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Friction inhomogeneities in cold rolling
Journal of Materials Processing Technology 125±126 (2002) 392±397
Friction inhomogeneities in cold rolling Hartmut Pawelski* SMS Demag AG, Metal Forming Technology, Postfach 230229, 40088 DuÈsseldorf, Germany Received 15 December 2001; accepted 24 February 2002
Abstract The friction conditions between strip and work roll are practically never homogeneous. Three different kinds of friction inhomogeneities, typical for technical strip rolling applications, are discussed: The ®rst one is the increase of the friction coef®cient from entry to exit of the roll gap. Measured force and forward slip data is used to recalculate this increase by applying an enhanced Bland±Ford theory. The second one is the case of different friction over the strip width. The in¯uence on ¯atness is shown. The third one is the effect of frictional instabilities like stick-slip, which may induce time-dependent asymmetry between top and bottom side, and therefore corrugations. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Strip rolling; Cold rolling; Friction; Flatness; Corrugations
1. Introduction Typically in a ®rst layout calculation for a strip rolling mill, the friction coef®cient between work roll and strip is assumed to be constant, although this is practically never the case. This constant value is chosen according to the conditions of the speci®ed rolling case. Important characteristics in this context are type of lubrication and rolling speed. A physically based modelling of friction in cold rolling gives a deeper insight, not so much into the exact value of the friction coef®cient, but into the dependence of the friction coef®cient on various additional parameters, e.g. temperature, roughness of strip and work roll (including kind of surface texture), diameter of work roll, reduction, and viscosity of the lubricant. Besides its global predictions, this modelling is also helpful to understand the development of friction inhomogeneities for a speci®c rolling case itself. Friction models for cold rolling, see e.g. [1±4], typically consist of a part which describes the hydrodynamic situation at the inlet zone into the roll gap to calculate the thickness of the entrapped lubricant ®lm, and a part which predicts the change of surface contact conditions from entry to exit of the roll gap. An important prediction is that the fractional area of contact of surface asperities and therefore the friction coef®cient itself is increasing from entry to exit of the roll gap. In general, friction inhomogeneities can be classi®ed as inhomogeneities in time and space. The described increase * Tel.: 49-211-881-5307; fax: 49-211-881-4997. E-mail address: [email protected] (H. Pawelski).
of friction from entry to exit is a spatial change in rolling direction and is case number 1 to be examined. The next case considers a spatial change in width direction, which can be induced by a variation of the mentioned friction-relevant parameters in width direction. In this context one immediately thinks of temperature or roughness differences, which can lead to ¯atness problems. The third case to be discussed is a mixture of time-dependent stick-slip behaviour and asymmetry between top and bottom side of strip. All three examples are taken from cold rolling, but the basic behaviour is also found at hot strip mills in principal, although the methods of calculation have to be adapted to the different friction behaviour. 2. Increase of friction from entry to exit The theoretical requirement for an increase of the friction coef®cient from entry to exit of the roll gap is very obvious in the case of aluminium foil rolling, because the measured forward slip data is much lower (e.g. about 25% for a reduction of thickness from 72 to 34 mm) than that estimated with constant friction (about 35%); [4] gives an example calculation. From the equations of static equilibrium, one can directly conclude that only high friction coef®cients and therefore shear stresses near the exit allows to come down from the high pressure at the neutral zone to the low pressure at the exit. The elastic exit zone with a comparably high friction coef®cient is additionally stabilising the rolling process, so
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 3 5 0 - 3
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
393
Fig. 1. Cold rolling of copper strip (width: 1250 mm) on a two-stand tandem mill from approximately 15 to 0.623 mm thickness in five passes. Measured roll force, torque and forward slip (crosses) and recalculated average values, fitted to force and forward slip (circles connected with lines).
that even rolling cases with forward slip values around zero (the exit strip speed is then identical to the circumferential speed of the work roll) are in most cases tolerable. But even in classical rolling cases far away from foil rolling, the increase predicted by theory can be noticed. In the following we want to analyse measured process data for cold rolling of copper and copper alloys on a two-stand tandem mill using rolling oil. Fig. 1 shows these data for copper, and similar data exists for brass (CuZn37) and bronze (CuSn6). For every pass, each consisting of two reduction steps in stands 1 and 2, the average for the period of constant speed has been taken. This has been repeated for several coils to get a statistically meaningful data set. To include the increase of friction an enhanced form of the classical Bland±Ford rolling theory (an introduction using the same symbol notation can be found in [5]) has been used,
Fig. 2. The elastic roll ¯attening is relatively small, so that using the Hitchcock approximation is suf®cient here. The difference to standard theory is the assumption that the friction coef®cient changes linearly from the entry (mE) to the neutral point (mN) and also from the neutral point to the exit (mA) of the roll gap, ®rst line of Fig. 2. The solutions for the corresponding pressure distributions for the entry and exit branch are given below. If roll force, torque and forward slip are given, it would in principle be possible to get three independent process quantities by a least-square ®t. If we suppose that the deformation-dependent yield stress of the material is known, these quantities could be mE, mN and mA. Unfortunately, due to the uncertainties in the torque data, this leads to nonmeaningful results. It can be expected from the theory of the change of the fractional area of contact of surface asperities
394
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
Fig. 2. Normal pressure in roll gap according to Bland±Ford theory, but enhanced by assuming a non-constant friction coefficient. It changes linearly from entry (mE) to neutral point (mN) and also from neutral point (mN) to exit (mA).
that the increase of friction from the entry to the neutral zone is steeper than from the neutral point to the exit [4]. The main reason is that the maximum of normal pressure is reached at the neutral point. Therefore as the most simple but realistic onset, we assume mN and mA to be equal, and only use force and forward slip data for the recalculation. The results are summarised in Fig. 3. A statistically signi®cant increase of the friction coef®cient can be seen for all three materials. An acceptable coincidence with the measured data is achieved in all cases, see Fig. 1 for copper. This is true even for the torque data, which has not been used for the ®ts. The torque at the work rolls in fact is only approximately known from the motor current of the main
Fig. 3. Increase of friction coefficient from entry (mE) to neutral point and exit (mN mA ) for cold rolling of copper, brass and bronze on a two-stand tandem mill. Mean value and standard deviation of values recalculated from roll force and forward slip for both stands and all passes.
drives. It seems that there is a small systematic error in the factor of this calculation, which is different for stand 1 and stand 2. 3. Friction inhomogeneities and flatness Nowadays, the control of strip ¯atness is a very important part of rolling technology. Therefore it is of interest to estimate the in¯uence of friction inhomogeneities in width direction on strip pro®le and ¯atness. Reasons for different friction coef®cients are, for example, differences in surface structure of roll or strip, and differences in temperature or amount of lubricant. In this context, the multi-zone cooling, which is typically used as actuator for ¯atness control, has to be mentioned. Based on the work of Beisemann [6], SMS Schloemann± Siemag has developed a program system for calculating the deformation of the roll stack, the contour of the roll gap in width direction, and the distribution of strip stress as function of the width coordinate at entry and exit of the roll gap. The exit stress distribution is an important indicator as it can be measured online using a so-called ¯atness roll. Fig. 4 gives the results of an example calculation. The parameters which have been applied are listed below the ®gure. First we want to discuss the case of constant friction (solid lines): a positive work roll bending has been used to compensate the de¯ection of the roll stack. Therefore the exit thickness is nearly constant, only near the strip edges it decreases rapidly; this is the so-called edge drop. In the edge
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
395
drop region a width ¯ow of material to the edge occurs, which has a noticeable effect on the strip stress. Due to higher reduction near the edge it decreases, but very near to the edge, due to a growing amount of width ¯ow, it increases again. Within a zone of about 150 mm width, we now change the friction coef®cient by 10% (dashed lines in Fig. 4). As expected, higher friction gives less reduction, but the amount of change itself is small, since the possibility of width ¯ow, which would allow more different reduction values, is mainly restricted. On the other hand, for the same reason, the effect on the stress distribution is more distinct. For more friction the mean value of entry and exit stress increases, which ®ts to less reduction, but the tendencies are different at entry and exit; while the entry stress is up to 7 N/mm2 higher than for constant friction, the exit stress is about 4 N/mm2 smaller. The explanation is that: more friction wants to move the neutral point to the entry of the roll gap. This has to be compensated by a partial shift of exit stress to entry stress. 4. Generation of stick-slip induced corrugations
Fig. 4. Effect of friction inhomogeneity in width direction on flatness of strip. Example calculation based on an algorithm of Beisemann [6] for a 6Hi mill (cylindrical rolls with diameters 470, 550, 1350 mm, strip width: 1250 mm, entry thickness: 14 mm, average exit thickness: 10 mm, average entry strip tension: 10 N/mm2, average exit strip tension: 30 N/mm2, yield stress: 390 N/mm2, elastic modulus: of strip 100,000 N/mm2, positive work roll bending: 400 kN).
The friction inhomogeneities mentioned above are stationary phenomena. Now we want to discuss how a timedependent periodic change of the friction coef®cient in the roll gap may cause unstable rolling. For cold rolling of brass CuZn37 (thickness range: 4±15 mm) on a 6-Hi mill with one drive, depending on the type of lubricant, a severe instability has been observed: the material leaves the roll gap as corrugated sheet. The peaks and valleys of the corrugations are transverse to rolling direction. The vibrations were so strong that damage to the rolling mill could not be excluded.
Fig. 5. Strip drawing test on brass CuZn37, width: 40 mm, thickness is reduced from 13 to 10 mm, drawing semi-angle: 68. The right diagram shows a small part of the left in higher resolution in time. The limiting lines have been calculated by standard strip theory.
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H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
It has been shown by applying the strip drawing test with large plastic deformation [7] that insuf®cient lubrication was the reason. The experiments were carried out by the author at the Max-Planck-Institut fuÈr Eisenforschung, DuÈsseldorf, Germany. For this type of strip drawing test, the material is drawn through a pair of wedge-shaped dies. Normal force and drawing force are measured so that one is able, by considering the equilibrium of forces only, to directly calculate the friction coef®cient without the need of knowing anything about the material behaviour. The amount of plastic deformation is similar to that of rolling (15±30%) so that tribological similarity can be expected.
In Fig. 5 the results for drawing of brass with two different lubricants are shown. For the conventional rolling oil, a strong instability of the friction coef®cient connected with noisy chattering has been observed. On the other hand the friction coef®cient is stable for an additive concentrate mainly consisting of tri-esters. The situation at the rolling mill is identical: the ®rst lubricant gives corrugations, while the second does not. Some combinations of different types of additives in different concentrations have been tested in detail [8]. It is only important here that there is a strong correlation between the occurrence of chattering at the strip drawing test and corrugations at the rolling mill.
Fig. 6. Model for corrugations induced by friction instabilities. Stationary finite element calculation with 40 15 quadrilateral elements, work roll diameter: 500 mm, strip width: 1000 mm, entry thickness: 10 mm, exit thickness: 8 mm, yield stress: 500 N/mm2, strip tensions have been neglected. In the lower right corner a result of the simulation after 40 mm length of rolled strip is shown. The darkness of the plot is proportional to the strain rate (white means 0 and dark grey 16 s 1).
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
Let us have a closer look on the forces of the strip drawing test when chattering is observed, (Fig. 5, diagram on the right side). The drawing force FZ increases while the normal force on the drawing dies FQ decreases, giving an increase of the calculated friction coef®cient m. Then suddenly (one interval of data acquisition, 0.01 s) they go back to their starting values. This is repeated periodically. The limiting values (dashed lines), calculated by standard strip theory, see e.g. [5], ®ts very well into the measured data, which means that we have a quasi-static increase of friction up to a maximum value and then an abrupt decrease to the minimum value: this behaviour is well known as stick-slip. One open question remains: How does an unstable friction coef®cient cause corrugations? Fig. 6 illustrates a possible mechanism. This example calculation is based on a stationary ®nite element calculation of the two-dimensional plane strain material ¯ow in the roll gap [9]. Since the form of the corrugations is identical over the width of the strip, it is not necessary to consider a ¯ow of material in width direction. The simulation starts by assuming an eventual increase of the friction coef®cient between strip and the bottom work roll caused by the stick-slip capability of the lubricant. The torque on the bottom side increases, which will slow down the circumferential speed on that side for a short time. This leads to a decrease of the friction coef®cient. This periodic asymmetry between top and bottom side gives a periodically changing angular speed of strip at the exit of the roll gap (ski up and down) and therefore the observed corrugations. It is interesting that the simulated change of roll force is very small compared to the change of torque on each side. This ®ts the observation that the strip with corrugation has no signi®cant thickness deviations, which is contrary to the phenomenon of shattering at rolling mills. The wavelength of the corrugations (25±75 mm) is 1±3 times longer than the
397
contact length in the roll gap. Their exact length is somewhat arbitrary and not deterministically depending on speed. 5. Conclusion All three kinds of friction inhomogeneities mentioned above are important effects in strip rolling. They all demonstrate the practical need for theories with non-constant friction coef®cients. A suitable modelling of each of them affords a different kind of simulation technique. References [1] M.P.F. Sutcliffe, K.L. Johnson, Lubrication in cold strip rolling in the mixed regime, Proc. Inst. Mech. Eng. 204 (1990) 249±261. [2] D. Chang, N. Marsault, W.R.D. Wilson, Lubrication of strip rolling in the low-speed mixed regime, Tribiol. Trans. 39 (2) (1996) 407±415. [3] W. Rasp, P. HaÈfele, Investigation into tribology of cold strip rolling, Steel Res. 69 (45) (1998) 154±160. [4] H. Pawelski, Evolution of surface roughness and corresponding friction during cold rolling, in: Advanced Technology of Plasticity, Proceedings of the Sixth ICTP, Vol. 3, NuÈrnberg, Springer, Berlin, 1999, pp. 1931±1936. [5] H. Pawelski, O. Pawelski, Technische Plastomechanik, Verlag Stahleisen, DuÈsseldorf, 2000, pp. 122±127. [6] G. Beisemann, Theoretische Untersuchungen der mechanisch einstellbaren Bereiche fuÈr die Walzspaltform an unterschiedlichen Walzwerksbauarten, Umformtechnische Schriften, B and 7, Verlag Stahleisen, DuÈsseldorf, 1987. [7] O. Pawelski, Ein neues GeraÈt zum Messen des Reibungsbeiwertes bei plastischen FormaÈnderungen, Stahl und Eisen 84 (20) (1964) 1233±1243. [8] H. Pawelski, R. de Sutter, E. DoÈtterl, Paxisgerechte Bewertung von WalzoÈladditiven mit Hilfe des Streifenziehversuchs, Tribologie und Schmierungstehnik 49 (3) (2002) 24±27. [9] H. Pawelski, Comparison of methods for calculating the influence of asymmetry in strip and plate rolling, Steel Res. 71 (12) (2000) 490±496.
Friction inhomogeneities in cold rolling Hartmut Pawelski* SMS Demag AG, Metal Forming Technology, Postfach 230229, 40088 DuÈsseldorf, Germany Received 15 December 2001; accepted 24 February 2002
Abstract The friction conditions between strip and work roll are practically never homogeneous. Three different kinds of friction inhomogeneities, typical for technical strip rolling applications, are discussed: The ®rst one is the increase of the friction coef®cient from entry to exit of the roll gap. Measured force and forward slip data is used to recalculate this increase by applying an enhanced Bland±Ford theory. The second one is the case of different friction over the strip width. The in¯uence on ¯atness is shown. The third one is the effect of frictional instabilities like stick-slip, which may induce time-dependent asymmetry between top and bottom side, and therefore corrugations. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Strip rolling; Cold rolling; Friction; Flatness; Corrugations
1. Introduction Typically in a ®rst layout calculation for a strip rolling mill, the friction coef®cient between work roll and strip is assumed to be constant, although this is practically never the case. This constant value is chosen according to the conditions of the speci®ed rolling case. Important characteristics in this context are type of lubrication and rolling speed. A physically based modelling of friction in cold rolling gives a deeper insight, not so much into the exact value of the friction coef®cient, but into the dependence of the friction coef®cient on various additional parameters, e.g. temperature, roughness of strip and work roll (including kind of surface texture), diameter of work roll, reduction, and viscosity of the lubricant. Besides its global predictions, this modelling is also helpful to understand the development of friction inhomogeneities for a speci®c rolling case itself. Friction models for cold rolling, see e.g. [1±4], typically consist of a part which describes the hydrodynamic situation at the inlet zone into the roll gap to calculate the thickness of the entrapped lubricant ®lm, and a part which predicts the change of surface contact conditions from entry to exit of the roll gap. An important prediction is that the fractional area of contact of surface asperities and therefore the friction coef®cient itself is increasing from entry to exit of the roll gap. In general, friction inhomogeneities can be classi®ed as inhomogeneities in time and space. The described increase * Tel.: 49-211-881-5307; fax: 49-211-881-4997. E-mail address: [email protected] (H. Pawelski).
of friction from entry to exit is a spatial change in rolling direction and is case number 1 to be examined. The next case considers a spatial change in width direction, which can be induced by a variation of the mentioned friction-relevant parameters in width direction. In this context one immediately thinks of temperature or roughness differences, which can lead to ¯atness problems. The third case to be discussed is a mixture of time-dependent stick-slip behaviour and asymmetry between top and bottom side of strip. All three examples are taken from cold rolling, but the basic behaviour is also found at hot strip mills in principal, although the methods of calculation have to be adapted to the different friction behaviour. 2. Increase of friction from entry to exit The theoretical requirement for an increase of the friction coef®cient from entry to exit of the roll gap is very obvious in the case of aluminium foil rolling, because the measured forward slip data is much lower (e.g. about 25% for a reduction of thickness from 72 to 34 mm) than that estimated with constant friction (about 35%); [4] gives an example calculation. From the equations of static equilibrium, one can directly conclude that only high friction coef®cients and therefore shear stresses near the exit allows to come down from the high pressure at the neutral zone to the low pressure at the exit. The elastic exit zone with a comparably high friction coef®cient is additionally stabilising the rolling process, so
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 3 5 0 - 3
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
393
Fig. 1. Cold rolling of copper strip (width: 1250 mm) on a two-stand tandem mill from approximately 15 to 0.623 mm thickness in five passes. Measured roll force, torque and forward slip (crosses) and recalculated average values, fitted to force and forward slip (circles connected with lines).
that even rolling cases with forward slip values around zero (the exit strip speed is then identical to the circumferential speed of the work roll) are in most cases tolerable. But even in classical rolling cases far away from foil rolling, the increase predicted by theory can be noticed. In the following we want to analyse measured process data for cold rolling of copper and copper alloys on a two-stand tandem mill using rolling oil. Fig. 1 shows these data for copper, and similar data exists for brass (CuZn37) and bronze (CuSn6). For every pass, each consisting of two reduction steps in stands 1 and 2, the average for the period of constant speed has been taken. This has been repeated for several coils to get a statistically meaningful data set. To include the increase of friction an enhanced form of the classical Bland±Ford rolling theory (an introduction using the same symbol notation can be found in [5]) has been used,
Fig. 2. The elastic roll ¯attening is relatively small, so that using the Hitchcock approximation is suf®cient here. The difference to standard theory is the assumption that the friction coef®cient changes linearly from the entry (mE) to the neutral point (mN) and also from the neutral point to the exit (mA) of the roll gap, ®rst line of Fig. 2. The solutions for the corresponding pressure distributions for the entry and exit branch are given below. If roll force, torque and forward slip are given, it would in principle be possible to get three independent process quantities by a least-square ®t. If we suppose that the deformation-dependent yield stress of the material is known, these quantities could be mE, mN and mA. Unfortunately, due to the uncertainties in the torque data, this leads to nonmeaningful results. It can be expected from the theory of the change of the fractional area of contact of surface asperities
394
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
Fig. 2. Normal pressure in roll gap according to Bland±Ford theory, but enhanced by assuming a non-constant friction coefficient. It changes linearly from entry (mE) to neutral point (mN) and also from neutral point (mN) to exit (mA).
that the increase of friction from the entry to the neutral zone is steeper than from the neutral point to the exit [4]. The main reason is that the maximum of normal pressure is reached at the neutral point. Therefore as the most simple but realistic onset, we assume mN and mA to be equal, and only use force and forward slip data for the recalculation. The results are summarised in Fig. 3. A statistically signi®cant increase of the friction coef®cient can be seen for all three materials. An acceptable coincidence with the measured data is achieved in all cases, see Fig. 1 for copper. This is true even for the torque data, which has not been used for the ®ts. The torque at the work rolls in fact is only approximately known from the motor current of the main
Fig. 3. Increase of friction coefficient from entry (mE) to neutral point and exit (mN mA ) for cold rolling of copper, brass and bronze on a two-stand tandem mill. Mean value and standard deviation of values recalculated from roll force and forward slip for both stands and all passes.
drives. It seems that there is a small systematic error in the factor of this calculation, which is different for stand 1 and stand 2. 3. Friction inhomogeneities and flatness Nowadays, the control of strip ¯atness is a very important part of rolling technology. Therefore it is of interest to estimate the in¯uence of friction inhomogeneities in width direction on strip pro®le and ¯atness. Reasons for different friction coef®cients are, for example, differences in surface structure of roll or strip, and differences in temperature or amount of lubricant. In this context, the multi-zone cooling, which is typically used as actuator for ¯atness control, has to be mentioned. Based on the work of Beisemann [6], SMS Schloemann± Siemag has developed a program system for calculating the deformation of the roll stack, the contour of the roll gap in width direction, and the distribution of strip stress as function of the width coordinate at entry and exit of the roll gap. The exit stress distribution is an important indicator as it can be measured online using a so-called ¯atness roll. Fig. 4 gives the results of an example calculation. The parameters which have been applied are listed below the ®gure. First we want to discuss the case of constant friction (solid lines): a positive work roll bending has been used to compensate the de¯ection of the roll stack. Therefore the exit thickness is nearly constant, only near the strip edges it decreases rapidly; this is the so-called edge drop. In the edge
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
395
drop region a width ¯ow of material to the edge occurs, which has a noticeable effect on the strip stress. Due to higher reduction near the edge it decreases, but very near to the edge, due to a growing amount of width ¯ow, it increases again. Within a zone of about 150 mm width, we now change the friction coef®cient by 10% (dashed lines in Fig. 4). As expected, higher friction gives less reduction, but the amount of change itself is small, since the possibility of width ¯ow, which would allow more different reduction values, is mainly restricted. On the other hand, for the same reason, the effect on the stress distribution is more distinct. For more friction the mean value of entry and exit stress increases, which ®ts to less reduction, but the tendencies are different at entry and exit; while the entry stress is up to 7 N/mm2 higher than for constant friction, the exit stress is about 4 N/mm2 smaller. The explanation is that: more friction wants to move the neutral point to the entry of the roll gap. This has to be compensated by a partial shift of exit stress to entry stress. 4. Generation of stick-slip induced corrugations
Fig. 4. Effect of friction inhomogeneity in width direction on flatness of strip. Example calculation based on an algorithm of Beisemann [6] for a 6Hi mill (cylindrical rolls with diameters 470, 550, 1350 mm, strip width: 1250 mm, entry thickness: 14 mm, average exit thickness: 10 mm, average entry strip tension: 10 N/mm2, average exit strip tension: 30 N/mm2, yield stress: 390 N/mm2, elastic modulus: of strip 100,000 N/mm2, positive work roll bending: 400 kN).
The friction inhomogeneities mentioned above are stationary phenomena. Now we want to discuss how a timedependent periodic change of the friction coef®cient in the roll gap may cause unstable rolling. For cold rolling of brass CuZn37 (thickness range: 4±15 mm) on a 6-Hi mill with one drive, depending on the type of lubricant, a severe instability has been observed: the material leaves the roll gap as corrugated sheet. The peaks and valleys of the corrugations are transverse to rolling direction. The vibrations were so strong that damage to the rolling mill could not be excluded.
Fig. 5. Strip drawing test on brass CuZn37, width: 40 mm, thickness is reduced from 13 to 10 mm, drawing semi-angle: 68. The right diagram shows a small part of the left in higher resolution in time. The limiting lines have been calculated by standard strip theory.
396
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
It has been shown by applying the strip drawing test with large plastic deformation [7] that insuf®cient lubrication was the reason. The experiments were carried out by the author at the Max-Planck-Institut fuÈr Eisenforschung, DuÈsseldorf, Germany. For this type of strip drawing test, the material is drawn through a pair of wedge-shaped dies. Normal force and drawing force are measured so that one is able, by considering the equilibrium of forces only, to directly calculate the friction coef®cient without the need of knowing anything about the material behaviour. The amount of plastic deformation is similar to that of rolling (15±30%) so that tribological similarity can be expected.
In Fig. 5 the results for drawing of brass with two different lubricants are shown. For the conventional rolling oil, a strong instability of the friction coef®cient connected with noisy chattering has been observed. On the other hand the friction coef®cient is stable for an additive concentrate mainly consisting of tri-esters. The situation at the rolling mill is identical: the ®rst lubricant gives corrugations, while the second does not. Some combinations of different types of additives in different concentrations have been tested in detail [8]. It is only important here that there is a strong correlation between the occurrence of chattering at the strip drawing test and corrugations at the rolling mill.
Fig. 6. Model for corrugations induced by friction instabilities. Stationary finite element calculation with 40 15 quadrilateral elements, work roll diameter: 500 mm, strip width: 1000 mm, entry thickness: 10 mm, exit thickness: 8 mm, yield stress: 500 N/mm2, strip tensions have been neglected. In the lower right corner a result of the simulation after 40 mm length of rolled strip is shown. The darkness of the plot is proportional to the strain rate (white means 0 and dark grey 16 s 1).
H. Pawelski / Journal of Materials Processing Technology 125±126 (2002) 392±397
Let us have a closer look on the forces of the strip drawing test when chattering is observed, (Fig. 5, diagram on the right side). The drawing force FZ increases while the normal force on the drawing dies FQ decreases, giving an increase of the calculated friction coef®cient m. Then suddenly (one interval of data acquisition, 0.01 s) they go back to their starting values. This is repeated periodically. The limiting values (dashed lines), calculated by standard strip theory, see e.g. [5], ®ts very well into the measured data, which means that we have a quasi-static increase of friction up to a maximum value and then an abrupt decrease to the minimum value: this behaviour is well known as stick-slip. One open question remains: How does an unstable friction coef®cient cause corrugations? Fig. 6 illustrates a possible mechanism. This example calculation is based on a stationary ®nite element calculation of the two-dimensional plane strain material ¯ow in the roll gap [9]. Since the form of the corrugations is identical over the width of the strip, it is not necessary to consider a ¯ow of material in width direction. The simulation starts by assuming an eventual increase of the friction coef®cient between strip and the bottom work roll caused by the stick-slip capability of the lubricant. The torque on the bottom side increases, which will slow down the circumferential speed on that side for a short time. This leads to a decrease of the friction coef®cient. This periodic asymmetry between top and bottom side gives a periodically changing angular speed of strip at the exit of the roll gap (ski up and down) and therefore the observed corrugations. It is interesting that the simulated change of roll force is very small compared to the change of torque on each side. This ®ts the observation that the strip with corrugation has no signi®cant thickness deviations, which is contrary to the phenomenon of shattering at rolling mills. The wavelength of the corrugations (25±75 mm) is 1±3 times longer than the
397
contact length in the roll gap. Their exact length is somewhat arbitrary and not deterministically depending on speed. 5. Conclusion All three kinds of friction inhomogeneities mentioned above are important effects in strip rolling. They all demonstrate the practical need for theories with non-constant friction coef®cients. A suitable modelling of each of them affords a different kind of simulation technique. References [1] M.P.F. Sutcliffe, K.L. Johnson, Lubrication in cold strip rolling in the mixed regime, Proc. Inst. Mech. Eng. 204 (1990) 249±261. [2] D. Chang, N. Marsault, W.R.D. Wilson, Lubrication of strip rolling in the low-speed mixed regime, Tribiol. Trans. 39 (2) (1996) 407±415. [3] W. Rasp, P. HaÈfele, Investigation into tribology of cold strip rolling, Steel Res. 69 (45) (1998) 154±160. [4] H. Pawelski, Evolution of surface roughness and corresponding friction during cold rolling, in: Advanced Technology of Plasticity, Proceedings of the Sixth ICTP, Vol. 3, NuÈrnberg, Springer, Berlin, 1999, pp. 1931±1936. [5] H. Pawelski, O. Pawelski, Technische Plastomechanik, Verlag Stahleisen, DuÈsseldorf, 2000, pp. 122±127. [6] G. Beisemann, Theoretische Untersuchungen der mechanisch einstellbaren Bereiche fuÈr die Walzspaltform an unterschiedlichen Walzwerksbauarten, Umformtechnische Schriften, B and 7, Verlag Stahleisen, DuÈsseldorf, 1987. [7] O. Pawelski, Ein neues GeraÈt zum Messen des Reibungsbeiwertes bei plastischen FormaÈnderungen, Stahl und Eisen 84 (20) (1964) 1233±1243. [8] H. Pawelski, R. de Sutter, E. DoÈtterl, Paxisgerechte Bewertung von WalzoÈladditiven mit Hilfe des Streifenziehversuchs, Tribologie und Schmierungstehnik 49 (3) (2002) 24±27. [9] H. Pawelski, Comparison of methods for calculating the influence of asymmetry in strip and plate rolling, Steel Res. 71 (12) (2000) 490±496.