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3DFiniteElementModelingofanAssemblyProcessWithThreadFormingScrew

ARTICLE·JANUARY2009

DOI:10.1115/1.3160377

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AlainDaidié

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Florestan Mathurine-mail: florestan.mathurin@insa-toulouse.fr

Jean Guillote-mail: jean.guillot@insa-toulouse.fr

Pierre Stéphane-mail: pierre.stephan@toulouse.iufm.fr

Alain Daidiée-mail: alain.daidie@insa-toulouse.fr

Laboratoire de Génie Mécanique de Toulouse,Institut Clément Ader,

Université de Toulouse,135 Avenue de Rangueil,

31077 Toulouse Cedex 04, France

3D Finite Element Modeling of anAssembly Process With ThreadForming ScrewThis paper presents a 3D finite element (FE) model of a thread forming screw assemblyprocess based on the ABAQUS 6.5.4 Explicit software program. The model consists of twoprincipal elements: an M10�12 thread forming screw and a lower 4 mm plate intowhich the screw taps its threads. The aim was to develop a robust industrial dimensioningtool; the model can be extended to establish the preload and investigate other types ofassemblies. A 45 deg sector, which represents 1/8 of the joint, was modeled to maintain agood compromise between calculation time and an accurate representation of the threadforming process. The intent of the study was to analyze the material flow throughout thethread forming process; a parametrical study was also conducted to identify the mostinfluential process parameters. To validate the model, FE numerical simulation resultsare compared with published experimental results. The study shows that the lead holediameter has an important influence on the screwing torque. �DOI: 10.1115/1.3160377�

Keywords: thread forming screws, finite element simulations, chipless assembly, tapping

IntroductionThread forming screws are one of the most frequently used

ssembly procedures in the automotive industry. Self tappingcrews are also commonly used for assemblies made of materials,hich transmit minimal exterior loadings, such as wood or ther-oplastic materials. Thread forming screws are suitable for highly

uctile metallic materials, which consequently transmit high load-ngs. They are designed to perform direct assembly by a threadorming process in the lower part of the assembly to avoid thenishing operations that are necessary with traditional screws.oreover, the chip evacuation problems, which are encounteredith self tapping screws, can be avoided.However, until recently, few studies related to auto forming

crews have been presented in part due to the fact that no dimen-ional specifications exist for these kinds of screws except for ISO085 �1�. In fact, most of the existing published works concerningorm tapping are based on experimental studies and on mechani-al models for load calculation during the finishing processes.ayama �2� analyzed autoforming screws and established a me-

hanical model using the minimal energy method and a theoryased on the study of a partially plastically deformed thick cylin-er. Simultaneously Henderer and Von Turkovich �3,4� developedn approximation model by considering the tapping process as anndentation problem, whereas Chowdhary et al. �5,6�, in a latertudy, took into consideration the elastic reversal process for cal-ulating the tapping forces. It should be noted that the applicabil-ty of the results from these studies is limited to their experimentalests, since several coefficients were obtained by reverse identifi-ation from the experiment.

Seneviratne et al. �7,8� investigated an assembly made up oflates of vulnerable materials using M4 and M6 thread formingcrews to monitor the tightening torque in an automated assemblyhain. This study was carried out considering that the ideal screwnsertion process can be discretized into three main phases: screwngagement, screw advancement, and tightening. For each phase,model based on a quasistatic analysis was set up to establish the

Contributed by the Manufacturing Engineering Division of ASME for publicationn the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedebruary 14, 2007; final manuscript received October 21, 2008; published online

uly 15, 2009. Review conducted by Zhongqin Lin.

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respective tightening torque, screw engagement torque, and screwadvancement torque, which can be further decomposed into threadforming and friction resistance components. Two experimentalsamples, one made of ABS plates and the other of polycarbonate,with circular core screws and triangular cross section threads wereused to validate the model.

Fromentin �9� conducted experimental investigations on tap-ping based on the deformation of different materials and notablyhigh strength steels. In this study, the material flow during thedeformation process and the shape and mechanical characteristicsof the threads were inspected.

Recently, Warington et al. �10� used an indentation processbased on an experimental study on tapping to study the shape ofthe hole at the crest of the threads.

It is worth nothing that the finite element �FE� simulationsmade so far tend to be indentation �11,12�, forming, forging, orextrusion simulations. Martin �13,14� developed 3D FE modelingof the rolling process on a plate of ACME screws using MSC

software. In this same framework, Domblesky and Feng �15,16�built 2D and 3D models for thread rolling screw under “DEFORM

3D,” whereas Pater et al. �17� used “SUPER FORGE 2000” to model anew rolling process. Finally, Warrington et al. �18� established FEmodels under DEFORM 3D software to improve tap design in formtapping and to highlight the hole phenomenon at the crest of thethread by considering form tapping to be equivalent to linearscratch experiment.

A review of the literature has revealed that no FE simulationsappear to have been published for thread forming screw assem-blies. Consequently, the intent in the current work was to developa 3D model of such assemblies. The main objective was to deter-mine displacements during the forming process and the shape ofthe threads and to establish the screwing or torque function basedon different parameters such as screw rotation speed and the di-ameter of the lead hole.

2 Modeling of the Assembly ProcedureIn recent years, FE simulation codes have developed consider-

ably with advances in the computer hardware technology and nu-merical resolution methods. Consequently, numerical models forsimulating certain processes, such as rolling, forging, or hydro-

forging, have become commonplace because they are accurate

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nd, moreover, reduce the computational time. The numericalimulation of the thread forming assembly process presented inhis paper was conducted using ABAQUS 6.5.4 FE software �19�.BAQUS is a powerful FE code built on finite elements method and

s suitable for a range of simulations from relatively simple linearroblems to complex nonlinear ones. The simulations presented inhis paper were conducted using the Explicit solver of ABAQUS

.5.4, which had proved to be efficient for solving 3D quasistaticroblems with very complex contact conditions and very largeeformations such as are encountered in the thread forming pro-ess.

General geometry of the thread forming screws. Since no pre-criptive dimensional guidelines have been developed for threadorming screws, their geometry and the assembly mountings ofteniffer from one manufacturer to another. Nevertheless, this studyonsiders only screws with ISO threads, as shown in Fig. 1, be-ause in the automotive industry, defective thread forming screwsre replaced with standard ISO screws.

The cross section A-A of a thread forming screw �Fig. 1� maye either circular or trilobed. Moreover, the screw can be subdi-ided into two distinct areas: a tightening zone and a thread form-ng zone. The latter, usually made up of three to five threads, haslinear profile allowing progressive penetration in the subassem-

ly during the tapping phase, whereas the tightening zone is simi-ar to a standard ISO screw.

Loading and simulation parameters. The model used in thetudy was composed of three principal elements, as shown in Fig.: a thread forming screw with a circular cross section M1012, a lower 4 mm plate �plate 1� in which the screw tapped its

hreads, and a 1 mm plate �plate 2� mounted 0.5 mm above plateto simulate the preloading phase and to set the preload for sev-

ral types of assemblies and different tightening torques. This wille presented in a further paper. The two plates were both modeleds AISI 1018 steel, which is commonly used in the mass produc-ion of these assemblies. However, as a 360 deg model wouldave required an estimated calculation time of around one month,45 deg sector, representing 1/8 of the joint was modeled toaintain a good compromise between calculation time and an

ccurate representation of thread forming.The contact surfaces of the thread forming screw were case

ardened to obtain a screw hardness greater than the hardness ofhe deformed plate. In addition to this, deformation in the subas-embly was only described along the two plates. Under these con-itions, the screw could be modeled as a rigid body without dis-egarding the real behavior of the assembly during the assemblyrocess. Consequently, the CPU calculation time was reduced,ince the displacement of the screw, considered as a discrete rigidody, was guided by a unique reference point, as shown in Fig. 2.

However, the two main concerns of this study were the step by

Fig. 1 Geometry of ISO thread forming screws

tep displacement of the plate surfaces during the tapping phase

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and the variation in the tapping torque via the lead hole diameterand the rotational speed of the screw. Note that the tapping torque,also called torque required to advance the screw, incorporates thethread forming torque and the friction torque.

The following cases and assembly parameters were investigated�Table 1�.

It is computationally impractical under ABAQUS to model qua-sistatic events such as the metal forming process in its naturaltime period. Literally millions of time increments would be re-quired. Thus, it was necessary to increase the speed of the processfor an economical solution. There are two possible approaches:the time scale of the process can be artificially reduced by increas-ing the loading rate or the stable time increment can be increasedby using a mass scaling factor. In this paper, the latter is used

Table 1 Finite element models

ModelLead hole diameter

�mm� Operating rotation speed N of the screw

Model 1.1 9.16 N=200 rpm, 1 pitch per revolutionModel 1.2 9.26 N=200 rpm, 1 pitch per revolutionModel 1.3 9.48 N=200 rpm, 1 pitch per revolutionModel 1.4 9.6 N=200 rpm, 1 pitch per revolutionModel 2.1 9.48 N=200 rpm, 1 pitch per revolutionModel 2.2 9.48 N=300 rpm, 1 pitch per revolutionModel 2.3 9.48 N=400 rpm, 1 pitch per revolutionModel 2.4 9.48 N=500 rpm, 1 pitch per revolutionModel 2.5 9.48 N=600 rpm, 1 pitch per revolution

Fig. 2 Geometrical parameters used in the modeling

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ince the subassemblies are made of sensitive strain-rate material.n a first approach, an operating rotation speed of 200 rpm wasonsidered for the study of the lead hole diameter, since it corre-ponds to the basic rotation speed for the M10 electrical spindle.

9.48 lead hole diameter was chosen for the rotation speed studyecause it corresponds to a typical process value for the set ofonditions simulated.

Meshing. The Explicit solver of ABAQUS 6.5.4 operates by con-idering a wave propagation problem. Thus, out-of-balance forcesre propagated as stress waves between neighboring elements, andbounded solution is obtained only when the time increment is

ess than the stable time increment. The stable increment is theinimum time that a dilatational wave takes to move across any

lement in the model. Thus, the CPU time for calculating thencrement increases as the element size decreases. However, theccuracy of the solution strongly depends on the mesh refinement,specially in highly deformed zones. Consequently, it is necessaryo optimize the calculation process by compromising betweenPU calculation time and the mesh size. The screw, modeled as aiscrete rigid body, was meshed with C3D4 quadrangle elementsecause it was impossible to define the screw by an analyticaligid surface. The plates were meshed with C3D8R reduced inte-ration bricks, as these elements are usually recommended foreformable structures. Using a rigid body is advantageous andconomical because its motion is completely driven by the refer-nce point with a maximum of six active degrees of freedom. Thehoices of C3D8R elements provided a good compromise be-ween the accuracy of the solution and CPU calculation time.ote that meshing was refined on the lower plate of the assembly,here thread forming occurs, whereas the elements length was

ncreased in the nondeformable areas, as shown in Fig. 3.Finally, an adaptive meshing was established using the ALE

BAQUS technique to comply with the large deformations that areenerated during the thread forming process and to improve theccuracy of the solution in the thread forming zone.

Behavior law. The simulations used the Johnson–Cook materialodel �20�, which represents the material flow stress �y as a func-

ion of strain, strain-rate, and temperature, as shown in Eq. �1�

�y��, �̇,T� = �A + B�n��1 + C ln� �̇

�̇0���1 − � T − Tr

Tm − Tr�m� �1�

here A, B, n, C, and �̇0 are all model parameters, Tm is theaterial melting temperature, and Tr is room temperature. Theodel parameters corresponding to the mechanical behavior of

018 steel �18�, which was used in the screwing experiments, are

Fig. 3 Assembly and plate 1 meshing

hown in Table 2.

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First, in order to represent the material behavior of 1018 steelover such a large range of strain-rates, slight modifications weremade to the original Johnson–Cook material constitutive modelusing the studies of Vural et al. �21�. Vural et al. modified theJohnson–Cook constant C and �̇0 so that they are dependent onthe strain-rate.

Second, thermal phenomena were not taken into considerationin the models, and isothermal behavior was used to simulate thethread forming. As the screw was modeled by a rigid body, theheat generated during the forming process could not be diffusedthrough the screw but only by the deformed plate. Kapoor andNemat-Nasser �22� made experimental investigations of theamount of heat generated during high strain-rate plastic deforma-tion in 1018 steel. The heat generated is either lost to the sur-roundings or causes localized heating in the workpiece. The in-crease in temperature, in turn, lowers the flow stress in thematerial. This is known as thermal softening. The use of isother-mal material data in the numerical simulations assumes that noheat is generated and may overpredict the flow stress by ignoringthe thermal softening effect. So, a coefficient was calculated fromthe experimental results to correct the screwing torque value ob-tained from the numerical simulation and the isothermal materialconstitutive data.

In order to be closer to reality, as the thread forming process isvery fast, FE models could be improved by using the new coeffi-cients proposed by Vural et al. and by employing adiabatic mate-rial data.

Boundary conditions. As mentioned previously, the displace-ments of the screw nodes were monitored using a single referencepoint, since the screw was modeled as a rigid body. Thus, thescrew motion was in advance by 1 pitch per revolution for arotation speed between 200 rpm and 600 rpm at the referencenode. During each simulation, the displacements of the lower

Table 2 Coefficients of the Johnson–Cook constructive model†10‡

A�MPa�

B�MPa� n C

�̇0�s−1�

Tr�K�

Tm�K� m

560 300 0.32 0.022 1 298 1773 0.55

Fig. 4 Boundary conditions imposed on plate 1

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late’s nodes were restricted on the free external surface �Fig. 4�.symmetry condition was applied on the face where the forming

rocess occurred, whereas the displacement of all the remainingaces was left free to visualize the 3D material flux. Moreover,nly translation along the screw axis was allowed at the upperlate of the assembly.

However, the relevance of the boundary conditions at the lowerubassembly is open to discussion. First, during the real tighteningrocess, plate 1 lies on its lower face and is fastened on its upperace. In the model, a clamping condition is defined. This is justi-ed by the fact that it does not affect the subassembly behavioruring the thread forming process, since enough material is keptadially. Furthermore, in the case of thick plates, radial extensiondilation� is negligible, and thus thread forming occurs only byaterial displacement. Moreover, as a result of the clamping con-

ition, material flows along the Z direction, which is the case inhe real word. The symmetry condition is so restrictive that no

aterial flow is possible radially, which is contrary to the realituation, since material can flow radially with the helicoidal mo-ion of the screw. However, the symmetry condition is better thanfree edge condition. This fact has been highlighted by numerical

imulations. In this framework, radial material flow with a freedge condition is opposite to the rotation of the screw, which ishysically impossible. Finally, a free edge condition is defined athe face where the screw crosses the subassembly in the radialirection. In a first approach, a symmetry condition was defined.onsequently, the material radial flow was prevented, and calcu-

ation convergence failed due to the excess of material not evacu-ted radially. Thus, the free edge condition was chosen. However,t should be noted that, with this condition, the radial materialow is too large. To counter the influence of the boundary condi-

ions defined above, two portions of 11.25 deg were subtractedrom the surrounding of the boundary conditions area. Thus, thengular sector of 45 deg was cut into a 22.5 deg sector during theostprocessing phase. Under these conditions, the effects of theoundary conditions were altered since results were investigatedway from the boundary condition areas.

Finally, contact conditions at the interface between the screwnd the lower plate were modeled using the ABAQUS “contactair” option, based on a Coulomb model with an arbitrary coeffi-ient of friction equal to 0.1. This friction coefficient of 0.1 cor-esponds to the average theoretical coefficient measured on theanufacturer’s M10 thread forming screws. The models presented

n this study were subsequently experimentally tuned to identifyhe coefficient of friction for each plate/thread forming screw con-guration.

Modeling of the Assembly ProcedureABAQUS simulations were carried out using a PC biprocessor

MD opteron 252–2.6 GHz equipped with 4 GB DDR 400 MHzam. CPU calculation times ranged between 32 h and 107 h de-ending on the conditions simulated. Note that only the formingith screw insertion process was simulated. Simulation was

topped as soon as the head of the screw was determined to beithin 0.1 mm of the contact zone of the upper plate.Results comparison. The thread forming process using a thread

orming screw is somewhat similar to a form tapping operation.ince the only available research on micrographic works concern

apping-deformation process, the FE results were compared withxperimental results obtained from these studies. Figure 5 showsicrographs obtained from a tapping-deformation process carried

ut through an M12 machinery tap �Protodyn M12�1.5�. Theseicrographs were taken from the Fromentin’s experimental study

9�, which is one of the few papers studying the step by stephread forming process. The results of this experiment and theesults of the FE simulation �model 1.1� are compared qualita-ively. Figure 5 retraces the forming of the thread section from theimulation results. At first glance, the experimental and FE results

ppear to be in good agreement. In order to further valid these

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results, an experimental study will be conducted using the sameconditions and the same material.

At step 1, the thread forming screw initially contacts the mate-rial and thus starts progressively forming the right flank of thethread, which reaches its final shape at step 8. At step 5, the screwwould have achieved a complete first rotation, and the threadforming screw would have started forming the left flank simulta-neously with the right flank. At step 12, the thread forming iscompleted.

It should be noted that screwing the screw induces thread for-mation by material displacement. Subsequently, a hollow shapecan be seen at the peak of the thread due to the material flow. Thisparticular shape is similar to the form observed in the experimen-tal study.

Moreover, the bottom of the thread is rounded. One cannotgeneralize and assume that this rounded shape is an intrinsic char-acteristic of the thread since the shape of the bottom is directlyrelated to the geometry of the thread forming screw. Also notethan the lead hole diameter D0 �Fig. 6� is not materialized on thewhole thread, since it corresponds to the middle line between thepeak and the bottom of this thread.

Under the effect of the thread forming screw, material flowsfrom areas located at diameters greater than the hole diameter toareas located at smaller diameters. Thus, it can be concluded thatthe material flow is inversely proportional to the lead hole diam-eter and, consequently, the final geometry of the thread and theheight of the hollow peaks differ considerably. This fact highlights

Fig. 5 Qualitative comparison between experimental †9‡ andnumerical FE study

the high dependence between the thread and the lead hole diam-

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Fig. 6 Hole diameter before and after thread forming

process between the experimental study †9‡ a

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eter, which will further analyzed. Finally, the five experimentallyidentified zones related to the material flux can be also studied inFE simulations �Fig. 7�.

From the displacement plot and the meshing shape, it can beseen that the material at the core of zone 1 �Z1� did not undergoany deformation, which is expected. Zone 2 �Z2�, where the headof the screws acts directly, is strongly deformed. In zone 3 �Z3�,material flows along the tap flanks. The core of the thread, iden-tified as zone 4 �Z4�, is slightly deformed. Finally, zone 5 �Z5�,which represents material on the free edge, undergoes the greatest

nt of material during the thread forming

Fig. 7 Comparison of the radial displaceme nd FE simulations

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isplacements. However, one can note that the core of this zone isbserved to be only slightly deformed, while the material basi-ally flows from the thread flanks.

Energy balance. It is possible, in ABAQUS Explicit, to monitorhe calculation increment, the maximal values of the outputs, andhe energy balance. In this framework, it is necessary to check thenergy conservation at every step of the simulation to validate theumerical model. The energy equilibrium is given in ABAQUS byq. �2�

EI + EVD + EFD + EKE − EW = ETOT = constant �2�

here EI is the internal energy �elastic, inelastic and hourglassnergy�, EVD is the energy absorbed by viscous dissipation, EFD ishe frictional dissipation energy, EKE is the kinetic energy, EW ishe energy linked to the work of external forces, and ETOT is theotal energy in the FE model.

The different energies presented in this model are the energiesn the overall model. In this study, they are relative to the lowerlate since the screw is considered to be rigid. Besides, it is im-ossible to simulate the forming process on the real time scaleince millions of increments and thousands of calculation hoursould be necessary due to the size of the meshing elements. Thus,

orming simulations were conducted considering a quasistaticroblem, and consequently CPU calculation time was improvedy reducing the increment time to around 10−6 s. This value isptimal for this study, since it prevents discontinuities between thelements. Note that the increment time is reduced under ABAQUS

y using the “mass scaling” option.From Fig. 8, which represents the different energy functions

ver time, it can be observed that the energy equilibrium is ap-roximately conserved. The figure also points out the fact that therictional dissipation energy is preponderant in comparison withhe viscous energy dissipated. On all the models presented in thisaper, the frictional dissipation energy always represents about0% of the energy linked to the work of external forces, where theriction coefficient f equals 0.1.

It is necessary to monitor the ratio of kinetic energy/internalnergy, which should not exceed 1–5% if the simulation is toemain in the conditions of a quasistatic process. Moreover, theatio of hourglass energy/internal energy should not exceed 10%,here hourglass energy is the energy loss in the model. It is in-

roduced during calculation to monitor the numerical parasite dis-ortion modes principally induced by double integration elementsuch as C3D8R elements. As shown in Fig. 9, the above condi-ions were respected in this study.

ABAQUS gives the energy balance at each predefined time inter-al of the simulation. Looking at the results of this energy bal-nce, the screw forming torque can be calculated for each incre-ent using Eq. �3�. This method was inspired from the calculation

Fig. 8 Model 1.1 energy balance

f the outflow rate for hydraulic pumps �23�

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Ct=i =EWti+1

− EWti

ti+1 − ti�

1

N�3�

where Ct=i is the instantaneous screwing torque calculated at timei in the simulation, N is the rotation speed in radians per second,EWti+1

and EWtiare the energy linked to the work of external forces

at the time i+1 and i, ti+1 and ti are the time values in seconds. Forexample, the results of the screwing torque are plotted versus timefor model 2.3. However, the numerical models presented in thispaper correspond to 45 deg angular sectors of the assembly. Thescrewing torque of the whole plate is obtained by adding thescrewing torques of each sector. Moreover, the curves have to beshifted at time intervals of �t corresponding to the angular shiftsof the sectors �Fig. 10�.

Figure 11 illustrates this method, which is represented in theresults for model 2.3. Note that using a screw with a trilobularrather than a circular shape reduces the contact areas during thethread forming process, and thus the screwing torque.

Influence of the lead hole diameter. Under the action of thedevice, material flows from the zones with a diameter greater thanthe lead hole diameter to areas with smaller diameters, as shownin Fig. 6. Subsequently, the lead hole diameter considerably af-fects the shape of the threads and, therefore, the thread formingtorque. Figure 12 shows the evolution of the tightening torque asa function of time and the final thread shape for models 1.1–1.4.

Fig. 9 Ratios of hourglass energy/internal energy and kineticenergy/internal energy relative to model 1.1

Fig. 10 Torque time curve relative to model 2.3

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As shown in Fig. 12, the lead hole diameter has a direct impactn the maximum tightening torque. Thus forming a thread from aole diameter of 9.15 mm instead of 9.6 mm induces a 2.5 timesreater torque �11 N m for 9.6 mm and 28 N m for 9.15 mmith a friction coefficient of 0.1�. Eight other simulations were run

n order to confirm the impact of the lead hole diameter with twother friction coefficients. On these models, thread formation in a.15 mm lead hole diameter led to a maximum screwing torqueultiplied by 2.5. These simulations show the importance of the

riction coefficient in screw forming: The energy dissipated byriction always represented about 90% of the energy linked to theork of external forces in all the simulations. Consequently, theesigner must compromise between a minimal and a maximalead hole diameter in order to supply mechanical resistance foroad transmission and limit the torque to advance the screw re-pectively.

Influence of the operating rotation speed. When optimizing therocess in an assembly chain, the influence of the operating rota-ion speed on the screwing torque should be investigated. In fact,n increase of this speed considerably decreases the cycle dura-ion. Thus, a 9.48 lead hole diameter was chosen for this study, ast corresponds to the process value. Besides, if the effect of thisarameter is negligible, the CPU calculation times can be consid-rably reduced. For this purpose, the models 2.1–2.5 were inves-igated. Figure 13 features the variation in the screwing torqueith time together with the final shape of the threads. Note that

he advance is fixed to 1 pitch per revolution, and thus the dis-lacement velocity of the screw must be monitored.

The increase in the rotational speed of the screw comes alongith an ascending time on the time/forming torque curves. How-

ver, the results also suggest that this speed has little impact on

ig. 11 Transition between the curves of the tightening torqueelative to 45 deg sector to the curve and relative to the com-lete plate

he screwing torque/insertion depth curve. Moreover, the final

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Fig. 12 Influence of the hole diameter on the tightening torqueand the final thread shape

Fig. 13 Influence of the rotation speed of the screw on the

tightening torque, the final thread shape, and the CPU time

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hape of the threads remains intact. This small influence of theotational speed is explained by the importance of the energy dis-ipated by friction, which always represents about 90% of thenergy related to the work of external forces in the energy balancen all simulations. Moreover, 1018 steel is not highly dependentn strain rate. Thus, the slight influence of the rotational speedight be case-specific. The differences between the various mod-

ls for the ratios of kinetic energy/internal energy and hourglassnergy/internal energy are advantageous for monitoring these ra-ios. Model 2.5 �N=600 rpm� presents the most favorable energyalance with a kinetic energy/internal energy ratio lower than 1%nd an hourglass energy/internal energy ratio of less than 4%. Theatio of kinetic energy/internal energy was also very accurate forodels 2.1, 2.2, 2.3, and 2.4, whereas the hourglass/internal ratioas less successful with a value of around 11% for model 2.1, as

hown in Fig. 14.

Conclusion and PerspectivesThis paper presents a simulation study of the material flux and,ore particularly, the step by step displacements during the as-

embling procedure of a thread forming process.A parametric study with a friction coefficient of 0.1 showed the

mportant impact of the lead hole diameter on the thread screwingorque, whereas the effect of the screw operating rotation screwas relatively small. Consequently, it would be interesting to set ainimal hole diameter during the design phase to provide suffi-

ient mechanical resistance of the threads along with minimalcrewing torque. The study shows that the screw rotational speedas negligible influence on the maximum screwing torque. Thisesult is probably the consequence of the material behavior lawypothesis. This material behavior could be refined even thoughhe ratio between the screw forming energy and the frictionalnergy is low.

In the aim of developing a robust industrial dimensioning tool,his model can be extended for other types of assemblies and alsoor establishing the preload. In this framework, the operating ro-ation speed of the screw �600 rpm� in model 2.5, which is the

Fig. 14 Ratio of hourglass energy/internal energy

41015-8 / Vol. 131, AUGUST 2009

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most economical in terms of CPU time, presents the most favor-able energy balance. Therefore, it will be used in future FE mod-els. An experimental campaign is also planned for validation andadjustment.

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