Correlating process parameters to thrust forces and torque in the friction stir processing of AZ31B

Abstract

Introduced in this work are correlations that capture the behavior of thrust force and torque vs. input process parameters in friction stir processing (FSP) of twin-roll cast (TRC) AZ3 IB. The correlations are based on the findings of an experimentally validated robust 3D FE model that was used to simulate the FSP process at different values of tool rotational and traverse speeds. The findings are fitted into simple power equations relating thrust force and torque to input parameters of spindle speed and feed. An experimental test matrix was used to validate the proposed correlations. The correlation equations were found to be able to predict the experimentally measured forces during friction stir processing with good statistical significance with average estimate errors of 6.2% and 5.4% for the thrust force and torque, respectively. The thrust force and torque exhibited opposite trends with increasing tool rotational speed. The thrust force increased while the torque decreased as the tool rotational speed increased. Copyright © (2014) by the Society of Manufacturing Engineers All rights reserved.

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Proceedings of NAMRI/SME, Vol. 42, 2014
Correlating Process Parameters to Thrust Forces and Torque
in the Friction Stir Processing of AZ31B
Ali H. Ammouri and Ramsey F. Hamade
Department of Mechanical Engineering
American University of Beirut
PO Box 11-0236 Beirut, Lebanon
ABSTRACT
Introduced in this work are correlations that capture the behavior of thrust force and torque vs. input process parameters in
friction stir processing (FSP) of twin-roll cast (TRC) AZ31B. The correlations are based on the findings of an experimentally
validated robust 3D FE model that was used to simulate the FSP process at different values of tool rotational and traverse
speeds. The findings are fitted into simple power equations relating thrust force and torque to input parameters of spindle
speed and feed. An experimental test matrix was used to validate the proposed correlations. The correlation equations were
found to be able to predict the experimentally measured forces during friction stir processing with good statistical
significance with average estimate errors of 6.2% and 5.4% for the thrust force and torque, respectively. The thrust force and
torque exhibited opposite trends with increasing tool rotational speed. The thrust force increased while the torque decreased
as the tool rotational speed increased.
KEYWORDS
Friction stir processing, AZ31B, thrust, torque, speed, feed
INTRODUCTION
Friction stir processing (FSP) is a microstructure
reforming processes originally proposed by Mishra [1] and
is based on the same principles of friction stir welding
(FSW). Whereas FSW welds separate plates, FSP is used to
refine the microstructure. Both processes utilize a rotating
tool that comprises a shoulder and a pin. The tool is first
plunged into the material to be processed and is, then,
traversed across areas of interest to be modified. Severe
mechanical deformation and frictional heating associated
with FSP initiates dynamic recrystallization (DRX) that is
the main mechanism behind grain refinement.
Magnesium alloy AZ31B is one of the light weight alloys
that have potential future in being adopted by the automotive
industry. FSP of magnesium AZ31B is desirable due to the
improvements it grant to the material’s mechanical
properties. These improvements are mainly achieved by
grain refinement and homogeneity that results in superplastic
behavior of alloys. Fine and more homogenized grain
structure of AZ31 was attained by friction stir processing [2].
Ultrafine-grained microstructures with an average grain size
of 100-300 nm were achieved in solution-hardened AZ31
alloy prepared by friction stir processing equipped with a
rapid heat sink [3]. The same approach was followed by
another author who used two-pass FSP to achieve an average
grain size of 85 nm [4]. A recent publication by [5] presented
AZ31 magnesium alloy prepared by friction stir processing
which exhibited 268% elongation at 723K and 10-2 s-1
indicating that high strain rate superplasticity could be
achieved.
The forces exerted on the FSP tool highly depend on the
process parameters especially the tool rotational speed and
feed. Establishing relations between the forces exerted on the
tool and the process parameters of FSP is important for
successful control of the process especially for temperature
sensitive alloys such as the AZ31B. Relationships between
FSP processing parameters and torque for several aluminum
alloys can be found in the literature [6, 7]. Other state
variables such as grain size has been previously reported [8].
In this work we present 2 correlations that relate the
thrust force and torque during FSP to the tool rotational and
traverse speeds using a multiplicative power law which is
commonly used in machining operations. The behavior of
the process thrust force and torque for the considered AZ31B
was found to be similar to what other authors reported for
Aluminum alloys [6, 7]. The correlations were constructed
from the simulation results of an experimentally validated
3D FE model that was constructed using the commercial
DEFORM 3D software. The FE model utilized the physical
based Zerilli-Armstrong material model for HCP material
which is capable of predicting accurate state variables [9].
The proposed correlations are only valid for the range of
process parameters described by the test matrix and for the
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Proceedings of NAMRI/SME, Vol. 42, 2014
geometries of the tool and workpiece adopted in the FE
model.
THE FE MODEL
A 3D thermo-mechanically coupled FE model was
developed using the commercial FEA software DEFORM-
3D™ (Scientific Forming Technologies Corporation, 2545
Farmers Drive, Suite 200, Columbus, Ohio 43235 [10]). The
meshed model shown in Figure 1 consists of a tool, a
workpiece, and backing plate. Both the tool and the backing
plate were modeled as rigid un-deformable bodies where
only heat transfer was accounted for while the workpiece
was modeled as a plastic body subject to both deformation
and heat transfer.
The considered tool had a 19 mm cylindrical shoulder
with a 6.4 mm diameter smooth unthreaded pin that extrudes
2.7 mm from the bottom of the shoulder. Both the workpiece
and the backing plate had an area of 90x40 mm2 and a height
of 3 mm. Materials used in the FEM model were H13 steel
for the tool, AISI-1025 steel for the backing plate and AZ31B
for the workpiece.
Figure 1. The meshed FEM model used in the simulations.
Selecting a proper material model for describing the
mechanical behavior of any material is key for a successful
simulation of friction stir processing where temperature,
strain, and strain rate gradients vary abruptly within, and
when moving away, from the stirring zone. The Zerilli-
Armstrong (ZA) is a physical based constitutive relation that
holds advantages over the empirical constitutive relations
that are usually used as “de-facto” in the simulation of
friction stir processes [11-13]. The ZA model is such a model
that is based on thermally activated dislocation mechanics. It
accounts for strain hardening, strain rate hardening, and
temperature softening as well as the grain size effect. The
HCP-specific ZA material model is described by
 

 
 
 

0 0 1
0 0 1
exp ln
1 exp exp ln
rr
T
T
CB
Ba

   
  


   

(1)
where

is the flow stress,

is the strain rate, T is the
temperature,

is the plastic strain, and C0, B, β0, β1, B0, εr,
α0, and α1 are determined experimentally (see [13] for
detailed explanation of the derivation of the constant terms).
Non-linear regression analysis was used to fit published
[14] experimental tensile test data for wrought twin roll cast
AZ31B into the ZA equations described in Equations 1. The
resulting fit had an R2 value of 0.917 and the corresponding
coefficients are summarized as:
Table 1. Fit coefficients for ZA of TRC wrought AZ31B.
C0
B
β0
β1
B0
εr
α0
α1
0
590
3.6 e-3
3.6e-5
653
0.089
6.1e-4
1.7e-4
Tetrahedral elements were used in the FEM model with
active local re-meshing triggered by a relative interference
ratio of 70% between contacting edges. This would ensure
the integrity of the workpiece geometry during deformation.
The tool and the backing plate were meshed for thermal
analysis purposes with each containing around 6000 and
5000 elements respectively while the workpiece had around
16000 elements. To further capture the state variables at the
tool-workpiece interface, a rectangular mesh control window
was applied around the processing area of interest where
finer mesh elements were created. The conjugate gradient
iterative solver with direct iteration method was used in
deformation calculations whereas the sparse solver was used
for temperature.
Heat transfer with the environment was accounted for all
the three meshed objects with a convective heat coefficient
of 20 W/(m2 ºC) at a constant temperature of 293K. The heat
transfer coefficient between the tool-workpiece and backing
plate-workpiece interfaces was set to 11 kW/(m2 ºC) [15].
Friction at the tool-workpiece interface is a significant
factor in any FSP/FSW simulation. It is determined that 86%
of the heat generated is due to frictional forces [16].
Determination of the friction factor is a daunting challenge
due to the variation of temperature, strain rate, and stress.
Different publications found in literature investigated the
value of friction coefficient in magnesium alloys [17-19].
Most authors use the ring upsetting and compressions tests
for determining the coefficient of friction. It is agreed that
the friction factor increases with temperature [20]. However,
this increase of friction factor with temperature is valid until
the liquidus temperature of AZ31B (630°C) is reached where
the friction drops drastically. The values of experimental
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Proceedings of NAMRI/SME, Vol. 42, 2014
data [17] were entered to the model and then extrapolated by
tuning different runs and analyzing state variables. The
friction coefficient vs. temperature used in the FE model is
shown in Figure 2. This is based on experimental data [17]
as well as on sensitivity analysis for model calibration as
previously published by the authors [21].
Figure 2. Friction coefficient VS temperature as used in the
FE model; shown compared with experimental data [17].
The FE model was used to run FSP simulations for the
24 test cases shown in Table 2. The label shown under each
feed rate is used to refer to matrix test cases. To reduce
simulation times, only the traverse phase of the friction stir
process was considered. The temperature rise from the
skipped plunging phase was accounted for by adding a
dwelling phase of 1 second was to each simulation.
Table 2. The FEM test matrix.
Tool rotational speed, RPM
600
800
1000
1200
1400
1600
1800
2000
Feed rate
,mm/min
75
(A1)
100
(B1)
100
(C1)
150
(D1)
300
(E1)
350
(F1)
400
(G1)
500
(H1)
100
(A2)
125
(B2)
150
(C2)
250
(D2)
500
(E2)
550
(F2)
600
(G2)
700
(H2)
125
(A3)
150
(B3)
200
(C3)
350
(D3)
700
(E3)
750
(F3)
800
(G3)
900
(H3)
SIMULATION RESULTS
Thrust force and torque exerted on the FSP tool were
extracted from the simulation results of each of the test
matrix cells. The values of these variables highly depend on
the instantaneous contact area between the tool and
workpiece and thus a lot of noise is expected in their reported
values. A moving average filter was applied to the force and
torque signals to reduce the noise and to present the data in a
readable format. The dwelling section of each signal was
discarded and only the steady state traverse phase values
were considered. Figures 3 and 4 show a sample of the thrust
force and torque for test cases A2. A similar procedure was
repeated for each of the test cases of Table 2.
Figure 3. Sample of thrust force data resulting from the
FEM simulation of test case A2.
Figure 4. Sample of the torque data resulting from the FEM
simulation of test case A2.
Figures 5a and 5b show a summary of the resulting thrust
force and torque for the test cases of Table 2. It can be
noticed that the thrust force and torque had opposite trends
with increasing tool rotational speed. The thrust force
increased while the torque decreased as the tool rotational
speed increased. The decrease of the thrust force can be
justified by material softening due to the increase in process
temperature whereas the increase in torque could be due to
the extra sticking caused by the increased temperature.
0
0.1
0.2
0.3
0.4
200 400 600 800 1000
Friction Coefficient
Temperature (K)
Friction coefficient variation
Experimental data [17]
As used in FE model
0
4
8
12
16
20
04812 16
Thrust force, kN
Time, sec
Raw data
Resampled and averaged data
0
10
20
30
40
0 4 8 12 16
Torque, Nm
Time, sec
Raw data
Resampled and averaged data
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Proceedings of NAMRI/SME, Vol. 42, 2014
(a)
(b)
Figure 5. FEM simulations of the (a) Thrust force and (b)
Torque of the 24 test cases of Table 2.
PROPOSED CORRELATION EQUATIONS
The steady state thrust force (F) and torque (τ) of FSP
were related to the tool rotational speed (N) and feed (f)
according to a multiplicative power law which is commonly
used in machining operations:
12
nm
SV A P P  
(2)
where SV is the state variable to be related, P1 and P2
being the process parameters (speed and feed in this case),
with A, n, and m being the fit coefficients of the power law.
In this work, coefficients A, n, and m were determined
by non-linear regression fitting of the simulation results to
Equation 2 using MS Excel solver. The fit coefficients of the
thrust force power relation were 15.11, -0.329, and 0.261
with an R-squared value of 0.76 whereas the coefficients of
the torque were 144.22,
-0.465, and 0.165 with an R-squared value of 0.824.
Equations (3) and (4) describe the proposed correlations
between force and torque from one side and the feed and
speed process parameters from the other side using the power
law described by Equation (2).
0.329 0.261
15.11F N f

  
(3)
0.465 0.165
144.2 Nf


  
(4)
A comparison between the values of the thrust force and
torque obtained from the FEM results and those obtained
from Equations 3 and 4 is shown in Figure 6. It can be
noticed that the proposed mathematical relation accurately
captures the FEM predicted values.
(a)
(b)
Figure 6. Comparison between the results of the proposed
correlations and FEM simulations for (a) Thrust force and
(b) Torque of the 24 test cases of Table 2.
EXPERIMENTAL VALIDATION
The two proposed correlations were experimentally
validated by running single FSP passes for each of the cells
of the test matrix described in Table 2. The runs were
conducted on a HAAS VF6 vertical machining center retrofit
with external hardware to perform friction stir processes.
The tool and workpiece fixture had the same dimensions
of those used in the FEM simulations. Figure 7 shows two
samples of the processed test cases.
(a)
(b)
Figure 7. Friction stir processed samples; Test cases (a) A2
and (b) C2.
Force measurements were collected using the Kistler’s
type 9123C rotary 4-Component (Fx, Fy, Fz, and Torque)
dynamometer. The Kistler 5223B charge amplifier acquires
and amplifies the signal emanating from the dynamometer
which is then collected by a custom developed LabVIEW
0
3
6
9
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Thrust force, kN
0
7
14
21
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Torque, Nm
0
3
6
9
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Thrust force, kN
Obtained from FEM Calculated from Equation 3
0
7
14
21
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Torque, Nm
Obtained from FEM Calculated from Equation 4
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Proceedings of NAMRI/SME, Vol. 42, 2014
software through four analog input channels of a National
Instruments USB-6251 data acquisition card.
During the plunging phase in FSP, the rotating tool is
“plunged” into the workpiece at a constant feed rate until the
tool shoulder engages into the top surface of the workpiece.
Since the plunging speed was fixed for all the test cases, the
maximum thrust force and torque during the plunging phase
depended solely on the tool rotational speed which resulted
in similar peaks for the test cases with the same letter prefix.
Figures 8 and 9 show typical thrust force and torque
behaviors during FSP for two different tool speeds. It can be
clearly noticed from both figures that the plunging part
(initial part prior to the vertical dashed line) had the same
amplitude of forces and torques for the considered test cases.
(a)
(b)
Figure 8. Experimental thrust forces for test cases (a) A1 –
A3 and (b) H1 – H3.
(a)
(b)
Figure 9. Experimental torques for test cases (a) A1, A2,
A3 and (b) H1, H2, H3.
The traverse thrust force and torque starts from the
reached plunging values and decrease to constant steady state
values. These values depend of the feed of the considered test
case. Both steady state torques and forces increased with
increasing feed at constant tool rotational speeds due to less
material softening as feed increased (less heat is generated at
faster feeds). The steady state force and torque had opposite
trends with increasing tool rotational speed. The thrust force
increased while the torque decreased as the tool rotational
speed increased. The decrease of the thrust force can be
justified by material softening due to the increase process
temperature (as determined earlier from the FEM results)
whereas the increase in torque could be due to the extra
sticking caused by the increased temperature (which
correlates to the friction factor adopted in the FEM
simulations).
Figures 10a and 10b compare the experimental steady
state traverse thrust force and torque results of the 24 cells of
the test matrix with the results of the proposed correlations
(Equations 3 and 4).
(a)
(b)
Figure 10. Comparison of the correlations’ results and the
experimental results of (a) Thrust force and (b) Torque
Good agreements can be noted between the
experimentally determined results and the values obtained
from the proposed correlations. The percent prediction error
of the correlations which is the percentage of variation of the
correlation predictions from the experimental results was
calculated for quantitative assessment. The average,
maximum, minimum, and standard deviation of errors were
6.2%, 17.7%, 0.5%, and 5.4% for the thrust forces and 5.4%,
13.3%, <0.1%, and 3.8% for torques and which indicate good
statistical agreement.
CONCLUSION
Developed in this work are correlation equations that
capture the behavior of thrust force and torque during friction
stir processing (FSP) of AZ31B as function of the process
parameters (namely tool rotational speed and traverse feed).
The equations utilized the results of 3D FEM simulation runs
of a test matrix covering a wide range of process parameters
ranging from 600 – 2000 RPM for tool rotational speed and
75 – 90 mm/min for tool traverse feed. Experimental test
cases were used to demonstrate the validity of the proposed
correlations.
Since multiplicative power law is widely used in the
modeling of fabrication operations, the correlation equation
0
5
10
15
20
020 40 60
Thrust force, kN
Time, sec
A1
A2
A3
0
5
10
15
20
020 40 60
Thrust force, kN
Time, sec
H1
H2
H3
0
15
30
020 40 60
Torque, Nm
Time, sec
A3
A2
A1
0
15
30
020 40 60
Torque, Nm
Time, sec
H3
H2
H1
0
3
6
9
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Thrust force, kN
Calculated from Equation 3 Experimental
0
7
14
21
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3
Torque, Nm
Calculated from Equation 4 Experimental
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Proceedings of NAMRI/SME, Vol. 42, 2014
was assumed to take on this form. The resulting power
equations were shown to be capable of successfully fitting
the results of the FEM simulations with R2 values of 0.76 and
0.824 for the thrust force and torque, respectively. The better
fit coefficient of the torque could be due to the lower signal
to noise ratio when compared to the thrust force. This
variation arises from the re-meshing approximation and
frequency which is utilized quite often in the modeling of
FSP due to the severe deformation undergone by the work
material during the process.
When tested, the proposed correlations were able to
predict the experimental thrust force and torque for the 24
test cases with an average estimate error (percentage of
variation of the correlation prediction to the experimental
result) of 6.2% and 5.4% with a standard deviation of 5.4%
and 3.8%, respectively..
The thrust force and torque had opposite trends with
increasing tool rotational speed. The thrust force increased
while the torque decreased as the tool rotational speed
increased. The decrease of the thrust force can be justified by
material softening due to the increase process temperature
whereas the increase in torque could be due to the extra
sticking caused by the increased temperature.
The proposed correlations are valid for the range of
process parameters described by the test matrix and for the
geometries of the tool and workpiece adopted in the FE
model.
ACKNOLEDGEMENTS
This publication was made possible by the National
Priorities Research Program (NPRP) grant #09-611-2-236
from the Qatar National Research Fund (a member of The
Qatar Foundation). The statements made herein are solely
the responsibility of the authors. The first author gratefully
acknowledges the support of Consolidated Contractors
Company (CCC) through the CCC Doctoral Fellowship in
Manufacturing.
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