Abdenour Abdelli

Bruno Sareni
email: sareni@leei.enseeiht.fr

Xavier Roboam

X Roboam Leei

Optimization of a small passive wind turbine generator with multiobjective genetic algorithms

Keywords: Multiobjective Optimization, Genetic Algorithms, Wind Energy, Vertical Axis Wind Turbine

In this paper Multiobjective Genetic Algorithms (MOGAs) are used for the design of a small wind turbine generator (WTG) coupled to a DC bus through a diode bridge. The originality of the considered system resides in the suppression of the Maximum Power Point Tracker (MPPT). The poor efficiency of the corresponding passive structure is considerably improved by optimizing the generator characteristics associated with the wind turbine in relation to the wind cycle. The optimized configurations are capable of matching very closely the behavior of active wind turbine systems which operate at optimal wind powers by using a MPPT control device.

Introduction

The optimization of wind energy transfer is generally achieved by controlling the speed of a Wind Turbine Generator (WTG). In particular, the rotor speed should vary in accordance with the wind speed by maintaining the tip speed ratio to the value that maximizes aerodynamic efficiency. For that purpose, many different Maximum Power Point Tracking (MPPT) control strategies have been developed, allowing to regulate the Permanent Magnet Synchronous Generator (PMSG) voltage [START_REF] Mirecki | Comparative study of maximum power strategy in wind turbines[END_REF] [START_REF] Chen | A fuzzy logic controlled power electronic system for variable speed wind energy conversion systems[END_REF]. The high efficiency of these generators is counterbalanced with higher costs and greater complexity of the electronic devices. On the other hand, simpler system structures consist in only using a passive rectifier directly connected to the DC bus (see Fig 1). Such system is characterized by very low cost but usually offers poor efficiency relatively to the wind power.

However, thanks to a suitable choice of the system design variables associated with the wind turbine generator sizing (especially electrical and geometrical parameters) it is possible to improve significantly the global system efficiency. In this paper, we propose an original approach based on Multiobjective Genetic Algorithms for sizing a small passive WTG. The whole system mass and the extracted output power are considered as optimization criteria. The obtained power efficiency is finally close to the one offered by active WTGs coupled with MPPT control devices.

The Sizing and Simulation Models of the Wind Turbine Generator

Two classes of models have been developed for sizing and simulating the WTG. On the one hand, fine accurate models based on the use of empirical equations, finite elements and a complete circuit representation of the WTG have been used for the system analysis and validation. On the other hand, surrogate models which approximate the system behavior have been employed in the optimization process in order to reduce computing times.

The Wind Cycle

The wind Cycle is represented by a typical wind speed sample

where O denotes the tip speed ratio, depending on the turbine rotational speed : and the wind speed

V W . W V R: O . ( 3
)
The associated wind turbine power can be expressed as:

3 2 1 W p WT AV C P U , ( 4
)
where U denotes the air density (U = 1.205 kg.m 3 ) and where the swept rotor area A is approximated as:.

A = 2RuH . ( 5
)
The corresponding torque T W produced by the wind turbine is:

:

WT WT P T (6)
and the electromagnetic torque of the generator is defined as:

: :

WT WT WT em F dt d J T T , (7)
where the wind turbine inertia and the damping coefficient are J WT = 16 kg.m² and F WT = 0.06. N.m.s/rad.

Note that the wind power is maximum when the power coefficient is maximum (C p * ≈ 0.22), i.e. for the optimal tip speed ratio (O * ≈ 0.82). For various wind speed values, the rotor speed should be adapted to operate at the optimal tip speed ratio. Therefore, in order to extract the maximum wind power, a MPPT strategy associated with a static converter structure is generally employed to control the rotor speed according to the wind speed such as : O * V W /R. This can be made by using a PWM Voltage Source Rectifier or a passive diode bridge coupled with a DC-DC chopper that tunes the extracted power [START_REF] Mirecki | Comparative study of maximum power strategy in wind turbines[END_REF].

The Permanent Magnet Synchronous Generator

An analytical model allows us to extract all sizing variables of the PMSG from geometrical features (i.e. the radius length ratio R rl , the number of pole pairs p, the number of slots per pole per phase N spp ) and energetic characteristics (the sizing voltage V b , the current density J c in a slot, the magnetic flux density B y in the yoke, the typical sizing power P b at the base point). For reason of complexity and space limitation, this model is not explained in detail in the paper. We invite the reader to refer to [START_REF] Slemon | Modeling and design optimization of permanent magnet motors[END_REF], [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF] for more information. Note that contrary to [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF] the generator is sized for a specific base speed:

R V W b ! : * O , (8)
where <V W > denotes the average speed of the wind cycle. The PMSG electric parameters (i.e. main inductance, stator resistance, magnetic flux, base current) are then deduced from empirical relations [START_REF] Slemon | Modeling and design optimization of permanent magnet motors[END_REF] or by using the Finite Element Method (FEM). For the system simulation, the PMSG is represented in a ABC reference frame and the diode rectifier is modeled in instantaneous value by considering ideal switches but taking into account the diode overlapping during the commutation interval. Furthermore, this model includes the thermal behavior of the synchronous generator in each component (slot copper, slot insulators, stator yoke) evaluated from the magnetic and electrical losses. Joule losses are classically computed from the generator current and the stator resistance, and magnetic losses are estimated from hysteresis and eddy current losses in the stator parts (i.e. yoke and teethes) according to [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF]. Since the computational cost associated with this global circuit model and the use of finite elements is rather high, surrogate models have been developed for the optimization process in order to reduce computing times. In particular, for the system simulation, a simplified causal model is used where the synchronous generator with the diode bridge association is replaced with an energetically equivalent DC model valid in average value. The synoptic of this model is given in Fig. 2b. Note that the causality is symbolized by arrows specifying which physical variables (energetic efforts or flows) are applied in each part of the system.

The correspondence of this model with the synchronous generator circuit of Fig. 2a is given in Table 1. We also mention in the following the characteristics of each block in the synoptic. The electromechanical conversion is represented by: °°® : )

) DC sDC sDC DC em p E I p T ' , (9)
where p denotes the pole pair number of the generator. The armature reaction in the generator is modelled with a voltage drop without power losses:

°°® sDC sDC sDC sDC sDC DC sDC sDC E I E I I L E E / ) ( ' ' 2 2 ' Z , ( 10
)
where Z denotes the electric angular pulsation associated with the rotor. The transient electric mode leads to a DC current in the generator defined as:

DC sDC sDC DC sDC DC E E I R dt dI L ' . (11)
Finally, the diode overlapping during the commutation interval is represented by a power conservative voltage drop:

°°® DC sDC DC DC DC s DC DC U I E I I L E U / 3 Z S . (12) E s E s ' L s R s V s I s E s E s ' E s ' L s R s V s I s (a)
) ) S 6 3 Inductance L s s DC L L 2 6 3 1 • © § S Resistance R s s DC R R 2 6 3 1 • © § S Electromotive Force E s s sDC E E S 6 3

Multiobjective Optimization of the Wind Turbine Generator by Genetic Algorithms

Design Variables, Objectives and Constraints

The design variables considered for the wind turbine optimisation and their associated bounds are shown in Table 2. Note that five variables are continuous parameters (i.e. R rl , P b , V b , B y , and J c ) and two are discrete (i.e. p and N spp ). Two conflicting objectives have to be improved: the useful power has to be maximized while minimizing the total mass of the system. The useful power is defined as the power extracted from the wind cycle reduced from all losses in the wind turbine system (i.e. mechanical losses in the turbine, Joule and iron losses in the generator and conduction losses in the diode rectifier). As underlined previously, all losses in the synchronous generator are computed according to [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF] and the conduction losses P cond in a diode of the rectifier are classically evaluated as follows:

2 d d d d cond i R i u P , (13)
where u d .denotes the diode voltage drop and R d represents the diode internal resistance (typically R d 3.4 m:

and u d 0.8 V). Note that switching losses have been neglected. The total mass of the system is obtained by considering the wind turbine mass as constant (M WT ≈ 48 kg) and the generator mass. This mass is computed from the volume of each constitutive component (iron, magnet, copper windings) and the corresponding mass density according to [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF]. Note that the rectifier mass has been neglected. Moreover, five constraints have to be fulfilled to ensure the wind turbine feasibility and to allow complying with the wind cycle. These constraints concern the number of wires per slot, the maximum temperature associated with the copper windings in the generator, the demagnetization limit of the magnets and the maximum temperature in the semiconductor junctions. They are computed similarly to [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF].

The Optimization Process

The Nondominated Sorting Genetic Algorithm (NSGAII) [START_REF] Deb | A fast-elitist non-dominated sorting genetic algorithm for multiobjective optimization: NSGA-II[END_REF] is applied for the optimization of the full passive wind turbine generator. To take into account the design constraints in the NSGA-II, the Pareto-dominance rule is modified as follows:

-if two individuals are non-feasible, the Pareto-dominance is considered in the constraint space.

-if two individuals are feasible, the Pareto-dominance is considered in the objective space.

-if one individual is feasible and the other non-feasible, the feasible individual dominates the non-feasible individual.

In this manner, Pareto ranking tournaments between individuals include the constraint minimization as well as the objective minimization. Note that in the case of the NSGA-II, for non-feasible individuals belonging to a given front in the constraint space, the computation of the I-distance density estimator [START_REF] Deb | A fast-elitist non-dominated sorting genetic algorithm for multiobjective optimization: NSGA-II[END_REF] is carried out in relation to all constraints [START_REF] Sareni | Integrated Design of Heterogeneous Electrical Energetic Systems using Multiobjective Genetic Algorithms[END_REF]. In this way, niching will occur in the two different spaces (i.e. constraint and objective spaces) and diversity will be preserved to avoid premature convergence.

Five independent runs are made to take into account the stochastic nature of the NSGA-II. The population size and the number of non-dominated individuals in the archive are set to 100 and the number of generations is G=200. Mutation and recombination operators are similar to those presented in [START_REF] Sareni | Recombination and Self-Adaptation in Multi-objective Genetic Algorithms[END_REF]. They are used with a crossover probability of 1, a mutation rate on design variables of 1/m (m denoting here the total number of design variables in the problem) and a mutation probability of 5% for the X-gene parameter used in the selfadaptive recombination scheme. The surrogate sizing and simulation models described in the previous section are exploited to evaluate the constraints and the objectives (i.e. the useful power and the total wind turbine mass) associated to the individuals in the NSGA-II population.

Results

The Pareto-optimal configurations determined from the five independent runs are displayed in Fig. 3a. Note that the global Pareto-optimal front is obtained by merging all fronts associated to these runs. We also represent in Fig. 3a the characteristics of three typical solutions and the initial configuration of the WTG which is actually used in our lab [START_REF] Mirecki | Comparative study of maximum power strategy in wind turbines[END_REF]. This generator is able to operate at optimal wind powers when it is associated with a MPPT control device but presents a "poor" efficiency if the MPPT is suppressed. As shown in Fig 3b, the power extracted from the wind cycle is strongly reduced in this case. The WTG optimization considerably improves both objectives. As it can be seen in Fig. 3, these passive optimized solutions can match very closely the behavior of active WTGs operating at optimal wind powers by using a MPPT control device. Some Paretooptimal solutions are even slightly better than the initial configuration of the generator with an MPPT control device since all losses in the system are reduced thanks to the global optimization process (see Table 3 for justification).

Model Sensitivity

To validate these results obtained with the surrogate sizing and simulation models, we compute the characteristics of the specific Pareto-optimal solutions of Fig. 3 with the accurate corresponding models. In particular, we compare in Table 4 the electric parameter values of the generator (typically the leakage and main inductances computed for one conductor per slot) obtained with the fully Analytical Model (AM) and the Finite Element Method (FEM). Moreover, we indicate the useful power computed from the FEM sizing and the classical synchronous model represented in a ABC frame. It can be noted that the results are globally in accordance since differences between the surrogate and accurate models are rather small. We also mention in this table the computing time associated with both models for a standard PC. Note that it is about 8 times higher for the accurate model. This justifies the use of the surrogate model in an optimization context since 100 000 runs have been performed to obtain the Pareto-optimal configurations.

Conclusions

In this work, Multiobjective Genetic Algorithms have been applied to the design of a small passive WTG. For this purpose, surrogate and accurate models have been developed for the sizing and the simulation of the WTG.

An optimization process based on the use of the NSGA-II in association with the implemented surrogate models has been exploited to improve the useful power and the mass of the WTG. Three Pareto-optimal solutions have been analyzed and compared with the accurate sizing and simulation models. Results show that the optimized configurations of the full passive WTGs are able to match very closely the behavior of active WTGs which operate at optimal wind powers by using a MPPT control device. In the outlooks of this work, the Pareto-optimal solution sensitivity to the wind cycle will be studied in order to take statistical information related to the WTG location. Note also that this problem can constitute an original benchmark for investigating design methodologies based on model hybridization such as Space Mapping Methods.

Fig. 1 :

 1 Fig. 1 : Synoptic of the passive wind turbine generator (without MPPT control system)

Fig. 2 :

 2 Fig. 2 : The energetic equivalent DC model for the synchronous generator

Fig. 3 :

 3 Fig. 3 : Pareto-optimal configurations compared with a non-optimized wind turbine

  Savonius Vertical Axis Wind Turbine of radius R = 0.5 m and height H = 2 m is considered as case study. Its power coefficient C p is defined by the following empirical interpolation:

	2.2. The Wind Turbine Characteristics
	A O O O 4540 . 0 1168 . 0 1299 . 0 2 3 p C	,
	relation
	V W	( t	)	10	2 . 0	105 . 0 sin( t	)	2	367 . 0 sin( t	)	293 . 1 sin( t	)	2 . 0	665 . 3 sin( t	)	.	(1)

V W (t) which is approximated with the empirical

  The synchronous generator equivalent circuit

	: :	Electromechnanic Electromechnanic Electromechnanic	E sDC E sDC	Armature Armature Armature	E sDC ' E sDC	Transient Transient Transient	E DC	Commutation Interval	U DC
		Conversion Conversion Conversion		Reaction Reaction Reaction		Electric Mode Electric Mode Electric Mode		in the Diode Rectifier
	T em T em	Voltage Source Voltage Source Voltage Source	I sDC ' I sDC	Voltage Drop Voltage Drop Voltage Drop	I sDC I sDC	Power Loss Power Loss Power Loss	I sDC	Voltage Drop	I DC

Table 1 :

 1 Correspondence between the synchronous generator circuit and the equivalent DC model

	Variable	Synchronous Generator	Equivalent DC -Model
	Voltage	V s	U	DC	S 3	6	V	s
	Current	I s	I	DC	S 6	I	s
	Flux	) s	DC					s

Table 2 :

 2 Design Variable Characteristics

	Design Variable	Nature	Bounds
	Sizing Voltage [V]	Continuous	V b [1, 200]
	Radius/Length Ratio	Continuous	R rl [0.1, 10]
	Number of Pole Pairs	Discrete	p {1,.., 60}
	Current Density [A/mm 2 ]	Continuous	J c [0.5, 10]
	Sizing Power [W]	Continuous	P b [1, 700]
	Yoke Induction [T]	Continuous	B y [1.2, 2.2]
	Number of Slots per Pole per Phase	Discrete	N spp {1,..,6}

Table 3 :

 3 Power assessment associated with the particular solutions of Fig 3

	Solution	Extracted Wind Power (W)	Electromagnetic Power (W)	Iron Losses (W)	Joule Losses (W)	Conduction Losses (W)	Useful Power (W)
	Initial Configuration (without MPPT)	124	123	19	16	3	85
	Initial Configuration (with MPPT)	291	274	33	18	3	220
	c	281	266	7	21	2	236
	d	281	266	8	27	2	229
	e	276	263	11	29	3	220

Table 4 :

 4 Surrogate and accurate model comparison for the particular solutions of Fig.3

		Main Inductance L p [PH]	Leakage Inductance L l [PH]	Useful Power [W]
	Solution					AM sizing +	FEM sizing +
		AM	FEM	AM	FEM	Equivalent DC	Synchronous
						Model	Model
	c	33.8	33.4	2.4	2.7	236	231
	d	29.5	29.7	5.8	6.4	229	220
	e	25.6	26.5	14.3	15.6	220	207
	Computing Time (s)	Negligible	120	Negligible	120	40	310


Maher Baili
email: amaher.baili@enit.fr

Vincent Wagner
email: bvincent.wagner@enit.fr

Gilles Dessein
email: cgilles.dessein@enit.fr

Julien Sallaberry
email: djulien.sallaberry@hotmail.fr

Daniel Lallement
email: edaniel.lallement@messier-dowty.com

An experimental investigation of hot machining with induction to improve Ti-5553 machinability

Keywords: Titanium alloy Ti-5553, induction, temperature, machinability, cutting force, wear

The manufacturing of aeronautic parts with high mechanical properties requires the use of high performance materials. That's why; new materials are used for landing gears such as the titanium alloy Ti-5553. The machining of this material leads to high cutting forces and temperatures, and poor machinability which requires the use of low cutting conditions. In order to increase the productivity rate, one solution could be to raise the workpiece initial temperature. Assisted hot machining consists in heating the workpiece material before the material removal takes place, in order to weaken the material mechanical properties, and thus reducing at least the cutting forces. First, a bibliography review has been done in order to determine all heating instruments used and the thermal alleviation that exists on conventional materials. An induction assisted hot machining was chosen and a system capable to maintain a constant temperature into the workpiece during machining (turning) was designed. Trails permit to identify the variation of cutting forces according to the initial temperature of the workpiece, with fixed cutting conditions according to the TMP (Tool-Material-Pair) methodology at ambient temperature. Tool life and deterioration mode are identified notably. The results analysis shows a low reduction of specific cutting forces for a temperature area compatible with industrial process. The reduction is more important at elevated temperature. However, it has consequences on quality of the workpiece surface and tool wear.

Introduction

For aeronautic field, new high performance materials are used because of their low density, their excellent properties at room and elevated temperature, such as resistance to fatigue and corrosion and specific strength. Indeed, for the manufacture of their landing gears, Messier-Dowty uses a new titanium alloy: Ti-5Al-5Mo-5V-3Cr (Ti-5553). However, this new refractory material presents a poor machinability compared to steel or the more known titanium alloy: Ti-6Al-4V (Ti-64) [START_REF] Arrazola | Machinability of titanium alloys (Ti6Al4V and Ti-5553)[END_REF]. When machining Ti-5553, the cutting speed is low and the tool life is short. So, this results increase cycle time and manufacturing cost becomes a major problem. Proposing improved solutions is possible only by understanding the cutting Ti-5553 alloy phenomena and the degradation modes of cutting tool, according to the assistants allowing increasing machinability. The aim of this paper is to study the impact of the initial temperature of the material being machined about the evolution of cutting forces and modes of degradation of tool. This is based on hypothesis that a potential gain in cutting force will positively affect the machinability. The methodology of the approach is based on Tool-Material Pair (AFNOR: COM [START_REF] Norm | Working zones of cutting tools -Couple tool-material[END_REF]). For this approach, the representative criterion of the optimization is the specific cutting energy Kc. Indeed, heating the workpiece material reduces plastic flow stress of the material, thereby, causing the thermal softening phenomenon (well known in high speed machining), which leads to the reduction of Kc. However, this temperature will affect the tool life (increasing of thermal stresses, flank wear, abrasion of the coating ...). This heating can cause a microstructural transformation of the material and generates a reduction in mechanical properties of the workpiece surface. Therefore, it's necessary to analyze the gains and limitations of hot machining approach.

State of the art for hot machining

The low machinability of titanium alloys is mainly due to its mechanical properties. Indeed, its poor thermal conductivity concentrates more heat at the tool-workpiece interface. This creates a high temperature tool-material contact. In addition to that, by high temperatures, titanium alloys react chemically with many materials of cutting tools. With increasing temperature, mechanical properties of all materials decrease (figure 1). So, heating lowers the plastic flow stress of metals.

Figure 1 Evolution of tensile strength as a function of temperature for different materials [START_REF] Malot | Laser crazing machining of boron[END_REF] The principle of assisted hot machining consists in taking advantage of the material mechanical properties decrease due to the increase in the workpiece initial temperature. Since the 70s, many studies have been conducted on this topic. Moore [START_REF] Moore | Hot machining in industry[END_REF] carried researches on different metallic materials and ceramics. He noted the improved machinability of aerospace materials such as titanium and nickel alloys. Gains generally observed are lower cutting forces, vibration and tool wear and improved surface finish. Studies have been conducted by Ozler [START_REF] Ozler | Theoretical and experimental determination of tool life in hot machining of austenitic manganese steel[END_REF] on the tool life when hot machining of austenitic-manganese steel. It was concluded that the tool life is proportional to the workpiece temperature to 600°C. However, it's inversely proportional to cutting speed. These results show that hot machining allows the use of higher cutting speeds for a given tool life. Melhaoui's researches [START_REF] Melhaoui | Contribution study of cutting tool wear during laser assisted machining and machinability of ceramics (zinc oxide)[END_REF] also confirm the interest of heating the workpiece in order to increase the tool life. In fact, with thermal assistance, he showed that 80% of the flank wear and 60% of the crater wear have been reduced. For hot machining of Ti-64, Sun [START_REF] Sun | Laser-assisted machining of titanium alloys[END_REF] have observed that the plasma assistance degrades the tool life, despite the reduction of cutting forces. Bi [START_REF] Bi | Crater Wear Modeling in Conventional Speed Machining[END_REF] explains that the thermal assistance does not necessarily reduce wear of the tool. As depicted in figure 2, we note that at low temperature, adhesion and abrasion are preponderant. However, at high temperature, diffusion, corrosion and plastic deformation occur. According to machined materials and cutting parameters, thermal assistance has contrasting effects on the wear of cutting tools. Depending on the temperature, the wear may have mechanical origins (abrasion) or chemical ones (diffusion). In addition to that, the physico-chemical properties of materials play an important role. Indeed, the high temperature reduces the material stress, but it activates the chemical reactions between tool and material.

To raise the temperature of the machined material, several methods are possible: the piece is entirety heated before being machined or local heating techniques are used. The plasma heating technique allows increasing the local workpiece temperature upstream of the tool path with a plasma torch. This method has been used in [START_REF] Leshock | Plasma enhanced machining of Inconel 718: Modeling of workpiece temperature with plasma heating and experimental results[END_REF] to heat Inconel 718.

Figure 2 Tool wear depending on temperature Another heating method that can be used: the laser heating [START_REF] Armitage | Laser Assisted Machining of Hard-to-Wear Materials[END_REF]. The principle of this method is similar to that of plasma method one. However, the power density obtained is much greater. The last heating method used is the induction heating one. Indeed, the workpiece is immersed in a magnetic field. So, the heating is done without any contact with the workpiece and can easily be compatible with the machining. It allows increasing a titanium alloy temperature at 1000°C in only 2 minutes. Moreover, it does not cause any danger because only the workpiece is heated and the thermal radiation remains very low. If increasing temperature of the machined material decreases its resistance and improves its machinability, it has a bad impact on the material surface integrity: microstructural changes and residual stresses ( [START_REF] Ding | Laser-assisted of hardened steel parts with surface integrity analysis[END_REF][START_REF] Chang | Evaluation of surface roughness in laser-assisted maching of aluminium oxide ceramics with Taguchi method[END_REF]). Indeed, Germain [START_REF] Germain | Comprehension of chip formation in laser assisted machining[END_REF] observed microstructural changes due to heat treatment caused by surface heating. Thus, α and β material phases change their structures. Thereby, rapid cooling of the surface generates stresses and cracks appear. Their presence affects the fatigue strength of the workpiece during its use. Jones [START_REF] Jones | Thermomechanical processing of Ti-5Al-5Mo-5V-3Cr[END_REF] studied the impact of temperature on the Ti-5553 structure. At room temperature, the titanium alloy has a β metastable structure. This structure evolves into (α + β) structure since crossing the β-transus at around of 845°C. The mechanical and thermal stresses caused by machining generate dilation of the superficial layer of the machined material. The difference of expansion between the material layers creates residual stresses. Mastered residual stresses (excessive value ones generate a fractured surface) improves the mechanical properties of the material. By heating the Ti-64, Germain [START_REF] Germain | Comprehension of chip formation in laser assisted machining[END_REF] presents relation between the surface residual stresses and the temperature reached. Indeed, the residual stresses due to tension increases at the expense of those due to compression. About cutting forces, all research carried out with laser assistance show a significant reduction of the specific cutting force. By turning a hard steel (AISI 4130), Ding [START_REF] Ding | Laser-assisted of hardened steel parts with surface integrity analysis[END_REF] obtained a reduction of Kc about 20%. For a metal matrix composite material, Wang [START_REF] Wang | An investigation of laser-assisted machining of Al203 particle reinforced aluminium matrix composite[END_REF] shows a significant reduction from 30 up to 50% of cutting forces while the tool life is improved. Braham-Bouchnak [START_REF] Bouchnak | Study of extreme stress behavior and machinability of a new aeronautical titanium alloy: the Ti555-3[END_REF] studied two assistance methods to machining the Ti-5553 material: laser assistance and high pressure water jet assistance. For the first method, it shows a reduction for specific cutting force of 35% with low cutting speeds (outside the area of usual V c,min according to TMP Method) to 19% for high speeds. His researches also show an increasing V c,min from 50 to 70 m/min through the laser assistance. Moreover, the roughness does not seem affected, but he noted increasing residual stresses to tensile strength and a reduction of strain hardening as the local heating caused by the laser only generates an expansion in a plastic surface layer.

Nowadays, researches carried out are limited to study the influence of increased temperature on the cutting forces, tool life, ductility, and surface integrity of the material independently. However, they don't reach an overall and industrial conclusion by comparing contributions of this technology on the machinability compared to its disadvantages. The goal of our work is to complete the literature in order to affirm if the heating of Ti-5553 represents a path of improvement and optimization of machinability and if it can find an industrial application.

Experimental set-up

The experimental set-up allows performing turning tests of Ti-5553 with stabilized temperature of the workpiece. In a first approach, the cutting parameters and the tool are settled down and only the temperature varies. We note the cutting force, roughness, wear of the cutting tool and the microhardness of the machined surface. The procedure consists in getting the workpiece at a controlled temperature, to carry the machining and to recover the measured information. The machinied workpiece is constituted of a piece of material at the initial state changed at each machining test. The choice of cutting tools and cutting conditions is determined by a previous study detailed in [START_REF] Wagner | Experimental study of coated carbide tools behavior[END_REF] giving an optimal result at room temperature presented as following:

• cutting speed Vc: 35 m/min (the cutting speed was selected according to the TMP (Tool-Material-Pair) methodology at ambient temperature), • feedrate f : 0.15 mm/rev, • depth of cut Ap: 3 mm, • machining time: 10 s, • tool insert: Sandvik CNMG 16 06 12 -QM 1105 (Rake angle = 13 °, backing edge of 0.12mm at 13 ° combined with a honing of 0.02mm), • dry machining. However, these conditions are not critical since the goal is to observe a differential of cutting forces and not to seek an optimum. If we observe the heat treatment cycle of Ti-5553 depicted in figure 3, and in terms of temperature, the material behavior can be divided into three clearly zones: the first zone corresponds to temperatures below 300°C, hot machining should not alter the effects of heat treatment as the Ti-5553 is in its stable area. Between 300 and 640°C, the stress relaxation zone seems particularly interesting. Indeed, it is in this zone that the prospects for reducing cutting forces and tool wear are expected. The last zone corresponds to temperatures above 640°C. In this case, there are irreversible microstructural changes affecting the mechanical properties of the material. Therefore, all heated material above 580°C must be removed from the cutting operation, in order to avoid a reduction in mechanical properties.

Figure 3 Range of heat treatment of Ti-5553

As specified previously, the best heating mean compatible with machining, allowing reaching quickly high, controlled, and stabilized temperatures is induction assisted hot machining method. The trials to be performed are turning tests under high temperature; this temperature must be maintained during machining. Thus, the experimental device consists of a semi-circular "pancake" inductor partially enveloping the workpiece during the turning, specifically designed for our tests (figure 4).

Figure 4 Material heating by semi-circular inductor

The geometry of the rotating workpiece was designed to integrate thermocouples inside and closer to the cutting zone. During the machining, the signal recoveries from thermocouples are carried through a rotating collector across the chuck of the lathe. Furthermore, a thermal camera was used to compare its temperature measurements to those provided by thermocouples. A dynamometer platform has been used for the cutting forces measurements (Kistler 9263-A). Figure 5 illustrates the device used for machining. For machining, a protocol for raising and maintaining the temperature of the rotating workpiece in the inductor, with temperature measurement by both thermocouples and thermal imaging camera determines the heating process. So, it ensures the stabilization at the desired temperature workpiece. We note that the delay of temperature rising is under 3 seconds.

Experimental results and discussion

Cutting forces.

Table 1 shows the evolution of the cutting forces and the specific cutting energy based on the initial temperature of the workpiece before machining. By observing figure 6, we can see that the evolution of cutting forces and specific cutting force Kc presents 3 phases: at temperatures lower than 100°C, the effort remains constant. When the heating temperature is between 100°C and 500°C, cutting force reducing is poor (about 10%). This reduction became significant only when heating temperature exceeds 500°C. Consequently, if we consider only the specific cutting force parameter, this domain would be of interest to optimize machinability (right picture on figure 6).

Temperature Reference -1% -5% -6% -7% -9% -13% -28% -34% Compared to heating laser technique on Ti-5553 [START_REF] Bouchnak | Study of extreme stress behavior and machinability of a new aeronautical titanium alloy: the Ti555-3[END_REF] where the heating zone remains superficial in the cut thickness, the Kc reduction is here significantly higher (figure 6: approximately 30% against 19% with laser) since in our configuration all machined thickness is at the elevated temperature. However, thermal stresses supported by tool are also higher than in laser heating case.

Average error = 5%

The decrease observed in cutting forces caused by the high initial temperature of workpiece is mainly due to thermal softening of the material. For the Johnson-Cook law (presented in equation 1) that can characterize the material behavior in context heating machining [START_REF] Shi | Identification of Material Constitutive Laws for Machining-Part II: Generation of the Constitutive Data and Validation of the Constitutive Law[END_REF], the third term of this law illustrates this trend.

( ) However, all tests were carried at constant cutting speed. It would be interesting on future experimental campaign to check the influence of workpiece temperature on the optimum cutting speed according to the COM approach [START_REF] Norm | Working zones of cutting tools -Couple tool-material[END_REF]. It would quantify the potential effect of temperature elevation on the cycle time.

0 0 0 . 1 ln . 1 m n f T T A B C T T ε σ ε ε       -     = + + -      -        (1)

Tool wear.

For the three temperature phases identified above, wear tests for quasi-orthogonal cutting were performed. At room temperature (workpiece at 25°C), there was a slight cutting edge chipping at limit the depth of cut. This degradation mode is resulted from various factors: severe abrasion on the rake face, effort and pressure on the workpiece caused by chip friction, difference of pressure on the free zone of the tool (cracking appearing in this zone) and possibility of inclusion in the material. When the temperature increases, a second degradation mode is observed: a built-up edge grows. It becomes more relevant as the workpiece temperature increases (figure 7). This mode reflects a very high temperature at tool-chip interface and a lower pressure in this zone. At high heating temperature (750°C), built-up edge is present across whole width of cut and a flank wear appears. Unlike the results depicted in literature about tool wear when hot machining of different materials, the influence of Ti-5553 initial temperature on tool wear is predominant. If the cutting forces are reduced, chipping and flank wear becomes significant as the temperature increases. Relationship between chip morphology and temperature. Machining Ti-5553 generates long and continuous chip. This chip morphology is an aggravating factor on tool life. The heat machining may be a means of segmentation of the chips [START_REF] Sun | Laser-assisted machining of titanium alloys[END_REF]. The chips obtained without thermal assistance are wavy with a high strain rate. For machining with laser assistance, the material is less resistant to shear forces. However, for the Ti-5553 and whatever the workpiece temperature, the chip does not remain segmented. This is due to poor thermal softening effect compared with hardening induced in the primary shear plane. In figure 8, we observe different chip morphology. At low temperature, shear bands are more pronounced. However, for high cutting temperature, the chip does not seem formed by shearing but seems repulsed.

Surface integrity.

The micro-hardness depicted in figure 9 is representative of the surface integrity of machined material. This micro-hardness tends to increase with heating temperature, but very weakly (about 40 Hv on average). Beyond 500°C, the structure is modified, resulting from significant changes at micro-hardness of the surface. The peak at 250°C is not significant. Figure 9 Influence of the temperature on the Vickers hardness and surface roughness Residual stresses in surface of machined material are the result of a competition between mechanical phenomena and thermal phenomena. In turning, cutting forces (mechanical phenomena) generate compressive residual stress. However, the heat flux (thermal phenomena) caused by the machining, i.e. plastic expansion of the heated and cooled superficial layer, generates tensile residual stresses. In laser heating, Germain [START_REF] Germain | Comprehension of chip formation in laser assisted machining[END_REF] and Braham-Bouchnak [START_REF] Bouchnak | Study of extreme stress behavior and machinability of a new aeronautical titanium alloy: the Ti555-3[END_REF] note a trend towards the tensile residual stresses that can be explained by the localized heating of the beam. By heating all the workpiece (as in induction assisted hot machining method), this phenomenon does not appear and the difference between temperature caused by cutting and initial heating temperature is lower. So, we can imagine, even if supplementary residual stress measurements have to be made to reinforce this analysis, that either we should get a stress relaxation, either a tendency toward compressive residual stresses. The increase of micro-hardness according to initial temperature of the material seems to correlate with this analysis; since the micro-hardness increases depending on temperature (the machined surface undergoes compression or strain hardening). Figure 9 shows too the evolution of roughness as a function of temperature. As depicted, roughness varies from Ra 1.6 µm to Ra 0.8 µm for the machining carried at temperatures above 200°C. It's difficult to explain the peak at 400°C, maybe due to a chip adhering. As shown in [START_REF] Ding | Laser-assisted of hardened steel parts with surface integrity analysis[END_REF] on hard materials and unlike laser assistance on the Ti-5553 [START_REF] Germain | Comprehension of chip formation in laser assisted machining[END_REF], we see a significant improvement in the roughness of the surface material around 50%. This decrease can be explained by the higher ductility of the material machined at high temperatures. Furthermore, the reduction of cutting forces involved in the limitation of the disturbing phenomena of the surface such as bending or vibration cutting. Reducing the frequency of the shear plane on the chip (as illustrated in figure 8) leads to an improvement of surface roughness, because cutting force variations are reduced with a more flexible and repulsed chip.

Summary

The aim of this paper is to study the influence of temperature on the machinability of Ti-5553. In this work, a induction assisted hot machining system was designed. Based on cutting conditions defined in a previous study, the impact of temperature on specific cutting force, wear of the tool and surface integrity was studied. The Ti-5553 is a brittle material. So, heating it can bring closer its behavior of more conventional materials such as hardened steels. Compared to room temperature, a 13% reduction of specific cutting force for a temperature of 500°C was measured. For a temperature of 750°C, the decrease reaches 34%. However, the material structure is irreversibly changed and the tool life is reduced. To overcome this problem, a cooling system of the cutting edge (cryogenic machining) will be tested using the results of [START_REF] Venugopal | Tool wear in cryogenic turning of Ti-6Al-4V alloy[END_REF]. Another optimization track is possible: varying the cutting speed, which was fixed during this study (equal to V c,min determined at room temperature). Indeed, V c,min varies according to temperature and seems to be higher at high temperature, thereby this may reduce cycle time. In addition, assistance by high pressure lubrication [START_REF] Braham-Bouchnak | High pressure water jet assisted machining of duplex steel: machinability and tool life[END_REF] is also an interesting mean to improve the Ti-5553 machinability. Indeed, this approach leads to chip fragmentation, low friction and the tendency is to obtain residual stresses in compression. But, this approach may be incompatible with some processes (dry machining required or milling case with a pilot on the cutting zone is very difficult to achieve). Finally, this research was foccused to the surface micro-hardness xith regards to surface integrity issues. Thus, in future work, more detailed study of surface integrity (residual stresses, strain hardening) has to be conducted.

Figure 5

 5 Figure 5 Experimental set-up

Figure 6

 6 Figure 6 Evolution of cutting forces and Kc depending on the temperatureIn this interesting domain, reduction values of specific cutting force correspond to the bibliography results. Indeed, Kc reduction values reach from 13 to 34% for a temperature range of 500 to 750°C. Compared to heating laser technique on Ti-5553[START_REF] Bouchnak | Study of extreme stress behavior and machinability of a new aeronautical titanium alloy: the Ti555-3[END_REF] where the heating zone remains superficial in the cut thickness, the Kc reduction is here significantly higher (figure6: approximately 30% against 19% with laser) since in our configuration all machined thickness is at the elevated temperature. However, thermal stresses supported by tool are also higher than in laser heating case.

  With: σ : Von Mises flow stress, ε : deformation, 0 ε ε : plastic strain rate, 0 T : room temperature, f T : melting temperature and A, B, C, n et m: constants. In Johnson-Cook law, m> 1. Consequently, if the temperature T of the material increases, the stress σ and hence the cutting force decreases, and vice versa.

Figure 7

 7 Rake wear (a) and flank wear (b)

Figure 8

 8 Chip morphology at 250°C (a) and 750°C (b)

Table 1

 1 Experimental set-up