16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 441

Modeling, Design & Control of Disc Type Stepper Motor

K. S. Denpiya and A.B. Patel S. H. Chetwani and M. K. Shah Electrical Engineering Department Electrical Research & Development Association Institute of Technology, Nirma University ERDA Road, GIDC, Ahmedabad -382 481 INDIA Vadodara- 390 010 INDIA as UC3717, UC3770, LM297 and LM298 generally limit the Abstract -This paper presents the modeling & design of bipolar current of motor below three Ampere, as a consequence these micro stepping control for a disc rotor type permanent devices cannot be used in the application fields of large power. stepper motor. Disc rotor type permanent magnet stepper motor DSP or FPGA base controllers are costly hence they are in shows the advantages of higher torque at high speed, high torque limited applications [3]. The technique of microstepping is to weight ratio, very low moment of inertia, and high torque to adopted as it reduces the stepper motor resonance problem and inertia ratio, low power consumption, ironless rotor and offers other advantages like smooth movement and constant having minimum iron loss using SiFe laminations. This paper torque . describes the design, FEM modeling & analysis of disc rotor type stepper motor. Here torque angle profile and inductance profile II. DESIGN AND CONSTRUCTION: is calculated using FEM analysis. This paper also presents a design of two phase bipolar microstepping drive for disc rotor type stepper motor. The microstepping control system improves The basic construction of disc rotor magnet stepper motor is the positioning accuracy and eliminates low speed ripple and shown in figure 1. Rotor consists of thin rare earth magnet resonance effects in a stepper . The same disc. There is large number of alternate N and S impressed on microstepping system is ideal for robotics, printers, and CNC rotor disc as shown in figure.1. Stator is made up of CRGO machines and can facilitate the construction of very sophisticated lamination and has a number of poles winding place on tip of positioning control system while significantly reducing stator poles. The width of the angular zone of the disc is such component cost, design time and system cost. that the whole width of disc is in the air gap formed by the stator segments. The stator consists of groups of C shaped I. INTRODUCTION: segment. Each group comprises a number of elementary magnetic circuits and at least 2 electric coils coupled to said Disc rotor type permanent magnet stepper motor offers elementary circuit. Each elementary circuit consists of 2 U many advantages such as higher torque at high speed, high shaped thin segments of high magnetic permeability The end- torque to weight ratio, very low moment of inertia, high torque faces of the inner arms of the two U segments are spaced from to inertia ratio, low power consumption, ironless rotor and each other to form an air-gap between them for the free stator having minimum iron loss using SiFe laminations [1]. movement of the disc within the air gap. Arrangement of U They are extremely reliable and compact having better segment of the stator pole is shown in figure 1. The coils are dynamic performance than other stepper motors. Fig.1 shows wound around the inner arms of the U segments, which the view of disk rotor type stepper motor. The rotor of such encloses the air-gap between them. Thus magnetic poles can motors consists of a rare earth magnet having the shape of a be created by passage of current in the windings. Selection of thin disc which is axially magnetized. 3D model of disc rotor the stator segment is considered depends on the step angle. type stepper motor is shown in Fig.1. The disc rotor motor is These 20 individual elementary circuits are grouped to form a very well suitable for high performance and high volume single phase. The other phase is formed by another set of 20 applications such as computer peripherals, robotics, and CNC elementary circuits, each having the construction as stated machines [1], [2]. above. There may be more than 2 groups of elementary circuits and the number of elementary circuits in each group can be decided further and need not be 20 in that case. These 20 stator segments is equally angularly spaced by 2πk/N degrees apart (k is an integer). The 2 groups of stator segments are further angularly shifted by 2πr/N ± πr/2N (r =3, 4). This shifting of the group is done so that when one pole is completely inside the air gap in one of the groups, the air gap

Fig.1.Basic construction of Disc magnet motor in the other group does not envelops one complete pole there remains some offset in the pole pitch which provides a higher However, conventional drive system of stepping motors resolution . Width of each elementary circuit = (π / N)*Ri, (Ri= based on the specific integrated circuit for motor control such inner radius of rotor)[5].

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA. 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 442

III. MODELLING OF DISC STEPPER MOTOR µ pCosHD γ )( B = 0 pmpm 2 (3) R δ

Some of the designing parameters have been stated in the r0 π 2/ p design. Here torque and flux, modelling of disc rotor type φ = .dABp stepper motor in this magnetic circuit is divided in two parts. ∫ ∫ −π 1. The flux due to stator segment. 2. The flux due to PM disc, ri 2/ p (4) considering an elemental magnetic circuit and applying amperes law to it we get [1] After calculations we get the flux as µ 2 − 2 pCosRRHD γ )()( φ = 0 pmpm 0 i (5) δ δ fefe pm pm ∗=∗+∗+∗ IWDHIHH (1) δ

Hδ = magnetic field strength in the gapair The magnetic energy in the air gap is ψ A ψ B H Pm = magnetic field strength in the iron = ψ + dIdIW ψ H fe = magnetic field theofstrength rotor disc mag ∫AA ∫ BB δ = gapair 0 0 (6)

l fe = lengthiron Thus the torque developed is Tm = dWmag / dγ D = thickness theof rotor disc Pm Hence finally we get the W = turnsofnumber 2 2 Pµ 0 pmpm 0 − )(( bi cos( γ ) − A sin(PIPIRRHD γ )) I = winding current Tm = (7) δ Thus the magnetic flux density in the air gap due to an elemental magnetic circuit consisting of a single stator IV. STEPPER MOTOR MODEL element is µ Wµ0 I 0 HD pmpm Based on above modeling, the basic dimensions of motor Bδ −= δ δ (2) were calculated. The major dimensions are given in table I.

Let’s consider two different coordinate systems, γ1 fixed to TABLE I

the stator and γ2 to the rotor. γ is the difference between these PARAMETER OF DISC ROTOR TYPE STEPPER MOTOR two coordinates. (γ2 = γ1 – γ.) This is shown in Fig. 2. INPUTS Angle between two Step Angle(deg) 1.8 phases(deg) 36 Holding Torque(kg- cm) 10.8 Width of stator segment(cm) 0.75 Air gap between the stator No. of Phases 2 segment(cm) 0.5 Stator Dimensions Rotor Dimensions Inner diameter(cm) 4.293 Outer Diameter(cm) 5.793 Outer diameter(cm) 8.12 Inner Diameter(cm) 4.293 Length(cm) 4.06 Width(cm) 0.1 Thickness of stator segment(cm) 0.138 No. of rotor pole 50 Shift of stator segment(deg) 7.2 No. of turns 114

Fig. 2.Top view of Stator Half Fig. 3 shows 3D model of stepper motor based on dimension of Table I. This shows 3D isometric view of stepper motor with finite element mesh and top view with Thus the air gap flux due to the one phase can be calculated nodes. It shows stator segments with exciting coil and rotor by integrating. So we get disc. In the rotor disc alternating N and S pole are arranged. When a pole is inside the air gap, the working point of the φ = .dAB magnet on the BH curve is very high and the magnetic ∫ induction is maximum. When a pole is outside of the air gap, = γ dA rd 1dr the magnet is in the air and the working point is then very low. It means that it needs a magnet with linearity in the second In the distribution of flux density due to the permanent quadrant of the BH curve. This is possible with rare earth magnet disc will be alternating in direction due to the permanent magnet so rare earth magnet is used in disc rotor alternating North & South poles. It will vary like a cosine type stepper motor. function with maximum at an interval of π/p degrees. (p=no of pole pairs). Hence the flux density due to the PM disc can be found to be

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA. 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 443

vica & versa. Torque is varying with the change in rotor position. This motor is specially design for micro stepping. In micro stepping drives one phase current is on sinusoidal while another phase current is 90 degree phase shifted as a cosine. Torque angle profile is calculated theoretically and it’s verified with FEM analysis. Figure 5 shows finite element with boundary condition and results. Rotor disc is exciting with magnetic field strength of rare earth magnet material such as NdFeB(39H) and coil is excited with current density as considering of that of micro stepping. Based on this FEM torque angle profile is obtained and it is verified with the theoretical result as shown in Fig. 6. Here resultant magnetic vector potential shows maximum flux line in the stator segments. That is uniform in all of stator segment because the flux flow is axial in disc rotor type stepper motor. Based on this model inductance profile is also calculated.

Fig. 3. 3D of stepper motor with finite element mesh and nodes

Rare earth magnet are available in different grades. Table 2 shows the theoretical and FEM results for different grades of PM materials. Based on this result NdFeB (39H) is used for the rotor disc. Fig. 4 shows the resultant flux density of magnet with all three PM .

Fig. 5. Finite element meshes with boundary condition and resultant magnetic vector potential

Fig.4. Resultant flux density of magnet.

TABLE II COMPARISON OF THEORITICAL AND FEM RESULTS FOR PM MATERIALS Hc Theoretical FEM Material Grade (AT/m) (mWb/m^2) (mWb/m^2)

NdFeb 39H 12300 1.029 1.286 Fig. 6. Torque angle profile. Smco 26 9200 0.879 0.971 NdFeb B10N 5780 0.489 0.497 V. CONTROL SYSTEM DESCRIPTION A. Configuration of the controller: Motor torque varies with one rotor pole. When rotor pole and stator segment are aligned, the torque is maximum and The block diagram of the bipolar microstepping drive for disc rotor type stepper motor using microcontroller TMC401

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA. 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 444 is shown in Fig. 7. In this diagram, cycle is generated in are N-channel enhancement mode silicon gate power field TMC401 and given to the TMC239 driver in which required effect . They are advanced power MOSFETs PWM signals are generated. The current has to be as much designed to withstand a specified level of energy in the sinusoidal as possible in the two phases of the stepper motor to breakdown avalanche mode of operation. It is required to raise obtain microstepping mode. the current level up to 4.6 ampere. So additional power drivers are used. This is satisfied by attaching a weak additional charge pump oscillator and pumping Vs up to the high supply. IR2110 developed by International rectifier company is high voltage, high speed power MOSFET & IGBT driver with independent high & low side referenced output channels. Proprietary HVIC and latch immune CMOS technologies enable ruggedized monolithic construction. The logic input is compatible with standard CMOS or LSTTL output, down to 3.3v logic. The output driver feature a high pulse current buffer stage designed for minimum driver cross-conduction. The floating channel can be used t o drive an N-channel power MOSFET or IGBT in the high side configuration up to 600 volts.

Fig.7. Block diagram of proposed drive system

TMC401 is a 32-pin enhanced controller developed by Trinamic , and its high computational performance with additional excellent peripherals such as high speed A/D converter and I/O ports makes it an ideal choice for many high performance power control and motion control application. Based on TMC 401, a new disc rotor type stepper motor driver system is designed as shown in Fig. 8. TMC 401 is the most crucial element of the whole control system which receives the external signals such as start or stop command, forward or reverse direction and pulse signals. The TMC 401 converts step/direction signals into SPI datagram that can be used to drive a TMC 239 stepper motor driver chip directly.

Fig. 9. Schematic of driver circuit for one phase

VI. EXPERIMENTAL RESULTS

The implementation & analysis was carried out on disc rotor motor in Electrical Research & Development Association, where a high performance microstepping system for disc rotor type stepper motor is realized effectively. The two phase disc rotor type stepper motor has following parameters: • Step angle θs = 1.8° (200 steps/revolution); • Rated supply voltage = 24 - 40 V ac; • Current per phase = 4.6 A; • Resistance per phase = 1.013 Ω ;

Fig. 8. Schematic for TMC 401 control circuit • Inductance per phase = 3.1 mH ; • Electrical time constant = 3.06 ms; B. Design of the driver Various waveforms of current in motor winding for different Fig.9 shows the drive circuit for one phase of disc rotor type stepping modes are shown in the following figures. stepper motor. IRF630 developed by Fairchild semiconductor

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA. 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 445

Fig. 10. Winding current in Full Step Mode Fig. 13. Winding current in half Step Mode

Fig. 14. Winding current in 1/4 Step Mode Fig. 11. Winding current in Full Step Mode

Fig. 12. Winding current in one phase on Mode Fig. 15. Winding current in 1/8 Step Mode

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA. 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 446

verification of design of stepper motor. Inductance profile is used for development of drives for stepper motor.

VI. REFERENCES

[1] K. S. Denpiya, S. H. Chetwani, Amit N. Patel, M.K.Shah “Modelling of Disc Rotor type Stepper Motor”, 3rd National Conference on Current Trends in Technology, NUCONE 2008, 27-29 November,2008. [2] C Obermeier, “Modelling of a Permanent Magnet disc Stepper Motor and Sensorless field oriented speed control using an extended kalman filter’’, IEEE Proceedings of International Conference on Power Electronics and Drive Systems , Vol. 2, May 1997, pp.714-720. [3] V. V.Athani “Stepper Motors – Fundamentals, Applications and Design” New Age International Publishers, 1997. [4] Norbert Veignat “Advances in Stepper Motors: The Disc Magnet Technology ’’ Application note, Portescap, Switzerland; October 1991. [5] Kuo, B.C’’Design of step motor”, SRLPubl., champaign,1979. [6] Claude Oudet ‘Electric Step motor’, US Patent no – 4330727, May 18, 1982 C Obermeier, “Modelling of a Permanent Magnet disc Stepper Motor [7] and Sensorless field oriented speed control using an extended kalman Fig. 16. Winding current in 1/16 Step Mode filter’’,IEEE,Proceedings of International Conference on Power

Electronics and Drive Systems , Volume 2, May 1997, pp.714-720. [8] Claude Oudet ‘Multipolar magnetization Device’ US Patent no – 4, 707, 677, Nov, 17, 1987. [9] Y.N.Zhilichev “Precise Multipole Magnetization of Disc Magnet for Sensor Application” IEEE transactions on magnetics, vol.39, no 5, sep 2003

Fig. 17. Winding current in 1/32 Step Mode

VII. CONCLUSION

Looking to the increasing use of these types of stepper motors in different applications viz. CNC, Robotics, more and more miniature and light weight motors with quick incremental motion without compromising on the torque needs is required. Hence the modeling and optimization of these types of motor is required to improve the dynamic performance of motor to suit their applications. The basic segment of disk type stepper motor is optimized. Complete model is optimized using optimized basic segment. Based on this inductance profile and torque angle profile are calculated. Torque angle profile gives performance of motor and

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.