Statistical research on forming of threaded holes in thin plates

P. Krasauskas*, S. Kilikevičius**, R. Česnavičius***, R. Dundulis**** *Kaunas University of Technology, Studentų 56, 51424 Kaunas, Lithuania, E-mail: povilas.krasauskas@ktu.lt **Kaunas University of Technology, Studentų 56, 51424 Kaunas, Lithuania, E-mail: sigitas.kilikevicius@ktu.lt ***Kaunas University of Technology, Studentų 56, 51424 Kaunas, Lithuania, E-mail: ramunas.cesnavicius@ktu.lt ****Kaunas University of Technology, Studentų 56, 51424 Kaunas, Lithuania, E-mail: romualdas.dundulis@ktu.lt


Introduction
Thread machining is widely used operation in various industries; however, it is difficult to tap a hole in thinwalled 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.Scientific works on fluteless manufacturing technologies usually deal with tool wear [1][2][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.

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°, respectively.High speed steel fluteless tappers of an M6×1.0 mm and M8×1.25 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.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: -3.7 pC/N for force, -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.

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 onesin Figs.7 and 8. Spindle speeds of 2000, 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.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.

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 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 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 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 2 (Table 4).A high value of R 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 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 α = 0.05, for drilling F0.05 = 2.69 while for tapping F0.05 = 3.26.Since the calculated F value for drilling maximum force Fcalc = 62.5 >> F0.05 = 2.69, for drilling torque Fcalc = 34.2>> F0.05 = 2.69 and for tapping torque Fcalc = 29.9>> F0.05 = 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  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.
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.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.

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 2 .A good correlation between the experimental and the predicted maximum values of axial force T was observed.The regression analysis showed that the calculated F value for drilling maximum force Fcalc = 62.5 >> F0.05 = 2.69, for drilling torque Fcalc = 34.2>> F0.05 = 2.69 and for tapping torque Fcalc = 29.9>> F0.05 = 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.

Fig. 1
Fig. 1 Stages of hole and thread forming in a thin plate: ainitial contact; bformer-tip penetration into the material; cmaterial flow and hole forming; dformer withdrawal; efast travel of the tapper to the workpiece; fextrusion tapping; gtapper withdrawal
conclude that regression model Eq. (

Table 1
Mechanical material properties

Table 2
Matrix of the drilling and tapping experiments

Table 3
Drilling force and torque regression matrix and results mm Fdmax, kN Fdmax, kN Tdmax,