Investigation of chatter prediction in end milling using morphological studies on aluminum alloy (Al6061)

Abstract

Future machine tools have to be highly powerful systems to maintain the needed intellectual performance and stability. The machine tool systems such as Spindle/Tool-holder/Tool assembly are necessary to be optimized for their functionality or cutting performance to meet the productivity and accessibility requirements of the user. Prediction of the dynamic behavior at the spindle tool-tip is, therefore, an important criterion for assessing the machining stability of a machine tool at the design stage. In commercial practice, the machine tool system is extensively influenced by the dynamic rigidity of the spindle system. In this work, a realistic dynamic high-speed spindle/milling tool holder/tool system model is elaborated based on rotor dynamics predictions. Using the finite element modeling with the Timoshenko beam theory, the frequency response at the tool-tip has arrived initially. Further, the numerical model is validated with 3D ANSYS and experimental modal testing. The theoretical stability lobe diagram (SLD) depends on the stiffness and damping properties of the cutting tool and distinguishes the stable and unstable cutting conditions. The mechanism of chatter formation is investigated experimentally during the end milling of Aluminum alloy (Al6061) by two different techniques. Experimental cutting tests are conducted at different depths of cuts, the corresponding vibration signals and cutting samples are examined using the Scanning electronic microscope (SEM) and optical microscope. These studies provide a detailed investigation to predict the stable and unstable cutting zones at different machining conditions.

Keywords

Frequency response modal testing spindle design milling stability morphological studies scanning electronic microscope

Introduction

In several applications of the aerospace industry, material removal operations are essentially required for the fabrication of products. Therefore, it is necessary to focus the research efforts on the parameters like cutting stability as well as the maximization of material removal rate. To achieve these objectives, the spindle-tool holder-tool couplings were having a key role. Moreover, these are the most flexible parts in the entire structure of the high-speed machine tool with the highest mode of fundamental frequencies. To develop a better design of this coupled structure, the identification of frequency responses at various positions is essentially needed. The primary cause for the chatter vibrations in the milling is due to the flexible coupling between the spindle-tool holder-tool interfaces. Several authors proposed works related to better designs for the integrated spindle-tool unit to improve the surface morphology of the workpiece. Yang and Nelson^1-3 investigated the analysis to improve the rigidity of the integrated spindle tool unit. Bosmanns et al. and Lin et al.^4,5 developed the integrated thermo-mechanical model for the high-speed spindles to resist the lateral deformations. Similarly, using the finite element modeling the various interactions of the spindle tool system over the machine frame were analyzed to improve the dynamic stability of the system.^6-9

Aluminum alloys are easily machinable and at the same time, they lead to burrs on the machined surfaces with an improper selection of cutting tool material and other cutting conditions. The MRR is limited by the spindle power availability and/or by the occurrence of the instability of the cutting process leads to the chatter phenomenon. Higher metal removal rates are essentially needed during the rough machining at the expense of the higher spindle power which further leads to cutting vibrations and the reduction of the tool life. In this line, several authors developed mathematical models to evaluate the correct stability of lobe boundaries.

Altintas and Budak¹⁰ evaluated the stability boundaries for different machining conditions during the high-speed milling operations. Further, the three-dimensional lobes arrived for various cutting conditions. Altintas and Weck^11,12 revealed the cutting process of the self-excited vibrations in different machining processes like grinding and milling. Simulated models were evaluated both in the time and frequency domain and these are validated with experiments.

Mingder and Fonga¹³ designed a novel architecture using the Taguchi method by considering different geometrical parameters of the coupling systems of the machine tool structure. Using the regression analysis, the optimal process conditions were obtained at various levels and were further validated with the regression analysis. Gagnol et al. ¹⁴ estimated the different ranges of stability boundary for the high-speed milling spindles. Songa and Tanga¹⁵ implemented the multi-degree of freedom model for different cases of the high-speed spindles to arrive at the responses at the tool-tip and further it was effectively utilized to plot the boundaries of the stability lobes. Suzuki et al.¹⁶ identified the inverse analysis approach to estimate the frequency response at the tool-tip and to reduce the excitations during the machining process. Raphael and Reginaldo¹⁷ investigated the methods of identifying the correct position of the spindle by the electronic transducers. Gao and Meng, Ozturk et al., and Erturk et al.^18-20 investigated the different design parameters such as the span of the bearings and the tool overhang effect over the responses at the tool-tip. Lin and Tu, Jiang and Zheng, and Peng et al.^21-23 introduced various novel methods to estimate the dynamic and thermal characteristics of the high-speed spindles at different machining conditions. Using spectral analysis, the dynamic motion of the spindle structure is obtained in terms of vibration signals. Sulaiman et al. ²⁴ studied various chip morphology to identify the chatter prediction. An SEM micro-photograph shows the surface roughness values at various depths.

It is observed that very limited works have been identified related to the morphological surface analysis of the workpiece to investigate the proper stability points. In the present paper, an attempt was made to estimate the correct stability boundaries for the machining of Al6061 alloy during the end milling process. Initially, the spindle-tool assembly was analyzed using the finite element method to arrive at frequency response at the tool-tip. Further, with numerical data, the boundaries were estimated correctly with the cutting tests at different depths of cuts.

Modeling of the spindle-tool unit

To estimate the dynamic performance of a machine tool, the coupling of the spindle and tool holder plays a key role. The stability in terms of its machining capacity is particularly dependent upon the taper portions of the spindle and its holder. This coupling is one of the flexible zones in the entire structure of the machine tool with the total deformation around 25–55% at the tool-tip. To ensure this stability during the machining process, the dynamic response has to be estimated at the tool-tip in essentially required. The entire model of the spindle tool system is discretized with the Timoshenko elements with shear and rotary deformations. All the beam elements were assumed to be collinear with the centroidal axis before getting deformed. In the present work, the entire spindle-tool structure is discretized into eight elements as shown in Figure 1. At each node, 5° of freedom are considered in which three linear translations and two rotational degrees with a total of 45° of freedom are considered for the modeling, and bearing stiffness value is added at the corresponding node position.

Figure 1.

Equivalent spindle tool unit for FEM analysis.

The bearing preload is provided at the two different positions on the spindle nodes to make the spindle in the self-balanced state in an axial direction. The combined governing equation for the integrated spindle tool system is defined as follows:

[M] {\overset{\cdot\cdot}{q}} + [[C] - Ω [G]] {\overset{\cdot}{q}} + ([K] - Ω^{2} [M_{c}]) {q} = {F}

(1)

where {q} is the vector with nodal displacements, the complete mass, viscous, and stiffness matrices are represented by the [M], [C], and [K], respectively. Similarly, the gyroscopic, centrifugal, and force vector matrices are represented by [G], [M_c], and {F}, respectively. Viscous damping matrix for the spindle tool unit is taken as $[C] = α [M] + β [K]$ where the alpha and beta are true scalar values. In general, 1% is taken as a structural damping factor and is used to arrive at the alpha and beta values as 17.32 and 3.67e^-6. An empirical relation is used to provide the preload at the spindle-bearing positions as given by the expression (2). The standard bearing parameters are taken to evaluate the stiffness at the bearing position is as follows: diameter of ball (D_b)=9 mm, axial preload (F_a) =1500N, the contact angle of balls (θ)=25°, and the number of balls (N_b)=20.

K_{x x} = Κ_{y y} = 1.77236 \times 1 0^{7} \times {(N_{b}^{2} . D_{b})}^{\frac{1}{3}} \frac{\cos^{2} θ}{\sin^{1 / 3} θ} F_{a}^{\frac{1}{3}}

(2)

The frequency response at the tip of the tool with the bearing stiffness is evaluated by the following expression²⁵:

[H (i ω_{c})] = {[- [M] ω_{C}^{2} + i ω_{c} [[C] - Ω [G]] + [[K] - Ω^{2} [M_{c}]]]}^{- 1}

(3)

Two-dimensional cutting force model

In the present work, the cutting force displacements for a two-dimensional milling model in radial and tangential directions are shown in Figure 2.

Figure 2.

Two degrees milling model.

The variable chip thickness for a time period (t) is considered as where ohm is the angular speed of the spindle and is represented as:

h (φ_{j}) = {f_{t} \sin (φ_{j}) + δ \sin (φ_{j}) + δ y \cos (φ_{j})} * l (φ_{j})

(4)

Here, δx and δy are the relative displacements of the present and previous tooth periods. The switching function, that is, $l (φ_{j})$ is taken as^26,27

l (φ_{j}) = {\begin{cases} 1 when φ_{s} \leq φ_{j} \leq φ_{e} \\ 0 when φ_{j} < φ_{j} o r φ_{j} > φ_{e} \end{cases}

(5)

where the cutter engagement angle at the starting and exit of the working piece is ϕ_s and ϕ_e, respectively. The radial and tangential directional cutting forces are for an axial depth of cut (b) and are represented as follows:

F_{r, j} (φ) = \cos (β) K_{s} b h (φ_{j}) = K_{r} b h (φ_{j})

(6)

F_{t, j} (φ) = \sin (β) K_{s} b h (φ_{j}) = K_{t} b h (φ_{j})

(7)

The final cutting force expressions from the tooth j to the number of teeth N_t is conveniently taken as follows:

F_{x} (φ) = \sum_{j = 1}^{N_{t}} F_{x, j}

(8)

F_{y} (φ) = \sum_{j = 1}^{N_{t}} F_{y, j}

(9)

The final force expressions are conveniently represented in the matrix form as follows:

{F} = {\begin{matrix} F_{x} \\ F_{y} \end{matrix}} = \frac{1}{2} b K_{t} [A (t)] {\begin{matrix} Δ x \\ Δ y \end{matrix}}

(10)

Initially, these cutting force expressions are time-dependent and these are changed into the frequency domain by considering the mean values with tooth period $τ = 60 / Ω N_{t}$ and tooth pitch $φ_{p} = 2 π / N_{t}$ (rad) as follows:

[A_{0}] = \frac{N_{t}}{2 π} [\begin{matrix} α_{x x} & α_{x y} \\ α_{y x} & α_{y y} \end{matrix}]

(11)

The corresponding directional orientation as follows:

α_{x x} = \frac{1}{2} {[(\cos (2 φ) - 2 K_{r} φ + K_{r} \sin (2 φ))]}_{φ_{s}}^{φ_{e}}

(12)

α_{x y} = \frac{1}{2} {[- \sin (2 φ) - 2 φ + K_{r} \cos (2 φ)]}_{φ_{s}}^{φ_{e}}

(13)

α_{y x} = \frac{1}{2} {[(- \sin (2 φ) + 2 φ + K_{r} \cos (2 φ))]}_{φ_{s}}^{φ_{e}}

(14)

α_{y y} = \frac{1}{2} {[(- \cos (2 φ) - 2 K_{r} φ - K_{r} \sin (2 φ))]}_{φ_{s}}^{φ_{e}}

(15)

The above equations are further represented in terms of oriented frequency as:

\det ([I] + Λ [H_{o} (i ω_{c})]) = 0

(16)

where $Λ = - N_{t} / 4 π b K_{t} (1 - e^{- i ω_{c}^{τ}})$

Finally, the average stable depth of cut for the number of cutting teeth is represented as follows:

b_{\lim} = - \frac{2 π}{N_{t} K_{t}} Λ_{Re} (1 + κ^{2})

(17)

Where $κ = Λ_{Im} / Λ_{Re} = \sin ω_{c} τ / 1 - \cos ω_{c} τ$

where $τ = 1 / ω_{c} (ε + γ 2 π)$ is the tooth passing period and γ represents the number of lobes (0, 1, 2. . .) and the corresponding phase shift is $ε = π - 2 μ$ and $μ = \tan^{- 1} (κ) .$ The final expression for the spindle speed in terms of the number of teeth and tooth passing period is taken as follows:

Ω = \frac{60}{N_{t} τ} (rpm)

(18)

Using the above expressions (equations (17) and (18)), the stability lobe diagram is plotted for the various spindle speeds and average stable depth of cuts using the frequency responses arrived at the tip of the tool.

Results and discussions

Finite element modeling

The self-excited vibration levels during the machining process are induced between the cutting tool and workpiece. To model this spindle tool system, the material properties of the cutting tool and the geometrical dimensions of the entire unit are taken from the user manuals of the MTAB MAXMIILL vertical machining center. The parameters required to model the integrated spindle-tool unit are provided in the Table 1.

Table 1.

Elemental properties and dimensions of the FEM model.

	Number of the elements
S. No	E1	E2	E3	E4	E5	E6	E7	E8
Length (mm)	30	30	85	51	60	45	45	47
Outer. Dia (mm)	12	12	40	75	75	75	75	75
Inner. Dia (mm)	0	0	0	40	0	0	0	0
E(Pa)	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹	2.8 × 10¹¹
Density(Kg/m³)	7972	7850	7850	7850	7850	7850	7850	7850

A MATLAB program is written according to the geometrical dimensions of the integrated spindle tool unit to arrive at the frequency response at the tool-tip by considering all the connections along with bearing positions as shown in Figure 3. It is observed from the numerical simulations, the first dominant mode is at 2056 Hz. Figure 3B, represents the real and imaginary parts of the absolute frequency response.

Figure 3.

Frequency response at the tool-tip. (a) Absolute FRF, (b) Real and Imaginary FRF.

Three dimensional FE model

In this section, the entire spindle unit is modeled using the SOLIDWORKS software to validate the results obtained from the finite element model as shown in Figure 4. The dimensions of the spindle and the positions of angular contact bearings are considered as per the MTAB CNC vertical milling machine.

Figure 4.

Components of the integrated spindle unit using SOLID WORKS.

The modeled spindle-tool unit is imported into the ANSYS WORKBENCH for the simulation. For meshing of the entire model (i.e. spindle, bearings, tool holder, tool, etc.) a higher order Tetrahedral 3-D SOLID 187 element (consists of 10 nodes having three degrees at each node with translations in the nodal X, Y, and Z directions) is considered for the analysis. The material properties, as well as the geometrical dimensions, are considered to be the same as of the Timoshenko beam theory. In performing simulations, the inner races of the bearing are provided with free-free boundary conditions whereas the outer races of the bearing are provided with the fixed boundary condition as it was assumed to be fixed with the hub. Modal analysis is performed on the solid model of the spindle tool unit and the corresponding few natural frequencies as 2047.3 Hz, 2054.6 Hz, 2665.4 Hz, 2762.9 Hz, 4481.6 Hz, and 4711.1 Hz. The corresponding six mode shapes are shown in Figure 5.

Figure 5.

Mode shapes of the integrated spindle-tool model. (a) First mode shape, (b) second mode shape, (c) third mode shape, (d) fourth mode shape, (e) fifth mode shape, and (f) sixth mode shape.

It is observed that the first fundamental frequency from the ANSYS (i.e. 2047.3 Hz) has a close agreement with the one-dimensional finite element analysis.

Experimental modal analysis

To arrive at the frequency responses experimentally, sine-sweep modal testing is conducted on the vertical CNC MTAB vertical machining center with the FANUC system. The machine tool is having a provision for three axes with a single-phase motor to operate at different spindle speeds required for the machining process. A four-channel digital oscilloscope (Model-DPO43034) is used to record the output time histories, while a vibration shaker is used to excite the tool-tip. A signal generator is used to provide the various input frequencies to the vibration shaker to excite the tool-tip. Furthermore, a tri-axial accelerometer (PG109M0) is used at the tool-tip to capture these excitations. The list of this equipment is shown in Figure 6.

Figure 6.

Modal testing experimental setup with sample signal plots.

The sine-sweep testing on the CNC vertical spindle with different input frequencies is tabulated and the corresponding amplitudes are recorded in the oscilloscope. These various frequencies are generated by the signal generator at the constant amplitude with the help of a power amplifier. Each experimental test is repeated thrice and average readings are noted and a smooth curve is drawn with the obtained average set. Frequency is altered with a signal generator, which excites the tip of the tool, and the corresponding voltage signal in mill volts is taken in the oscilloscope. The amplitude in terms of the voltage signals is plotted against the corresponding input frequencies and is shown in Figure 7.

Figure 7.

Experimental modal frequency responses.

It has been observed from this plot, there are two sweeping range frequencies of 2039 Hz–2590 Hz, respectively. This first mode is having a better agreement with the earlier stiffened frequency response obtained from the finite element approach and with the three-dimensional approaches.

Stability lobe development and testing

A program is written in MATLAB software to develop the stability lobe diagrams (by utilizing the tool-tip frequency response obtained by the numerical methods. The cutting data and the modal coefficients are given in Table 2.

Table 2.

Modal and geometric parameters.

Cutting coefficients (K_x & K_y)	2.1 × 10⁸ N/m
Natural frequencies (ω_x=ω_y)	2056.5 Hz
Damping ratio (ξ_x & ξ_y)	0.01
Diameter of the cutting tool	12 mm
Specific cutting energy (K_s)	750 N/mm²
Number of cutting teeth (N_t)	4

For the down/up milling process the corresponding start and exit angles are considered as follows.

\begin{array}{l} φ_{s} = 180^{o} - \cos^{- 1} (\frac{r - a}{r}), φ_{s} = 180^{o} for down milling \\ φ_{e} = \cos^{- 1} (\frac{r - a}{r}), φ_{s} = 0^{o} for up milling milling \end{array}

where ‘a’ represents the depth of cut in a radial direction and ‘r’ represents the cutting tool radius respectively. To evaluate the correctness of the stability lobe boundaries, experimental cutting tests are performed on the CNC machining center. The vertical machine tool has a speed range of 4000 rpm with 3-Axis movement and a provision to accommodate different types of tool accessories. In the present, experimentation an end mill cutter with a diameter of 12 mm with four flutes has been used for the machining of aluminum alloy (Al-6061). The cutting displacements at specific depths and speeds during the machining process were recorded with an accelerometer with a frequency range of 1–10 KHz. These data were measured and recorded in a four-channel digital oscilloscope with a provision of a hard drive (USB) as shown in Figure 8.

Figure 8.

Experimental set-up for vibration and sound testing.

The displacements of the cutting tool during the machining process were recorded in the four-way channel digital oscilloscope and stored in time-domain signals in the USB drive. Further, this time-domain data is used to plot the corresponding FFT’s at the same specified speeds and depths 0.07 mm and 0.17 mm and are plotted in Figure 9. It is evident from these plots, as an increase in the cutting depth with the same spindle speed, the amplitudes of the tool displacements level increase which in turn forms the tool indentation marks. Further, it is also clearly observed that there is a change in the range of the chatter frequencies( ) from 1300 Hz to 1100 Hz, which clarifies that the chatter appears early during the machining process.

Figure 9.

Tool displacement levels and FFT diagrams at different depths of cut. (a) Depth of cut 0.07 mm (Stable) and (b) Depth of cut 0.17 mm (Unstable).

Furthermore, a microphone interfaced with the LABview software is utilized to get the sound spectrographs during the machining of the Al alloy. Figure 10 shows the sound pressure intensities are measured in the time-domain scale along with the equivalent power spectral density plots. From these plots, the peak chatter frequencies are identified and are indicated with star marks. It is evident from these PSD plots, the chatter frequency of 1350 Hz was observed at a depth of cut 0.07 mm. As the depth of cut is slightly increased to 0.17 mm, there is a change in the frequency range to 1090 Hz which leads to a possibility of early occurrence of chatter.

Figure 10.

Time-domain and PSD plots at different depths of cut. (a) Depth of cut 0.07 mm (stable), (b) Depth of cut 0.17 mm (unstable).

Using the Scanning electron microscope (SEM), the machining areas are scanned with a magnification scale of 100 μm at different cutting zones. Furthermore, the same samples are examined with an optical microscope, with a zoom factor of 10X were also observed at the specified depths of cuts and spindle speeds. It is evident that with these SEM and optical images at speed of 2200 rpm and an axial depth of 0.07 mm, the surface is observed with no chatter marks as shown in Figure 11B. As the depth of cut enhanced to more than 0.07 mm at the same spindle speed, the machining surfaces were observed with tool indentation marks on the surface, and well as large-sized pits were identified at the micro-level as shown in Figures 11C and 11D, respectively.

Figure 11.

Optical surface images at different depths of cut. (a) SEM image at 0.07 mm, (b) optical microscope image at 0.7 mm, (c) SEM image at 0.17 mm, and (d) optical microscope image at 0.17 mm.

The stability lobe boundaries are analytically plotted for a down milling process at full immersion and are shown in Figure 12. Further, the correctness of these analytical boundaries to estimate chatter-free regions is verified with the experimental cutting tests at the same cutting conditions. Few points are considered above and below the boundary lines and their corresponding SEM and optical images, sound spectrographs, and tool displacements levels were analyzed. Further, these cutting points were superimposed on the analytical stability lobe diagrams. These points are represented as circles (o) stating the stable cutting with no chatter marks, and with squares () representing the unstable with chatter marks. Based on the images and online measurement techniques, it is possible to estimate the chatter at the early stages of the machining process.

Figure 12.

Analytical stability lobe diagram with experimental verification.

Conclusions

This work presents a novel method of identifying the chatter phenomenon in the machining of Al alloys at the microscopic level in an end milling process. The numerical approach of identifying the tool-tip frequency responses with Timoshenko beam elements provides a valid method and it has been further validated with the experimental approaches as well. These methods were facilitating, to use extensively to arrive at the responses for the different combinations of tool and holder arrangements and this avoids the costly experimental trials. The tool-tip FRF’s obtained from the beam theory were utilized to plot the theoretical stability lobes. The following are some conclusion of the present work:

It was observed that for Al6061, the combination of smaller depths of cut, low feed, and higher spindle speeds are the key factors in reducing the chatter marks on the surface in the slot milling process.

The experimental investigations such as the tool vibration levels and sound pressure intensities provided in this paper present a different approach of online identification of the chatter frequencies at various depths of cut and spindle speeds.

Further, Micro-level deep investigation methods such as SEM and optical microscope are used to examine the machined surfaces and it was proved to be the predominant method of identifying the chatter marks both on the surface level as well as deeply for the Al6061.

Supplemental Material

sj-docx-1-nvw-10.1177_09574565221093232 – Supplemental material for Investigation of chatter prediction in end milling using morphological studies on aluminum alloy (Al6061)

Supplemental material, sj-docx-1-nvw-10.1177_09574565221093232 for Investigation of chatter prediction in end milling using morphological studies on aluminum alloy (Al6061) by Jakeer H Shaik, Rajasekhara R Mutra, Ahmed M Galal and Sinivasa R Tanneeru in Noise & Vibration Worldwide

Footnotes

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 iDs

Rajasekhara R Mutra

Ahmed M Galal

Supplemental material

Supplemental material for this article is available online.

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