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Friction measurement apparatus for sheet metal forming
Wear 224 Ž1999. 1–7
Friction measurement apparatus for sheet metal forming S. Hao, B.E. Klamecki ) , S. Ramalingam Department of Mechanical Engineering UniÕersity of Minnesota, Minneapolis, MN, 55455-0111, USA Received 19 February 1998; revised 21 August 1998; accepted 21 August 1998
Abstract Friction at the tooling–workpiece interface is very important in sheet metal forming operations. Accurate knowledge of friction at such interfaces is needed for process design and analysis, numerical process simulation and validation and control of forming processes. Two physical models or friction simulators, based on the stretching of a strip around a pin, were developed to characterize sheet metal forming friction. In contrast to other test apparatus which use measurements of strain to infer friction forces, these apparatus use direct measurements of forces. Effects of strain, stretching speed, lubrication, pin radius and wrap angle on coefficient of friction were determined. q 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Friction measurement; Test apparatus; Metal forming
1. Introduction In sheet metal forming, a workpiece or blank is formed between a punch and die. As the punch draws the blank into the die, frictional forces at the die shoulder and over the punch face influence workpiece deformation. In addition to inherent friction forces, in many cases additional friction forces are introduced into the forming process. In situations such as the forming of large radius, shallow parts, additional workpiece deformation may be needed to achieve the desired final part shape and control springback. A holddown or binder plate is used to apply a load to the blank and friction between the binder and workpiece and workpiece and die restrains workpiece movement and causes increased plastic deformation of the workpiece. Additional local blank restraint can be produced by drawbeads which are protrusions on the die face. The bending of the workpiece as it moves over the drawbead and drawbead–work friction restrain workpiece flow and induce plastic deformation in the workpiece. Since friction is important in determining and controlling workpiece deformation in forming processes, detailed knowledge of friction forces is needed for process design and control. In addition, in sheet metal forming frictional forces are important boundary conditions and so must be known for accurate analytical and numerical process modeling. Accu-
)
Corresponding author.
rate measurements of friction forces can provide valuable information for process model development and validation. There are unique features of sheet metal forming which determine the tooling–workpiece coefficient of friction and can make the frictional behavior different from conventional sliding friction. The workpiece experiences bulk plastic deformation, new surfaces are created and local surface deformation occurs on a plastically deforming substrate. The importance and unique features of friction in sheet metal forming have led to the development of friction measurement apparatus which simulate the workpiece deformation in forming operations. A widely used concept is the measurement of coefficient of friction as a metal strip is pulled over the cylindrical surface of a metal pin. The development of this concept into new friction test apparatus and the description of the effects of test variables on the measured coefficient of friction are reported here. The tensile strip test developed by Duncan et al. w1x is widely used. In this test, shown schematically in Fig. 1, a strip specimen of sheet metal is pulled over the cylindrical surfaces of pins to simulate stretching and drawing processes. The pulling force on one side of the pin is measured along with the strain in a section of the test specimen on the other side of the pin. The strip force on this second side of the pin is calculated from the measured strain using the stress–strain characteristics of the test material. Assuming that the coefficient of friction is constant over the pin surface, the strip tensions are used in the capstan friction
0043-1648r99r$ - see front matter q 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 8 . 0 0 2 8 8 - 9
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S. Hao et al.r Wear 224 (1999) 1–7
tus itself, a drawback of the tensile strip test is that the load on one portion of the strip is estimated from measurement of strain. In the work described here, two different, simpler, test configurations were developed. The apparatus allow strip tensions on both sides of the pin to be measured directly. Using these apparatus, tests were performed to determine the effects of strain, stretching speed, lubrication, pin radius, pin material, and wrap angle on coefficient of friction.
2. Strip friction measurement apparatus
Fig. 1. Tensile strip test for measurement of coefficient of friction.
model to calculate the coefficient of friction. In subsequent studies, Wang et al. w2x showed that the coefficient of friction increased with strip sliding distance and that increasing the pin radius resulted in a small increase in measured coefficient of friction. Zheng and Overby w3x showed that the coefficient of friction decreased with increasing sliding speed and increasing pin radius. Bhonsle and Weinmann w4x developed an expression for the coefficient of friction in terms of measured strains, rather than forces, in their study of friction in elasticrelastic, plasticrelastic, and plasticrplastic deformations in the strip on different sides of the pin. To account for severe deformation conditions, Weinmann et al. w5x suggested use of the friction factor to describe tool–work friction. In the expression for the friction factor in terms of measured strain, the pin radius appears explicitly and experimental results show that friction factor decreases with increasing pin radius. Wilson et al. w6x developed a sheet metal forming simulator to investigate the relationships between friction and process variables such as sliding speed, interface pressure, workpiece strain and strain rate. Schurman and Wright w7x used a physical model simulating the binder and drawbead regions and studied the effects of workpiece surface characteristics and tooling topography on friction. The friction force acting on the blank holder in cup drawing was measured by Lin and Wang w8x using a split blank holder and measuring the change in gap due to the flow of the workpiece over it. Weinmann et al. w9x and Kernosky and Weinmann w10x built an instrumented strip drawing machine to study sheet forming. The part of the apparatus which simulates the die shoulder is instrumented with strain gages and was used to measure strip tensions on both sides of the die shoulder so that coefficient of friction can be calculated. There are questions that arise when the strip friction test, and other process simulation tests, and experimental results are considered. Some of the results reported indicate a dependence of coefficient of friction on the test configuration, e.g., pin radius. In terms of the test appara-
In the strip friction test, the coefficient of friction is estimated from measurements of strip tensions on each side of the pin using the capstan or belt friction model. Force and moment equilibrium on an element of the strip result in the following descriptions of the average contact pressure, p, the average friction stress, f, and the coefficient of friction, m. ps fs
F1 q F2 2WR F1 y F2
ms
WR f 1
f
ln
F1 F2
Ž 1. Ž 2. Ž 3.
In these equations F1 and F2 are the strip tensions, W is the width of the strip, R is the radius of the pin and f is the wrap angle of the strip on the pin. A schematic representation of the ‘U’ shape sheet forming friction test is shown in Fig. 2. The strip specimen is pulled over two pins and around a surface which is mounted on a load cell. This apparatus is set up in a tensile test machine and the pulling force, F1 , is measured by the test machine load cell. The strip tension on the other side of the pins, F2 , is measured with the load cell in the apparatus. The radius and location Žthe dimension shown as 77 mm in Fig. 2. of the pins can be changed to investigate the effects of the pin radius and wrap angle on friction.
Fig. 2. Schematic of the ‘U’ shape strip friction test.
S. Hao et al.r Wear 224 (1999) 1–7
Fig. 3. Schematic of the ‘L’ shape strip friction test.
Fig. 3 shows the setup for the ‘L’ shape sheet forming friction test. A test strip is held at one end in a grip supported by a load cell. The specimen is wrapped around a cylindrical pin and loaded in a tensile testing machine. The strip tensions and F1 and F2 are measured simultaneously during the test. An extensometer is used to monitor strain and to determine strain rate during the test. A major advantage of the test apparatus is that strain does not have to be measured to measure coefficient of friction. For some testing the effect of strain on coefficient of friction may be of interest. In the ‘L’ shape apparatus tests an extensometer was used as shown in Fig. 3 to measure strain during testing. In other cases the use of an extensometer may not be reasonable or warranted. In most cases it is expected that the uniform deformation region is of interest so only a measurement of specimen elongation is needed to calculate specimen strain away from the grip and pin regions. The ‘U’ shape apparatus was used in this way. The variation of strain over the apparatus pin and near the grip of the test machine was not considered in this work.
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oil, mineral oil with 1% oleic acid, mineral oil with 1% stearic acid. An argument is presented in Appendix A that mixed lubrication conditions existed during the testing. Stretching speed is the speed of the test machine head. In the ‘L’ shape apparatus tests strain was measured and strain rate was calculated for the section of the test strip between the machine head and pin assuming that strain was uniform over this length of test material. For the tests run using the ‘U’ shape apparatus strip elongation was measured. In both types of tests the initial strip length between the pin and the test machine grip was 120 mm. Specimens were carefully prepared to assure constant width and that they were burr free and were cleaned with acetone. The pins were polished with fine abrasive papers Ž600 grit. and cleaned with acetone after each test. The test apparatus were set up on a tensile test machine. During each test, outputs from the load cells, and the extensometer in the ‘L’ test, were sampled with a computer-based data acquisition system. Data acquired were processed to calculate the coefficient of friction using Eq. Ž3.. Initial testing showed that tests run under similar conditions on both apparatus gave similar results for coefficient of friction and for changes in coefficient with changes in experimental variable values, w11x.
4. Results An initial series of tests were performed at different stretching speeds. At low stretching speeds, stick–slip motion occurred at the beginning of some test runs. With an increase in stretching speed stick-slip motion was greatly reduced. No stick–slip was observed at stretching speeds of 200 mmrmin and greater. Initial stick–slip behavior was not included in test results. Both apparatus gave the same results for tests when the testing conditions were the same w11x.
3. Experimental conditions and materials The ‘U’ shape friction test was used to investigate the effects of pin radius, pin material, strip material and wrap angle on coefficient of friction. Specimen material: aluminum strips Ž0.47 mm thick, 10.2 mm wide., steel strips Ž0.57 mm thick, 12.7 mm wide., galvanized steel strips Ž0.64 mm thick, 12.7 mm wide., pin material: steel, copper, and teflon, pin radius: 6.35 mm, 12.7 mm, wrap angle: 908, 758, 608, stretching speed: 20 mmrmin, lubrication: dry. The ‘L’ shape friction test was used to investigate the effects of stretching speed and lubrication on friction. Specimen material: steel strips Ž0.57 mm thick, 12.7 mm wide., pin radius: 12.7 mm, pin material: steel, Wrap angle: 908, stretching speed Žmmrmin.: 5, 10, 20, 50, 100, 200, 500, corresponding strain rate Ž%rs.: 0.046, 0.090, 0.198, 0.499, 0.956, 1.872, 3.731, lubrication: dry, mineral
4.1. Variations of coefficient of friction with strain and strain rate The variation of coefficient of friction with strain for stretching speeds between 5 and 500 mmrmin is shown in Fig. 4. The results are for steel strip specimens, steel pins, pin radius of 12.7 mm, wrap angle of 908 and no lubricant. The coefficients of friction are in the commonly quoted range of 0.2–0.4 for metal working processes and increase by 10–15% over the test range. The coefficient of friction decreases as the stretching speed increases. Coefficient of friction decreased by about 30% as stretching speed was increased from 5 to 500 mmrmin. However, this large change in coefficient of friction is due to the large difference between the lowest and highest strain rates. All test results are shown in Fig. 4 with very similar results for stretching speeds of 20, 50,
S. Hao et al.r Wear 224 (1999) 1–7
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pressure curve is not constant, that is, the coefficient of friction varied in the tests. There are two regions in which the coefficient of friction changes at much different rates. Over most of the range of pressure, the coefficient of friction changes slowly. The range of pressure between about 9.5 MPa and 12 MPa corresponds to the data shown in Fig. 4. For larger pressure the coefficient of friction rises rapidly. 4.3. Effect of lubrication
Fig. 4. Variation of coefficient of friction with strain and stretching speed in strip friction tests Žsteel strip, steel pin, pin radiuss12.7 mm, wrap angles908, dry..
100 and 200 mmrmin and many data points overlapping. These results show that if the increase in coefficient of friction with strain is due to the formation of new surface area, as long as the new area forms the rate of formation has very little influence on the change in coefficient of friction. 4.2. Friction stress Õersus contact pressure Contact pressure and friction stress can be calculated from the measured forces using Eqs. Ž1. and Ž2.. Fig. 5 shows the variation of the friction stress with contact pressure for test conditions of Fig. 4 and 200 mmrmin stretching speed. The slope of the friction stress–contact
Fig. 5. Friction stress vs. contact pressure in strip friction tests.
The three lubricants used were straight mineral oil, mineral oil with 1% Oleic acid, and mineral oil with 1% Stearic acid. The test results presented in Fig. 6 are for a stretching speed of 100 mmrmin and are representative of the speeds used in this work. As shown in the Appendix, boundary lubrication conditions existed. The results indicate that straight mineral oil has little effect on friction because there is essentially no hydrodynamic action at the pinrstrip interface. Polar additives of 1% oleic acid or 1% stearic acid greatly reduce sheet forming friction, by about 50% in this case. These additives can react with the surfaces to form tightly adhering boundary lubricant films which promote stable boundary lubrication and decrease friction force. 4.4. Effect of pin radius, material and wrap angle The results presented in Fig. 7 are the average coefficients of friction for varying strain tests with different test materials. The results show that the coefficient of friction increases as the steel pin radius decreases for aluminum, steel and galvanized steel strip materials. Use of the smaller pin with the diameter half that of the larger pin produced
Fig. 6. Effect of lubrication on friction in strip friction tests Žsteel strip, steel pin, pin radiuss12.7 mm, wrap angles908, speeds100 mmrmin..
S. Hao et al.r Wear 224 (1999) 1–7
Fig. 7. Effect of pin radius in strip friction tests Žsteel pin, wrap angles908, speeds 20 mmrmin, dry..
increases of coefficient of friction of about 13%, 25% and 29%. Changes in coefficient of friction were also seen with changes in strain and the effect of pin radius on specimen strain is discussed in Section 5. A series of tests were performed with aluminum strips using steel, copper, and Teflon pins. The results are shown in Fig. 8 and indicate that the pin material has a significant influence on coefficient of friction. As expected, friction between aluminum and teflon is very low. This first reported use of a very low friction material for the pin indicates potential simplification of other sheet metal tests. Workpiece bending and very low friction situations in sheet metal forming are usually studied by pulling the strip specimen over a pin which is free to rotate. The small
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Fig. 9. Variation of coefficient of friction with wrap angle Žgalvanized steel strip, steel pin, pin radiuss12.7 mm, speeds 20 mmrmin..
friction effects shown in the results for the fixed teflon pin point toward usefulness of fixed, low friction material pins in investigations of sheet metal deformation and friction. The effect of wrap angle on coefficient of friction was investigated in a series of tests using galvanized steel strips. The results are presented in Fig. 9. For small strains there is little difference in coefficients of friction for different strip wrap angle. As test specimen strain increases coefficient of friction decreases with increasing wrap angle. Eq. Ž3. describes the relation between the force ratio, F1rF2 , and the wrap angle, f , for constant coefficient of friction.
5. Discussion
Fig. 8. Results from strip friction tests with different pin materials Žsteel strip, wrap angles908, speeds 20 mmrmin, dry..
The results presented fall into the two categories of those related to the test apparatus and those which are results of friction tests. The two sheet forming friction test apparatus developed can be used to characterize frictional behavior for the design, modeling and operation of sheet metal forming processes. The test apparatus are simple and offer the advantage that strip tensions are measured directly. Difficulties with measuring strain and uncertainties about material deformation descriptions needed to calculate forces from measured strains are eliminated. Friction test results show that coefficient of friction Ži. increases with increasing test specimen strain, Žii. increases with increasing local contact pressure, Žiii. decreases with increasing stretching speed, i.e. strain rate, and Živ. decreases with increasing pin radius. The test results correspond to published results and show that at the large strains used to simulate strains imposed in metal working processes significant changes in
S. Hao et al.r Wear 224 (1999) 1–7
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indentation for bulk plane strain plastic deformation. They found that the effective hardness of the surface is reduced by plastic flow in the bulk. These deformation induced surface and bulk material modifications can explain changes in frictional behavior. The change in coefficient of friction with test strip strain shows that contact conditions and material state vary continuously throughout the test. The implication is that potentially large difference in friction conditions can occur over the workpiece in metal forming operations since differences in strain and strain rate exist at different locations. Work-tool coefficient of friction will vary during sheet metal forming processes complicating process modeling and process control.
Fig. 10. Geometry of the strip–pin interface.
coefficient of friction occur with changes in test conditions. Large, process specific effects are clearly seen in the increase in coefficient of friction with strain shown in Fig. 4 which correspond to results of Wang et al. w2x. During strip stretching new surface area is created. In the strip–pin contact area the new strip surface area is in intimate contact with the pin and high friction is expected. The large effects of polar lubricants seen in Fig. 6 where lubrication reduces coefficient of friction by about 50% add strength to this interpretation. New, active surface area with strong lubricant binding sites is created during large strain stretching and this area increases with amount of strain. With measured strip tensions and known test apparatus characteristics the average contact pressure and average friction stress can be calculated using Eqs. Ž1. and Ž2.. Fig. 5 is another representation of the changing coefficient of friction and also indicates another unique feature of sheet forming processes and work–tool friction. Changes of coefficient of friction occur even at low contact pressure. The contact pressure, p, is p s t srR
6. Biographies Dr. S. Hao is currently the manager of the Advanced Lapping Technology department in Seagate Recording Heads, Minneapolis, MN. He obtained his PhD in Mechanical Engineering at the University of Minnesota in 1994. His main areas of research are related to advanced slider fabrication process development and engineering, including process optimization, sensor height control, lapping fundamentals, surface finish and process automation. Dr. B.E. Klamecki is Associate Professor of Mechanical Engineering at the University of Minnesota, MN. He teaches a course in Tribology and conducts research in basic aspects of friction and wear. His other research areas are sensor development for monitoring manufacturing processes and the analysis and modeling of the mechanics of material removal processes. Dr. S. Ramalingam is a professor of Mechanical Engineering at the University of Minnesota, Minneapolis, MN, USA. He obtained his PhD degree in 1967. His main areas
Ž 4.
where s is the tensile stress, R is the pin radius and t is the strip thickness. For strip specimens and sheet forming t < R and so p is small. The local contact pressure is relatively small even though the underlying material is in bulk plastic flow. The increase in average coefficient of friction with decreasing pin radius seen in Fig. 7 indicates that even though bending strain is compressive on the pin side of the strip, the large stretching strains in these tests produce large deformation and surface related effects. For example, the extreme case of the smaller pin radius of 6.35 mm and thick strip thickness of 0.57 mm gives a bending strain of 4.3% compared to the stretching strains of 10–25% imposed in the tests. All these results are consistent with the models proposed by Sheu and Wilson w12x, Wilson and Sheu w13x and Sutcliffe w14x. In their work, they used upper-bound methods to investigate workpiece asperity flattening or surface
Fig. 11. Pressure distribution.
S. Hao et al.r Wear 224 (1999) 1–7
of research are related to mechanical engineering: surface coating and surface inspection for flaws.
Acknowledgements This work was supported by the National Science Foundation under Award Number DDM-9022550.
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The fluid parameter values correspond to typical mineral oils. The pressure distribution is shown in Fig. 11. For a film thickness of 0.4 mm, the maximum pressure is less than 0.16 MPa. Let h be the film thickness and l the composite roughness at the interface. When 3l ) h, the contact is boundary lubricated. In the experimental work, l pin s 0.09 mm; lstrip s 1.18 mm; l s Ž l2pin q lstrip 2 . s 1.18 mm ; 3 l 4 0.4 mm. Therefore, the contact between the strip and the pin is boundary-lubricated at the test speeds used.
(
Appendix A. Hydrodynamic analysis of the strip r pin interface An analysis is presented here to describe the lubrication state at the interface between the strip and the cylindrical pin. The geometry of the striprpin interface for a pin of unit diameter is shown in Fig. 10. The hydrodynamic pressure distribution can be determined using force equilibrium and flow continuity. For the boundary conditions uŽ0. s U, uŽ h. s 0, where u is fluid speed and U is the sliding speed of the strip, the governing ŽReynolds. equation for the pressure distribution is dp dx
s 6h U
h y h0
Ž A1.
h3
where p is the pressure of the fluid, h 0 is the film thickness at x s 0 and h is the fluid viscosity. At time t s 0, there is no relative motion and h 0 s 0. At t ) 0, the strip is stretched and pulled around the pin of radius R. Eq. ŽA1. can be solved for the pressure distribution. Using the approximation h s h0 q
x2
Ž A2.
2R
for a cylindrical pin, Eq. ŽA1. gives x2
3h U
dp s dx
R
ž
h0 q
x2 2R
Ž A3.
3
/
The following incremental form was used to obtain the pressure distribution. pi y piy1 q
2 3h U x iy1 Ž x i y x iy1 .
R
ž
h0 q
2 x iy1
2R
3
Ž A4.
/
The pressure distribution was calculated using the following parameter values. x 0 s -12.5 mm; p 0 s 0 Pa; kinematic viscosity h s 25.5 Cs; density of the fluid r s 0.857 kgrl; R s 12.5 mm; U s 500 mmrmin; h 0 s 0.4 mm.
References w1x J.L. Duncan, B.S. Shabel, J.G. Filho, A tensile strip test for evaluating friction in sheet metal forming, SAE Technical Paper, No. 780391, 1978, 8 pp. w2x X.J. Wang, J.L. Duncan, M.L. Devenpeck, Punch friction tests for sheet metal forming, J. Applied Metalworking 3 Ž1983. 3–11. w3x R. Zheng, D. Overby, Strip Friction Experimental Study on Galvanized Steel Sheet, Proceedings of the 15th Biannual Congress of the International Deep Drawing Research Group, 1988, Dearborn, MI, pp. 85–90. w4x S.R. Bhonsle, K.J. Weinmann, The significance of elastic deformation of the workpiece sample in the strip–tension friction test, Transactions of the North American Manufacturing Research Institution 18 Ž1990. 46–51. w5x K.J. Weinmann, S.R. Bhonsle, J. Gerstenberger, On the determination of the coefficient of friction and the friction factor by the strip–tension friction test, Annuals of the CIRP 30 Ž1990. 263–266. w6x W.R.D. Wilson, H.G. Malkani, P.K. Saha, Boundary friction measurements using a new sheet friction metal forming simulator, Transactions of North American Manufacturing Research Institution 19 Ž1991. 37–42. w7x T.S. Schurman, R.N. Wright, Micro-Mechanistic Interpretation of ToolrWorkpiece Interactions, SAE Technical Paper, No. 920631, 1992, 7 pp. w8x J.F. Lin, L.Y. Wang, Friction in deep drawing of aluminum sheet, Wear 156 Ž1992. 189–199. w9x K.J. Weinmann, J.R. Michler, V.D. Rao, A.R. Kashani, Development of a computer-controlled drawbead simulator for sheet metal forming, Annals of the CIRP 43 Ž1994. 257–261. w10x S.K. Kernosky, K.J. Weinmann, A sensing system for real-time control of the sheet metal drawing process, Transactions of the North American Manufacturing Research Institution 25 Ž1997. 37– 41. w11x S. Hao, Optimal and Intelligent Computer Controlled Sheet Metal Forming, PhD Thesis, University of Minnesota, 1994. w12x S. Sheu, W.R.D. Wilson, Flattening of workpiece surface asperities in metal forming, Proceedings of the North American Manufacturing Research Institution 11 Ž1983. 172–178. w13x W.R.D. Wilson, S. Sheu, Real area of contact and boundary friction in metal forming, International Journal of Mechanical Sciences 30 Ž1988. 475–489. w14x M.P.E. Sutcliffe, Surface asperity deformation in metal forming processes, International Journal of Mechanical Sciences 30 Ž1988. 847–868.
Friction measurement apparatus for sheet metal forming S. Hao, B.E. Klamecki ) , S. Ramalingam Department of Mechanical Engineering UniÕersity of Minnesota, Minneapolis, MN, 55455-0111, USA Received 19 February 1998; revised 21 August 1998; accepted 21 August 1998
Abstract Friction at the tooling–workpiece interface is very important in sheet metal forming operations. Accurate knowledge of friction at such interfaces is needed for process design and analysis, numerical process simulation and validation and control of forming processes. Two physical models or friction simulators, based on the stretching of a strip around a pin, were developed to characterize sheet metal forming friction. In contrast to other test apparatus which use measurements of strain to infer friction forces, these apparatus use direct measurements of forces. Effects of strain, stretching speed, lubrication, pin radius and wrap angle on coefficient of friction were determined. q 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Friction measurement; Test apparatus; Metal forming
1. Introduction In sheet metal forming, a workpiece or blank is formed between a punch and die. As the punch draws the blank into the die, frictional forces at the die shoulder and over the punch face influence workpiece deformation. In addition to inherent friction forces, in many cases additional friction forces are introduced into the forming process. In situations such as the forming of large radius, shallow parts, additional workpiece deformation may be needed to achieve the desired final part shape and control springback. A holddown or binder plate is used to apply a load to the blank and friction between the binder and workpiece and workpiece and die restrains workpiece movement and causes increased plastic deformation of the workpiece. Additional local blank restraint can be produced by drawbeads which are protrusions on the die face. The bending of the workpiece as it moves over the drawbead and drawbead–work friction restrain workpiece flow and induce plastic deformation in the workpiece. Since friction is important in determining and controlling workpiece deformation in forming processes, detailed knowledge of friction forces is needed for process design and control. In addition, in sheet metal forming frictional forces are important boundary conditions and so must be known for accurate analytical and numerical process modeling. Accu-
)
Corresponding author.
rate measurements of friction forces can provide valuable information for process model development and validation. There are unique features of sheet metal forming which determine the tooling–workpiece coefficient of friction and can make the frictional behavior different from conventional sliding friction. The workpiece experiences bulk plastic deformation, new surfaces are created and local surface deformation occurs on a plastically deforming substrate. The importance and unique features of friction in sheet metal forming have led to the development of friction measurement apparatus which simulate the workpiece deformation in forming operations. A widely used concept is the measurement of coefficient of friction as a metal strip is pulled over the cylindrical surface of a metal pin. The development of this concept into new friction test apparatus and the description of the effects of test variables on the measured coefficient of friction are reported here. The tensile strip test developed by Duncan et al. w1x is widely used. In this test, shown schematically in Fig. 1, a strip specimen of sheet metal is pulled over the cylindrical surfaces of pins to simulate stretching and drawing processes. The pulling force on one side of the pin is measured along with the strain in a section of the test specimen on the other side of the pin. The strip force on this second side of the pin is calculated from the measured strain using the stress–strain characteristics of the test material. Assuming that the coefficient of friction is constant over the pin surface, the strip tensions are used in the capstan friction
0043-1648r99r$ - see front matter q 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 8 . 0 0 2 8 8 - 9
2
S. Hao et al.r Wear 224 (1999) 1–7
tus itself, a drawback of the tensile strip test is that the load on one portion of the strip is estimated from measurement of strain. In the work described here, two different, simpler, test configurations were developed. The apparatus allow strip tensions on both sides of the pin to be measured directly. Using these apparatus, tests were performed to determine the effects of strain, stretching speed, lubrication, pin radius, pin material, and wrap angle on coefficient of friction.
2. Strip friction measurement apparatus
Fig. 1. Tensile strip test for measurement of coefficient of friction.
model to calculate the coefficient of friction. In subsequent studies, Wang et al. w2x showed that the coefficient of friction increased with strip sliding distance and that increasing the pin radius resulted in a small increase in measured coefficient of friction. Zheng and Overby w3x showed that the coefficient of friction decreased with increasing sliding speed and increasing pin radius. Bhonsle and Weinmann w4x developed an expression for the coefficient of friction in terms of measured strains, rather than forces, in their study of friction in elasticrelastic, plasticrelastic, and plasticrplastic deformations in the strip on different sides of the pin. To account for severe deformation conditions, Weinmann et al. w5x suggested use of the friction factor to describe tool–work friction. In the expression for the friction factor in terms of measured strain, the pin radius appears explicitly and experimental results show that friction factor decreases with increasing pin radius. Wilson et al. w6x developed a sheet metal forming simulator to investigate the relationships between friction and process variables such as sliding speed, interface pressure, workpiece strain and strain rate. Schurman and Wright w7x used a physical model simulating the binder and drawbead regions and studied the effects of workpiece surface characteristics and tooling topography on friction. The friction force acting on the blank holder in cup drawing was measured by Lin and Wang w8x using a split blank holder and measuring the change in gap due to the flow of the workpiece over it. Weinmann et al. w9x and Kernosky and Weinmann w10x built an instrumented strip drawing machine to study sheet forming. The part of the apparatus which simulates the die shoulder is instrumented with strain gages and was used to measure strip tensions on both sides of the die shoulder so that coefficient of friction can be calculated. There are questions that arise when the strip friction test, and other process simulation tests, and experimental results are considered. Some of the results reported indicate a dependence of coefficient of friction on the test configuration, e.g., pin radius. In terms of the test appara-
In the strip friction test, the coefficient of friction is estimated from measurements of strip tensions on each side of the pin using the capstan or belt friction model. Force and moment equilibrium on an element of the strip result in the following descriptions of the average contact pressure, p, the average friction stress, f, and the coefficient of friction, m. ps fs
F1 q F2 2WR F1 y F2
ms
WR f 1
f
ln
F1 F2
Ž 1. Ž 2. Ž 3.
In these equations F1 and F2 are the strip tensions, W is the width of the strip, R is the radius of the pin and f is the wrap angle of the strip on the pin. A schematic representation of the ‘U’ shape sheet forming friction test is shown in Fig. 2. The strip specimen is pulled over two pins and around a surface which is mounted on a load cell. This apparatus is set up in a tensile test machine and the pulling force, F1 , is measured by the test machine load cell. The strip tension on the other side of the pins, F2 , is measured with the load cell in the apparatus. The radius and location Žthe dimension shown as 77 mm in Fig. 2. of the pins can be changed to investigate the effects of the pin radius and wrap angle on friction.
Fig. 2. Schematic of the ‘U’ shape strip friction test.
S. Hao et al.r Wear 224 (1999) 1–7
Fig. 3. Schematic of the ‘L’ shape strip friction test.
Fig. 3 shows the setup for the ‘L’ shape sheet forming friction test. A test strip is held at one end in a grip supported by a load cell. The specimen is wrapped around a cylindrical pin and loaded in a tensile testing machine. The strip tensions and F1 and F2 are measured simultaneously during the test. An extensometer is used to monitor strain and to determine strain rate during the test. A major advantage of the test apparatus is that strain does not have to be measured to measure coefficient of friction. For some testing the effect of strain on coefficient of friction may be of interest. In the ‘L’ shape apparatus tests an extensometer was used as shown in Fig. 3 to measure strain during testing. In other cases the use of an extensometer may not be reasonable or warranted. In most cases it is expected that the uniform deformation region is of interest so only a measurement of specimen elongation is needed to calculate specimen strain away from the grip and pin regions. The ‘U’ shape apparatus was used in this way. The variation of strain over the apparatus pin and near the grip of the test machine was not considered in this work.
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oil, mineral oil with 1% oleic acid, mineral oil with 1% stearic acid. An argument is presented in Appendix A that mixed lubrication conditions existed during the testing. Stretching speed is the speed of the test machine head. In the ‘L’ shape apparatus tests strain was measured and strain rate was calculated for the section of the test strip between the machine head and pin assuming that strain was uniform over this length of test material. For the tests run using the ‘U’ shape apparatus strip elongation was measured. In both types of tests the initial strip length between the pin and the test machine grip was 120 mm. Specimens were carefully prepared to assure constant width and that they were burr free and were cleaned with acetone. The pins were polished with fine abrasive papers Ž600 grit. and cleaned with acetone after each test. The test apparatus were set up on a tensile test machine. During each test, outputs from the load cells, and the extensometer in the ‘L’ test, were sampled with a computer-based data acquisition system. Data acquired were processed to calculate the coefficient of friction using Eq. Ž3.. Initial testing showed that tests run under similar conditions on both apparatus gave similar results for coefficient of friction and for changes in coefficient with changes in experimental variable values, w11x.
4. Results An initial series of tests were performed at different stretching speeds. At low stretching speeds, stick–slip motion occurred at the beginning of some test runs. With an increase in stretching speed stick-slip motion was greatly reduced. No stick–slip was observed at stretching speeds of 200 mmrmin and greater. Initial stick–slip behavior was not included in test results. Both apparatus gave the same results for tests when the testing conditions were the same w11x.
3. Experimental conditions and materials The ‘U’ shape friction test was used to investigate the effects of pin radius, pin material, strip material and wrap angle on coefficient of friction. Specimen material: aluminum strips Ž0.47 mm thick, 10.2 mm wide., steel strips Ž0.57 mm thick, 12.7 mm wide., galvanized steel strips Ž0.64 mm thick, 12.7 mm wide., pin material: steel, copper, and teflon, pin radius: 6.35 mm, 12.7 mm, wrap angle: 908, 758, 608, stretching speed: 20 mmrmin, lubrication: dry. The ‘L’ shape friction test was used to investigate the effects of stretching speed and lubrication on friction. Specimen material: steel strips Ž0.57 mm thick, 12.7 mm wide., pin radius: 12.7 mm, pin material: steel, Wrap angle: 908, stretching speed Žmmrmin.: 5, 10, 20, 50, 100, 200, 500, corresponding strain rate Ž%rs.: 0.046, 0.090, 0.198, 0.499, 0.956, 1.872, 3.731, lubrication: dry, mineral
4.1. Variations of coefficient of friction with strain and strain rate The variation of coefficient of friction with strain for stretching speeds between 5 and 500 mmrmin is shown in Fig. 4. The results are for steel strip specimens, steel pins, pin radius of 12.7 mm, wrap angle of 908 and no lubricant. The coefficients of friction are in the commonly quoted range of 0.2–0.4 for metal working processes and increase by 10–15% over the test range. The coefficient of friction decreases as the stretching speed increases. Coefficient of friction decreased by about 30% as stretching speed was increased from 5 to 500 mmrmin. However, this large change in coefficient of friction is due to the large difference between the lowest and highest strain rates. All test results are shown in Fig. 4 with very similar results for stretching speeds of 20, 50,
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pressure curve is not constant, that is, the coefficient of friction varied in the tests. There are two regions in which the coefficient of friction changes at much different rates. Over most of the range of pressure, the coefficient of friction changes slowly. The range of pressure between about 9.5 MPa and 12 MPa corresponds to the data shown in Fig. 4. For larger pressure the coefficient of friction rises rapidly. 4.3. Effect of lubrication
Fig. 4. Variation of coefficient of friction with strain and stretching speed in strip friction tests Žsteel strip, steel pin, pin radiuss12.7 mm, wrap angles908, dry..
100 and 200 mmrmin and many data points overlapping. These results show that if the increase in coefficient of friction with strain is due to the formation of new surface area, as long as the new area forms the rate of formation has very little influence on the change in coefficient of friction. 4.2. Friction stress Õersus contact pressure Contact pressure and friction stress can be calculated from the measured forces using Eqs. Ž1. and Ž2.. Fig. 5 shows the variation of the friction stress with contact pressure for test conditions of Fig. 4 and 200 mmrmin stretching speed. The slope of the friction stress–contact
Fig. 5. Friction stress vs. contact pressure in strip friction tests.
The three lubricants used were straight mineral oil, mineral oil with 1% Oleic acid, and mineral oil with 1% Stearic acid. The test results presented in Fig. 6 are for a stretching speed of 100 mmrmin and are representative of the speeds used in this work. As shown in the Appendix, boundary lubrication conditions existed. The results indicate that straight mineral oil has little effect on friction because there is essentially no hydrodynamic action at the pinrstrip interface. Polar additives of 1% oleic acid or 1% stearic acid greatly reduce sheet forming friction, by about 50% in this case. These additives can react with the surfaces to form tightly adhering boundary lubricant films which promote stable boundary lubrication and decrease friction force. 4.4. Effect of pin radius, material and wrap angle The results presented in Fig. 7 are the average coefficients of friction for varying strain tests with different test materials. The results show that the coefficient of friction increases as the steel pin radius decreases for aluminum, steel and galvanized steel strip materials. Use of the smaller pin with the diameter half that of the larger pin produced
Fig. 6. Effect of lubrication on friction in strip friction tests Žsteel strip, steel pin, pin radiuss12.7 mm, wrap angles908, speeds100 mmrmin..
S. Hao et al.r Wear 224 (1999) 1–7
Fig. 7. Effect of pin radius in strip friction tests Žsteel pin, wrap angles908, speeds 20 mmrmin, dry..
increases of coefficient of friction of about 13%, 25% and 29%. Changes in coefficient of friction were also seen with changes in strain and the effect of pin radius on specimen strain is discussed in Section 5. A series of tests were performed with aluminum strips using steel, copper, and Teflon pins. The results are shown in Fig. 8 and indicate that the pin material has a significant influence on coefficient of friction. As expected, friction between aluminum and teflon is very low. This first reported use of a very low friction material for the pin indicates potential simplification of other sheet metal tests. Workpiece bending and very low friction situations in sheet metal forming are usually studied by pulling the strip specimen over a pin which is free to rotate. The small
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Fig. 9. Variation of coefficient of friction with wrap angle Žgalvanized steel strip, steel pin, pin radiuss12.7 mm, speeds 20 mmrmin..
friction effects shown in the results for the fixed teflon pin point toward usefulness of fixed, low friction material pins in investigations of sheet metal deformation and friction. The effect of wrap angle on coefficient of friction was investigated in a series of tests using galvanized steel strips. The results are presented in Fig. 9. For small strains there is little difference in coefficients of friction for different strip wrap angle. As test specimen strain increases coefficient of friction decreases with increasing wrap angle. Eq. Ž3. describes the relation between the force ratio, F1rF2 , and the wrap angle, f , for constant coefficient of friction.
5. Discussion
Fig. 8. Results from strip friction tests with different pin materials Žsteel strip, wrap angles908, speeds 20 mmrmin, dry..
The results presented fall into the two categories of those related to the test apparatus and those which are results of friction tests. The two sheet forming friction test apparatus developed can be used to characterize frictional behavior for the design, modeling and operation of sheet metal forming processes. The test apparatus are simple and offer the advantage that strip tensions are measured directly. Difficulties with measuring strain and uncertainties about material deformation descriptions needed to calculate forces from measured strains are eliminated. Friction test results show that coefficient of friction Ži. increases with increasing test specimen strain, Žii. increases with increasing local contact pressure, Žiii. decreases with increasing stretching speed, i.e. strain rate, and Živ. decreases with increasing pin radius. The test results correspond to published results and show that at the large strains used to simulate strains imposed in metal working processes significant changes in
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indentation for bulk plane strain plastic deformation. They found that the effective hardness of the surface is reduced by plastic flow in the bulk. These deformation induced surface and bulk material modifications can explain changes in frictional behavior. The change in coefficient of friction with test strip strain shows that contact conditions and material state vary continuously throughout the test. The implication is that potentially large difference in friction conditions can occur over the workpiece in metal forming operations since differences in strain and strain rate exist at different locations. Work-tool coefficient of friction will vary during sheet metal forming processes complicating process modeling and process control.
Fig. 10. Geometry of the strip–pin interface.
coefficient of friction occur with changes in test conditions. Large, process specific effects are clearly seen in the increase in coefficient of friction with strain shown in Fig. 4 which correspond to results of Wang et al. w2x. During strip stretching new surface area is created. In the strip–pin contact area the new strip surface area is in intimate contact with the pin and high friction is expected. The large effects of polar lubricants seen in Fig. 6 where lubrication reduces coefficient of friction by about 50% add strength to this interpretation. New, active surface area with strong lubricant binding sites is created during large strain stretching and this area increases with amount of strain. With measured strip tensions and known test apparatus characteristics the average contact pressure and average friction stress can be calculated using Eqs. Ž1. and Ž2.. Fig. 5 is another representation of the changing coefficient of friction and also indicates another unique feature of sheet forming processes and work–tool friction. Changes of coefficient of friction occur even at low contact pressure. The contact pressure, p, is p s t srR
6. Biographies Dr. S. Hao is currently the manager of the Advanced Lapping Technology department in Seagate Recording Heads, Minneapolis, MN. He obtained his PhD in Mechanical Engineering at the University of Minnesota in 1994. His main areas of research are related to advanced slider fabrication process development and engineering, including process optimization, sensor height control, lapping fundamentals, surface finish and process automation. Dr. B.E. Klamecki is Associate Professor of Mechanical Engineering at the University of Minnesota, MN. He teaches a course in Tribology and conducts research in basic aspects of friction and wear. His other research areas are sensor development for monitoring manufacturing processes and the analysis and modeling of the mechanics of material removal processes. Dr. S. Ramalingam is a professor of Mechanical Engineering at the University of Minnesota, Minneapolis, MN, USA. He obtained his PhD degree in 1967. His main areas
Ž 4.
where s is the tensile stress, R is the pin radius and t is the strip thickness. For strip specimens and sheet forming t < R and so p is small. The local contact pressure is relatively small even though the underlying material is in bulk plastic flow. The increase in average coefficient of friction with decreasing pin radius seen in Fig. 7 indicates that even though bending strain is compressive on the pin side of the strip, the large stretching strains in these tests produce large deformation and surface related effects. For example, the extreme case of the smaller pin radius of 6.35 mm and thick strip thickness of 0.57 mm gives a bending strain of 4.3% compared to the stretching strains of 10–25% imposed in the tests. All these results are consistent with the models proposed by Sheu and Wilson w12x, Wilson and Sheu w13x and Sutcliffe w14x. In their work, they used upper-bound methods to investigate workpiece asperity flattening or surface
Fig. 11. Pressure distribution.
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of research are related to mechanical engineering: surface coating and surface inspection for flaws.
Acknowledgements This work was supported by the National Science Foundation under Award Number DDM-9022550.
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The fluid parameter values correspond to typical mineral oils. The pressure distribution is shown in Fig. 11. For a film thickness of 0.4 mm, the maximum pressure is less than 0.16 MPa. Let h be the film thickness and l the composite roughness at the interface. When 3l ) h, the contact is boundary lubricated. In the experimental work, l pin s 0.09 mm; lstrip s 1.18 mm; l s Ž l2pin q lstrip 2 . s 1.18 mm ; 3 l 4 0.4 mm. Therefore, the contact between the strip and the pin is boundary-lubricated at the test speeds used.
(
Appendix A. Hydrodynamic analysis of the strip r pin interface An analysis is presented here to describe the lubrication state at the interface between the strip and the cylindrical pin. The geometry of the striprpin interface for a pin of unit diameter is shown in Fig. 10. The hydrodynamic pressure distribution can be determined using force equilibrium and flow continuity. For the boundary conditions uŽ0. s U, uŽ h. s 0, where u is fluid speed and U is the sliding speed of the strip, the governing ŽReynolds. equation for the pressure distribution is dp dx
s 6h U
h y h0
Ž A1.
h3
where p is the pressure of the fluid, h 0 is the film thickness at x s 0 and h is the fluid viscosity. At time t s 0, there is no relative motion and h 0 s 0. At t ) 0, the strip is stretched and pulled around the pin of radius R. Eq. ŽA1. can be solved for the pressure distribution. Using the approximation h s h0 q
x2
Ž A2.
2R
for a cylindrical pin, Eq. ŽA1. gives x2
3h U
dp s dx
R
ž
h0 q
x2 2R
Ž A3.
3
/
The following incremental form was used to obtain the pressure distribution. pi y piy1 q
2 3h U x iy1 Ž x i y x iy1 .
R
ž
h0 q
2 x iy1
2R
3
Ž A4.
/
The pressure distribution was calculated using the following parameter values. x 0 s -12.5 mm; p 0 s 0 Pa; kinematic viscosity h s 25.5 Cs; density of the fluid r s 0.857 kgrl; R s 12.5 mm; U s 500 mmrmin; h 0 s 0.4 mm.
References w1x J.L. Duncan, B.S. Shabel, J.G. Filho, A tensile strip test for evaluating friction in sheet metal forming, SAE Technical Paper, No. 780391, 1978, 8 pp. w2x X.J. Wang, J.L. Duncan, M.L. Devenpeck, Punch friction tests for sheet metal forming, J. Applied Metalworking 3 Ž1983. 3–11. w3x R. Zheng, D. Overby, Strip Friction Experimental Study on Galvanized Steel Sheet, Proceedings of the 15th Biannual Congress of the International Deep Drawing Research Group, 1988, Dearborn, MI, pp. 85–90. w4x S.R. Bhonsle, K.J. Weinmann, The significance of elastic deformation of the workpiece sample in the strip–tension friction test, Transactions of the North American Manufacturing Research Institution 18 Ž1990. 46–51. w5x K.J. Weinmann, S.R. Bhonsle, J. Gerstenberger, On the determination of the coefficient of friction and the friction factor by the strip–tension friction test, Annuals of the CIRP 30 Ž1990. 263–266. w6x W.R.D. Wilson, H.G. Malkani, P.K. Saha, Boundary friction measurements using a new sheet friction metal forming simulator, Transactions of North American Manufacturing Research Institution 19 Ž1991. 37–42. w7x T.S. Schurman, R.N. Wright, Micro-Mechanistic Interpretation of ToolrWorkpiece Interactions, SAE Technical Paper, No. 920631, 1992, 7 pp. w8x J.F. Lin, L.Y. Wang, Friction in deep drawing of aluminum sheet, Wear 156 Ž1992. 189–199. w9x K.J. Weinmann, J.R. Michler, V.D. Rao, A.R. Kashani, Development of a computer-controlled drawbead simulator for sheet metal forming, Annals of the CIRP 43 Ž1994. 257–261. w10x S.K. Kernosky, K.J. Weinmann, A sensing system for real-time control of the sheet metal drawing process, Transactions of the North American Manufacturing Research Institution 25 Ž1997. 37– 41. w11x S. Hao, Optimal and Intelligent Computer Controlled Sheet Metal Forming, PhD Thesis, University of Minnesota, 1994. w12x S. Sheu, W.R.D. Wilson, Flattening of workpiece surface asperities in metal forming, Proceedings of the North American Manufacturing Research Institution 11 Ž1983. 172–178. w13x W.R.D. Wilson, S. Sheu, Real area of contact and boundary friction in metal forming, International Journal of Mechanical Sciences 30 Ž1988. 475–489. w14x M.P.E. Sutcliffe, Surface asperity deformation in metal forming processes, International Journal of Mechanical Sciences 30 Ž1988. 847–868.