Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys
In this study, a stir tool force measuring dynamometer was designed and manufactured to be suitable for use during the process of friction stir welding. The dynamometer meets the requirements needed for actual force measurements, with error percentage values in the x-, y-, and z-axis directions of 1...
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irk-123456789-1735962020-12-13T01:26:16Z Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys Wang, H.F. Wang, J.L. Zuo, D.W. Song, W.W. Научно-технический раздел In this study, a stir tool force measuring dynamometer was designed and manufactured to be suitable for use during the process of friction stir welding. The dynamometer meets the requirements needed for actual force measurements, with error percentage values in the x-, y-, and z-axis directions of 1.1, I.3, and 1.2%, respectively, and a three-directional sensitivity range of 0.4-2.1%. At the same time, stir tool forces were measured under different process parameters using the manufactured dynamometer. The stir tool force mathematical model, to be used for friction stir welding processes, was established by function approximation and regression analysis methods. The model was set up with a significance level under 90%. Finally, a comparison between the model-calculated values and experimental values yielded a stir tool force average error of 10.4, 4.66,, and 7.11% in the x, y, and z axes direction, respectively. Therefore, calculated and experimental values are in agreement. 2017 Article Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys / H.F. Wang, J.L. Wang, D.W. Zuo, W.W. Song // Проблемы прочности. — 2017. — № 1. — С. 181-189. — Бібліогр.: 12 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173596 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Wang, H.F. Wang, J.L. Zuo, D.W. Song, W.W. Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys Проблемы прочности |
| description |
In this study, a stir tool force measuring dynamometer was designed and manufactured to be suitable for use during the process of friction stir welding. The dynamometer meets the requirements needed for actual force measurements, with error percentage values in the x-, y-, and z-axis directions of 1.1, I.3, and 1.2%, respectively, and a three-directional sensitivity range of 0.4-2.1%. At the same time, stir tool forces were measured under different process parameters using the manufactured dynamometer. The stir tool force mathematical model, to be used for friction stir welding processes, was established by function approximation and regression analysis methods. The model was set up with a significance level under 90%. Finally, a comparison between the model-calculated values and experimental values yielded a stir tool force average error of 10.4, 4.66,, and 7.11% in the x, y, and z axes direction, respectively. Therefore, calculated and experimental values are in agreement. |
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Article |
| author |
Wang, H.F. Wang, J.L. Zuo, D.W. Song, W.W. |
| author_facet |
Wang, H.F. Wang, J.L. Zuo, D.W. Song, W.W. |
| author_sort |
Wang, H.F. |
| title |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys |
| title_short |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys |
| title_full |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys |
| title_fullStr |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys |
| title_full_unstemmed |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys |
| title_sort |
application of stir tool force measuring dynamometer for friction stir welding of aluminum alloys |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2017 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/173596 |
| citation_txt |
Application of Stir Tool Force Measuring Dynamometer for Friction Stir Welding of Aluminum Alloys / H.F. Wang, J.L. Wang, D.W. Zuo, W.W. Song // Проблемы прочности. — 2017. — № 1. — С. 181-189. — Бібліогр.: 12 назв. — англ. |
| series |
Проблемы прочности |
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AT wanghf applicationofstirtoolforcemeasuringdynamometerforfrictionstirweldingofaluminumalloys AT wangjl applicationofstirtoolforcemeasuringdynamometerforfrictionstirweldingofaluminumalloys AT zuodw applicationofstirtoolforcemeasuringdynamometerforfrictionstirweldingofaluminumalloys AT songww applicationofstirtoolforcemeasuringdynamometerforfrictionstirweldingofaluminumalloys |
| first_indexed |
2025-07-15T10:20:35Z |
| last_indexed |
2025-07-15T10:20:35Z |
| _version_ |
1837707910877020160 |
| fulltext |
UDC 539.4
Application of Stir Tool Force Measuring Dynamometer for Friction Stir
Welding of Aluminum Alloys
H . F. W a n g ,ab1 J . L . W an g ,a D. W . Z uo ,b an d W . W . Songa
a College of Mechanical and Electrical Engineering, Huangshan University, Huangshan, China
b College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and
Astronautics, Nanjing, China
1 wanghnfeng@163.com
In this study, a stir tool force measuring dynamometer was designed and manufactured to be suitable
fo r use during the process o f friction stir welding. The dynamometer meets the requirements needed
fo r actual force measurements, with error percentage values in the x-, y-, and z-axis directions o f 1.1,
I.3, and 1.2%, respectively, and a three-directional sensitivity range o f 0.4-2.1%. At the same time,
stir tool forces were measured under different process parameters using the manufactured
dynamometer. The stir tool force mathematical model, to be used fo r friction stir welding processes,
was established by function approximation and regression analysis methods. The model was set up
with a significance level under 90%. Finally, a comparison between the model-calculated values and
experimental values yielded a stir tool force average error o f 10.4, 4.66,, and 7.11% in the x, y, and z
axes direction, respectively. Therefore, calculated and experimental values are in agreement.
Keywords', friction stir welding, dynam ometer, octagonal ring, stir tool force model,
regression analysis method.
In tro d u c tio n . A lthough octagonal ring dynam om eters were first used in the field of
m achine tool cutting, they w ere later w idely adopted in agricultural engineering [1-5].
Some examples o f how dynam om eters have been used in agricultural engineering include
the w ork o f X u et al. [6], w here an octagonal ring dynam om eter was used to measure
three-directional w ood cutting forces; the w ork o f K arabay [7], where an octagonal ring
m anufacturing dynam om eter was used to m easure three-directional drill forces; and the
work o f Chen et al. [8], where a double extended octagonal ring manufacturing dynamometer
was implemented to measure tractor traction. However, to the best o f the authors’ knowledge,
there are no studies, except for [9], on application o f a dynam om eter to m easuring stir tool
forces in a friction stir welding process. The stir tool forces exerted during the process o f
friction stir welding determ ine the perform ance o f the welding region; therefore, the study
o f stir tool forces is important. In this study, based on the principles o f octagonal ring
measuring forces, a dynamometer was designed specifically for stir tool force measurements
during friction stir welding. In addition, a stir tool force m odel w as established using the
dynamometer. It is expected that the data obtained can be used for subsequent finite
elem ent analysis o f friction stir welding.
1. D y nam om ete r D esign fo r F ric tio n S tir W elding. The design o f an octagonal ring
dynam om eter revolves around the ring, and so its w orking principle is the same as that o f a
cylindrical ring. However, an octagonal ring is m ore easily processed than a circular ring,
and under the same sensitivity conditions, its stiffness is higher than that o f a circular ring.
The octagonal ring w orking principle is the following: w hen a horizontal force is
applied to the circle, the ring w ill produce the m axim um strain at 45° to the vertical
direction, as shown in Fig. 1a. The strain can be represented as [10]:
s a = ± 313 E U - (1)
© H. F. WANG, J. L. WANG, D. W. ZUO, W. W. SONG, 2017
ISSN 0556-171X. Проблемы прочности, 2017, № 1 181
mailto:wanghnfeng@163.com
H. F. Wang, J. L. Wang, D. W. Zuo, and W. W. Song
Fig. 1. The circular ring force analysis [5].
where R is the average radius o f the octagonal ring, E is the elastic m odulus, b is the
octagonal ring width, and h is the thickness o f the octagonal ring.
The horizontal force can be calculated by the deform ation that takes place in A and
A ', w hich is determ ined using an attached strain gauge.
W hen a vertical force is applied to the ring, the later w ill produce the m axim um strain
along four directions (up, down, left, and right) separated by an interval o f 90°, as shown in
Fig. 1b. The strain can be represented as [10]:
£ B = 1.09
K R
Ebh 2 • (2)
Because the up and down directions are not convenient for strain gauge measurements,
the strain gauge is placed in the B and B ' positions.
The octagonal ring body is the elastic elem ent o f the dynamometer. The resistance
strain gauge is placed in such a w ay that w hen the ring ’s body undergoes some force
deformation, the strain gauge resistance w ill also change. To m easure the value o f the
octagonal ring strain and calculate the force, the data acquisition instrum ent w ill collect the
signal using an electrical bridge circuit. Fig. 2a illustrates the shape o f a single octagonal
ring w ith eight strain gauges used to m easure force in two directions. The resistance strain
gauges No. 1 to No. 4 can measure the force in the z-axis direction (F z ) as shown in Fig. 2b,
while strain gauges No. 5 to No. 8 can m easure the vertical force (Fx) as shown in Fig. 2c.
The friction stir w elding dynam om eter is com posed o f four octagonal rings, staggered
around each other, to m easure the force in three directions, as is shown in Fig. 3.
A drawing o f the dynam om eter is shown in Fig. 4.
a b c
Fig. 2. Single octagonal ring measuring force principle [4]: (a) a single octagonal ring; (b) electric
bridge circuit to measure the horizontal force; (c) electric bridge circuit to measure the vertical force.
182 ISSN 0556-171X. npodneMbi nponnocmu, 2017, № 1
Application o f Stir Tool Force Measuring Dynamometer
Fig. 3 Dynamometer gauge placement schematic.
Fig. 4. The dynamometer drawing of friction stir welding: (a) octagonal ring drawing; (b) workbench
drawing; (c) base drawing.
2. T he M easu rin g F orce Device an d I ts C a lib ra tio n . The dynam om eter dimensions
are determ ined according to the three-directional force required and the alum inum alloy
plate size needed for the friction stir w elding force m easurem ent experiment. Before
m anufacturing the dynam ometer, the octagonal ring size, precision, roughness, and position
are determ ined according to the sensitivity requirem ents. The dynam om eter is divided in
three parts: base, single octagonal ring, and workbench. The parts are connected by eight
M8 X 50 bolts. W hen the force is measured, the dynam om eter connects a TST5915
dynam ic strain testing system to computers for data acquisition, as shown in Fig. 5. The
pressure (F z ), x-axis (Fx) and y-axis (Fy) forces are calibrated by a pressure sensor on the
dynamometer.
c
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H. F. Wang, J. L. Wang, D. W. Zuo, and W. W. Song
Fig. 5. Dynamometer calibration site photo.
The m ain principle behind the octagonal ring dynam om eter’s force m easurem ent is
that it indirectly m easures the force by m easuring the m icrostrain, caused by an external
load, o f the octagonal ring. Therefore, the dynam om eter needs to be calibrated when
running an actual force m easurem ent. The force is m easured by using a calibration value
obtained from the m easured microstrain. In this study, the x-, y-, and z-axis direction forces
(Fx , F y , and F z ) are m easured using the dynamometer. In the calibration process, the
same directional forces are m easured three tim es, and the average value is the final
calibration value. The applied static load was 10, 20, 30, 35, 65, 95, or 130 kg, respectively.
The directional force calibration curves for the x -, y -, and z -axis directions are shown in
Fig. 6. For an applied load in the x-axis direction, (Fig. 6a), it can be seen that the
deform ation in the y- and z-axis directions w as small enough to be neglected. For an
applied load in the y -axis direction, (Fig. 6b), it is observed that deform ation in the x - and
z-axis directions were small enough that it could be neglected. Similarly, for an applied load
in the z -axis direction, (Fig. 6c), the deform ation in the x - and y -axis directions are small
enough to be neglected. From linear tests, the calculated error percentages o f Fx , F y , and
F z are 1.1, 1.3, and 1.2%, respectively (Table 1). The three-directional cross sensitivity
range is 0.4~2.1% (Table 2), w hich meets the dynamometer design requirements. Therefore,
the x-, y-, and z-axis direction forces (Fx
b, and c, respectively.
F y, and F z ) are calibrated according to Fig. 6a,
T a b l e 1
The Linear Test Results o f the Dynamometer
Load direction Load (kg) Testing
microstrain pe
Calibration
microstrain pe
Error (%)
x 50 30.3 30.7 1.1
y 50 10.4 10.3 1.3
z 50 40.9 41.4 1.2
T a b l e 2
Dynamometer Cross Sensitivity Test Results
Load
direction
Load
(kg)
Testing microstrain pe Average error (%)
X Y Z X Y Z
x 50 30.3 0.13 0.15 - 0.4 0.5
y 50 0.04 10.4 0.22 0.4 - 2.1
z 50 0.73 0.31 40.9 1.8 0.8 -
184 ISSN 0556-171X. npoÔMeMbi nponnocmu, 2017, № 1
Application o f Stir Tool Force Measuring Dynamometer
20-
o K m — ■“ - ! — ■ I * ■ I ■ * I ■ I " I
0 20 40 60 80 100 120 140
F> kgf
c
Fig. 6. Dynamometer calibration lines for: (a) x-axis direction, (b) ^-axis direction, and (c) z-axis
direction.
3. M a th em atic a l M odel o f th e S tir Tool F orce in a F ric tio n S tir W eld ing Process.
3.1. The Force M easurem en t E xperim ent. The four m ain process param eter for
friction stir w elding are: stir tool rotational speed (w), w elding speed (v), under press value
(A), and tilt angle (6). Generally, in the w elding process, due to the influence o f the welding
plate thickness and w elding region quality, the plate thickness attained fixed A and 6
values. In this work, four 10 m m thick 7022 alum inum alloy plates were used, keeping
A = 0.1 m m and 6 = 2.5°. The stir tool force direction used in the experim ent is shown in
Fig. 7. The results are shown in Table 3.
Fig. 7. The stir tool force direction.
ISSN 0556-171X. Проблемы прочности, 2017, № 1 185
H. F. Wang, J. L. Wang, D. W. Zuo, and W. W. Song
T a b l e 3
Test Results o f the Stir Tool Force Experiment
Test No. « , rpm v, mm/min Fx, N Fy , N Fz , N
1 300 30 8387 1062 34650
2 300 50 16060 1452 35680
3 300 100 17190 2313 36130
4 400 30 4130 905 28000
5 400 50 7242 937.7 27680
6 400 100 4401 1001 23860
7 600 30 11980 953.4 24100
8 600 50 14930 913.6 20750
9 600 100 4187 580 9252
3.2. E stab lishm ent o f the S tir Tool Force M athem atica l M odel in the Friction S tir
W elding Process. There have not been any relevant reports that deal w ith a stir tool force
m athem atical m odel for friction stir welding processes. In this study, based on the
experim ental results and a regression analysis method, a stir tool force m athem atical model
for a friction stir welding process was established. A ny function, at least in a small range,
can be approxim ated by an arbitrary polynom ial. Therefore, often in the m ore com plex
practical problem s, regardless o f the relationship betw een the dependent variable and each
independent variable, a polynom ial regression analysis is used.
Generally, in the field o f science and technology, the quadratic polynom ial
approxim ation is accurate enough [11, 12]. In this paper, the stir tool force m athem atical
m odel for the friction stir welding process o f a 10 m m thick 7022 alum inum alloy was,
2 2
Fx = ao + « 1« + # 2v + a 3®v+ a 4« + a 5v ,
• Fy = bo + &1 « + &2 V + &3 « v + ^ 4« 2 + &5 v 2 , (3)
2 2F z = Co + C1 (« + C2v+ C 3« v + C4« + C5v .
The stir tool force m athem atical m odel for the friction stir welding o f a 10 m m thick
7022 alum inium alloy, Eq. (4), was obtained by substituting onto Eq. (3) the experimental
results from Table 3, and using regression analysis,
Fx = 4 9 2 8 0 - 300.9« + 9 1 7 .2 v -0 .7 6 6 « v + 0.372« 2 - 4.455v2 ,
• F y = 4 4 5 7 -1 9 .1 3 « + 36 .42v- 0.067«v+ 0.023« 2 - 0.029v2 , (4)
F z = 6 5 1 1 0 - 161.6« + 368 .9v- 0 .766«v+ 0.165« 2 - 0.926v2.
To test the regression effect o f Eq. (4), two aspects o f Eq. (4) should be analyzed: one
is the overall effectiveness o f the regression equation, and the second is the effect o f each
independent variable on the effectiveness o f the regression.
First o f all, Eq. (5) is used to solve for the R SS and E SS values,
TSS = 2 (7 ; - 7 ) 2 + 2 ( 7 ; - Y )2 = R S S + E S S , (5)
186 ISSN 0556-171X. npoôëeMbi npounocmu, 2017, N2 1
Application o f Stir Tool Force Measuring Dynamometer
where TSS is the total sum o f deviation square, R S S = 2 (Y; — Yi ) 2 is the residual sum o f
squares, and E S S = 2 (Y ; — Yi )2 is the regression sum o f squares.
Because E SS is the regression sum o f squares o f the five independent variables, it has
5 degrees o f freedom, while the R SS degrees o f freedom is calculated using (n — 1)— 5 =
= n — 6. In this test, n = 9, so RSS has 3 degrees o f freedom.
U sing m athem atical statistics formulas, the F -test value is obtained using the
following calculation:
= E S S / 5
= R S S / 3. (6)
The F a (5 3) value is obtained from a look-up table, and then the validity o f the
regression equation can be assessed.
A ccording to Eqs. (5) and (6), the relevant variance analysis o f Eq. (4) is listed in
Table 4.
T a b l e 4
Analysis o f Variance
Eq. Source
of variance
The sum
of deviation
square
Degree of
freedom
Variance F F0.1,(5,3) Significant
Fx ESS 2.23-108 5 4.46-107 34.30 5.31 *
RSS 4.00-106 3 1.30 -106
TSS 2.27-108 8
Fy ESS 1.69-106 5 3.38-105 6.26 5.31 *
RSS 1.62-105 3 5.40-104
TSS 1.85 -106 6
Fz ESS 6.03-108 5 1.21-108 1480 5.31 *
RSS 2.45 -105 3 8.17-104
TSS 6.03-108 8
In Eq. (4), for the analysis o f linear regression equation, a = 0.1. In Table 4, three
force linear equations were established under a 90% significance level.
A n effectiveness analysis is perform ed for each independent variable w ith a t -test,
w ith the variable t i being the calculated value for each independent variable.
The t-test quation is
f P t
f i J R / S p f ’ (7)
where f is the RSS degrees o f freedom ( f = 3) and p i is the partial regression sum o f
squares. In a linear regression, p i is an independent variable o f the partial regression sum
o f squares that is used to get rid o f the independent variables in the regression equation, and
to reduce the regression sum o f squares o f the values. In other words, it does not contain
the independent variable o f the regression equation. W hen independent variables are added,
ISSN 0556-171X. npoôëeMbi 2017, N2 1 187
H. F. Wang, J. L. Wang, D. W. Zuo, and W. W. Song
the regression sum o f squares increases. The p t term reflects the im portance o f the
independent variables in the regression equation. Each variable o f the partial regression sum
o f squares and t values is listed in Table 5.
From Table 5, it can be seen that for each o f the three regression equations, one for
each o f the direction forces, the independent variables had t > 1, except the F y equation,
w hich had t v < 1. For the Fx equation, each independent variable’s im pact on Fx should
not be neglected, w ith m2 being m ore im portant on F x than other independent variables
because it had a greater effect on F x than the other variables, while v 2 had the least
impact. A lthough t v < 1 for F y shows that the v variable had the least im pact on F y , it
cannot be ignored, as it w as observed that the value o f mv is m ore im portant for F y than
all the other independent variables. In the F z equation, the influence o f each independent
variable on F z cannot be ignored, w ith v 2 having the strongest effect, while m and v
have the low est t values.
T a b l e 5
The Independent Variable o f the Partial Regression Sum of Squares and t Values
Eq. Pœ Pv Pœv Pœ2 P 2v
Fx 8.1 -107 7.6-107 7.2-107 1.03-108 3.80-107
Fy 9.0-104 5.0-104 5.3-105 1.20-105 1.00-105
Fz 2.7-107 2.7-107 9.0-107 2.20-107 3.06-108
Eq. tœ tv 1œv 1 2 œ2 lv 2
Fx 7.89 7.650 7.44 8.90 5.41
Fy 1.29 0.964 3.14 1.49 1.36
Fz 18.00 18.000 33.20 16.40 61.20
In order to validate the correctness o f the model, the m odel-based predictions and
experim ental values are listed in Table 6, w here it can be seen that the stir tool force
average error in the x-, y-, and z-axis directions w as 10.4, 4.66, and 7.11%, respectively.
This im plies that the values predicted by the established m odel coincide well w ith the
experim ental values, dem onstrating the m odel accuracy. These results grant the model
feasibility for subsequent friction stir welding finite elem ent analysis.
T a b l e 6
Comparison of Model Predictions and Experimental Values
No. The process
parameters
Fx > N Fy , N Fz ,N
œ v jztheor
Fx F<xp Error
(%)
rptheor
Fy
FeXP
Fy Error
(%)
theor
Fz FzexP Error
(%)
1 500 30 3847 3541 8.64 703.5 740.2 4.96 24300 21679 12.1
2 500 40 6070 6828 11.1 712.4 752.3 5.30 23510 22176 6.02
3 500 60 7844 7516 4.36 712.8 738.1 3.43 21380 19872 7.59
4 500 80 6054 7345 17.6 690 725.8 4.93 18500 19021 2.74
Average error (%) 10.4 4.66 7.11
188 ISSN 0556-171X. npoôëeubi 2017, N2 1
Application o f Stir Tool Force Measuring Dynamometer
C o n c l u s i o n s
1. A dynam om eter suitable for friction stir welding w as designed and m anufactured.
The dynamometer was calibrated, and the calibration results show that the error percentages
for Fx , F y , and F z are 1.1, 1.3, and 1.2%, respectively. The three-directional cross
sensitivity range is 0.4~2.1%.
2. A m athem atical m odel for the stir tool force exerted in friction stir welding
processes was established.
3. For each axis direction, the m odel error betw een the predicted and experimental
values fall w ithin 18%, w hich suggests that the established stir tool force m odel is
applicable for the available friction stir welding equipm ent and technique. The predicted
stir tool force theoretical value is reliable and provides the guaranteed accuracy for the
finite elem ent analysis o f friction stir welding.
Acknow ledgm ents. This study is supported by the National Natural Science Foundation
o f China (Grantes Nos. 51175255 and 51305199); the Excellent young talents fund key
project o f the A nhui H igher Education Institutions o f China (Grant No. 2013SQRL089ZD);
and the Starting Foundation for Talents from H uangshan University o f China (Grant No.
2013xkjq003).
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