Stepper-Motor Operation and Interfacing Fundamentals Prepared by: P. David Fisher and Diane T. Rover

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1 tepper-motor Operation and Interfacing Fundamentals Prepared by: P. David Fisher and Diane T. Rover mpere s Law & iot-avart Law n electrical current I in a ware causes (induces) a magnetic field. The direction of is given by the right-hand rule. I R Magnetic Fields for a Long Thin Wire For a long thin wire, the strength of the magnetic field a distance R from the wire is = (U 0 I)/(2πR) (1) where µ 0 = permeability of vacuum, µ 0 = 4πx10-7 henry/meter The olenoid coil of wire with turns creates a magnetic field in the direction illustrated, where = ki, (2) with k being a constant. Hence, is proportional to and I. I Magnetic Field Lines 1 st_mot_3.doc

2 The Electromagnet (outh) (orth) Iron Core If you place a compass and in the vicinity of the iron core, you would discover that one end (say ) would be similar to the outh Magnetic Pole of the earth, while the other end (say ) would be similar to the Earth s orth Magnetic Pole. Two important properties of electromagnets are the following: 1. ll Electromagnets are dipoles; i.e., they have a orth Pole () and a outh Pole (). 2. The position of the Poles (at or ) is determined by the direction of the current I and the direction of the winding. 2 st_mot_3.doc

3 asic Model for a tepper Motor Consider the four electromagnets physically arranged as illustrated. P1(L11,L12) P4(L41,L42) P2(L21,L22) P3(L31,L32) where R 11 L 11 L 31 R 31 i 11 R 12 L 12 v a i 31 L 32 R 32 Windings for P1 & P3 i 12 i 32 v b R 21 L 21 L 41 R 41 1 i 21 R 22 L 22 v c i 41 L 42 R 42 Windings for P2 & P4 i 22 i 42 v d 3 st_mot_3.doc

4 Controlling Magnetic Polarities with Winding Voltages (v a, v b, v c and v d ) The magnetic polarities of the electromagnets can be controlled by varying the winding voltages v a, v b, v c and v d. Consider the following two cases. Case I P1 and P3 P1(L11,L12) i ll > 0 v a = 5V i l2 = 0 v b = 0V P(L31,L32) i 3l > 0 v a = 5V i 32 = 0 v b = 0V P1(L11,L12) i ll = 0 v a = 0V i l2 > 0 v b = 5V P3(L31,L32) i 3l = 0 v a = 0V i 32 > 0 v b = 5V ote: Winding voltages v a and v b control the polarities for electromagnets P1 and P3. 4 st_mot_3.doc

5 Case II P2 & P4 P2(L21,L22) i 2l > 0 v c = 5V i 22 = 0 v d = 0V P4(L41,L42) i 41 > 0 v c = 5V i 42 = 0 v d = 0V P2(L21,L22) i 2l = 0 v c = 0V i 22 > 0 v d = 5V P4(L41,L42) i 4l = 0 v c = 0V i 42 > 0 v d = 5V ote: Winding voltages v c and v d control the polarities of electromagnets P2 and P4. 5 st_mot_3.doc

6 Controlling tepper-motor tate Transitions The state of a stepper motor can be controlled by controlling the winding voltages of the electromagnets. Consider the following example. Present tate P1 P 1 & P 3 v a = 0V v b = 5V P4 C P3 P 2 & P 4 P2 v c = 5V v d = 0V ext tate P1 v a = 5V P4 C P3 P 1 & P 3 P 2 & P 4 v b = 0V P2 v c = 5V v d = 0V ote: The polarities of electromagnets P1 and P3 can be reversed by simultaneously changing v a from 0V to 5V and v b from 5V to 0V. 6 st_mot_3.doc

7 Important Questions and Conclusions With respect to the previous example, answer the following questions. 1. ssume that the stepper motor is in its initial state. If a compass is positioned with the pivot point of its needle at point C, in what direction would the needle point? 2. ssume that the stepper motor is in its next state. If a compass is positioned with the pivot point of its needle at point C, in what direction would the needle point? 3. Did the compass needle move clockwise or counter clockwise? 4. What voltages do we need to change to have the compass needle rotate in the opposite direction? 5. How many steps does it take to make a 360 rotation? 6. How might you add the number of steps for a 360 rotation? Identify two distinct approaches. 7. Why might you want to add steps? 8. What are the engineering design considerations that must be addressed as a new stepper-motor assembly is designed for a new commercial application? 7 st_mot_3.doc

8 tepper-motor Interface Circuit Model There are a number of significant challenges facing the computer engineer who must interface a stepper motor to a microcontroller. For example, consider the following transient circuit response problem. 1 V R 1 + V 1 - i 11 R 11 L 11 + V L11 - R 1 = hunt Resistance of witch R 1 >> R 11 Case 1: witch closes at t = 0 i 11 (0 - ) = i 11 (0 + ) = V /R 0 (3) i 11 (t) = (V /R 11 )e -t/τ, where τ = R 11 /L 11 (4) V L11 (t) = V s e -t/τ (5) Case 2: witch Opens at t = 0 ecause currents through an inductor cannot change discontinuously, i ll (0 + ) = i 11 (0 - ) = V /R 11 (6) pplying Kirchhoff s Voltage Law (KVL) around the loop at time t = 0 + yields: -V + V 1 + R 11 i 11 + V L11 = 0 (7) -V + R 1 i 11 + R 11 i 11 + V L11 = 0 (8) V L11 = V (R 1 + R 11 )i 11 V (R 1 /R 11 )V, when R 1 >> R 11 (9) V L11 -(R 1 /R 11 )V -(1MΩ/0.1kΩ)V V (10) These large voltages will destroy the solid-state switch. 8 st_mot_3.doc

9 Diode Protection There exists a very standard solution to the problems which arise due to the desire to rapidly switch electrical currents in circuits containing inductive loads. The following example illustrates the solution. The winding of an electromagnet can be modeled as a resistance in series with an inductance, as illustrated in the figure. Under computer control, current i 11 is to be controlled by controlling voltage v 1. s we saw with the stepper-motor example, i 11 will assume one of two steady-state values i.e., i 11 = 0 and i 11 = V /R 11. In the circuit illustrated, diode D 1 protects the interface logic from large transient voltages. Computer Interface Logic D 1 v 1 R 11 L 11 i11 Case 1: v 1 = 0V The voltage drop across the diode is v 1 = 0V, and the diode is turned off (an open circuit). lso, i 11 = 0. Case 2: v 1 = V, where V > 0V The voltage drop across the diode is v 1 = V, and the diode is turned off (an open circuit). lso, i 11 = V /R 11. Case 3: t t = 0 -, v 1 = V, where V > 0V. Then at time t = 0, the interface logic switches and presents a high impedance to the rest of the circuit. t time t t = 0 +, the current i 11 = V /R 11 and passes through the diode. The diode is forward biased with v 1 = -0.7V. With time, i 11 drops to 0, v 1 returns to 0V and the diode is turned off (an open circuit). This is the solution to only one interfacing problem. nother common problem is the fact that actuators, such as the stepper motor, do not operate at standard logic voltages. This problem will be discussed as we investigate the electrical properties of a specific stepper motor and its computer-interface requirements. 9 st_mot_3.doc

Material World: Electricity

Material World: Electricity 17. Coulomb s Law The force, F, between two objects with charge q1 and q2, is given by: k q q 1 2 F -, where r = distance between the two charges in meters 2 r k = Coulomb's constant = 9 X 10 9 m 2 /C