Optimization of the functional geometry of cutting tools using the finite element method (FEM) to reduce vibrations in steel machining

Abstract

The research presented in this paper analyses the numerical simulation using the Finite Element Method (FEM) to study the vibration and performance of cutting tools during steel turning. The main objective is to optimize the functional geometry of the tools in order to reduce vibrations affecting the quality of the machined surfaces and the tool life. The FEM model was applied to carry out static, modal and harmonic analyses which allowed determining the eigenmodes (natural modes of vibration) and critical frequencies. The modeling was performed using a 42CrMo4 steel which is widely used for the manufacturing of bearing retaining parts, high strength parts in compressors, turbines, working parts of heavy machinery for surface and underground operations, as well as parts of agricultural machinery. Research has shown that the functional geometry of the tools and their construction are critical factors greatly influencing vibration parameters. This paper presents three types of cutting tools: a classical one (T01) and two improved ones (T02 and T03) with integrated spring washers that allow obtaining an optimal functional geometry. The conclusions emphasize that the FEM method is an effective tool for the dynamic analysis of cutting tools, and highlight the fact that tools which allow obtaining an optimal functional geometry offer better stability in terms of vibration, especially when machining steels with high mechanical properties.

Keywords

Vibration control numerical simulation finite element method steel turning

1. Introduction

The Finite Element Method (FEM) is a powerful numerical technique used to model the dynamic behavior of complex mechanical systems, including cutting tools (Davim, 2011). It allows a complex model to be divided into simpler elements, which are analyzed separately in order to determine the global response of the system (Cheng and Liu, 2017).

Previous studies (Siddhpura and Paurobally, 2012; Zatarain et al., 2018) demonstrated that vibrations in turning negatively affect the quality of the machined surface, the tool life, and the efficiency of the process. Numerous FEM models have been proposed in literature (Shuvam et al., 2019; Yan et al., 2024), with the purpose of analyzing cutting tool vibrations. In general, these models include:

• The studies focused on developing a model consisting of a tool and holder, considering the geometrical effects of the tool.

• Other studies investigated the effects of the interaction forces between the cutting tool and the workpiece, for example, during high-speed turning processes.

• FEM is also used to model the entire mechanical system of the turning machine, including the holders and the workpiece, to investigate how they contribute to the amplification of vibrations.

FEM modeling is usually validated by comparing numerical results with experimental data. In numerous studies (Ho et al., 2023), accelerometers and vibration analysis techniques have been used to measure the dynamic behavior of cutting tools under real machining conditions and to verify the predictions of the FEM models.

For example, the study, Swain et al. (2020) and Airao and Nirala (2021), used a combined FEM and experimental testing approach to analyze vibrations at high cutting speeds. By comparing simulated results with experimental data, the authors demonstrated that FEM is capable of providing accurate predictions of the dynamic behavior, provided that all relevant aspects are modeled correctly, such as boundary conditions and used materials (Liu et al., 2017, 2019).

For example, the study (Ullah and Chan, 2024) showed that the tool geometry and tool holder length are critical factors directly affecting vibrations and the quality of the machined surface. The use of FEM allowed the simulation and identification of the critical tool holder length (60 mm) above which vibrations increase exponentially, affecting the surface roughness. When turning, cutting tools are subjected to self-excited and forced vibrations. Self-excited vibrations, such as chatter, are the most dangerous as they can lead to instability, but FEM can be used to predict chatter behavior (Jasiewicz and Miądlicki, 2019). Literature studies (Jabłońska and Łastowska, 2024) suggest that FEM analysis of the natural frequencies of the tools is essential to identify the critical modes of vibration. FEM models developed for cutting tools are used to determine the eigenmodes and to identify the critical frequencies where undesirable vibrations may occur. Research presents multiple approaches to FEM modeling of cutting tools. For example, in Parida and Maity K. (2019), a 3D model of a turning tool was modeled using FEM for the purpose of analyzing how the natural frequencies vary with tool geometry and material. This study showed how geometrical changes (e.g., tool bracket length) and material properties influence vibrations and natural frequencies.

Other studies, such as Iglesias et al. (2022), Duan et al. (2023), and Sun and Yan (2022) used FEM to simulate the vibrational behavior of turning tools with carbide inserts. Their model allowed the analysis of the dynamic behavior during contact with the workpiece under the influence of varying cutting forces. In recent literature (Shao et al., 2022; Aydin, 2024), FEM remains an essential tool for analyzing cutting tool vibrations during turning, especially when combined with experimental methods and advanced technologies, such as ultrasonic vibration-assisted machining and Machine Learning. Integrating these methods enables a better understanding of the factors influencing vibration and optimizes cutting parameters in order to improve machining quality and tool life (Fu et al., 2024; Yang et al., 2021).

Following the analysis of the aspects presented in literature, the main objective of the research is determined, namely the optimization of the functional geometry of cutting tools used in steel turning with the aim of reducing vibrations using the FEM. Thus, FEM is used to analyze the eigenmodes and critical frequencies of these tools, on the basis of which several constructive models, both classical and improved, are compared in order to identify solutions for vibration control. The ultimate objective is to identify optimal functional geometries that provide superior vibration performance under real-life operating conditions of cutting tools.

2. Materials and methods

2.1 Materials

An essential parameter for the FEM analysis of turning consists of the physical-mechanical properties of the materials and in particular the modulus of elasticity, Poisson’s ratio and density, all of which have an influence on the vibrational behavior. Both the properties of the material being processed and the properties of the materials of the cutting tool components were taken into consideration in the modeling, and these properties are presented in Table 1.

Table 1.

Properties of the work material and of the material of the component parts of the cutting tool (Callister and Rethwisch, 2018).

Material	Material properties
Material	Tensile strength, MPa	Modulus of elasticity, GPa	Poisson’s ratio	Brinell hardness	Density, Kg/m³
Material to be processed—42CrMo4	680–690	190–210	0.27–0.30	197–200	7510
Material of the cutting tool body—steel C45	610–630	195–205	0.27–0.29	205–207	7715
Material of the clamping screw—steel C15	330–460	190–200	0.27–0.29	130–150	7700
Material of the elastic washer—steel A2 1.4305	450–600	195–205	0.28–0.30	185–190	7900
Material of the cutting insert—PCBN	2600–2800	95–105	0.18–0.21	13–15 GPa	1445

2.2 Tools used for turning

A lathe turning tool was selected for the FEM analysis, consisting of a body with a special profile and a removable CCGT insert, PVD-coated, supplied by Seco Tools. The geometry of the insert had a rake angle γ of 8°, a clearance angle α of 6°, an entering (declination) angle χ_r of 90°, and an edge inclination angle λ of 8°. In order to assess the complexity of the longitudinal turning process, especially for workpieces made of materials with high physico-mechanical properties, the changes that may occur in the functional geometry of the tools during machining, affecting the stability and quality of the process, were taken into account. Given this context, the FEM modeling considered three constructive variants of cutting tools: T01 (classical version), T02 (improved constructive variant with one spring washer), and T03 (improved constructive variant with two spring washers), presented in Figure 1. Three cutting tools (T01, T02, T03) were selected to assess how functional geometry influences dynamic performance, and based on FEM simulations—including static, modal, and harmonic analyses—tool T03, equipped with two elastic washers, demonstrated the best results by achieving the lowest vibration amplitudes and ensuring stable behavior well outside the operational frequency range.

Figure 1.

(a) classical cutting tool (T01); (b) improved cutting tool with one spring washer (T02); (c) improved cutting tool with two spring washers (T03); 1—tool body; 2—screw; 3—turning insert; 4—spring washer.

2.3. FEM analysis

Numerical methods have been used since ancient times to compute certain geometric quantities (length and area of a circle, for example) and later to simulate various physical phenomena. Among the most commonly used numerical methods are the finite difference method, the finite element method and the boundary element method. These are connected to each other at points called nodes. The unknown function or functions, which are applicable throughout the entire domain of study, are approximated by a set of functions which are only applicable over the domain of the finite element. In the case of static analyses the loads and constraints are independent of time. For each of the three tool models, the classical tool T01 and the two optimized tools, T02 and T03, the geometrical models were created as shown in Figure 1. After importing these models, the meshing step was performed. Figure 2 shows the meshed geometric models as well as images showing that the finite element is free of any distorted elements which could cause significant errors in the analysis.

Figure 2.

The mesh used for the static as well as the modal and harmonic analyses and its quality: (a) the mesh for cutting tool T01; (b) the quality of the mesh for cutting tool T01; (c) the mesh for cutting tool T02; (d) the quality of the mesh for cutting tool T02; (e) the mesh for cutting tool T03; (f) the quality of the mesh for cutting tool T03.

For the construction of the finite element network a combination of two finite elements was used, more precisely a combination of two types of meshing, namely free and controlled. The two types of finite elements used are Solid 92, a tetrahedral element with four nodes, and Solid 45, a parallelepiped element with eight nodes. The mesh was constructed in such a way that the element side size did not exceed 1.5 mm and the transition from small to larger elements was made slowly. The materials used for the present analysis were a quality carbon steel for the tool body and the clamping screw, sintered metal carbide for the turning insert and a spring steel for the spring elements used in the construction of the two optimized tools.

2.4. Modal analysis

The modal analysis belongs to the eigenvalue-determining analyses, as does the flow analysis which determines the type of flow of a fluid, whether laminar or turbulent. This type of analysis is of particular importance because it determines the eigenmodes or natural frequencies of bodies or assemblies. For engineers, their knowledge is obviously of particular importance because vibrations are crucial in engineering.

However, knowledge of the eigenmodes or natural frequencies is not only important for mechanical engineers. Another application of the modal analysis is widely recognized in civil engineering where buildings, bridges in particular, are frequently subjected to vibratory motions. Recently, the modal analysis is also showing its importance in the field of occupational health because, just as mechanical parts have their own modes of vibration, so do the organs of the human body (heart, liver, brain). It is important that humans do not work in a vibrating environment where the frequencies come close to the natural frequencies of the human body organs. It is important to know the values of the eigenmodes in order to avoid the resonance phenomenon that occurs when the analyzed body or assembly is subjected to a load that varies sinusoidally (harmonically) with a certain amplitude and frequency close to one of the eigenmodes.

2.5. Harmonic analysis

If the modal analysis provides information regarding the frequencies at which resonance might occur, the harmonic analysis is the one that clarifies the matter. First of all, in contrast to the modal analysis, the harmonic analysis is an analysis in which both constraints (which must be the same as the ones in the modal analysis) and loads are introduced. What is specific to this type of analysis is the fact that the loads applied are no longer constant in time as in the case of static analyses, but they vary according to a sinusoidal (harmonic) law of variation. This type of analysis is necessary in all situations involving rotating bodies or assemblies, as it is known that they introduce loads which vary sinusoidally.

In the turning process, cutting forces are not perfectly constant but have variable components due to the interaction between the tool and the material. By applying the harmonic analysis, one can model how these variable forces affect the tool and can identify the frequencies at which the vibrations are amplified. For example, if the harmonic analysis indicates that for a given rotational speed a resonant frequency is present, the operator can adjust the cutting speed to avoid this frequency, thereby reducing vibration and improving the quality of the machined surface.

3. Results and discussion

3.1. Results and discussion for the static analysis

Since all three geometric models were made of several component parts, it was also necessary to create the contacts between them. A “bonded” type contact was defined between all component parts. Figures 3 –5 show the loads, constraints and results obtained from the static analysis. It is worth mentioning that, to simplify the three-dimensional modeling, the coordinate planes and, implicitly, the axes of the coordinate systems are chosen to be different from the real axes in the cutting process, as can be seen in Figures 3 –5.

Figure 3.

The loads and results obtained from the static analysis for tool T01: (a) loads and constraints; (b) Von Mises equivalent stress; (c) total nodal displacement; (d) total nodal displacement in X direction; (e) total nodal displacement in Y direction; f–total nodal displacement in Z direction.

Figure 4.

The loads and results obtained from the static analysis for tool T02: (a) loads and constraints; (b) Von Mises equivalent stress; (c) total nodal displacement; (d) total nodal displacement in X direction; (e) total nodal displacement in Y direction; f–total nodal displacement in Z direction.

Figure 5.

The loads and results obtained from the static analysis for tool T03: (a) loads and constraints; (b) Von Mises equivalent stress; (c) total nodal displacement; (d) total nodal displacement in X direction; (e) total nodal displacement in Y direction; (f) total nodal displacement in Z direction.

According to the previously presented, the constraints were applied by canceling all degrees of freedom on the clamping area of the tools in the tool holder and the loads applied were the maximum loads measured during the machining process for the alloyed steel. These loads were chosen because they are the maximum loads occurring in the cutting process. The clamping screws of the inserts were preloaded with a load of 30 N. The results were centered on determining the equivalent Von Mises stress, the resulting total displacement and the directional displacements in the X, Y, and Z axes. Table 2 summarizes the results of the static analysis for the three tools considered (T01, T02, T03).

Table 2.

Static analysis results for the three types of tools.

No.	Result type	Tool T01	Tool T02	Tool T03
1	Von Mises equivalent stress (MPa)	295.28	288.91	282
2	Total nodal displacement (mm)	0.0217	0.0354	0.0391
3	Displacement in X direction (mm)	0.0026	0.0068	0.0089
4	Displacement in Y direction (mm)	0.0164	0.0269	0.0298
5	Displacement in Z direction (mm)	0.0022	0.0035	0.0028

As can be seen from the sequence of Figures 3 –5 and the results presented in Table 2, the maximum load present in the case of the classical tool, T01, leads to the highest equivalent stress value (295.28 MPa) but it is located at the cutting insert. There is no danger from this point of view because the sintered metal carbide inserts withstand stresses of the order of GPa, depending on the type of insert. However, in the case of nodal displacements, under hypothetical static loading, the maximum nodal displacement is found for tool T03—0.0298 mm, followed by tool T02—0.0269 mm, and tool T01—0.0164 mm, respectively. This is due to the fact that in the case of a static loading, the damping effect of the elastic elements placed under the cutting insert does not take place.

It could also be observed that, in all three cases, the maximum displacement is measured in the Y direction, which is normal because the loading is also predominant in this direction.

3.2. Results and discussion for the modal analysis

From a practical point of view, running a modal analysis is not significantly different to running a static analysis, essentially performing the same steps as for the static one. Thus, the body or assembly in our case is imported and then meshed. It should be noted that in the Ansys program all the analyses were coupled so that the mesh remains the same. Since it is known that the eigenmodes or natural frequencies are not dependent on the applied loads but only on the geometrical shape of the model, its mass and the supporting method, there is no need to introduce the loads stressing the body or assembly but only the constraints. In addition to the static analysis, the density of materials was taken into account in order to calculate the mass of the parts in the assembly. Figure 6 shows the modal analysis results for tool T01.

Figure 6.

Eigenmodes and vibration tendencies for tool T01: (a) vibration mode I; (b) vibration mode II; (c) vibration mode III; (d) vibration mode IV; (e) vibration mode V; (f) vibration mode VI.

For all three types of tools the first six eigenmodes were analyzed, without limiting the maximum frequency value. Figure 7 shows a plot of the eigenmodes or natural frequencies for tool T01.

Figure 7.

Numerical values of the eigenmodes for tool T01.

In the process of identifying the eigenmodes through modal analysis, the actual magnitude of the displacement corresponding to each resonant frequency is not the primary focus. Instead, what holds greater significance is the behavior or pattern of vibration associated with each mode—commonly referred to as the vibration tendency—and the exact frequency at which that mode occurs. This information is crucial for assessing the potential risk of resonance. The precise numerical values of the displacements, which are influenced by external loads, will be computed and analyzed in detail in the subsequent section dedicated to harmonic analysis.

Figures 8 and 9 present the modal analysis results for tools T02 and T03, respectively, highlighting their eigenmodes and corresponding vibration patterns. Figures 10 and 11 present the values of the eigenmodes or natural frequencies for tools T02 and T03.

Figure 8.

Eigenmodes and vibration tendencies for tool T02: (a) vibration mode I; (b) vibration mode II; (c) vibration mode III; (d) vibration mode IV; (e) vibration mode V; (f) vibration mode VI.

Figure 9.

Eigenmodes and vibration tendencies for tool T03: (a) vibration mode I; (b) vibration mode II; (c) vibration mode III; (d) vibration mode IV; (e) vibration mode V; (f) vibration mode VI.

Figure 10.

Numerical values of the eigenmodes for tool T02.

Figure 11.

Numerical values of the eigenmodes for tool T03.

An analysis of the graphs in Figures 7, 10, and 11 clearly indicates that in all three cases the first eigenmode occurs somewhere around the value of 1470 Hz, which is well above the working frequency for turning. Similarly, since the frequency values for the eigenmodes are increasing, the remaining five eigenmodes are also beyond the working range of the turning tool. Thus, it can be stated that there is no danger of resonance in any of the models presented.

Figure 9 shows the results of the modal analysis for tool T03, considering both the eigenmodes and the vibration tendencies.

Based on the analysis of the results obtained for the three types of tools, it was found that the classical tool, T01, has the highest eigenmode values compared to the other two, followed by T02 and, of course, T03. This demonstrates the fact that introducing elastic elements under the insert increases its slenderness and thus a decrease in the frequency value is obtained. In conclusion, even if the eigenmode values decrease for tools T02 and T03 compared to the initial tool T01, the decrease is of only 5…6 Hz for the first two eigenmodes, therefore there is no danger of resonance, as the frequency value is high enough not to interfere with the working frequency range of the turning tool.

Although the modal analysis indicates that all eigenfrequencies are significantly higher than the actual operating frequency in turning—thus eliminating the risk of resonance—other factors can still affect the tool’s dynamic behavior during machining. These include variable cutting forces caused by material heterogeneity, tool wear, improper clamping, thermal expansion, and machine-tool structural flexibility. Such factors can induce forced vibrations even below the natural frequencies, leading to surface irregularities or unstable cutting conditions. Therefore, the harmonic analysis included in this study is essential, as it simulates the system’s response to sinusoidal loading and helps identify amplitude peaks that might still occur due to these external influences.

3.3. Results and discussion for the harmonic analysis

For harmonic analyses the results can be plotted in amplitude-phase or real part-imaginary part “coordinates.” In the case of this analysis the results were obtained in amplitude-phase “coordinates” as they are easier to understand. For this reason the sequence of Figures 12 –14 contains two figures for each type of result, one with the frequency measured in Hz on the abscissa and the vibration amplitude measured in mm on the ordinate, and a second with the frequency measured in Hz on the abscissa and the phase angle measured in radians on the ordinate. The analysis of the results presented in Figures 12 –14 shows that the phase angle varies over the entire range for the X and Z directions but only over range [0, +π] for the Y direction. It can also be noted that the largest amplitudes are found in the Y direction for all materials and all tool models. Resonance occurs, as mentioned earlier, where the amplitude increases asymptotically. As can be seen in all cases the first peak occurs at the first eigenfrequency in the Y direction, which is both the direction of the vibration tendency and the main loading direction.

Figure 12.

Harmonic analysis results for tool T01: (a) amplitude variation in X direction; (b) phase angle variation in X direction; (c) amplitude variation in Y direction; (d) phase angle variation in Y direction; (e) amplitude variation in Z direction; (f) phase angle variation in Z direction.

Figure 13.

Harmonic analysis results for tool T02: (a) amplitude variation in X direction; (b) phase angle variation in X direction; (c) amplitude variation in Y direction; (d) phase angle variation in Y direction; (e) amplitude variation in Z direction; (f) phase angle variation in Z direction.

Figure 14.

Harmonic analysis results for tool T03: (a) amplitude variation in X direction; (b) phase angle variation in X direction; (c) amplitude variation in Y direction; (d) phase angle variation in Y direction; (e) amplitude variation in Z direction; (f) phase angle variation in Z direction.

Thus, the obtained results are in agreement with those obtained in [24, 25], that is, it is confirmed that significant phase changes are closely related to changes in the dynamic behavior of a system and can be an early indicator of possible deterioration or instability.

Table 3 summarizes the results of all nine analyses carried out.

Table 3.

Maximum amplitude obtained in harmonic modeling.

Y Direction			X Direction			Z Direction
Tool T01	Tool T02	Tool T03	Tool T01	Tool T02	Tool T03	Tool T01	Tool T02	Tool T03
8.2957	7.2923	6.9014	1.4866	1.4293	0.7428	0.5068	0.5393	0.3821

As can be seen from the results presented in Table 3 the maximum value of the amplitude is obtained in the Y direction. This allows concluding that the amplitude in this direction depends on the properties of the processed material. For the other two directions, X and Z, it can be observed that, in addition to the peaks occurring in the vicinity of the first mode of vibration, local peaks also occur in certain situations, for example, when machining with tool T03 in the vicinity of modes 4 and 6, creating the danger of resonance there also. Local maxima also occur in the vicinity of the third eigenmode when machining with tool T02. However, it should be noted that these frequencies are around 5300 Hz for tool T02 and 8000–9000 Hz for tool T03, respectively, meaning that there is no chance of them interfering with the working regime.

Furthermore, the results presented in Table 3 show that tool T03 has the smallest amplitude values and therefore it best damps the vibrations caused by the harmonic stress. In conclusion, even though as mentioned, there is no risk of resonance because the eigenmodes are outside the working range, by extrapolating for frequencies within the working range it can be stated that the optimized tool T03 can be successfully used for steels with high mechanical properties while tool T02 can be used for steels with medium mechanical properties, both producing better results than the original tool, T01.

The optimization of tools T02 and T03 is based on modifying the functional geometry by integrating elastic elements (spring washers) beneath the cutting insert. This design change aims to improve vibration damping by allowing controlled micro-movements that absorb part of the dynamic loads during machining. The basis for this improvement stems from the hypothesis—validated through FEM analysis—that introducing compliant elements in the tool structure can reduce the amplitude of forced vibrations and enhance dynamic stability, without compromising tool stiffness under static loading. The simulation results confirm this, as tools T02 and especially T03 show lower vibration amplitudes and improved performance compared to the classical design T01.

The T03 tool demonstrated the best performance in the processing of high-strength steel, particularly in terms of vibration damping and dynamic stability. This conclusion is supported by the results of the harmonic analysis, which show that T03 recorded the lowest vibration amplitudes in all directions compared to T01 and T02. Specifically, as presented in Table 3 of the manuscript:

• In the Y direction (the main loading and vibration direction), T03 had a maximum amplitude of 6.9014 mm, compared to 7.2923 mm for T02 and 8.2957 mm for T01.

• In the X direction, T03 reached only 0.7428 mm, significantly lower than 1.4866 mm for T01.

• In the Z direction, it also had the smallest amplitude: 0.3821 mm.

These results indicate that T03 is most effective at reducing forced vibrations during cutting, which leads to better machining stability, improved surface quality, and extended tool life when working with high-strength steels. Additionally, the modal analysis confirmed that T03’s eigenfrequencies remain well above the operational frequency range, ensuring no risk of resonance. The tool’s enhanced performance is attributed to the integration of two spring washers beneath the insert, which provide superior damping compared to the other configurations.

The results of the numerical simulations confirm that optimizing the functional geometry of cutting tools—especially by incorporating elastic elements such as spring washers beneath the cutting insert—can significantly enhance their dynamic behavior. This structural improvement contributes to better vibration damping and increased stability during machining operations. Among the three tool configurations analyzed, tool T03, which includes two elastic washers, exhibited the lowest vibration amplitudes across all directions in the harmonic analysis. These findings validate the effectiveness of this design approach in reducing dynamic disturbances, particularly when machining steels with high mechanical properties.

Vibrations during turning negatively affect the machining process by causing surface roughness deterioration, dimensional inaccuracies, and chatter marks on the workpiece, while also accelerating tool wear, insert chipping, and even tool breakage due to fluctuating cutting forces and thermal stress. These effects reduce the efficiency, precision, and economic life of both the tool and the machined component.

4. Conclusions

Following the numerical simulations conducted using the finite element method for the three cutting tool models, the key findings can be summarized as follows:

• Numerical methods, particularly the finite element method (FEM), have proven to be effective for the dynamic analysis of tools utilized in metal cutting processes, delivering satisfactory results across the board;

• The static analysis, which involved applying a maximum time-independent load, indicates that all three cutting tool models exhibit excellent performance under static stress. Specifically, both the nodal displacements and the associated stresses and strains remain well within the allowable limits for the materials used.

• The modal analysis applied to the three tool models demonstrates that the eigenmode values are all outside the operational frequencies typically encountered in the turning process, which indicates that none of the tools are at risk of entering into resonance during normal machining conditions. The three tools analyzed—T01 (classical version), T02 (with one spring washer), and T03 (with two spring washers)—were selected to evaluate how changes in the functional geometry, particularly the integration of elastic elements, influence the vibrational behavior. While tool T01 serves as the baseline configuration, tools T02 and T03 represent progressively optimized designs aimed at improving dynamic stability. The comparison between these configurations reveals that the addition of elastic components slightly lowers the eigenfrequencies, but they remain safely above the working frequency range, confirming the effectiveness of the design improvements without introducing resonance risks.

• The harmonic analysis reveals some slight variations in the vibrational behavior of the three tool models. Tool T03 demonstrated superior performance when used for turning high-strength steels, while T02 showed the best results for medium or low-strength steels. Notably, both improved tool designs (T02 and T03) outperformed the original tool (T01) in terms of vibration amplitude.

These research directions aim to advance the understanding and control of tool vibrations, thereby improving the efficiency, longevity, and stability of cutting tools in industrial applications.

Footnotes

Authorship contribution

M.T.: Conceptualization, methodology, writing—review and editing, and validation. D.D.: Visualization, validation and investigation. V.O and G.G.: Methodology, data curation, validation, resources, writing—original draft, software, and formal analysis. M.T., D.D., V.O. and G.G.: Project administration and supervision.

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Dan Dobrotă

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(2024) Cutting conditions dependent adjustment of dynamic responses for slender tools in internal turning with a flexible vibration suppression device. Journal of Manufacturing Processes 113: 76–94. DOI: 10.1016/j.jmapro.2024.01.053.

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Gao

Liu

(2021) Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic. Journal of Vibration and Control 28(19–20): 2531–2543. DOI: 10.1177/10775463211014414.

23.

Zatarain

Alvarez

Gomez

(2018) FEM analysis of tool vibration reduction by optimizing cutting parameters. International Journal of Machine Tools and Manufacture 65: 50–60.