Study on micro-forming taps with unequal fluteless spacing

Tools with unequal fluteless spacing (UFS) feature are used to cut different materials. The UFS tool and a traditional tool differ in terms of the angle between the two cutting edges. The UFS tool experiences smaller axial and radial cutting forces than the traditional tool so cutting vibration is reduced, tool life is increased, and the surface roughness of the workpiece increases. This study uses the smaller hole diameter (D), spindle speed (N), and cutting fluid concentration (C) for the central composite design (CCD). Minitab statistical software is used for the second-order response surface modeling of the maximum thread-filling rate (f) and the minimum torque (T) for micro-forming M1.2 mm taps using UFS on AL-7075 aluminum alloy. The analysis of variance (ANOVA) results for f and T show that D and C are the important parameters that affect f, and D, N, and C significantly affect T. Compared with the predicted conditions, the errors in f and T for the experiment are 2.51% and 2.25%, respectively. This study shows that the two second-order mathematical models that are derived using CCD and the response surface method (RSM) feature good prediction accuracy.


Introduction
A tap is frequently used to generate an internal thread. Taps are used in the aerospace, machinery, electrical, electronics, and construction industries. Smart electronic products, such as mobile phones, tablet computers, or smart watches, are becoming lighter, thinner, and smaller and have multiple functions, such as networks, global positioning systems, accelerometers, and digital audio-visual leisure. There is limited internal space in smart electronic products, so specific functional components must be firmly locked in the casing, which demands a small blind internal thread (SBIT). The machining of a SBIT is often the last process in the production cycle, so if the tap breaks in the hole during tapping, the entire product is ruined. Smart electronic products use a M1.2 mm thread, which is formed using a micro-formed tap. If a micro-forming tap is used for extrusion tapping, there is no need for rotary chip breaking or chip removal, so a micro-forming tap is more efficient and has a longer service life than a traditional tap. Unlike a traditional tap, a micro-forming tap gradually squeezes the material on both sides of the ridged teeth of the micro-forming tap during the thread-forming process, so a U-shaped notch or crack is created at the top of the thread, as shown in Fig. 1. The ridges of this tooth may be in danger and can break when the part is manipulated or assembled, so the geometric dimensions of a microforming tap and its processing conditions have a significant impact on the results of micro-forming tapping. A microforming tap is extruded using the ridged teeth to form the SBIT, so it can only be used with ductile materials.
Torque is an important indicator of the quality of tapping and has a significant impact on tool wear, tool life, machining accuracy, and machined surface quality. Studies show that the torsion force due to extrusion between the ridged teeth of the tap and the workpiece is the main reason for breakage of the tap in the threaded hole. The main factors that affect torque for traditional taps are the geometry of the tap, the material for the tap, the type of material to be processed, the smaller hole diameter, tapping speed, the type and concentration of the cutting fluid, a coated surface for the tap, and the use and type of auxiliary vibration device. The geometry of the tap is the main factor that affects tapping torque, followed by the tapping speed, the smaller hole diameter, and the type and concentration of the cutting fluid. The tapping torque affects the extrusion into the material to be processed and depends on tool angle and the clearance between the tool and a hole with a smaller diameter. A micro-forming tap is designed with no chips and no flutes, so its core diameter is greater than that for a traditional tap and it better bears the torque caused from tapping.
Warrington et al. [1] showed that the factors affecting thread forming for extrusion taps are the material properties, process parameters, and tap geometry. Agapiou [2] determined the relationship between the smaller hole diameter and the thread-filling rate using the tools at different torque settings for high-speed tapping. The results show that an increase in the spindle speed (or feed rate) for the forming tap does not affect torque during tapping. Ivanov [3] studied the geometrical design of forming taps for small-diameter internal threads and used regression mathematical equations to determine the relationship between the process parameters for forming taps and the geometry of the tool to increase tool life and threading efficiency. Chowdhary et al. [4] studied the relationship between the contact area between the tool and the workpiece and proposed a mathematical model to predict the internal thread-forming force and torque during extrusion tapping and corrected the accuracy of the mathematical model using experiments. Chowdhary et al. [5] developed this mathematical model [3] to determine the effect of the elastic recovery of ductile materials on tapping quality after forming, in order to predict changes in the torsion force and the axial force during extrusion tapping. The geometrical dimensions of the tool were parameterized, and their effect on the friction force and the forming force during extrusion tapping was determined. Fromentin et al. [6] studied the surface quality characteristics of threads that are produced using traditional taps and extruded taps and showed that high strain hardening is the most important quality characteristic for tapping steel, and lubrication is the most significant influencing factor. High strain hardening of the thread surface is most affected by the thickness and hardness of the tooth surface deformation layer. Fromentin et al. [7] conducted an experimental study using C27 carbon steel with M12 taps to compare the results for a traditional tap and an extrusion tap in terms of tapping quality and precision and used two different cutting fluids to determine the effect of lubricity on the tapping quality. Stéphan et al. [8] noted that the smaller hole diameter is one of the most important influencing factors for tapping, and determined the selection conditions for tapping. The study used an ISO standard screw formula to calculate the empirical formula for the torque when the tap presses. Stéphan et al. [9] used a slip-line method to determine the pressure on the flank of the thread and described the physical displacement of the extruded material during the tapping process. Carvalho et al. [10] studied the effect of different coatings on tools, the smaller hole diameter, and feed rate on the torsion force, the axial force, the hardness, and the threadfilling rate during the formation of an extrusion thread. The experimental results show that the smaller hole diameter has the greatest effect on the torsion for extrusion tapping, and the tool coating has a lesser effect on the torsion. At high feed rates, the axial force during the formation of an extrusion thread formation decreases. For the smaller hole diameter, the axial force during the formation of an extrusion thread increases. Huang et al. [11] proposed a set of mathematical theoretical formulas to determine the maximum torque for an extrusion tap during thread forming and determined the effect of the geometry of an extrusion tap on the torque during the extrusion thread-forming process. Experiments showed that when the length of an invalid tooth increases, the maximum torque when the tapping tooth is squeezed increases. Pereira et al. [12] studied the effect of pitch and thread length for forming taps and traditional taps and showed that as the feed rate of the forming tap increases, the axial force l also increases, and its effect on the torque for the forming tap is not significant. Dias et al. [13] conducted experiments using an extruded tap with no helix angle and an outer diameter that Fig. 1 The tooth profile that is formed using a micro-forming tap is much smaller than the outer diameter of the final formed thread and showed that as the circumferential speed of the horizontal plane increases, the torsion force and the vertical axial force decrease and the profile of the thread is relatively poor. Landeta et al. [14] analyzed the wear on the threadtapping edge teeth, the torque value, and the axial-forming force for the tapping process, a metallographic study of the thread, and the effect of the coating and tool geometry on the forming tap and showed that a tool with six ridges (type 1) has better extrusion-tapping performance than a tool with five ridges (types 2 and 3). An even number of teeth concentrates the extruding during tapping, and when there are a large number of invalid teeth on the front chamfer, the torsional deformation of the workpiece is gradual and gentle, so wear resistance is greater. Oliveira et al. [15] studied the effect of feed rate, coating, and cutting edge chamfer on the torsion force and the axial force during extrusion tapping using a design of experiment and showed that the feed rate has a significant effect on the torsion force and the axial force during extrusion tapping. Monka et al. [16] studied tool breakage or failure for a forming tap by measuring the rotational angle of the tool and the tool wear. The experimental system used three different rotary angle tools for extrusion tapping with different feed rates. The feed rate and the rotational angle are the respective variables for thread length and tool life, and the tool wear model was measured for vibration to predict tool wear when the tool is squeezed and tapped. Pereira et al. [17] demonstrated the effect of cutting parameters, tool geometry, and process characteristics on torque and temperature during internal tapping. Swissi et al. [18] developed an experimental setup to determine the intrinsic properties of threads and their effect on the tapping process. Ren and Yan [19] used a quasistatic model to predict and simulate the difference in radial pitch diameter during tapping for different chamfer lengths and spindle speeds. Brandão et al. [20] reviewed the literature to demonstrate the evolution of the tapping process over the past 20 years, but the diameters that are used for forming and machining internal threads range from 3 to 10 mm. Forming taps with a thread diameter of less than 3 mm (micro-forming taps) are widely used for smart electronic products, so microforming taps are of significance to future developments.
Previous studies on forming taps are mainly based on perforation and tapping. The thickness of a case for modern smart electronic products is only about 1.5 ~ 2.0 mm, and 0.2 mm must remain intact to prevent puncturing of the case so small blind holes are used. Most systems use 4 extruded tapping blades, and the angle between each blade is 90°. This equal-spacing angle increases friction and torque for the extruded tap during tapping and creates resonance at high spindle speeds. Non-equidistant forming taps resolve the problems of equal fluteless spacing (EFS)-forming taps. Few studies concern micro-forming taps with UFS.

Design of a micro-forming tap
Micro-forming taps with EFS have spiral cutting edges (ridged teeth and arced sides), so ductile materials plastically deform without any chips, as shown in Fig. 2. At the front end of the tapping edge of a micro-forming tap with EFS, there is a taper of 10 ~ 20°. An invalid tooth is identified by the pitch. The invalid tooth range for a micro-forming tap with EFS for hole tapping is about 1 to 3 pitches. In terms of the invalid teeth on a micro-forming tap with EFS in the blind hole that is tapped in a mobile phone or tablet case, the invalid tooth range is about 1 pitch (0.25 mm).
During thread forming, each ridge tooth is a gradual forming tool. The outline of the entire internal thread is continuously generated by a row of tapping teeth in a direction into the cut material [1]. Studies on the thread-forming process for micro-forming taps with EFS show that many cracks form during thread cutting, and the shape of the thread that is formed depends on the attack angle (α 1 ) and the lobe length (L), as shown in Fig. 3 [1]. Ridges with larger angles of attack incur larger overall crack top areas and perimeters so contact areas are smaller. Reducing the attack angle increases the strength of the overall thread and reduces the severity of fatigue wear and the amount of full thread top area. The angle of attack angle affects the saturated area that is formed by the top of the thread and the size of the hole at the time of tapping. The optimal angle of attack is different for different materials. Cutting fluid is used when micro-forming taps with EFS are used to tap a blind hole to reduce the cutting torque that is generated by the friction between the cutting edge and the material during tapping. However, the cutting edge of a micro-forming tap with EFS is completely wrapped with the material to be cut, and the diameter of the micro-forming tap with EFS is small without a flute, so the pressure in the hole increases, and cutting fluid does not easily enter the hole and the cutting torque is not reduced. Unequal fluteless spacing (UFS) is used for the cutting of end mills. End mills with UFS have a smaller axial and radial cutting force than end mills with EFS, so they are used in less powerful machines and non-rigid machines, or for milling in unstable cutting conditions (such as thin-walled part processing or unstable fastening methods), for which the durability of the tool has a significant impact. In a UFS tool, the angles between the two cutting edges are not equal, so the angle of attack, the clearance angle, and the position of the ridge teeth on a micro-forming tap with UFS are changed. The change in the angle of attack, the clearance angle, and the ridge tooth position affects the tapping quality in terms of the cutting force, the cutting torque, the tooth profile, the thread-filling rate, and tool wear for a micro-forming tap with UFS. However, no studies determine the effect of micro-extrusion tapping with UFS or which UFS tools best suit different materials. This study uses D, N, and C at a lower concentration and changes the geometric shape and size of the micro-forming tap with UFS, using CCD. The experiment involves micro-extrusion tapping with UFS on AL-7075 aluminum alloy. The geometry of a micro-forming tap with EFS and a micro-forming tap with UFS is shown in Fig. 4. The space for the oil for a micro-forming tap with UFS is larger than that for a micro-forming tap with EFS, so a micro-forming tap with UFS is better lubricated and cooled than a micro-forming tap with EFS. The geometric data for the M1.2-mm micro-forming taps with UFS for this study is shown in Table 1.

Central composite design (CCD)
To determine the maximum thread-filling rate (f) and minimum tapping torque (T) for a micro-forming tap with UFS for specific processing parameters, the smaller hole diameter (D), spindle speed (N), and cutting fluid concentration (C) are the quality factors. The level of the quality factor has values of − 1, 0, and 1. Table 2 shows a comparison of the quality factor-coded variables and the natural variables. The optimal design for a micro-extrusion tapping with UFS increases the value of f and reduces the value of T. The values of f and T  affect the quality of the SBIT and the service life of the tool and the production cost. The CCD for micro-extrusion tapping with UFS uses three factors at three levels, as shown in Table 3. Numbers 1 ~ 8 are corner experimental points, nos. 9 ~ 12 are center experimental points, and nos. 13 ~ 18 are axial experimental points. To reduce the experimental error, the experiment uses a random test. The RSM uses a design of experiment and regression methods to solve a multi-factor optimization quality problem to determine the most important quality characteristic data at the least experimental cost. The RSM determines the effect of individual factors and the effect of interaction factors using a statistical system test and residual analysis to ensure the reliability and accuracy of the overall experiment. This method is widely used in industry and academia. Regression analysis is a numerical method to establish a mathematical model of a problem that is solved using statistical induction. It is used to determine the functional relationship between one or more independent variables and strain numbers using experimental values, and the least squares method is used to establish an approximate mathematical function model to determine the interaction between the quality factors and the quality characteristics. In order to accurately represent and explain the model for micro-extrusion tapping using UFS, this study uses a CCD to establish a second-order RSM polynomial function model with f and T to obtain the best quality. A combination of factor levels is used for a characteristic. The second-order polynomial function of RSM is expressed as where, y is the strain number, x i is the ith experimental parameter, 0 is the coefficient of the constant term, i is the coefficient of the ith experimental parameter, ij is the coefficient of the interaction term between the ith and jth experimental parameters, ii is the second-order term of the experimental parameter, and ε is the model error.

Experiments
This study uses a Brother S500X1 machining center for the UFS micro-extrusion tapping experiment, and an AL-7075 aluminum alloy plate of 40 mm x 40 mm x 5 mm is the workpiece. The process parameters for the tapping experiment are shown in Table 4. The torque that is generated by the UFS micro-extrusion tapping experiment is measured using a Kistler 9273 dynamometer, which measures the tapping torque that the tool exerts on the workpiece. The dynamometer outputs the torque that is generated by the micro-forming tap with UFS as an analog signal, and this is fed to a Kistler 5011 charge amplifier using an anti-interference transmission line. The Kistler 5011 charge amplifier amplifies the analog signal 50 times and uses a NI-6110S data capture card to convert the analog signal into a digital signal, which is input to a computer hard disk for data calculation and analysis. The equipment and wiring diagram that are required to measure the load signal for   Fig. 5.
All tapping experiments were conducted three times. Digital optical devices are used to capture physical images, which are then used for processing, analyzing, measuring, and deciphering information about physical objects using an image processing software. For this study, the workpiece was milled using a Brother S500X1 machining center after the UFS micro-extruded tapping experiment. After milling, the workpieces were ultrasonically cleaned, and SBIT images were captured using an optical microscope (Micro-Vu Vertex 220). The SBIT image was then binarized using an image processing software (ImageJ) and a grayscale threshold. The Renyi entropy algorithm was used to calculate the values for f after the UFS micro-extrusion tapping process [21]. The value of f is calculated as where A ET is the experimental thread area and A IT is the ideal thread area, which is calculated as 0.01974 mm 2 .

Factorial analysis
The experimental results for micro-forming taps with UFS are shown in Table 5. To determine the relationship between the parameters and the quality characteristics for microforming taps with UFS for tapping in an AL-7075 aluminum alloy, a second-order regression model was established using   Minitab software, which generates the prediction equations for the thread-filling rate (f 1 ) and the minimum torque ( T 1 ). These second-order regression models for f 1 and T 1 are expressed as where D is the smaller hole diameter (mm), N is the spindle speed (rpm), and C is the cutting fluid concentration (wt.%). Equation (3) shows that D and N are negatively correlated with f 1 , and C is positively correlated with f 1 . Equation (4) shows that as the values of D, N, and C increase, the T 1 value for a UFS micro-forming tap decreases. Therefore, increasing the values of D, N, and C reduces the value of T 1 for a UFS micro-forming tap. These results are consistent with practical experience in the industry. Table 6 shows the results for the analysis of variance (ANOVA) for f 1 and T 1 . The results of the ANOVA show that the determination coefficients ( R 2 ) for f 1 and T 1 are 99.63% and 99.09%, respectively, so the two second-order models are significant. The factor confidence level is 95% so the T-value is less than T (0.05/2,7) = 2.36 and is an insignificant factor. The results in Table 6 show that D and C are the significant parameters for f 1 and that D, N, and C are the important parameters for T 1 . D has the greatest effect, C has the second greatest effect, and N has the least effect. As the value of D increases, the thread-filling rate decreases and the tapping torque decreases. In terms of the strength of a microforming tap with UFS, the D value for a micro-forming tap (3) with UFS must be sufficiently large, but the value of N has an insignificant effect on the thread-filling rate because there is a material push delay during tapping using a microforming tap with UFS. The smaller the N, the larger is the thread-filling rate, and the larger is the minimum torque. The value of C has a similar effect to the value of D. The results in Table 6 also show that the first-order interaction factor DN has a significant effect on f 1 and T 1 . However, the first-order interaction factor DC has a significant effect on T 1 . Table 7 shows a comparison of the experimental values and prediction data (in Eqs. (3) and (4)) for the f 1 and T 1 . The respective errors (%) in f 1 and T 1 are less than 1.0% and 5.0%, so the two second-order models are satisfactory.

Optimization analysis
Machining quality affects the manufacturer's cost and reputation and the service life of the product. The geometric parameters for micro-forming tap with UFS for f 1 and T 1 are optimized using the two second-order models that are established. In terms of the minimum torque for a micro-forming tap with UFS, the thread-filling rate is easily calculated to ensure optimal machining quality for a lower torque. The process parameter (D) and the tapping parameters (N and C), as shown in Table 4, are used to optimize the thread-filling rate. However, the optimal solution must allow the limiting condition for the objective function, which is expressed as where T 2s is the optimal solution for the minimum torque, f 2s is the optimal solution for the thread-filling rate, and E f 2s is the expected value for f 2s , which is 85%. According to Eq. (5), the optimized thread-filling rate ( f 2s ) must be less than or equal to 85%. The coded variables for the optimal solution that is obtained using Minitab software are shown in Table 8. The code value for D is 0.59 (1.09 mm). The greater the value of D, the smaller is the contact surface (or friction force) between the tool and the workpiece, so the smaller the contact surface between the tool and workpiece, the smaller is the tapping torque and the greater is the thread-filling rate. The code value of N is − 1.0 (1000 rpm). Reducing the spindle speed reduces the friction force between the tool and the workpiece, so the tool is not damaged by overheating. The material-pushing delay during tapping is also significant so the value of f 1 increases. However, the value of T 1 increases as the spindle speed decreases. If the code value of C is 0.23 (19 wt.%), T 1 decreases, but the value of f 1 (T-value) decreases more slowly, as shown in Table 6.
In order to confirm the accuracy of the prediction model, the optimal solution is experimentally tested. The error between (5) Objective function ∶ MinT 2s Limiting condition ∶ E f 2s − f 2s ≤ 0 the predicted and measured values for the thread-filling rate (f 2S ) and the minimum torque (T 2S ) is shown in Table 9. The results in Table 9 show that the measured results for the optimal solution are 87.13% and 20.46 N-mm for f 2S and T 2S , respectively. Compared to the predicted condition, the error results for the measurements for thread-filling rate and minimum torque are 2.51% and 2.25%, respectively. The prediction models are shown to be valid. The modeling results agree with practical experience in the industry.
To determine the difference in the tool parameters for micro-forming taps with EFS and UFS (Table 1) under the optimal tapping conditions, the experimental values for f 2s and T 2s are compared, as shown in Table 10. The experimental results in Table 10 show that the UFS micro-forming tap shows an increase of 0.80% for f 2s and a decrease of 17.10% for T 2s , compared with an EFS micro-forming tap.

Conclusions
SBIT is used by manufacturers of smart electronic products. A micro-forming tap with EFS is used for SBIT tapping, but fractures are possible and costs are high. A central composite design (CCD) with RSM is an experimental approach for solving exactly constrained optimization problems. The optimization of tapping parameters (D, N, and C) for UFS micro-forming tapping of AL-7075 aluminum alloy uses the Minitab software. The results allow the following conclusions to be drawn: 1. The results of the ANOVA show that the coefficients of determination (R 2 ) for f 1 and T 1 are 99.63% and 99.09%, respectively, so the two second-order models are significant. However, D and C are significant parameters for f 1 , and D, N, and C are important parameters for T 1 . 2. The measured results allow better control of the quality error than the prediction results. The error in f 1 and T 1 has a maximum value of about 2.51% and 2.25%, respectively. CCD, RSM, and Minitab software are used to optimize the tapping of an AL-7075 aluminum alloy with a UFS micro-forming tap to obtain reliable results for f 1 and T 1 .