Hybrid Search for Faster Production and Safer

Process Conditions in Friction Stir Welding

Cem Celal Tutum1, Kalyanmoy Deb2, and Jesper Hattel1

1 Technical University of Denmark (DTU), Department of Mechanical Engineering,Produktionstorvet, 2800, Kgs. Lyngby, Denmark

2 Kanpur Genetic Algorithms Laboratory (KanGAL),Indian Institute of Technology Kanpur, PIN 208016, Kanpur, India

cctu@mek.dtu.dk, deb@iitk.ac.in, jhat@mek.dtu.dk

Abstract. The objective of this paper is to investigate optimum processparameters and tool geometries in Friction Stir Welding (FSW) to min-imize temperature difference between the leading edge of the tool probeand the work piece material in front of the tool shoulder, and simultane-ously maximize traverse welding speed, which conflicts with the formerobjective. An evolutionary multi-objective optimization algorithm (i.e.NSGA-II), is applied to find multiple trade-off solutions followed by agradient-based local search (i.e. SQP) to improve the convergence of theobtained Pareto-optimal front. In order to reduce the number of functionevaluations in the local search procedure, the obtained non-dominatedsolutions are clustered in the objective space and consequently, a post-optimality study is manually performed to find out some common designprinciples among those solutions. Finally, two reasonable design choiceshave been offered based on several process specific performance and costrelated criteria.

Keywords: Evolutionary multi-objective optimization, gradient-basedlocal search technique, ε-constraint method, hybrid search, friction stirwelding, thermal simulation, material flow.

1 Introduction

The FSW process is an efficient solid-state, i.e. without melting, joining tech-nique that is invented by Wayne Thomas and a team of his colleagues at theWelding Institute (TWI), UK, in December 1991; especially for aluminium al-loys which are difficult to weld with traditional welding techniques [1]. Figure 1ashows a standard welding tool having a cylindrical shoulder and probe which arein general designed in different size and shapes with/out thread features or man-ufactured with different materials based on work piece and process specific needsor limitations. The process, which is schematically shown in Figure 1b, consistsof several subsequent procedures denoted as plunging, dwelling, actual weldingand pulling the tool out of the work piece. First, the tool is submerged verticallyinto the joint line with high rotational speed in the plunge period and then dwell

K. Deb et al. (Eds.): SEAL 2010, LNCS 6457, pp. 603–612, 2010.c© Springer-Verlag Berlin Heidelberg 2010

604 C.C. Tutum, K. Deb, and J. Hattel

Fig. 1. (a) A standard tool having a cylindirical shoulder and probe (pin) design. (b)Schematic view of the FSW process. (c) A welded structure having a key hole at theend.

period takes place, where the the tool is held steady relative to the work piecewhile keeping rotation and heating the surrounding work piece material locally.Following dwelling, the tool is moved forward while stirring two work piece ma-terial to be joint (welding period) and is pulled out of the work piece leavinga key hole behind as seen in Figure 1c. These sequences have also been repre-sented schematically in Figure 2 emphasizing different computational modellingapproaches with respect to different reference frames, i.e. the Lagrangian (alsoknown as ”global approach” [9], where transient effects are captured) and theEulerian (”local approach” [7], in general used for the steady-state conditions).

In FSW, heat is generated by friction (mainly at the interface between toolshoulder and upper surface of the work piece) and plastic deformation (by toolprobe or pin in plunging stage and during welding period via stirring two workpiece material along the joining line). The heat flows into the work piece as wellas the tool. The amount of heat conducted into the work piece influences thequality of the weld, distortion and residual stress in the work piece [7,8,9]. Insuf-ficient heat generation from the tool shoulder and the probe could lead to failureof the tool pin since the work piece material is not soft enough. Therefore, un-derstanding the heat aspect of the FSW process, which is the main driving forcefor all consequent coupled simulations, e.g. microstructure and solid mechanicsmodels, is extremely important, not only for understanding physical phenomena,but also for improving the process efficiency, e.g. welding faster and safer.

In the present paper, optimum process parameters and tool geometries in FSWare investigated to minimize the temperature difference between the leading edgeof the tool probe and the work piece material in front of the tool shoulder, i.e. tosoften the material enough to move the tool probe forward without failure, andsimultaneously to maximize traverse welding speed, therefore production rate,subjected to hot and cold weld conditions. More specifically, the choices of thetool rotational speed and the traverse welding speed together with the radii ofthe tool shoulder and the probe have been investigated in order to achieve the

Hybrid Search for Faster Production and Safer Process Conditions in FSW 605

Fig. 2. Lagrangian versus Eulerian approach for simulation of the FSW process

goals mentioned above which are in essence conflicting. A Steady-state Eulerianthermal finite element model with temperature dependent thermo-physical (i.e.heat treated aluminum alloy, AA2024-T3) material data has been implementedusing a commercial multi-physics simulation software COMSOL for the functionevaluations. An evolutionary multi-objective optimization (EMO) algorithm, i.e.non-dominated sorting genetic algorithm (NSGA-II) is initially performed to findthe Pareto-optimal front. The non-dominated solutions found so far have beenclustered based on their Euclidean distances (in the objective space) in a pre-fix grid structure to reduce the number of the solutions, which will in turn beserved as initial starting points for the gradient-based local search technique, i.e.sequential quadratic programming (SQP). The ε-constraint method is appliedby fixing the second objective (i.e. welding speed) as a constraint for each clus-tered non-dominated solutions independently to obtain the modified optimizedfront. Further improvement in accuracy and confidence in the convergence ofthe Pareto-optimal front is achieved, and following this, a brief post-optimalitystudy is performed to unveil some common design principles among members ofthe clustered Pareto-optimal set. Finally, two reasonable design solutions amongthose multiple trade-off solutions have been selected based on different charac-teristics of the temperature distribution under the tool shoulder induced by thematerial flow, tool selection and production rate preferences.

2 Thermal Model

Due to relatively high heat generation contribution from the surface of the toolshoulder, an assumption based only on modelling the tool shoulder is taken intoaccount. The radius or in other words location of the tool probe is hypotheti-cally included as a design variable to compute the first objective function (i.e.temperature difference) and temperature variation under the tool, between thetool shoulder and the probe, to be used in the decision making step. Modellingthe whole welding process, i.e. plunge, dwell and pull out periods, holds somenotable complexities. In order to reduce the computational cost regarding mov-ing heat source, meanwhile preserving the applicability, only the welding period

606 C.C. Tutum, K. Deb, and J. Hattel

is taken into account and a moving coordinate system (i.e. Eulerian referenceframe) which is located on the heat source is applied. The shear layer formedbelow the tool shoulder due to high tool rotational speed is also included; hencean asymmetric temperature field along the joint line is obtained in the presentnumerical model. Equation 1, on the right side, describes the steady-state heattransfer in the plate (transient term on the left side disappears),

ρcp∂T

∂t= ∇(k∇T ) + qvol − ρcpu∇T ⇒ ρcpu∇T −∇(k∇T ) = qvol (1)

where T denotes the temperature field to be solved, ρ, cp and k are the density,the specific heat capacity and the heat conductivity of the AA2024-T3 (the work-piece material), respectively, besides u prescribing the flow vector and qvol is thevolumetric stationary heat source representing the tool as a circle in Figure 3a.

(a) (b)

Fig. 3. (a) 2-D Eulerian Steady state thermal model. (b) Mathematical modelling ofthe flow field under the tool shoulder in detail.

In the present model, heat generation is a function of the tool radius andthe temperature dependent yield stress of the work piece material (σy(T ) ofAA2024-T3) and assumed to be uniform through the thickness (t=3 mm) of theplates to be welded, as given below in Equation 2.

qvol(r(x, y), T ) =ω r(x, y) σy(T )√

3

t= (

nrev2π

60)√

x2 + y2σy(T )t√

3(2)

The details of this temperature and position dependent heat source model en-titled as Thermal-Pseudo-Mechanical (TPM) model are given in detail elsewhere[2]. The traverse motion of the tool and the relatively complex flow field underit are modelled by prescribing a material flow through the rectangular plate re-gion, as shown in Figure 3a. Due to this flow prescription, Equation 1 includesa convective term (u) in addition to the conductive term. The derivation of themathematical prescription of the material flow is also schematically representedin Figure 3b and components of the flow vector in the welding and the transverse

Hybrid Search for Faster Production and Safer Process Conditions in FSW 607

directions are formulated for an arbitrary point on the periphery of tool shoul-der as a function of θ (i.e. θ = arccos( x√

x2+y2) in Cartesian reference frame).

Equation 3 generalizes the flow field description (u(θ) = u(x, y) = (vx, vy)) forthe whole domain as follows,

u ={

(uweld − sin(θ)wRshoulder , cos(θ)wRshoulder) if r(x, y) ≤ Rshoulder

(uweld, 0) if r(x, y) > Rshoulder(3)

where r(x, y) is the radius or the position vector, cos(θ) = x√x2+y2

and sin(θ) =y√

x2+y2. As a boundary condition, the room temperature (20◦C) is defined at

the left edge of the rectangular region where the tool is assumed to be movingtowards. The heat flux on the right edge of the plate region, where the materialleaves the computational domain, is dominated by convection. On the upper andlower edges of the plate boundaries, thermal insulation is enforced.

3 Hybrid EMO

Although evolutionary computation has become an important problem solvingmethodology with its population-based collective learning process, self-adaptation, and robustness, the performance of the algorithms still depend onproper selection of various parameters (e.g. probabilities, selection and mutationschemes, etc.), namely the proper relationship between the exploration and theexploitation capabilities avoiding premature convergence, as mentioned above.Moreover, the computational speed is relatively slow as compared to the classi-cal (deterministic) algorithms. Therefore, as expected, the need for hybrid algo-rithms, which combine an evolutionary algorithm with e.g. a local search method,emerges aiming at both robust and accurate solutions with (if possible at all) lesscomputational cost. Local search methods may be incorporated within the pop-ulation members (parents) or among the offsprings. The architectures of hybridevolutionary algorithms have been summarized by [5] as follows: hybridizationbetween two different EAs (a GP asisted GA), an EA with a neural network,a particle swarm optimization (PSO) or an ant colony optimization (ACO) aswell as hybridization between EA and other heuristics (such as local search, tabusearch, simulated annealing, hill climbing, etc.). However, as the No Free LunchTheorem proposes, on average, all black-box algorithms have identical behavior,thus there is not a definite answer for which local search procedure to use forany sort of problems.

4 Hybrid EMO for the Thermal FSW Model

In this section, the multi-objective optimization problem (MOP), briefly de-scribed in section 1 that is related to the thermal aspects of the FSW process,is formulated. Optimum process parameters, i.e. the tool rotational and tra-verse welding speeds (nrev and uweld), and geometrical tool parameters, i.e. tool

608 C.C. Tutum, K. Deb, and J. Hattel

shoulder and probe radii (Rshoulder and Rprobe), are investigated to minimizethe temperature difference (ΔT ) between the leading edge of the tool probeand the work piece material in front of the tool shoulder, and simultaneouslyto maximize traverse welding speed. The second objective, based on the dualityprinciple, is reformulated as the minimization of -uweld due to the way of imple-mentation of the EMO algorithm, i.e. MATLAB implementation of the originalNSGA-II [3] algorithm by the first author [6]. This MOP problem is constrainedwith hot and cold weld conditions, geometrical constraints (the tool shoulderradius is desired to be 5 mm larger than the tool probe radius), besides lowerand upper limits of the design variables. In order to evaluate hot and cold weldconditions, average temperature (Tavg) is computed under the tool shoulder, inother words, the temperature values on each element inside the circular region(i.e. Area = πR2

shoulder) are integrated and divided by the number of elements.The constrained multi-objective optimization problem is given below,

Minimize : f1(x) = ΔT = Tprobe − Tahead,Minimize : f2(x) = −uweld,subject to : 450◦C ≤ Tavg ≤ 500◦C,

Rprobe + 5 mm ≤ Rshoulder ,8 mm ≤ Rshoulder ≤ 17 mm,3 mm ≤ Rprobe ≤ 12 mm,100 rpm ≤ nrev ≤ 1250 rpm,0.5 mm/s ≤ uweld ≤ 15 mm/s.

(4)

As mentioned above, NSGA-II, which is an EMO algorithm [3] enabling find-ing well-spread multiple Pareto-optimal solutions for an MOP by incorporatingthree substantial features, i.e. elitism, non-dominated sorting, and diversity pre-serving mechanism (crowding distance), is used for the proposed constrainedproblem. Population size is 100 and the number of generations is fixed to 10 dueto relatively high computational cost of the function evaluations, i.e. simulationtime for each set of designs is approximately 10 minutes on a PC having Core2 CPU, 2.33 GHz, 2 GB of RAM. Real variable-coding is used for the designvariables. Therefore the simulated binary crossover (SBX) and the polynomialmutation [4], with a distribution indices of 5 and 10, are used as a crossover andmutation operators, respectively. Figure 4a shows all NSGA-II (non-dominated)solutions composing a non-convex Pareto-optimal front, having −uweld on thehorizontal axis and ΔT on the vertical axis. As expected, the higher weldingspeeds results in higher temperature difference indicating steeper gradients infront of the tool, which is not desirable in case of limitations due to impropertool or machine designs. More detailed analysis of these trade-off designs is per-formed after the local search procedure which aims for further improvement inthe convergence of the obtained trade-off frontier.

Prior to the local search step, the non-dominated solutions found so far are clus-tered simply based on their Euclidean distances (i.e. minimum di) with respect totheir mean, which is computed in each cell and in each axes, in a prefix grid struc-ture to reduce the number of the solutions (for the sake of computational cost), as

Hybrid Search for Faster Production and Safer Process Conditions in FSW 609

−0.015 −0.01 −0.005 020

40

60

80

100

120

140

160

180

−uweld [m/s] (minimize)

del

ta T

[C]

(min

imiz

e)

Pareto−optimal Set

(a) (b)

Fig. 4. (a) The non-convex Pareto-optimal front obtained with NSGA-II. (b) Cluster-ing scheme.

represented in Figure 4b on a hypothetically distributed points in the objectivespace. Figure 5a shows 17 clustered solutions, indicated by cross markers, out of72 non-dominated solutions for the FSW problem in a 10-by-10 grid.

In the next step, before investigating some common manufacturing process ordesign principles in the FSW process among the members of the Pareto-optimalset, NSGA-II solutions are sought to be further improved or at least validatedto be true Pareto-optimum solutions. ε-constraint method [10] is a very suit-able approach to alleviate the difficulties faced in non-convex objective spaces(a weighted objective or a Tchebyscheff metric or any other metric which willconvert multiple objectives into a single objective can also be used). In this ap-proach, the MOP is reformulated by just keeping one of the multiple objectivesand restricting the rest of the objectives within user-specified values (i.e. uweld

is transformed into a constraint by considering ε = 10−6 in the present case).More details are given in [4]. In order to solve the scalarized optimization prob-lem by means of searching the minimum of the aggregated objective function,a gradient-based local search technique, i.e. sequential quadratic programming(SQP; fmincon function in MATLAB Optimization Toolbox), is used. The mod-ified front is shown with the blue curve in Figure 5b. The change in the conver-gence is not exaggerated, but on the other hand, it enhances the confidence inthe trade-off front obtained by NSGA-II.

After completing the multi-objective optimization task, a set of optimal so-lutions specifying the design variables and their trade-offs is obtained. If theseoptimal solutions are sorted according to the worse order of the first objective(min. ΔT ), they would also get lined up in the second objective (min. -uweld) inan ascending order. Having such a wide variety of solutions make the decision-making process much easier compared to having only one optimal solution. Thisenables engineers or designers to judge or plan the performance of a productor a process in a larger perspective in terms of sacrifices and gains with re-spect to multiple criteria [4]. Moreover, a basic post-optimality study can unveil

610 C.C. Tutum, K. Deb, and J. Hattel

interesting design knowledge that is common to all of these trade-off solutionsor a partial set of them [11]. This design methodology, which was originallyformulated as ”innovization” (innovation through optimization) [12,13], has alsobeen applied manually to the current FSW problem. A set of design variablescorresponding to some of the solutions on the Pareto-curve have been listedin Table 1.

−0.015 −0.01 −0.005 020

40

60

80

100

120

140

160

180 12

34

56

78

9

10

1112

1314

15

16

17

−uweld [m/s] (minimize)

del

ta T

[C

] (m

inim

ize)

Non−dominated SolutionsClustered Solutions X

(a)

−0.015 −0.01 −0.005 020

40

60

80

100

120

140

160

180 12

34

56

78

9

1011

1213

1415

16

17

−uweld [m/s] (minimize)

del

ta T

[C

] (m

inim

ize)

NSGA−II Results

After Local Search (SQP)

(b)

Fig. 5. (a) Clustered non-dominated solutions indicated by crosses and the correspond-ing numbers on top of them. (b) Pareto-optimal front modified after the local searchon each clustered non-dominated solutions.

Table 1. Set of designs corresponding to some of the members on the modified Pareto-optimal front in Figure 5b

Rshoulder [mm] Rprobe [mm] uweld [mm/s] nrev [rpm]

10.932 5.155 13.224 1037.810.819 5.377 12.359 1014.910.896 5.831 11.261 1119.6

14.959 9.887 9.694 974.3313.793 8.263 7.171 856.0713.579 8.005 4.304 718.17

10.998 5.74 3.672 1057.711.113 5.527 1.539 880.3310.694 4.581 0.643 968.65

Three intervals can be distinguished looking at Table 1, i.e. 0.5mm/s ≤uweld < 4mm/s, 4mm/s ≤ uweld < 10mm/s and 10mm/s ≤ uweld < 14mm/s.In the first and the third intervals, tool shoulder and probe radii are approxi-mately same (10 mm and 5 mm, respectively). In the middle interval, there is asignificant increase in the tool dimensions, but there is also a common tendencyto have a 5 mm difference in the radius dimensions (second constraint is active)along the Pareto-front. Moreover, in the middle interval, since the tool shoulderis getting larger, therefore heat generation is increasing due to the increase inthe frictional surface area (consequently, the hot weld condition becomes active),

Hybrid Search for Faster Production and Safer Process Conditions in FSW 611

Fig. 6. Thermal field for a parameter set: uweld=11.3 mm/s, Rshoulder=10.5 mm,Rshoulder=5.5 mm, nrev=1100 rpm

tool rotational speed (nrev) shows a decrease compared to other two intervals onthe Pareto-curve. In most of the designs, distribution of the temperature fieldunder the tool is almost uniform (i.e. cold weld condition is not active), thusstandard deviation is close to the mean value, which is a desired process con-dition. Main criterion for the manufacturer to select one or two designs out ofthese possibilities would be welding speed which is related to investment andoperating cost of different kinds of tool-machine combinations. In case of limitedfinancial resources, manufacturer or engineer would like to weld slower (needto sacrifice in production rate) in order to improve the lifetime of the tools. Inthis case, such a design set: uweld=2-3 mm/s, nrev=700-800 rpm, Rshoulder=9-10mm and Rprobe=4-5 mm would be preferable. In an opposite case, where finan-cial limitations are negligible, the production rate would be a dominant criterion(e.g. uweld >11 mm/s), but similar tool geometries with higher rotational speedswould be sufficient (e.g. Figure 6).

5 Conclusions and Discussions

Optimum FSW process parameters and tool geometries are investigated to min-imize temperature difference between the leading edge of the tool probe and thework piece material in front of the tool shoulder, and simultaneously to maxi-mize traverse welding speed, which are in essence conflicting. An evolutionarymulti-objective optimization algorithm (i.e. NSGA-II), is applied to find multipletrade-off solutions followed by a gradient-based local search (i.e. SQP) on clus-tered non-dominated solutions to enhance the confidence in the convergence ofthe obtained Pareto-optimal front. A brief post-optimality study is performed tofind out some common design principles among those trade-off solutions. Threeintervals in the design space have been distinguished looking at these optimalsolutions. Finally, production rate is found to be a dominant criterion, and con-sequently, two reasonable choices have been made to solve the manufacturer’sdilemma (faster production versus safer process conditions which can also berelated to cheaper solutions).

612 C.C. Tutum, K. Deb, and J. Hattel

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