd (4) Ar in qualitative agreement with the experimental relation ( 1) when assilimilating/-tO to ltd. The final conclusion, when comparing (1) and (4), is that the area fraction Ar~l should Ar be proportional to 8Rz. This is altogether coherent when, in analogy with the macroscopic equivalence for Rpm 2) ~Rz is interpreted as the volume of load carrying lubricant trapped on the plateaux. Fig. 11 is a clear indication of microhydrodynamic lubrication as a major mechanism controlling tool/sheet friction and associated sheet surface damage. With communicating valleys in the sheet surface morphology, oil pressure build-up in the valleys is insufficient to share load carrying as occurring on the oil pockets of the plateaux. On the contrary, with isolated valleys as for sheet T1 dynamic seal-off of these valleys and associated oil pressure build-up should occur. Thus the microhydrodynamic mechanism can be transposed to this larger scale and the considerably better friction behaviour, in spite of over-critical sliding lengths for debris build up, would then be a natural consequence.
Surface asperity flattening in sheet metal forming
175
(total applied load) P (normal pressure) (tool)
Ft (friction force)
(shear stress)
P
q
q~
q
]
(sheet)
ii:
(real s°lid/s°lid ,,j bearing area whereAfrdcti°n i ind;red ,.[ metal shearing ° c c u r s ) / I A [(tt
Ar (total load carrying bearing area) :~"
Aa
....
"-
(apparent macroscopic bearing area) Fig. 12 ." contact mechanical definitions : A a ." apparent macroscopic bearing area. Ar : total load carrying bearing area. Ard : real area of dry solid bearingwhere friction induced shearing OCCURS.
CONCLUSION In a first part we have given experimental surface topographical evidence that mild steel laser textured sheets with isolated valleys are superior in deep drawing simulation than those with communicating valleys : Asperity truncation as well as wear particle generation are less severe in the first case. In a second part we study microhydrodynamic lubrication owing to dynamic seal-off of pressurised oil pockets on the load carrying plateaux. We finally conclude, by transposition, that the superior friction and surface damage behaviour of the first type of laser textured sheets in deep drawing is dominated by hydrodynamic load carrying of the oil trapped in the isolated valleys. Quantitative statistical and relocation profilometry is seen to be a fundamental tool for micromechanical understanding in conatct mechanics. REFEREN(~ES 1) 2) 3) 4)
5)
R. Hill : The mathematical theory of plasticity. Oxford Press (1950) pp. 128-181. J. von Stebut : Modification of a surface profile's height parameters during strip drawing. Wear. Vol. 109 (1986) p. 145. J. yon Stebut : Modification of a surface profile's horizontal spacing during strip drawing. Wear. Vol. 108 (1987) pp. 329-340. G. Monfort and J. Defourny : Tribological factors in the stamping of coated and uncoated steel sheets. 16th biennal congress of the IDDRG (1990) BorRtnge. R. Rault and M. Entringer : Antigalling roughness profile permitting a reduction of a blankholder pressure and the required amount of lubricant during the forming of sheets. 9th biennal congress of the IDDRG (1976) Ann Arbor.
Table Ra
Rq
Rim
1
1(°) l.ss
F.k
Sk ]
6)
7)
8)
9)
10)
11) 12) 13)
TI
2.1
3
T2
2.2
2.8
13.9 550 500
4.6 I -1
12.8 80
3.2 +0.6
580
J. yon Stebut and B. Moul~ne : The choice of meaningful parameters obtained from the surface profile analysis in order to characterize the deep drawing capacity of a metal sheet. 13th biennal congress of the IDDRG (1984) Melbourne. J. von Stebut and J. Merk : Dispositif de mesure de forces de frottement et de l'usure h mouvement alternatif permettant de fortes charges et des surfaces de contact importantes. French patent no 82 13921. X. Roizard and J. von Stebut : The influence of contact temperature on metal transfert and galling in strip drawing. 16th biennal congress of the IDDRG (1990) Borl~inge. L.H. Butler : The effects of interposed lubricants on the surface deformation of metals during plasting working. Journal of the Institute of Metals. Vol. 88 (1960) pp. 337-343. L.H. Butler : The influence of lubricants on the grows of surface-contact areas during plastic deformation of metals. Journal of the Institute of Metals. Vol. 89 (1961) pp.116-123. T. Nellemann, N. Bay, T. Wanheim : Real area of contact and friction stress - The role of trapped lubricant. Wear. Vol. 43 (1977) pp. 45-53. Y. Berthier : Communication ~ la Socirt6 Tribologique de France (1992). J. yon Stebut and B. Moul~:ne : Determination of the real bearing area after friction by means of surface profile analysis. IDDRG Working group meeting WG I/4 (1988) Helsinki.
Int. J. Mach. Tools Manufact. Vol. 35, No.2. pp. 169-175, 1995 Elsevier Science Ltd. Printed in Great Britain 0890-6955/9557.00 + .00
S U R F A C E A S P E R I T Y F L A q T E N I N G I N S H E E T M E T A L F O R M I N G - A 3-D R E L O C A T I O N STYLUS PROFILOMETRIC STUDY
X. ROIZARDf AND J. VON STEBUT~ tLM.I.T., I.U.T. D~T. GflNIE MI~,CANIQUEEl" PRODUCTIQUE B. P. 1559, F-25009 BESAN(~ONCEDEX, FRANCE. *L.S.G.S., I~XZOLEDES MINES, F-54042 NANCY, CEDEX, FRANCE.
SUMMARY Among the laser textured steel sheets retained for difficult stamping situations those with isolated, non communicating valleys are shown to be especially interesting. Such isolated valleys act simultaneously as traps for wear debris and as practically frictionless, high pressure oil pockets, participating in overall load carrying. These results are substantiated by 3D profilometry before and after friction to analyse specific residual roughness and friction-induced surface damage on the load carrying plateaux. difference consists in a different average plateau length 1", INTRODUCTION while plateau spacing Lss is similar. In addition, there is a significant difference in skewness : negative for T1 and Sheet surface roughness is known to be important positive for T2. for friction and galling in the press shop. From first principles in contact mechanics it is clear t) that the Friction experiments die/sheet surface asperity contact angle will dominate the amount of sheet surface shearing. Thus both roughness Strip drawing was done by means of a test rig (height) parameters 2) and horizontal spacing 3) must be (fig.2) described in detail in 7). A 50 mm wide and 0.7 mm considered for sheet surface topography optimisition in thick boundary lubricated (1) mild steel sheet was stamping. Montfort and al. have introduced the compound squeezed in between two non rotating O 20 ram, 60 mm parameter 4) which allows for clear empirical selection of long high speed steel dies (Ra _< 0.I iam) leading to a sheets correlating well with stamping behaviour. In perfectly symmetrie, extended ( = 0.3 mm wide at 4 kN) addition, negatively skewed surfaces (cf. abrasively worn double "line" contact. Normal loads of 4 kN were applied surfaces) also decrease the tool/sheet contact angle. by means of a pneumatic actuator. Friction experiments Another functional approach has been chosen by were run in the unidirectional multipass mode. This Rault and Entringer s). Their antigalling roughness profile implies return to the starting position with the dies "liffed is based on the valleys' capacity of trapping wear debris. off" in between two consecutive passes. Contact When embedded on the roughness plateaux these debris temperature was varied by means of heating elements lead to galling. This work showed in particular that there powered by a P!D controller. is a critical plateau length beyond which such debris embedding becomes important. Laser textured sheets, with RESULTS AND DISCUSSION a regular array of load carrying plateaux have brought about an economic solution in the same line as proposed Asperity truncation : debris generation and by Rault, with the additional advantage of being trapping practically isotropic and allowing for tailored plateau and valley lateral spacing. Fig. 3 shows how friction is successively modified In the present work we address both the wear in multipass operation. While there is only a slight debris trapping and the lubrication aspect. While the advantage of sheet T1 at room temperature this difference amount of lubricant stored in the sheet surface can be is patent at 100 °C where static friction increase after the quantified by the empty volume identical with the average 4 th pass indicates the onset of galling phenomena s). Some peak height Rpm 6) particular attention will be paid to the insight into the associated micromechanical modifications fact whether the roughness valleys communicate or not. can be gained from fig. 4, where surface topography of the virgin sheets is compared with that observed after 5 I~XPERIMENTAI,, DETAILS consecutive strip drawing passes. When looking at the beginning of the 50 mm Sheet surface morphology sliding distance it is clear that T1 resists much better to friction-induced surface truncation. This conclusion is The specimens retained for this study were two backed up by 2D relocation profilometry (fig. 5). types of uncoated, laser textured mild steel sheets Tl and Quantitative, statistical analysis (fig. 6-a) T2. For the first set the surface morphology consisted in substantiates these findings. an array of isolated valleys within essentially During the first pass the rate of surface truncation communicating plateaux, while the second set had of sheet T2 is twice that of Tl (60 % as compared to 30 isolated, flat continuous plateaux separated by a network %). Even though this rate decreases with pass number, the of communicating valleys (fig. 1). 3D topographic plots residual security margin in empty volume, likely to feed in were assessed by means of standard PC driven tactile lubricant and to trap wear particles is reduced to 20 % for profilometry 2,3) with a Talysurf l0 as pick-up. T2 (as compared to 40 % for TI). Corresponding quantitative data are compiled in table 1. (I) Our standatt sheet oiling procedure for boundat), lubrication From inspection of this table it is patent that the corresqxmdsto 4g of oil per m2 sheet surface. This amountsto roughness parameters are practically identical. The major approximately half of the empty surface volume Rpm 169
170
X. ROlZnRD and J. von STEBUT
(a)
(b) Depth distribution 0
,
---.___
-5
Sheet TI
~m ~
Total depth Mean depth
: 16.32 ~m : 5.92 ~m
Depth distribution 0 15
-5 I0
Sheet T2
-10
5
-
-15 ~m.,
o
Total depth Mean depth
: 11.64 ~m : 6.05 ~tm
Fig. 1 ." steel sheet surface morphology ," a - bearing (white) areas ; b - corresponding height distributions. ,,
be concluded for T2 that this is due to the joint effect of a higher rate of debris generation and to an insufficient residual empty volume for debris trapping. Asperity truncation : lubrication aspects
-.,d--
sheet /
I
Fig. 2 ." synoptic o f the friction test rig
Fig. 7 gives more morphological information on the modifications resulting from the first pass. For T2 secondary asperities have emerged giving rise to a net decrease in average peak spacing and, above all, leading to high contact angle asperity shearing, likely to generate more wear debris than for T1 where surface morphology changes are negligible. Wear particles contin ously generated will accumulate preferentially ahead of the advancing dies. At the end of a 50 mm friction pass when lifting the dies off the surface before going back to the beginning of the track, only those debris sticking to the dies will be recycled. Thus the abrasive action of debris will be much less effective in the beginning of a pass. The severely scratched surface at the end of pass # 5 for sheet T2 is therefore a consequence of wear part.cle ploughing. It can
Clearly the rates of asperity truncation and debris generation are fundamental aspects of tool/workpiece interaction in metal forming operations. However, if this is so why don't we find more debris entrapping on the largely continous plateaux of sheet # 1 with an array of isolated valleys ? This is what should be expected from Rault's results 5) concerning a critical sliding length for wear particle embedding. The reason of this could be related to a fundamental difference in morphology-specific lubrication efficiency. Therefore the remainder of this study is dedicated to potential microhydrodynamic mechanisms as conjectured in the literature 9,10.11). For reasons of simplicity we shall only retain the "unfavourable" T2 morphology with isolated plateaux and communicating valleys. As shown 9.ma2) high pressure lubricant pockets may form on the plateaux and participate in load carrying. Fig. 8 illustrates such entrapped oil pockets on a T2 type plateau. If this mechanism applies there should be a residual, persisting plateau roughness intimately related to the basic lubrication parameters like contact pressure, sliding speed, and temperature of the lubricant : In fig. 9 an fig. 10 the effect of one single 50 mm pass on the surface height distributions and associated "Abbott bearing plots" is shown as a function of contact temperature and sliding speed. As discussed in 13) the upper part left of the bend-over in the Abbott bearing plot corresponds to surface areas having been modified during strip drawing. The corresponding height difference 6Rz is the persistent, residual plateau roughness. Clearly 5Rz decreases with increasing contact temperature (fig. 9-c) implying that contact becomes more severe. On the
Surface asperity flattening in sheet metal forming
T1
T2
J
J
171
T2
T2
J
J
Ill,
T1
0,2
T2 T2
> ,;2
J
2
TI
0,2
1
2
3
4
5
passnumb~
Fig. 3 : Friction response during 5 consecutive muhipass S.D. routines for T1 and 7"2..
contrary, an increase in sliding speed and thus the fraction of hydrodynamic lubrication decreases contact severity and enhances persistent plateau roughness. Naturally these modifications in sliding contact conditions should be accompanied by modifications in friction. The friction values corresponding to the 6 situations studies in fig. 9 and fig. 10 are plotted out in fig. 11 as a function of 8Rz. It is striking that all friction data points both for varying contact temperature and sliding speed fit on to apractically linear empirical master plot : la = la0 - k ARz (k being a constant) (1) With these results and Amontons' second law of friction in mind a simple law of mixture model can be set up : overall friction is supposed to result from the junction shearing o f dry metal/metal contacts while the isolated pressurised lubricant pockets are assumed to share load carrying without substantial contribution to friction. The tangential friction F t f o r c e is w r i t t e n as :
Ft = 5". ard • "td + ~ arl • ql (2) with the overall load carrying,_.real bearing area : Ar = Y. ard + 2 . arl = Ard + Arl The weight coefficients ard and arl in (2) correspond to the load carrying areas of dry contact and lubricant pockets, 't d and ql being the respective shear strengths of the sheet metal and the lubricant (cf fig. 12). With ql << 'td we get from (2) : Ft = Ard. "td As generally admitted we shall suppose for the sheet hardness H = Fn / Ar, Fn being the overall contact load. Thus we get for the overall friction coefficient : Ft ( A t - Arl ) "t:d la = F--'-n Ar H (3) Xd is a sheet metal material constant describing pure H adhesive, dry friction : lad = ~_.d_. H
172
X. RoIzAm~and J. ,,on SlEiat i
@ a-1
®
Jl
a-2
y b-1
b-2
c-I
c-2
o e-
e~.
E !
~" 500 ~m
Fig. 4 ." 3-D projections o f sheets surface topology. a - 1, 2 ." "virgin" state (as received). b - 1, 2 : beginning of the 5 th pass. c - 1, 2 ." end of the 5t h pass.
T1
(a) Beginning of pass I(X),. ARz/Rz0 (%)
T2
:'~'~
-,_ f.~.'. . . . . LL '
' i'
Virgin
80 i 6O
/
(b)
End of pass
~
'
4O 20 ~
Pass #5 ~",j
1
',."
,
"'. ~"....
~
/ -
I
-
/ ]
-
I
~
1
-
I
!~
!:
!
:
!
:
!
0 1 2 3 4 5
pass # Fig. 5 .' two dimensional relocation profilometry f o r both sheets. Fig. 6 ." zSRz/RzO vs. sliding distance after 5 consecutive S.D. passes (50 turn each). Rz 0 ." total peak to valley roughness amplitude af the virgin sheet.
Surfaceasperityflatteningin sheetmetalforming
173
8.02 [am
I 82.68% ~-~
Residualpersisting 10t.tm plateaurougbn~'~
Vnlley
17.32%
4.97
300)am
Ilrn
1"
Fig. 8 ."plateat~ morphology of sheet T2
44.08%
~]
55.92%
Fig. 7 : major and secondary peaks on T2 surface sheet.
@
1[
((afterfriction))
(heightdistribution functions)
@
curves)(C°rresp°nding Abbottbearing ]
~ 8R~ i
~1
~
60°C 8R ml,
i
A h (tam)
l h
o
(~.m) ~ ' ~
5
T 8Rz
I
I
i
0
50
100 (%)
0
(
8 R z = f(T) )
1
50
100
Ar m(%) Aa
Fig. 9 : residual plateau roughness g)Rz derived from the corresponding Abbott curves as a function of tool temperature. Strip drawing with cylindrical tools ; sliding speed ." 10 rnm/min.
174
X. ROIZARDand J. von STEBUT
II
Q
rfrci°n' aI
(height distribution functions)
F
l
mm/min
(corresponding Abbott bearing curves)
8R z 10 ram/rain
I
,
J ~
5R
I(X) ram/rain
l
h (pro)
I h (~m)
[_looo ~m/m~. I !
F
iI
~
I
0
1(hgt) ram/rain
i
50
~oo (%)
50
lOO Ar --(%) Aa
8R z =f(V) ) II Fig. 10 : residual plateau roughness 6Rz derived from the corresponding Abbott curves as a function of sliding speed. Strip drawing with cylindrical tools ," tool temperature • 20 °C
0,3C
O O •
(Variation of sliding temperature)
20 °C 60 °C 100°C
[] [] []
(Variation of 20 mm/min sliding 200 mm/min speed) 2000 mm/min
0,25
0,213
~),15
I
I
0,5
1
t= 1,5
5Rz
Fig. 11 : friction coefficient during the first pass of strip drawing sliding friction as a function of the resulting persistent plateau roughness 6Rz in turn induced by different contact conditions.
A_, Expression (3) finally becomes It = ltd - 2 - ~ gd (4) Ar in qualitative agreement with the experimental relation ( 1) when assilimilating/-tO to ltd. The final conclusion, when comparing (1) and (4), is that the area fraction Ar~l should Ar be proportional to 8Rz. This is altogether coherent when, in analogy with the macroscopic equivalence for Rpm 2) ~Rz is interpreted as the volume of load carrying lubricant trapped on the plateaux. Fig. 11 is a clear indication of microhydrodynamic lubrication as a major mechanism controlling tool/sheet friction and associated sheet surface damage. With communicating valleys in the sheet surface morphology, oil pressure build-up in the valleys is insufficient to share load carrying as occurring on the oil pockets of the plateaux. On the contrary, with isolated valleys as for sheet T1 dynamic seal-off of these valleys and associated oil pressure build-up should occur. Thus the microhydrodynamic mechanism can be transposed to this larger scale and the considerably better friction behaviour, in spite of over-critical sliding lengths for debris build up, would then be a natural consequence.
Surface asperity flattening in sheet metal forming
175
(total applied load) P (normal pressure) (tool)
Ft (friction force)
(shear stress)
P
q
q~
q
]
(sheet)
ii:
(real s°lid/s°lid ,,j bearing area whereAfrdcti°n i ind;red ,.[ metal shearing ° c c u r s ) / I A [(tt
Ar (total load carrying bearing area) :~"
Aa
....
"-
(apparent macroscopic bearing area) Fig. 12 ." contact mechanical definitions : A a ." apparent macroscopic bearing area. Ar : total load carrying bearing area. Ard : real area of dry solid bearingwhere friction induced shearing OCCURS.
CONCLUSION In a first part we have given experimental surface topographical evidence that mild steel laser textured sheets with isolated valleys are superior in deep drawing simulation than those with communicating valleys : Asperity truncation as well as wear particle generation are less severe in the first case. In a second part we study microhydrodynamic lubrication owing to dynamic seal-off of pressurised oil pockets on the load carrying plateaux. We finally conclude, by transposition, that the superior friction and surface damage behaviour of the first type of laser textured sheets in deep drawing is dominated by hydrodynamic load carrying of the oil trapped in the isolated valleys. Quantitative statistical and relocation profilometry is seen to be a fundamental tool for micromechanical understanding in conatct mechanics. REFEREN(~ES 1) 2) 3) 4)
5)
R. Hill : The mathematical theory of plasticity. Oxford Press (1950) pp. 128-181. J. von Stebut : Modification of a surface profile's height parameters during strip drawing. Wear. Vol. 109 (1986) p. 145. J. yon Stebut : Modification of a surface profile's horizontal spacing during strip drawing. Wear. Vol. 108 (1987) pp. 329-340. G. Monfort and J. Defourny : Tribological factors in the stamping of coated and uncoated steel sheets. 16th biennal congress of the IDDRG (1990) BorRtnge. R. Rault and M. Entringer : Antigalling roughness profile permitting a reduction of a blankholder pressure and the required amount of lubricant during the forming of sheets. 9th biennal congress of the IDDRG (1976) Ann Arbor.
Table Ra
Rq
Rim
1
1(°) l.ss
F.k
Sk ]
6)
7)
8)
9)
10)
11) 12) 13)
TI
2.1
3
T2
2.2
2.8
13.9 550 500
4.6 I -1
12.8 80
3.2 +0.6
580
J. yon Stebut and B. Moul~ne : The choice of meaningful parameters obtained from the surface profile analysis in order to characterize the deep drawing capacity of a metal sheet. 13th biennal congress of the IDDRG (1984) Melbourne. J. von Stebut and J. Merk : Dispositif de mesure de forces de frottement et de l'usure h mouvement alternatif permettant de fortes charges et des surfaces de contact importantes. French patent no 82 13921. X. Roizard and J. von Stebut : The influence of contact temperature on metal transfert and galling in strip drawing. 16th biennal congress of the IDDRG (1990) Borl~inge. L.H. Butler : The effects of interposed lubricants on the surface deformation of metals during plasting working. Journal of the Institute of Metals. Vol. 88 (1960) pp. 337-343. L.H. Butler : The influence of lubricants on the grows of surface-contact areas during plastic deformation of metals. Journal of the Institute of Metals. Vol. 89 (1961) pp.116-123. T. Nellemann, N. Bay, T. Wanheim : Real area of contact and friction stress - The role of trapped lubricant. Wear. Vol. 43 (1977) pp. 45-53. Y. Berthier : Communication ~ la Socirt6 Tribologique de France (1992). J. yon Stebut and B. Moul~:ne : Determination of the real bearing area after friction by means of surface profile analysis. IDDRG Working group meeting WG I/4 (1988) Helsinki.