9.9 Light Chopper Drive Motor

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1 9.9 Light Chopper Drive Motor This application is for a motor to drive a slotted wheel which in turn interrupts (chops) a light beam at a frequency of 200 H z. The chopper wheel has only a single slot and an inertia of 0.2 gcm. Supply voltage available is 4 Vdc. Given: V o = 4 Vdc Max M L = 0.2 gcm (2 x 10-4 NM ) Chopper freq. = 200 H z Solution: ω = 2πf ω = 2π x 200 = P in = M L ω = 2 x 10-4 x x 10 3 = 0.25 Watts Propose to use 16 C Motor From catalog: K = 23 x 10-4 Nm/A R =7.5Ω l o = 0.015A Now: V o = Rl + Kω V o = (7.5 x 0.102) + 23 x 10-4 x 1257 = 3.66 volts 4 Volt supply is acceptable and motor choice checks out REVIEW OF ESCAP STEP MOTORS 10.1 Description The Escap family of permanent magnet step motors are the result of a unique patented technology. The motors can be built with one phase per stack, with two or more phases per stack (each phase-covers a given angular sector) or with two or more phases imbricated in one single stack. Patents are protecting these different designs. The-following described motor has two phases arranged in one single stack. This new step motor design is based upon a homoheteropolar structure. Figure 25 illustrates the motor's design in a simplified mechanical schematic. 390

2 The motor is in the form of a thin axially magnetized disc made from somarium cobalt magnetic alloy. A special magnetization process allows for a high number of magnetic poles and small step angles. The magnetic path is closed by the use of "C" shaped silicon iron lamination cores. These cores are symmetrically arranged in the two stator halves. These lamination cores act as the stator "teeth" and are surrounded with a "bean" shaped coil for each electrical phase. The magnet is fixed to a shaft by virtue of two end-bells thus, forming the rotor assembly. It should be obvious that the inertia of such a rotor assembly is very low an advantage of this motor. Figure 26 shows the construction of the Escap step motor. The two stator halves forming the housing are precision molded of Ryton. This material has a very good modulus of elasticity, low shrinkage, and excellent thermal stability. The four bean shaped coils are identical and are manufactured by standard winding methods Advantages and Unique Features The advantages and unique features of the Escap P series motors can be summarized as follows: Very low rotor inertia (12 x 10-7 kgm 2 for P532) High torque Low mass Low volume High power/mass ratio (150 W/kg -1 for P532) Excellent acceleration (140,000 rad/s 2 for P532) High efficiency 391

3 Low resonant frequency (250 H z for P532) Low system cost (motor/control package) Linear torque vs. ampere-turns characteristic Capable of very high step rates Low mechanical time constant No risk of demagnetization Compatible with simple low cost drive circuitry 10.3 Detent Torque The P series step motor does provide some holding torque with the windings do-energized. This torque is the result of an interaction between the rotor poles and the stator poles. For this motor design the detent torque is a fourth harmonic of the fundamental sinusoid torque curve and is defined as T q = 2T 4 Sin (4Nα φ 4 ) During manufacture of the motor it is possible to increase or decrease the detent torque over a range of almost zero to about 10% of the one-phase-on holding torque Holding Torque The P series motor is a two phase step motor. With one phase energized with a dc current, the rotor poles will align themselves with the corresponding stator poles of the energized phase. A motor so aligned is in a position of stable equilibrium. If an external torque is applied to the motor shaft causing the rotor and stator poles to misalign, a counteracting torque is developed which tends to restore the original condition of equilibrium. This restoring torque is called the static holding torque and its value varies with rotor position. This torque is zero when the rotor and stator poles are aligned and increases with the angle of misalignment up to some maximum value for the particular motor (static torque characteristics). With two phases energized the static holding torque is obtained by adding the torques of the two phases energized separately. Theoretically the two-phase-on scheme produces 2 times the torque developed with one-phase-on. In practice the actual static torque is less because the individual torque curves are not sinusoidal. Under conditions of negligible detent torque the mathematical expression for Static holding torque (one-phase-on) is given by: T = γ ni sin Nα where N = number of pole pairs (25 for 100 steps per revolution) γ = torque per ampere-turn (a motor constant) ni = number of ampere-turns α = total mechanical displacement (0 to 360º) The torque curves of Figures 27 and 28 present a graphic explanation of the various torques under one and two-phase-on operation. A review of these curves yields the following helpful observations: (A) One-phase-on The stable equilibrium positions of the detent torque and the holding torque are the same. The stiffness of the stable equilibrium positions is increased by the detent torque. (B) Two-phases-on The stable equilibrium positions of the holding torque (phase and 1 2) are unstable positions of the detent torque. The stiffness of the stable equilibrium positions is decreased by the detent torque. 392

4 T 1 T 2 T 3 T 4 T 5 DETENT TORQUE AMPLITUDE THEORETICAL MAXIMAL DYNAMIC TORQUE WITH ONE PHASE ENERGIZED THEORETICAL MAXIMAL DYNAMIC TORQUE WITH TWO PHASE ENERGIZED HOLDING TORQUE AMPLITUDE WITH ONE PHASE ENERGIZED HOLDING TORQUE AMPLITUDE WITH TWO PHASES ENERGIZED A, B STABLE EQUILIBRIUM WITH ONE PHASE ENERGIZED C, D STABLE EQUILIBRIUM WITH TWO PHASES ENERGIZED A, C, B, D SUCCESSIVE ROTOR POSITIONS WHEN HALF-STEPPING (8 STEP SWITCHING SEQUENCE) Figure 27 Descriptive Torque Curves 393

5 T 2 T 4 L TL A, B A', B' THEORETICAL MAXIMAL DYNAMIC TORQUE WITH ONE PHASE ENERGIZED HOLDING TORQUE AMPLITUDE WITH ONE PHASE ENERGIZED AMOUNT OF APPLIED LOAD COUNTERACTING TORQUE WHEN LOAD L IS APPLIED STABLE EQUILIBRIUM WITH ONE PHASE ENERGIZED STABLE EQUILIBRIUM WHEN LOAD L IS APPLIED Figure 28 Descriptive Torque Curves 10.5 Dynamic Characteristics The performance curves of the P312 and P532 step motors are shown in Figure 29. It should be noted that the start-stop torque versus speed will be affected by both the load inertia and friction. However, the pull-out torque is usually affected by friction alone. It should be realized however, that in some cases static friction and running friction are often different values. A good dynamic behavior can be claimed when this motor is compared to equivalent hybrid type 3.6º motors with a rare-earth cobalt magnet, or even to traditional hybrid type 1.8º motors. For the same number of steps per second, the P532 is rotating twice as fast as a 1.8º motor; the mechanical work is therefore equivalent, as long as torque is at least half the torque of the competition motor. It is effectively the case, even though the volume and the mass 394

6 395

7 are respectively 27% and 42% lower. The rotor inertia is 5 times lower but, as a matter of fact, should be multiplied by 4 in order to compare the inertia of both motors on a shaft which runs at the same speed. As far as mechanical power is concerned, the P532 motor is equivalent to a size 22 motor, 2" long, with 1.8 times more volume, 2.4 times more mass and 2.5 times more equivalent inertia. The reason why the P532 has good performances with regard to its volume and its mass is essentially because of its low inertia and low magnetic losses (due to a total silicon-iron magnetic circuit which weighs only 50g). At 1000 steps per second, the P532 needs 0.4W and conventional 1.8º motors need 0.7W to 1.1W. At 2000 steps per second, this becomes 1.1W against 1.9 and 2.9W. At 5000 steps per second, the P532 needs 4W, of which 1W is due to friction in the ball bearings viscous friction of the magnet in the air gap. Referred to a chopper drive, the Joule power in the coils represents about 6W. A total of 10W power losses can so be figured out. This rough calculation gives an idea of the motor efficiency, since the available mechanical power is more than 20W Damping Considerations At low speed, the P532 and P312 have less losses than other step motors. Thus, the damping of the settling oscillations will need longer time. However, the damping effect created by the short-circuit of the coils or simply by connecting the coils across a low source impedance is better, up to 3000 steps/s. At 1600 steps/s for example, an 80% power loss increase can be achieved by short-circuit of only one coil or by connecting one phase across an adapted low resistance. Similar measurements with size 22 by 2" long hybrid typemotors, shows that no damping effect occurs after 800 to 1500 steps/s under the same circumstances. The effect on damping by increasing the load inertia is to increase the settling time and overshoot amplitude. Likewise the effect on damping by increasing the load friction is to decrease the settling time and overshoot amplitude. Friction sometimes improves system performance Resonance The mechanical resonance of a P532 motor with no load inertia is about 190 Hz. It is calculated by the following expression: where: T is the holding torque, N is number of pole pairs J is total inertia From this formula it can be observed that load inertia will reduce the primary resonant frequency. In applications where the motor must be operated near its primary resonance the addition of load inertia may provide a safer operating speed range. However, higher order harmonics may appear at higher speeds as inertia is increased. The addition of friction can sometimes be used to reduce the severity of resonance Accuracy Step accuracy is defined as a non-cumulative error which represents the step to step error in one full revolution. Inertia and viscous friction do not affect step accuracy. Friction does however, create a dead band around the normal resting position of the motor. This is due to the fact that the rotor comes to rest in a position where the static torque matches the friction 396

8 torque of the system. Thus, the rotor is offset from its ideal rest position by an angle where the static torque curve equals the friction. This is called position accuracy and is not to be confused with step accuracy which is really a mechanical property of the motor. It should be obvious that the steeper the static torque curve the better will be the position accuracy. This is very important in selecting the proper step motor Motor Drive Techniques The performance of a step motor is greatly influenced by the type of drive circuitry utilized. An obvious advantage of any step motor is its compatibility with digital electronics. The motor making a fixed incremental displacement (step) for each single pulse of energy supplied to it. Although step motors can be run closed loop, they have the cost saving advantage of being able to operate quite satisfactorily in open loop mode. Provided, of course, that the response characteristics (torque, speed, etc.) of the motor are not exceeded. The three types of driver configuration recommended for the Escap steppers are: resistance limited, (unipolar or bipolar), or a bipolar chopper type. The unipolar drive system is low cost and most commonly used in lower performance applications. Its disadvantage is due to the fact that only one winding per phase is in use at any particular time. The bipolar drive developes higher motor performance since both windings per phase are utilized. This requires either series or parallel connected windings. Also the bipolar requires a dual polarity power supply or a transistor bridge for each motor phase. Bipolar driving yields a 2 increase in low speed torque for the same electrical input power as delivered by a unipolar drive. The bipolar chopper drive is known for its high performance and improved efficiency (due to the absence of external resistance). This type of drive is best used at higher speeds. A chopper drive may cause audible noise due to the motor laminations vibrating at the chopper frequency. Single step motion is with a high acceleration due to the short current rise time of a chopper drive. The response therefore can be more oscillatory especially at speeds near the natural resonance of the motor. Half step techniques usually reduces resonant effects, and microstepping schemes will completely eliminate resonance and speed instability problems Application Example Description The application is a matrix dot printer carriage drive. The carriage is moving along a metallic bar; its weight is 5 oz. and the friction is 4 oz. in. The motor has a 3.6º step angle and has to be able to drive the carriage at 1200 steps per second. The motion is transferred from the motor shaft to the carriage through a pulley and a cable. An acceleration time of 100 ms is allowed from standstill to 1200 steps per second. The supply voltage is specified below or equal to 24V Mechanical Requirements When the P532 has to replace a 1.8º motor without any change in the electronics, especially the number of pulses per second, or in the carriage travel speed, one has to provide the system with a half diameter pulley. This sometimes creates a problem as far as the cable is concerned. In the present application, no pulley diameter is specified but we don't want the reflected inertia to be higher than 4 times the motor inertia. This will lead to the same kind of cable problems. 397

9 The motor inertia is J M = 1.2 x 10-6 kg.m 2 The load inertia should be less than 4 x 1.2 x 10-6 kg.m 2 J L 4.8 x 10-6 kg.m 2 If the pulley diameter is D = 0.45", then x 5 x 28 x 10-3 = 4.6 x 10-6 kg.m 2 The stress on each cable strand due to this radius of curvature is d is the diameter of a single cable strand E = 2 x N/m 2 (Young's modulus of elasticity) A good steel will tolerate η = 1500 N/mm 2 ; let's use η = 700 N/mm 2 for a more conservative calculation. Then In addition, there will be a stress on the cable during the acceleration phase. It will be negligible, because there is no drastic acceleration requirement. Nevertheless if the P532 is used with a high acceleration rate like 10 5 steps/s 2, there will be an additional force on the cable: F = m.γ = (5 x 28 x 10-3 ) Using a 0.5 mm cable diameter, the steel section will be approximately 0.12 mm 2. This means an additional stress of Then Finally, each strand diameter must be as low as ". In addition, the cable should be teflon coated. It may be easier to find a steel band in that thickness, instead of a cable. The following design may be used in that case 398

10 Electrical Requirements Each motor coil has 320 turns and R = 12Ω resistance. One should decide now if the coils will be connected in series, or in parallel. If a series connection is chosen, then the back emf will be (peak value) γ = Torque per ampere-turns = 4.6 x 10-4 Nm n = Number of turns per coil = 320 E emf = 22V If a parallel connection is chosen, then the back emf will only be The requirement made about the supply voltage assigns the coil connection to be parallel. Suggested driving technique: drive the P532 with constant voltage applied to an IC (SGS L 293), using a 2-phases-on scheme. This supply voltage calculation can be done as the following. a) Required torque = Nm (4.56 oz. in.) Let's use a 1.5 factor to get a more conservative system. It becomes: T s = 1.5 x = Nm (6.76 oz. in.) b) The required number of ampere-turns; torque is related to the number of ampere-turns in the coils. With the influence of the detent torque subtracted out, the running torque, which is times lower than the holding torque, is Nm. A running torque of Nm consequently needs the holding torque to be x 2 = Nm (9.57 oz. in.) This torque can be reached if the number of ampere-turns in the 2 phases is 100 A-T. C) Required supply voltage The voltage calculation is referred to It is difficult to use this differential equation as it is. Our purpose is to get an idea of the supply voltage and the following approximation will give it close enough E = Rl + E emf 399

11 Normally is not negligible above 1000 steps/s. but it is hard to figure out. With 100 A-T input power, the temperature raise is approximately 10ºC, the phase resistance the becomes R = 6 ( x 10) 6.25 ohms then The voltage drop in the transistor is about 1V; finally E = 14V The experiment shows that the actual value must be E = 15V If a 10Ω series resistor is used to improve dynamic performances, then An analog experiment indicates E = 19V A further experiment result is the maximum running torque Nm (5.92 oz.in.) slight less then expected. The difference represents the losses inside the motor which we did not take cared of.* The above calculation is only a guide and cannot replace experiment. An undesirable resonace frequency cannot especially be predicted by the above formulas. *If the motor is running at 400 steps/s with 15V supply voltage (400 steps/s is the frequency when the acceleration ramp starts), then the back emf is only 3.6V. It means that the current will raise to 1.6A. The chip cannot tolerate this current very long; consequently one should not leave this frequency for more than one step. If the motor is suddenly stopped, the current becomes very high and must be switched off by using the inhibit function of the IC. When the series resistor is connected this situation is not as critical. 400

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