electrospindle design for high speed machining

ELECTROSPINDLE DESIGN FOR HIGH SPEED MACHINING∗

Jean-François Antoine† , Gabriel Abba† , Codrut Visa‡ , Christophe Sauvey‡ † LGIPM-CEMA,

Ecole Nationale d’Ingénieurs de Metz, Île du Saulcy, 57045 Metz Cedex 1, Tél +33(0)387346947, fax +33(0)387344279, [email protected], [email protected] ‡ LGIPM-CEMA,

University Paul Verlaine-Metz, Île du Saulcy, 57000 METZ, Tél +33(0)382820637, fax +33(0)382820606, [email protected], [email protected]

Abstract : High speed machining process requires sufficient cutting speed to involve its thermomechanical phenomena and improve cutting conditions. To obtain such a cutting speed at the edge of small drill or mill tools (2 mm in diameter), an ultra-fast actuator is being designed for turning up to 200,000 rpm with switched reluctance motor principle. Keywords : high speed machining (HSM), switched reluctance motor (SRM), design

1 Introduction For more than 20 years, High Speed Machining (HSM) is offering new high productivity solutions to manufacturers with a better fabrication quality [Vigneau, 1991, DUGV, 1995, UGV, 2003]. Fabrication processes and machine tools had to be developed to reach the minimum requirements of cutting speed and feed rate required. The high rotational speed and feed rate needed create new demands in terms of actuators (linear actuators, electro-spindles). Research works on technologies (actuators, guiding systems) or materials were born from these requirements in order ∗

We thank the Conseil Régional de Lorraine for its financial support

Fifth International conference on High Speed Machining

March 14-16, 2006

to keep the best working conditions as long as possible. Even if lots of machine tools allowing High Speed Machining with great diameter tools are still proposed by manufacturers [Fos, 1993, Fayard, 1999, Fos et al., 2001], removing material by drilling or milling with tools of a tiny diameter (about 2 mm) with sufficient cutting speed (about 1.500 meters per minute) is not yet possible because ultra fast actuators with enough power have never been launched or designed. The design of such a motor is rather complex because ultra high rotational speeds involve some great mechanical, thermal and electromagnetical problems. In an electric motor, rotor and stator are usually designed to develop a given torque at specific rotational speed. At low speed, the electrical and magnetic design are decoupled of the mechanical one. Since our motor is to be used in high speed range, all physical problems become coupled by material that has to present electromagnetical, mechanical and thermal performances of good relevance. All these viewpoints have to be taken into account at the same time. Different modes of rotor vibrations become excited by unbalanced forces especially concerning the Switched Reluctance Motor (SRM) [Miller, 1993, BesBes, 1995, Camus et al., 1997], which is used here as an actuator. Catastrophic failure due to resonance may occur [Ede et al., 2002]. The high centrifugal forces substantially modify rotor and tools dimensions, and excessively solicited parts may break. The choice of material and dimensions has to take into account vibrations behavior, stresses and magnetic properties, which are essential to create motion. [Antoine et al., 2003a] The thermal problem is also of importance, since cooling has to balance the electrical losses, magnetic losses (Eddy currents and iron losses) and mechanical losses (ball bearing friction) [Abba et al., 2002, Antoine, 2004]. All these technological constraints are modelized to perform the design of a ultra high speed SRM for HSM [Sauvey et al., 2005a, Sixdenier et al., 2005]. The control of such a reluctance motor is tough since it requires power supply at high frequency [Visa, 2004]. The paper presents some of these aspects of the design of a 2kW / 200, 000 rpm machine. First, the motor principle that was chosen in this project is presented. Then, the electromagnetical design is described. Later on, the thermomechanical design is presented. In the end, real-time environment and control systems are detailed.

2 Motor principle The motor chosen to move the electrospindle was the switched reluctance principle. Our prototype is composed on a six-pole stator and a bipolar "cold" rotor, because it has no windings. Consequently, the rotor can consist in a simple and reliable structure made of fewer parts. These properties allow this kind of synchronous motor to reach high rotational speed and make it able to equip an HSM electro-


March 14-16, 2006

Figure 1. Structure 6/2 of a Switched Reluctance Motor

spindle [Miller, 1993]. Figure 1 presents the structure of a 6/2 SRM. θ parameter is the mechanical angle between the rotor axis and the stator supplied pole axis. The torque of such a motor is given by T = 12 ∂L I 2 , where L and I are respectively ∂θ the inductance and the current of the supplied phase. The inductance variation is obtained by rotor teeth profile. Figure 2 presents the design problem of a ultra high speed electrospindle. The design of an electrospindle could be defined as the achievement of a machining power, thanks to the product of the motor torque by the rotational speed. The motor torque is obtained by the choice of materials and geometries of the rotor and stator. Extreme rotational speeds cause the material of the rotor to be centrifuged and generate high mechanical stresses that could results in reliability problems. The rotor is supported by bearings and is submitted to excitation forces (electromagnetical, unbalance and machining forces), that create vibrations and stability problems. The rotor and stator materials are also submitted to the high supply frequency required for high rotational speed. It creates electromagnetical losses, that contributes with mechanical losses to global motor heating and thus decrease its efficiency.

3 Electromagnetical design 3.1 Rotor/stator design. Figure 3 presents the two structures of bipolar rotor that have been tested in our laboratory. The first one is composed of a


Electrospindle Power P

Rotor geometry

Mechanical stresses

=

Motor Torque C

´

Rotational Speed W

High supply frequency

Stator geometry

Materials Properties Electromagnetical

r, E, n, smax…

Losses

reliability

Vibrations

March 14-16, 2006

Bearings

Mechanical Losses

Heating DT

Stability Excitation forces

Figure 2. Ultra High Speed Electrospindle Design Problem

Figure 3. Bipolar Rotor Design

shaft passing through the ferromagnetic core and a Kevlar-Epoxy reinforcement. The second one consists in two parts (except bearings): a lamination stack inserted and stuck in a composite peripheral shaft. The magnetic circuit is designed to offer the best inductance variation with minimal losses and thus the highest torque for a given current. The material has to be chosen to generate minimal losses at high frequency (iron losses). Lamination thickness is chosen to reduce Eddy current losses. Figure 4 presents the simultaneous influence of rotor profile (teeth) on motor torque wave (according to position) and mechanical stresses calculated by analytic model. The main result in this design field is that precise location of corner point directly induces the torque vs rotor angular position curve [Antoine et al., 2003b]. Electrically, very high speeds have a direct influence on the phase feeding current shapes. Indeed, what is usually considered as square current becomes trapezoidal with increased rotational speed


March 14-16, 2006

Figure 4. Rotor Profile Modelization, Stress Results and Torque for 4A current

[Sauvey et al., 2005b]. 3.2 Power electronics. SRM is supplied by three-phase asymmetric power converter. In order to perform a current control of the motor phases, the converter which supplies the phases is operated with a current controlled by pulse width modulation (PWM). PWM frequency has to be much higher than the 6.6 kHz supply frequency to allow the waveform control of current (typically 100-150 kHz). High-frequency commutations under high power require high performance electronic components and circuits. Since the motor phases are widely inductive cut of the phase current is problematic: As this cut has to be done when the inductance is maximal, some commutation helping circuits have been designed, so that commutation cells can work at high speed without damageable heating.

4 Thermomechanical design 4.1 Vibratory behavior evaluation. An SRM functioning at ultra high speed generates excitation forces that cause the motor to vibrate[Miller, 1995]. To avoid stability problems, the design of such a motor has to take vibration into account in geometry and material choice [Bigret, 1980, Lalanne et al., 1986]. The vibratory behavior of the rotor is calculated thanks to classical Lagrangian methods. In a first step, kinetic and potential energy have been analytically modelized


March 14-16, 2006

through the used materials and a generic geometry to obtain, in a few seconds, the dynamic and vibratory behavior of a new geometry [Antoine et al., 2003a]. Thanks to mass, stiffness and gyroscopic damping matrixes, Bode diagrams associated to an excitation forces set (synchronous or asynchronous forces) are obtained. The result allow to modify the design to obtain the best vibratory performances. 4.2 Mechanical stresses. The mechanical stresses are evaluated in the rotor ferromagnetic materials. The rotor laminations are first designed to produce the highest possible torque. At ultra high speed, the material is submitted to high centrifugal forces that impose to take them into account in the design of lamination profile [Antoine et al., 2003b]. By the use of strength of material and of theory of elasticity [Timoshenko et al., 1974] and specially developed stress intensity factors [Peterson, 1974, Antoine, 2004], we have obtained an analytical model of the maximal stresses at critical points A and B (Fig.4) of the rotor lamination as a function of rotor profile (inner, outer radii, fillet). One of the main problems is to obtain sufficient mechanical information from manufacturers, who develop their products to be electrically and magnetically high performers, to the detriment of mechanical properties, that are inaccurate.

A

B

Figure 5. FEM study on a quarter of rotor lamination (critical stress points A and B) 4.3 Bearing choice and settings. Depending on the room available in the motor to place bearings, the best solution often consists in using classical ball bearings. Angular-contact ball bearings with ceramic balls (silicon nitride) are commonly used to improve performances, increase electrospindle stiffness and reduce friction torque. An important study of this mechanical element has been realized to determine its functioning conditions at high speed. Dynamic stiffness matrix and friction torque have been modelized. The most important setting parameter is the bearing preload, that must be elastically applied (by spring or compressive element) to allow the bearing to be faster (dilatation allowed). This value is of importance to keep the stiffness to a sufficient value. For example 706 angular-contact ball bearing have been shown to lose more than 80 percent of its static stiffness when turning


Imposed Temperatures

Te PFc

Tc

Timpe

feoo

HOUSING

fce

Covers

Td

PAi

fic

fie

TEETH 6 f di (Stator) fbd 6 f bi PFd Windings Tb (Stator) f PJb

Tn PFn

ni

Rotor core PEfq

Timpf

ff oo

2 ffe

STATOR 6 fdc

March 14-16, 2006

Tf PMbo

2 ffi

Ti

Tbo f fbo Outer 2 fboi Ring

Inner air

2Z feli

2 ffqi Fnfq

fna

2 fbii

Tfq

fboel

Balls fbiel

Inner Ring fbia

Shaft

Tbi Faoo

Covers fai fafq

Tel

Ta

PMbi

Outer air Temperature

Timpa Temperature

Figure 6. Thermal Flux Network in the SRM

at 200,000 rpm under insufficient preload (4N instead of 8N manufacturer minimal preconization). 4.4 Thermal considerations. A thermal resistance network has been computed, taking account the whole material properties and part dimensions to built the matrix equation modeling the linear-assumed thermic behavior of the SRM. The model takes into account all mechanical and electromagnetical losses to link motor temperatures distribution and heat sources (electromagnetical and frictional losses).


March 14-16, 2006

5 Spindle control This nonlinear behavior of an SRM explains the difficulty in modeling and controlling SRM drives. Related works about SRM modeling have been reported by our team. Off-line parameters identification of an SRM from input-output data using analytical methods and optimization techniques has been studied in [Visa et al., 2004a, Visa et al., 2004b]. The interest in accurate parameters identification lies on high precision SRM control laws design. Non linear control laws are presented in [Visa et al., 2004a, Visa et al., 2002]. All control laws are tested using a real-time control system. 5.1 Real-time environment. Real Time Linux kernel (RTAI - Real Time Application Interface) [RTAI, 2005] has been chosen for digital implementation of the control laws. Figure 7 shows the block diagram of the experimental setup. Two acquisition boards(1) have been preferred to DSP to perform D/A and

Figure 7. Block diagram of the control system. A/D acquisitions. The first acquisition board, NI-6070E, performs eight-channel 12 bits A/D conversions. Voltages, currents and other analog information can be sampled with a maximum frequency of 1.25MHz. The second board, NI-6711, performs three-channel 12 bits D/A. Control signals are sent to the PWM converter with a maximum frequency of 1.25MHz. The acquisition boards are synchronized through the RTSI National Instruments policy. The control PC used has two processors at 2.4GHz. One of the processors is dedicated to A/D and D/A real time tasks acquisitions, while the second one is dedicated to computations and other tasks. Eight A/D and three D/A acquisitions can be performed with this hardware solution with a maximum frequency of 50kHz. The real-time system has been recently used to estimate the machining torque during an high speed machining operation. 1

National Instruments Inc.


March 14-16, 2006

5.2 Control system. Continuous rotor position information is required using advanced control methods, for example to determine the turn-on and the turnoff angle of each stator phase. A shaft encoder or resolver can be used for accurate measure of the rotor position. However, this solution adds extra costs and reduces the reliability of the drive. Moreover, high speed implies high centrifugal stresses and thus the development of a position sensor becomes difficult. Alternatives to the position sensors must then be developed to perform the right excitation of the phases. Several solutions for sensorless control of an SRM have been proposed during the last years. The sensorless methods we propose use the actual excitation of the SRM to calculate the rotor position. Based on general non-linear observers’ theory exposed in [Thau, 1973] and the works presented in [Solsona et al., 1999] we have developed a reduced-order observer to estimate the rotor position. The observer uses the measurements of the phase voltages and currents to estimate all unavailable information: rotor position, speed and the unknown torque. Experimental results are presented in fig. 8 when an unknown load torque in used. Figure 8 shows the experimental observer dynamics under an unknown load torque perturbation. On these figures we can remark three different areas. Each one corresponds to a realistic machining operation point. The first area is related to the starting procedure of the SRM. During this phase the observer convergence is achieved. The SRM velocity is about 30, 000 rpm and the load torque is −0.6 Nmm. In the second area, an external perturbation (unknown load torque) is applied. This phase corresponds to the real case when the machining starts. Since there is no speed controller, the SRM reduces the velocity at about 16, 000 rpm in order to produce more torque. The estimated load torque will give the value of the unknown load torque. During the third area, there is no more load torque perturbation. Thus the SRM speed increases to get back to the initial value 30, 000 rpm.

6 Conclusion The development of an SRM-based electrospindle used for high speed machining has been presented. Thermomechanical, electrical and magnetic designs, power supply and control system principles have been skimmed over. These studies allowed us to optimize the magnetic and mechanical assemblies of the prototype. Best control integration should allow to improve really obtained performances. The mechanical link between tool and tool-holder is problematic in the targeted rotational speed range, and required complementary studies of vibratory behavior and a global optimization of tool-machine system. Damping properties that could offer some magnetic coupling structures will be taken into account. Ma-


March 14-16, 2006

4

4

x 10

0.01

3.5

0.008

0.006

3

0.004

0.002 Torque (Nm)

Speed (rpm)

2.5

2

0

−0.002

1.5

−0.004

1 −0.006

0.5 −0.008

0

0

1

2

3

4 Time (s)

5

6

7

(a) Rotational Speed estimation.

8

−0.01

0

1

2

3

4 Time (s)

5

6

7

8

(b) Load torque estimation.

Figure 8. Experimental estimations under unknown load torque.

chining tests will be soon performed and will give valuable information about real vibratory behavior and about different losses in the motor.

References [Abba et al., 2002] Abba, G., Visa, C., Antoine, JF., Fayard, H. and Sauvey, C. (2002). Design and control of a high speed electrospindle for metal cutting. Pre-proceedings of PRASIC’ 02, Brasov, Roumania. [Antoine, 2004] Antoine, JF. (2004). Conception et Modélisation d’une Electrobroche Grande Vitesse : Résolution de problèmes couplés. PhD Thesis. Université de Metz, 8 juillet 2004. [Antoine et al., 2003a] Antoine, JF., Abba, G. and Sauvey, C. (2003a). Approximate explicit calculation of first vibration frequencies of an unsymmetrical high speed rotor. IMECE 2003 Congress, Washington D.C., USA. 55133.pdf. [Antoine et al., 2003b] Antoine, JF., C.Sauvey, Visa, C. and Abba, G. (2003b). Optimisation de la forme d’un rotor de MRV 6/2 pour l’UGV. Electrotechnique du Futur 2003, Gif sur Yvette, France. [BesBes, 1995] BesBes, M. (1995). Contribution à la modélisation numérique des phénomènes couplés magnétoélastiques–Application à l’étude des vibrations d’origines magnétiques dans les MRV. PhD Thesis. Université de Paris VI, juin 1995. [Bigret, 1980] Bigret, R. (1980). Vibrations des machines tournantes et des structures. Technique et Documentation - Lavoisier. Paris. Tomes I à IV.


March 14-16, 2006

[Camus et al., 1997] Camus, F., Humeau, B., Besbes, M. and Gabsi, M. (1997). Reduction des vibrations des machines à réluctance variable. action sur la commande. Actes de la Journée Vibrations et bruits acoustiques des machines électriques, LESIR, Cachan, France pp. 47–56. [DUGV, 1995] DUGV (1995). Dossier usinage grande vitesse. Usine Nouvelle p. 47. [Ede et al., 2002] Ede, J.D., Zhu, Z.Q. and Howe, D. (2002). Rotor resonances of high speed permanent magnet brushless machines. IEEE transaction on Industry Applications 38(6): 1542–1548. [Fayard, 1999] Fayard, H. (1999). Procédés à réluctance variable pour la conversion d’énergie électromécanique directe–application à l’usinage grande vitesse. PhD Thesis. Université de Metz, 10 mars 1999. [Fos, 1993] Fos, R. Vives (1993). Étude d’électrobroches à Réluctance Variable pour l’Usinage à Très Grande Vitesse. PhD Thesis. Conservatoire National des Arts et Métiers, mai 1993. [Fos et al., 2001] Fos, R. Vives, Sánchez, R., Sánchez, A., Rubio, J., Aucejo, V., Fayard, Henry and Abba, Gabriel (2001). Present technologies, limits and researches in progress for high speed spindles in machine tool. Proceedings of third international conférence on metal cutting and high speed machining, ENIM, University of Metz, France 1: 427–444. [Lalanne et al., 1986] Lalanne, M., Berthier, P. and Der Hagopian, J. (1986). Mécanique des vibrations linéaires. seconde Ed. Masson. Paris. [Miller, 1993] Miller, T.J.E. (1993). Switched Reluctance Motors and their control. Oxford. U.K.: Clarendon. [Miller, 1995] Miller, T.J.E. (1995). Faults and unbalanced forces in the switched reluctance machine. IEEE trans on Industry Applications 31(2): 319–328. [Peterson, 1974] Peterson, R.E. (1974). Stress Concentration Factors. John Wiley & Sons. New York. [RTAI, 2005] RTAI (2005). WebSite : http://www.rtai.org. [Sauvey et al., 2005a] Sauvey, C., Abba, G., Antoine, J-F. and Visa, C. (2005a). Optimisation et dimensionnement d’une MRV 6/2 à très grande vitesse. In: EF’2005 Electrotechnique du Futur. 14-15 septembre. Grenoble, France. pp. II– 01.pdf. [Sauvey et al., 2005b] Sauvey, C., Antoine, JF., Visa, C. and Abba, G. (2005b). Optimisation of the design for a switched reluctance drive controlled by trapezoidal shaped currents. In: 44th IEEE conf. on decision and control (CDC). 12-15 december. Sevilla, Spain. pp. 3892–3897.


March 14-16, 2006

[Sixdenier et al., 2005] Sixdenier, F., Morel, L., Masson, J.P., Visa, C. and Sauvey, C. (2005). Vers des outils de validation pour actionneurs grande vitesse. In: EF’2005 Electrotechnique du Futur. 14-15 septembre. Grenoble, France. pp. II– 03.pdf. [Solsona et al., 1999] Solsona, J., Etchechoury, M., Valla, M.I. and Muravchik, C. (1999). Position and speed estimation of a switched reluctance motor. International Journal of Electronics 86(4): 487–507. [Thau, 1973] Thau, F.E. (1973). Observing the state of non-linear dynamic systems. International Journal of Control 17(3): 471–479. [Timoshenko et al., 1974] Timoshenko, S., Young, D.H. and Weaver, W. (1974). Vibration Problems in Engineering. fourth Ed. Wiley. New York. [UGV, 2003] UGV (2003). Ugv : des travaux courants à des vitesses dépassant celles habituelles. Revue Technique du travail des métaux (70): 29–34. [Vigneau, 1991] Vigneau, J. (1991). Usinage à grande vitesse. SNECMA pp. 1–3. [Visa, 2004] Visa, C. (2004). Commande non linéaire et observateurs: application à la MRV en grande vitesse. PhD Thesis. Université de Metz, 11 décembre 2004. [Visa et al., 2002] Visa, C., Abba, G. and Léonard, F. (2002). Asservissement de vitesse par commande non linéaire d’un moteur à réluctance variable. In: Conférence Internationale Francophone d’Automatique - CIFA’02. Vol. CdRom p973.pdf. 8-10 July. Nantes, France. pp. 973–978. [Visa et al., 2004a] Visa, C., Abba, G., Léonard, F., Antoine, J.-F. and Sauvey, C. (2004a). Nonlinear identification and control of a switched reluctance motor. In: 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS). 1-3 September. Stuttgart, Germany. pp. 1463–1468. [Visa et al., 2004b] Visa, C., Abba, G, Léonard, F., Antoine, J.-F. and Sauvey, C. (2004b). Parameters identification of the switched reluctance motor without position sensor. In: 11th IFAC Symposium on automation in Mining, Mineral and Metal processing (MMM). 8-11 September. Nancy, France.