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Coefficient of friction at interface of lubricated upsetting process
Wear 286–287 (2012) 3–7
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Coefficient of friction at interface of lubricated upsetting process Akira Azushima a,∗ , Shigeki Yoneyama a , Hiroshi Utsunomiya b a b
Dept. of Mechanical Engineering, Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogya-ku, Yokohama 240-8501, Japan Dept. of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
a r t i c l e
i n f o
Article history: Received 12 November 2010 Received in revised form 12 April 2011 Accepted 14 April 2011 Available online 22 April 2011 Keywords: Friction Lubrication Upsetting
a b s t r a c t In the lubricated upsetting process, it is well known that the coefficient of friction over the contact surface between the tool and the workpiece is distributed nonuniformly and changes with the reduction in height and the position at the interface. In order to increase the reliability of the numerical simulation of cold forging processes, more precise input data of the coefficient of friction at the tool–workpiece interface have become necessary. In this study, in order to predict the coefficient of friction at the interface lubricated cylinder upset tests are carried out using a specimen of commercially pure aluminum and a liquid lubricant. The displacements of the points located at the interface are measured. The normal stress and the tangential stress acting on the interface are calculated by the finite element method, using the measured displacement. Then, the coefficients of friction are estimated using Amonton–Couloumb’s friction law. The coefficients of friction depend on the reduction in height and the position at the interface. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recent societal circumstances have led to new innovations for metal forming process, namely those in harmony with the environment. In the field of cold forging, they include the development of new lubricants to replace phosphates and soap lubricants. Biodegradable lubricants have been developed as environmentally friendly lubricants for cold metal forming processes [1]. It is well known that the liquid lubricant is entrapped at the interface between the tool and the workpiece in an upsetting process and the entrapped lubricant affects on the coefficient of friction at the interface [2]. The authors [3] attempted to measure the lubricant behavior between the tool and the workpiece of the end surface in upsetting of the cylinder accompanied by a reduction in height, using a newly developed upsetting experimental apparatus which consisted of a transparent die made of quartz, a microscope with a CCD camera, a video system and an image processor. They observed directly that at the beginning of upsetting, the lubricant was trapped between the tool and the workpiece, and then the asperities generated with surface roughening during plastic bulk deformation were flattened by the flat tool. They found that the fraction of real contact depended on the reduction in height and the point in the surface at the interface, and at the same time the coefficient of friction depended on the reduction in height and the point in the surface at the interface.
∗ Corresponding author. Tel.: +81 45 339 3861; fax: +81 45 331 6593. E-mail address: [email protected] (A. Azushima). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.04.008
In the numerical simulation using FEM in metal forming, the friction models were considered [4,5]. For improved reliability of the numerical simulation of cold forging processes, more precise input data of the coefficient of friction at the tool–workpiece interface have become necessary. If the highly precise solution in the numerical simulation using FEM is desired, the distribution of the coefficient of friction at the interface between tool and workpiece in upsetting process must be given. Either a constant Amonton–Coulomb coefficient [6] or a constant friction factor [7] is practically applicable to most forming processes. However, for unsteady forming processes such as forging, the use of a constant value of coefficient of friction is not usually possible. A friction model which can be used in the numerical simulation of cold forging processes with high accuracy must be derived. In particular, it is necessary to investigate quantitatively the dependence of the coefficient of friction on the reduction in height and the position at the interface in order to obtain the distribution of the coefficient of friction using the new friction model [8]. In this paper, for the purpose of developing the new friction model in cold forging processes, the displacements of points at the interface in the lubricated aluminum cylinder upset tool are measured at several levels of the reduction in height after upsetting. Then, the normal stress and the tangential stress at the point accompanied with reduction in height in upsetting of cylinder are calculated by the elastic-plastic finite element method, using the measurements by assuming the Amonton–Coulomb’s friction law. The dependence of the coefficient of friction on the reduction in height and the point at the interface are measured. The new mixed
4
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 3. Geometry and finite element discretization of specimen.
lattice points of eight circular patterns at each reduction in height is derived by the elongation of each element. 3. Modeling for calculation
Fig. 1. Master of circular lattice pattern.
lubrication model at the interface between tool and workpiece in upsetting process with lubricants is proposed. 2. Experimental procedure The workpiece material used is commercially available pure A1050H aluminum. Cylindrical specimens with a diameter of 16 mm and a height of 4 mm are machined from a cold drawn rod and are annealed for 1 h at 350 ◦ C. The top and bottom surfaces of the specimens are polished to a smooth surface of Ra 0.2 m. Then, a scribed pattern is printed on the top end surface of the cylindrical specimen by a photograph image method using a film with a circular lattice as shown in Fig. 1. The interval of the circular patterns is 1 mm and the diameters of the circular patterns range from 2 mm to 16 mm. The photograph of the specimen is shown in Fig. 2. The upsetting experiments between flat tools are carried out at a constant speed of approximately 0.6 mm/min at up to four levels of reduction in height ranging from 10 to 40%. The surface roughness of the tools is measured. Paraffinic oils having three levels of viscosity (P400: 1460 cSt, P30: 80 cSt, P8: 24 cSt at 20 ◦ C) are used as a lubricant. The experiments are carried out at room temperature (20 ◦ C). After carrying out the upsetting tests at up to four levels of reduction in height of 10, 20, 30 and 40%, the displacements of the
Fig. 2. Photograph of the specimen.
The ABAQUS/Standard version 6.2 is used for calculating the coefficient of friction at the lattice points accompanying the reduction in height in the upsetting process. The cylindrical specimen with a diameter of 16 mm and a height of 4 mm is used and the geometry and the finite element discretization of the specimen are shown in Fig. 3. In the quarter of the specimen, the height is 2 mm and the radius is 8 mm. The model workpiece is compressed between the two flat parallel tools. The computations are carried out under axisymmetrical conditions. The stress–strain curve of the workpiece is measured by the repetitive compression testing under lubricated conditions [9]. The relationship between the stress and the strain obtained by the experiment is shown in Fig. 4. The stress–strain curve used for calculation is given by = 157ε0.27
(1)
where is the flow stress and ε is the true strain. At the first stage of calculation, for the boundary conditions the tool is assumed to move at a constant compression speed and Amonton–Couloumb’s friction law at the tool–workpiece interface is used as the frictional boundary condition. The frictional shear stress f is expressed using a coefficient of friction as f = p
(2)
where p is the normal pressure. The values of the coefficient of friction are 0.1, 0.2 and 0.3. At the second stage of calculation, for the boundary conditions the tool is assumed to move at a constant compression speed and the displacements in the horizontal direction at the nodal points at the interface accompanied with the reduction in height are given by experimental data. The normal stress and the tangential stress at the nodal points are calculated, and the coefficients of friction
Fig. 4. Constitutive equation used in the analysis.
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 5. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 1460 cSt.
accompanying the reduction in height are estimated from these values assuming Amonton–Couloumb’s friction law. 4. Results 4.1. Measurement of displacement at point at interface The displacements at the eight points in the internal region of the interface after upsetting tests up to four levels of reduction in height of 10, 20, 30 and 40% for P400 having a viscosity of 1460 cSt are illustrated in Fig. 5. Similar distributions of the displacement are illustrated in Fig. 6 for P30 having a viscosity of 80 cSt and in Fig. 7 for P8 having a viscosity of 24 cSt. For P400 having high viscosity,
Fig. 8. Calculated displacement at nodal point ( = 0.1).
the distributions of the displacement up to a reduction in height of 20% are nearly uniform and at 40%, the displacement becomes larger from the center point to the peripheral point. For P30 and P8 having low viscosity, in the internal region, the displacement at each reduction in height becomes larger from the center point to the peripheral point and in the peripheral region, it decreases and then increases in the peripheral direction. 4.2. Calculation of displacement at nodal point Next, the displacements at the eight nodal points after upsetting tests at up to four levels of reduction in height of 10, 20, 30 and 40% for a coefficient of friction of 0.1 are illustrated in Fig. 8. Similar distributions are illustrated in Fig. 9 for a coefficient of friction of 0.2 and in Fig. 10 for a coefficient of friction of 0.3. For the lower
Fig. 6. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 80 cSt. Fig. 9. Calculated displacement of nodal point ( = 0.2).
Fig. 7. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 24 cSt.
5
Fig. 10. Calculated displacement of nodal point ( = 0.3).
6
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 11. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P400).
coefficient of friction, the distributions of the displacement at each reduction in height are nearly uniform. For the higher coefficient of friction, the distributions become nonuniform. In the internal region, the displacement becomes larger from the center point to the outside point and in the peripheral region, it decreases and then increases in the peripheral direction. On comparing with the calculated displacements at nodal points shown in Figs. 8–10 and the measured displacements shown in Figs. 5–7, the large difference between them are observed. From these comparisons, it is estimated that the coefficient of friction depends on the reduction in height and the position at the interface in the lubricated upsetting process. 4.3. Calculation of coefficient of friction at nodal point In order to estimate the distribution of the coefficient of friction at the interface at each reduction in height, the normal stress and the tangential stress at the nodal point accompanying the reduction in height in upsetting of the aluminum cylinder are calculated by the elastic-plastic finite element method, using the measured displacement as shown in Figs. 5–7. The coefficients of friction estimated by assuming the Amonton–Couloumb’s friction law are shown in Figs. 11–13. From the calculated results, it can be understood that the coefficient of friction depends on the reduction in height and the position at the interface. For P400, the coefficient of friction at reductions in height of 10 and 20% is nearly uniform with a value of approximately 0.05 and at reductions in height of 30 and 40% it becomes larger from the center point to the peripheral point. The coefficient of friction increases with increasing reduction in height. In the central region, the dependence of the coefficient
Fig. 13. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P8).
of friction on the reduction in height is small and in the peripheral region, it is large. For P30 and P8, the coefficients of friction at each reduction in height become larger in the peripheral direction and they increase with increasing reduction in height.
5. Discussion It is understood that the coefficients of friction depend on the reduction in height and the position of the surface at the interface of the cylindrical specimen from Figs. 11–13. However, if the contact model at the interface between the tool and the workpiece is considered, the coefficient of friction must be given as a function of the ratio of the real contact area ˛, the radius of the surface position of the end surface a and the reduction in height r. Generally, the ratio of the real contact area can be estimated using following parameters of the oil film thickness trapped between the tool surface and the end surface of cylindrical specimen, the surface roughness of the end surface which various with the reduction in height and the flattening of the asperity on the end surface, using the Greenwood analysis [10]. The oil film thickness between the tool surface and the end surface at low compression speed will be predicted using Osakada’s micro elasto-hydrodynamic model [11]. The central thickness h0 is given by
V 1/3
h0 = 10.6
E
(3)
where is the viscosity of lubricant, V is the speed of the tool approach, E is Young’s modulus of the specimen and R is the radius of the cylindrical specimen. The oil film thickness h(a, r) at a given position during compression can be estimated from Eq. (3) and the experimental results of the distribution of the oil film thickness measured by Azushima [12]. The end surface deforms plastically and randomly and the surface roughness on the end surface Rrms(r) = (r) increases with increasing reduction in height. The deformation of the asperity on the end surface is constrained by the smooth tool surface. Consequently, it is assumed that the flattening mechanism is similar to one in the compression testing using the specimen with a random rough surface [13], the ratio of the real contact area ˛(a, r) at a given position and a given reduction in height is expressed by a following equation proposed by Watanabe [14],
Fig. 12. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P30).
R2/3
∞
˛(a, r) = 2
ϕ(z) dz h(a,r)
(4)
A. Azushima et al. / Wear 286–287 (2012) 3–7
where
7
From Eq. (4), the coefficient of friction (a, r) at a given position and a given reduction in height is given by
uniform. For the lubricant having low viscosity, the distribution became nonuniform and it increased from the center point to the peripheral point. (2) The coefficient of friction depended on the reduction in height and the surface position at the interface. The dependence was significant for the lubricant having low viscosity.
(a, r) = ˛(a, r)b
References
(z) =
1
exp
2 (r)
−
2 (r) z2
(5)
(6)
where b is the coefficient of friction in the boundary lubrication. The value of b can be measured using fundamental tribo testers such as a pendulum testing machine. In Figs. 11–13, it is estimated that the coefficient of friction in the edge of the end surface are larger than b by the reason why the side of the cylindrical specimen. It is assumed that the metal contact will be occur in this area. In near future, the ratio of the real contact area expressed by Eq. (4) must be quantitatively and experimentally developed in order to construct the new friction model expressed by Eq. (6). 6. Conclusions In order to develop a new friction model in cold lubricated forging processes, the normal stress and the tangential stress acting on the interfacial surface accompanying the reduction in height in the upsetting of the cylinder specimen were calculated by the elastic–plastic finite element method, using the experimentally measured displacement of points at the interface between the tool and the workpiece. Then the coefficients of friction were estimated by assuming Amonton–Couloumb’s friction law. The results obtained are as follows: (1) For the lubricant having high viscosity, the distributions of the measured displacement at each reduction in height were nearly
[1] F. Klocke, Environmentally friendly lubricants for cold forging process, Proc. ICTP (2003). [2] L.H. Butler, Surface conformation of metal under high normal contact pressure, Metallurgia 58 (1960) 167–174. [3] A. Azushima, S. Yoneyama, T. Yamaguchi, H. Kudo, Direct observation of micro contact behavior at the interface between tool and workpiece in lubricated upsetting, Ann. CIRP 45–1 (1996) 205–210. [4] X. Tan, Comparison of friction models in bulk metal forming, Tribol. Int. 35 (2002) 385–389. [5] M.S. Joun, H.G. Moon, I.S. Choi, M.C. Lee, B.Y. Jun, Effects of friction laws on metal forming processes, Tribol. Int. 42 (2009) 311–319. [6] F.P. Bowden, D. Tabor, The Friction and Lubrication of Solids, Part 1, Oxford Clarendon Press, 1953, pp. 98–100. [7] J.A. Schey, Tribology in Metalworking, A.S.M., Metal Park, OH, 1983. [8] P. Becher, H.J. Jeon, C.C. Chang, A.N. Bramley, A geometric approach to modelling friction in metal forming, Ann. CIRP 52 (1) (2003) 209–212. [9] N.H. Polakowski, The compression test in relation to cold rolling, J. Iron Steel Inst. 163 (1949) 250–276. [10] J.A. Greenwood, The area of contact between rough surfaces and flats, J. Lubr. Technol. Trans. ASME 20 (1977) 55–63. [11] K. Osakada, A mechanism of lubricant trapping in slow speed compression, Int. J. Mech. Sci. 19 (1977) 413–421. [12] A. Azushima, In situ 3D measurement of lubrication behavior at interface between tool and workpiece by direct fluorescence observation technique, Wear 260 (2006) 243–248. [13] A. Azushima, S. Kuba, S. Tani, D.D. Olsson, Direct observation of asperity deformation of specimens with random rough surfaces in upsetting and indentation process, Wear 260 (2006) 258–264. [14] K. Watanabe, Direct observation of asperity deformation under lubricated condition using fluorescence method, Undergraduate thesis of Yokohama National University, 2000.
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Coefficient of friction at interface of lubricated upsetting process Akira Azushima a,∗ , Shigeki Yoneyama a , Hiroshi Utsunomiya b a b
Dept. of Mechanical Engineering, Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogya-ku, Yokohama 240-8501, Japan Dept. of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
a r t i c l e
i n f o
Article history: Received 12 November 2010 Received in revised form 12 April 2011 Accepted 14 April 2011 Available online 22 April 2011 Keywords: Friction Lubrication Upsetting
a b s t r a c t In the lubricated upsetting process, it is well known that the coefficient of friction over the contact surface between the tool and the workpiece is distributed nonuniformly and changes with the reduction in height and the position at the interface. In order to increase the reliability of the numerical simulation of cold forging processes, more precise input data of the coefficient of friction at the tool–workpiece interface have become necessary. In this study, in order to predict the coefficient of friction at the interface lubricated cylinder upset tests are carried out using a specimen of commercially pure aluminum and a liquid lubricant. The displacements of the points located at the interface are measured. The normal stress and the tangential stress acting on the interface are calculated by the finite element method, using the measured displacement. Then, the coefficients of friction are estimated using Amonton–Couloumb’s friction law. The coefficients of friction depend on the reduction in height and the position at the interface. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recent societal circumstances have led to new innovations for metal forming process, namely those in harmony with the environment. In the field of cold forging, they include the development of new lubricants to replace phosphates and soap lubricants. Biodegradable lubricants have been developed as environmentally friendly lubricants for cold metal forming processes [1]. It is well known that the liquid lubricant is entrapped at the interface between the tool and the workpiece in an upsetting process and the entrapped lubricant affects on the coefficient of friction at the interface [2]. The authors [3] attempted to measure the lubricant behavior between the tool and the workpiece of the end surface in upsetting of the cylinder accompanied by a reduction in height, using a newly developed upsetting experimental apparatus which consisted of a transparent die made of quartz, a microscope with a CCD camera, a video system and an image processor. They observed directly that at the beginning of upsetting, the lubricant was trapped between the tool and the workpiece, and then the asperities generated with surface roughening during plastic bulk deformation were flattened by the flat tool. They found that the fraction of real contact depended on the reduction in height and the point in the surface at the interface, and at the same time the coefficient of friction depended on the reduction in height and the point in the surface at the interface.
∗ Corresponding author. Tel.: +81 45 339 3861; fax: +81 45 331 6593. E-mail address: [email protected] (A. Azushima). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.04.008
In the numerical simulation using FEM in metal forming, the friction models were considered [4,5]. For improved reliability of the numerical simulation of cold forging processes, more precise input data of the coefficient of friction at the tool–workpiece interface have become necessary. If the highly precise solution in the numerical simulation using FEM is desired, the distribution of the coefficient of friction at the interface between tool and workpiece in upsetting process must be given. Either a constant Amonton–Coulomb coefficient [6] or a constant friction factor [7] is practically applicable to most forming processes. However, for unsteady forming processes such as forging, the use of a constant value of coefficient of friction is not usually possible. A friction model which can be used in the numerical simulation of cold forging processes with high accuracy must be derived. In particular, it is necessary to investigate quantitatively the dependence of the coefficient of friction on the reduction in height and the position at the interface in order to obtain the distribution of the coefficient of friction using the new friction model [8]. In this paper, for the purpose of developing the new friction model in cold forging processes, the displacements of points at the interface in the lubricated aluminum cylinder upset tool are measured at several levels of the reduction in height after upsetting. Then, the normal stress and the tangential stress at the point accompanied with reduction in height in upsetting of cylinder are calculated by the elastic-plastic finite element method, using the measurements by assuming the Amonton–Coulomb’s friction law. The dependence of the coefficient of friction on the reduction in height and the point at the interface are measured. The new mixed
4
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 3. Geometry and finite element discretization of specimen.
lattice points of eight circular patterns at each reduction in height is derived by the elongation of each element. 3. Modeling for calculation
Fig. 1. Master of circular lattice pattern.
lubrication model at the interface between tool and workpiece in upsetting process with lubricants is proposed. 2. Experimental procedure The workpiece material used is commercially available pure A1050H aluminum. Cylindrical specimens with a diameter of 16 mm and a height of 4 mm are machined from a cold drawn rod and are annealed for 1 h at 350 ◦ C. The top and bottom surfaces of the specimens are polished to a smooth surface of Ra 0.2 m. Then, a scribed pattern is printed on the top end surface of the cylindrical specimen by a photograph image method using a film with a circular lattice as shown in Fig. 1. The interval of the circular patterns is 1 mm and the diameters of the circular patterns range from 2 mm to 16 mm. The photograph of the specimen is shown in Fig. 2. The upsetting experiments between flat tools are carried out at a constant speed of approximately 0.6 mm/min at up to four levels of reduction in height ranging from 10 to 40%. The surface roughness of the tools is measured. Paraffinic oils having three levels of viscosity (P400: 1460 cSt, P30: 80 cSt, P8: 24 cSt at 20 ◦ C) are used as a lubricant. The experiments are carried out at room temperature (20 ◦ C). After carrying out the upsetting tests at up to four levels of reduction in height of 10, 20, 30 and 40%, the displacements of the
Fig. 2. Photograph of the specimen.
The ABAQUS/Standard version 6.2 is used for calculating the coefficient of friction at the lattice points accompanying the reduction in height in the upsetting process. The cylindrical specimen with a diameter of 16 mm and a height of 4 mm is used and the geometry and the finite element discretization of the specimen are shown in Fig. 3. In the quarter of the specimen, the height is 2 mm and the radius is 8 mm. The model workpiece is compressed between the two flat parallel tools. The computations are carried out under axisymmetrical conditions. The stress–strain curve of the workpiece is measured by the repetitive compression testing under lubricated conditions [9]. The relationship between the stress and the strain obtained by the experiment is shown in Fig. 4. The stress–strain curve used for calculation is given by = 157ε0.27
(1)
where is the flow stress and ε is the true strain. At the first stage of calculation, for the boundary conditions the tool is assumed to move at a constant compression speed and Amonton–Couloumb’s friction law at the tool–workpiece interface is used as the frictional boundary condition. The frictional shear stress f is expressed using a coefficient of friction as f = p
(2)
where p is the normal pressure. The values of the coefficient of friction are 0.1, 0.2 and 0.3. At the second stage of calculation, for the boundary conditions the tool is assumed to move at a constant compression speed and the displacements in the horizontal direction at the nodal points at the interface accompanied with the reduction in height are given by experimental data. The normal stress and the tangential stress at the nodal points are calculated, and the coefficients of friction
Fig. 4. Constitutive equation used in the analysis.
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 5. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 1460 cSt.
accompanying the reduction in height are estimated from these values assuming Amonton–Couloumb’s friction law. 4. Results 4.1. Measurement of displacement at point at interface The displacements at the eight points in the internal region of the interface after upsetting tests up to four levels of reduction in height of 10, 20, 30 and 40% for P400 having a viscosity of 1460 cSt are illustrated in Fig. 5. Similar distributions of the displacement are illustrated in Fig. 6 for P30 having a viscosity of 80 cSt and in Fig. 7 for P8 having a viscosity of 24 cSt. For P400 having high viscosity,
Fig. 8. Calculated displacement at nodal point ( = 0.1).
the distributions of the displacement up to a reduction in height of 20% are nearly uniform and at 40%, the displacement becomes larger from the center point to the peripheral point. For P30 and P8 having low viscosity, in the internal region, the displacement at each reduction in height becomes larger from the center point to the peripheral point and in the peripheral region, it decreases and then increases in the peripheral direction. 4.2. Calculation of displacement at nodal point Next, the displacements at the eight nodal points after upsetting tests at up to four levels of reduction in height of 10, 20, 30 and 40% for a coefficient of friction of 0.1 are illustrated in Fig. 8. Similar distributions are illustrated in Fig. 9 for a coefficient of friction of 0.2 and in Fig. 10 for a coefficient of friction of 0.3. For the lower
Fig. 6. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 80 cSt. Fig. 9. Calculated displacement of nodal point ( = 0.2).
Fig. 7. Measured displacement of nodal point in each reduction in height for lubricant with viscosity of 24 cSt.
5
Fig. 10. Calculated displacement of nodal point ( = 0.3).
6
A. Azushima et al. / Wear 286–287 (2012) 3–7
Fig. 11. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P400).
coefficient of friction, the distributions of the displacement at each reduction in height are nearly uniform. For the higher coefficient of friction, the distributions become nonuniform. In the internal region, the displacement becomes larger from the center point to the outside point and in the peripheral region, it decreases and then increases in the peripheral direction. On comparing with the calculated displacements at nodal points shown in Figs. 8–10 and the measured displacements shown in Figs. 5–7, the large difference between them are observed. From these comparisons, it is estimated that the coefficient of friction depends on the reduction in height and the position at the interface in the lubricated upsetting process. 4.3. Calculation of coefficient of friction at nodal point In order to estimate the distribution of the coefficient of friction at the interface at each reduction in height, the normal stress and the tangential stress at the nodal point accompanying the reduction in height in upsetting of the aluminum cylinder are calculated by the elastic-plastic finite element method, using the measured displacement as shown in Figs. 5–7. The coefficients of friction estimated by assuming the Amonton–Couloumb’s friction law are shown in Figs. 11–13. From the calculated results, it can be understood that the coefficient of friction depends on the reduction in height and the position at the interface. For P400, the coefficient of friction at reductions in height of 10 and 20% is nearly uniform with a value of approximately 0.05 and at reductions in height of 30 and 40% it becomes larger from the center point to the peripheral point. The coefficient of friction increases with increasing reduction in height. In the central region, the dependence of the coefficient
Fig. 13. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P8).
of friction on the reduction in height is small and in the peripheral region, it is large. For P30 and P8, the coefficients of friction at each reduction in height become larger in the peripheral direction and they increase with increasing reduction in height.
5. Discussion It is understood that the coefficients of friction depend on the reduction in height and the position of the surface at the interface of the cylindrical specimen from Figs. 11–13. However, if the contact model at the interface between the tool and the workpiece is considered, the coefficient of friction must be given as a function of the ratio of the real contact area ˛, the radius of the surface position of the end surface a and the reduction in height r. Generally, the ratio of the real contact area can be estimated using following parameters of the oil film thickness trapped between the tool surface and the end surface of cylindrical specimen, the surface roughness of the end surface which various with the reduction in height and the flattening of the asperity on the end surface, using the Greenwood analysis [10]. The oil film thickness between the tool surface and the end surface at low compression speed will be predicted using Osakada’s micro elasto-hydrodynamic model [11]. The central thickness h0 is given by
V 1/3
h0 = 10.6
E
(3)
where is the viscosity of lubricant, V is the speed of the tool approach, E is Young’s modulus of the specimen and R is the radius of the cylindrical specimen. The oil film thickness h(a, r) at a given position during compression can be estimated from Eq. (3) and the experimental results of the distribution of the oil film thickness measured by Azushima [12]. The end surface deforms plastically and randomly and the surface roughness on the end surface Rrms(r) = (r) increases with increasing reduction in height. The deformation of the asperity on the end surface is constrained by the smooth tool surface. Consequently, it is assumed that the flattening mechanism is similar to one in the compression testing using the specimen with a random rough surface [13], the ratio of the real contact area ˛(a, r) at a given position and a given reduction in height is expressed by a following equation proposed by Watanabe [14],
Fig. 12. Distribution of coefficient of friction estimated by calculated normal stress and tangential stress at nodal points (P30).
R2/3
∞
˛(a, r) = 2
ϕ(z) dz h(a,r)
(4)
A. Azushima et al. / Wear 286–287 (2012) 3–7
where
7
From Eq. (4), the coefficient of friction (a, r) at a given position and a given reduction in height is given by
uniform. For the lubricant having low viscosity, the distribution became nonuniform and it increased from the center point to the peripheral point. (2) The coefficient of friction depended on the reduction in height and the surface position at the interface. The dependence was significant for the lubricant having low viscosity.
(a, r) = ˛(a, r)b
References
(z) =
1
exp
2 (r)
−
2 (r) z2
(5)
(6)
where b is the coefficient of friction in the boundary lubrication. The value of b can be measured using fundamental tribo testers such as a pendulum testing machine. In Figs. 11–13, it is estimated that the coefficient of friction in the edge of the end surface are larger than b by the reason why the side of the cylindrical specimen. It is assumed that the metal contact will be occur in this area. In near future, the ratio of the real contact area expressed by Eq. (4) must be quantitatively and experimentally developed in order to construct the new friction model expressed by Eq. (6). 6. Conclusions In order to develop a new friction model in cold lubricated forging processes, the normal stress and the tangential stress acting on the interfacial surface accompanying the reduction in height in the upsetting of the cylinder specimen were calculated by the elastic–plastic finite element method, using the experimentally measured displacement of points at the interface between the tool and the workpiece. Then the coefficients of friction were estimated by assuming Amonton–Couloumb’s friction law. The results obtained are as follows: (1) For the lubricant having high viscosity, the distributions of the measured displacement at each reduction in height were nearly
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