A Dadouche

M J Conlon

W Dmochowski

B Liko

J.-P Bedard

EXPERIMENTAL EVALUATION OF ABRADABLE SEAL PERFORMANCE AT HIGH TEMPERATURE

Abradable seals have been used in aero-engines and landbased gas turbines for more than three decades. They are applied to various sections of the engine in order to reduce gas leakage by optimizing the gap between rotating and stationary parts. This optimization represents a significant increase in efficiency and decrease in fuel consumption. Performance evaluation of any abradable seal includes measurement of its mechanical properties, abradability tests and (ultimately) tests in engines. The aim of this paper is to study the effect of temperature on the rub performance of abradable seals. A series of experiments has been carried out in order to evaluate a commercially available seal material at different operating conditions. The effect of operating temperature on contact force, abrasion scar appearance and blade wear is examined and analyzed. A microstructural analysis of the rub scar has also been performed.

INTRODUCTION

Abradable seals are widely used in aero-engines and landbased gas turbines (for power generation) to minimize gas leakage between the blades and the casing. Abradable application on stationary parts results in an optimal gas path and increased efficiency. Reducing leaks around the rotating parts serves to maximize the amount of working gas and minimize power loss. Fuel consumption represents 53% of the operating cost of an aircraft [START_REF] Novinski | THSP coatings save aircraft engines[END_REF][START_REF] Stern | Aircraft propulsion -a key to fuel conservation: An aircraft manufacturer's view[END_REF], emphasising the importance of implementing a good seal with minimal gap. Abradables have to be carefully designed to accommodate rub situations that might result from maneuver-ing and landing loads, vibration of casing and rotor, thermal expansion of the engine rotor, centrifugal and gyroscopic forces, as well as poor assembly and machining tolerances, without damage to the engine components. To illustrate the importance of a good seal, an extra gap of five thousandths of an inch (0.127 mm or 0.005 in) can increase the fuel consumption by 0.5% [START_REF] Ferguson | Use of coatings in turbomachinery gas path seals[END_REF]. On the other hand, a gain of 0.3 to 1% in power output and up to 5% in efficiency could be realized through seal system improvements [START_REF] Chupp | Development of higher temperature abradable seals for gas turbine applications[END_REF][START_REF] Schmid | 1200 • reached[END_REF].

Typically, metallic abradable coatings are used in the compressor side of a gas turbine and ceramic materials are used in the turbine side. The choice of material for a given application depends on the operating environment, particularly the temperature to which the coating will be exposed, rubbing element material and geometry, seal durability and economics [START_REF] Hajmrle | Abradable seals for gas turbines and other ro-tary equipment[END_REF]. A variety of seals have been developed over the last few decades and are now commercially available, however, as engine technology evolves towards higher power density there is a need to develop abradables capable of performing under severe operating conditions such as extremely high temperatures and abrasive environments. Most aircraft engines operate with temperatures greater than 1000 • C in their turbine sections; the F110, M88, F100 and EJ200 have turbine inlet temperatures of 1427 • C, 1570 • C, 1399 • C and 1477 • C, respectively [START_REF]Gas Turbine Forecast[END_REF].

A typical abradable seal material is purchased in powder form, and may be deposited by several different thermal spray techniques. These techniques are well established in the industry and include deposition by combustion (flame), plasma, and highvelocity oxyfuel (HVOF) spray. Thermal spray offers several advantages, including simple overhaul and repair, and a variety of coating materials are available [START_REF] Novinski | THSP coatings save aircraft engines[END_REF]. Examples of some of the abradables already on the market are:

• Aluminum-alloy-polyester that can be either plasma or HVOF sprayed and is suitable for service at temperatures as high as 343 • C (650 • F), • Aluminum-alloy-graphite that can be either combustion or plasma sprayed and is suitable for service at temperatures up to 482 Abradable materials must satisfy many requirements to be considered as an efficient seal system, and these have been extensively discussed in the literature. Novinski [START_REF] Novinski | The selection and performance of thermal sprayed abradable seal coatings for gas turbine engines[END_REF][START_REF] Novinski | The design of thermal sprayed abradable seal coatings for gas turbine engines[END_REF] summarizes the design criterea for abradables, their microstructure and application to various gas turbine sections. From a design point of view, abradable seals must meet the following expectations:

• Be abradable and durable:

• Be readily abradable • Have a consistent microstructure • Be resistant to impact from abrasive particles traveling through the engine at high velocity and to degradation at elevated temperatures • Be resistant to salt water and engine fuel • Be resistant to oxidation

• Rub and age well with stable mechanical properties in the harsh environment of gas turbine engines • Wear by disintegrating into fine particles; debris must not damage any components downstream within the gas turbine • Cause minimal wear of blade tips or knife edges • Generate low contact friction • Maintain a smooth surface in order to reduce aerodynamic losses, despite releasing wear debris • Rubbing should break the bond between particles rather than melt the particles themselves Some of those requirements such as abradability and durability are contradictory; however, designing a seal system that performs well involves striking a balance between these opposing requirements.

There is no standard method or procedure for testing abradable materials. Mechanical properties of an abradable material, such as hardness and ultimate tensile strength, are not guarantees of good performance [START_REF] Hajmrle | Abradable seals for gas turbines and other ro-tary equipment[END_REF], therefore additional testing must be carried out to establish which materials would be good candidates for further development. These other testing methods may include a porosity analysis through imaging on cross-sectional micrographs, erosion resistance testing (ASTM G76), oxidation life and abradability testing. Abradability tests could be performed at room temperature or in an environment similar to that seen during service. Usually results from abradable testing provide sufficient confidence to apply coatings to engine sections for testing. To-date, there has been good correlation between wear rig results and engine results [START_REF] Hajmrle | Abradable seals for gas turbines and other ro-tary equipment[END_REF].

This paper presents the results of an experimental investigation carried out to determine the effects of temperature on the wear performance of a commercially available abradable seal. Some realistic service conditions such as thermal growth and dynamic loading have been simulated during tests on the National Research Council Canada's abradable test rig.

RIG DESCRIPTION AND TEST PARAMETERS

The wear rig used to carry out the tests is shown in Fig. 1. This rig simulates operational wear using a simulated turbine blade or knife-edge. It consists of a rotor driven by an air turbine and supported on hybrid rolling-element bearings. The rotor can be spun up to 40, 000 rpm, which corresponds to a blade tip speed of 425 m s -1 (1400 f t s -1 ). The motion of the table on which the test coupon holder is mounted is controlled axially and radially through two servomotors. Its speed varies from 0.0025 mm s -1 to 0.76 mm s -1 (0.0001 in s -1 to 0.03 in s -1 ). The test coupon's fixture is adaptable for testing both flat and curved profiles. The rig is also capable of testing heated abradables up to a temperature of 600 • C using a ceramic-encased, wire-wound resistor located at the back of the test coupon.

The rig is equipped with various sensors measuring rub temperature, rubbing forces (both radial and tangential), speed and seal incursion rate. After each test, blade and abradable seal wear is measured. Other parameters such as vibration and bearing and environment temperatures are monitored while testing. All data are acquired using a computerized data acquisition system.

As mentioned earlier, the abradable seal analyzed in this study is commercially available; it is a Cobalt-Nickel-based material (Co 25Ni 16Cr 6.5Al 0.5Y ) used in the high pressure compressor section of gas turbines where the temperature could reach 600 • C. The powder was sprayed on flat Hastelloy X substrates, ground flat to produce a smooth seal surface and then heat treated to burn off the polymer, resulting in a porous material (Fig. 2). The tests were performed using untipped Inconel 718 material blades with a tip width of 6.35 mm (0.25 in). The most important test parameters when evaluating abradable seal performance are blade tip speed, incursion rate and environment temperature. These parameters must replicate the operating conditions that abradable seals are normally subjected to. Usually such parameters are specified by end users or manufacturers; for this study, a test matrix has been selected to cover various conditions encountered in gas turbines such as thermal growth, excessive external loading and engine vibration. Table 1 shows the test parameters used in this study. It is important to mention that only the seal was heated during the high temperature tests and, depending on the disk's rotational speed, the seal surface temperature drops due to the windage generated by the disk rotation. It is also worth mentioning that all tests were carried out using a single working blade with a total of 1 mm (0.040 in) seal incursion. A second, shorter and thicker blade, located 180 degrees from the test blade was used for balancing. In a real application, multiple blades rub against the seal material; using a single blade creates an extreme operating condition.

DATA ANALYSIS AND DISCUSSION BLADE AND SEAL WEAR

Quantification of the blade and seal wear due to their interference during the abrasion process is rather difficult because of the complexity of the rubbing phenomenon. In Fig. 3, an estimation of the blade material loss is presented for different incursion rates and blade speeds for tests done at room temperature. As the wear bars show, for blades speed of 152 m s -1 and 305 m s -1 , the material loss is only marginally affected by the incursion rate. However, for a speed of 396 m s -1 the material loss is noticeably affected by incursion rate; the wear at the lowest incursion rate (0.00254 mm s -1 ) is only 12% of that at the higher incursion rate (0.762 mm s -1 ). It is important to highlight that the measured blade material loss represents an estimation rather than a quantification; in many cases seal material or wear fragments were transferred to the blade tip, filling some of its gouges and furrows (Fig. 4). For an incursion rate of 0.127 mm s -1 and blade speed of 305 m s -1 (Fig. 3), the masses of the blades after testing were slightly higher than the baseline mass, which is an indication of seal transfer to the blade tip. As a result of that, the wear bar for this specific case is negative. During the tests, the blades become slightly polished at their leading and trailing cutting edges and seal particles adhere to the blade tip, appearing as gray and burnt (high temperature oxidation) areas throughout the tip surface (Fig. 5a and5b). In Fig. 5a and5b, one can notice a small number of vertical streaks which were formed during manufacturing; Fig. 5c shows an untested blade tip.

Figures 6 and7 present a comparison between the blade material loss at room-and high-temperature for various incursion rates and a blade speed of 152 m s -1 and 305 m s -1 , respectively. Generally the room temperature tests exhibit higher blade wear compared to the heated tests for all incursion rates. (The cases where the room temperature tests show lower or no blade wear were discussed in the previous paragraph.) The examination of the blades following the tests revealed that those tested at high temperature appeared better both in terms of wear and severity of the scratches. As an example, Fig. 8 shows two blades tested at room and high temperature at a relatively high incursion rate of 0.381 mm s -1 and a low speed of 152 m s -1 . The blade tested at room temperature (Fig. 8a) is characterized by deep grinding marks, discoloration, burning, and material deformation at the blade edges, whereas the blade tested at high temperature suffered minimal wear and only slight discoloration. The abradable seal at room temperature must be harder and its mechanical properties must be higher than those at high temperature. This may lead to a severe interaction with the blade during the abrasion where the hard microscopic abradable particles score the blade tip as the seal moves towards it. Estimating the seal material lost during the abrasion is challenging due to the porosity of the abradable and the irregularities of the rub scar; this is especially true for the high temperature tests. However, measurement of the scar depth at its mid section produced consistent values ranging from 0.9 mm to 1.14 mm throughout its width depending on the test conditions.

The scar appearance represents but one of the important criteria when evaluating abradable seals. All room temperature tests produced smoother rub grooves when compared with the high temperature tests, which produced scars which were typically rough and irregular. Moreover, the room temperature tests at the lowest incursion rate resulted in a better scar finish than the higher incursion rate tests, especially for higher blade tip speeds. Figures 9 and10 show the different scars obtained for room temperature and heated tests at a low blade tip speed of 152 m s -1 and various incursion rates. A comparison between the two figures highlights the significant differences in terms of scar appearance and uniformity: the room temperature test scars are mostly regular and uniform, whereas all the high temperature scars are irregular with a large number of gouges due to tearing and spalling rather than disintegration into fine particles.

Figure 11 shows scanning electron microscope (SEM) images of a small portion of the rub scar tested at the highest incursion rate (0.762 mm s -1 ) and lowest blade tip speed (152 m s -1 ). As the images show, the room temperature test (Fig. 11a) results in a smother rubbing surface when compared to the high temperature test (Fig. 11b).

CUTTING FORCES

There are three control parameters that can affect the cutting forces in these tests: incursion rate, blade speed and temperature. It is useful to look at the test data in terms of each parameter in turn. We normalize the time data using the incursion interval. This means that the area under the force curve is a sort of "specific impulse" for the duration of the rub. This facilitates comparison between rubs at different incursion rates. For an idealized rub, we would expect the reaction forces to increase nonlinearly as

F r (t) ∝ arccos 1 - i(t) r (1)
where F r is the net reaction force, i is the incursion distance and r is the rotor radius. In reality we see this predictable force increase only at the lowest incursion rate, 0.00254 mm s -1 , as shown in Fig. 12. Figure 12 presents the tangential component of the rub force plotted versus rub interval fraction for three different blade tip speeds.

THE EFFECT OF INCURSION RATE

For higher incursion rates we would expect larger rubbing forces, however the incursion itself happens over a much shorter time interval, which illustrates the utility of normalizing the incursion time with respect to the rub interval. Table 2 outlines the percent change in specific impulse for different blade speeds, comparing the highest incursion rate with the lowest. We see that for all but the lowest blade speed the specific impulse is higher at the higher incursion rate. The trend is parabolic with respect to blade tip speed, as might be expected.

THE EFFECT OF BLADE SPEED

As seen in Fig. 12, the specific impulse of the lowest-speed incursion increases with blade speed. This is not the case for the highest incursion rate, as outlined in Tab. 3, where the higher blade speed produces a lower specific impulse. This may be due to the abrasion mechanism; the higher incursion rate is two orders of magnitude larger than the lowest-speed incursion, and one could expect a substantial difference in the two abrasions. Indeed, as discussed previously, there is a distinct difference in the scar appearance for the two abrasion rates. The low-speed incursion rate produces a much smoother scar than the high incursion rate.

THE EFFECT OF TEMPERATURE

Table 4 presents the effect of temperature on the specific impulse for the four incursion rates. For all but the lowest incursion rate increasing the seal temperature results in decreased cutting forces. This effect is independent of blade speed, as seen in Fig. 13-16 which compare ambient and high-temperature cutting forces for the two extreme incursion rates, and two different blade speeds. Figures 13 and 14 present the tangential cutting force for ambient and high temperature tests with an incursion rate of 0.00254 mm s -1 and blade speeds of 152 m s -1 and 305 m s -1 (respectively). For this low incursion rate both the ambient and high temperature force profiles display the trend predicted by Eq. 1. The forces recorded during the high-temperature testing are more variable, which corresponds well with the rougher scar appearance. In Fig. 14 in particular, we see that the high temperature cutting force drops suddenly just under halfway through the rub. The force eventually recovers to the expected level, suggesting that perhaps a chunk of seal material broke off at that point during the rub.

In Figures 15 and16 we see the tangential force profiles for ambient and high temperature tests with an incursion rate of 0.762 mm s -1 and blade speeds of 152 m s -1 and 305 m s -1 (respectively). For this incursion rate, the cutting forces are higher for the ambient tests and similarly higher for the lower blade speeds, as previously summarized in Tab. 3 and Tab. 4.

CONCLUSIONS

The effect of testing abradable seals at high temperature was studied and analyzed in this paper for a better evaluation of their performance characteristics. Blade material loss, rub scar and interaction forces were analyzed for different test conditions and parameters. However, there is a need to complement this study by heating both seal and blade for an accurate assessment. The main conclusions drawn from this study are as follows:

• Testing abradables at high temperature affects the rub characteristics. • Heating the seal results in less blade wear and a rougher scar surface. • The blade tip may sustain severe wear at room temperature, especially at high incursion rates. • Evaluation of abradable seal performance at room temperature should be followed by testing at high temperatures. • Rub forces are substantially affected by temperature, and in a less-than-intuitive manner, which necessitates hightemperature testing. • Forces are also affected by blade speed and incursion rate, and larger forces seem to correlate well with rougher scar appearance.

Figure 1 .Figure 2 .

 12 Figure 1. Abradable test rig

Figure 3 .Figure 4 .Figure 5 .

 345 Figure 3. Blade material loss at room temperature

Figure 6 .

 6 Figure 6. Blade material loss at 152 m s -1 blade tip speed

Figure 7 .

 7 Figure 7. Blade material loss at 305 m s -1 blade tip speed

Figure 8 .

 8 Figure 8. Blade tips after abrasion at test conditions of 0.381 mm s -1 and 152 m s -1 (a) room temperature, and (b) high temperature

Figure 9 . 1 Figure 10 . 1 Figure 11 .

 9110111 Figure 9. Rub scar appearance for a room temperature test at a blade speed of 152 m s -1 and incursion rate of (a) 0.00254 mm s -1 , (b) 0.127 mm s -1 , (c) 0.381 mm s -1 , and (d) 0.762 mm s -1

Figure 12 .

 12 Figure 12. Force versus rub interval fraction for a 0.00254 mm s -1 incursion rate

  • C (900 • F), • Nickel-graphite (15 to 25 weight % graphite) that can be used up to 343 • C (650 • F) and offers better corrosion resistance and, • Ni-Cr-Fe-Al-BN abradables that are combustion sprayed and used for engine sections that reach temperatures of up to 816

• C (1500 • F).

Table 1 .

 1 Test conditions

					Room Temperature	High Temperature
	Blade Speed (m s -1 )	{152, 305, 396}	{152, 305}
		Test	Test	Horizontal
	Air turbine Disc	blade	coupon	load cell
	Pyrometer	Vertical	Axial incursion	Radial incursion
		load cell	controller	controller

Incursion Rate (mm s -1 ) {0.00254, 0.127, 0.381, 0.762} {0.00254, 0.127, 0.381, 0.762}

Blade Material Loss for Various Incursion Rates Blade Material Loss [mm 3 ]

	3.467
			152 m s -1
	2.575		305 m s -1 396 m s -1
	2.19
	1.582 1.338 1.156 0.912
	0.243
	-0.7
	0.0025	0.127	0.381	0.762
		Radial Incursion Rate [mm s -1 ]

Radial Incursion Rate [mm s -1 ] Blade Material Loss for Higher Tip Speed Blade Material Loss [mm 3 ]

	2.575 2.494
	2.19
				Room temperature
				High temperature
	1.338
	0.73
	0.547
	0.304
	0.0025	0.127	0.381	0.762

Table 2 .

 2 Relative change in specific impulse with increased incursion rate (for different blade speeds)

	Blade Speed Specific Impulse
	(m s -1 )	(% Change)
	152	-400
	305	+20
	396	+70

Table 3 .

 3 Relative change in specific impulse with blade speed (for different incursion rates)

	Blade Speed		Incursion Rate
	(m s -1 )		(mm s -1 )
		0.00254 0.127 0.381 0.762
	152	-	-	-	-
	305	+90%	-	-	-70%
	396	+200%	-	-	-80%

Table 4 .

 4 Relative change in specific impulse with increased temperature (for different incursion rates)

						2.	Force vs. Rub Interval Fraction
						1.8
						1.4 1.6	Ambient Temperature
		Blade Speed (m s -1 )	Incursion Rate (mm s -1 )	Force [N]	0.8 1. 1.2
			0.00254 0.127 0.381 0.762	0.6
		152	+70%	-90% -60% -40%	0.2 0.4	High Temperature
		305	+60%	-	-	-40%
						0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
						Rub Interval Fraction
		0.6	Force vs. Rub Interval Fraction	Figure 15. Force versus rub interval fraction for a 0.762 mm s -1 incur-sion rate and 152 m s -1 blade speed at different temperatures
			High Temperature
	Force [N]	0.4				0.6	Force vs. Rub Interval Fraction
		0.2		Ambient Temperature	0.4	Ambient Temperature
		Rub Interval Fraction 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9	Force [N]	0.2
						High Temperature
	Figure 13. Force versus rub interval fraction for a 0.00254 mm s -1 in-
	cursion rate and 152 m s -1 blade speed at different temperatures	0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
						Rub Interval Fraction
		1.	Force vs. Rub Interval Fraction	Figure 16. Force versus rub interval fraction for a 0.762 mm s -1 incur-sion rate and 305 m s -1 blade speed at different temperatures
		0.8
			High Temperature
	Force [N]	0.4 0.6
				Ambient Temperature
		0.2
		0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
			Rub Interval Fraction

Figure 14. Force versus rub interval fraction for a 0.00254 mm s -1 incursion rate and 305 m s -1 blade speed at different temperatures


Marion Cuny

Sylvain Philippon

Pierre Chevrier

François Garcin

Experimental Measurement of Dynamic Forces Generated during Short-Duration Contacts: Application to Blade-Casing Interactions in Aircraft Engines

Keywords: Experimental set-up, High speed interaction, Orthogonal cutting, Abradable, Dynamic force measurement Nomenclature

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Increasing efficiency and reducing fuel consumption of aircraft engines require optimization of the clearance between the rotating parts (blades) and the engine case [START_REF] Demasi-Marcin | Protective coatings in the gas turbine engine[END_REF]. To achieve reduced clearance without endangering the blading, abradable seals are deposited inside the casing of the different engine stages. This type of coating was designed to wear out in case of contact with the blade tip [START_REF] Dalzell | Abradable seal with improved properties[END_REF][START_REF] Dorfman | Gas turbines use abradable coatings for clearance-control seals[END_REF] and to thermally insulate the engine casing.

The abradable seals present in the low-pressure compressor stage are generally composed of metal phase and self-lubricating non-metal phase with high porosity [START_REF] Faraoun | Improvement of thermally sprayed abradable coating by microstructure control[END_REF]. This material, deposited by Atmospheric Plasma Spraying (APS), is known for its good balance between erosion resistance and abradability [START_REF] Bounazef | The wear, deterioration and transformation phenomena of abradable Bn-SiAlcoating bounding organic element, caused by the friction between the blades and the turbine casing[END_REF][START_REF] Yi | Erosion wear behaviour and model of abradable seal coating[END_REF] as well as its simple manufacturing process and good sealing effectiveness. In case of contact with the blade tip, it produces fine particles which can be safely ingested by the engine and generates a smooth new surface which is beneficial to the aerodynamics properties.

However, important thermal and mechanical solicitations undergone by the turbomachines, particularly during transient states, lead to high speed interactions between the moving parts and the casing. These interactions can not be avoided in the case of reduced clearance. They have strong consequences on the blade vibratory behavior and may rapidly cause damages to the blading. Thus, characterization and understanding of the different phenomena which take place during interactions are essential to prevent premature wear or failure of the blading and to increase the reliability and service life of engines.

From a phenomenological point of view, wear mechanisms occurring during interaction were identified by Borel [START_REF] Borel | The wear mechanisms occuring in abradable seals of gas turbines[END_REF] and can be separated in two categories: mechanisms occurring without contact (erosion, corrosion and oxidation) and those occurring with contact (cutting, deformation, adhesive transfer, melting and tribo-oxidation). The mechanisms of the first category are undesirable because they increase the clearance between the blading and the seals and therefore decrease engine efficiency. They can be detected when the roughness, the chemistry or the color of the seal surface changes. As for the mechanisms of the second category, deformation appears when the blade plastically deforms the abradable material, smearing the non-metal phase on the metal phase. It can lead to unwanted densification of the material and creates a striated surface. These phenomena are prejudicial to the aerodynamic airtightness and to the abradability. Adhesive transfer corresponds to the transfer of material from the blade onto the seal and reciprocally. Melting produces a hard layer on the abradable seals. Adhesive transfer and melting affect the behavior of the abradable seal and can damage the blading. They should be avoided. On the contrary, the cutting mechanism is the only desirable abradable seal wear process: the blade acts like a cutting tool. This interaction leads to a brittle rupture of the abradable material without damaging the blade tip and generates a very smooth and shiny surface particularly favorable to aerodynamic properties.

From a quantitative point of view, the basic mechanical properties of abradable material are poorly known. These materials are highly anisotropic and a have layered structure resulting from successive deposits of molten/ semi-molten powder. Their mechanical properties are strongly influenced by the shape of these individual deposits, by interactions between the coating and the substrate, and between the different layers. Moreover, a majority of mechanical testing on coatings provides results on the couple coating/substrate. However, quasi-static tensile tests realized by Johnston and Evans [START_REF] Johnston | Freestanding abradable coating manufacture and tensile test development[END_REF] on self-supporting freestanding abradable specimens sprayed on dissolvable molds show that the materials have plastic behavior without elastic response. Mechanical and thermal properties of abradable materials are also estimated analytically thanks to a finite element modeling built on analysis of micro-structure [START_REF] Faraoun | Modelisation des proprietes thermomecaniques des materiaux abradables[END_REF]10].

As for the rotor/stator interaction phenomenon understanding, a first approach consists in studying the property of abradable material to wear out easily. The abradability is experimentally tested thanks to rub test machines allowing a large range of interaction speed (< 400 m/s) and temperature (< 500 • C) [START_REF] Bounazef | Blade protection and efficiency preservation of a turbine by a sacrificial material coating[END_REF][START_REF] Rathmann | Sealing Technology-Rub test Rig For Abrasive/Abradable Systems ASME Turbo Expo[END_REF][START_REF] Steinke | Process design and monitoring for plasma sprayed abradable coatings[END_REF]. However this type of experiments is mainly performed to compared abradable materials in order to optimize manufacturing process, to establish wear maps and for phenomenological studies. It does not provide information on the interaction forces applied on the blade tip nor allows to create wear laws. More precisely, it does not provide data suitable to calibrate and validate analytical or numerical models of the blade-casing contact or the abradable materials behavior under dynamical conditions. And these models are essential to optimise the design of new aircraft engines.

From this perspective, two other approaches seem more appropriate. The first one investigates the wear process by means of dry friction experiments. For instance, Yi et al. [START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF] give experimental values of the friction coefficient for different normal loads but for a low sliding velocity (V = 0.377 m/s) much inferior to those of compressor blade tips. The authors also establish an inverse correlation between the abradability of a given abradable material and its hardness. However, they also show that the hardness alone can not be consider as a criterion of abradability since the abradability varies from one material to another regardless of their hardness.

The second approach considers the blade to be a complex cutting tool. In this way, orthogonal cutting of abradable coating by titanium tools was studied by Sutter et al. [START_REF] Sutter | Dynamic analysis of the interaction between an abradable material and a titanium alloy[END_REF] for various interaction speeds ( from 10 m/s to 107 m/s), incursion depths (from 0.05 mm to 0.5 mm) and radii of the tool edge (from 0.001 mm to 0.03 mm). They show that mean interaction force increases when speed, incursion depth and radius of the tool edge increase and can be defined as the sum of two forces: a component force induced by friction and another one generated by the cutting interaction process. To generate high speed interaction, various technique are used. Their performances are very different in terms of range of interaction speed, incursion depth, materials involved, and duration of measurement. For the most part, they use machine tools, particularly those designed to study high speed machining (turning, milling, drilling) of metal. Interaction speeds are only limited by the capacity of the machine tool (up to 160 m/s in high speed turning [START_REF] Velasquez | Etude des copeaux et de l'integrite de surface en usinage grande vitesse de l'alliage de titane ta6v[END_REF]). But they generate long duration processes while the rotor/stator contact lasts only a few microseconds. Hydraulic high speed tensile testing machines are also used to generate shortduration contacts [START_REF] Faure | Design of a dynamometer capable of capturing the dry friction force in dynamic conditions[END_REF][START_REF] Philippon | A device enhancement for the dry sliding friction coefficient measurement between steel 1080 and vascomax with respect to surface roughness changes[END_REF] but their performances in terms of interaction velocity are limited (< 5 m/s). We chose to use a ballistic bench which allow to generate a short and unique interaction and to obtain a large range of interaction speed (from 3 m/s to 600 m/s) [START_REF] Guegan | Analyse experimentale de la coupe orthogonale sur dispositif equipe d'une barre d'hopkinson et de cameras videos rapides. 17eme Congres Franc ¸ais de Mecanique[END_REF][20][START_REF] Espinosa | Dynamic friction measurements at sliding velocities representative of high-speed machining processes[END_REF][START_REF] Philippon | An experimental study of friction at high sliding velocities[END_REF][START_REF] Lodygowski | Dry sliding friction experiments at elevated velocities[END_REF][START_REF] Chevrier | Mecanique et mesomecanique de l'ecaillageessais experimentaux et critere de rupture-etude d'un alliage d'aluminium et d'un acier de blindage[END_REF].

Accurate measurement of interaction force under dynamic conditions is difficult as well and requires dynamometers with a high bandwidth. The scientific literature presents a large range of measurement technologies, such as optical systems [25], load cells [START_REF] Seker | Design and construction of a dynamometer for measurement of cutting forces during machining with linear motion[END_REF][START_REF] Gunay | Design and construction of a dynamometer to evaluate the influence of cutting tool rake angle on cutting forces[END_REF], strain gauges [START_REF] Karabay | Analysis of drill dynamometer with octagonal ring type transducers for monitoring of cutting forces in drilling and allied process[END_REF][START_REF] Karabay | Performance testing of a constructed drilling dynamometer by deriving empirical equations for drill torque and thrust on SAE 1020 steel[END_REF][START_REF] Korkut | A dynamometer design and its construction for milling operation[END_REF][START_REF] Yaldiz | A dynamometer design for measurement the cutting forces on turning[END_REF][START_REF] Yaldiz | Design, development and testing of a four component milling dynamometer for the measurement of cutting force and torque[END_REF][START_REF] Totis | Development of a dynamometer for measuring individual cutting edge forces in face milling[END_REF][START_REF] Oraby | High-capacity compact threecomponent cutting force dynamometer[END_REF] sometimes associated with accelerometers [START_REF] Kim | Development of a combined-type tool dynamometer with a piezo-film accelerometer for an ultraprecision lathe[END_REF], and piezoelectric sensors [START_REF] Martinez | Identification des sources de vibration en usinage. Etude experimentale et numerique[END_REF]. However, these dynamometers remain limited by their bandwidth (varying between 130 Hz and 2,35 kHz). That is why various signal correction methods, principally based on modal analysis, has been developed and are implemented [START_REF] Martinez | Identification des sources de vibration en usinage. Etude experimentale et numerique[END_REF]37] to reduce the parasitic phenomena induced by the dynamic behavior of the sensor.

To sum up, the understanding of phenomena occurring during rotor/stator interactions in aircraft engines offers potential for the improvement of their efficiency and reduce their fuel consumption. Aircraft engineering requires numerical simulation tools to optimize design and performance of new engines and to increase their reliability and service life. But models on which these numerical simulation tools are built need to be validated by experimental data. However these data are not easily accessible by standard experimental devices because of the complexity of interactions and the extreme conditions in which they occur. In this paper, a new device is described and adapted to a ballistic bench where interaction velocities can reach up to 500 m/s. A set of experiments were carried out to investigate the orthogonal cutting process for a couple of materials composed of abradable material M601 and steel 42MoCr4. The velocities and forces of the interactions as well as the incursion depths were measured. A dynamic correction method based on the modal analysis principle was successfully applied. New interesting experimental data, meant to be used to calibrate and validate numerical models of the abradable material and to optimize the design of the blades, are reported for ranges of velocities and interaction depths varying from 60 m/s to 270 m/s and from 0.13 mm to 0.35 mm respectively. It appears that the mean interaction force increased in a non-linear way as a function of the interaction velocity and the incursion depth. Postexperiment observations highlighted the presence of two wear mechanisms identified by Borel [START_REF] Borel | The wear mechanisms occuring in abradable seals of gas turbines[END_REF]: cutting and plastic deformation.

The Experimental Set-Up

Experimental Set-Up Description Interaction between the blade and the abradable coating was experimentally simulated by projecting a sample of abradable material against a tool representing the blade tip by means of a ballistic bench (Fig. 1(a)). The propulsion device [START_REF] Chevrier | Mecanique et mesomecanique de l'ecaillageessais experimentaux et critere de rupture-etude d'un alliage d'aluminium et d'un acier de blindage[END_REF] was designed to reach extreme velocity up to 500 m/s corresponding approximately to the tangential velocity of the blade in the first compressor stage. However, for this work, the projectile velocity was limited to 300 m/s to preserved some sensitive part of the device, especially the guiding system (launch tube and rail). The device is mainly made of a pneumatic gun using the sudden expansion of compressed nitrogen to launch a semi-cylindrical projectile made of aluminum alloy. This projectile (Fig. 2) supports a sample of abradable material. It is guided along a launch tube and impacts an instrumented tool generating a short interaction. This instrumented tool which will be referred in this paper as the blade. After interaction, a shock absorber, placed in the receiving tank, captures the projectile without damaging the sample of abradable material in order to carry out post-experiment analysis. The experiments are performed under vacuum conditions to minimize blast phenomena perturbing the measurement before and during the interaction process.

Interaction Force Measurement

The axial force generated during the interaction was measured in the same time by a piezoelectric force sensor (PCB Piezotronic 260A01) connected to an ICP signal conditioner and a strain gauge glued onto the blade (Fig. 3), connected to a Wheatstone bridge in a quarter-bridge configuration. Both signals of the strain gauge and the piezoelectric force sensor were simultaneously recorded by a computer equipped with an acquisition card with a large bandwidth (0 to 480 kHz, Fig. 4).

The blade shape and the position of the strain gauge were determined by means of numerical simulations performed with a finite element code (Abaqus®, Fig. 5). A compromise between sensitivity and stiffness had to be found to maximize the sensor bandwidth as well as to limit the blade edge displacement and the influence of its dynamic behavior. Eventually, a static calibration was performed to find sensitivities of the measurements by the strain gauge (0.31 mV/N) and the piezoelectric force sensor (7.3 mV/N).

Interaction Velocity Measurement

The projectile velocity during the interaction process is controlled by adjusting the gas pressure. It was precisely calculated in two different ways thanks to the signals recorded during cutting tests (Fig. 6). First, three laser diodes, placed at the launch tube exit and spaced with a known distance, allowed to measure interaction velocity at few instants before and during the interaction and to calculate mean interaction velocity V i . The measuring accuracy of this method slightly increased with the interaction speed. Indeed, the voltage drops observed on diodes signals, when the projectile cut the laser beams off, had a logically shorter duration T td and the relative error committed during interaction velocity calculation decreased in the case of high projectile velocity (Table 1). The analysis of the laser diodes signals and the calculation of interaction velocity at various instants before and during interactions underlined that the velocity variations were insignificant regarding the absolute measuring error. So the sample velocity was assumed to be constant during the interaction process.

The second method consisted in analyzing the force sensors recordings. Assuming a constant velocity of the projectile during the process and knowing precisely its length L p , the value of the velocity V MF R was given by the ratio of length L p to duration of interaction T i . The main difficulty of this method consisted in determining precisely the duration of the interaction on the force sensors raw signals.

The piezoelectric force sensor recordings were too dynamically perturbed to be used for that task. One the other hand, the strain gauge signals allowed to calculate mean interaction velocity in three experimental cases. Nonetheless, the results concerning the mean interaction velocity given by both methods (diode laser signal analysis and strain gauge recordings analysis) for these three cases (M01, M02 and M05) were of the same order. They confirmed that the velocity was constant during interactions and validated the first velocity measurement method.

Incursion Depth Measurement

Adjust and control the incursion depth required to master the projectile position in the launch tube during the interaction. In order to do that, a semi-cylindrical rail was rigidly fixed in the launch tube to insure a precise guiding of the projectile. To verify the perfect alignment of the different guiding parts as well as the good accuracy of the tolerance of their geometry, validation tests involving launching projectiles without sample were carried out. Indeed, geometrical tolerances and surface roughness of the guiding parts had to be very accurate to ensure precise guiding of the projectile and a repeatable and quasi-constant incursion depth during interaction process. But the slight misalignments of the guiding parts can lead to shocks during the accelerating stage of the projectile. These shocks generated elastic waves transmitted through the device to the force sensors which created perturbations in force measurement. These tests permitted to adjust the device. They eventually showed that alignment was good enough for measuring only force generated during the interaction process without being perturbed by dynamic phenomena occurring when the projectile is sliding through the device (shocks, parasitical contacts due to micrometric variation of the launch tube diameter, etc). The incursion depth t 1 was set up before each experiment by adjusting the relative position of the blade from the upper face of the sample. The sample, mounted on the projectile, was machined in order to impose a known distance between the upper face of the sample and the sliding face of the projectile using this last one as a reference. The blade was positioned precisely with a standard piece placed on the guiding rail. Then the theoretical incursion depth t 1t was obtained by the difference between the sample upper surface height and the reference piece height. The real experimental incursion depth was calculated in ten points of the sample regularly spaced comparing the sample upper face height before and after interaction.

For all experiments presented in this paper, the theoretical incursion depth was set to 0.2 mm. However, as shown in Table 4, mean incursion depth t 1 varied between 0.12 mm and 0.18 mm for the samples made of polycarbonate and between 0.13 mm and 0.35 mm for the M601 samples. Note that during interaction, the incursion depth was not constant. Its variation t 1 fluctuated between 0.032 mm and 0.048 mm for the samples made of polycarbonate and between 0.022 mm and 0.069 mm for the samples made of M601. Both these variations could be explained by error committed during the sample preparation, the positioning of the blade, the experimental incursion depth measurement and the dynamic behaviors of the blade, of the sample and of the projectile. Nevertheless, it is interesting to note that these variations were lower for the polycarbonate than for the M601. It leads to think that the material behavior of the sample, particularly the mechanical properties could have an influence on the cutting process, the blade tip displacement and the sample roughness after the experiment. This could partially explain the variations of incursion depth around the theoretical value and during interaction.

Interaction Force Correction

Sensors Dynamic Behavior

Traditionally, sensors dedicated to dynamic measurement are built as rigid as possible to obtain the highest first mode frequency and the largest bandwidth [START_REF] Totis | Development of a dynamometer for measuring individual cutting edge forces in face milling[END_REF]. Indeed, maximal frequencies excited by mechanical phenomena have to be inferior to the upper limit of the sensor bandwidth to ensure a precise force measurement. The high frequency noise and the vibratory behavior of the sensor are filtered off by applying a low pass filter with a cut-off frequency corresponding to the upper limit of the bandwidth. In this case, a static calibration is sufficient and well-adapted. In this work, the dynamic response of the sensors was investigated by means of pulse tests to determine their bandwidth. The tip of the blade was excited by using an impact ram and the excitation force was measured by a piezoelectric force sensor (PCB Piezotronic 208C02), see Fig. 7. The input (excitation force imposed by the ram) and the outputs (forces measured by piezoelectric force sensor PCB Piezotronic 260A01 and by the strain gauge) were recorded simultaneously. Then, modal analysis was performed to calculate frequency response functions (FRFs, equations ( 2) and ( 3)) and the bandwidth was defined when the amplitude of the FRFs exceeded ±3 dB, see Fig. 8.

These experiments showed that the device bandwidth was inferior to 2 kHz, therefore it was not sufficient to accurately measure interaction forces such as those generated during high speed cutting. Indeed, the maximum frequency contained in the studied phenomenon was estimated to be inferior to 10 kHz according to the interaction velocity and duration. Nevertheless, the necessary bandwidth is not obtainable in practice. In fact, if sensors can reach this bandwidth when they are tested alone, it is very difficult Fig. 7 Experimental set-up for pulse tests to design a complete set-up which does not have natural frequencies under 10 kHz. Consequently, as the dynamic behavior of the mechanical system could not be optimized enough, the traditional way of performing dynamic measurement (restricted to the static approach) was not adapted to this application and another approach had to be found. So, a correction method, detailed in the next section, was implemented to clean up the sensors signals.

Signal Correction

To virtually enlarge the bandwidth of the measuring system and to eliminate the dynamic and vibratory behavior of the device, the signals were mathematically treated with the method presented by Castro et al. [START_REF] Martinez | Identification des sources de vibration en usinage. Etude experimentale et numerique[END_REF] based on the principle of the Frequency Response Function (FRF) [START_REF] Ewins | Modal testing: theory, practice and application[END_REF][START_REF] Harris | Shocs and vibration handbook[END_REF]. The system response is described by forces or more precisely by output voltages proportional to forces rather than displacements or accelerations. The whole device considered as a linear system is described by equation [START_REF] Demasi-Marcin | Protective coatings in the gas turbine engine[END_REF].

{O(j ω)} = [T (jω)]{I (jω)}

(1)

Fig. 8 Dynamic response of the experimental set-up

Transmissibility matrix [T] was determined experimentally. During a calibration step, the device was excited with a white noise and both the excitation force, {i(t)}, and response signals provided by the sensors, {o(t)}, were recorded. Using the modal analysis approach, transmissibility matrix [T] was calculated as the FRF H 1 (equation ( 2)), which is the ratio between input-response cross-spectrum (G I O ) and input auto-spectrum (G I I ). Accuracy of the signal correction depended directly on the quality of FRF components which were evaluated thanks to the coherence function γ 2 calculated for each component (equation ( 4)). A good quality of the FRF corresponds to a coherence function equal to 1 for the whole frequency range.

H 1 (j ω) mn = G I O (j ω) G I I (j ω) = < O(jω) m • Ī (jω) n > < I (jω) n • Ī (jω) n > (2) H 2 (j ω) mn = G OO (j ω) G OI (j ω) = < O(jω) m • Ō(j ω) m > < I (jω) n • Ō(j ω) m > (3) γ 2 (j ω) mn = H 1 (j ω) mn H 2 (j ω) mn (4)
During the interaction tests, {O(j ω)} was known and {I (jω)} had to be determined reversing (equation ( 1)).

As the transmissibility matrix was a complex rectangular matrix, it could not be reversed directly. Consequently, the hermitian transpose, defined by equation ( 5), was necessary to obtain relation (equation ( 7)).

[T (jω)] H = [ T (jω)] T (5) [H (jω)] = [T (jω)] H • [T (jω)]

-1

• [T (jω)] H (6)

{I (jω)} = [H (jω)] • {O(j ω)} (7)
In order to improve their quality, FRF components were calculated by parts. In fact, the experimental set-up was excited with a white noise filtered by a located frequency band (LFB) and the transmissibility matrix sub-components were calculated for the frequency band excited. Then, the FRF matrix components were constructed from the combination of sub-components obtained by all tests. The coherence functions were constructed in the same way. LFB width was a major parameter for the correction method accuracy. Indeed, coherence quality increases and noise quantity decreases when LFB width reduces [START_REF] Martinez | Identification des sources de vibration en usinage. Etude experimentale et numerique[END_REF]. However, decreasing LFB width requires the realization of additional measurements. Thus, it was necessary to find a good compromise between the FRF quality and the number of tests. There were a lot of other parameters which had to be carefully fixed because of their influence on the correction functions and their quality. For example, the correction matrix [H] depends on the dynamic behavior of the whole structure supporting the sensor. So it was important to ensure good repeatability of positioning and tightening of the different parts of the device. The correction procedure is summed up in Fig. 9.

Dynamical Calibration

In order to correct the signals recorded during the cutting experiments, it was essential to characterize the dynamic behavior of the device and to calculate the transmissibility matrix. Thus, a series of tests was carried out using a known excitation force. The presented configuration of the experimental set-up allowed to measure only the axial force component with two different kinds of sensors. So equation ( 1) can be written in two unidirectional systems (equation ( 8)) which makes the comparison between the two measurement technologies possible (equations ( 9) and ( 10)).

O g (j ω) O p (j ω) = T g (j ω) T p (j ω)

• I a (j ω) [START_REF] Johnston | Freestanding abradable coating manufacture and tensile test development[END_REF] Where: I a (j ω): Fourier transformed input signal of axial force imposed on the blade tip O g (j ω) and O p (j ω): Fourier transformed output signals delivered by the strain gauge and by the piezoelectric sensor respectively T g (j ω) and T p (j ω): and o p (t)) by the strain gauge and by the piezoelectric force sensor 260A01 respectively. These three signals were recorded with the same acquisition system and with the same parameters as the ones used during the cutting experiments. Modal analysis and calculus of frequency response functions were performed with a special software developed with Mathematica. FRFs between the reference force sensor and the two sensitive parts of the experimental set-up (strain gauge and piezoelectric force sensor) were obtained between 0 to 8 kHz with a LBF width of 400 Hz.

The coherence function associated with the correction function of the strain gauge signal (not presented here) showed that the FRF quality was not good enough to ensure an accurate correction of the signal recorded by the strain gauge. In a lesser scale and for low frequencies, the FRF of the strain gauge obtained thanks to the pulse tests (Fig. 8) showed the same lack of quality. The sensitivity of the strain gauge was too weak and due to the shaker energy limitation, the excitation force was much smaller than the force that the device was designed to measure. So the amplitude of the response signal during the calibration stage was too low to emerge from electronic noise and the ratio of the system response to the input was incoherent.

As for the piezoelectric force sensor, the results of the calibration provided evidence of good performance (Fig. 11). The FRF between the reference force sensor and piezoelectric force sensor composing the experimental set-up clearly presented resonance and antiresonance peaks and a low frequency dynamic behavior which were in good accordance with the results of the pulse test. However, as the coherence function showed, the FRF accuracy was not perfect for the whole frequency range. More precisely, coherence drops appeared close to the antiresonance peaks. As for the strain gauge FRF, because of the antiresonance, the amplitude of the response signal was too low to not be significantly disturbed by the electronic noise despite the good sensitivity of the force sensor explaining the low quality of the FRF. One way to avoid such coherence drops in future application could be to reduce peak amplitude at antiresonance by increasing the structure dampening by modifying the technical solution of fixing the blade on the sensor.

Results & Discussion

Measurement and Correction of the Interaction Force

The raw signals recorded all along the interaction process by the piezoelectric force sensor (Fig. 6) were highly perturbed by the dynamic behavior of the set-up even for the lowest interaction velocities. Oscillations visible on the raw force recording were not damped quickly enough to determine precisely the end of interaction or a mean value of the interaction force. As explained previously, conventional static post-treatment was not sufficient to ensure an accurate measurement of the interaction force. Therefore the correction method was applied to obtain the results presented in Fig. 12.

The corrected force signal showed a significant improvement allowing to observe the interaction duration, and to determine mean value of interaction force F m . But, corrected signals were disrupted by undamped oscillations before, during and after the process. The correction method uses Discrete Fourier Transform which allows to approximate a discontinuous non-periodic function with a sum of continuous periodic functions. It can generate a mathematical phenomenon of discontinuity amplification which creates damped oscillations in the vicinity of the discontinuity. So, oscillations were expected at the beginning and at the end of interaction. However oscillations observed on the post-treated force signal had great amplitude and persisted long after the interaction without being damped. So they could not have been due to this phenomenon. In addition, the frequency of these oscillations calculated by spectral analysis corresponded exactly to the coherence drop frequency observed on the FRF used for the dynamic correction. The authors concluded that they were mathematical artifacts due to the localized low quality of the correction function. The only solution to eliminate this artifact will be to improve the quality of the FRF by modifying the experimental set-up in order to reduce the peak amplitude at the antiresonance frequency. However, despite these artifacts, it is possible to calculate a significant mean value of interaction force. An offset was clearly observable after the interaction process on the piezoelectric force sensor raw signal and on the corrected signal, see Fig. 12(b). It increased with the interaction velocity and therefore was linked to the launching pressure which applied a force on the blade tip after the projectile passage. Its value was highly inferior to the interaction force. So, it did not pertubate the measurement or the interpretation of the corrected signal.

The strain gauge raw signal was less dynamically perturbed than the piezoelectric force sensor at least for the experiments performed with low interaction velocity (inferior to 100 m/s). For these experiments, the interaction duration was clearly visible and the force varied around a mean value. This mean value was coherent with the one obtained by correcting the piezoelectric force sensor signal. The elastic deformation rate measured by the strain gauge was too low to ensure good measurement precision. Indeed, electronic noise present on the recorded signals represented almost 30 % of the signal amplitude. Furthermore, the gauge signal was not dynamically corrected because of the very low quality of the correction function. So low deformation rate is a major problem which can be solved in two ways. A first solution could consist of modifying the blade geometry in order to increase its deformation, but it is not recommended. It would reduce the blade stiffness and increase the displacement of the blade tip as well as the variation of the incursion depth. A second way to achieve a greater sensitivity could be to replace the traditional strain gauge by a semiconductor strain gauge. However, the piezoelectric force sensor seemed more appropriate for future applications.

Finally, three cutting experiments were performed with polycarbonate samples in the same experimental conditions in order to study the repeatability of the process and the measurement system. The raw signals of the piezoelectric force sensor for the experiments PC01 and PC02 (Fig. 13) could almost have been superimposed demonstrating the good repeatability of the set-up. The slight differences were amplified by the dynamic correction explaining the two mean interaction force values. The first purpose of this project was to experimentally study blade-casing contacts phenomena and to extend the knowledge of the material behavior of a given abradable material under extreme conditions. A simplified approach where only orthogonal cutting conditions are investigated was carried on thanks to the experimental technique presented in the previous sections. New experimental data on the material behavior of M601 in high speed orthogonal cutting conditions have been obtained and those obtained for low interaction velocities have been compared to the data available in the literature.

The chosen abradable material was the M601, an abradable material developed by Sulzer Metco whose the chemical composition is presented in Table 2. As shown in Table 3, a set of cutting experiments on abradable material M601 were performed for a range of interaction velocities varying from 60 m/s to 270 m/s and of incursion depths from 0.13 mm to 0.35 mm. The blade was made of steel 42CrMo4 (Table 4). Its edge was regularly sharpened to maintain its radius at 25 µm. The tested materials couple (M601/42CrMo4) is not the same as the one found in the engines compressors (M601/TA6V). For this first approach, the hypothesis was made that, as the dynamical behavior of the blade is not considered, the material of the blade has a insignificant influence on the interaction force in regard of the mechanical and geometrical conditions of the interaction. Figure 14 presents the evolution of the mean interaction force per unit of width F m /W s generated during interaction process as a function of the interaction velocity V i and the incursion depth t 1 . Mean interaction force per unit of width values for the low interaction velocity experiments (inferior to 100 m/s) with a blade edge radius of 25 µm were in good agreement with data available in the literature, especially with those proposed by Sutter et al. [START_REF] Sutter | Dynamic analysis of the interaction between an abradable material and a titanium alloy[END_REF].

Figure 14 shows also that the interaction force increased with the interaction speed and the incursion depth. More precisely, the relation between the interaction force F m and the interaction velocity V i did not seem linear as the data available in the litterature [START_REF] Sutter | Dynamic analysis of the interaction between an abradable material and a titanium alloy[END_REF] suggest. Indeed, the relation between the interaction force F m , the interaction velocity V i and the incursion depth t 1 can be described by the empirical law (equation ( 11)).

F m (t 1 , V i ) = (a.t 1 + b)e c.V i (11)
These results clearly showed a viscous behavior of the abradable material Metco M601 and was consistent with a visco-plastic behavior such as the one describes by a model of Norton. Furthermore, it is interesting to note that this nonlinear behavior is very similar to the one described by Yi et al. [START_REF] Yi | Erosion wear behaviour and model of abradable seal coating[END_REF]. The authors, who performed erosion tests, show that for law impact angle, erosion can be assimilate to microcutting and that the erosion rate depends on the impact velocity following a power law for low impact angle. Finally, the powder of M601 found in the receiving tank as well as the observation of the post-experiment surfaces of the M601 samples gave evidence of two wear mechanisms described by Borel [START_REF] Borel | The wear mechanisms occuring in abradable seals of gas turbines[END_REF]: cutting with brittle rupture of the abradable material and plastic deformation. Indeed the created surfaces (Fig. 15) were striated and showed traces of smearing. These two elements are representative of the plastic deformation mechanism.

Conclusion

An experimental technique has been designed to study blade-casing contact phenomena. These interactions have been assimilated to high speed orthogonal cutting and the interaction force has been measured.

A correction method based on modal analysis principles has been developed in order to reduce the influence of the sensor dynamic behavior on the measured interaction force. This correction method allowed to precisely measure the mean force generated during interactions lasting less than 400 μs. However, this correction method remains to be optimized to permit to study the evolution of the force during the interaction. It will require to suppress the artifacts appearing during the correction and to improve the correction function quality. In order to do that, a modification of the experimental set-up-and consequently its dynamical behavior-is unavoidable. The device structural damping has to be increased by adding a damper to reduce the peak amplitude at the antiresonance frequency.

The experiments performed to characterize the abradable material Metco M601 showed a viscous behavior of the M601 and revealed a non-linear relation existing between the mean interaction force and the interaction velocity. This relation as well as the interaction force values measured for the experiments performed with low interaction velocities were in good agreement with the data available in the literature.

Finally, to extend the understanding of the blade-casing contact phenomena, it will be important to investigate the material behavior under experimental conditions more close to the real functioning conditions. This means simulating oblique cutting process for the highest interaction velocities (500 m/s) and the operating temperature (300 • C).

Fig. 1

 1 Fig. 1 Experimental set-up. (a) Ballistic bench. (b) Measurement system

Fig. 2

 2 Fig. 2 Projectile and the sample covered with abradable material M601

Fig. 3

 3 Fig. 3 Schematic description of the interaction process

Fig. 4

 4 Fig. 4 Data acquisition system of the experimental set-up

Fig. 5

 5 Fig. 5 Strain gauge location on the blade

Fig. 6

 6 Fig. 6 Typical raw signals obtained during orthogonal cutting experiment. Sample M02-Interaction speed: 90 m/s-Mean incursion depth: 0.26 mm

Fig. 9

 9 Fig. 9 Diagram of the correction method

Frequency

  Fig. 10 Experimental set-up for the dynamic calibration

Fig. 11

 11 Fig. 11 Piezoelectric force sensor FRF and coherence

Fig. 12

 12 Fig. 12 Typical force signals obtained after post-treatment. (a) Sample M02-Interaction speed: 90 m/s-Incursion depth: 0.26 mm. (b) Sample M09-Interaction speed: 269 m/s-Incursion depth: 0.25 mm

Fig. 13

 13 Fig. 13 Comparison of raw and corrected signals for two experiments performed with the same conditions. Samples PC01 and PC02: Interaction speed: 96 m/s-Incursion depth: 0.13 mm

Fig. 14 Fig. 15

 1415 Fig.[START_REF] Yi | Friction and wear behaviour and abradability of abradable seal coating[END_REF] Interaction force as a function of the interaction velocity and the incursion depth for abradable material M601 in orthogonal cutting conditions for a blade edge radius close to 0.001 mm

Table 1

 1

	Interaction velocity
	comparison	Sample	Force recording	Laser diode measuring method
			V MF R	V i	V min	V max	T td	Absolute error	Relative error
			[m/s]	[m/s]	[m/s]	[m/s]	[µs]	[m/s]	[%]
		M01	61	61.3	61.1	61.5	20	1.50	2.45
		M02	88	89.5	88.3	89.4	14	2.25	2.52
		M03	\	90.5	90.3	90.6	13	2.12	2.35
		M04	\	117.5	116.8	117.1	10	2.75	2.34
		M05	154	152.6	151.1	152.4	7	3.26	2.14
		M06	\	190.8	190.1	190.8	5	3.64	1.91
		M07	\	227.5	225.2	226.8	4	4.10	1.80
		M08	\	228.0	227.3	228.3	4	4.16	1.83
		M09	\	269.4	268.8	270.3	3	4.35	1.61

Table 2

 2

		Chemical composition of abradable material M601
	(Aluminum-silicon alloy and polyester) [15]
		Elements [%]
		Al	Si	Fe	C	Impurities	Polyester
	M i n	5 1	6 . 5	/	/	/	T h er e s t
	Max	55	8.5	0.5	0.2	0.35	The rest

Table 4

 4 Chemical composition of steel 42CrMo4

		Elements [%]
		C	C r	M o	M n	S i	S	P
	Min	0.38	0.9	0.15	0.6	/	/	/
	Max	0.45	1.2	0.25	0.9	0.4	0.035	0.025
	Abradable Material M601/ Steel 42CrMo4 Interaction

Table 3

 3

	Testing conditions
	and experimental results		Interaction velocity	Incursion depth	Interaction force
	Tests	Sample	V i	t 1	t 1	F m
	N •	Materials	[m/s]	[mm]	[mm]	[N]
	PC01	Polycarbonate	96	0.13	0.042	378
	PC02	Polycarbonate	96	0.12	0.032	407
	PC03	Polycarbonate	97	0.18	0.048	422
	PC04	Polycarbonate	123	\	\	524
	PC05	Polycarbonate	184	0.18	0.043	873
	M01	M601	61	0.30	\	230
	M02	M601	90	0.26	0.040	287
	M03	M601	90	0.35	0.053	362
	M04	M601	118	0.13	0.032	411
	M05	M601	153	\	\	436
	M06	M601	191	0.26	0.049	740
	M07	M601	226	0.28	0.060	1060
	M08	M601	228	0.15	0.022	778
	M09	M601	269	0.25	0.069	1306

Acknowledgments This work takes place in the framework of the MAIA mechanical research and technology program sponsored by SNECMA of SAFRAN Group. The authors are grateful for the financial support to develop this project. They would also like to acknowledge David Stinger, engineer at the National Engineering School of Metz (E.N.I.M.), for his contribution to the device design.