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Linköping University Electronic Press

  

Report

  

  

  

  

Decentralized Friction Stir Welding Control on Canisters for

Spent Nuclear Fuel

  

  

Isak Nielsen, Olof Garpinger and Lars Cederqvist

  

  

  

  

  

  

  

  

  

  

  

  

  

  

 

LiTH-ISY-R, 1400-3902, No. 3062

 

Available at: Linköping University Electronic Press

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-91571

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Technical report from Automatic Control at Linköpings universitet

Decentralized Friction Stir Welding

Control on Canisters for Spent Nuclear

Fuel

Isak Nielsen, Olof Garpinger, Lars Cederqvist

Division of Automatic Control

E-mail: isani82@isy.liu.se, olof.garpinger@control.lth.se,

lars.cederqvist@skb.se

23rd April 2013

Report no.: LiTH-ISY-R-3062

Address:

Department of Electrical Engineering Linköpings universitet

SE-581 83 Linköping, Sweden

WWW: http://www.control.isy.liu.se

AUTOMATIC CONTROL REGLERTEKNIK LINKÖPINGS UNIVERSITET

Technical reports from the Automatic Control group in Linköping are available from http://www.control.isy.liu.se/publications.

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Abstract

The Swedish nuclear waste will be stored in copper canisters and kept iso-lated deep under ground for at least 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is utilized. To repetitively pro-duce high quality welds, it is vital to use automatic control of the process. A decentralized solution is designed based on an already existing temperature controller and a proposed linear plunge depth controller. The plunge depth control is challenging mainly because of deection in the machine, thermal expansion and cross couplings in the process. The decentralized controller has been implemented and evaluated on the real system with good results, keeping the plunge depth within the necessary ±0.1 mm of its setpoint at the same time as the temperature specications are met.

Keywords: Decentralized Control, Plunge Depth Control, Stir Zone Tem-perature Control, Friction Stir Welding, Copper Canisters, Nuclear Waste, SKB

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Decentralized Friction Stir Welding Control on

Canisters for Spent Nuclear Fuel

Isak Nielsen (Linköping University), Olof Garpinger (Lund University)

and Lars Cederqvist (SKB AB)

2013-04-26

Abstract

The Swedish nuclear waste will be stored in copper canisters and kept isolated deep under ground for at least 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is utilized. To repetitively produce high quality welds, it is vital to use automatic control of the process. A decentralized solution is designed based on an already exist-ing temperature controller and a proposed linear plunge depth controller. The plunge depth control is challenging mainly because of deection in the machine, thermal expansion and cross couplings in the process. The decentralized controller has been implemented and evaluated on the real system with good results, keeping the plunge depth within the necessary ±0.1mm of its setpoint at the same time as the temperature specications are met.

1 Introduction

The Swedish Nuclear Fuel and Waste Management Company (SKB) is respon-sible for research and development of a long term storage for Sweden's nuclear waste. The proposed solution consists of multiple protective barriers. The spent fuel is rst encapsulated in 50 mm thick copper canisters which are then embed-ded in bentonite clay about 500 meters below ground in the Swedish bedrock, see Fig. 1.

The repository must keep the spent fuel safe for at least 100,000 years. To ensure a suciently thick copper corrosion barrier, it is important that the canisters are sealed properly. SKB is currently investigating use of Friction Stir Welding (FSW) for sealing lids to the 5 m long and 1 m diameter canisters. The plunge depth and weld temperature must be controlled within certain limits to produce the corrosion barrier demanded by Swedish authorities.

If the weld tool plunges too shallow or too deep into the material, there is an increased risk that defects will form inside the copper. The plunge depth has previously been controlled only indirectly by keeping a constant axial force, but this solution have shown insucient. The weld temperature has, on the other hand, been controlled directly using a cascaded solution, Cederqvist et al. [2]. This paper describes the design of a linear plunge depth controller and the evaluation of the combined decentralized control solution.

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There are several dicult process properties to take into consideration when designing the plunge depth controller, such as deections in the machine, eccen-tricity of the canister and thermal expansion of the workpiece.

Parallel to this research on the decentralized controller, the authors are also investigating an alternative solution using a more advanced multivariable Nonlinear Model Predictive Controller (NMPC). The theoretical results of the NMPC controller are presented in Nielsen et al. [13].

2 The Friction Stir Welding Process

The sealing of the canisters are made using FSW, which is a solid state welding method invented in the early 90's by The Welding Institute (TWI), Thomas et al. [1]. This has become a popular method for forging dierent metals, such as aluminum, titan, steel and copper. The welding is made at temperatures below the melting temperature and it is an energy ecient method, Mishra et al. [3].

2.1 Friction Stir Welding

The basic setup in FSW is seen in Fig. 2, where two metal plates are welded. The rotating, non-consumable, tool consists of a probe and a shoulder. It generates heat and is traversed along the joint line when the metal is warm enough, stirring the material from the two pieces into a weld. The heat is a result from friction and plastic deformation of the material.

2.2 Friction Stir Welding in Copper Canisters

In contrary to many FSW applications where the workpieces are relatively thin and at, the sealing of the canisters involves thick, cylindrically shaped, met-als. A purpose-built welding machine, that copes better with high forces and torques than a standard FSW robot, was installed at the Canister Laboratory in Oskarshamn in 2003. Even so, there are still small machine deections that the depth measurements must be compensated for.

The tool used in SKB's application consists of a probe that is approximately 50 mm long, and a convex scroll shoulder with a diameter of 70 mm. The choice of a convex shoulder instead of the commonly used concave shoulder was investigated by Cederqvist et al. [4]. This choice gives smaller variations in plunge depth and spindle torque, which is desirable from a control point of view.

Mayeld et al. [5] conclude that there are three axes in FSW with an eort and a ow, and only one of these two can be manipulated for each axis. The other one is determined by the process. In SKB's application, the axial force acting on the tool (Fz), the spindle rotation speed (ω) and the tool traverse

speed (vw) are possible control signals. These variables are depicted in Fig. 3.

The corresponding variables plunge depth (Pz), spindle torque (Mspindle) and

traverse force (Ft) are then given by the process. It was decided to keep the

traverse speed constant at vw = 86 mm/min and use the other two variables

as control signals since their inuence on the temperature and plunge depth is greater. The stir zone temperature (T ) and power input (P ) are also very

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important process variables. The power input is determined by multiplying spindle torque with spindle rotation speed.

Fig. 4 shows how the process variables are related. The plunge depth af-fects the spindle torque, which in turn inuences the stir zone temperature. The plunge depth depends on the temperature and, hence, there is a triangle of dependences between the process variables. Changing the axial force will aect both plunge depth and spindle torque, while the spindle rotation speed inuences the temperature. Observations reveal that the spindle rotation speed inuences the torque as well, but this is not accounted for in this article. Similar observations was made by Cui et al. [14].

A full circumferential weld consists of ve dierent stages; dwell, start, down-ward, joint line and parking sequences. The weld starts in the dwell sequence, where the tool is inserted in a drilled hole 75 mm above the joint line. The tool rotates and heats the copper, and when a certain threshold temperature is reached, the tool starts to traverse parallel to the joint line such that the start sequence is initiated. When the tool has accelerated and yet another temper-ature threshold is reached, the tool starts moving downward. The downward sequence is ended when the tool reaches the joint line. The tool is then traversed 360 degrees to produce the weld that seals the canister and the lid. Finally, the parking sequence is initiated and the tool travels up into the lid again.

3 Controller Goals

In order to produce welds without defects, the process needs control. Defects are mainly formed due to incorrect plunge depth or stir zone temperature. The previously mentioned temperature cascade controller has an inner loop that controls the power input. This controller has proved to work well with the rapid torque disturbances and slow temperature disturbances that are common in this FSW application, Cederqvist et al. [2].

To cope with defects that are related to plunge depth, this variable must be controlled as well. It is particularly important that the plunge depth is close to its setpoint when the tool reaches the joint line, since the rest of the weld is often controlled suently well using a constant force. For this reason and in order to keep the control problem as small as possible in the beginning, it is assumed that the depth controller will only be active during the start-, downward- and beginning of the joint line sequence.

The main control goal of the plunge controller is to keep the plunge depth within ±0.1 mm from the setpoint when the tool reaches the joint line. This should be achieved while keeping the axial force roughly within the interval 78 to 93 kN. The lower bound is introduced to avoid wormhole defects forming at higher temperatures than normal, see Cederqvist [10], while the upper bound is introduced to avoid deep welds that are hard to recover from. At the same time as the plunge depth specications are met, the stir zone temperature must also be kept within an interval of 790-910◦C to avoid temperature related defects.

In some FSW applications with welding robots, position control of the tool is used, but this induces problems with compliance in the robots' linkages, Longhurst et al. [7]. A related research topic is force control, since this is sup-posed to solve the problem with machine exibility. The idea is that a constant force equals a constant depth, but this is not always true. Investigations on

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using torque as an indicator of plunge depth have been made by Longhurst et al. [8] and Lammlein et al. [9], and they state that torque is a better predictor of plunge depth than axial force. The controller proposed in this article will use the axial force as control signal, but modify the process output to give the actual plunge depth rather than the tool position.

4 Modeling

The controller design used in this paper is model based, but research results regarding plunge depth modeling are quite sparse. Mandal et al. [6] developed a numerical model using the constitutive temperature dependent Johnston-Cook law and simulations using the Finite Element Method with promising results. This type of models are, however, not useful in real-time control applications due to their computational complexity.

Since the model will be used for decentralized controller design alone, only the dynamics from axial force to plunge depth will modeled in this section. The temperature is controlled using the existing cascade controller. Possible interactions between the two control loops are neglected, and will be handled as disturbances by the two controllers. For a thorough model of the whole process, see Nielsen et al. [13].

The plunge depth is measured using a position sensor that measures the distance from the welding machine to the tool. The sensor is calibrated to the canister surface before the weld, so the origin is well dened before the dwell sequence. However, since this is not a measure equivalent to plunge depth, the signal has to be transformed before it can be used in the controller.

The position measurements are composed of four dierent parts; plunge depth, deection, eccentricity and thermal expansion, see Fig. 5. The eccen-tricity is almost zero during the short start and downward sequences. Based on experimental observations, the thermal expansion is assumed constant during the same time period. Pein Fig. 5 is therefore approximated as a constant that

does not aect the control. The plunge depth and deection will, however, be described by linear dynamic models in this section.

4.1 Plunge Depth Model

The plunge depth model proposed in this article is based on rheology models which are approximate descriptions of visco-elastic materials, and metals at high temperatures can be modeled as such, Flügge [11]. In this paper, a model without creep is investigated, while in Nielsen et al. [13] creep is also part of the model used for NMPC.

The rheology model is based on a 1-D deformation of the material, and to use it some assumptions are needed. The tool is considered a rigid body that does not deform at all. Furthermore, it is assumed that the copper closest to the tool have a homogenous temperature and that the copper outside this region is completely sti. The strain (t) is described as

(t) = c · ∆l(t), (1)

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that the contact area is constant, the stress σ(t) can be expressed as σ(t) = F (t)

A , (2)

where A is the contact area and F (t) is the force acting on the tool. The deformation is the same as the deviation in plunge depth, i.e.

∆l(t) = Pz(t) − ¯Pz,

where ¯Pz is the plunge depth around which the system is linearized.

The simplest Kelvin material model is used, and together with the assump-tions above the expression relating stress and strain is

σ(t) = ¯K(t) + ¯B ˙(t), (3)

where ¯K and ¯B are constants. Using (1)-(3) the force exerted on the tool by the copper can be written as

F (t) = K∆l(t) + B∆ ˙l(t).

The deformation is created by the motion of the tool and spindle, and this motion is subjected to Newton's second law, giving

m∆¨l(t) = ∆Fz(t) − F (t) = ∆Fz(t) − K∆l(t) − B∆ ˙l(t),

where m is the mass of the moving parts and ∆Fz(t) = Fz(t) − ¯Fz is the

devi-ation in axial force from the linearizdevi-ation point ¯Fz. This is a linear dierential

equation and the corresponding transfer function is Gz(s) =

1 ms2+ Bs + K,

from the change in axial force ∆Fz, to the deviation from the plunge depth ¯Pz.

Using measured data and the System Identification Toolbox in Mat-lab, a second order process model was estimated giving,

Gz(s) =

1

14.8s2+ 58.6s + 36.2.

The estimation data were obtained by measuring the response for a step in axial force when the cascaded temperature controller was active.

4.2 Deection

The deection was investigated by pushing the tool shoulder towards the canis-ter surface and measuring how much the position measurements changed. Using this data, a deection model was created. The resulting model is a rst order linear time invariant model, described by the transfer function

Gd(s) =

0.0304 0.56s + 1.

The gain in the deection model is of the same order of magnitude as the plunge depth model, and it is therefore crucial to compensate for it.

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Combining the plunge depth model and the deection model gives a model for the tool position measurements. A discrete time validation of this model, with a sampling time of 0.1 s, is seen in Fig. 6, where the change in the measured depth is shown during a 2 kN change in the axial force. Hence, all changes origi-nate from the deection and plunge depth responses. Notice that the oscillatory behaviour is a result of an oscillating axial force, which is a built-in property of the machine and nothing that can easily be changed.

5 Controller Design

The choice of the decentralized controller assumes that the cross couplings in the process can be handled well enough as disturbances. The plunge depth controller is a PI controller, which is a reasonable controller to start out using. Simulations of the closed loop system have also shown that the increase in performance using a PID controller instead of a PI was not big enough to justify the extra degree of complexity that comes with the D-part.

The controller has the structure given by Fig. 7, where Hr(s)and Hy(s)are

low-pass lters on the reference and measurements respectively. The measure-ment lter is used to attenuate noise on the sensor readings, and the reference lter is added to get another degree of freedom when tuning the controller. By using this structure, the closed loop disturbance suppression and reference tracking performances can be separated.

The control law for the PI controller using this conguration is then Fz(t) = KPe(t) + K˜ I

Z t

0

˜ e(τ )dτ

where KPis the proportional gain, KI the integral gain and ˜e the ltered control

error.

There are several tuning methods for nding suitable values of the PI-parameters with rules of thumb on how to choose the controller gains. Here, the controller is designed using a technique by Garpinger [12].

5.1 Disturbance Suppression and Robustness

Garpinger's algorithm focuses on disturbance suppression and robustness of the closed loop system. The latter property is closely connected to the sensitivity function S(s) and the complementary sensitivity function T (s), dened by

S(s) = 1

1 + Fy(s)Gz(s)

T (s) = Fy(s)Gz(s) 1 + Fy(s)Gz(s)

,

where the transfer function Fy(s) represents a PI or PID controller. The idea

with the algorithm is to specify upper bounds on |S(iω)| and |T (iω)|, where ω is the angular frequency, and nd the stabilizing controller that minimizes the Integrated Absolute Error (IAE) during a unit step disturbance. That is, to solve the following optimization problem

min KP,KI IAE = Z ∞ 0 |e(t)|dt,

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subject to

|S(iω)| ≤ MS, ∀ ω ∈ R+

|T (iω)| ≤ MT, ∀ ω ∈ R+,

where e(t) is the control error and MS, MT are robustness bounds. At least one

of the inequalities above must hold for some angular frequency ωS and/or ωT.

In Garpinger [12], IAE is calculated for a disturbance entering the system at the process input, but in this paper the disturbance is entering at the process output in order to reect the real process more accurately.

A PI-controller is not very sensitive to noise, if the proportional gain KP

is reasonably small, and therefore the measurement lter was not used. Using MS = MT = 1.2, which is known to give good robustness, in Garpinger's

algorithm results in KP = 11.3, KI = 7.86.

5.2 Reference Tracking

The lter Hr(s)was designed to achieve the desired reference tracking

perfor-mance. Since the reference will be constant most of the time in this application, the reference tracking is not as important as the robustness and disturbance suppression. A low-pass lter of low order was chosen, with its time constant as a tuning parameter that could be changed based on experimental observations. Currently, a rst order low-pass lter with time constant Tf = 30s and a static

gain of 1 is used.

6 Experimental Evaluation

The PI controller has been evaluated during ve dierent welds showing good performance. In Fig. 8 the ltered control error, ˜e, is plotted for the welds. When the tool reaches the joint line after approximately 135 seconds, all welds are within ±0.1 mm from the reference. The large transient at the beginning of the dark blue weld is due to an initialization error in the controller, and should not be considered.

The corresponding axial forces for the welds are presented in Fig. 9 and it is clear that to keep the desired plunge depth, a varying force is needed. Three of the ve welds saturate at their upper limits, although the weld marked with a dark blue curve use a lower maximum force limit.

Since the control structure does not consider cross couplings in the pro-cess, it is interesting to investigate how the plunge depth controller aects the temperature control. In Fig. 10, the measured torques are plotted for the ve welds. They vary over approximately 200 Nm during the start and downward sequences. By comparing Fig. 9 and 10 it is evident that there is a strong correla-tion between changes in the axial force and the torque. The torque changes will make the work of the cascaded temperature controller harder since the torque is directly related to the power input. Fig. 11 shows the stir zone temperatures and the corresponding rotation speeds during the ve welds. The cascade controller changes the spindle speed to compensate for the torque disturbances to keep the power input constant. The control is denitely bothered by the cross coupling, but the temperature is still held well within the bounds 790-910◦C when the

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joint line is reached. The relation between spindle rotation and plunge depth is, however, much weaker and one can assume that the plunge depth controller handle these disturbances without problems.

7 Conclusions

The research results presented show that the proposed control strategy can be used to successfully regulate the FSW process at SKB. Five dierent welds have been made using the full decentralized controller, and the results are good. The main controller goals are met for all welds, with both the plunge depth error and the temperature well within their specied boundaries. However, there have also been some observations suggesting that both the thermal expansion and the deection can change between the welds. This must be thoroughly investigated before the control strategy can be fully trusted. Since both these parameters are a result of the current position measurements, the control would benet greatly by a sensor that can measure the actual plunge depth directly.

Acknowledgments

This research was founded by the Swedish Nuclear Fuel and Waste Management Company.

References

[1] Thomas WM, Nicholas ED, Needham JC, Murch MG, Temple-Smith P, Dawes CJ. Friction stir butt welding, Patent PCT/GB92/02203,1991 [2] L. Cederqvist, O. Garpinger, T. Hägglund, A. Robertsson. Cascade

con-trol of friction stir welding process to seal canisters for spent nuclear fuel. Control Engineering Practice, Jan. 2012.

[3] R.S. Mishra, Z.Y. Ma. Friction stir welding and processing. Materials Sci-ence and Engineering R 50, Aug. 2005.

[4] L. Cederqvist, C.D. Sorensen, A.P. Reynolds, T. Örberg. Improved process stability during friction stir welding of 5 cm thick copper canisters through shoulder geometry and parameter studies. Science and Technology in Weld-ing and JoinWeld-ing 46(2).

[5] D.W. Mayeld C.D. Sorensen. An improved temperature control algorithm for friction stir welding. In 8th International Symposium on Friction Stir Welding, Timmerdorfer Strand, Germany, May 2010.

[6] S. Mandal, J. Rice, A.A. Elmustafa. Experimental and numerical investiga-tion of the plunge depth stage in fricinvestiga-tion stir welding. Journal of Materials Processing Technology (203), 2008.

[7] W. R. Longhurst, A. M. Strauss, G.E. Cook. Enabling Automation of Fric-tion Stir Welding: The ModulaFric-tion of Weld Seam Input Energy ny Traverse SPeed Force Control. Journal of Dynamic Systems, Measurement, and Con-trol, Jul. 2010.

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[8] W. R. Longhurst, A. M. Strauss, G. E. Cook, P. A. Fleming. Torque con-trol of friction stir welding for manufacturing and automation. The Inter-national Journal of Advanced Manufacturing Technology, Apr. 2010. [9] D. H. Lammlein, W. R. Longhurst, D. R. DeLapp, P. A. Fleming, A. M.

Strauss, G. E. Cook. The friction stir welding of hemispheres - a technique for manufacturing hollow spheres. International Journal of Pressure Vessels and Piping, Aug. 2010.

[10] L. Cederqvist, Friction Stir Welding of Copper Canisters Using Power and Temperature Control, PhD. Thesis, Lund University, 2011

[11] W. Flügge, Viscoelasticity, Springer-Verlag, 1975.

[12] O. Garpinger, Design of Robust PID Controllers with Constrained Control Signal Activity, Lic. Thesis, Lund University, 2009

[13] I. Nielsen, O. Garpinger, L. Cederqvist. Simulation based Evaluation of a Non-Linear Model Predictive Controller for Friction Stir Welding of Nu-clear Waste Canisters. European Control Conference, July, 2013.

[14] S. Cui, Z. W. Chen, J. D. Robson. A model relating tool torque and its associated power and specic energy to rotation and forward speeds during friction stir welding/processing. International Journal of Machine Tools & Manufacture 50, Sep. 2010.

[15] O. Garpinger, T. Hägglund, K. J. Åström. Criteria and Trade-os in PID Design. In IFAC Conference on Advances in PID Control, Brescia, Italy, 2012.

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Figure 1: Multiple protective barriers ensure a safe long term storage of the Swedish nuclear waste.

Figure 2: A gure from TWI depicting the tool and workpiece conguration in a common FSW application. The tool is plunged into the material and traversed along the joint line.

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Figure 3: The manipulated variables are 1) Spindle rotation speed (ω), 2) Tra-verse speed (vw) and 3) Axial force acting on the tool (Fz). The upper part is

the lid, and the lower part is the canister.

M

Pz T

Fz ω

Figure 4: The relation between the process variables and the manipulated vari-ables in the process. The arrows represent which varivari-ables are inuencing the others.

Plunge Depth Deection Eccentricity & Thermal Exp.

+ Fz

Pd

Pz Pt

Pe

Figure 5: Block diagram of the four components in the position measurements. The thermal expansion and the eccentricity are independent of the axial force.

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0

5

10

15

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Change in position measurement

Time (s)

Change in P

t

(mm)

Measured position

Simulated position

Figure 6: Validation of the plunge depth model. The gure shows the estimated and measured change in tool position after a 2 kN step change in the axial force.

Process PI -1 Hy(s) + Hr(s) + −Gd(s) Pz,r P˜z,r E˜ Fz Pt Pz − ˜Pz −Pd

Figure 7: Block diagram of the control structure with a PI controller together with lters for the reference and measurements. The Process block represents the FSW process from axial force to the tool position measurements. The plunge depth is extracted by subtracting the deection model output from the measurements.

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0

50

100

150

−0.2

−0.1

0

0.1

0.2

0.3

Control error for several welds

Time (s)

Control error (mm)

Figure 8: Five welds with plunge depth control have been produced. The re-sulting control error is plotted during the start and downward sequences. The joint line is reached at approximately 135 seconds.

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0

50

100

150

80

82

84

86

88

90

92

Axial force applied by the controller

Force (kN)

Time (s)

Figure 9: Axial forces commanded by the PI controller during the welds. It is clear that a varying axial force is required to achieve the desired plunge depth.

0

50

100

150

950

1000

1050

1100

1150

1200

1250

Torque exterted by the motor

Torque (Nm)

Time (s)

Figure 10: Changes in axial force will induce changes in the torque exerted by the tool.

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0

50

100

150

750

800

850

Stir zone temperature

Time (s)

Temperature (°C)

0

50

100

150

300

400

500

Tool rotation speed

Time (s)

Rotation speed (RPM)

Figure 11: The temperature controller is aected by the plunge depth con-troller through variations in the torque. To compensate for these, the cascaded controller changes the rotation speed.

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Avdelning, Institution Division, Department

Division of Automatic Control Department of Electrical Engineering

Datum Date 2013-04-23 Språk Language  Svenska/Swedish  Engelska/English   Rapporttyp Report category  Licentiatavhandling  Examensarbete  C-uppsats  D-uppsats  Övrig rapport  

URL för elektronisk version http://www.control.isy.liu.se

ISBN  ISRN



Serietitel och serienummer

Title of series, numbering ISSN1400-3902

LiTH-ISY-R-3062

Titel

Title Decentralized Friction Stir Welding Control on Canisters for Spent Nuclear Fuel

Författare

Author Isak Nielsen, Olof Garpinger, Lars Cederqvist

Sammanfattning Abstract

The Swedish nuclear waste will be stored in copper canisters and kept isolated deep under ground for at least 100,000 years. To ensure reliable sealing of the canisters, friction stir welding is utilized. To repetitively produce high quality welds, it is vital to use automatic control of the process. A decentralized solution is designed based on an already existing tem-perature controller and a proposed linear plunge depth controller. The plunge depth control is challenging mainly because of deection in the machine, thermal expansion and cross cou-plings in the process. The decentralized controller has been implemented and evaluated on the real system with good results, keeping the plunge depth within the necessary ±0.1 mm of its setpoint at the same time as the temperature specications are met.

References

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