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Journal of the Korean Society for Precision Engineering - Vol. 34 , No. 12

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Journal of the Korean Society for Precision Engineering - Vol. 34, No. 12, pp. 917-926
Abbreviation: J. Korean Soc. Precis. Eng.
ISSN: 1225-9071 (Print) 2287-8769 (Online)
Print publication date 01 Dec 2017
Received 24 Apr 2017 Revised 26 Oct 2017 Accepted 13 Nov 2017
DOI: https://doi.org/10.7736/KSPE.2017.34.12.917

A Study on the Design Model of Passive Tunable Damped Boring Bar
Jun-Hee Hong1, # ; Yang-Yang Guo2 ; Doo-Sang Song3
1School of Mechanical Engineering, Chung-Nam University
2Department of Ultra Precision Machines & System, Korea Institute of Machinery & Materials
3Division of Technology, Dae-Myung Tech.

패시브 튜너블 방진 보링바의 설계모델에 대한 연구
홍준희1, # ; 곽양양2 ; 송두상3
1충남대학교 기계공학과
2한국기계연구원 초정밀시스템실
3대명테크
Correspondence to : #E-mail: hongjh@cnu.ac.kr, TEL: +82-42-821-5642


Copyright © The Korean Society for Precision Engineering
This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract

Boring depth is limited by the overhang on which the vibration frequency depends. To improve the process, a passive boring bar with dynamic vibration absorber has been used, but is effective only for a limited length of overhangs. In this study, a tunable damped boring bar was devised to cope with a variable length of overhangs. Vibration parameters arising from the various overhangs were analyzed using Euler’s beam theory. The proposed bar contains a cantilever-type dynamic vibration absorber to suppress the vibration amplitudes of the overhangs. The absorber adjusts the natural frequency of the bar by adjusting the spring stiffness. The proposed bar was fabricated and tested by impact excitation and its capability to suppress vibration was demonstrated.


Keywords: Tunable damped boring bar, Overhang, Dynamic vibration absorber
키워드: 튜너블 방진 보링바, 보링바 돌출길이, 동흡진기

1. Introduction

The extended length of a boring bar used in the boring process depends on the depth of the bore, called the overhang.1 Since the overhang is of cantilever form, it receives tensile stress and compression stress simultaneously during the process. Thus, dynamic rigidity varies with the overhang, and the magnitude of the vibration that occurs during the process affects cutting conditions.2-14

Vibration is intimately related with the natural frequency of the overhang. As cutting takes place when the boring bar contacts the structure under fabrication, the vibration has frequency slightly higher than the natural frequency.3 This vibration lowers the roughness and dimensional accuracy of the structure and brings about tool wear and deficiencies.11 Studies of vibration-free boring bars for enhancing stability in the boring process started in 1989. One approach is to enhance the rigidity of the boring bar using the complex material; however, this approach is not effective if the overhang, L, is longer than 6d.4 The other approach is to adopt a dynamic vibration absorber (DVA) at the tip of the boring bar.5 This method was developed in the USA and EU and is being applied in industry. However, it is not easy to oppress the frequencies of the various overhangs, which require various sizes of boring bars to be prepared. In addition, vibration-damping boring bars should be altered to cope with the inner radii of the structure, leading to increased idling time and cost. To solve these problems, a new type of tunable13 damping bar is needed to oppress vibrations due to the presence of various overhangs. In this paper, a design model of a tunable damping bar is proposed. The dynamic characteristics of the proposed bar are analyzed with a mathematical model based on the Euler beam theory.6

The analysis results are compared with results from the CAE program (Ansys Workbench) simulation for validation. In addition, impulsive excitation tests are conducted to verify the damping effects of various overhang with DVA inserted in the body.


2. Analysis Using the Mathematical Model
2.1 Proposed Model

The schematic of the dynamic model of the proposed passive tunable boring bar is depicted in Fig. 1(a) and its structure is shown in Fig. 1(b). In the Fig. 1, F, X(a), and X(b) denote the external force, and the absolute displacements of the DVA and the boring bar, respectively. The body consists of a shank, connector, and head. The shank has an inner hole to accommodate the DVA, the connector fixes the DVA, and the head combines the inserted blade. The DVA is of an adjustable spring cantilever form. Its function is to absorb the vibration energy of the structure’s movement by creating a resistant force in the opposite direction to the excitation force. This can be achieved by adjusting the DVA spring length. The vibration frequency varies with the overhang.


Fig. 1 
Concept model of tunable damped boring bar

2.2 Analysis Using Euler’s Beam Theory

Fig. 2 depicts the computation flow chart for modeling a tunable damped boring bar based on Euler’s beam theory. The bar has multiple cross sections, as shown in Fig. 3. The lengths of the head, connector, tube, and shank are l4, l3, l2, and l1, respectively.


Fig. 2 
Flow chart of theoretical analysis


Fig. 3 
Structure of tunable boring bar body

The insert tip is assembled into the head section. The connector adjusts the position of the DVA in the tube section. l5 is the distance between points ⓒ and ⓔ. The elasticity “E” at point ⓒ is an important design parameter required to determine the effective mass and stiffness of the DVA.7

The body of the tunable damped boring bar has multiple cross sections consisting of several beam elements. In this study the body was modeled with 5 nodes and 4 beam elements as in Fig. 4 to solve the mass and rigidity of the tunable damped boring bar body.


Fig. 4 
Element of tunable damping boring bar body

Equation matrices in terms of the mass and stiffness of each element are solved and combined to produce those of the body. The matrices are expressed in Eqs. (1) and (2).

Mi=ρiAili42015622li54-13li22li4li213li-31li25413li156-22li-13li-3li2-22li4li2(1) 
Ki=EiIili3126li-126li6li4li2-6li2li2-12-6li12-6li6li2li2-6li4li2(2) 

In the equations, “E” is the elasticity coefficient, ρ is the density, and “l ” is the length of the beam element.

The subscript i denotes the index of each beam element (1 = shank, 2 = tube, 3 = connector, 4 = head). To simplify the analysis, the matrices of Eqs. (1) and (2) can be divided into four sections as shown in Eqs. (3) and (4).8-10

Mi=MaiMbiMbiTMci(3) 
Ki=KaiKbiKbiTKci(4) 

Combining the matrices of the four elements in Eqs. (3) and (4) results in Eqs. (5) and (6):

M = Ma1Mb1Mb1TMc1+Ma2Mb2Mb2TMc2+Ma3Mb3Mb3TMc3+Ma4Mb4Mb4TMc4(5) 
K= Ka1Kb1Kb1TKc1+Ka2Kb2Kb2TKc2+Ka3Kb3Kb3TKc3+Ka4Kb4Kb4TKc4(6) 

If the displacement and rotation angle of the boring bar are assumed to be 0, which is the case for the boundary conditions of a cantilever,8-10 Eqs. (7) and (8) are obtained.

M=Mc1+Ma2Mb2Mb2TMc2+Ma3Mb3Mb3TMc3+Ma4Mb4Mb4TMc4(7) 
K  =Kc1+Ka2Kb2Kb2TKc2+Ka3Kb3Kb3TKc3+Ka4Kb4Kb4TKc4(8) 

Applying Eqs. (7) and (8) to the momentum Eq. (9), the natural frequency can be obtained.8-10

Mx¨+Cx˙+Kx=f(9) 

Where [M] is the mass matrix Eq. (7), [C] is the attenuation matrix, [K] is the stiffness matrix Eq. (8), {x} is the displacement vector, and {f} is the force vector. If the force vector and attenuation matrix are assumed to be 0, the characteristic can be expressed as.8-10

-λM+Kx=0(10) 

Then, the mode can be analyzed from the solution of the characteristic equation. λ obtained in the process of solving Eq. (10) is called the eigenvalue. Multiplying [M]-1, which is the transposed matrix of [M], on each side of Eq. (10) produces

-λI+Dx=0(11) 

Where [I] is the unit vector and [D] is the dynamic matrix defined as

D=M-1K(12) 

For the solution of {x} to be valid, the characteristic matrix must become 0 and is expressed as

Δ=-λI+D=0(13) 

Eq. (13) can be developed into an n-dimensional polynomial. As λ = ω2 in the characteristic or oscillation equation, the mode configuration and eigenvector {x} can be obtained through λ.

ω2 is referred to as the natural frequency of the oscillation system, and the matrix consisting of the eigenvectors is referred to as the modal matrix appearing in Eq. (14).

ϕji=x1x2xn=ϕ11ϕ12ϕ1nϕ21ϕ22ϕ2nϕn1ϕn2ϕnn(14) 

Where ϕji is the mode matrix, j is the nodal point, and i is the dimension number of the mode. Hence, the equivalent mass and stiffness of the nodal point can be obtained as

Meq=1ϕjiϕji(15) 
Keq= ω2Meq(16) 

In the analysis, the outer radius of the body shank, d, is 25 mm, and the lengths of the overhangs are entered sequentially into the computation as values from 7d to 12d in intervals of 1d.

Table 2 shows the calculated natural frequencies utilizing Eqs. (15) and (16) and the input parameters in Table 1. MATLAB software, and the input parameters in Table 1.

Table 1 
Input parameter of tunable boring bar body
Parameter Name Quantity
Head length (l4) 40(mm)
Connector length ( l3) 28(mm)
Tube length (l2) 100(mm)
Vibration output position (l5) 68(mm)
Boring bar’s diameter (d) 25(mm)
Boring bar’s tube inner dia. (D) 16(mm)
Boring bar’s young’s modulus (E) 2E+11(pa)
Boring bar’s density (ρ) 7850(Kg/m3)
Boring bar’s material SCM440
Boring bar’s hardness 33~38(HRC)
Boring Bar overhang(L ) 7d ~ 12d(mm)

Table 2 
Theoretical analysis result of tunable damping boring bar body with euler beam theory
Overhang of boring bar : L (mm) Frequency (Hz)
7d (175mm) 538.26
8d (200mm) 431.21
9d (225mm) 351.31
10d (250mm) 290.77
11d (275mm) 244.06
12d (300mm) 207.40

2.3 Design of a DVA Based on Boring Bar Overhang

The DVA consisting of a single-spring.15structure was designed based on a tunable bar body. The mass and stiffness for the DVA are expressed in the following Eqs. (17) and (18).

m=ρV(17) 
k=kKeqMeq11+μ2(18) 

Where Meq and Keq are the equivalent mass and stiffness of the body. The DVA is a cylinder of radius ds suitable for adjusting and fixing ls. dm and ds in Table 3 are set as constants considering the spaces of the inner diameter D (16 mm) and l2 (100 mm) of the bar. The length of the DVA, lm, is obtained in Eq. (19).

lm=2mπρdm2(19) 

Fig. 5 
Analysis model of DVA

Table 3 
Input parameter of DVA
Parameter Name Quantity
Mass’s Diameter (dm) 14(mm)
Spring’s Diameter (ds) 5(mm)
Young’s modulus (E) 1.4312E+11(pa)
Density (ρ) 7850(Kg/m3)
Material SCM440
Hardness 55~60(HRC)

Since the second cross-sectional moment Id and stiffness kd of the DVA are obtained in Eqs. (20) and (21), the tunable spring length of the DVA, ls, and the frequency can be solved in Eq. (22).

Id=πds464(20) 
kd=3EIdls3(21) 
ls=3EIdk13(22) 

The calculated results for ls for a DVA suitable for each overhang are shown in Table 4.

Table 4 
Tuning result of spring length (ls) on DVA
Overhang of boring bar : L (mm) ls (mm)of DVA
7d (175mm) 15
8d (200mm) 21
9d (225mm) 26
10d (250mm) 33
11d (275mm) 38
12d (300mm) 43


3. Simulation Using the CAE Program
3.1 CAE Simulation of a Tunable Boring Bar Body

In the simulation of a complex structure, which is basically a continuous system, an approximation is needed to convert it into a system with multiple degrees of freedom. For this purpose, the finite element approach using the CAE program is beneficial.

In this study, the CAE program was used. The bar body was modeled as shown in Fig. 6.


Fig. 6 
Analysis model of body on CAE program

The body consisting of the head, connector, and shank was assembled into a chuck. The simulation was performed with changing overhangs. The input variables are listed in Table 1.

The overhangs were adjusted from 7d to 12d in 1d intervals as shown in Fig. 7. Six modes were analyzed, but only the results of the first mode are presented in this paper because this mode represents the principal force11,12 most closely related to the vibration. The results are summarized in Table 5.


Fig. 7 
1th Mode analysis result of overhang for body

Table 5 
Natural frequencies of boring bar body on CAE
Overhang of boring bar : L (mm) Frequency (Hz)
7d (175mm) 582.76
8d (200mm) 465.91
9d (225mm) 378.31
10d (250mm) 309.25
11d (275mm) 260.71
12d (300mm) 220.81

3.2 CAE Simulation of DVA

The CAE simulation model of the DVA is shown in Fig. 8. The DVA is attached to the connector, which adjusts and fixes the spring length ls of the DVA. The parameters in Tables 3 and 4 were applied for the DVA analysis. The simulation was conducted with regard to the first-mode natural frequencies of the spring lengths, ls, alone, and the results are presented in Table 6.


Fig. 8 
Analysis model of DVA on CAE program


Fig. 9 
1 th Mode analysis result of DVA

Table 6 
Natural frequencies of spring length (DVA) on CAE
Spring Length ls (mm) Frequency (Hz)
15 (mm) 585.13
21 (mm) 407.51
26 (mm) 343.83
33 (mm) 266.54
38 (mm) 221.14
43 (mm) 197.16


4. Test of a Passive Tunable Damped Boring Bar
4.1 The Manufacture of Design Model

The design model of a tunable damped boring bar is shown in Figs. 10 and 11 is a photograph of each manufactured part and assembled state. The experimental method is to apply the impact hammer and analyze the signal by applying the impact of the boring bar.


Fig. 10 
Design model of tunable damped boring bar


Fig. 11 
Photo of passive tunable damped boring bar

4.2 Impulse Excitation Test of Boring Bar Body

An impulse excitation was applied to the test bar to determine the natural frequency of the body. As Fig. 12 indicates, the test was conducted with the boring bar attached to the chuck but without the DVA. The natural frequency was measured under the same conditions used in the CAE simulation in section 3.1. Test results are presented in Fig. 13 and Table 7.


Fig. 12 
Photo of experiment setup for boring bar body


Fig. 13 
Natural frequency of overhang 7d-12d

Table 7 
Natural frequencies of boring bar body on experiment
Overhang of boring bar : L (mm) Frequency (Hz)
7d (175mm) 520
8d (200mm) 420
9d (225mm) 340
10d (250mm) 270
11d (275mm) 230
12d (300mm) 195

4.3 Impulse Excitation Test of DVA

In this test, ls was adjusted using the results in Table 4. The natural frequency was measured by a non-contact optic fiber sensor with a resolution of 0.28 μm, as shown in Fig. 14. The measured values are presented in Table 8.


Fig. 14 
Photo of experiment setup for DVA

Table 8 
Natural frequency of DVA on experiment
Spring Length ls (mm) Frequency (Hz)
15 (mm) 530
21 (mm) 415
26 (mm) 325
33 (mm) 265
38 (mm) 225
43 (mm) 190

4.4 Comparison of Analysis and Test Results

The results of the theoretical analysis in Table 2 based on Euler’s beam theory, the simulation in Table 8 using the CAE program, are all compared in Table 9.

Table 9 
Comparison between frequency domain of theoretical review and experimental result in boring bar body
Boring bar overhang L (mm) Natural frequency of boring bar body
Theoretical analysis (Hz) CAE analysis (Hz) Experiment (Hz)
7d (175) 538.26 582.76 520
8d (200) 431.21 465.91 420
9d (225) 351.31 378.31 340
10d (250) 290.77 309.25 270
11d (275) 244.06 260.71 230
12d (300) 207.40 220.81 195

The differences in natural frequencies between the theoretical analysis and the CAE simulation for the various overhangs are approximately 7% while those between the theoretical analysis and test results are approximately 6%, as shown in Table 9.

Similarly, the difference in the obtained natural frequencies between the theoretical analysis and the CAE simulation with variation of the spring length of the DVA, ls, are approximately 6% while those between the theoretical analysis and test results are approximately 8%, as shown in Table 10. Therefore, it can be seen that the boring bar design is possible through the theoretical analysis presented in this paper.

Table 10 
Comparison between natural frequencies of CAE and theoretical review in ls for DVA
Spring length ls (mm) Natural frequency of DVA (ls)
Theoretical analysis (Hz) CAE analysis (Hz) Experiment (Hz)
15 538.26 585.13 530
21 431.21 407.51 415
26 351.31 343.83 325
33 290.77 266.54 265
38 244.06 221.14 225
43 207.40 197.16 190


Fig. 15 
Adjusting setup for tunable damped boring bar

4.5 Impulse Excitation test of Damping Capability

Together with the results in section 4.4, the DVA was inserted inside the tunable damped boring bar body and an impulse excitation test was applied as shown in Fig. 12. The overhang was adjusted to the benchmarks by adjusting the spring length ls inside the body as in Table 2.

An impact hammer provided an impact at the end tip of the boring bar. An oscilloscope was used to measure the absorption capability of the DVA.

The test results are the same as those of the passive control simulation.8 Part of the test results are shown in Fig. 16.


Fig. 16 
FFT analysis of passive tunable damped boring bar for overhang 9d

Table 11 indicates that the damping effect reaches a maximum of 73.8% at position 9d (225 mm) and more than 50% at all positions.

Table 11 
Comparison between impulse test of general system and passive system in tunable damped boring bar
Tunable damped boring bar overhang L (mm) Frequency Domain Damping rate (%)
Amplitude without DVA (m/N) Amplitude with DVA (m/N)
7d (175) 1.18 0.55 53.4%
8d (200) 1.55 0.41 73.5%
9d (225) 1.64 0.43 73.8%
10d (250) 1.19 0.59 50.4%
11d (275) 0.89 0.42 52.8%
12d (300) 0.94 0.35 62.7%

It is indicated that the proposed tunable damped boring bar can control the vibration of the internal DVA by adjusting the overhang, hence offering a better damping effect than the existing passive boring bar design.

The proposed design can also control a wider frequency band such as that generated from various overhangs, while the existing design can damp oscillations within only a limited frequency band. More applications can be anticipated with future work.

4.6 Cutting Test of Tunable Damped Boring Bar

Based on the results in section 4.5, Cutting test was carried out for tunable damped boring bar as shown in Fig. 17. Experimental methods for cutting were performed under the same conditions as Tables 12 and 13 shows the equipment, materials and cutting conditions.


Fig. 17 
Photo of experiment setup for cutting process

Table 12 
Tunable condition of tunable damped boring bar on cutting process
Tunable damped boring bar overhang L (mm) Spring length of DVA ls (mm)
7d (175) 15
9d (225) 26
11d (275) 38

Table 13 
Cutting condition of boring process
Process condition Quantity
Cutting speed (V) 80(m/min)
Feed (f) 0.132(mm/rev)
Depth (mm) 0.5(mm)
Workpiece (material) SM45C
Workpiece size (Tube type) Inside 60(mm)
Outside 100(mm)
Machine Type Lathe (HL-380)
Tool of insert tip CCMT 09T304


Fig. 18 
Comparison between steel bar and tunable damped bar in frequency domain

For the cutting test method, the overhang (L) of the boring bar was adjusted to the benchmarks by adjusted the spring length (ls) of DVA inside the boring bar as Table 12.

In addition, the vibration frequency and surface roughness of the workpiece were measured to compare the performance of the steel boring bar and a tunable damped boring bar. The cutting test results showed that the vibration frequency amplitude of the tunable damped boring bar was reduced.

The improvement effects are shown in Table 14.

Table 14 
Comparison between cutting process of steel bar and tunable damped boring bar on frequency domain
Boring bar overhang L (mm) Frequency domain Damping rate (%)
Amplitude of steel bar (m/N) Amplitude of tunable bar (m/N)
7d (175) 6.52 4.45 31.7%
9d (225) 11.28 3.25 71.2%
11d (275) 7.98 2.17 72.8%

Table 14 indicates that the damping effect of tunable damped boring bar reaches a maximum of 72.8% at position 11d (275 mm) and more than 30% at all positions. Based on the result of cutting test, the roughness of the workpiece was measured. The measurement results are shown in Fig. 19.


Fig. 19 
Comparison between steel bar and tunable damped bar in surface roughness (Ra)

The measurement of surface roughness was carried out in accordance with ISO1997. Fig. 19 indicates that the improvement effect of surface roughness reaches a maximum of 50.9% at position 11d (275 mm) and more than 40% at all positions.


5. Conclusion

A new type of tunable damped boring bar has been proposed to suppress vibrations occurring in the boring process. The dynamic characteristics of its body were modeled using Euler’s beam theory. The analysis results were supported by comparison with the results of CAE simulation and experimental tests. The following conclusions are drawn.

(1) The model showed less than 7% error compared to the predictions of simulations, assuring its validity.

(2) Based on the analysis, a new DVA design was proposed. Additionally, the spring length, which is the tuning parameter, ls, was determined. The designed length showed approximately 8% inaccuracy compared with measurements.

(3) Based on the analysis and simulation, a tunable damped boring bar was manufactured and impulse excitation tests were performed. Adjustment of the DVA spring length for the given overhang was able to tune the frequency accordingly.

(4) The tuning test between 7d to 12d at 1d intervals showed that vibration was attenuated by more than 50% over the entire range, with a maximum effect of 73.8% at 9d.

(5) Through the cutting experiment, general steel boring bar and tunable damped boring bar was compared. And the cutting test between 7d to 11d at 2d intervals showed that vibration amplitude was attenuated by more than 30% ~ 70% over the entire range, with a maximum effect of 72.8% at 11d.

(6) Based on the cutting test, the surface roughness of workpiece indicated that improvement effect was confirmed a maximum of 50.9% at position 11d and more than 50% at all positons.

(7) The cutting test of tunable damped boring bar between 7d to 11d at 2d intervals showed that surface roughness was constant as a micro value and the standard deviation was 0.181μm. Therefore, the effectiveness of tunable damped boring bar design was verified.

The proposed passive damped boring bar offers better frequency-damping capability by adjusting the length of the inserted spring ls compared with existing boring bars, which respond only to limited overhangs. Improvement in the proposed design elements and the addition of external attenuation elements could produce further advancement in future research.


NOMENCLATURE
DVA : Dynamic vibration absorber
L : Overhang of bring bar
d : Diameter of bring bar
D : Inner diameter of bring bar
dm : Diameter of DVA
ds : Spring length of DVA
k : Spring stiffness of dynamic absorber
m : Spring mess of dynamic absorber
ω : Natural frequency
lm : Length of mass for DVA
ls : Length of spring for DVA
Meq : Effective mass of “E” point on boring bar body
Keq : Effective stiffness of “E” point on boring bar body

Acknowledgments

This work supported by Research Program supported by Chung-Nam National University academic policy of 2015.


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