# Experimental Research on the Dynamic Stability of Internal Turning Tools for Long Overhangs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/D

^{4}) represents the tool’s slenderness coefficient (TSC) [16,17].

## 2. Materials and Methods

_{p}= 0.1 mm, feed f = 0.14 mm, and cutting speed v

_{c}= 360 mmin

^{−1}.

^{3}/D

^{4}), called the TSC in this paper and given in mm

^{−1}, which means the tool’s slenderness coefficient. The conditions employed in the experiments are a contact tool diameter (D) for all tools D = 16 mm and different TSCs = 1.68, 4, 7.81, 13.50, 21.43, 32, and 45.56 mm

^{−1}.

- Stable cut: The vibrations present acceleration signals that are inferior to 100 m/s
^{2}; at the same time, the roughness of the machined surface was less than 0.8 µm. - Unstable cut: The vibrations present acceleration signals of more than 100 m/s
^{2}; at the same time, the roughness of the machined surface was more than 0.8 µm.

^{3}, area of the cross-section (A) of 1.64 × 10

^{−4}m

^{2}and inertia of the cross-section (I) of 2.84 × 10

^{−9}m

^{4}, a Poisson ratio of 0.33 and Young’s modulus of the tool (E

_{t}) equal to 2.0 × 10

^{11}N/m

^{2}were used. One anti-vibrating tool (Silent tool), code 570-SCLCL-16-06, was used for the support, and code 570-3C 16 156 was used for the anti-vibrational bar and passive damping system shown in Figure 4a where L is the tool overhangs and the parametric values are k

_{TMD}= 703,744.74 N/m and c

_{TMD}= 61.7 Ns/m. The rubber of the TMD system is 0.05 < ζ

_{TMD}< 0.12, and we used ζ

_{TMD}= 0.08. Similarly, Figure 4b shows a replica of the ID designed in the paper [14]. A boring bar, code A16R SCLCR 09-R, was used, and a cavity (diameter 8.32 mm × 180 mm) manufactured internally was filled with steel spheres, which have a diameter of 8 mm, a mass of 0.0021071 kg, and a Poisson ratio of 0.33, and Young’s modulus of the ball (E

_{b}) equals 2.0 × 10

^{11}N/m

^{2}, resulting in a gap (G) between the ball’s surface and cavity wall of 0.32 mm.

_{2}O

_{3}+ TiCN (Sandvik CC 650), insert grain size 0.3–2.0 µm with rectangular geometry with hole for clamping, nose radius r

_{ε}= 0.8 mm, chamfer 0.1 mm, x = 20°, entering angle χ

_{r}= 95°, rake angle γ = +6°, rake angle λ = −6°, nose angle ͛ = 80°, and clearance angle α = 7° [58]. It has lower toughness than inserts with a higher CBN content, but is still sufficient to maintain cutting-edge integrity. The advantage of this CBN class over the class with the highest CBN content is its greater chemical stability with iron. They were used to turn a hardened DIN EN 1.2842 (ISO 90MnCrV8) steel material workpiece with 55 HRC, and it comprises a ring workpiece geometry with the following properties: internal diameter of 30 mm, external length of 76 mm, length of 30 mm, 5 mm chamfers at the edges with a general dimensional, and roundness tolerance of +/− 0.01 mm and roughness limited to class N6.

^{−1}and incrementing at 0.25 until the clamping limit of the ID and Silent tool (TSC = 1.68 mm

^{−1}) was v

_{c}= 300 m/min, f = 0.1 mm, and a

_{p}= 0.1 mm without using a coolant. The acceleration of the boring bars was measured at 20 mm before the tip of the tool during the cutting process with a triaxial piezoelectric accelerometer positioned in the x direction of the tool where the roughness is more affected. The measured vibration time was 4 s, and the sampling rate was 12,800 Hz. The signal of the accelerometer was filtered below 4500 Hz, while a Mitutoyo portable roughness meter, SURFCOM 1900SD2, was used to measure the roughness in the workpiece’s internal surface; an average of 3 measurements were taken with a cutoff of 0.8 mm and a total length of measurement of 4 mm relative to parameters (Ra) and (Rz).

## 3. Results

_{a}) and natural frequency (ω) at a certain overhang. Afterward, to obtain the compliance FRF amplitude (h

_{c}), Equation (4) [62,63] was applied in order to understand the interaction between the reacceptance amplitude at the main resonant peak and the tool’s overhang:

_{d}is the dynamic stiffness of the tool in the corresponding overhang in Equation (4). According to [64], the experimental static stiffness, k

_{s}, can also be calculated as follows:

^{−1}.

^{−1}(see Figure 7a) and in unstable conditions at TSC = 21.43 mm

^{−1}(see Figure 7b).

^{−1}in 2D (Figure 8a) and in 3D (see Figure 8b), and in unstable conditions at TSC = 21.43 mm

^{−1}in 2D (see Figure 8c) and in 3D (Figure 8d).

- (1)
- The turning process was stable: No vibration marks were visible on the workpiece’s surface, and at the same time, the value of the mean arithmetic deviation (Ra) was less than 0.8 μm (see Figure 9a).
- (2)
- The turning process was unstable: There were visible signs of chatter on the surface of the workpiece, and at the same time, the value of the arithmetic mean deviation (Ra) was greater than 0.8 μm. Tool marks on the surface of the workpiece (internal hole) during an unstable turning process can be observed in Figure 9b.

^{2}) are substantially higher compared to the stable ones (RMS acceleration amplitude lower than 50 m/s

^{2}), except for the ID bar that did not show significant amplitudes relative to the long overhangs (RMS acceleration amplitude lower than 3 m/s

^{2}); because of this, there are no unstable signals in Figure 11.

## 4. Discussion

^{−1}, 29.09 mm

^{−1}, and 32 mm

^{−1}. This proves the efficiency of the damper mechanisms of carbide due to the higher Young’s modulus of the tool, the tuned mass damper system in the Silent tool, and the multitude of balls inside the cavity of the ID tool that can minimize the vibration amplitude of the tool during internal turning operations with respect to hardened materials. In the same way, for short holes, most tools can be used except for the Silent tool, which cannot operate in short overhangs at TSC ≤ 7.81 mm

^{−1}. Another point to be mentioned is that when Table 2 and Table 3 are compared, the efficiency of the ID with respect to forced vibrations (during cutting) is superior compared to the TMD in free vibration conditions. This can be explained by the dynamics of the bouncing balls as the excitation amplitude increases and more balls are activated within the cavity to decrease the tool’s vibration amplitude. When a ball is actively participating in the suppression of a tool’s vibration, it performs an approximately circular motion in the cavity. In other words, the ball is not spinning purely on the wall of the cavity but bounces over it as it moves along a non-smooth circular path.

^{−1}to TSC of 45.56 mm

^{−1}, the natural frequency for all tools decreases significantly, i.e., the carbide boring bar reduces the frequency from 4630 Hz to 640 Hz, which results in a decrease in the static stiffness for all tools of at least eight times by using Equations (3) and (4). Then, in long overhangs, the tool is more vulnerable to chatter than in short overhangs. After this analysis, to avoid undesirable vibrations with a TSC of over 13.50 mm

^{−1}, it is necessary to construct an antivibration system in the tool in order to increase the damping ratio of the tool and consequently, the dynamic stiffness of the tool. The better choice for that is the Silent tool and the ID bar, which activate the damping system of the tool with respect to forced vibrations.

^{−1}, no abrupt increase in the acceleration signal was detected. However, for this condition, roughness increased abruptly when the bar exceeded TSC = 32 mm

^{−1}, where the unstable regime was present. The most accepted hypothesis for explaining how roughness grew significantly without growth in acceleration comes from the vibration theory: for simple harmonic motions, acceleration is proportional to the displacement amplitude, and it is proportional to the square of the frequency. In that case, the acceleration amplitudes can be equal for short and long overhangs, as it was experimentally experienced, but the displacement amplitudes exhibit a different behavior because of their different natural frequencies. Hereafter, one can conclude that the ratio of the roughness is reciprocally proportional to the ratio of the square of the natural frequency of the tool.

## 5. Conclusions

^{−1}, the standard holder exhibited stable cuts; at TSC ≤ 10.40 mm

^{−1}, the carbide holder exhibited stable cuts; at 5.69 mm

^{−1}≤ TSC ≤ 29.09 mm

^{−1}and ID TSC ≤ 32 mm

^{−1}, the silent holder exhibited stable cuts. The roughness and the acceleration amplitude remained practically constant.

- The tool vibration remains practically constant with the growth of the overhang until it suddenly increases in a certain overhang value—small changes in the overhang near the limit region already cause this variation, showing that the bar is very sensitive to the change in its stiffness in this overhang range;
- The use of balls on the ID bar provided an increase in the limit overhang, that is, it provided the machining of deep holes;
- It is essential to remember that the variables that cause excitation at the tooltip are generally the tool’s dynamic parameters totally dependent on time. Therefore, to reduce the vibration amplitude of the system, it was necessary to interfere with the inertial and elastic conditions of the tool. These modifications caused an increase in the damping capacity due to the cavity dimensions (Ø 8.43 × 180 mm) and also the Ø 8 mm spheres inside. In this way, the flow of vibrational energy generated by the tool’s harmonic movement is significantly reduced. The energy flow contours of the vibration spectrum become smoother since the kinetic energy dissipation of the bar is reduced by rapidly transferring linear momentum from the spheres in a combination of multiple inelastic collisions, friction between spheres, and between spheres and cavity walls to achieve damping. It is enough to observe the equation of the total mechanical energy of simple harmonic motion, which establishes that the energy of vibration is proportional to the square of the amplitude of oscillation, given a conservative system (constant mechanical energy).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BUE | build-up-edge |

CBN | Cubic nitride bor |

D | diameter |

DVA | dynamic vibration absorber |

FRF | frequency response function |

ID | impact damper |

IRF | impulse response function |

L | length |

TMD | tuned mass damper |

TSC | tool’s slenderness coefficient |

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**Figure 3.**The measurement equipment: (

**a**) modal hammer and accelerometer; (

**b**) boring bar and lathe parts used during the experiments.

**Figure 5.**IRF and FRF for boring bars in TSC = 7.81 mm

^{−1}(

**a**) standard boring bar; (

**b**) carbide boring bar; (

**c**) TMD boring bar; (

**d**) ID boring bar.

**Figure 6.**Comparison of the maximum FRF values of the standard, carbide, TMD (Silent Tools), ID ball impact damper bars.

**Figure 7.**Roughness profile of the workpiece when cutting with a carbide boring bar: (

**a**) in stable conditions at TSC = 4 mm

^{−1}; (

**b**) in unstable conditions at TSC = 21.43 mm

^{−1}.

**Figure 8.**Circularity profile of the workpiece when cutting with a carbide boring bar: (

**a**) in stable condition in 2D; (

**b**) in stable condition in 3D at TSC = 4 mm

^{−1}; (

**c**) unstable condition in 2D; (

**d**) unstable condition in 3D at TSC = 13.50 mm

^{−1}.

**Figure 9.**Arithmetic average roughness (Ra) for the workpiece when cutting with a carbide boring bar (

**a**) in stable conditions at TSC = 4 mm

^{−1}; (

**b**) in unstable conditions at TSC = 13.50 mm

^{−1}.

**Figure 10.**Excitation signals in stable TSC = 4 mm

^{−1}and unstable TSC = 7.81 mm

^{−1}conditions with a standard boring bar: (

**a**) acceleration; (

**b**) velocity; (

**c**) displacement amplitudes.

**Figure 11.**Excitation signals in stable TSC = 21.43 mm

^{−1}conditions with an ID boring bar: (

**a**) acceleration; (

**b**) velocity; (

**c**) displacement amplitudes.

**Figure 12.**Excitation signals in stable TSC = 21.43 mm

^{−1}conditions with a TMD boring bar: (

**a**) acceleration; (

**b**) velocity; (

**c**) displacement amplitudes.

**Figure 13.**Excitation signals in stable TSC = 21.43 mm

^{−1}conditions with a carbide boring bar: (

**a**) acceleration; (

**b**) velocity; (

**c**) displacement amplitudes.

Name | Code | Material |
---|---|---|

Insert for Standard, Carbide, and ID bars | CCGW09T308S01020F 7015 (class ISO H10) | CBN |

Insert for Silent tool | CCGW060208S01030F 7015 | CBN |

Bushing | 132L-4016105-B | Steel |

Standard | A16R SCLCR 09-R | Steel |

Carbide | E16R SCLCR 09 R | Tungsten |

Silent tool support | 570-SCLCL-16-06 | Steel |

Silent toolbar | 570-3C 16 156 | Steel |

ID bar | A16R SCLCR 09-R | Steel |

Tool Type | Damping Ratio (ζ) | Static Stiffness × 10^{6} (N/m) | Natural Frequency (Hz) |
---|---|---|---|

Standard | 0.900 | 0.203 | 1348.406 |

Carbide | 0.814 | 1.000 | 2234.394 |

TMD * | 0.161 | 3.886 | 1353.312 |

ID ** | 0.915 | 0.211 | 1397.589 |

**Table 3.**Measured parameters are in terms of the average values of roughness (deviation ± 0.02 mm) and acceleration amplitude (deviation ± 0.1 m/s

^{2}) of the tip of the tool.

Tool Type | TSC (mm^{−1}) | Stability | Ra (μm) | Ra (μm) | RMS (m/s^{2}) |
---|---|---|---|---|---|

Standard | <5.69 | Stable | 0.36 | 1.860 | 16.189 |

≥5.69 | Unstable | 1.507 | 7.002 | 347.795 | |

Carbide | <10.40 | Stable | 0.350 | 2.000 | 5.189 |

≥10.40 | Unstable | 1.832 | 9.444 | 350.578 | |

TMD * | 5.69 ≤ TSC ≤ 29.09 | Stable | 0.360 | 1.738 | 44.776 |

5.69 > TSC > 29.09 | Unstable | 1.300 | 6.010 | 362.977 | |

ID ** | ≤32 | Stable | 0.460 | 2.249 | 2.318 |

>32 | Unstable | 1.820 | 8.000 | 2.318 |

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## Share and Cite

**MDPI and ACS Style**

da Silva, W.T.A.; Peterka, J.; Vopat, T. Experimental Research on the Dynamic Stability of Internal Turning Tools for Long Overhangs. *J. Manuf. Mater. Process.* **2023**, *7*, 61.
https://doi.org/10.3390/jmmp7020061

**AMA Style**

da Silva WTA, Peterka J, Vopat T. Experimental Research on the Dynamic Stability of Internal Turning Tools for Long Overhangs. *Journal of Manufacturing and Materials Processing*. 2023; 7(2):61.
https://doi.org/10.3390/jmmp7020061

**Chicago/Turabian Style**

da Silva, Wallyson Thomas Alves, Jozef Peterka, and Tomas Vopat. 2023. "Experimental Research on the Dynamic Stability of Internal Turning Tools for Long Overhangs" *Journal of Manufacturing and Materials Processing* 7, no. 2: 61.
https://doi.org/10.3390/jmmp7020061