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On possibilities for the determination of the coefficient of friction in hydroforming of tubes
Journal of Materials Processing Technology 125±126 (2002) 412±420
On possibilities for the determination of the coef®cient of friction in hydroforming of tubes F. Vollertsen*, M. Plancak Department for Metal Forming Technologies, Universitat Paderborn, 33098 Paderborn, Germany Received 14 January 2002; accepted 24 February 2002
Abstract Tribology plays an important role in metal forming, especially in tube hydroforming. The tests available for the experimental determination of the coef®cient of friction (COF) are unsatisfying. This is especially true for the case of friction within the forming zone, i.e. where the workpiece is deformed plastically. A new measuring principle is developed. It is based on upsetting a tube. The comparison of experimental results and FEM simulation yields the COF without any undesired interference with the forming process. First results for a variation of the lubricant show the feasibility of the method. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydroforming; Tube forming; FEM simulation; Friction test; Tribology; Principle of measurement
1. Introduction Hydroforming of tubes is a technology which is been expanding its applications continuously, especially in the automotive industry. Many applications of this technology are based on the possibility to generate thin-walled hollow complex shaped parts. The main advantages of hydroforming are, e.g. low weight and high stiffness of the product. In order to reduce weight of the component the wall thickness should be reduced. This is connected with an increasing role of the friction, as the friction forces have to be transferred by a decreasing cross-section during the forming process. As the contact pressure is high and the contact surface is large, the friction forces make a dominant portion of the punch forces. Due to that the friction coef®cient should be measurable in order to enable the development of the strategies for a reduction of the coef®cient of friction (COF). According to Fig. 1, there are two different kind of zones in hydroforming, the so-called feed zone and the forming zone. The feed zone is meant to be a kind of reservoir for material which is pushed into the forming zone. The deformation of the tube in this zone is, in a ®rst rough approximation, pure elastic compression. At the beginning of the process, there has to be a clearance between the outer diameter of the tube and the inner diameter of the tool in *
Corresponding author. Tel.: 49-525-160-2372; fax: 49-525-160-3419. E-mail address: [email protected] (F. Vollertsen).
order to ensure that, despite of the scatter in the diameter, the workpiece can be inserted into the tool and closing of the tool will not result in undesired plastic deformation of the tube. This insertion gap is eliminated during pressurizing of the tube at the beginning of the hydroforming process. Even for very low gap sizes, this results in plastic deformation of the tube. So, the deformation condition within the feed region is characterized by small plastic tensile strain in circumferential direction. Depending on the friction conditions, the strains remain constant or increase during the further forming action. In the forming zone, a three-dimensional strain occurs. Depending on the ratio of the axial stress, produced by the punch forces and reduced by the friction forces in the feed region, and the tangential stress generated by the inner pressure, a thickening or thinning of the wall can take place. In some casesÐfor instance when the workpiece has a de¯ected shapeÐit is almost impossible to introduce compressive axial stress from the punches to the feed zone. In that case, a two-dimensional tensile stress with a low radial compressive stress results, yielding a thinning of the tube wall. The strains in the forming zone are large compared to those in the feed zone, yielding a continuous change of the surface micro geometry. In turn, this produces different changes of the friction conditions. As in many cases of metal forming, the validity of Coulomb's law of friction is anticipated. The problem of the contact pressure was discussed elsewhere [1±3]. As the differences between the contact pressure and the inner
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 2 9 2 - 3
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413
Fig. 1. Definition of the different zones in hydroforming.
pressure is typically in the order of 10%, it is assumed that the inner pressure is equivalent to the contact pressure. This simpli®cation gives lower errors than the introduction of some calculation rules without having the boundary conditions exactly de®ned. In Fig. 2, the in¯uences on the COF and the contact pressure are shown. While it is possible to determine the local contact pressure by FEM, as the in¯uence parameters are direct input values, the determination of the COF by the FEM is not possible. It is a result of the contact conditions including the effects of the lubricant and surface micro geometry. Therefore, the COF has to be determined by measurements and taken as an input parameter for the FEM. It is evident that in the tribological aspect of hydroforming technology, there is a certain scarcity of knowledge. The present paper provides closer insight into this ®eld, with the particular focus on the possibilities for determination of the COF in the forming zone of an hydroforming process.
2. COF measurement 2.1. Principles There are different methods which have been applied for the measurement of the COF in hydroforming [3±5]. One class of methods are the push through tests, see Fig. 3. These tests simulate the feed region of the hydroforming process. A tube is expanded by an internal pressure against the tool wall. By pushing the tube through the tool, a friction force at the contact surface between the tube and the tool occurs. This force can be measured either as a difference of the punch forces or as a resulting force on the tool, measured in a horizontal or vertical test layout. The measured friction force is divided by the nominal contact force, i.e. the contact area times the internal pressure, to get the COF. In all three cases, it has to be ensured that there is no friction between the punch and the die directly, as this would affect the
Fig. 2. Influential parameters on the friction in hydroforming.
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Fig. 3. Friction tests for the feed area in hydroforming.
measurement result. Different tool coatings, lubricants and forming conditions (punch speed, internal pressure) were investigated by this method. With the exception of the contact pressure the experimental boundary conditions can be varied and determined exactly. Even different insertion clearances can be realized, yielding a small plastic deformation of the tube at the beginning of the test, as it is observed in the real forming process. The difference between the two vertical variants shown in Fig. 3 is the position of force measurement. The ®rst method is based on the direct measurement of the difference in punch force, while the second is based on the force measurement on the tool, i.e. only one force has to be determined, which minimizes the possible errors. In the case of the horizontal layout, the die is split parallel to the tube axis. The closing force Fp is measured and load cells between the two die halves measure the tool contact force. The difference of the two forces is taken as contact force between the tube and the die. The disadvantage of this method is that the die and the closing force must be beard by linear bearings. This requires a correction of the measured values by the value of friction forces in the bearings.
Fig. 4 shows various principles for the determination of the COF for the forming zone. The ®rst principle is one variant of the direct measurement of the friction force in the forming zone [3,6]. A ring segment, which is placed at the position where the dome of the part is formed, can be shifted by the friction force against load cells. The problems which occur with this method are typical for that kind of measurements: due to the elasticity of the load cell, a gap between the ring section and the remainder of the tool occurs. As the workpiece material in this zone is in the condition of plastic deformation it can easily ¯ow into that gap. This results in severe disturbances or even errors in the measurement. A second problem is that the dome has to have a minimum length, as the material has to be formed so far that it covers the tool radius. Before the radius is formed, it is not possible to measure any friction force in this test. A systematic variation of the processing parameters (internal pressure, sliding speed) is dif®cult, as these parameters have to be adjusted to enable proper forming of the part. Another principle of the measurements of the COF in the forming zone is the calibration test, see Fig. 4. A round tube is expanded by inner pressure into a rectangular tool.
Fig. 4. Friction tests for the forming zone in hydroforming.
F. Vollertsen, M. Plancak / Journal of Materials Processing Technology 125±126 (2002) 412±420
Depending on the friction conditions the development of the radius and the wall thickness in the edges differs. The test can be terminated at a certain pressure, using the edge radius as a measure for the COF. The radius should be proportional to the COF [7]. Alternatively, the wall thickness distribution can be analyzed at the end of the test and correlated, e.g. by using FEM calculations, with the COF. It was shown that there are large differences in the wall thickness distributions after this test for different lubricants [5]. The advantages of the test are the plastic deformation of the specimen during the whole test and that the forming process is not affected by the testing method itself, like it is the case in the direct measurement method shown in Fig. 4. The disadvantage is that there is very little sliding of the specimen against the tool surface and that the contact pressure is not constant but increases during the test. The third test shown in Fig. 4, the tube upsetting test, was developed to overcome these dif®culties. It is presented in this paper in more details. 3. Push through test 3.1. Experiments Experiments for the feed range were done using the equipment shown in Fig. 5. Lubrication was carried out by using oil without additives. An amount of 6 g/m2 was applied and checked by a weight control of the dry and lubricated tube. The tube was positioned between two punches. To ensure a de®ned compression of the tube, which simulates the adaption process at the beginning of the real forming process to overcome the insertion gap, a mechanical distance was inserted between the two punches inside the workpiece. The tube was compressed by 0.5%. Besides the
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insertion gap ®lling, this method yields also a metallic sealing without wedge shaped punch ends, which would increase the local pressure between the tube and the tool due to additional radial pressure. After that, the internal pressure was slowly increased up to pressures of 200 MPa. The internal pressure was measured by pressure transducers. During this increase, both punches were moved downwards by the same velocity. The resulting friction forces were measured at the force transducer. A piezoelectric transducer was used. These measurements provided information about the friction force as a function of the internal pressure. The COF was calculated according to the Coulombs law. In this work, the internal pressure was taken as the contact pressure. The error by doing so is assumed to be below 10% and can be corrected as soon as there is more relevant information regarding the real contact pressure. One approach to determine the contact pressure is a FEM simulation. A second approach to the contact pressure problem could be an experimental one, using the method published in [8], which uses ultrasonic waves for the determination of the real contact area. It seams feasible by calibration of this method to determine the contact pressure too. Different materials of the tube were tested, such as low carbon steel, high alloyed steel and an aluminum alloy. The tool was made from hardened tool steel and coated by plasma nitriding or a hard coating from combined PVD± CVD coatings. 3.2. Experimental results Typical results from push through measurements are shown in Fig. 6. It is obvious that the problems concerning friction are more evident in forming of aluminum tubes than in steel materials. The COF is three times higher for the aluminum tubes than for low alloyed steel tubes. Using
Fig. 5. Test equipment for the vertical push through test.
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Fig. 6. Results for the feed area for different tool coatings and workpiece materials [9].
modi®ed coatings, the COF can be reduced to an amount comparable to that of steel in sliding against a nitrided tool. Further results of these tests are published elsewhere [1,3,9,10]. 4. Tube upsetting method 4.1. Principle A new principle for the measurement of the COF in the forming zone is proposed and shown in Fig. 7. A tube is continuously upset in a closed die, while it is elastic± plastically expanded towards the tool wall by an internal pressure. Due to the friction forces the wall thickness increases non-homogeneously. The biggest increase of the wall thickness occurs near the punch with the higher velocity. The shape of the wall cross-section is a function of the
COF m, the strength and strain hardening behavior (characterized by the strain hardening coef®cient C and strain hardening exponent n from Ludwik±Hollomons law) and the compression ratio. Depending on these parameters, different shapes can develop: (A) m 0, n 0: a homogeneous thickening of the whole tube occurs, the wall thickness is a function of the compression ratio only. (B) m 0, n > 0: same as in case (A). (C) m > 0, n 0: the wall thickness increases linearly from one end to the other, while the largest thickness occurs at the tube end which is in contact with the punch having the higher velocity. (D) m > 0, n > 0: the wall thickness is similar to that of the case (C), but the difference in thickness along the tube wall is smaller as the hardening coefficient increases.
Fig. 7. Basic principle of the tube upsetting test for the friction measurement.
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Depending on the hardening behavior, the course can be non-linear. The principle of the test is similar to that of the ring compression test or the combined forward±backward extrusion test. The COF is determined from the geometry of the test piece after forming, using a suitable diagram. Such diagrams can be calculated from analytical solutions, which are under development and will be published elsewhere. An alternative is the determination of the diagrams by FEM calculations. This method is presented in the current paper. Compared to the other test principles which are mentioned above, this methods has the following advantages: The processing parameters (internal pressure, sliding velocity, deformation speed and upsetting grade) can be chosen freely during this test. The equipment used for this test is simple compared to some of the other tests and does not interfere with the process itself. By changing the length of the tube, the test can be adapted to different friction conditions. In the case of a low COF, long tubes would be beneficial, as the friction stresses are accumulated to forces which significantly influence the thickening of the tube. 4.2. FEM simulation 4.2.1. FEM model The FEM simulation was done using PAM Stamp (Version 2000). The tool was considered as rigid body, while the tube had the material properties according to that of steel or an aluminum alloy. Proper stress±strain curves were used in the simulation. Shell elements were applied. The contact
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conditions were modeled by the Langrangrian contact type. The calculation time was about half an hour on a SUN Ultra 60 workstation. 4.2.2. FEM results Fig. 8 shows an example of the calculated shape of the tube wall after the compression test. It is interesting to note that the wall thickness distribution is nearly linear. In the case of a very high COF m 0:5, the lower part of the tube remains unchanged (wall thickness s s0 ). This is so, because the friction reduces the axial stress which acts in the tube cross-section. At a high COF, the stress is reduced below the ¯ow stress, resulting in pure elastic compression of the lower end of the tube. For mild steel and for an aluminum alloy a diagram was calculated, see Fig. 9. The wall thickness distribution was characterized by the slope of the wall thickness strain x Des =Dh, where es is the tube wall thickness strain and h the height of the tube after compression. The COF was varied between the smallest COF which is believed to occur in hydroforming and the largest value which theoretically occur in metal forming if Tresca's yield criterion is applied (i.e. m 0:5). 4.3. Experiments Experiments were done using the same equipment as for the friction tests for the push through test. The velocity of the lower punch was set to zero, while the upper punch velocity was 5 mm/s. Mild steel tubes (German standard St34-2) were upset by 15% except one tube. That experiment (lower curve in Fig. 10) was not considered in the following examination of the results. The wall thickness distribution of the upset tubes is shown in Fig. 10. The curves were
Fig. 8. Calculated wall thickness distribution after upsetting of a steel tube at different COFs.
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Fig. 9. Calculated slope x±COF m curves for different material behavior.
Fig. 10. Measured wall thickness distribution after tube upsetting for different lubricants.
linearized in order to determine the slope x for a comparison with the results given in Fig. 9. Due to the sealing method, the punch ends showed a different thickening behavior than the main body of the tube. Additional radial stresses also lead to increased friction forces in these regions. As the test is not based on force measurements, these effects do not affect the result concerning the COF directly, but the effective length of the tube is shortened. Three different lubricants were tested: mixture of grease and molybdenum disul®de (common name: Molykote) was applied by painting, molybdenum disul®de by spraying and oil by rolling. From other tests, it is known that the best lubrication is derived from Molykote, while oil showed the poorest behavior.
5. Discussion It is worth mentioning that there is a linear relationship between the slope of the wall thickness x and the COF m when plotting the results from the FEM in a double logarithmic plot. This shows that there is a power law relationship between the two values. This gives a helpful hint for the analytical description of this test. If one compares the curve for the aluminum alloy with that of the steel, it is obvious that the steel tubes show a steeper slope than aluminum. It can be understood as follows. In the tube upsetting test, there is only one intended forming zone in the area starting at the punch having the higher velocity. Provided that the COF and the contact
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419
Fig. 11. Slope x±COF m diagram with experimental results.
pressure are equal for steel and aluminum alloy, i.e. the friction force has the same value, there will be the same stress gradient in the tubes. Thickening will occur in that region where the effective stress seff seff
Fp
FR p=4pi d0 2s0 2 p=4 d02 di2
(where Fp is the punch force; FR the friction force; pi the inner pressure; d0, di the outer and inner tube diameter; s0 the wall thickness) is equivalent to the ¯ow stress. As the aluminum alloy has a lower ¯ow stress than steel, the point below which no thickening occurs will be at a position with a larger distance from the movable punch than for steel. As the punch travels, and therefore the overall compression is equal for all data points in Fig. 9, the slope for the steel tube must be steeper as the compression concentrates on a smaller length of the tube. The simulation of tube upsetting of steel tubes was performed by using materials with different strain hardening behavior. The resulting difference in the x±m curves is small. The curve for the material with the smaller strain hardening exponent has a slope which is steeper than that for the material with higher strain hardening exponent n. This is consistent with the prediction for case (D) compared to case (C) above. In Fig. 11, the results of the tube upsetting tests are plotted into the slope±friction diagram. The COFs, which are identi®ed in this way, are in the expected order of magnitude. The value of the COF in the case when Molykote was applied as lubricant, is very small and lies below 0.01, but this can be understood from the pressure dependence which is observed in push through tests. The highest m-value is obtained for oil as lubricant, yielding a COF in the order of 0.015. While these are only some preliminary results which have to be veri®ed by further
measurementsÐpartly the scatter was undesirable high, see Fig. 10Ðthey show that the concept of the test is reliable and can be used for friction measurements in the forming zone at different conditions. 6. Conclusions Although a number of different tests for the determination of COF for hydroforming of tubes exist, there is still a lack of information related to that subject. There exist a number of different tests for the determination of the COF for hydroforming of tubes. While the push through test seems to be well established for the feed area, no standard test seems to exist for the forming area. The differences in friction behavior for the friction between different workpiece material and different tool coatings are shown by friction tests using the push through test. Aluminum shows detrimental effects, resulting in high COFs. The tube upsetting test was defined. It is shown that reliable results for the COF can be deduced from that test for the case of plastic deformation of the workpiece. The differences between obtained COFs for three different lubricants were determined. The COF was in the order of 0.01. Further work must be done in order to reduce the scatter of the results. Diagrams for the identification of the COF can be calculated using the FEM simulation. As this is time consuming, an analytical model is desired and under development. Acknowledgements The authors like to express their gratitude to the DAAD for the ®nancial support of the research visit of Prof. Plancak
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in Germany. Special thanks are to Dipl.-Ing. J. Woitschig for conducting the FEM simulation. They also thank Dipl.Ing. T. Prange and MSc. A. Zarin for conducting the experiments.
[5] [6]
References [1] F. Vollertsen, T. Prange, M. Sander, Hydroforming: needs, developments and perspectives, in: M. Geiger (Ed.), Advanced Technology of Plasticity, Vol. 2, Springer, Berlin, 1999, pp. 1197±1210. [2] Ch. Hartl, Ein Beitrag zur Flexibilisierung der Innenhochdruckumformung, Shaker, Aachen, 1995. [3] W. Meyer, Ein Beitrag zur Tribologie der Innenhochdruckumformung, Vol. 2, Fortschritt-Berichte VDI, 1999, p. 509. [4] D. Schmoeckel, C. Hielscher, M. Prier, Developments and perspectives of internal high-pressure forming of hollow sections, in: M. Geiger (Ed.), Advanced Technology of Plasticity, Proceed-
[7] [8] [9] [10]
ings of the Sixth ICTP, Vol. 2, Springer, Berlin, 1999, pp. 1171± 1182. A. Birkert, Herstellung von Strukturbauteilen durch InnenhochdruckUmformen, BeitraÈge zur Umformtechnik, MAT-INFO Informationsgesellschaft DGM, Vol. 25, Frankfurt, 2000. F. Dohmann, W. Meyer, Tribologie in der Innenhochdruckumformung, Blech Rohre Profile 44 (10) (1997) 36±39. M. Nielsen, in: Proceedings of Symposium on New Coatings for Hydroforming Tooling, Next Generation Solutions, Vol. 10, Nashville, USA, 2000, pdffiles/papers/0.18. pdf. M. Geiger, U. Engel, F. Vollertsen, In situ ultrasonic measurement of the real contact area in bulk metal forming processes, Ann. CIRP 41 (1) (1992) 255±258. F. Vollertsen, Challenges and Chances of Hydroforming of Aluminum Alloys, German±Chinese Ultralight Symposium, Vol. 218, DVS-Berichte, 2001, pp. 71±79. F. Vollertsen, Reibung beim Innenhochdruckumformen, in: F. Vollertsen, M. Kleiner (Eds.), Idee-Vision-Innovation, Meisenbach Bamberg, 2001, pp. 463±472.
On possibilities for the determination of the coef®cient of friction in hydroforming of tubes F. Vollertsen*, M. Plancak Department for Metal Forming Technologies, Universitat Paderborn, 33098 Paderborn, Germany Received 14 January 2002; accepted 24 February 2002
Abstract Tribology plays an important role in metal forming, especially in tube hydroforming. The tests available for the experimental determination of the coef®cient of friction (COF) are unsatisfying. This is especially true for the case of friction within the forming zone, i.e. where the workpiece is deformed plastically. A new measuring principle is developed. It is based on upsetting a tube. The comparison of experimental results and FEM simulation yields the COF without any undesired interference with the forming process. First results for a variation of the lubricant show the feasibility of the method. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydroforming; Tube forming; FEM simulation; Friction test; Tribology; Principle of measurement
1. Introduction Hydroforming of tubes is a technology which is been expanding its applications continuously, especially in the automotive industry. Many applications of this technology are based on the possibility to generate thin-walled hollow complex shaped parts. The main advantages of hydroforming are, e.g. low weight and high stiffness of the product. In order to reduce weight of the component the wall thickness should be reduced. This is connected with an increasing role of the friction, as the friction forces have to be transferred by a decreasing cross-section during the forming process. As the contact pressure is high and the contact surface is large, the friction forces make a dominant portion of the punch forces. Due to that the friction coef®cient should be measurable in order to enable the development of the strategies for a reduction of the coef®cient of friction (COF). According to Fig. 1, there are two different kind of zones in hydroforming, the so-called feed zone and the forming zone. The feed zone is meant to be a kind of reservoir for material which is pushed into the forming zone. The deformation of the tube in this zone is, in a ®rst rough approximation, pure elastic compression. At the beginning of the process, there has to be a clearance between the outer diameter of the tube and the inner diameter of the tool in *
Corresponding author. Tel.: 49-525-160-2372; fax: 49-525-160-3419. E-mail address: [email protected] (F. Vollertsen).
order to ensure that, despite of the scatter in the diameter, the workpiece can be inserted into the tool and closing of the tool will not result in undesired plastic deformation of the tube. This insertion gap is eliminated during pressurizing of the tube at the beginning of the hydroforming process. Even for very low gap sizes, this results in plastic deformation of the tube. So, the deformation condition within the feed region is characterized by small plastic tensile strain in circumferential direction. Depending on the friction conditions, the strains remain constant or increase during the further forming action. In the forming zone, a three-dimensional strain occurs. Depending on the ratio of the axial stress, produced by the punch forces and reduced by the friction forces in the feed region, and the tangential stress generated by the inner pressure, a thickening or thinning of the wall can take place. In some casesÐfor instance when the workpiece has a de¯ected shapeÐit is almost impossible to introduce compressive axial stress from the punches to the feed zone. In that case, a two-dimensional tensile stress with a low radial compressive stress results, yielding a thinning of the tube wall. The strains in the forming zone are large compared to those in the feed zone, yielding a continuous change of the surface micro geometry. In turn, this produces different changes of the friction conditions. As in many cases of metal forming, the validity of Coulomb's law of friction is anticipated. The problem of the contact pressure was discussed elsewhere [1±3]. As the differences between the contact pressure and the inner
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 2 9 2 - 3
F. Vollertsen, M. Plancak / Journal of Materials Processing Technology 125±126 (2002) 412±420
413
Fig. 1. Definition of the different zones in hydroforming.
pressure is typically in the order of 10%, it is assumed that the inner pressure is equivalent to the contact pressure. This simpli®cation gives lower errors than the introduction of some calculation rules without having the boundary conditions exactly de®ned. In Fig. 2, the in¯uences on the COF and the contact pressure are shown. While it is possible to determine the local contact pressure by FEM, as the in¯uence parameters are direct input values, the determination of the COF by the FEM is not possible. It is a result of the contact conditions including the effects of the lubricant and surface micro geometry. Therefore, the COF has to be determined by measurements and taken as an input parameter for the FEM. It is evident that in the tribological aspect of hydroforming technology, there is a certain scarcity of knowledge. The present paper provides closer insight into this ®eld, with the particular focus on the possibilities for determination of the COF in the forming zone of an hydroforming process.
2. COF measurement 2.1. Principles There are different methods which have been applied for the measurement of the COF in hydroforming [3±5]. One class of methods are the push through tests, see Fig. 3. These tests simulate the feed region of the hydroforming process. A tube is expanded by an internal pressure against the tool wall. By pushing the tube through the tool, a friction force at the contact surface between the tube and the tool occurs. This force can be measured either as a difference of the punch forces or as a resulting force on the tool, measured in a horizontal or vertical test layout. The measured friction force is divided by the nominal contact force, i.e. the contact area times the internal pressure, to get the COF. In all three cases, it has to be ensured that there is no friction between the punch and the die directly, as this would affect the
Fig. 2. Influential parameters on the friction in hydroforming.
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Fig. 3. Friction tests for the feed area in hydroforming.
measurement result. Different tool coatings, lubricants and forming conditions (punch speed, internal pressure) were investigated by this method. With the exception of the contact pressure the experimental boundary conditions can be varied and determined exactly. Even different insertion clearances can be realized, yielding a small plastic deformation of the tube at the beginning of the test, as it is observed in the real forming process. The difference between the two vertical variants shown in Fig. 3 is the position of force measurement. The ®rst method is based on the direct measurement of the difference in punch force, while the second is based on the force measurement on the tool, i.e. only one force has to be determined, which minimizes the possible errors. In the case of the horizontal layout, the die is split parallel to the tube axis. The closing force Fp is measured and load cells between the two die halves measure the tool contact force. The difference of the two forces is taken as contact force between the tube and the die. The disadvantage of this method is that the die and the closing force must be beard by linear bearings. This requires a correction of the measured values by the value of friction forces in the bearings.
Fig. 4 shows various principles for the determination of the COF for the forming zone. The ®rst principle is one variant of the direct measurement of the friction force in the forming zone [3,6]. A ring segment, which is placed at the position where the dome of the part is formed, can be shifted by the friction force against load cells. The problems which occur with this method are typical for that kind of measurements: due to the elasticity of the load cell, a gap between the ring section and the remainder of the tool occurs. As the workpiece material in this zone is in the condition of plastic deformation it can easily ¯ow into that gap. This results in severe disturbances or even errors in the measurement. A second problem is that the dome has to have a minimum length, as the material has to be formed so far that it covers the tool radius. Before the radius is formed, it is not possible to measure any friction force in this test. A systematic variation of the processing parameters (internal pressure, sliding speed) is dif®cult, as these parameters have to be adjusted to enable proper forming of the part. Another principle of the measurements of the COF in the forming zone is the calibration test, see Fig. 4. A round tube is expanded by inner pressure into a rectangular tool.
Fig. 4. Friction tests for the forming zone in hydroforming.
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Depending on the friction conditions the development of the radius and the wall thickness in the edges differs. The test can be terminated at a certain pressure, using the edge radius as a measure for the COF. The radius should be proportional to the COF [7]. Alternatively, the wall thickness distribution can be analyzed at the end of the test and correlated, e.g. by using FEM calculations, with the COF. It was shown that there are large differences in the wall thickness distributions after this test for different lubricants [5]. The advantages of the test are the plastic deformation of the specimen during the whole test and that the forming process is not affected by the testing method itself, like it is the case in the direct measurement method shown in Fig. 4. The disadvantage is that there is very little sliding of the specimen against the tool surface and that the contact pressure is not constant but increases during the test. The third test shown in Fig. 4, the tube upsetting test, was developed to overcome these dif®culties. It is presented in this paper in more details. 3. Push through test 3.1. Experiments Experiments for the feed range were done using the equipment shown in Fig. 5. Lubrication was carried out by using oil without additives. An amount of 6 g/m2 was applied and checked by a weight control of the dry and lubricated tube. The tube was positioned between two punches. To ensure a de®ned compression of the tube, which simulates the adaption process at the beginning of the real forming process to overcome the insertion gap, a mechanical distance was inserted between the two punches inside the workpiece. The tube was compressed by 0.5%. Besides the
415
insertion gap ®lling, this method yields also a metallic sealing without wedge shaped punch ends, which would increase the local pressure between the tube and the tool due to additional radial pressure. After that, the internal pressure was slowly increased up to pressures of 200 MPa. The internal pressure was measured by pressure transducers. During this increase, both punches were moved downwards by the same velocity. The resulting friction forces were measured at the force transducer. A piezoelectric transducer was used. These measurements provided information about the friction force as a function of the internal pressure. The COF was calculated according to the Coulombs law. In this work, the internal pressure was taken as the contact pressure. The error by doing so is assumed to be below 10% and can be corrected as soon as there is more relevant information regarding the real contact pressure. One approach to determine the contact pressure is a FEM simulation. A second approach to the contact pressure problem could be an experimental one, using the method published in [8], which uses ultrasonic waves for the determination of the real contact area. It seams feasible by calibration of this method to determine the contact pressure too. Different materials of the tube were tested, such as low carbon steel, high alloyed steel and an aluminum alloy. The tool was made from hardened tool steel and coated by plasma nitriding or a hard coating from combined PVD± CVD coatings. 3.2. Experimental results Typical results from push through measurements are shown in Fig. 6. It is obvious that the problems concerning friction are more evident in forming of aluminum tubes than in steel materials. The COF is three times higher for the aluminum tubes than for low alloyed steel tubes. Using
Fig. 5. Test equipment for the vertical push through test.
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Fig. 6. Results for the feed area for different tool coatings and workpiece materials [9].
modi®ed coatings, the COF can be reduced to an amount comparable to that of steel in sliding against a nitrided tool. Further results of these tests are published elsewhere [1,3,9,10]. 4. Tube upsetting method 4.1. Principle A new principle for the measurement of the COF in the forming zone is proposed and shown in Fig. 7. A tube is continuously upset in a closed die, while it is elastic± plastically expanded towards the tool wall by an internal pressure. Due to the friction forces the wall thickness increases non-homogeneously. The biggest increase of the wall thickness occurs near the punch with the higher velocity. The shape of the wall cross-section is a function of the
COF m, the strength and strain hardening behavior (characterized by the strain hardening coef®cient C and strain hardening exponent n from Ludwik±Hollomons law) and the compression ratio. Depending on these parameters, different shapes can develop: (A) m 0, n 0: a homogeneous thickening of the whole tube occurs, the wall thickness is a function of the compression ratio only. (B) m 0, n > 0: same as in case (A). (C) m > 0, n 0: the wall thickness increases linearly from one end to the other, while the largest thickness occurs at the tube end which is in contact with the punch having the higher velocity. (D) m > 0, n > 0: the wall thickness is similar to that of the case (C), but the difference in thickness along the tube wall is smaller as the hardening coefficient increases.
Fig. 7. Basic principle of the tube upsetting test for the friction measurement.
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Depending on the hardening behavior, the course can be non-linear. The principle of the test is similar to that of the ring compression test or the combined forward±backward extrusion test. The COF is determined from the geometry of the test piece after forming, using a suitable diagram. Such diagrams can be calculated from analytical solutions, which are under development and will be published elsewhere. An alternative is the determination of the diagrams by FEM calculations. This method is presented in the current paper. Compared to the other test principles which are mentioned above, this methods has the following advantages: The processing parameters (internal pressure, sliding velocity, deformation speed and upsetting grade) can be chosen freely during this test. The equipment used for this test is simple compared to some of the other tests and does not interfere with the process itself. By changing the length of the tube, the test can be adapted to different friction conditions. In the case of a low COF, long tubes would be beneficial, as the friction stresses are accumulated to forces which significantly influence the thickening of the tube. 4.2. FEM simulation 4.2.1. FEM model The FEM simulation was done using PAM Stamp (Version 2000). The tool was considered as rigid body, while the tube had the material properties according to that of steel or an aluminum alloy. Proper stress±strain curves were used in the simulation. Shell elements were applied. The contact
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conditions were modeled by the Langrangrian contact type. The calculation time was about half an hour on a SUN Ultra 60 workstation. 4.2.2. FEM results Fig. 8 shows an example of the calculated shape of the tube wall after the compression test. It is interesting to note that the wall thickness distribution is nearly linear. In the case of a very high COF m 0:5, the lower part of the tube remains unchanged (wall thickness s s0 ). This is so, because the friction reduces the axial stress which acts in the tube cross-section. At a high COF, the stress is reduced below the ¯ow stress, resulting in pure elastic compression of the lower end of the tube. For mild steel and for an aluminum alloy a diagram was calculated, see Fig. 9. The wall thickness distribution was characterized by the slope of the wall thickness strain x Des =Dh, where es is the tube wall thickness strain and h the height of the tube after compression. The COF was varied between the smallest COF which is believed to occur in hydroforming and the largest value which theoretically occur in metal forming if Tresca's yield criterion is applied (i.e. m 0:5). 4.3. Experiments Experiments were done using the same equipment as for the friction tests for the push through test. The velocity of the lower punch was set to zero, while the upper punch velocity was 5 mm/s. Mild steel tubes (German standard St34-2) were upset by 15% except one tube. That experiment (lower curve in Fig. 10) was not considered in the following examination of the results. The wall thickness distribution of the upset tubes is shown in Fig. 10. The curves were
Fig. 8. Calculated wall thickness distribution after upsetting of a steel tube at different COFs.
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Fig. 9. Calculated slope x±COF m curves for different material behavior.
Fig. 10. Measured wall thickness distribution after tube upsetting for different lubricants.
linearized in order to determine the slope x for a comparison with the results given in Fig. 9. Due to the sealing method, the punch ends showed a different thickening behavior than the main body of the tube. Additional radial stresses also lead to increased friction forces in these regions. As the test is not based on force measurements, these effects do not affect the result concerning the COF directly, but the effective length of the tube is shortened. Three different lubricants were tested: mixture of grease and molybdenum disul®de (common name: Molykote) was applied by painting, molybdenum disul®de by spraying and oil by rolling. From other tests, it is known that the best lubrication is derived from Molykote, while oil showed the poorest behavior.
5. Discussion It is worth mentioning that there is a linear relationship between the slope of the wall thickness x and the COF m when plotting the results from the FEM in a double logarithmic plot. This shows that there is a power law relationship between the two values. This gives a helpful hint for the analytical description of this test. If one compares the curve for the aluminum alloy with that of the steel, it is obvious that the steel tubes show a steeper slope than aluminum. It can be understood as follows. In the tube upsetting test, there is only one intended forming zone in the area starting at the punch having the higher velocity. Provided that the COF and the contact
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Fig. 11. Slope x±COF m diagram with experimental results.
pressure are equal for steel and aluminum alloy, i.e. the friction force has the same value, there will be the same stress gradient in the tubes. Thickening will occur in that region where the effective stress seff seff
Fp
FR p=4pi d0 2s0 2 p=4 d02 di2
(where Fp is the punch force; FR the friction force; pi the inner pressure; d0, di the outer and inner tube diameter; s0 the wall thickness) is equivalent to the ¯ow stress. As the aluminum alloy has a lower ¯ow stress than steel, the point below which no thickening occurs will be at a position with a larger distance from the movable punch than for steel. As the punch travels, and therefore the overall compression is equal for all data points in Fig. 9, the slope for the steel tube must be steeper as the compression concentrates on a smaller length of the tube. The simulation of tube upsetting of steel tubes was performed by using materials with different strain hardening behavior. The resulting difference in the x±m curves is small. The curve for the material with the smaller strain hardening exponent has a slope which is steeper than that for the material with higher strain hardening exponent n. This is consistent with the prediction for case (D) compared to case (C) above. In Fig. 11, the results of the tube upsetting tests are plotted into the slope±friction diagram. The COFs, which are identi®ed in this way, are in the expected order of magnitude. The value of the COF in the case when Molykote was applied as lubricant, is very small and lies below 0.01, but this can be understood from the pressure dependence which is observed in push through tests. The highest m-value is obtained for oil as lubricant, yielding a COF in the order of 0.015. While these are only some preliminary results which have to be veri®ed by further
measurementsÐpartly the scatter was undesirable high, see Fig. 10Ðthey show that the concept of the test is reliable and can be used for friction measurements in the forming zone at different conditions. 6. Conclusions Although a number of different tests for the determination of COF for hydroforming of tubes exist, there is still a lack of information related to that subject. There exist a number of different tests for the determination of the COF for hydroforming of tubes. While the push through test seems to be well established for the feed area, no standard test seems to exist for the forming area. The differences in friction behavior for the friction between different workpiece material and different tool coatings are shown by friction tests using the push through test. Aluminum shows detrimental effects, resulting in high COFs. The tube upsetting test was defined. It is shown that reliable results for the COF can be deduced from that test for the case of plastic deformation of the workpiece. The differences between obtained COFs for three different lubricants were determined. The COF was in the order of 0.01. Further work must be done in order to reduce the scatter of the results. Diagrams for the identification of the COF can be calculated using the FEM simulation. As this is time consuming, an analytical model is desired and under development. Acknowledgements The authors like to express their gratitude to the DAAD for the ®nancial support of the research visit of Prof. Plancak
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in Germany. Special thanks are to Dipl.-Ing. J. Woitschig for conducting the FEM simulation. They also thank Dipl.Ing. T. Prange and MSc. A. Zarin for conducting the experiments.
[5] [6]
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