Simulation of Kinetic Friction in L-Bending of Sheet Metals

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1 World Aademy o Sene, Engineering and Tehnology Simulation o Kineti rition in L-Bending o Sheet Metals Maziar Ramezani, Thomas Neitzert, Timotius Pasang International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/ Abstrat This paper aims at experimental and numerial investigation o springbak behavior o sheet metals during L- bending proess with emphasis on Stribek-type rition modeling. The oeient o rition in Stribek urve depends on sliding veloty and ontat pressure. The springbak behavior o mild steel and aluminum alloy 6022-T4 sheets was studied experimentally and using numerial simulations with ABAQUS sotware with two types o rition model: Coulomb rition and Stribek rition. The inluene o orming speed on springbak behavior was studied experimentally and numerially. The results showed that Stribektype rition model has better results in prediting springbak in sheet metal orming. The E predition error or mild steel and 6022-T4 AA is 23.8%, 25.5% respetively, using Coulomb rition model and 11%, 13% respetively, using Stribek rition model. These results show that Stribek model is suitable or simulation o sheet metal orming espeally at higher orming speed. T Keywords rition, L-bending, Springbak, Stribek urves. I. INTRODUCTION HE most prominent eature o sheet metal orming proess is an elasti reovery phenomenon during unloading whih leads to springbak [1]. The ollowing statement best desribes springbak: A purely elastially bent sheet will return to its original oniguration upon removal o the bending moment. Ater partially plasti bending; permanent deormation and residual stress remain ater unloading [2]. Evidently, bending auses the metal on the outside o the neutral axis to be under a state o tension, whereas the inside is subjeted to ompression. During the bending proess, internal stresses are developed in the sheet and upon unloading; the internal stresses do not vanish. Ater bending, the extrados is subjeted to residual tensile stress and the intrados is subjeted to residual ompressive stress. These residual stresses produe a net internal bending moment whih auses springbak [3]. The sheet ontinues to springbak until the internal bending moment drops to zero. Despite the broad appliation o sheet metal orming, the design o the tools and the seletion o the sheet materials are still usually based on trial and error eorts, a very expensive and time onsuming proedure. Reliable inite element models M. Ramezani is a Researh ellow and Leturer at Centre or Advaned Manuaturing Tehnology (CAMTECH) o Aukland University o Tehnology, New Zealand (phone: ; maziar.ramezani@aut.a.nz). T. Neitzert is a Proessor o Mehanial Engineering and Diretor o Engineering Researh Institute (ERI) at Aukland University o Tehnology, New Zealand. T. Pasang is an Assoate Proessor and Head o Department o Mehanial Engineeringat Aukland University o Tehnology, New Zealand. or desribing the proess would be o great value in redung muh o the tool tryout work [4]. or these inite element simulations, aurate models o the material behavior under deormation as well as the rition between tool and metal are needed. or metal orming simulations, a good rition model is very important, as shown by [3] [5]. or most orming simulations the value o oeient o rition is hosen as a onstant, negleting the at that the parameters on whih this value depends might hange during the proess. Coulomb rition model is a simple model requently used in simulation. In this model, the ratio between rition ore and normal ore, deined as the oeient o rition, onsidered to be onstant, as used by [6], [7]. But, rition depends on a large number o parameters, e.g. the miro-geometry, the marogeometry, the lubriant and the operational parameters: veloty, temperature and normal load. I one o the parameters hanges; the oeient o rition will also hange [8]. In the present paper, the L-bending o mild steel and aluminum alloy 6022-T4 sheets is simulated with emphasis on Stribek-type rition modelling. rom the author s knowledge, there has been no previously published analysis o Stribek-type ritional behavior in L-bending. The springbak behavior o sheets was studied using numerial simulations by ABAQUS sotware with two types o rition model: Coulomb rition and Stribek rition. The results have been ompared with experimental results. The inluene o orming speed on springbak behavior o sheets is also studied experimentally and numerially. II. STRIBECK RICTION MODEL When a metal orming proess is observed, it is lear that the onditions in all the dierent ontats are very dierent. or most orming simulations the value o oeient o rition is hosen as a onstant, negleting the at that the parameters on whih this value depends might hange during the proess. Oten, several metal orming simulations with dierent values or the oeient o rition have to be perormed beore the simulation provides aeptable results. It is lear that these simulations have no prediting power at all [4]. rom this, it is obvious that a model whih desribes oeient o rition as a untion o loal ontat onditions is needed. The limiting strain o a material is not diretly hanged by rition, but rition hanges the stress and strain distribution. The redistribution o stress and strain, an aet deets on metal orming, suh as springbak. Stribek is redited or arrying out the irst systemati experiments unolding a lear view o the harateristi urve International Sholarly and Sentii Researh & Innovation 8(6)

2 World Aademy o Sene, Engineering and Tehnology International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/ o the oeient o rition versus speed [9]. In reognition o his ontribution, this urve is alled the Stribek urve [10]. The Stribek urve has also been proven to be useul or identiying boundary, mixed, elasto-hydrodynami and hydrodynami lubriation regimes [11]. In bending proess, ontat regions operate in boundary lubriation regimes. Only very extraordinary onditions (suh as high orming speed), make it possible or the ontat untions to be in mixed lubriation regime. In lubriated ontat surae between punh and sheet, the total normal load T is shared by the hydrodynami liting ore, H and the asperity interating ore, C. + T H (1) Similarly, the total rition ore is the sum o two omponents, H (the hydrodynami rition ore) and, C (the asperity interating rition ore). The hydrodynami rition ore, H is represented as τ e η ( u ) 2, H L C h τ L (1 ). ab (2) where B is the ontat length; u is the relative veloty; τ L is the limiting shear stress; h is the ilm thikness; and a is the hal width o Hertzian ontat. Assuming that the oeient o rition is onstant or all asperities, we arrive at the ollowing relationship or the rition ore, C N p da p i 1 i i 1 i A i N A da where is determined rom experiments. Hene, the oeient o rition an be obtained rom T + T (3), H (4) A ull desription o the Stribek theoretial model an be ound in [12]. III. INITE ELEMENT SIMULATION The inite element method has been used to simulate springbak in L-bending o sheet metals. To study the eet o rition model on springbak predition, the plane-strain bending proess was simulated in the ommeral EM sotware ABAQUS/Standard. Springbak is oten an important part o a orming analysis beause the springbak analysis determines the shape o the inal, unloaded part. ABAQUS provides the apability to import a deormed mesh and its assoated material state rom ABAQUS/Standard into Abaqus/Explit and vie versa. This apability is partiularly useul in manuaturing problems; or example, the entire sheet metal orming proess (whih requires an initial preloading, orming, and subsequent springbak) an be analyzed. In this ase the initial preloading an be simulated with ABAQUS/Standard using a stati proedure and the subsequent orming proess an be simulated with ABAQUS /Explit. inally, the springbak analysis an be perormed with ABAQUS/Standard. Sine springbak involves no ontat and usually inludes only mild nonlinearities, ABAQUS/Standard an solve springbak problems muh aster than ABAQUS/Explit an. Thereore, the preerred approah to springbak analyses is to import the ompleted orming model rom ABAQUS/Explit into ABAQUS /Standard. The rigid punh and die are modeled in ABAQUS/Standard as analytial rigid suraes with the *SURACE option in onjuntion with the *RIGID BODY option. The top and bottom suraes o the sheet are deined with the *SURACE option. Two rition model: Coulomb rition and Stribek rition, implemented to ABAQUS/Standard and the results have been ompared with the experimental results. Models or simulating sheet metal orming proesses onsist o dierent sub-models. Eah o these sub-models takes a spei aspet o the total proess into aount. The main two sub-models or sheet metal bending are material model and rition model. The entire analysis is arried out in ive steps. In the irst step the blank holder is pushed onto the blank with a presribed displaement to establish ontat. In the seond step the boundary ondition is removed and replaed by the applied ore o 100 kn on the blank holder. This ore is kept onstant during Steps 2 and 3. This tehnique o simulating the lamping proess is used to avoid potential problems with rigid body modes o the blank holder, sine there is no irm ontat between the blank holder, the blank, and the die at the start o the proess. The two-step proedure reates ontat beore the blank holder is allowed to move reely. In the third step the punh is moved toward the blank by speying a total displaement. This step models the atual bending proess. During this step the DISCONTINUOUS analysis option is inluded sine ontat with rition tends to reate a severely disontinuous nonlinearity and we wish to avoid premature utbaks o the automati time inrementation sheme. The last two steps were used to simulate springbak. In the ourth step all the nodes in the model are ixed in their urrent positions and the ontat pairs are removed rom the model. This is the most reliable method or releasing ontat onditions. In the ith, and inal, step the regular set o boundary onditions is reinstated and the springbak is allowed to take plae. Mild steel and aluminum alloy 6022-T4 were used or modeling. Simulations were arried out using Hill s plastity model. The dimensions used in simulation o L-bending aording to experimental work are shown in ig. 1. The thikness o the sheet is 1 mm. International Sholarly and Sentii Researh & Innovation 8(6)

World Aademy o Sene, Engineering and Tehnology International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/9998580 The punh and die material is H13 tool steel.

3 World Aademy o Sene, Engineering and Tehnology International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/ The punh and die material is H13 tool steel. In this simulation two ritional models were used in the analysis: Coulomb rition model with a onstant oeient o sliding rition 0.13 and Stribek rition model with initial oeient o sliding rition o 0.13 or lubriated surae between mild steel sheet and punh and 0.14 between 6022-T4 AA sheet and punh. The value o oeient o rition is based on historial data or similar ases [13] [15]. The Stribek urves used in this analysis are a untion o veloty and ontat pressure. These urves were implemented to model through ontat property options. ig. 1 Dimensions used in L-bending ig. 2 Variation o (a) sliding veloty and (b) Hertzian ontat pressure with time IV. RESULTS AND DISCUSSIONS As mentioned beore, oeient o rition hanges during the proess and has dierent values in dierent nodes and dierent time during the proess. The hange o sliding veloty and Hertzian ontat pressure with time during plane strain bending proess based on the Stibek urve is illustrated in ig. 2 or a sample point between punh and sheet or a period o 0.1s during the punhing strive. The variation o oeient o rition with time during plane strain bending proess based on the Stibek urve is shown in ig. 3 or a sample point between punh and sheet or a period o 0.1s during the punhing strive. As an be seen in ig. 3, the hange in oeient o rition varies between initial value o 0.13 redung to 0.11 at 0.07s and inreases aterward whih is signiiant and this aets the stress distribution in sheet whih in turn aets the springbak. As illustrated in ig. 3, the oeient o rition in dierent points between sheet and die hanges signiiantly during proess. So it is lear that using a onstant oeient o rition as uses by Coulomb model has no prediting power and may lead to poor results or prese sheet metal orming simulations. The amount o springbak or mild steel and 6022-T4 AA in L-bending was alulated numerially using inite element program ABAQUS/Standard. The relationship between springbak and the ratio o the tensile strength to the elasti modulus or u 20mm/ s, using dierent rition models is given in ig. 4. As an be seen rom ig. 4, as the ratio o the tensile strength inreases, the springbak inreases. The E predition error or mild steel and 6022-T4 AA is 22.5% and 25% respetively, using Coulomb rition model; and 13% and 16% respetively, using Stribek rition model. So, Stribek-type rition model predit springbak better than Coulomb model. The amount o springbak at dierent orming speeds was measured experimentally and ompared with inite element results and illustrated in ig. 5. Aording to ig. 5, the predition o springbak is improved by using Stribek ritional model. Espeally at higher orming speeds, the EM results are very lose to the experimental results. or mild steel at u 25mm/ s, the E springbak predition error using Coulomb model is 23.8%. Using Stribek rition model, this error dereases to 11%. or 6022-T4 AA at u 25mm/ s, the E predition error using Coulomb model is 25.5%. Using Stribek model, this error dereases to 13%. This is due to more hanges in oeient o rition at higher veloties, aording to Stribek urves. The oeient o rition ontributes to the amount o springbak. During bending, the metal is ored between the lower die setion and the orming punh. I the learane between these two setions is less than the metal thikness (as it usually is), intense rition is reated. The amount o rition determines how muh the bend will be strethed [16]. I the inside bend radius is large enough and the metal an be strethed over it, the amount o ompression is redued or eliminated. I ompression is eliminated, both sides o the radius are in tension, thus redung the amount o springbak International Sholarly and Sentii Researh & Innovation 8(6)

4 World Aademy o Sene, Engineering and Tehnology International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/ [17]. Although an inrease in rition may redue the amount o springbak, intense rition may results in severe wear to the die setions. or this reason, lubriants should be used. ig. 3 Variation o oeient o rition with time ig. 4 The relationship between springbak and the ratio o tensile strength to elasti modulus or u20mm/s ig. 5 Springbak angle obtained rom experimental and numerial analysis at dierent orming speeds V. CONCLUSION The predition o springbak in bending proesses has been a hallenging topi. or sheet metal orming proesses, the ritional behavior depends on several parameters suh as the ontat pressure, sliding speed, sheet and tool material, surae roughness, lubriant and onurrent deormation. Beause all o these variables inluene rition, the question arises as to whether the Coulomb simple rition model is apable o desribing the real ritional properties o sheet metal orming proesses. In the present paper, the Stribek rition model was used to investigate springbak behavior o sheet metals under L-bending. The Stribek urves an be alulated by varying the veloty while keeping the other operational onditions onstant. The ollowing onlusions were reahed regarding the hoie o stribek rition model. Coeient o rition hanges during the proess and has dierent values in dierent nodes and dierent time during the proess. An aurate rition model whih desribes oeient o rition as a untion o loal ontat onditions is needed. Stribek-type rition model has better results in prediting springbak in sheet metal orming. The E predition error at u 20mm/ s or mild steel and 6022-T4 AA is 22.5%, 25% respetively, using Coulomb rition model and 13%, 16% respetively, using Stribek rition model. These results show that Stribek model is suitable or simulation o sheet metal orming. Stribek-type rition model has better results at higher orming speeds. or 6022-T4 AA at u 25mm/ s, the E analysis shows 25.5% error using Coulomb model and 13% error using Stribek model. REERENCES [1] J.R. Cho, S.J. Moon, Y.H. Moon, S.S. Kang, inite element investigation on spring-bak harateristis in sheet metal U-bending proess, Journal o Materials Proessing Tehnology 141 (2003) [2] Mullan HB (2004) Improved predition o springbak on inal ormed omponents. J. o Materials Proessing Tehnology , pp [3] Li KP, Carden WP, Wagoner RH (2002) Simulation o springbak. Int. J. o Mehanial Senes 44, pp [4] M. Math, B. Grizelj, inite element approah in the plate bending proess, J. o Materials Proessing Tehnology (2002) [5] Lee BH, Keum YT, Wagoner RH (2002) Modeling o the rition aused by lubriation and surae roughness in sheet metal orming. J. o Materials Proessing Tehnology , pp [6] Y.E. Ling, H.P. Lee, B.T. Cheok, inite element analysis o springbak in L-bending o sheet metal, Journal o Materials Proessing Tehnology 168 (2005) [7].K. Chen, S.. Ko, Deormation analysis o springbak in L-bending o sheet metal, Journal o Ahievements in Materials and Manuaturing Engineering, Volume 18 Issue 1-2 September Otober [8] Matuszak A (2000) ators inluenng rition in steel sheet orming. J. o Materials Proessing Tehnology 106, pp [9] Jaobson B (2003) The Stribekmemorialleture. Tribology Int. 36, pp [10] Lu X, Khonsari MM, Gelink ERM (2006) The Stribek urve: experimental results and theoretial predition. ASME J. o Tribology, Vol. 128, Otober International Sholarly and Sentii Researh & Innovation 8(6)

5 World Aademy o Sene, Engineering and Tehnology [11] Gelink ERM, Shipper DJ (2000) Calulation o Stribek urves or line ontats. Tribology Int. 33, pp [12] Ramezani M, Ripin ZM, Ahmad R (2009) Computer aided modelling o rition in rubber-pad orming proess. Journal o Materials Proessing Tehnology 209 (10), pp [13] W. Wang, R.H. Wagoner,X.J. Wang, Measurement o rition under Sheet orming Conditions, Metallurgial and Materials Transations A, Volume 27A, Deember [14] Wang Z, Nakamura T, Dohda K, Obika T (2003) EM analysis o ontat mehanism in press-orming o lubriant pre-oated steel sheet. J. o Materials Proessing Tehnology 140, pp [15] Hao S, Klameki BE, Ramalingam S (1999) rition measurement apparatus or sheet metal orming. Wear 224, pp [16] Kuzman K (2001) Problems o auray ontrol in old orming. J. o Materials Proessing Tehnology 113, pp [17] Gusel L, Anzel I, Brezonik M (2005) Eet o lubriation on the stress distribution in an extruded material. Int. J. o Advaned Manuaturing Tehnology, pp. 25: International Sene Index, Industrial and Manuaturing Engineering waset.org/publiation/ International Sholarly and Sentii Researh & Innovation 8(6)

M. E. Kinsella 1, B. W. Lilly 2, N. Bhagavatula 2, K. G. Cooper 3 OH Abstract

Appliation o solid reeorm abriation proesses or injetion molding low prodution quantities: proess parameters and ejetion ore requirements or SLS inserts M. E. Kinsella 1, B. W. Lilly 2, N. Bhagavatula