Feasibility studies for an enhanced flat bottom drill tool design considering modal and resonance us

Abstract

Keywords: Flat bottom drill; finite element methods; modal analyses; natural frequency.

Introduction

Drilling is one of the most commonly used operations for making holes for different purposes in various types of materials including metals, ceramics, composites, etc. Having a significant economic benefit in terms of rapidity, it contributes for 40–60% of the total material removal processes in industry [1]. In recent years, with the developing technology the interbedded and complex shapes of the designed components used in industrial applications

require different types of cutting tools beyond the conventional twist drills one of which is the flat bottom drills. Flat bottom drills are used in making holes on the sloped surfaces, counterboring, thin plate, pre hole of blind tapping, cross hole, eccentric hole corrections, counterboring at deep hole position, deep half circle, continuous thin plates, deep position cross hole machining as demonstrated in Figure 1. The geometry of the designed cutting tools has a supreme influence on the chip morphology, cutting forces, workpiece quality, tool and machine components life cycle.

*Corresponding author. *E-mail address: nima.zoghipour@gmail.com Published by Yıldız Technical University Press, İstanbul, Türkiye This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Figure 1. Various applications of flat bottom drills [2]. Table 1. Geometrical parameters of the designed cutting tools Tool no.

Table 2. The calculated masses of the designed flat bottom drills Tool no.

Table 3. Technical specifications of the used carbide in the manufacture cutting tools Grade Classification Co% WC incl. Density Hardness Tensile Fracture doping (g/cm3) HV30 strength Toughness (Kg/mm2) (MPa) KIC, (MPa.m1/2) DK500UF

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Figure 2. The studied geometrical parameters on the designed cutting tools. Table 4. The calculated natural frequencies in different shape modes of the designed flat bottom drills Mode no.

Table 5. The calculated total displacements in different shape modes of the designed flat bottom drills Mode no.

Undesired vibrations are the dynamical phenomenon leading to experience an unstable cutting process [3]. Lateral chatter, torsional-axial chatter and whirling are three types of vibrations that arise in drilling [4]. Chatter vibrations evolve at tight range of frequencies of the cutting tool to the close natural ones. This type of vibration is generally

Figure 3. The applied boundary conditions to the cutting tools.

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Figure 4. Modal analysis results for tool No. 1; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 6. The calculated stiffness values for different shape modes of the designed flat bottom drills

Table 7. The calculated oscillation period time for different shape modes of the designed flat bottom drills

observed with dimensional accuracy error and tool failures. However, whirling occurs at the multiples of spindle frequency and uneccentric hole shapes, dimensions are representative of this type of vibration [4].

Ema et al. [5] investigated the frequency, amplitude, initiation boundary, and measured unstable range of chatter vibration at various cutting parameters for several drills with different overhang lengths and special drills

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Figure 5. Modal analysis results for tool No. 2; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 8. ANOVA results of first mode natural frequencies Source

with different pieces of additional masses. Their experimental results showed that the vibration is a regenerative chatter, and its frequency is equal to the bending natural frequency of the drill when the drill point is supported in a machined hole. Zhai et al. [6] studied different axial rake angle and radial rake angle combination under certain load deformation using finite element analysis for plunge

milling cutters. Fujii et al. [7] studied the whirling vibrations in a workpiece with a pilot hole. In another work [8], they focused on the interactions between the effect of the drill geometry and the drill flank, in starting whirling. Tekinalp et al. [9] studied the dynamics of drill bits under different geometries, rotational speeds and boundary conditions using FEM (Finite Element Methods). Razika

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Figure 6. Modal analysis results for tool No. 3; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 8. ANOVA results of first mode natural frequencies Source

et al. [10] conducted a study of vibration and of deformation between a tool without defect and a tool with two cases of defects. These defects have a random shape (any form), and the contact length tool-work piece, is considered the length of defects as 1 mm and the height of wear has been studied for two cases: VB=0.1 and 0.2 mm. Ji et al. [11] performed a modal analysis using FEM for

optimization of layer face milling cutting tool structural and analysis of restrain vibration. Kashyzadeh et al. [12] utilized computer simulation for identifying the effect of cutting tool construction and damping material on its natural frequency. Liu et al. [13] focused on the dynamic characteristics analysis and the stiffness contribution on a face-milling tool system by using Finite Element Modal

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Figure 7. Modal analysis results for tool No. 4; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 9. ANOVA results of second mode natural frequencies Source

Analysis (FEMA). Tobias [14] investigated machine-tool dynamics. He reported that a certain type of chatter vibration which causes a relative displacement of the saddle in relation to the machine table may be observed only in certain speed ranges. Considering the executed studies on literature, the importance of identifying the dynamic characteristics of the cutting tools is undeniable in order to minimize the trail, reworks and also scraps. Furthermore, it is seen

that there is no available research paper on the newly developed cutters having different sorts of applications. Therefore, in this research it has been attempted to study various flat bottom drills’ dynamic characteristics by focusing on the cutting tool design with combination of radial and rake angle. The natural frequencies, mode shape, displacements, rigidity, stiffness, oscillation periods of the designed flat bottom drills have been studied using finite element methods.

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Figure 8. Modal analysis results for tool No. 5; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 9. ANOVA results of second mode natural frequencies Source

Modeling of the Flat Bottom Drills The designed flat bottom drills with the illustrated geometrical parameters in Table 1 have been modeled in Solidworks 2021 as depicted in Figure 2. The mass and mechanical properties of the designed carbide cutting tools are given in Table 2 and 3, respectively. Thereafter, the feasibility of the designed tools has been studied considering the resonance and modal analysis properties for an enhanced

drilling operation using Finite Element Methods. For this reason, the modal analyses of the designed flat bottom drills have been executed in Explicit solver of Abaqus 2017 program to improve cutting tool performance and capabilities, especially for vertical and inclined drilling operations of metallic materials. The tetrahedral element types were deployed for the meshing process. The element numbers for the designed tool were between 91610 and 92650. Since

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Figure 9. Modal analysis results for tool No. 6; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 10. ANOVA results of third mode natural frequencies Source

cutting tool design necessitates an understanding of the application challenges that can be experienced during the machining process, counting; setup inflexibility – critical to dimensional accuracy and finish quality of the part, in order to have an actual close condition to industrial applications, U1=U2=U3=RU1=RU3=0 boundary conditions have been applied to the shank of the flat bottom drills as tool holder assembled simulation as demonstrated in Figure 3.

Results And Discussions

Finite Element Analysis Modal analysis was carried out by considering the boundary conditions described in the previous section. The obtained analyzes outcomes for the designed cutting tools are shown from Figure 4 to Figure 12. The results of six natural frequencies, maximum total displacements,

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Figure 10. Modal analysis results for tool No. 7; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 11. ANOVA results of fourth mode natural frequencies Source

and mode shapes of the flat bottom drill tools are given in Table 4, 5, respectively. The stiffness of the system in each frequency has been calculated by the below given expressions. 

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Figure 11. Modal analysis results for tool No. 8; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 12. ANOVA results of fifth mode natural frequencies Source

where; ω, ƒ are the angular and natural frequencies for the mode shape., m, k, T and N represent the mass, stiffness, oscillation period, and rotational speed in rpm, respectively. The lowest natural frequency has been calculated as 361.20 Hz for tool number 9 at first mode. However, the highest one was for tool number 1 with 1590.20 Hz at sixth mode. It must be noted that the metallic materials are be-

ing machined using carbide tools at maximum 20000 rpm in industrial applications. Ideally, the calculated natural frequencies for the tools are higher than the industrial application conditions and also tool manufacturers’ recommendations which is an implicant of a sufficient cutting tools design considering the modal dynamic analyses and can be used with no failure or damages to the framework such as machine tools. The calculated stiffness and oscilla-

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Figure 12. Modal analysis results for tool No. 9; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. Table 13. ANOVA results of sixth mode natural frequencies Source

tion period for the mode shapes of the designed flat bottom drills are exposed in Table 4, 5, respectively. The stiffness values for each mode shape expresses the ability of the tool against elastic deformation in order to provide an accurate cut. Meanwhile, the machining power is transmitted by this property [15]. The higher value of stiffness leads the framework to lower elastic deformations or faster stop of the oscillation.

The variation of the natural frequencies for six modes of the designed flat bottom drills with radial and axial rake angles are demonstrated in Figure 13. The effects of these parameters on natural frequency are shown in Figure 14. It is seen that although small values, the natural frequencies of the cutting tool have decreased with increase in the radial rake angle for all of the shape modes. This can be attributed to the change in the cutting tool

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Figure 13. The variation of the natural frequencies with radial and axial rake angle of flat bottom drill; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes. mass and stiffness. However, no dominant trends were observed for both natural frequencies and total maximum displacements with the change in the axial rake angle of

the cutting tool. The effects of radial and axial rake angles on total maximum displacement are shown in Figure

15. In order to observe the influence of the cutting tool

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Figure 14. The variation of the natural frequencies with radial and axial rake angle of flat bottom drill; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes.

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Figure 15. The variation of the natural frequencies with radial and axial rake angle of flat bottom drill; (a) first, (b) second, (c) third, (d) fourth, (e) fifth, (f) sixth modes.. geometrical design parameters on the natural frequencies for each mode shape, analysis of variance (ANOVA) as a statistical technique has been used. Statistical significance

of the fitted model and terms was assessed by the P-values of ANOVA results. The analysis results are given in Tables 8 to 13 for six modes of natural frequencies, respective-

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Table 14. The quadratic order developed regression model for different shape modes of the designed flat bottom drills Mode No.

ly. The A and B parameters stand for the radial and axial rake angles in the tables, respectively. For all the mode shapes, the high model F-values imply that the analyzes are significant. The chances of error due to noise are less than 1%. P-values less than 0.0500 indicate model terms are significant. Values greater than 0.1000 indicate the model terms are not significant. In order to predict the natural frequencies for different shape modes of the designed flat bottom drills quadratic order regression models have been developed and illustrated in Table 14. The A, B, and R2 parameters stand for the radial, axial rake angles and model accuracy, respectively.

Conclusion

In order to achieve a comprehensive knowledge on the cutting tool dynamics, modal analyzes of flat bottom drill with various geometrical parameters have been studied using finite element methods. The obtained conclusions from the simulation are mentioned in below: • The Finite elements method analysis is a powerful and functional tool which provides the designers with realistic results for complex geometrical shapes. • Modal analysis does not have any restrictions in definition of the angular frequencies. Therefore, it can be said that it is a universal and sufficient analysis method for definition of the natural frequencies. • The result of modal analysis reveals that the calculated natural frequencies for the tools are higher than the industrial application conditions and also tool manufacturers’ recommendations. Therefore, they can be used in metallic materials material removal processes. • The natural frequencies for all the mode shapes intensify with increase in the radial rake angle. • The stiffness, maximum total displacement and oscillation period has been calculated for each mode shape of the designed flat bottom drills. • Regression models have been presented in order to predict the natural frequencies of the designed flat bottom drills with radial and axial rake angles as geometrical inputs. The accuracy of these models is higher than 93% and can be used for faster prediction.

Acknowledgements

The authors thank TÜBİTAK (The Scientific and Technological Research Council of Türkiye) for partially supporting this work under project number 118C069.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request. Author’s Contributions Nima Zoghipour: Cutting tool design, performing the finite element analysis, preparing the article. Yusuf Kaynak: Supervisor.

Conflict of Interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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