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Nanomanufacturing and Metrology

, Volume 1, Issue 4, pp 236–247 | Cite as

A Finite Element Modeling Prediction in High Precision Milling Process of Aluminum 6082-T6

  • A. Davoudinejad
  • S. Doagou-Rad
  • G. Tosello
Original Articles
  • 129 Downloads

Abstract

This study investigates micro-end-milling machining prediction using three-dimensional finite element modeling method. The FE model was developed for contouring up-milling operation for prediction of chip flow, burr formation, cutting temperature and cutting forces in an integrated model. The flow stress behavior of the workpiece was modeled by the Johnson–Cook material constitutive model. Different cutting conditions were simulated to consider the effect of the process variables that might be difficult or impossible to follow in the physical experiments at this scale. The tool was precisely 3D modeled to describe the detailed geometry of the tool which is one of the critical aspects of the model and is characteristic of the cutter tool micro-geometry design. Furthermore, the tool deflection was studied using a FE model under the experimental cutting forces measured in the different cutting conditions in order to consider the micro-end-mill deviation from the nominal position. 3D simulations of chip flow and temperature distribution are compared in various cutting conditions. The results of the burr formation, temperature distribution and cutting forces in three directions predictions are compared against the experiments. Simulations were able to predict the burr height with an accuracy between 1 and 4 µm depending on cutting parameters settings. The results of this study are beneficial to comprehend the micro-end-milling chip and burr formation to increase the machinability of the workpiece and to understand the influence of cutting parameter in order to prevent several experimental tests prior to the final machining.

Keywords

3D finite element modeling Burr formation Chip formation Cutting force Deflection Micro-end-milling Temperature distribution 

1 Introduction

The micro-end-milling has become an established high-performance process within the last three decades. Various industries such as aerospace, automotive, medical, precision die and mold manufacturing use micro-milling for manufacturing complex miniaturized structure with high precision [1]. A number of experimental studies have investigated micro-machining by evaluating the cutting parameters to improve the process performance in terms of surface roughness, cutting force, chip and burr formation, tool wear, tool life [2, 3, 4, 5, 6]. However, the predictive models are also used and can be combined as a supplementary tool into the process planning system to increase productivity and improve product quality [7, 8].

FE modeling of machining process has been reported by different studies. For example, 2D FEM was used for high-speed cutting (up to 200,000 rpm) to predict burr formation on Ti–6Al–4V in micro-end-milling process [9].

Another study evaluated the stress distribution in the vicinity of the cutting edge [10]. Microstructural texture evolution by 2D FEM was investigated in high-speed machining of Ti–6Al–4V alloy, and plastic deformation of the machined surface was analyzed [11]. The same workpiece material was used to investigate the stress distribution on the tool surface and friction coefficients between the tool and the formed chip on the tool rake face with FE simulations [12].

In addition to 2D analysis, the 3D FEM method provides additional analysis material to explore the effect of the cutting tool on chip flow and burr formation [13]. A 3D FEM in dry micro-milling process studied chip formation such as plastic chip flow, plastic strain, principle stresses and temperatures of titanium alloy Ti–6Al–4V [14]. Another study [13] with 3D FEM investigated the effect of the cutting edge radius on temperature distribution, effective stress and simulated cutting forces in Al2024-T6 micro-milling. Abouridouane et al. [15] studied microstructure-based multiphase FEM of micro-drilling ferritic-pearlitic carbon steels. Various size effects and chip formation were predicted with experimental tests, and more than 60% improvement in feed and torque with FEM computation was observed. Chip formation and cutting forces were predicted with a developed 3D multiphase FEM. A comparable cutting forces and chip formation prediction tool was validated against the experiments [16].

The micro-burr formation was investigated in the past decades mainly with experimental, analytical and numerical methods. Different studies classified burrs formation according to its location in milling process, namely entrance burr, exit burr, side burr, top burr and bottom burr [17, 18]. Micro-milling FEM simulations were conducted for controlling the burr formation by vibration-assisted machining on the top burr generation results [19]. The 3D FE simulation was used to investigate the prediction capability of the model on different types of burr formations in micro-ball milling of Ti–6Al–4V alloy [17].

This study presents 3D FE simulations of contouring operation micro-up-milling by considering tool helix angle and corner radius. Different cutting conditions are simulated in order to evaluate the possible prediction capability. Various aspects of machining process were assessed, and the model is used to study the chip flow, burr formation and temperature distribution. The burr formation, cutting forces and temperature predictions are validated by comparing the FEM results with experiments. The design of experiments analysis DOE is carried out on the burr formation to clarify the parameters contribution and to show the experimental and simulation comparison. Additionally, the tool deflection under the acquired experimental cutting forces was studied using a structural finite element modeling.

2 3D FE Modeling

2.1 FE Model

The FE model for micro-milling of aluminum 6082-T6 has been established using a Lagrangian FE formulation for implementing coupled thermo-mechanical transient analyses by AdvantEdge® FEM software [20]. The calculations were carried out on with 8 threads parallel simulation mode to speed up the simulation time. The computing time was 25–35 h long based on the selected conditions. Figure 1 presents the setup and the geometry of the model.
Fig. 1

Up-milling setup and tool cutting edge

2.2 Tool and Workpiece

Considering the proper geometry of the tool is a significant factor for modeling accuracy as it was investigated and demonstrated in the previous study on the influence of the tool cutting edge solid modeling [21]. In this context, the accuracy of the micro-end-mill model is critical. A CAD model was generated based on the points cloud obtained by a 3D optical microscope in order to demonstrate and reproduce the actual topology of the micro-end-mill. The geometry of the mill (Table 1) was scanned and reconstructed by using an Alicona G5 focus variation 3D microscope. A four-node tetrahedral elements type was used for meshing tool and workpiece which is one of the most proper mesh types for 3D modeling [22]. The rigid micro-end-mill was meshed using 58,205 brick elements and 15,042 nodes. The workpiece was meshed with total number of 27,870 elements and 5458 nodes. After earliest tests [23, 24], the element sizes for the workpiece were set to 2 mm and 1 µm. A finer mesh was defined in the region of the contact on the micro-end-mill (Fig. 1b, d) and the workpiece cutting zone area.
Table 1

Tool characteristics [23]

 

Actual dimensions

Tool manufacturer

Dormer

Code

S150.05

Tool material

Carbide

Flute number

2

Diameter

493 µm

Cutting edge radius (re)

3 μm

Helix angle

27.26°

Rake angle

Relief angle

Corner radius (rε)

22 µm

The tool element size was fixed at 1 mm and 1 µm. The quality of the mesh was continuously monitored in the run and, when the element distortion reached a certain threshold, adaptive remeshing was applied. A reliable material model is critical in machining simulation performance [25]. Among various material models, the Johnson–Cook (JC) model [26] is broadly applied for machining simulations for equivalent behavior of material as a function of strain, strain rate and temperature [27]. The JC material model used in this study is expressed in Eq. (1):
$$\sigma = (A + B(\varepsilon )^{n} )\left[ {1 + C\ln \left( {\frac{{\dot{\varepsilon }}}{{\dot{\varepsilon }_{0} }}} \right)} \right]\left[ {1 - \left( {\frac{{T - T_{\text{a}} }}{{T_{\text{m}} - T_{\text{a}} }}} \right)^{m} } \right]$$
(1)
where σ is the material flow stress, ε is the plastic strain, \(\dot{\varepsilon}\) is the strain rate, \(\dot{\varepsilon}_{0}\) is the reference strain rate. T is the material temperature, Tm is the melting point and Ta is the room temperature. The JC constants are as follows: A is the yield stress, B is the pre-exponential factor, C is the strain rate factor, n is the work hardening exponent, and m is the thermal softening exponent. Tables 2 and 3 list the JC material constants and the physical properties of material, respectively.
Table 2

Material constants for the JC model [24, 28]

A (MPa)

B (MPa)

C

m

n

Tm (°C)

Ta (°C)

214.25

327.7

0.00747

1.3

0.504

582

21

Table 3

Material properties for Al6082-T6 [24]

Property

Unit

Value

Young’s modulus E

GPa

70

Poisson ratio v

0.33

Density ρ

g/cm2

2.70

Thermal conductivity K

W/m K

180

Specific heat Cp

J/Kg °C

700

Thermal expansion coefficient

°C

24 × 10−6

Coulomb law (Eq. 2) was used as friction model. This model considers frictional stresses τ on the tool rake face relative to the normal stresses \(\sigma_{n}\) with a friction coefficient µ [29]. The constant value of coefficient of friction was assigned as µ = 0.7 based on the experimental study on Al6061-T6 [30]. These two aluminum Al6082-T6 and Al6061-T6 are popular alloys that sometimes are used to replace each other in the industrial practice due to the similar characteristics.
$$\tau = \mu \sigma_{n}$$
(2)

2.3 Deflection Model

The tool deformation was also studied using FE simulations. The simulations are conducted using the commercial FE code ABAQUS Implicit. Quadratic tetrahedral elements (C3D10) were used to mesh the FE models. Mesh-seed lengths of 0.5 μm were used around the tip of the tool. The convergence studies led to the construction of FE models comprising 700,000 elements. Figure 2 shows the full length of end mill with fine mesh on the region of interest. The processing unit similar to the aforementioned FE simulations was used. Figure 2 shows the constructed FE model and the implemented mesh distribution.
Fig. 2

Tool FE model in ABAQUS

3 Experimental Method

Experiments were carried out on a Kern EVO ultra precision 5-axis machine (Fig. 3) with the positioning tolerance on the workpiece equal to ± 2 μm as stated by the manufacturer. The workpiece was especially designed to carry out the machining near the geometrical center of the dynamometer flange as shown in Fig. 3. The carbide micro-end-mill (Dormer S150.05) details are presented in Table 1. The infrared ThermaCAM Researcher camera with waveband in the electromagnetic spectrum (in the range of 8–9 μm) has been used for measuring the temperature at the cutting area. All of the experimental data have been normalized to a room temperature of 21 °C. The camera was adjusted with standard blackbodies at different temperatures [31]. Figure 3c shows the experimental temperature measurements in the cutting area at different cutting conditions.
Fig. 3

a Experiment setup, b cutting area (top view), c experimental temperature measurements

The cutting edges were measured with a 3D optical microscope (Alicona) before machining with the following measurement parameters: 10× magnification, exposure time = 1.206 ms, contrast = 1, coaxial light, estimated vertical and lateral resolutions = 0.083 μm and 4 μm, respectively. A good agreement between nominal and measured value was found for the characteristics angles (Table 1). Table 4 shows the experimental conditions of the tests. The cutting parameters were selected with consideration of previous studies on the process parameters and burr formation [22, 32]. The test plan was a 22 full factorial DOE. The tests were repeated two times. The cutting conditions (feed per tooth, depth of cut, width of cut) were selected to stay around the cutting edge radius, this way, to appreciate the minimum uncut chip thickness effect.
Table 4

Experimental conditions

Cutting parameters

Unit

Test 1

Test 2

Test 3

Test 4

Depth of cut

µm

50

100

50

100

Width of cut

µm

125

250

Feed per tooth

µm/(tooth·rev)

4

Cutting speed

m/min

28.27

Approach

 

Up-millings

The micro-slots were acquired with an Infinite Focus Alicona G5 focus variation 3D microscope (with the following measurement parameters: 10× magnification, exposure time = 110 ms, contrast = 1, coaxial light, estimated vertical and lateral resolutions = 3.6 μm and 2.4 μm). Concerning the cutting force, a miniature piezoelectric three-axial dynamometer Kistler 9317B was used and amplified by three Kistler 5015A charge amplifiers.

The force signal compensation [19] was applied to remove the dynamic contribution of the sensor resonance. The frequency response functions (FRF) of the dynamometer were recognized from impact tests applied on the force directions as detailed in [33].

4 Results and Discussion

Different chip shapes were found after 360° tool rotation in different cutting conditions. Figure 4 presents the plastic strain distribution in the cutting area. The plastic strain has a slight reduction in comparison with the highest cutting condition. The variation of the plastic strain is more visible on the burr formation and machine wall. It was noticed that the degree of plastic deformation on the machined surface area increases considerably in the lowest cutting condition as represented in Fig. 4a. Figure 5 shows different phases of the tool engagement and the distribution of temperature in the tool and cutting area. The simulation predicted temperature reaches its maximum of ≈ 35.5 °C in the chip and workpiece zone at highest engagement angle. It is visible in the simulations, where the chip thickness starts at zero and increases toward the end of the cut. Highest temperature distribution was observed in Test 4 (Fig. 5d) with higher axial and radial depth of cut. It can be noticed that the chip shows the highest temperature mainly due to its intensive plastic deformation. In the higher cutting conditions, temperature rises mainly due to the heat generation of the workpiece (mechanical energy) in the deformation zones and the friction between the tool–chip and tool–workpiece interface. Therefore, more heat is generated in the chip area at Test 4 (Fig. 5d) and more in the machined surface wall at Test 1 (Fig. 5a) which is correlated with increased plastic deformation in the cutting interface.
Fig. 4

Plastic strain distribution in the cutting zone. a Test 1 (ap = 50 μm, ae = 125 μm), b Test 2 (ap = 100 μm, ae = 125 μm), c Test 3 (ap = 50 μm, ae = 250 μm), d Test 4 (ap = 100 μm, ae = 125 μm)

Fig. 5

Simulated chip temperature distribution in different angular positions and along the cutting edge at the end of cut

Simulated temperature on the tool corner is presented (on the right side) in Fig. 5 at the end of cut for (Test 1, 2 θ ≈ 50° and Test 3, 4 θ ≈ 125°). The heat is determined in the chip and contact area of the workpiece and for the tool mainly in cutting edge radius. Lower temperature distribution in the cutter area vicinity recorded than the chip and workpiece.

4.1 Burr Formation

Burrs formation at various cutting conditions in FEM (end of the cut) and in real experiments from the side and the top, respectively, is shown in Fig. 6. Based on the burrs classification defined in [17, 18], top burrs were formed on the top side of the machined slot. The simulations were carried out for both teeth engagements, and the pictures of FEM results illustrate the end tool engagements arc. However, the experimental results indicate several teeth engagements. Figure 7 shows the top burr height comparison from experimental and simulation results. The results indicate that machining conditions influence the burrs.
Fig. 6

Burr formation in different cutting conditions. a Test 1 (ap = 50 μm, ae = 125 μm), b Test 2 (ap = 100 μm, ae = 125 μm), c Test 3 (ap = 50 μm, ae = 250 μm), d Test 4 (ap = 100 μm, ae = 250 μm)

Fig. 7

Burrs height assessment at different conditions

Based on the selected machining conditions, the depth of cut and width of cut affected the top burr height. Top burr size is higher for lower ap values (Test 1, Fig. 6a and Test 3, Fig. 6c). The smallest top burr is obtained for high depth and width of cut (Test 4, Fig. 6d).

The design of experiments (DOE) technique was applied to investigate the different parameters’ effect. The interaction and main effect plots are presented in Fig. 8. The main effect plot (see Fig. 8a) shows the burr height variation which by increasing depth and width of cut smaller burr was formed on the machined wall. The interaction plot in Fig. 8b shows experimental and simulation in different depths of cut, widths of cut and burr measurement positions. The simulation results were underestimated between 8 and 17% in evaluation with the experimental results; nevertheless, parallel trends were predicted for all simulations. The deviation of height was in the range of 2–4 μm. It was noticed with respect to the experimental cutting conditions, the prediction of burr height was rather poor in lower setting (depth of cut 50 µm and width of cut 125 µm).
Fig. 8

a Main effects plot of burr height and b interaction plot of burr height

4.2 Cutting Forces

A low-pass filter with a fifth-order Butterworth was used for the simulated cutting force signals. Similar experimental cut-off frequency to the bandwidth of the dynamometer (about 7000 Hz) was applied to the signals for the comparable results with experimental tests [24]. In the previous experiments with similar cutting speed, similar sampling frequency was applied [33]. The assessments were performed with the results obtained from the FEM and the experiments for one tooth engagement as shown in Fig. 9. The shapes of the first tooth forces acquired for two different cutting conditions, Test 1 and Test 2, are presented. Feed force Fx is the main component and presented the highest force value and shows similar trends for FEM in comparison with experiments. In the up-milling approach the force directions the initial of the cut start at zero and increases by the engagement of the tooth toward the end of machining path. Fx starts decreasing faster and with a lower inclination in case of FEM. In the experiments with this approach the cutting edge forced into the workpiece and cutting forces push the cutter. The difference might be due to the fact that during the experiments, the cutting edge slides on the workpiece. Another issue that generated problems was represented by the influence of the built-up edge (BUE) on the tool which alters the geometry of the cutting edge and also increases the deviation between real and nominal spindle speed in the machine tool, and as a consequence it could affect the tool engagement. The Fy forces for both results show a minor decrease and a positive increase at the end of the cut. The force in Z direction (Fz) has very small value in comparison with other force directions, so it is frequently neglected in the models. The cutting forces evaluation presents a similar trend of profile curve shapes, for three forces components. A slightly relevant over-estimation of the forces in X and Y directions is recorded in the simulated conditions. The mismatching in the validation of cutting force can be explained by the tool static deflection during machining since the model does not include the simulation of cutting deflection. The spindle and the cutter run-outs were not considered in the FE model.
Fig. 9

Cutting forces comparison, process settings for Test 1 and 2

4.3 Deflection

Acquiring the cutting forces from experiments and simulation enables us to study the deflection behavior of the tool under the accompanying loads during the process [34]. In order to achieve high-quality part geometry and desirable tolerances, the sources and levels of errors should be completely understood. In fact, one of the major sources of the error in the process is originated from the tool deflection. Therefore, the tool deflection under the actual loads in the process is investigated using structural finite element. Two loading scenarios with the two described depths of cuts are considered in the simulations (See Fig. 9). In the second loading case, the depth of cut is twice as that of the first scenario. Figure 10 shows the maximum deflections of the tip under the achieved experimental forces.
Fig. 10

The maximum total deflection considering the loading and depth of cuts, process settings for a Test 1 and b 2. Deflections in the pictures are scaled up 100 times. (The depicted magnitudes are in millimeters)

In addition, considering the forces in one cycle, the deflections of the tool along the length of the tip under the two applied loads were studied. Figure 11 presents the average deflections of the tool in one cycle along the whole length of the tool under individual and total loading directions. As it can be clearly seen from the results, the deflection of the tip increases notably with increasing cutting depths. In fact, under second loading forces the maximum deflection increases up to 4.5 μm. It is also noteworthy to mention that since the tip deforms elastically, the deflection of the tip follows the similar path observed in Fig. 9.
Fig. 11

Deflection of central axis of the tool, process settings for a Test 1 and b 2

5 Conclusion

A numerical model has been developed to investigate the micro-milling process of the aluminum alloy Al6082-T6. The JC material model was employed with modified coefficients for the specific workpiece material. 3D FE simulations were utilized for predicting different machining aspects. The tool CAD model was generated based on the actual geometry by using the micro-end-mill cloud of points. The model was validated with experimental tests carried out in various conditions. The tool deflection was also investigated under the acquired experimental cutting forces to find out the deformation of the tool position regarding the nominal geometry. In addition, the influence of the cutting depth on the deflection of the tool was studied. The evolution of chip generation and the cutting temperature distribution were demonstrated. The predicted temperature along the cutting edge and machining was determined. The maximum temperature that was observed was approximately of 35.5 °C. The simulated burrs revealed comparable results with respect to the corresponding experiments. Burrs characteristics were affected by the different cutting conditions as shown by the DOE analysis that was in fact conducted to clarify the effects of the different machining settings. The simulation results were underestimated between 8 and 17% in comparison with the experiments. The proposed 3D FE model demonstrated a good matching with experiments force profiles shape, mostly in the two major directions Fx and Fy and comparable cutting forces amplitude in all directions.

Notes

Acknowledgements

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. 609405 (COFUNDPostdocDTU). The authors would also like to acknowledge the Politecnico di Milano (Italy) for funding the PhD project “3D finite element modeling of micro end-milling by considering tool run-out, temperature distribution, chip and burr formation” by Dr. Ali Davudinejad.

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Copyright information

© International Society for Nanomanufacturing and Tianjin University and Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark

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