Anna Carla Araujo

Adriane Lopes Mougo

Fabio De Oliveira

Micro milling cutting forces on machining aluminium alloy ICOMM 2013 64

Keywords: micro milling, mechanistic models, cutting forces

INTRODUCTION

Miniaturization has increased over the last decade and, as a consequence, manufacturing of micro parts for bioengineering and aerospace applications are one of the areas there is a need of research and development. Micro milling is a flexible machining process that allows the fabrication of high quality parts. Cutting force analysis plays a vital role in studying the micro milling processes. The stress variation on the shaft of a micro-tool is much higher than that on a conventional tool, as in micro milling operations the feed per tooth to tool radius ratio has to be higher than in conventional milling to keep productivity at a reasonable level [START_REF] Bao | Modeling micro-end-milling operations. Part I: analytical cutting force model[END_REF]. Due to the small size of the micro-tools, it is very difficult to notice the damage in the cutting edges and an inappropriate selection of the cutting conditions can cause the tool to brake unexpectedly. The micro-tools used in this operation have a diameter of less than 2 mm. In machining of metallic components, the size of the part plays an important role, called size effects. Even if the relationship between the main geometrical features is kept constant, the process behavior changes. Vollertsen et al. [START_REF] Vollertsen | Size effects in manufacturing of metallic components[END_REF] presented a review on effects of size effect and their use: the article presents the typology of size effects, a description of size effects on strength and tribology and size effects on formability and machinability. Camara et al. [START_REF] Câmara | State of the Art on Micromilling of Materials, a Review[END_REF] presented a state of art on micromilling with emphasis on the work material requirements, tool materials and geometry, cutting forces and temperature, quality of the finished product, burr formation, process modeling and monitoring and machine tool requirements. Two process mechanisms, ploughing and chip formation , are involved in micromachining. A critical cutting thickness needs to be exceeded to involve both phenomena. Ramos et al. [START_REF] Ramos | Characterization of the transition from ploughing to cutting in micro machining and evaluation of the minimum thickness of cut[END_REF] studied the minimum uncut chip thickness. Besides the ploughing mechanism, where part of the material is plastically pushed against the workpiece surface when tc<tcmin, there is also the mechanism of elastic deformation, when the deformation forces are proportional to the interference volume between the tool and the workpiece when tc<<tcmin [START_REF] Vogler | On the modeling and analysis of machining performance in micro-endmilling, Part II: Cutting force prediction[END_REF]. Similarly, Malekian et al. [START_REF] Malekian | Modeling of minimum uncut chip thickness in micro machining of aluminum[END_REF] used the minimum uncut chip thickness, under which the material is not removed but ploughed, and claimed that this effect causes an in increase of machining forces that affect the surface integrity of the workpiece. Microstructure has a significant effect on microscale cutting. Simoneau et al. [START_REF] Simoneau | Grain Size and Orientation Effects When Microcutting AISI 1045 Steel[END_REF] investigates the effect of grain size and orientation during microcutting in FE modeling of the primary shear zone. Their research group [START_REF] Simoneau | Chip formation during microscale cutting of a medium carbon steel[END_REF] analyzed the orthogonal cutting in microscale. Tests were conducted on steel and the resulting chips examined, showing that the chip formation changes from continuous to "quasi-shear-extrusion" chip due to the uncut thickness size. The results indicate that the pearlite and softer ferrite grains play distinct roles in the plastic deformation process. Abouridouane et al. [START_REF] Abouridouane | Size Effects in Micro Drilling Ferritic-Pearlitic Carbon Steels[END_REF] investigate size effects by down scaling the twist drilling using a Lagrangian formulation proposed in the implicit code. He also presented a new three-dimensional multiphase finite element computation model for the simulation of micro drilling two-phase ferritic-pearlitic carbon steels [START_REF] Abouridouane | A new 3D multiphase FE model for micro cutting ferritic-pearlitic carbon steels[END_REF]. This article analysed the cutting mechanism, the ploughing phenomena, tribological and heat transfer mechanisms at the microscale. Jin and Altintas [START_REF] Jin | Prediction of micro-milling forces with finite element method[END_REF] presents the prediction of micro-milling forces using cutting force coefficients evaluated from the finite element simulations of orthogonal micro-cutting process and compared to experimental turning results. The milling forces in their model are calculated based on the local geometry and chip load. Bao and Tansel [START_REF] Bao | Modeling micro-end-milling operations. Part I: analytical cutting force model[END_REF] proposed an analytical force model for micro end milling process based on Tlusty's model [START_REF] Tlusty | Dynamics of cutting in end milling[END_REF] but using a new expression for the chip thickness. They computed by the trajectory of the tool tip and observed that the model gives a good result at higher feed rate which supports his assumption that feed per tooth to tool radius is larger in micro end milling than in the conventional end milling operation. Zaman et al. [START_REF] Zaman | A three-dimensional analytical cutting force model for micro end milling operation[END_REF] established a new concept to estimate the cutting force in micro end milling by estimating the theoretical chip area instead of undeformed chip thickness. Pérez et al. [START_REF] Pérez | Estimation of cutting forces in micromilling through the determination of specific cutting pressures[END_REF] developed a new model for the estimation of cutting forces in micromilling based on specific cutting pressure. The proposed model includes three parameters which allow to control the entry of the cutter in the workpiece and which consider also the errors in the radial position of the cutting edges of the tool. The new mechanistic force model determines the instantaneous cutting force coefficients using experimental data processed for one cutter revolution. The model has been validated through experimental tests over a wide range of cutting conditions. The re-sults obtained show good agreement between the predicted and measured cutting forces. Rodriguez e Labarga [START_REF] Rodríguez | A new model for the prediction of cutting forces in micro-end-milling operations[END_REF] developed a new cutting force prediction model in micromilling operations for application on machining monitoring systems, considering the most influents factors of the process, like tool deflection, runout, scale effect and . Experiments carried out on Aluminum 7075 and AISI 1045 steel presented a good concordance with simulated results. Kang et al. [START_REF] Kang | A mechanistic model of cutting force in the micro end milling process[END_REF] developed a mechanistic model to predict the cutting force in micro milling and its influence on tool wear and superficial roughness of Al 7075 alloy. Experimental results showed good concordance and the raise of the feed per tooth indicated a raise of the cutting force values. This article compares mechanistic models for micro milling process considering homogeneous grain properties. It is not taken into account dynamic behavior of tool and interactions between tool-workpiece due to stiffness or grain variation. Experimental data is used to calculate specific pressure in different approaches and compare results between models.

CUTTING FORCE MODELLING

The knowledge of cutting forces is fundamental for tool optimization and it is very important to avoid tool breakage and instability. In micro milling, those factors are even more relevant due to the high cost of tools, that breaks very easily. Meso and micromilling models are presented.

A. CHIP LOAD CUTTING MODEL

Elemental normal and frictional forces are required to the determination of cutting forces for a given geometry. The mechanistic modeling approach is a combination of analytical and empirical methods in which the forces are proportional to the chip load [START_REF] Kline | The prediction of cutting forces in end milling with application to cornering cuts[END_REF]. The specific cutting pressure, K n , K f and K z , have been shown as a function of chip thickness t c in mesoscale milling process and it is used for calculation of dF n , dF f and dF z on each angular position θ of the discretized cutting edge, proportional to the chip load area dA as shown in [START_REF] Bao | Modeling micro-end-milling operations. Part I: analytical cutting force model[END_REF].

𝑑𝐹 ! 𝜃 = 𝐾 ! 𝑑𝐴 𝜃 𝑑𝐹 ! 𝜃 = 𝑚 ! 𝐾 ! 𝑑𝐴(𝜃) 𝑑𝐹 ! 𝜃 = 𝑚 ! 𝐾 ! 𝑑𝐴(𝜃) (1)
Using a semi empirical modeling as [START_REF] Tlusty | Dynamics of cutting in end milling[END_REF], relating specific cutting pressures by empiric factors m1 and m2.

Chip area is calculated based on uncut chip thickness 𝑡 ! 𝜃 , that is called Martellotti equation:

𝑡 ! 𝜃 = 𝑓 ! 𝑠𝑖𝑛 𝜃 (2)
The specific cutting pressure is calculated as:

ln 𝐾 ! = 𝑎 ! + 𝑎 ! ln 𝑡 ! + 𝑎 ! ln 𝑉 ! + 𝑎 ! ln 𝑡 ! ln 𝑉 ! (3)
The coefficients a 0 , a 1 , a 2 and a 3 are called specific cutting energy coefficients. They are dependent on the tool and workpiece materials and also on the cutting speed and the chip thickness. They are determined from calibration tests for a given tool work piece combination and for a given range of cutting conditions.

B. CHIP LOAD AND CUTTING EDGE MODEL

The differential tangential, radial and axial cutting forces can be separated in cutting area dependent part and cutting edge part, as in (3) [START_REF] Pérez | Estimation of cutting forces in micromilling through the determination of specific cutting pressures[END_REF].

dF ! θ = K !" 𝑡 ! 𝜃 db + 𝐾 !" 𝑑𝑏 dF ! θ = m ! 𝐾 !! 𝑡 ! 𝜃 𝑑b + 𝐾 !" 𝑑𝑏 𝑑𝐹 ! 𝜃 = 𝑚 ! 𝐾 !! 𝑡 ! 𝜃 𝑑b + 𝐾 !" 𝑑𝑏 (4)

C. CHIP THICKNESS CORRECTION IN MICRO CUTTING MODEL

Bao [START_REF] Bao | Modeling micro-end-milling operations. Part I: analytical cutting force model[END_REF] developed a more precise expression then Martelotti calculation for uncut chip thickness 𝑡 ! 𝜃 used by Newby et al. [START_REF] Newby | Empirical analysis of cutting force constants in micro-end-milling operations[END_REF] to calculate average uncut thickness.

𝑡 ! 𝜃 = 𝑓 ! 𝑠𝑖𝑛 𝜃 - ! !!" 𝑓 ! ! 𝑠𝑖𝑛 𝜃 𝑐𝑜𝑠 𝜃 + ! ! ! !! 𝑐𝑜𝑠 ! 𝜃 (5)

D. SIZE EFFECT BY PLOUGHING

Ploughing effect under minimum uncut chip thickness, which was modeled by different approaches. Liu et al. [START_REF] Liu | An Analytical Model for the Prediction of Minimum Chip Thickness in Micromachining[END_REF] modeled considering analytical model using slip line theory and Johnson-Cook model. Malekian et al. [START_REF] Malekian | Modeling of minimum uncut chip thickness in micro machining of aluminum[END_REF] presented an article on micromilling of aluminium, which is used in this article based on the edge radius 𝑟 ! and on a critical or stagnant angle, 𝜑 ! .

t !" = r ! (1 -cos φ ! ) (6)
The stagnant angle is considered equal to the friction angle between the material and the rake face, regardless of the other parameters involved in the process.

EXPERIMENTAL SETUP

In order to analyze micro milling forces and compare to modeled results, experiments were performed.

E. MATERIAL, TOOLS AND EXPERIMENTS

The workpiece material selected for the experiments is an aluminum alloy (Al 6351-T6), which is an AlMgSi alloy usually applied in the automotive, construction engineering and shipbuilding industries. The overall workpiece dimensions are 47x50x15 mm, in which a small area is faced to be subjected to the experimental machining.

It was used a carbide micro-milling tool, very often applied in medical, aerospace and electronic areas, with 0.381 mm diameter and 1.143 mm flute length, as showed in Figure 1 based in manufacturer information. The cutting tool was measured in SME microscopy. As the cutting edge radius has strong influence on the cutting force model chosen, the images presented on Figure 2 were taken.

Using those SEM images, the helix angle, point radius and cutting edge radius is measured. The tool has point tip radius of 2,5µm, cutting edge radius of 0,5µm and β=30° helix angle.

Figure 2: SEM Microscopy of the cutting tool presenting the cutting edge radius (rε)

The micro machine used on the experiments was the CNC Mini Mill/GX from Minitech Machinery Corporation. The machine uses NSK 60K RPM Precision Spindle with 3 Axis Controller. Its standard resolution is 0.00078125mm using dual linear ball bearing slides on each axis, sealed for the table mechanism (THK linear slides -RSR15 series, Caged-ball technology). The drive mechanism THK Ball Screw actuator -preloaded and sealed, achieves low torque fluctuation and no backlash.

A mini-dynamometer is used for cutting force measurement.

The MiniDyn KISTLER 9256C2 used cable 1697A5, as shown in Figure 3. The cutting force components are presented in the Figure . It was used a charge amplifier 5070A10100 and a data acquisition board NI USB 6251. Table 1 summarizes the equipment used on the set-up. x 20 mm was faced using a 3mm milling tool, 18m/min cutting velocity and feed rate equals to 200 mm/min. The micro milling tool performed a surface trajectory before each pass to guarantee the axial depth of cut designed. The axial depth of cut chosen is 20 times higher then the point radius, 100µm. That is why the main cutting edge has more significance impact on the cutting model. The secondary cutting edge was neglected.

Considering the cutting edge radius of 0,5µm, three feed per tooth (f t ) values were planned for tests from 1-5µm, almost 10 times higher then the radius. This choice was made in order to use cutting models that does not considers ploughing as the main component of the cutting force. Two replicates were run for each level of feed per tooth and 20 revolutions of the signal were taken. Table 2 presents the cutting parameters used on the experiments.

RESULTS AND DISCUSSION

In this section it is presented the experimental data, the simulated curves and a basic specific cutting pressure is calculated.

G. EXPERIMENTAL RESULTS

The experimental data was averaged using 20 revolutions for each test. Is is presented on Figure 4, 5 and 6 three representative curves for the experiments using 0,002 mm/th, 0,004mm/th and 0,005 mm/th respectively. The force components presented (Fx and Fy) represents the components on the plane normal to the spindle, as presented on Figure 3a.

No filter is applied and 2N/V amplification is used in the charge amplifier, the maximum rate. Using all experiments, the resultant force is calculated and the higher value is taken on each revolution. All results are taken into account to produce the graphic presented on Figure 7. This figure shows that the maximum resultant force remains linearly distributed if the feed is increased. Although when the feed is doubled, the force does not increase in this same rate. For comparison purposes, simulations were performed using the cutting data presented on Table 2. Specific pressure 𝐾 ! is considered as 5000N/mm 2 using the value taken from [START_REF] Pérez | Estimation of cutting forces in micromilling through the determination of specific cutting pressures[END_REF].

The radial specific pressure is considered as 40% of 𝐾 ! . Figure 8 presents the results calculated for the three levels of feed rate used on experiments. Figure 8a uses ft=0,002mm/th, Figure 8b uses ft=0,004mm/th and ft=0,005 is used on Figure 8c. Figure 9 shows the three resultant forces, one for each case.

In the model, the force is proportional to the area and it is not considered tool run-out, as the experiments did not shown strong differences between the two cutting flutes. Specific pressure 𝐾 ! considered for aluminium in the simulation is over estimated. Using experimental data and considering only the maximum resultant force, the specific cutting pressure calculated is four times less the simulated one. The value of 1000 N/mm 2 is nearer the meso scale specific force for aluminium.

CONCLUSIONS

This article deals with micro milling of an aluminium alloy using three levels of feed rate and constant cutting velocity, axial depth of cut and same tool. First effort on experimental cutting force is challenged in our laboratory. Experimental and simulated forces are qualitatively compared. The specific pressure considered based on previous articles is over estimated, as values around 1kN/mm 2 is calculated from experiments.

Figure 1 :

 1 Figure 1: Tool Dimensions

  Figure 3: Experimental Set-up

Figure 4 :

 4 Figure 4: Experimental Cutting Components F x and F y using f t =0,002 mm/th.

Figure 5 :

 5 Figure 5: Experimental Cutting Components F x and F y using f t =0,004 mm/th.

Figure 6 :

 6 Figure 6: Experimental Cutting Components F x and F y using f t =0,005 mm/th.

Figure 7 :

 7 Figure 7: Effect of feed per tooth on Resultant Forces

Figure 8 :Figure 9 :

 89 Figure 8: Simulated Cutting Components F x and F y

Table 2 : Cutting Parameters

 2

	Spindle revolution	20,000 rpm -clockwise
	Cutting Velocity	18 m/min
	Feed per tooth	2, 4 and 5 µm/tooth (Three Levels)
	Axial depth of cut	100µm
	Width of cut	381 µm (full immersion)
	Length of cut	15 mm
	Workpiece material	Al 6351 T6

ACKNOWLEDGE

The authors thanks to: the support of the CAPES for acquiring the equipment used in this article thru Pro-equipamentos resources, to the kindly services of UFRJ importation department and for the Mechanical Engineering Department.


Gabriel Bezerra De Menezes

Silva Anna

Carla Araujo

COMPUTATIONAL ALGORITHM BASED ON ALTINTAS MODEL FOR CUTTING DYNAMICS OF END MILLING PROCESS

Keywords: Metal cutting, End milling, Chatter, Vibration stability

The study of cutting dynamics is important to predict regenerative vibration to avoid tool breakage and bad surface quality. In this study the critical stability condition of an end milling operation is simulated based on Altintas Model for dynamics of metal cutting. This analytical model considers the milling tool and the workpiece as system of two degrees of freedom. The required routine calculates the depth of cut that defines the stable and unstable region for all the possible spindle speed disposable on the machine. Using all the results for the limit depth of cut is possible to build the diagram of stability lobes. The algorithm considers as input parameters: the tool geometry, workpiece material, specific cutting forces and dynamic coefficients of the tool. Using the algorithm it is possible to evaluate the contribution of each parameter to reduce chatter and in this study some parameter contribution are analyzed by comparing the different lobes diagrams. Material removal rate is considered to compare different situations for the exit angle. For the specific parameters described, it was possible to find one value for the exit angle, and consequently the width of cut, that maximizes the removal rate without chatter.

INTRODUCTION

The manufacturing scientific research usually focus topics that involves the analysis of materials, tool wear, geometry, mechanics and dynamics of the process. Several machining operations are executed by a large variety of machine-tools in order to produce all needed shapes and tolerances. Being under the desired tolerances is a target for the machine tools to produce non rejected pieces. Machined pieces presents dimensional or geometry error as a function of the inherent process and also due to vibrations and misplacing of tool and workpiece. Controlling the workpiece is a problem when chatter appears due to low stiffness of tool-machine-tool system or workpiece specially when using high cutting velocities values, as in high speed milling -HSM [START_REF] Patel | Uncharted islands of chatter instability in milling[END_REF].

The chatter, or self-excited vibration, is one of the greater limiters of the metal cutting processes since the increase in the amount of removed material can induce instabilities that may forego the tool to breakage. The presence of this type of vibration in processes like milling may cause bad superficial workpiece quality, low dimensional tolerance, decrease in the life cycle of the tool, or even damage in the bearing of the machine. Thus, the study and modeling of the chatter are essential for the tool optimization and increase of productivity in machining industry [START_REF] Araujo | Dynamical analysis of an end milling process[END_REF]. [START_REF] Tobias | Machine-tool vibration[END_REF] and [START_REF] Koenigsberger | Machine Tool Structures -Vol. I: Stability Against Chatter[END_REF] were first researchers to publish analytical models explaning the regenerative mechanism of chatter and its prediction for the case of orthogonal cut. Afterwards [START_REF] Altintas | Analytical prediction of stability lobes in milling[END_REF] developed the analytical model prediction of chatter for the two degree of freedom and applied to end milling process. The model considered the average cutting forces and it was able to achieve the prediction of chatter conditions valideted with experiments. The analytical model however did not reach good results for the prediction when radial depth of cut was small compared to the milling tool diameter. The stability of the milling process was investigated by Zhao andBalachandran (2001), and[START_REF] Insperger | Stability of up-milling and down-milling, part 2: experimental verification[END_REF], by considering single and two degree of freedom systems for different experimental conditions and the mathematical model is represented by delay-differential equations [START_REF] Moon | Dynamics and chaos in manufacturing processes[END_REF].

The objective of this paper is to develop an algorithm in MATLAB software to generate the diagram of lobes of the end milling processes using Altintas model. Using this graphic tool, it is possible to analyze the influence of the parameters of the processes in this stability. The control of the stability can be done not only by choosing an optimal situation in the diagram, but also by choosing the correct input parameters which to stabilize the system. In this study it is presented a comparison with different values for these parameters and the results are compared to a reference.

ALTINTAS MODEL FOR CHATTER CONSIDERING TWO DEGREES OF FREEDOM

The end milling tool is dynamically similar to a cylindrical beam fixed in one extremity by the tool-holder and forced on the other side by the contact with the workpiece under cutting process. The dynamic of the system composed by the end milling tool, tool-holder, machine-tool and the workpiece can present complex nonlinear behavior associated to extreme conditions, as chatter, which can severely affect the quality of the machined workpiece. Modeling can be very useful for establish optimal operational conditions. Several authors proposed simple models to study tool dynamics during machining using one [START_REF] Insperger | Stability of up-milling and down-milling, part 2: experimental verification[END_REF] or two degrees of freedom mass-spring-dashpot mechanical system models [START_REF] Altintas | Analytical prediction of stability lobes in milling[END_REF].

When the tool is considered rigid, the tangential and radial forces acting in tooth j can be written as function of the uncut chip thickness h(t), the axial depht of cut a, the tangential specific cutting pressure K t and the radial cutting constant k r as can be noted in in Eq 1:

F tj (t) = K t .a.h(t) = K t .a.f t . sin(φ(t)), F rj (t) = k r .F tj , (1)
Note that the chip thickness for end milling is normally described by Martellotti equation as a function of f t the feed per tooth and the spindle angle φ. The forces can be decomposed in the x and y directions as:

F xj (t) = -F tj (t).cosφ j -F rj (t).sinφ j , F yj (t) = +F tj (t).sinφ j -F rj (t).cosφ j , (2)
where φ j is the position angle of tooth j and it vary according to the spindle speed n, as can be seen in Fig. 1. The cutting force is a function of time acting in the end milling tool is the sum of the contribution of each tooth:

F x (t) = N -1 j=0 F xj (φ j , t); F y (t) = N -1 j=0 F yj (φ j , t). (3)
Depending on the volume of material removed, the force can be distributed differently in one revolution. The material removal rate, or MRR, represents the volume of material removed by unit of time. The MMR is an usual parameter of control and optimization of the time of production. For the milling process the material removal rate is described for [START_REF] Cheng | Machining Dynamics: Fundamentals, Applications and Practices[END_REF] as:

M RR = a.b.n.N.f t , (4)
Where b is the radial depth of cut, n the spindle speed and N the number of teeth.

When the tool can no longer be considered rigid, it is necessary to analysis the dynamic of the cut in order to study the stability of the system. [START_REF] Altintas | Analytical prediction of stability lobes in milling[END_REF] modeled the cutting forces as can be seen in Fig. 1. The end milling tool is assumed to have N number of teeth with a zero helix angle. In the figure k x , k y , c x and c y are the modal parameters of the mass-spring-dashpot system in the x and y direction, and dF tj and dF rj are the tangential and radial cutting force respectively.

Figure 1. Milling model for two orthogonal degrees of freedom [START_REF] References Altintas | Manufacturing automation[END_REF].

The transfer function matrix of the two orthogonal degree of freedom mass-spring-dashpot mechanical system is trivial as it has only the diagonal terms G xx and G yy . The transfer function matrix then is obtained by doing the laplace transform in the caracteristic diferential equation as showed in the folowing steps:

mẍ + c x ẋ + k x x = F x , (5)
22nd International Congress of Mechanical Engineering (COBEM 2013) November 3-7, 2013, Ribeirão Preto, SP, Brazil

mÿ + c y ẏ + k y y = F y , (6)
where m is the mass, x and y are the current dynamic displacement of the cut in the time domain. In the frequence domain, the transfer function Φ(s) is write as

Φ(s) xx = X(s) F x (s) = 1 (ms 2 + c x s + k x ) = ω 2 nx k x (s 2 + 2ξ x ω nx s + ω 2 nx ) , (7)
Φ(s) yy = Y (s) F y (s) = 1 (ms 2 + c y s + k y ) = ω 2 ny k y (s 2 + 2ξ y ω ny s + ω 2 ny ) , ( 8
)
where s is the Laplace variable, X(s) and Y (s) are the current displacement in the frequence domain, ω nx and ω ny are the natural frequence in the x and y direction, ξ x and ξ y are the system damping ratio in the x and y direction. The last step in order to study the stability of the system is to obtain it caracteristic equation by developing a expression for the chip thickness h, that in the non rigid tool model it is a time varying variable. In his work, [START_REF] Altintas | Analytical prediction of stability lobes in milling[END_REF] shows that the chip thickness can be expressed by the static chip thickness h 0 , the difference between the previous and present dynamic displacement {∆x ∆y} T left by the tooth j -1 and j respectively, and the step funtion g(φ j ) which determines whether the thooth is in or out of cut as show in Eq.9.

g(φ j ) = 1, se φ s < φ j < φ e , 0, se φ j < φ s ou φ j > φ e , (9)
where φ s is the entry angle of the cut and φ e the exit angle, and they can be seem in Fig. 2.

Figure 2. Entry and exit angles of the cut.

To simplify, the static chip thickness h 0 is removed from the expression as it does not influence the regenerative mecanism, so only the dynamic chip thickness h(φ j ) is considered for chatter analysis

h(φ j ) = [∆xsinφ j + ∆ycosφ j ]g(φ j ). ( 10
)
With the cutting force model, the transfer function matrix and the time varying chip thickness relation, Altintas achieved in his work the caracteristic equation of the chatter regenerative mecanism which is

{F (s)} = 1 2 aK t [1 -e -sT ][A 0 ][Φ(s)]{F (s)}, ( 11
)
where T is the tooth passing period and A 0 is the average matrix of directional factors. The caracteristic equation only has a non trivial solution when the determinant is zero.

det = [ I ] - 1 2 K t a(1 -e -sT )[A 0 ][Φ(s)] = 0. ( 12
)
Using this approach and through the study of the stability of the Laplace constant done by Altintas, it is possible to calculate the depth of cut limit a lim for no chatter on a specific spindle rotations speed by using the Eq. 13 and Eq. 14 respectively:

a lim = - 2πΛ R N.K t (1 + κ 2 ), (13)
T = 1 ω c ( + 2kπ) -→ n = 60 N T . ( 14
)
where Λ R is the real part of the eigenvalue, κ = Λ R /Λ I is the phase of the eigenvalue, k is a integer, = π -2ψ is the phase shift between present and previous vibration marks and, where ψ = tan -1 κ.

The stability lobes diagram is the graphic that presents a lim in function of the spindle speed rotation n of each lobe k of the Eq. 14 as show in Fig. 3. For values of depht of cut a above the found for the stability limit a lim , the system is instable and chatter occurs. For values below, the system is found in the meter of stability and chatter does not occurs.

Figure 3. Diagram of stability lobes [START_REF] Faassen | Chatter Prediction and Control for High-Speed Milling[END_REF].

NUMERICAL SIMULATIONS

The stability lobe diagram is plotted using the equations presented. For the analytical prediction of chatter, it is necessary a programming routine using known parameters k y , ω n and ξ, and the diagram may be plotted following the steps described in [START_REF] References Altintas | Manufacturing automation[END_REF]:

• Select a frequency of chatter of the transfer function close to a dominating vibration mode.

• Solve the eigenvalues equation.

• Calculate the depth of cut limit a lim (Eq. 13).

• Calculate rotation of the tool for each stability lobe k. (Eq. 14)

• Repeat the procedure for other chatter frequencies close to the dominating vibration modes of the structure, made evident by the transfer function.

The necessary algorithm to run this routine was developed utilizing MATLAB software.

Case study

The objective of the case study is to analyze the influence of each parameter of the process on the diagram of lobes built by the algorithm. For this, a group of input data was used in conjunct with the standard data for comparison. This way, altering the values of the input parameters it is possible to compare both diagrams, standard and altered, and analyzing which influence this parameter exercise on the dynamic stability of the system. Parallel to the influences on stability, some other focus of interest also will be considered to determine parameters on input, such as strength of cut and material removal rate (MRR).

The table 1 presents the information of all data of standard input, as well as the changes that will be done for the study case. The altered input parameters will be the number of teeth in the milling tool N , the workpiece material, the stiffness of the set machine-tool, the damping of the set machine-tool, the enter angle φ s and the exit angle φ e .

Using the standard input parameters of the simulation it is obtained a diagram of lobes conform the Fig. 4. In this base model it is important to note that the depth of cut for any spindle speed is found around 1.5 mm and the last two spindle speed where it can be obtained a value of a lim much above the stable depth of cut for all rotations are 5000 RPM and 9000 RPM approximately.

a) Tools with different number of teeth

There is the possibility of work with mills with different number of teeth or inserts available in the market, and the decision of choice of tool to be used in the process may be taken based on the stability of the system. For the comparison were chosen two values of N distinct of the standard.

As can be seen in the Fig. 5, the multiplication of the number of teeth for an arbitrary value has an inversely proportional effect, thereby dividing the critical depth o cut and the equivalent spindle speed by the same factor, the shape of the graphic remain equal and differ by a scale factor. Thus, a tool with two teeth can reach a stable depth of cut for all spindle speed two times higher than that achieved with 4 teeth, while with 8 teeth reaches a depth of cut two times smaller. This effect on stability may be explained by the increased frequency of excitation, which increases the instability while the excitation amplitudes are lower.

Although the decrease in the number of teeth can provide a greater range of stability, as all other parameters were considered constant, stress on the tool in this new scenario is much higher, since more material will be removed once for each tooth, thereby increasing the chip area and hence the cutting force. Therefore, depending on the characteristics of the process and the operating point of the lobe diagram, the use of a greater number of teeth may be a better decision since their use saves life of the tool.

The material removal rate remains constant with the variation of the number of teeth, since the increase of N causes a reduction of f t and N reduction causes an increase of f t considering the same feed speed for both cases.

b) Different workpiece materials

Since it is not usually possible to vary the cutting constant K r without altering the specific cutting pressure K t , and vice versa, since both are mostly defined by the material of the workpiece and process parameters, their influences on the plot diagram will be evaluated by changing the material and then their combined effects can be predicted.

Changing the aluminum material for carbon steel 1095, the new values of K t and K r can be found in [START_REF] Kim | A cutting force model for face milling operations[END_REF]. By comparing the two graphs in the Fig. 6 it can be seen that the variation of the material significantly change the stability of the system. For higher strength materials can be observed a notable reduction in a lim for stability at any spindle speed rotation from about 2 times. The spindle speeds where the peaks of a lim occurs were also sensitive to the change of material and were shifted to the left. For higher speeds however, it is possible to obtain a higher value of a lim for the steel than for aluminum. pressure by the process parameters, it is still possible to make an analysis in terms of material removal rate (MRR).

According [START_REF] De Lima | Influência da profundidade de corte e do avanço na força de corte no fresamento de faceamento[END_REF] with the increase of the feed per tooth, the value of K t decreases, which would result in the increase of the stability range, thus enabling an increase in the material removal rate by increasing both the depth of cutting as the feed per tooth since increasing depth of cutting has little influence on the value of K t , allowing this large gain in MRR. As this gain occurs at the cost of greater effort on the tool and hence a lower life, it is necessary to do an economic analysis of the process to calculate the optimal point between increased MRR and reduced tool life.

c) Different modal parameters

The change of the modal parameters can be achieved for example by comparing two different machine tools. To analyze the effect of each parameter separately, stiffness and damping, its value was increased by 20 % and then its new natural frequencies were found.

Then plotting the lobe diagram, by the analysis of the Fig. 7 (a) it is possible to note a reduction in the occurrence of chatter with the increase of stiffness. One would expect a greater range of stability greater the rigidity of the system, but it is also important to note that this gain in stability occurs usually at the cost of larger/different machinery, and so stiffness is often a difficult parameter to be changed given availability of tools and machines. The variation of the damping constant was also made increasing its value by 20%. By varying the damping, the natural frequency remained constant.

Evaluating the diagram in Fig. 7 (b) the greater the damping that represents the ability to dissipate the energy of the system, the less is the occurrence of chatter and therefore the greater the stability range, although an increase of 20% of the value of ξ has only increased depth of cutting limit at 9.3%. It is also possible to notice that the great speed remain the same for different values of ξ. For the change of ξ, it is also necessary to replace the used tool or machinery.

d) Different cutting geometry

The variation of cutting geometry is done by using differents entry and exit angles. Looking at the diagram in Fig. 8 (a), the variation of φ s increases the value of the depth of cut in which it should operate. However, the increased entry angle usually depends on the geometry of the workpiece often occurs an entry angle greater than zero in up milling only by a short period of time a pass. Analyzing Fig. 8 (b) it is expected that the possible depths of cut are lower for a greater exit angle, because more teeth were in contact at once and so the excitation frequency of the system would be greater, effect similar to which occurs when increasing the number of teeth of the tool. However, the small difference between the diagrams of the exit angles of • and 180 • proved to be much less trivial, because a reduction of approximately 0.2 mm of the possible depths of cut, the largest exit angle of 180 • allows the removal of the double material in one pass due to radial depth of cut b be double, being possible a large increase in the volume of chips removed, which will be studied further. In general, the smaller the exit angle, the more sensitive is the stability lobe diagram to the variation of it.

MAXIMING THE MATERIAL REMOVAL RATE

To account the increasing in the MRR due to the variation of the exit angle, the MRR was calculated for different values of φ e . The MRR equation ( 4) can be further recast as the effect of the feed per tooth in the stability is small and can be dropped from the expression. A normalized material removal rate then can be written by the equation 15

M RR * = M RR f t = a.b.n.N. ( 15
)
To calculate the exit angle φ e which maximizes the material removal rate were calculated the depth of cutting stable for all spindle speeds for different exit angles.

As the values of a used are stable for any spindle speed, rotation will also be drawn from the equation 15 as it not alter the stability of the system. The exit angle that maximizes the MRR in the stability band can be seen in Fig. 9. By observing the figure it is possible to see that the angle that maximizes the MRR is 160 • . It was conducted a case study analysis of different input parameters, and it was concluded that it is often not possible to increase the range of stability without giving up a greater cutting force or a lower material removal rate. It is necessary to design the machining process analyzing the cost-benefit that offers the variation of each parameter to decide which should be changed to eliminate the chatter vibration. The study of the input parameters shows that:

• The increase of the teeth number, the using of higher strength materials and the increase in the exit angle increased the chatter band of occurrence, while the increase in the system stiffness, the increase in the system damping ratio and the increase in the entry angle decreased the chatter band.

• The using of higher strength materials and the increase in the exit angle increased the cutting force value, while the increase in the teeth number and the increase in the entry angle decreased the cutting force.

• The increase in the teeth number and the increase in the exit angle increased the material removal rate, while the increase in the entry angle decreased the material removal rate.

Besides the influence of each parameters in the stability lobe diagram, it was also possible to achieve an exit angle value of 160 degrees that maximize the material removal rate in a band of stability for all spindle speeds studied, making possible to optimize the manufacturing process by beyond the instability challenge.

22nd

  Figure 4. Stability lobes diagram using standard parameters (Reference values ofTable 1)

Figure 5 .

 5 Figure 5. Stability lobes diagram using different number of teeth.

Figure 6 .

 6 Figure 6. Stability lobes diagram using different material.

  (a) Stability lobes diagram using different stiffness. (b) Stability lobes diagram using different damping ratio.

Figure 7 .

 7 Figure 7. Stability lobes diagram using diferent modal parameters.

  (a) Stability lobes diagram using different entry angle. (b) Stability lobes diagram using different exit angle.

Figure 8 .

 8 Figure 8. Stability lobes diagram using diferent cutting geometry.

Figure 9 .

 9 Figure 9. Material removal rate as a function of the exit angle

Table 1 )Table 1 .

 11 Standard input data and variation data 1 and 2.

	Input Parameter	Reference Value	Option 1	Option 2
	Number of teeth N	4 teeth	8 teeth	2 teeth
	Workpiece material	Aluminium	Carbon steel 1095	-
	K r	0.07	0.67	-
	K t	600 MPa	2500 MPa	-
	Dynamic Proprieties
	k -
	ω nx	593.75 Hz	650 Hz	-
	ω ny	675 Hz	740 Hz	-
	ξ x	3.9 × 10 -2	4.68 × 10 -2	-
	ξ y	3.5 × 10 -2	4.2 × 10 -2	-
	Entry angle φ s	0 •	18 •	-
	Exit angle φ e	60 •	90 •	180 •

x 5.59 × 10 6 N/m 6.7 × 10 6 N/m k y 5.71 × 10 6 N/m 6.85 × 10 6 N/m

ACKNOWLEDGEMENTS

The authors thanks to the Mechanical Engineering Department to the academic support and for PR-3 UFRJ to the support on conference expenses.


Adriane Lopes
email: adriane.mougo@gmail.com

Mougo Fábio

Oliveira Campos

Anna Carla

Monteiro De Araujo

A STUDY OF THE INFLUENCE OF THE WIDTH OF CUT ON MICRO MILLING ALUMINUM ALLOY

Keywords: Micro milling, width of cut, cutting forces, tool wear, workpiece surface features

The minimum chip thickness is the lower limit value where cutting process occurs as it is studied in cutting metal. Below this value the process is usually modeled as forming. In micro end milling the chip thickness varies with the rotation angle from zero to the feed per tooth. This article presents a first effort to divide the cutting process in two phases: when the chip thickness is below the lower limit and when there is cutting mechanism. It is proposed to calculate differently those two forces: forming forces and cutting forces. It is presented an experimental study on micro milling aluminum alloy with different width of cut in order to identity the influence of the minimum chip thickness on the resultant forces. Using lower width of cut, the time during forming phase would be relatively higher. Experimental data is acquired using a micro dynamometer and the forces are analyzed. Tool wear and workpiece surface features were also investigated. The design of experiments considers one factor, the width of cut, with four levels. The machined workpiece showed good superficial quality for lower width of cut with less burr formation along the channel.

INTRODUCTION

Micro milling is a flexible machining process that allows the fabrication of high quality parts. Cutting force analysis plays a vital role in studying the micro milling processes. Micro milling is a suitable process for producing complex 3D geometries for a wide range of materials, so the understanding the physical phenomena affecting the process performance is essential in order to increase the quality of the micro-milled components [START_REF] Afazov | Effects of micro milling conditions on the cutting forces and process stability[END_REF].

The size of the part in machining of metallic components plays an important role in the force prediction. The fundamental process mechanisms between macro and microcutting can be different due to the substantial size reduction. This is known as the "size effect" in micro machining [START_REF] Aramcharoen | Size effect and tool geometry in micromilling of tool steel[END_REF]. The feed per tooth to tool radius ratio has to be higher than in conventional milling to keep productivity at a reasonable level [START_REF] Bao | Modeling micro-end-milling operations. part i: analytical cutting force model[END_REF]. Due to the small size of the micro-tools, which have a diameter of less than 2 mm, it is very difficult to notice the damage in the cutting edges and an inappropriate selection of the cutting conditions can cause tool breakage unexpectedly.

Even if the relationship between the main geometrical features is kept constant, the process behavior changes. [START_REF] Vollertsen | Size effects in manufacturing of metallic components[END_REF] presented a review on size effect and their use: the article presents the typology of size effects, a description of size effects on strength and tribology and size effects on formability and machinability. Camara et al. (2012) presented a state of art on micro milling with emphasis on the work material requirements, tool materials and geometry, cutting forces and temperature, quality of the finished product, burr formation, process modeling and monitoring and machine tool requirements. [START_REF] Afazov | Effects of micro milling conditions on the cutting forces and process stability[END_REF] studied the micro milling conditions on the cutting forces and process stability through the effects of the tool wear, rake angle, run-out and workpiece material.

At low feed rates, when chip thickness (t c ) is lower than the required minimum chip thickness (t cmin ), rubbing or ploughing occurs instead of cutting [START_REF] Bayesteh | 2-Dimensional ploughing simulation model development in micro flat end milling[END_REF]. A critical cutting thickness needs to be exceeded to promote the chip removal. [START_REF] Ramos | Characterization of the transition from ploughing to cutting in micro machining and evaluation of the minimum thickness of cut[END_REF] studied the transition from ploughing to cutting in micromachining and evaluated the minimum uncut chip thickness. In this study the changes of the surface roughness, surface topography and residual stress state after micro cutting have been also investigated. If the chip thickness is below this value (tc<t cmin ), the ploughing mechanism is present, where part of the material is plastically pushed against the workpiece surface. It is also possible to have the elasticity mechanism when the forces are lower. In this case, tc<<tcmín and the forces are proportional to the interference volume between the tool and the workpiece [START_REF] Vogler | On the modeling and analysis of machining performance in microendmilling, part ii: Cutting force prediction[END_REF]. Similarly, [START_REF] Malekian | Modeling of minimum uncut chip thickness in micro machining of aluminum[END_REF] used the minimum uncut chip thickness, under which the material is not removed but ploughed, and claimed that this effect causes an increase of machining forces that affect the surface integrity of the workpiece.

Microstructure has also a significant effect on microscale cutting. [START_REF] Simoneau | Grain size and orientation effects when microcutting {AISI} 1045 steel[END_REF] investigates the effect of grain size and orientation during microcutting in FE modeling of the primary shear zone. Their research group [START_REF] Simoneau | Chip formation during microscale cutting of a medium carbon steel[END_REF] analyzed the orthogonal cutting in microscale. Tests were conducted on steel and the resulting A. L. Mougo, A. C. Araujo, F. O. Campos Effect of Width of cut on Micro Milling Aluminum Alloy chips examined showing that the chip formation changes from continuous to "quasi-shear-extrusion" chip due to the uncut thickness size. The results indicate that the pearlite and softer ferrite grains play distinct roles in the plastic deformation process. [START_REF] Araujo | Micro milling forces on machining aluminum alloy[END_REF] studied the micro milling cutting forces on machining aluminum alloy and experimental results were compared to mechanistic model.

Literature review shows the assumption of non-homogeneity in workpiece material properties because the micrograin-structure size is of the same order of magnitude as the cutter radius of curvature and the grain structures will affect the cutting properties [START_REF] Afazov | Effects of micro milling conditions on the cutting forces and process stability[END_REF], Camara et al., 2012[START_REF] Simoneau | Grain size and orientation effects when microcutting {AISI} 1045 steel[END_REF]. However, the study of the size effect considering the homogeneous material properties is important to reduce the experimental and simulated conditions in micromachining.

This article presents an experimental study on micro milling aluminum alloy using different width of cut. Cutting Forces, burr formation and tool breakage is analyzed and presented. It is proposed to analyze forces reducing the width of cut with the aim to focus on influence of the ploughing phase in the total cutting force.

CUTTING FORCE IN MICRO MILLING

The knowledge of cutting forces is fundamental for tool optimization and it is very important to avoid tool breakage and instability. In micro milling, those factors are even more relevant due to the high cost of tools that breaks very easily. Meso and micro milling models are presented.

General chip load cutting model for cutting forces

Elemental normal and frictional forces are required to the determination of cutting forces for a given geometry. The mechanistic modeling approach is a combination of analytical and empirical methods in which the forces are proportional to the chip load [START_REF] Kline | The prediction of cutting forces in end milling with application to cornering cuts[END_REF].

The specific cutting pressure, K n , K f and K z (tangential, radial and axial coefficients respectively), have been shown as a function of chip thickness t c in mesoscale milling process and it is used for calculation of the differential cutting forces dF n , dF f and dF z on each angular position θ of the discretized cutting edge proportional to the chip load area dA as shown in Eq. 1. Using a semi empirical modeling as [START_REF] Tlusty | Dynamics of cutting in end milling[END_REF], relating specific cutting pressures by empiric factors m 1 and m 2 . Chip area is calculated based on uncut chip thickness t c (θ) that is called Martellotti equation.

( ) sin( ) ct tf   (2)
where f t is the feed per tooth.

The specific cutting pressure in mechanistic models is calculated as:

0 1 2 3 ln ln ln ln ln t c c c c k a a t a V a t V     (3)
where the coefficients a 0 , a 1 , a 2 and a 3 are called specific cutting energy coefficients and they need to be experimentally calculated. They are dependent on the tool and workpiece materials and also on the cutting speed and the chip thickness.

Those coefficients are determined from calibration tests for a given tool work piece combination and for a given range of cutting conditions.

Cutting force model using chip load and cutting edge

Other models consider that the cutting edge length influence the cutting force. The differential tangential, radial and axial cutting forces can be composed by one parcel that it is dependent of the cutting area and another that is proportional to the cutting edge db, as in Eq. 4 [START_REF] Pérez | Estimation of cutting forces in micromilling through the determination of specific cutting pressures[END_REF]. where k tc , k rc and k zc are the cutting forces coefficients in the tangential, radial and axial directions, and k te , k re and k ze are the edge forces coefficients in the same directions.

2.3

Cutting force model considering chip thickness correction for microcutting [START_REF] Bao | Modeling micro-end-milling operations. part i: analytical cutting force model[END_REF] developed a more precise expression than Martelotti calculation for uncut chip thickness t c (θ) used by [START_REF] Newby | Empirical analysis of cutting force constants in micro-end-milling operations[END_REF] to calculate average uncut thickness, as shown in Eq. 5. This equation can be used to replace t c (θ) in the Eq. ( 1) or (4).

t c t t f z t f f nr f         (5)
where z, n and r are the tool teeth, spindle speed and tool radius respectively.

Minimium uncut chip thickness for cutting force prediction

Under the minimum uncut chip thickness, ploughing mechanism is present and it needs to be modeled by different approaches than the presented cutting ones. [START_REF] Liu | An analytical model for the prediction of minimum chip thickness in micromachining[END_REF] modeled the minimum chip thickness, cutting temperature, strain, and strain rate simultaneously, considering analytical model using slip line theory and Johnson-Cook model. [START_REF] Malekian | Modeling of minimum uncut chip thickness in micro machining of aluminum[END_REF] presented an analytical models based on identifying the stagnant point of the workpiece material during the machining, based on the edge radius re and on a critical or stagnant angle, θ m to calculate t cm .

(1 cos )

cm e m tr   (6)
The stagnant angle is considered by [START_REF] Malekian | Modeling of minimum uncut chip thickness in micro machining of aluminum[END_REF] to be equal to the friction angle between the material and the rake face, regardless of the other parameters involved in the process and the edge radius can be either measured of by the tool manufacturer.

A trigonometric analysis is used to calculate the minimal width of cut (a emin ), using Eq. ( 2) and ( 7), that defines when the material begins to be removed. This calculation considers the tool radius (R) and the tool rotation angle θ m for this minimum width of cut. Figure 1 represents the relation between the width of cut a e and the tool rotation angle θ m for any case. The rotation angle assumes values from zero to 2 if there is full immersion, when a e =2R=D. In this case, for θ < θ m and θ > 2π -θ m the milling process contains only ploughing mechanism. When θ m < θ <2 -θ m , cutting process is running. For values of the width of cut smaller than D, the cutting force analysis must be aware on the impact of this

EXPERIMENTAL SETUP

In order to analyze the cutting forces involved in the process of micro milling with different width of cut, a series of experiments were performed.

Material, tools and experiments

The work material used on experiments is the alloy Al 6351 T6, which is an AlMgSi alloy. The workpiece dimensions were 47x50x15 mm. It was used a carbide micro milling tool, with 0.254 mm diameter and 0.762 mm flute length, as showed in Fig. 3.

Experimental procedure

Before the actual micro milling experiments started, a surface of 50 x 20 mm, the work area, was faced on the workpiece using a 3mm milling tool, as shown in the Fig. 5b. It was used 18 m/min as cutting velocity and feed rate equals to 200 mm/min. This facing operation is important because it ensures that the micro milling operation would be performed on a flat surface. If the surface to be machined was not flat, the axial depth of cut could vary during the cutting process and, consequently, the forces data would not be right.

The micro milling tool performed a surface trajectory before each pass to guarantee the axial depth of cut designed. The axial depth of cut chosen is 30 times higher than the point radius, 50 µm. The feed per tooth chosen is 4 times higher than the cutting edge radius, 2 µm, to ensure the removal of material. Table 1 presents the cutting parameters used on the experiments. Initially, four channels were machined with a micro-end-milling process, using full immersion and spaced by 1.5 mm in between, as shown in Fig. 6. For the design of experiment the values of a e were selected considering the cut tool diameter (D). The width of cut used to machine channels 1 to 4 were 12,5% D, 25% D, 50% D and 100% D, as presented in Tab. 2. The channel 4 remains with a e = D for the comparison with the others channels, as shown in Fig. 7. With Eq. ( 2) it is possible to calculate the value of θ min =0.268 rad, considering t c (θ)=0.53 µm and f t =2µm/tooth. With Eq. ( 6) and ( 7) it is possible to calculate the values of t cm= 0.02 µm and a emin = 4.57 µm, considering re=0.53 µm and R=127 µm.

RESULTS AND DISCUSSION

In this section, experimental cutting force, tool wear and micro-machined surfaces characteristics will be presented.

Cutting forces

The experimental cutting forces were obtained with a media of 20 rotations on each experiment. The signal was filtered using a high-pass filter with the cut-off frequency corresponding to the frequency of the spindle speed.

Tool wear

The wear and the modification in the geometry of the cutting edge increase the vibration during material removal, inducing the formation of burr. After the experiments, it was verified that the cutting point of the tool was broken, as showed in Fig. 9a. Figure 9b presents the EDS (Energy Dispersive Spectroscopy) at pt2, indicating the presence of aluminum chips on the cutting face.

Workpiece surface features

Figure 11 shows the 4 channels machined with width of cut variation. Channels 1, 2 and 3 present good surface finishing and channel 4, machined at full immersion of the tool (ae = D = 0.254 mm), showed high burr occurrence. Figure 12 presents the top view of channels 2 and 4 at the start and at the end of cutting. There was burr formation only at channel 4. The breakage of the tool point, the adhesion of aluminum on the cutting face and the selection of the cutting parameters can cause these burrs.

End End

Figure 13 presents the side view of channels 2 and 4 at the starting of the cutting of the channel. Channel 4 shows a e = 0.230 mm, though the tool diameter is 0.254 mm, and this value can be influenced by the presence of burrs. Channel 2 shows a e = 0.292 mm, because of this the difference between the two width of cut is 0.0621 mm. This result shows that the breakage of tool point did not harmed the surface machining of the workpiece.

CONCLUSIONS

In this article it was presented the cutting forces, the tool conditions and the workpiece surface features for micro milling of an aluminum alloy, varying the width of cut. The minimum width of cut calculated was 4.57 µm and in the work were used values between 254 µm and 32 µm. However, even with high values, the profile of the cutting forces presented influence of noise, indicating the necessity of an increase at the amplifying rate of the signals.

It was verified the breakage of the tool point, that can be consequence of the selected cutting parameters or of the length of the machined surface, which was 350 mm for the machining of the channels and the variation of the width of cut.

The machined workpiece showed good superficial quality for width of cut lower than the tool diameter. With width of cut equals to the diameter, there was burr formation along all channels, influenced by the breakage of the tool point. Therefore, with the conditions presented in this work, it is recommended the machined of the channel with a tool with lower diameter and, than, the variation of width of cut for the finishing.

Future works aim the development of a model that considers the different paths of the cutting edge on the workpiece, identifying the moments of ploughing and cutting during the process. For this work, it will be used an equipment with higher amplifying rate, enabling the force acquisition for lower values of feed per tooth and width of cut.

(Figure 1 .

 1 Figure 1. Relation between the width of cut a e and the tool rotation angle θ.

  . Mougo, A. C. Araujo, F. O. Campos Effect of Width of cut on Micro Milling Aluminum Alloy ploughing phase on process, as shown in Fig. 2. This article deals with experimental procedure with different values of a e in order to study the tool and process behavior on each case.

Figure 2 .

 2 Figure2. Shearing and ploughing areas when a e =2R=D[START_REF] Bayesteh | 2-Dimensional ploughing simulation model development in micro flat end milling[END_REF].

Figure 3 .

 3 Figure 3. Dimensions of the micro milling tool used on the experiments.The cutting tool was measured in SEM microscopy. As the cutting edge radius has strong influence on the cutting force, the images presented on Fig.4were taken. Using those SEM images, the helix angle, point radius and cutting edge radius are measured. The tool has point tip radius of 1.58 µm, cutting edge radius of 0.53µm and β=30° helix angle.

Figure 4 :

 4 Figure 4: SEM Microscopy of the cutting tool presenting the cutting edge radius and the point radius. CNC Mini Mill/GX from Minitech Machinery Corporation was used on the experiments. The machine uses NSK 60K RPM Precision Spindle with 3 Axis Controller. Its standard resolution is 0.78125µm using dual linear ball bearing slides on each axis, sealed for the table mechanism (THK linear slides -RSR15 series, Caged-ball technology). The drive mechanism THK Ball Screw actuator -preloaded and sealed, achieves low torque fluctuation and no backlash.A mini-dynamometer is used for cutting force measurement. The MiniDyn KISTLER 9256C2 used cable 1697A5 and the cutting forces components are presented in Fig.5a. It was used a charge amplifier 5070A10100 and a data

Figure 5 .

 5 Figure 5. Experimental set-up: (a) Miny Dyn and force components; (b) Feed directions.

Figure 6 :

 6 Figure 6: Scheme for channels machined for testing.

Figure 7 :

 7 Figure 7: Machining of channels with different a e .

  Figure 8 show the force signals in the X and Y directions. The force components presented (F x and F y ) represents the components on the plane normal to the spindle, as presented on Fig 5a. The profile of the cutting forces presented influence of noise for all channels, especially for values of cutting force with a e < D.

Figure 8 .

 8 Figure 8. Experimental cutting forces.

Figure 8

 8 Figure8shows that for very low values of a e or even with full immersion, the relation signal/noise is low, influenced either by the feed rate or by the spindle speed, or by both.

  (a) Breakage at the tool edge.(b) EDS of aluminum on the tool cutting region.

Figure 9 .

 9 Figure 9. Tool analysis on top view. Figures 10a and 10b present the break of the tool point in 0.0025 mm, in front view. Figures 10c and 10d show EDS at point pt2 and pt3, indicating the tungsten and the presence of aluminum on the tool.

Figure 10

 10 Figure 10. (a) and (b) Tool point broken; (c) and (d) EDS of the tool (W) and of the aluminum accumulated on the cutting face of the tool

Figure 11 .

 11 Figure 11. Front view of the channels. (a) Channel 1 with a e = 0.0318 mm, (b) Channel 2 with a e = 0.0635 mm, (c) Channel 3 with a e = 0.127 mm e (d) Channel 4 with a e = 0.254 mm.

Figure 12 .

 12 Figure 12. Start and end of channel cutting. (a) Channel 2 with a e = 0.0635 mm e (b) Channel with 4 a e = 0.254 mm.

Figure 13 .

 13 Figure 13. Side view of the workpiece. (a) a e = 0.0635 mm and (b) a e = 0.254 mmFigure14shows the topography measurements on each channel. Channel 1, 2, 3 and 4 presents the arithmetic average height (Sa) of 0.252 µm, 0.172 µm, 0.156 µm and 0.170 µm respectively. This results show that the width of cut has stronger effect on the surface quality, and that lower width of cut increases the values of Sa.

Figure 14 .

 14 Figure 14. Topography measurement.

Table 1 :

 1 Cutting parameters.

	Cutting Velocity (V c )	23.93 m/min -clockwise
	Feed per tooth (f z )	2 µm/tooth
	Axial depth of cut (a p )	50 µm
	Width of cut (a e )	254 µm (full immersion)
	Workpiece material	Al 6351 T6

Table 2 :

 2 Design of Experiments.

	Channel Relation with D	Value of a e (mm)	Value of θ (rad)
	1	12,5%	0.0318	0.72
	2	25%	0.0635	1.05
	3	50%	0.1270	1.57
	4	100%	0.2540	3.14

A. L. Mougo, A. C. Araujo, F. O. Campos Effect of Width of cut on Micro Milling Aluminum Alloy

ACKNOWLEDGEMENTS

The authors thank to the support of CAPES for acquiring the equipment used in this article thru Pro-equipment resources, to the kindly services of UFRJ importation department for the Mechanical Engineering Department.

RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.


domain: chim sde

text:
Valentina Valbi

Anne Perez

Aurélie Verney-Carron

Yoan Pechaud

Chloé Fourdrin

Claudine Loisel

Stéphanie Rossano

Understanding the browning phenomenon of medieval stained-glass windows: impact of bacteria and bacterial exudates on the dissolution of a Mn-bearing glass

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Previous studies revealed enrichment in Mn in the browned areas and some of them have suggested that manganese migration to the surface, oxidation and/or precipitation might be linked to biological activity.

In order to improve our understanding of this phenomenon and investigate the direct and indirect implication of microorganisms, weathering experiments of a model glass were designed. The browning of medieval stained glass windows appears as dark Mn-rich spots inside the altered layer on the surface of the glass. It leads to a loss of transparency.

The mechanisms leading to its formation are not understood yet.

The browning phenomenon

As Mn was introduced as a (de)colourant, the browning is often located on faces and purple shades

UNDERSTANDING THE BROWNING PHENOMENON OF MEDIEVAL STAINED GLASS WINDOWS: IMPACT OF BACTERIA AND BACTERIAL EXUDATES ON THE DISSOLUTION OF A Mn-BEARING GLASS

Valbi Valentina a , Perez Anne a , Verney-Carron Aurélie b , Fourdrin Chloé a , Pechaud Yoan a , Loisel Claudine c , Rossano Stéphanie a

Conclusion Acknowledgements

The results show that the presence of bacteria and bacterial exudates modifies the dissolution mechanisms and kinetics, increasing dissolution rates and changing dissolution stoichiometry. This highlights that a biological activity could be involved in the solubilisation of Mn in a Mn-bearing glass, which is the first step of the appearance of the browning phenomenon.

  windows have a potash-lime-silica composition because of the use of plant ashes as flux. Grinding and sieving: 100-200 µm fraction 25 °C -160 rpm 100 mg in 200 ml  S/V= 0,2 cm -1

a

  Laboratoire Géomatériaux et Environnement (LGE), University of Paris-Est Marne la Vallée, Champs sur Marne, France b Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), University of Paris-Est Créteil, Créteil, France c Laboratoire de Recherche pour les Monuments Historiques (LRMH), Champs sur Marne, France environment, bacteria have an important role in biogeochemical cycles of elements such as C, S, P, Ca, K, Fe, Mn. They strongly influence the weathering of minerals and the bio-mineralization. The glass support can be a source of micro and macro nutriments for micro-organisms. Micro-organisms sampling on stained glass windows  The glass follows a slightly incongruent dissolution in control conditions  Enhancement of dissolution rate in presence of bacterial exudates Results  Formation of the complex Mn(III)HDFOB + observed by UV-VIS  Few amounts of siderophore are sufficient to significantly enhance the dissolution rate  The more concentrated DFOB the faster the dissolution Glass casting at 1500 °C Production of glass representative of medieval stained glass windows in a high temperature furnace. NORMALIZED MASS LOSSES Concentration results are normalized to the reactive surface and to the glass composition: 𝑁𝐿 𝑖 = 𝑉 × 𝑖 𝑆 × 𝑥 𝑖 𝑖 : concentration in ppb 𝑆 : glass surface 𝑉: volume of solution 𝑥 𝑖 : mass fraction of the element i in the glass Versailles' Chapelle Royale

1 Biotic dissolution tests in bioreactor 3 Screening

 13 of glass-weathering potentials of sampled bacteria

wells: Control experiment glass in culture medium MM9 3 wells: Biotic dissolution experiment glass in culture medium MM9 and bacteria

2 This work was supported by grants from the Paris Ile-de-France Region -DIM « Matériaux anciens et patrimoniaux » and from the Université Paris-Est Marne la Vallée