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Friction measurement in cold rolling
Journal of Materials Processing Technology 111 (2001) 142±145
Friction measurement in cold rolling Y.J. Liua,*, A.K. Tieua, D.D. Wanga, W.Y.D. Yuenb a
Department of Mechanical Engineering, University of Wollongong, North®elds Avenue, Wollongong, NSW 2522, Australia b Steel Research Laboratories, BHP Steel, Port Kembla, NSW 2505, Australia
Abstract In order to study friction in the roll bite in the laboratory, a work roll with embedded pins is used in cold rolling. Friction and pressure are studied under dry and lubricated conditions. Aluminum alloy is used in the experiments. The results con®rm that the friction coef®cient in the roll bite is not uniform. The validity of the experimental data is con®rmed by comparing it with theoretical results. This indicates that the sensor roll can give reliable friction measurements. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Friction; Cold rolling; Sensor roll; Forward slip
1. Introduction Friction at the interfaces between two rolls and a strip being plastically deformed by the rolls is one of the most important considerations in both the theory and practice of plastic working. However, the nature of friction at the strip± roll interface is not clearly understood. The traditional approach is to assume that the frictional force in the roll bite is proportional to the normal force, with the friction coef®cient remaining constant in cold rolling. However, this affects the accuracy of the mathematical model and consequently the thickness and shape of the strip. The ratio of the interfacial frictional stress to the normal pressure is de®ned as the friction coef®cient. There are several ways to describe this coef®cient. These include Amonton's laws and the statement that t mk, where t is the frictional stress, k the shear yield strength, and m a constant multiplier between zero and unity. While both of these approaches lead to a reasonable prediction of process variables, they are, strictly speaking, incorrect. A limited number of cold rolling tests were reported in [1±3], all showing that the ratio of frictional to normal stress is indeed not constant during rolling, con®rming the suggestion of Shaw et al. [4] that for relatively high interfacial normal stresses, this ratio varies along the contact zone. The objectives of the present study is to understand the relationship between the friction coef®cient and the process parameters and how the friction coef®cient varies in the roll bite. Finally, experimental and calculated results were * Corresponding author. Tel.: 61-2-4221-4923; fax: 61-2-4221-3101. E-mail address: [email protected] (Y.J. Liu).
compared. Aluminum alloy H5052-H34 was used in all experiments. 2. Experimental equipment and material 2.1. The rolling mill and data acquisition A two-high rolling mill with rolls of 225 mm diameter and 254 mm length, driven by a variable speed DC motor of 75 hp, was used. The maximum rolling force, torque and speed are 1500 kN, 13 kN m and 70 rpm, respectively. The sensor roll nitrided surface hardness is 65±70 HRC. Two group of sensors are embedded in the roll, one with full-bridge strain gauges, the other with high sensitive, temperature-compensated load-cells. The pin diameter is 2 mm. The sensor roll overview and sectional view showing the pressure pins are given in Figs. 1 and 2, respectively. The rolling time can be less than 25 ms at a rolling speed of 70 rpm, so it is necessary to use a fast computer and data acquisition system to capture enough data points in the roll bite. A Pentium III computer was used in the experiments. The maximum sampling rate is 250 k/s. 2.2. Materials Aluminum alloy H5052-H34 and lubricant Rolkleen 485A were used in the experiments. The variation of the material resistance to deformation is obtained from the constitutive relationship, an expression similar to that in [5] as shown below being used: s 199:60 1 201:8e0:097 MPa
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 4 1 - 6
(1)
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
143
Nomenclature h1 h2 L
strip entry thickness strip exit thickness mark length left on strip after sensor roll turns one circle circumference of sensor roll deformed roll radius forward slip roll speed
L0 R0 Sf v
Fig. 2. Sensor roll section view.
Greek letters e reduction (%) s yield strength of material f1 bite angle at entry point friction coefficient
3. Results and discussion The determination of the friction coef®cient in the roll gap is done by an analysis of the equilibrium of forces acting on the radial and oblique pins. Here, the same analysis method adopted in [1,6] is used in calculating the friction coef®cient. The Orowan equation, solved according to Alexander [7], is used for determining the rolling pressure, rolling force and rolling torque. Variable friction coef®cient in the roll bite is also considered. In the results presented below, ``variable friction coef®cient'' refers to the friction coef®cients in the roll bite measured from the sensor roll and ``constant friction coef®cient'' refers to constant friction coef®cient calculated from the forward slip in [8] as shown in Eq. (2): 2 R0 f1 f1 2 Sf (2) h2 2 4m
Fig. 3. Force distribution e 29:48% (lubricated).
The force distributions from the radial and oblique pins are shown in Figs. 3 and 4 for 29.48 and 17.71% reduction,
respectively. The experiments for Figs. 3 and 4 were carried out under lubricated and dry condition, respectively. After analysis of the measured data, the pressure and friction coef®cient distribution in the roll bite shown in Figs. 5±8 are obtained. From Figs. 5 and 6, the pressure peak in the roll bite as predicted by the standard rolling theory cannot be detected. This could be due to the effect of the pin diameter (2 mm) compared with the contact length (10.1 mm for lubricated condition, 7.9 mm for dry condition). From Figs. 5±8, it can be seen that the location of the single pressure peak may not coincide with the location of the neutral point and that the friction coef®cient varies widely throughout the roll bite. In isolated instances, double or triple pressure peaks have been measured in [3,6] or predicted in [10,11]. During commissioning of our sensor roll, double pressure peaks
Fig. 1. Sensor roll overview.
Fig. 4. Force distribution e 17:71% (dry).
The forward slip in Eq. (2) is determined by the marking method [9] in the experiments. Eq. (3) shows how the forward slip is calculated: Sf
L
L0 L0
100%
(3)
144
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
Fig. 5. Pressure distribution e 29:48% (lubricated).
Fig. 6. Pressure distribution e 17:71% (dry).
Fig. 9. Pressure comparison e 29:48% (lubricated).
Fig. 10. Pressure comparison e 17:71% (dry).
Fig. 7. Friction coef®cient e 29:48% (lubricated).
for oblique pin was found to be caused by the segment movement. Comparison between the measured and calculated pressure distributions are shown in Figs. 9 and 10 for lubricated and dry rolling condition. The pressure from the mixed ®lm lubrication model [12] compares well with the measured radial pressure from the sensor roll. Calculation results show that the three curves in Figs. 9 and 10 give reasonable agreement. Finally, the rolling force and torque are shown in Figs. 11 and 12. From the two graphs, it can be seen that the measured rolling load and torque validate the pressures measured by the sensor roll.
Fig. 8. Friction coef®cient e 17:71% (dry).
Fig. 11. Rolling force comparison (dry).
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
145
Acknowledgements The ®nancial assistance of the Australian Research Council and BHP Steel Research are gratefully acknowledged. The authors also wish to thank the management of BHP Steel Research Laboratories for permission to publish the material contained in this paper. References Fig. 12. Rolling torque comparison (dry).
4. Conclusions 1. The friction coef®cient in the roll bite is not constant. 2. Determination of the friction coef®cient using a sensor roll has been validated by the experimental results. These values are found to be reasonable on comparing them with the theoretical calculation. 3. No obvious pressure peak was found over the roll bite, and the location of the single pressure peak does not coincide with the location of the neutral point.
[1] G.T. Van Rooyen, W.A. Backofen, J. Iron Steel Inst. 186 (1957) 235±244. [2] A. Banerji, W.B. Rice, Ann. CIRP 21 (1972) 53±54. [3] F.A.R. Al-Salehi, T.C. Firbank, P.R. Lancaster, Int. J. Mech. Sci. 15 (1973) 693±710. [4] M.C. Shaw, A. Ber, P. Mamin, J. Basic Eng. Ð ASME 82 (1960) 342±346. [5] A.N. Karagiozis, J.G. Lenard, Eurotrib 85 (1985) 1±7. [6] Lim Lai-Seng, J.G. Lenard, J. Eng. Mater. Technol. 106 (1984) 139±146. [7] J.M. Alexander, R.C. Brewer, G.W. Rowe, Manufacturing Technology, Vol. 2: Engineering Processes, Ellis Horwood, Chichester, UK, 1993. [8] H. Ford, D.R. Bland, J. Iron Steel Inst. 168 (1951) 57±72. [9] Y.J. Liu, A.K. Tieu, E.B. Li, W.Y.D. Yuen, in: Proceedings of the AFDM'99, Pusan, South Korea, 1999, pp. 495±500. [10] Li. Guo-ji, S. Kobayashi, J. Eng. Ind. Ð ASME 104 (1982) 55±64. [11] J.G. Lenard, in: Proceedings of the COBEM, Rio de Janeiro, 1981, pp. 13±24. [12] Z.L. Qiu, W.Y.D. Yuen, A.K. Tieu, J. Tribol. Ð Trans. ASME 121 (1999) 1±8.
Friction measurement in cold rolling Y.J. Liua,*, A.K. Tieua, D.D. Wanga, W.Y.D. Yuenb a
Department of Mechanical Engineering, University of Wollongong, North®elds Avenue, Wollongong, NSW 2522, Australia b Steel Research Laboratories, BHP Steel, Port Kembla, NSW 2505, Australia
Abstract In order to study friction in the roll bite in the laboratory, a work roll with embedded pins is used in cold rolling. Friction and pressure are studied under dry and lubricated conditions. Aluminum alloy is used in the experiments. The results con®rm that the friction coef®cient in the roll bite is not uniform. The validity of the experimental data is con®rmed by comparing it with theoretical results. This indicates that the sensor roll can give reliable friction measurements. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Friction; Cold rolling; Sensor roll; Forward slip
1. Introduction Friction at the interfaces between two rolls and a strip being plastically deformed by the rolls is one of the most important considerations in both the theory and practice of plastic working. However, the nature of friction at the strip± roll interface is not clearly understood. The traditional approach is to assume that the frictional force in the roll bite is proportional to the normal force, with the friction coef®cient remaining constant in cold rolling. However, this affects the accuracy of the mathematical model and consequently the thickness and shape of the strip. The ratio of the interfacial frictional stress to the normal pressure is de®ned as the friction coef®cient. There are several ways to describe this coef®cient. These include Amonton's laws and the statement that t mk, where t is the frictional stress, k the shear yield strength, and m a constant multiplier between zero and unity. While both of these approaches lead to a reasonable prediction of process variables, they are, strictly speaking, incorrect. A limited number of cold rolling tests were reported in [1±3], all showing that the ratio of frictional to normal stress is indeed not constant during rolling, con®rming the suggestion of Shaw et al. [4] that for relatively high interfacial normal stresses, this ratio varies along the contact zone. The objectives of the present study is to understand the relationship between the friction coef®cient and the process parameters and how the friction coef®cient varies in the roll bite. Finally, experimental and calculated results were * Corresponding author. Tel.: 61-2-4221-4923; fax: 61-2-4221-3101. E-mail address: [email protected] (Y.J. Liu).
compared. Aluminum alloy H5052-H34 was used in all experiments. 2. Experimental equipment and material 2.1. The rolling mill and data acquisition A two-high rolling mill with rolls of 225 mm diameter and 254 mm length, driven by a variable speed DC motor of 75 hp, was used. The maximum rolling force, torque and speed are 1500 kN, 13 kN m and 70 rpm, respectively. The sensor roll nitrided surface hardness is 65±70 HRC. Two group of sensors are embedded in the roll, one with full-bridge strain gauges, the other with high sensitive, temperature-compensated load-cells. The pin diameter is 2 mm. The sensor roll overview and sectional view showing the pressure pins are given in Figs. 1 and 2, respectively. The rolling time can be less than 25 ms at a rolling speed of 70 rpm, so it is necessary to use a fast computer and data acquisition system to capture enough data points in the roll bite. A Pentium III computer was used in the experiments. The maximum sampling rate is 250 k/s. 2.2. Materials Aluminum alloy H5052-H34 and lubricant Rolkleen 485A were used in the experiments. The variation of the material resistance to deformation is obtained from the constitutive relationship, an expression similar to that in [5] as shown below being used: s 199:60 1 201:8e0:097 MPa
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 4 1 - 6
(1)
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
143
Nomenclature h1 h2 L
strip entry thickness strip exit thickness mark length left on strip after sensor roll turns one circle circumference of sensor roll deformed roll radius forward slip roll speed
L0 R0 Sf v
Fig. 2. Sensor roll section view.
Greek letters e reduction (%) s yield strength of material f1 bite angle at entry point friction coefficient
3. Results and discussion The determination of the friction coef®cient in the roll gap is done by an analysis of the equilibrium of forces acting on the radial and oblique pins. Here, the same analysis method adopted in [1,6] is used in calculating the friction coef®cient. The Orowan equation, solved according to Alexander [7], is used for determining the rolling pressure, rolling force and rolling torque. Variable friction coef®cient in the roll bite is also considered. In the results presented below, ``variable friction coef®cient'' refers to the friction coef®cients in the roll bite measured from the sensor roll and ``constant friction coef®cient'' refers to constant friction coef®cient calculated from the forward slip in [8] as shown in Eq. (2): 2 R0 f1 f1 2 Sf (2) h2 2 4m
Fig. 3. Force distribution e 29:48% (lubricated).
The force distributions from the radial and oblique pins are shown in Figs. 3 and 4 for 29.48 and 17.71% reduction,
respectively. The experiments for Figs. 3 and 4 were carried out under lubricated and dry condition, respectively. After analysis of the measured data, the pressure and friction coef®cient distribution in the roll bite shown in Figs. 5±8 are obtained. From Figs. 5 and 6, the pressure peak in the roll bite as predicted by the standard rolling theory cannot be detected. This could be due to the effect of the pin diameter (2 mm) compared with the contact length (10.1 mm for lubricated condition, 7.9 mm for dry condition). From Figs. 5±8, it can be seen that the location of the single pressure peak may not coincide with the location of the neutral point and that the friction coef®cient varies widely throughout the roll bite. In isolated instances, double or triple pressure peaks have been measured in [3,6] or predicted in [10,11]. During commissioning of our sensor roll, double pressure peaks
Fig. 1. Sensor roll overview.
Fig. 4. Force distribution e 17:71% (dry).
The forward slip in Eq. (2) is determined by the marking method [9] in the experiments. Eq. (3) shows how the forward slip is calculated: Sf
L
L0 L0
100%
(3)
144
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
Fig. 5. Pressure distribution e 29:48% (lubricated).
Fig. 6. Pressure distribution e 17:71% (dry).
Fig. 9. Pressure comparison e 29:48% (lubricated).
Fig. 10. Pressure comparison e 17:71% (dry).
Fig. 7. Friction coef®cient e 29:48% (lubricated).
for oblique pin was found to be caused by the segment movement. Comparison between the measured and calculated pressure distributions are shown in Figs. 9 and 10 for lubricated and dry rolling condition. The pressure from the mixed ®lm lubrication model [12] compares well with the measured radial pressure from the sensor roll. Calculation results show that the three curves in Figs. 9 and 10 give reasonable agreement. Finally, the rolling force and torque are shown in Figs. 11 and 12. From the two graphs, it can be seen that the measured rolling load and torque validate the pressures measured by the sensor roll.
Fig. 8. Friction coef®cient e 17:71% (dry).
Fig. 11. Rolling force comparison (dry).
Y.J. Liu et al. / Journal of Materials Processing Technology 111 (2001) 142±145
145
Acknowledgements The ®nancial assistance of the Australian Research Council and BHP Steel Research are gratefully acknowledged. The authors also wish to thank the management of BHP Steel Research Laboratories for permission to publish the material contained in this paper. References Fig. 12. Rolling torque comparison (dry).
4. Conclusions 1. The friction coef®cient in the roll bite is not constant. 2. Determination of the friction coef®cient using a sensor roll has been validated by the experimental results. These values are found to be reasonable on comparing them with the theoretical calculation. 3. No obvious pressure peak was found over the roll bite, and the location of the single pressure peak does not coincide with the location of the neutral point.
[1] G.T. Van Rooyen, W.A. Backofen, J. Iron Steel Inst. 186 (1957) 235±244. [2] A. Banerji, W.B. Rice, Ann. CIRP 21 (1972) 53±54. [3] F.A.R. Al-Salehi, T.C. Firbank, P.R. Lancaster, Int. J. Mech. Sci. 15 (1973) 693±710. [4] M.C. Shaw, A. Ber, P. Mamin, J. Basic Eng. Ð ASME 82 (1960) 342±346. [5] A.N. Karagiozis, J.G. Lenard, Eurotrib 85 (1985) 1±7. [6] Lim Lai-Seng, J.G. Lenard, J. Eng. Mater. Technol. 106 (1984) 139±146. [7] J.M. Alexander, R.C. Brewer, G.W. Rowe, Manufacturing Technology, Vol. 2: Engineering Processes, Ellis Horwood, Chichester, UK, 1993. [8] H. Ford, D.R. Bland, J. Iron Steel Inst. 168 (1951) 57±72. [9] Y.J. Liu, A.K. Tieu, E.B. Li, W.Y.D. Yuen, in: Proceedings of the AFDM'99, Pusan, South Korea, 1999, pp. 495±500. [10] Li. Guo-ji, S. Kobayashi, J. Eng. Ind. Ð ASME 104 (1982) 55±64. [11] J.G. Lenard, in: Proceedings of the COBEM, Rio de Janeiro, 1981, pp. 13±24. [12] Z.L. Qiu, W.Y.D. Yuen, A.K. Tieu, J. Tribol. Ð Trans. ASME 121 (1999) 1±8.