A method to estimate the average temperature on the cutting edge of tools. Application on the milling process.

Transcription

1 A method to estimate the average temperature on the cutting edge of tools. Application on the milling process. aj Elmoussami and Jean-Luc Battaglia Laboratoire Energétique et Phénomènes de ransfert, Ecole Nationale Supérieure d Arts et Métiers, UMR 8508, Esplanade des Arts et Métiers, alence cedex, France. el : (+33) Fax : (+33) jlb@lept-ensam.u-bordeaux.fr - 1 -

2 Abstract In this work we present an experimental technique for the estimation of the average temperature on the cutting edge of each insert in a milling tool. he experimental device used thermistors, one by insert, and a rotational collector in order to ensure the transmission of the signals between the rotating tool and the acquisition device. Each thermistor is located at a point in the tool close to the tip of each insert. he average temperature on the cutting edge of each insert is estimated from the temperature at the nearest sensor and a model expressing these two temperatures. his model is achieved from the non-integer system identification method. eywords: machining, milling, temperature, thermistor, inverse method, system identification, non integer derivation

3 Introduction As it is represented on figure 1, the machining process by milling consists in removing the material from a fixed workpiece with a tool being in rotation around its axis of revolution. On the other hand, this tool moves by translation on the plane perpendicular to its axis. his process of machining is characterised by the following parameters: cutting speed V, feed rate V, radial depth a and cutting c f r depth a p. hese parameters are constant values in conventional milling. owever, they can vary during machining using a computer numerical controlled (CNC) machine. he mechanical power provided during machining is supposed to be completely converted into heat. Figure 2 presents the different regions of heat generation in the cutting domain. eat generation appears in Zone 1, called the dead zone, where the separation of the material takes place. Zone 2, called the primary shearing zone, comes from the change of direction of the material out-flow. It is the place of intense deformation and intense deformation rates that lead to strongly increase the temperature in this zone. Zone 3 is called the secondary shearing zone where the chip slides on the rake face of the tool. his zone is submitted to intense deformation rates and intense rubbing that also lead to greatly increase the temperature close to the cutting edge. Zone 4 denotes the domain where the machined surface slides on the clearance face of the tool. hese four heat sources generate heat fluxes in the workpiece, the chip and the tool, respectively w, c and t. he heat flux in the tool is weak in comparison with the fluxes in the chip and the workpiece. hat comes from the small contact surface between the chip and the tool and from the stationary of the contact surface in the tool referential. One observes high temperature on the cutting edge of the tool and high temperature gradient in the tool. Given that this temperature varies from point A to point C, we define the average temperature denoted t on the cutting edge. igh temperature on the cutting edge introduces undesirable effects a on the tool life and on the machined surface quality. Many studies in the literature concern the average temperature estimation on the cutting edge during a turning process. emperature measurements are achieved from thermocouples or thermal cameras in infrared or visible spectral domain. All of these techniques can be classified into two sets of methods

4 he first set consists embedding the sensor as close as possible to the cutting edge of the tool in order to directly measure the temperature in the cutting domain. erbert [1], Shore [2] and Stephenson [3] use the natural thermocouple formed by the workpiece and the tool when the two materials are electric conductors. As shown for example by Laraqi [12] a thermal resistance occurs at the sliding interface of two materials. hereby, the previous technique does not lead to the average temperature on the tool but on the average temperature at the tool-chip interface. Ay and Yang [4], Barlier and al. [5] and itagawa and al. [6] embed the thermocouples in the neighbourhood of the cutting edge by previous insert preparation. Given to the very high temperature gradient in the tool, this technique can not be used to estimate the temperature on the cutting edge even if the sensor is embedded very close to it. Jaspers and al. [7] and won and al. [8] use I.R. thermography in an orthogonal cutting process configuration. his measure is inaccurate given to the spatial variation of the emissivity coefficient on the cutting domain. Nevertheless, it gives very interesting qualitative information concerning heat transfer in this domain. he approach, presented by Stephenson [9], uses I.R. thermography and thermocouples together in order to calibrate the emissivity according to the temperature from the thermocouples. he second set of methods concerns the indirect methods based on the resolution of an inverse heat conduction problem. his approach consists in estimating the average temperature on the cutting edge from the temperature measured in one or several points in a neighbourhood domain from the techniques presented previously. Furthermore, it used the model of the transient thermal behaviour of the tool that expresses the temperature at the sensors according to the average temperature on the cutting edge. Stephenson [10] and Stephenson and Ali [11] measure the temperature in the workpiece by I.R. thermography and use the analytical solution of heat transfer in the workpiece to estimate the temperature in the shearing zone. As said previously, this temperature is not representative of the temperature on the cutting edge given to the thermal resistance at the tool-chip interface. he technique used by Groover and ane [13] consists in embedding two thermocouples under the insert. A model expressing the average temperature on the cutting edge and the temperature at these two thermocouples is achieved by a nodal method based on the thermoelectric analogy. An insulating element is placed between the insert and the tool holder. hen, one considers that the insert is - 4 -

5 thermally insulated from the tool holder that led to mark off the domain of modelling. A comparable methodology is proposed by Yen and Wright [14]. In their application, the temperature at the thermocouple is expressed according to the average temperature on the cutting edge from an exponential law. Parameters in this relation are identified from temperature measurements on a specific apparatus that permit simulating variations of the temperature on the cutting edge. here are few works in the literature concerning assessment of the cutting edge temperature in milling, and more generally in all processes with a tool being in rotation. im and al. [15] arrange a thermocouple in the workpiece and record the temperature when the flank face of the tool passes above the thermocouple. his measurement is very inaccurate with regard to the uncertainties on the sensor location in the insert. Lin [16] uses an indirect method leading to the temperature of the workpiece in the shearing zone. Its method is based on the temperature measurement at a point of the machined surface behind the tool using an I.R. pyrometer and a model of heat transfer in the workpiece. As noted previously, the influence of a thermal resistance at the tool-chip does not permit to accurately estimate the average temperature on the cutting edge. Our Approach Our approach is based on a non destructive indirect method. As shows on the figure 3, the temperature measurement is achieved by thermistors, one by insert, embedded far from some millimetres to the cutting edge. he recorded signal is transmitted toward the acquisition device by a rotating collector. he sensitivity of a thermistor is about 1000 times higher than a thermocouple and allows using a classical bearing. his experimental apparatus has been used notably by Broussely [17] in order to measure the temperature at different points of an asynchronous electric motor. he transient thermal behaviour model of the tool is obtained by the system identification approach. Measurements realise during the machining process show that the temperature at the sensor associated with its heated insert is only sensitive to the variation of the temperature on the cutting edge of this insert. herefore, each {insert-sensor} system can be considered as monovariable. Obviously that led to significantly simplify the system identification procedure given that the system is axially symmetric. hereby, this procedure consists in estimating the parameters of a linear model expressing the average - 5 -

6 temperature on the cutting edge t of one of the inserts and the temperature of the associated a c sensor t from measurements of these two quantities. his model is the same for all the {insertsensor} set. As it was demonstrated by Battaglia [20-21], the model is expressed from the successive derivatives of ½ multiple orders of these two quantities in the form: M 1 i0 D i ni / 2 c t M i0 D i ni / 2 a t (1) he value of M essentially depends on the distance between the cutting edge and the sensor. A great amount of system identification techniques are presented in the books of Ljung [18] and Soderström [19]. his approach presents many advantages. First, the model does not require knowledge of the thermal properties as thermal conductivity, thermal diffusivity, convection and radiation coefficients and thermal resistance, of the different parts of the system. It does not consider also as a constraint the complexity of the system morphology, given that different parts overlap others and the contact points are difficult to identify. It takes the same form (1) even if heat transfer in the system is one, two or three-dimensional. Finally, it takes into account the influence of the sensor on the dynamical behaviour of the tool, given that the dimensions of one sensor are comparable to the distance from the cutting edge. On the other hand, this approach is well suitable to the resolution of the inverse problem in order to evaluate a t. In fact, the same sensor is used in the system identification procedure and in the inversion procedure. hereby, uncertainties concerning the location of the sensors in the system vanish. If known boundary conditions, as the ambient temperature for example, remain constant between the system identification stage and the inversion stage, they do not appear in the model. Finally, in practice, the model is expressed from a weak number (2M+1) of parameters. his allows estimating a t in the real time process using a sequential method. Obviously, the system identification approach presents some difficulties, particularly from the experimental point of view. During the system identification stage, the average temperature on the cutting edge must be controllable and measurable. his constraint requires reproducing the real boundary conditions on the cutting edge. On the other hand, the device used to simulate the thermal - 6 -

7 boundary condition on the cutting edge must not modify the real thermal behaviour of the tool. In other words, it must not introduce some dynamical effects that lead to modify the estimated average temperature from the resolution of the inverse problem during machining. Finally, the confidence domain of the estimated average temperature depends on the confidence domains of the identified parameters in relation (1). Given that there is no modelling error, the confidence domain of the estimated average temperature only depends on the measurement errors at the sensor during the system identification stage and the inversion stage. he scheme represented on figure 4 summarises our approach. It clearly appears that it is based on the resolution of two inverse problems. he first concerns the identification of the parameters of the non integer model of the tool from the characterisation apparatus. Consequently, the impulse response can be then computed and used to solve the second problem, that is, the estimation of the average temperature on the cutting edge from temperature measurement at the sensors during the process. he plan of the article is as follows. First of all we present the mathematical method for resolution the inverse heat conduction problem for a monovariable system. hen, we present the experimental device used during machining. Subsequently, the method of the tool characterisation and the laboratory apparatus for the system identification stage is presented. Finally, results of applications are presented and commented. Sequential procedure for the resolution of the inverse problem he procedure of resolution of the inverse problem is sequential and permits the evaluation of system input, i.e., the average temperature on the cutting edge, in real time. he method, called the sequential function specification method, has been developed by Beck and Arnold [22]. It supposes, that at time t the average temperature t is constant from a t k t to t k rt. Integer number r denotes the number of future time steps and t is the sampling period. Estimation of the average temperature a, k, at time k t is carried out from temperature measurement by the sensor from c time k t to time k rt as described by the following relation: - 7 -

8 a, k r j1 c, k j1 r j1 ~ j i1 k j1 h i 2 j i1 h i (2) Where: ~ k 1 k j 1 hk j l a, l (3) a,0 l 1 In these relations, hi is the impulse response at time i t and is the initial value of the average a,0 temperature on the cutting edge. his sequential technique permits the estimation of the average temperature on the cutting edge in real time process machining. he shift from the real process only depends on the number of future time steps r which is equal 2 or 3 in practice. he value of the sampling period t is evaluated from the distance d between the sensor and the cutting edge and the thermal diffusivity of the tool that can be known approximately. herefore one has the following relation: 2 d t (4) hat means that the sampling period is equal to the diffusion time between the cutting edge and the sensor. he sampling period can be chosen smaller but in that case one must increase the number of future time steps in order to satisfy the relation: d r 1t (5) 2 Experimental device emperature measurement in rotating tools imposes the use of specific apparatus assuring the link between every sensor and the acquisition device. his apparatus must not disturb the measure by introducing heavy noise and thermal drift due to its warming-up. Concerning temperature measurement from thermocouple, Stephenson [3] and Bourouga and al. [23] use rings with mercury whose implementation requires a great amount of cautions. On the other hand, the measure in the real machining configuration is strongly perturbed given to the weak sensitivity of the thermocouple that is - 8 -

9 about some µv by C. he approach that has been developed by Broussely [17], is based on micro thermistors of micro series type. hese sensors can be used from 50 C to 150 C and are composed of a polyamide tube of 0.47 mm diameter and 4 mm length, filled with an Epoxy component. hese small dimensions confer a very weak inertia and therefore fast answer time of about 250 milliseconds. he resistance of the sensor vary with the temperature according to the non linear law of Steinhart-art that we express under its simplified form: R R 2 1 exp (6) 1 2 c c c In this relation, and are the temperatures corresponding to the resistances R and R2 respectively and is a constant to determine. he expression of the temperature according to its R resistance is obtained under the form: 2 c 1 c of the sensor c 1 ln 1 R R (7) he characteristic curve of the thermistor is plotted on figure 5. he measurement of the resistance consists in sending a current and to measure the corresponding voltage. he current generator for each thermistor is built around the LM334 component. he current is limited to 10 V in order to avoid the auto warming-up of the thermistor that modifies the temperature measurement in the tool. he sensitivity of this thermistor is of order of some millivolts, therefore about thousand times higher than a thermocouple. hereby, a collector with classic brooms can be used for the transmission of the signal issued from each thermistor toward the acquisition device. his high speed rotating collector is EC3848 type. It can be used for rotational speeds up to rpm. he complete experimental apparatus is represented on figure 6. he Labview software drives the acquisition device, which is a PCMCIA National Instruments, 16 bits, 6061E type. As it is described on figure 3, each thermistor is embedded in the tool holder close to the cutting edge of the associated insert. It led to improve the sensitivity of the temperature at the measurement location according to the variations of the average temperature on the cutting edge. Obviously, only the duration of variations greater to the sampling period t will be observed. On the other hand the - 9 -

10 location of the sensor in the tool holder permits to replace the insert. oles for the micro thermistors are made by an electro discharge machining with 0.6 mm diameter. he sensors are fixed with adhesive epoxy mono component contained silver type Loctite It is characterised by its excellent thermal conductivity. Identification of the system he length of a thermistor is comparable to the distance between the cutting edge and the sensor location. herefore it is clear that one must take into account the presence of the sensor in the heat transfer modelling of the tool. As we said in the introduction, the system identification approach appears to be the most adapted solution to establish a model that express the average temperature on the cutting edge according to the temperature at the sensor. his model takes the form of the relation (1). We denote t the temperature measured by a sensor at instant t and by e t the measurement error defined by: Y c Y c t t e t (8) c By replacing t by t from the relation ( 8), the relation (1) becomes: c Y c M i / 2 i / 2 Y t D t D Y t t c i0 i M 1 i1 i c (9) Residue t is expressed as a function of non integer derivatives of the measurement error with as: t M 1 i0 D i i / 2 e t (10) Relation (9) can be expressed on the form of the following linear regression: Y c t t θ t (11) where : t 1/ 2 nm / 2 n0 / 2 nm / 2 D Y t. D Y t D t.. D t 1 (12) c c a a and : θ 1. M 1 0 M. (13)

11 If one consider successive measurements and a constant sampling period, relation ( 1 t 11) becomes: (14) c E θ Y, With : et t t t t t.. t t t t t.. E (15) Estimation of the vector is given in the least linear square sense by: θ (16) c, 1 ˆ Y θ he confidence domain of the identified parameters arises from the covariance matrix defined by: ˆ ˆ ˆ cov E E E E E E E θ θ θ θ θ (17) Assuming that E E E 2, one finally obtains the confidence domain of the identified parameters from: (18) 2 1 ˆ cov θ As a classical result, the best estimator of is: 2 M n n J E 2, ˆ 2 θ (19) Nevertheless, one can easily demonstrate that the linear least square estimator is biased. It implies that the standard deviation of every parameter can not be defined rigorously by: i i i, ˆ cov θ, with i i i, (20) his value can only be viewed as an indicator of the identified parameter influence on the temperature. he instrumental variables method minimises this bias by whitening' the residues. In that case the

12 identification method is still linear but sequential. Battaglia and al. [21] give a complete description of this method for the non integer models. It clearly appears that the regression vector, relation (11), is expressed from the non integer derivatives of the measurements at each time of the acquisition. Given to the fact that derivation amplifies the measurement errors, this vector can not be computed directly with the measured data. One has to filter the data with a low-pass filter. he cut frequency must be equal to the Nyquist frequency 1 2 f t. Experimental device for characterisation of the milling tool he identification of the milling tool from relation (1) is achieved from a complementary specific apparatus which permits to control and measure the average temperature applied on the cutting edge. he cutting edge is heated by a micro resistance (5.7) formed by a platinum circuit embedded on an alumina plate of 250 µm thick. he contact between the insert and the micro-resistor is realised using a silver charge stick type Loctite As it is represented on figure 7, the small dimensions of the micro-resistor and the stick are designed to heat the insert on a surface corresponding to the cutting domain. On the other hand, the thermal inertia of the heating apparatus does not exceed 0.1 second. A thermocouple type (Chromel-Alumel), 40µV C -1 sensitivity, is embedded in the stick at the interface between the insert and the micro-resistor. It permits to measure the average temperature on the cutting edge. he signal issued from the thermocouple is amplified and recorded by the acquisition device. Applications and results Identification of the system Duration of the experiment is equal to 80 seconds and the sampling period is equal to 0.02 second. In order to improve the identification at the short times, successive steps of electric power in the microresistor are generated. For this purpose the switch represented on figure 7 is used. Only one insert need to be heated given to the axially symmetric of the tool. Figure 8 presents the temperature evolution on the cutting edge of the heated insert and on all the sensors. As we said in the introduction, only the

13 thermistor embedded in the neighbourhood of the heated insert is sensitive to the average temperature variations on the cutting edge. It confirms thus, that each {insert sensor} couple behaves like a monovariable system for the duration of the machining process. We identify the parameters in relation (1) from the method presented in chapter 4. he best identified model is expressed from four unknown parameters as: D 0,022 0,049 1/ 2 t D 1 1/ D 0, c 845 a t (21) Figure 9 shows the excellent agreement between the calculated temperature from the previous identified model and measured temperature at the sensor for the variation of the average temperature on the cutting tool plotted on figure 8. In order to validate this model another experiment is realised. We compute the value of c for the new variation of a represented on figure 10. As previously, results show an excellent agreement between calculated and measured temperature at the sensor. hese results demonstrate that model ( 21) is accurate for any variation of the temperature on the cutting edge. From the model (21) we compute the impulse response h t which is used in the procedure of resolution of the inverse problem, presented in chapter 2, in order to estimate the average temperature on the cutting edge of each insert during machining. his impulse response is represented on figure 11. Evaluation of the average temperature on the cutting edge during milling process he machining experiment is realised on a classic universal milling machine. he result of the operation is a flat surface obtained by removing a 2 mm thick layer of material. A Sandvik p Coromant R Q2711M tool with 7 carbide inserts Sandvik Coromant R M-PM type are used. wo different workpieces are machined. he first workpiece is an aluminium AL2017 type, and the conditions of machining are: cutting speed V c 100 m mn 1, feed speed V f 80 mm mn 1, radial depth a 80 mm and length of cutting r L p 90 mm. he temperatures measured by all the 7 sensors are plotted on figure 12 and the estimated average temperatures on the cutting edge of each insert are plotted on figure

14 he second workpiece is steel (hardness V234) and the conditions of machining are: cutting speed V c 100 m mn 1 1, feed speed V 80 mm mn, radial depth f ar 80 mm and length of cutting L p 90 mm. he temperatures measured by all the 7 sensors are plotted on figure 14 and the estimated average temperatures on the cutting edge of each insert are plotted on figure 15. hese two experiments indicate that the inserts does not have the same behaviour during the machining process. It clearly appears that some inserts work more than others. Because of these differences, the exact cutting edge location of each insert according to the revolution axis of the milling tool has been measured during the first machining. A mechanical comparator has been fixed on the table of the milling machine and the relative location of each cutting edge with respect to the insert number 3 has been measured. Results that are reported on the following table, confirm the difference in the average cutting temperature of each insert during the first machining represented on figure13. Insert number (ref.) 7 Relative location (mm) Before the second machining the inserts have been removed and replaced, that explain the little change in the inserts n {1,5,4} behaviour with regards to the first experiment as represented on figure 15. A sensitivity analysis of the average temperature on each cutting edge according to the cutting parameters has been realised. his analysis can be used to find the better cutting parameters considering given tool and material. he machined material is aluminium type AL2117. Figure 16 shows the relationship between the cutting depth when the cutting speed, the feed speed and the radial depth are respectively: V c 100 m mn 1 V f 80 mm mn 1 and a r 1mm. On the same figure we represent the influence of the radial depth when 100 m mn 80 mm mn and 2 mm. V c 1 V f 1 a p Finally, we represent the influence of the feed when V c 100 m mn 1 a 80 mm and 2 mm. r a p

15 Conclusion We have described a method devoted to the average temperature estimation on the cutting edge of each insert in the milling tool. his approach is an indirect method, based on the resolution of the inverse heat conduction problem in the tool. he sensors are placed in the tool holder close to the cutting edge of each insert. Considering the great temperature gradient in the tool, the thermal variations observed at the sensor remain small in comparison with that on the cutting edge. he choice of thermistor as a sensor comes from the temperature operating range and its great sensitivity. It allows using a classical rotating collector in order to transmit the signals toward the acquisition device. hereby, measurements are not disturbed by this device during real machining process. he model expressing the temperature at the sensor with that on the cutting edge of the associated insert is achieved from the non integer system identification method. Derivation orders must be equal to multiple values of ½ in thermal diffusion process. Nevertheless, this approach requires a specific characterisation apparatus in order to control and measure the thermal conditions applied to the cutting edge of the insert. he main difficulty comes from the realisation of the heating system which must not modify the thermal behaviour of the tool. We used a micro-resistor whose dimensions confer inertia smaller than the sampling period chosen during the system identification process. In our configuration, the identified model only requires 4 parameters in order to describe perfectly the evolution of the temperature at the sensor according to the variation of the average temperature on the cutting edge. his small number of parameters permits to estimate the average temperature on the cutting edge of each insert in a real time procedure. Results obtained during real processes show the gap between each average temperature of each insert according to the tool geometrical configuration. On the other hand, the method is applied to achieve the sensitivity analysis of the average temperature according to the cutting parameters. his method constitutes a practical tool in order to reach various objectives as for example: tool wear monitoring during machining, detection of incorrect insert arrangement in the tool, choice of optimal cutting parameters for given tools and materials, influence of coatings

16 Bibliography [1] erbert E. G., he measurement of cutting temperatures, Proc. Inst. Mech. Engr., vol. 1, 1926, p [2] Shore., hermoelectric measurement of cutting tool temperatures, J. Washington Academy of Sciences, vol. 15, 1925, p [3] Stephenson D. A., ool-work thermocouple temperature measurements-heory and implementation issues, Journal of Engineering for Industry, Vol. 115, 1993, p [4] Ay. and Yang W. J., Dynamics of cutting tool temperatures during cutting process, Experimental eat ransfer, Vol. 7, 1994, p [5] Barlier C., Lescalier C., Millet J.-M., Mesure en continue de l usure des outils de coupe par micro-sondes incorporées. Acquisition par Capteur de empérature Appliquée à la Recherche de l USure. Le système ACARUS. Nancy, 1997, [6] itagawa., ubo A., Maekawa., empérature and wear of cutting tools in high-speed machining of Inconel 718 and i-6a1-6v-2sn, WEAR, vol. 202, 1997, p [7] Jaspers S. P., Dautzenberg J.. and aminiau D. A., emperature measurement in orthogonal metal cutting, Int. J. Adv. Manuf. echnol., vol. 14, 1998, p [8] won P., Schiemann., ountanya R., An inverse estimation scheme to measure steady-state tool-chip interface temperatures using an infrared camera, International Journal of Machine ools & Manufacture, vol. 41, 2001, p [9] Stephenson D. A., Assessment of steady-sate metal cutting temperature models based on simultaneous infrared and thermocouple data, Journal of Engineering for Industry, vol. 113, 1991, p [10] Stephenson D. A., An inverse method for investigating deformation zone temperatures in metal cutting, Journal of Engineering for Industry, vol. 113, 1991, p [11] Stephenson D. A. and A. Ali, ool temperatures in interrupted metal cutting, Journal of Engineering for Industry, vol. 115, 1993, p [12] Laraqi N., Phénomène de constriction thermique dans les contacts glissants, International Journal of eat and Mass ransfer, Vol. 39, N. 17, 1996, p [13] Groover M. P. and ane G. E., A continuing study in the determination of temperatures in metal cutting using remote thermocouples, Journal of Engineering for Industry, 1971, p [14] Wey Yen D. and Wright P.., A remote temperature sensing technique for estimating the cutting interface temperature distribution, Journal of Engineering for Industry, vol. 108, 1986, p

17 [15] im S. W., Lee C. M., im J. S., Jung Y.., Evaluation of the thermal characteristics in high-speed ball-end milling, Journal of Materials Processing echnology, vol. 113, 2001, p [16] Lin J., Inverse estimation of tool-work inteface temperature in end milling, Int. J. Mach. ools Manufact., vol. 35, N. 5, 1995, p [17] Broussely M., Réduction de modèles thermiques par la théorie des réseaux, application à la surveillance d'une machine asynchrone par couplage d'un modèle thermique réduit avec un schéma équivalent électrique, hèse de l'université de Poitiers, [18] Ljung L., System identification: theory for the user, Prentice all, [19] Söderstrom., Stoïca P., System identification, Prentice all, [20] Battaglia J.-L., Le Lay L., Batsale J.-C., Oustaloup A., Cois O., eat flux estimation through inverted non integer identification models, Journal of hermal Science, vol. 39, N. 3, 2000, p [21] Battaglia J.-L., Cois O., Puigsegur L., Oustaloup A., Solving an inverse heat conduction problem using a non-integer identified model, International Journal of eat and Mass ransfer, vol. 14, N. 44, 2000, p [22] Beck J. V. and Arnold. J., Parameter estimation in engineering and science, John Wiley & sons, [23] Bourouga B., Briot J.-M., Bardon J.-P., Influence de la vitesse et de la charge sur la conductance thermique de transport entre les bagues d'un roulement à rouleaux, International Journal of hermal Sciences, Vol. 40, N. 7, 2001, p

18 V c Milling tool a p V f a r workpiece Figure 1: schematic description of the milling process, V : cutting speed, a : depth of cut, ar : radial depth, V : feed. f c p

19 Chip c 3 A P ool t M 2 Q B E C N Workpiece 1 4 w Figure 2: representation of the different heat sources generated during the machining process. Zone 1: dead zone, zone 2: primary shearing zone, zone 3: secondary sharing zone, zone 4: clearance zone

20 Figure 3 : representation of the experimental device. he average temperature on the cutting edge of each insert is estimated from the temperature measured at each thermistor embedded in the tool

21 Figure 4: Description of the estimation method. In a first stage, one identifies the parameters of the non integer model from experimental values of a t and t c using a specific heating apparatus. In a second stage the average temperature on the cutting edge of each insert is estimated from temperature measurements at the sensors, using the previous identified model

22 Figure 5: hermistor characteristic curve

23 Figure 6: schematic representation of the experimental apparatus for the estimation of the average temperature on the cutting edge of each insert during machining

24 Figure 7: description of the experimental apparatus devoted to the characterisation of the tool

25 sensor 1 thermocouple temperature ( C) sensor 2 to time (s) Figure 8: temperature measurements obtained during the system identification stage

26 temperature ( C) measure simulation time (s) Figure 9 : comparison between the measured and experimental values of the temperature at the sensor form the identified system

27 temperature ( C) measure simulation time (s) Figure 10: validation of the identified system considering another characterisation experiment

28 10-2 impulse response ( C) time (s) Figure 11: computation of the impulse response from the identified model

29 sensor 1 sensor 2 sensor 3 sensor 4 sensor 5 sensor 6 sensor 7 temperature ( c) time(s) Figure 12: temperature measured at all the sensors during a machining process of aluminium

30 250 estimated average temperature ( c) insert 1 insert 2 insert 3 insert 4 insert 5 insert 6 insert time(s) Figure 13: estimated average temperature at the cutting edge of each insert from the identified system and the temperature measurements at the sensors

31 sensor 1 sensor 2 sensor 3 sensor 4 sensor 5 sensor 6 sensor 7 temperature ( c) time(s) Figure 14: temperature measured at all the sensors during a machining process of steel

32 estimated average temperature ( c) insert 1 insert 2 insert 3 insert 4 insert 5 insert 6 insert time(s) Figure 15: estimated average temperature at the cutting edge of each insert from the identified system and the temperature measurements at the sensors

33 250 estimated average temperature ( C) ar=80 mm ar=35 mm ap=2 mm ap=1 mm Vf=80 mm/mn Vf=125 mm/mn time (s) Figure 16: sensitivity analysis of the average temperature on the cutting edge according to the cutting parameters