Statistical research on forming of threaded holes in thin plates.
Krasauskas, P. ; Kilikevicius, S. ; Cesnavicius, R. 等
1. Introduction
Thread machining is widely used operation in various industries;
however, it is difficult to tap a hole in thin-walled parts due to the
insufficient thickness. Therefore, an additional insert welding
operation is required to increase the overall thickness of the wall. In
order to avoid this problem, friction drilling along with fluteless
tapping can be used. These methods allow to produce threaded holes in
thin plates by using special tungsten carbide and HSS tools without
cutting edges. Applying this technique, the drilling tool penetrates the
material making a hole and simultaneously forming an additional molten
flange on the underneath side of the workpiece, which later is tapped
using a special tapper. The main stages of forming steps of threaded
holes are shown in Fig. 1.
[FIGURE 1 OMITTED]
Scientific works on fluteless manufacturing technologies usually
deal with tool wear [1-3], the surface quality of produced holes [4, 5]
and experimental investigations on the drilling force and moment [6, 7].
Paper [8] investigates the effect of fluteless tapping parameters on the
responses: torque, hardness, fill rate, and thrust force of the form
tapping process.
However, the fluteless tapping process of holes produced by
friction drilling was not widely studied and the influence of machining
data on the forces and moments which occurs during the process of
drilling and tapping is not yet completely investigated.
This paper presents an investigation of the influence of machining
data and workpiece thickness on the force and moment of drilling and
tapping during friction forming of threaded holes in thin plates along
with a multivariable linear regression analysis of the results. A proper
adjustment of machining data leads to an increase of forming performance
and decrease of tool wear.
2. Experimental technique of the extrusion drilling and tapping
The research on the force and moment during drilling and tapping in
thin plates was carried out using DC-01 steel sheets with 1.0 mm and 1.5
in thickness. The mechanical properties of the material are presented in
Table 1.
The experimental setup is shown in Fig. 2. The experiments were
carried out on a CNC milling machine "DECKEL MAHO DMU-35M" 1
with a "Sinumerik 810D/840D" controller and
"ShopMill" software using tungsten carbide fluteless drills
with diameters of 5.4 mm and 7.3 mm. The friction contact area ratio
(FCAR) and the friction angle the of the drills were 75% and
33[degrees], respectively. High speed steel fluteless tappers of an M6 x
1.0 mm and M8 x 1.25 mm were used for tapping. It should be noted that
the cross-sections of the working sections of the both tools are
polygonal shaped, in order to ensure better metal flow during the hole
forming and tapping.
[FIGURE 2 OMITTED]
The axial force and torque were measured using a universal
laboratory charge amplifier Kistler type 5018A 2 and a press force
sensor Kistler type 9345B 3 mounted on the CNC table. Measuring ranges
of the sensor: -10 ... 10 kN for force, -25 ... 25 Nm for torque;
sensitivity: [approximately equal to]-3.7 pC/N for force, [approximately
equal to]-200 pC/Nm for torque. The amplifier converts the charge signal
from the piezoelectric pressure sensor into a proportional output
voltage. The variation of the axial drilling force and torque was
recorded to a computer 4 using a "PICOSCOPE 4424" oscilloscope
5 and "PicoScope 6" software.
The holes with 5.4 and 7.3 mm in diameter were formed in the sheets
for further tapping of M6 and M8 threads.
3. Results and discussion of the experimental investigation
The results of the investigation of holes forming under different
spindle speed and feed are presented in Figs. 3 - 6, of thread tapping
ones - in Figs. 7 and 8.
[FIGURE 3 OMITTED]
Spindle speeds of 2000, 2500 and 3000 rpm were used and for each of
them three tool feed rates of 60, 100 and 140 mm/min were assigned in
order to investigate the influence of these parameters on the axial hole
forming and tapping forces as well as the torque along with a
statistical prediction.
The matrix of the drilling and tapping experiments is presented in
Table 2.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The experiment showed that the tool rotational speed has a
significant influence on the axial force and torque variation. An
analysis of the experimental results showed that the axial force, during
the drilling process (from the initial contact until the end of the hole
forming), varies in a very wide range. The axial force reaches its
maximum value when the conical part of the tool fully penetrates into
the plate. When the sheet is pierced, the axial force drastically
decreases, meanwhile the torsion moment increases. The maximum torque is
reached when the conical part of the tool is fully penetrated into the
plate.
The experimental results enabled to conclude that the optimal
machining data are spindle speed 2500-3000 rpm and forming feed rate 100
mm/min.
It was observed that the tapping force values are very low (less
than 90 N), therefore these results were not presented and discussed.
The negative torque values during tapper withdrawal in Fig. 7 and 8 are
not presented, because they are very low compared to the tapping torque.
When the spindle speed is 2000 rpm, the maximum torque is obtained
between 1 and 2 s, after that it gradually decreases. The tapping torque
was several times higher than the drilling torque.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
4. Multivariable linear regression analysis
The multivariable regression analysis was carried out in order to
identify the influence of the drilling and tapping machining data on the
maximum axial force [F.sub.dmax], maximum drilling and tapping torques
[T.sub.dmax], [T.sub.tmax].
Experimental matrix, on which base regression analysis was
performed, are presented in Tables 3 and 4.
It was assumed that the intervals of factors variation are tenuous,
iterations can be limited by linear approximation
Y = [a.sub.0] + [a.sub.1] [X.sub.1] + [a.sub.2] [X.sub.2] +
[a.sub.3] [X.sub.3] + ... + [a.sub.n] [X.sub.n], (1)
where [a.sub.0], [a.sub.1], [a.sub.2], [a.sub.3], ... , [a.sub.n]
are unknown parameters of the model (regression coefficients); n = 1, 2,
3, ... ,i are the factors of influence; [X.sub.1], [X.sub.2], [X.sub.3],
..., [X.sub.I] are independent variables.
Referring to this, a regression analysis was performed making
presumption that the drilling force and the torque are stipulated as the
entirety of drilling machining data, i.e. spindle rotational speed S,
feed rate F, tool diameter D and sheet thickness t and could be
expressed by a four variable regression model for [F.sub.dmax],
[T.sub.dmax] and [T.sub.tmax] respectively.
The summary output, analysis of variance, parameter values and
comparative four variable linear regression analysis for maximal axial
drilling force and torque and tapping torque are presented in Tables 5
and 6.
The regression model adequacy was evaluated taking into account the
value of the correlation coefficient [R.sup.2] (Table 4). A high value
of [R.sup.2] indicates that the obtained model adequately explains the
variation of the forming parameters.
As it is seen from Table 4, a good correlation between the
experimental and the predicted values of [F.sub.dmax], [T.sub.dmax] and
[T.sub.tmax] was observed. The analysis showed that the four variable
linear regression model with 89% confidence for [F.sub.dmax], 82%
confidence for [T.sub.dmax], and 92 % confidence for [T.sub.tmax]
adequately evaluates the magnitude of the forming parameters.
The results of the model validation are presented in Table 5.
The model significance was evaluated using the Fisher's
statistical method. From the F-criteria tables [9], under the confidence
interval [alpha] = 0.05, for drilling [F.sub.0.05] = 2.69 while for
tapping [F.sub.0.05] = 3.26. Since the calculated F value for drilling
maximum force Fcaic = 62.5 >> [F.sub.0.05] = 2.69, for drilling
torque [F.sub.calc] = 34.2 >> [F.sub.0.05] = 2.69 and for tapping
torque [F.sub.calc] = 29.9 >> [F.sub.0.05] = 3.26, the model can
be considered as significant and can be used for estimation of the axial
force and torque.
The coincidence of the experimental and calculated [F.sub.dmax] and
[T.sub.dmax] values enabled to conclude that regression model Eq. (1)
could be used to optimise friction drilling process for wide spectrum of
the structural materials.
The significance of the regression analysis factors was estimated
by normalising the factors using these expressions of normalised
parameters.
[X.sub.in] = 2([X.sub.i] - [X.sub.i0])/([X.sub.imax] +
[X.sub.imin]) and [X.sub.i0] = ([X.sub.imax] - [X.sub.imin]/2, (2)
where i is the number of factor X; n is the row number for the each
X factor in the column.
The normalised regression coefficients (Table 7) showed that the
thickness of the workpiece and the diameter of the tool have the highest
influence on the axial drilling force; the tool diameter and the feed
rate have the highest influence on the drilling torque, while the sheet
thickness has the highest influence on the tapping torque.
[FIGURE 9 OMITTED]
The regression analysis of thread forming has showed that the feed
rate during thread tapping has no influence, because the regression
coefficient of this variable is 0 (Table 4). It means that the influence
of the tapping parameters on the tapping torque can be approximated by
the three variable regression model. The latter model was also verified
and the regression statistics as well as the coefficients of the
regression model were obtained the same as in the four variables
regression.
4. Conclusions
An experimental analysis along with a multifactor regression
analysis of holes and threads forming in thin plates were carried out
and the axial force and torque variations were measured under different
hole forming and tapping parameters.
The regression model adequacy was evaluated taking into account the
value of the correlation coefficient [R.sup.2]. A good correlation
between the experimental and the predicted maximum values of axial force
[F.sub.dmax], drilling torque [T.sub.dmax] and tapping torque
[T.sub.tmax] was observed.
The regression analysis showed that the calculated F value for
drilling maximum force [F.sub.calc] = 62.5 >> [F.sub.0.05] = 2.69,
for drilling torque [F.sub.calc] = 34.2 >> [F.sub.0.05] = 2.69 and
for tapping torque [F.sub.calc] = 29.9 >> [F.sub.0.05] = 3.26, the
model can be considered as significant and can be used for estimation of
the axial force and torque.
The normalised regression coefficients showed that the thickness of
the workpiece and the diameter of the tool have the highest significance
on the axial drilling force; the most significant drilling parameter on
the drilling torque is the tool diameter and feed rate, while the
highest influence on tapping torque has the sheet thickness.
The research allows to predict optimal parameters for holes and
treads forming in thin plates in order to optimise the drilling and
tapping force along with the torque and, as a consequence, to decrease
tool wear and extend the lifetime of the tools.
References
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Received April 20, 2016
Accepted May 31, 2016
P. Krasauskas *, S. Kilikevicius **, R. Cesnavicius ***, R.
Dundulis ****
* Kaunas University of Technology, Studenty 56, 51424 Kaunas,
Lithuania, E-mail: povilas.krasauskas@ktu.lt
** Kaunas University of Technology, Studenty 56, 51424 Kaunas,
Lithuania, E-mail: sigitas.kilikevicius@ktu.lt
*** Kaunas University of Technology, Studenty 56, 51424 Kaunas,
Lithuania, E- mail: ramunas.cesnavicius@ktu.lt
**** Kaunas University of Technology, Studenty 56, 51424 Kaunas,
Lithuania, E- mail: romualdas.dundulis@ktu.lt
[cross.sup.ref] http://dx.doi.Org/10.5755/j01.mech.22.3.15263
Table 1
Mechanical material properties
Material Tensile Tensile Elongation Modulus of
strength, strength, at break, elasticity,
ultimate, yield, % GPa
MPa MPa
DC-01 280 160 28 201
(1.0330)
Table 2
Matrix of the drilling and tapping experiments
Drilling Tapping
Material Hole Plate Spindle Feed Spindle Feed
diameter, thickness, speed, rate, speed, rate,
mm mm rpm mm/ rpm mm/
min rev
Steel M06-5.4 1.0 2000 60 100 1.0
DC-01 1.5 2500 100 200
M08-7.3 1.0 3000 140 300 1.25
1.5
Table 3
Drilling force and torque regression matrix and results
S, rpm F, D, t, [F.sub.dmax],
mm/min mm mm kN
[X.sub.1] [X.sub.2] [X.sub.3] [X.sub.4] [Y.sub.exp]
2000 140 5.4 1.0 0.88
100 0.84
60 0.77
2500 140 5.4 1.0 0.82
100 0.69
60 0.75
3000 140 5.4 1.0 0.80
100 0.75
60 0.65
2000 140 5.4 1.5 1.06
100 1.21
60 1.09
2500 140 5.4 1.5 1.25
100 1.08
60 0.96
3000 140 5.4 1.5 1.33
100 1.07
60 0.97
2000 140 7.3 1.0 0.92
100 0.89
60 0.85
2500 140 7.3 1.0 0.89
100 0.67
60 0.74
3000 140 7.3 1.0 0.86
100 0.82
60 0.74
2000 140 7.3 1.5 1.46
100 1.32
60 1.24
2500 140 7.3 1.5 1.42
100 1.54
60 1.33
140 7.3 1.5 1.35
3000 100 1.29
60 1.26
S, rpm F, [F.sub.dmax], [T.sub.dmax], [T.sub.dmax],
mm/min kN Nm Nm
[X.sub.1] [X.sub.2] [Y.sub.calc] [Y.sub.exp] [Y.sub.calc]
2000 140 0.82 2.40 2.58
100 0.75 1.99 2.25
60 0.68 1.86 1.92
2500 140 0.79 1.72 2.17
100 0.73 1.63 1.83
60 0.66 1.68 1.51
3000 140 0.77 1.63 1.74
100 0.70 1.40 1.42
60 0.63 1.24 1.09
2000 140 1.26 3.94 3.05
100 1.19 2.72 2.72
60 1.12 2.62 2.39
2500 140 1.24 2.55 2.63
100 1.16 2.20 2.30
60 1.09 1.81 1.97
3000 140 1.21 2.28 2.21
100 1.14 1.94 1.88
60 1.07 1.74 1.55
2000 140 0.97 2.96 2.92
100 0.90 2.75 2.59
60 0.83 2.30 2.27
2500 140 0.94 2.60 2.50
100 0.87 2.25 2.17
60 0.80 1.91 1.85
3000 140 0.92 2.28 2.08
100 0.85 1.88 1.75
60 0.77 1.72 1.43
2000 140 1.41 3.83 3.39
100 1.33 2.63 3.60
60 1.26 2.68 2.73
2500 140 1.38 2.55 2.96
100 1.30 2.58 2.64
60 1.24 2.01 2.31
140 1.35 2.54 2.55
3000 100 1.28 2.19 2.22
60 1.21 1.78 1.89
Table 4
Thread tapping experiment matrix and regression results
S, rpm F, D, t,
mm/min mm mm
[X.sub.1] [X.sub.2] [X.sub.3] [X.sub.4]
200 1.0 6 1.0
250 1.0 6 1.0
300 1.0 6 1.0
200 1.25 8 1.0
250 1.25 8 1.0
300 1.25 8 1.0
200 1.0 6 1.5
250 1.0 6 1.5
300 1.0 6 1.5
200 1.25 8 1.5
250 1.25 8 1.5
300 1.25 8 1.5
S, rpm [T.sub.tmax], [T.sub.tmax],
Nm Nm
[X.sub.1] [Y.sub.exp] [Y.sub.calc]
200 2.13 3.08
250 3.4 2.84
300 3.12 2.60
200 8.41 8.82
250 9.57 8.58
300 8.89 8.34
200 4.65 4.39
250 4.51 4.15
300 4.41 3.91
200 10.82 10.13
250 11.31 9.89
300 7.66 9.65
Table 5
Regression Statistics
Regression data [F.sub.dmax] [T.sub.dmax] [T.sub.tmax]
Multiple R 0.94 0.90 0.96
R Square 0.89 0.82 0.92
Adjusted R Square 0.88 0.79 0.76
Standard Error 0.09 0.27 1.08
Observations 36 36 12
Table 6
Analysis of variance (ANOVA)
df
[F.sub.dmax] [T.sub.dmax] [T.sub.tmax]
Regression 4 4 4
Residual 31 31 8
Total 35 35 12
F 62.5 34.2 29.9
Table 7
Normalised regression coefficients
Regression coefficients
[F.sub.dmax] [T.sub.dmax] [T.sub.tmax]
Intercept -0.296 1.41 -12.3
Variable [X.sub.1] -0.131 -2.09 -1.21
Variable [X.sub.2] 0.177 0.82 0
Variable [X.sub.3] 0.486 1.12 20.9
Variable [X.sub.4] 1.096 0.22 3.27
