Motion System Design

Direct flight to power

Brushless motor construction includes stator windings and permanent-magnet rotors, similar to that of ac permanent-magnet synchronous motors. Too, in brushless dc motors the commutation (that process which converts input direct current to alternating and properly distributes it to each winding) is generated with non-wearing transistors and other semiconductor devices. However, brushless dc motors incorporate Hall elements, encoders, or optics to detect rotor position and produce signals for control.


Knowing actual motor position is essential for precision positioning. So say we have a three-phase unipolar-operated motor (a common and efficient design) that uses optical sensors (phototransistors) as position detectors. If three phototransistors are placed on the end plate at 120° intervals, they can be exposed to light in sequence through a revolving shutter on the motor shaft. Then the logic circuit can be set up so that when the north pole of the rotor faces salient pole P2 of the stator, phototransistor 1 detects light, and turns transistor 1 on. In this state, the south pole created at salient pole P1 by the electrical current flowing through winding W1 attracts the north pole of the rotor to move it. When the north pole comes to face the salient pole P1, the shutter (coupled to the shaft) shades phototransistor 1, exposes 2 to light, and current flows through the transistor 2.

When a current flows through the winding W2 and creates a south pole on salient pole P2, the north pole in the rotor revolves to face that pole. At this moment, the shutter shades phototransistor 2, and the phototransistor PT3 is exposed to light. This steers current from winding W2 to W3. Thus salient pole P2 is de-energized, while salient pole P3 is energized to create the south pole. Hence the north pole on the rotor travels from P2 to P3 without stopping.

Bipolar drive

When a three-phase brushless motor is driven by a three-phase bridge circuit, efficiency (ratio of mechanical output power to electrical input) is maximized. Why? An alternating current flows through each winding, a bit like that on an ac motor, as a bipolar drive — so windings are alternatively energized as south and north poles.

Say we're still using optics for detecting rotor position, and six phototransistors are placed on our motor's end plate. What is the relationship between the on/off transistor state and phototransistor signals? The simplest relation is when the logic sequencer is set to turn on a transistor when the corresponding phototransistor is exposed to light.

Picture electrical current through transistors 1, 4, and 5 on a motor with 3-connected windings, with battery voltage on terminals U and W, and zero potential at terminal V. In this state, current flows from U and W to V. The rotor is positioned such that field flux has a 90° angle with respect to the stator's magnetic field.

In such a state, clockwise torque is produced on the rotor. After it turns through 30° the phototransistor 5 is turned off and 6 on to make the stator's magnetic pole revolve 60° clockwise. Thus when the rotor's south pole approaches, the stator's south pole recedes to create a continuous clockwise rotation.

Rotational direction may be reversed — by arranging the logic sequencer so that when a certain photodetector is exposed to light, the corresponding transistor is turned off. (Then when a phototransistor is not exposed to light, the corresponding transistor is turned on.)

After 30° of rotation transistor 2 is turned off and 1 on. At this point, the field has rotated 60°. As the rotor produces another counterclockwise torque, the counterclockwise motion continues in the sequence of a→ b→ c→ d to produce continuous counterclockwise motion.

In other axis positioning systems, dc motor position is detected with a magnetic pulse encoder that emits so many pulses per rev — 256, for example. One setup includes a magnetic annular gear attached to the rotor, and a hybrid circuit. A sensor integrated into the circuit converts the magnetic field differences between the top land and the tooth root into electrical signals. This makes for two-phase quadrature rectangular pulse signals, which are then processed by system control.

These compact pulse encoders can be directly mounted on the motor, fitted to the free end of the motor shaft. And connections between the pulse encoder and the motor routed in a common ribbon cable simplify electrical connection considerably.

The speed-torque relationship

Still assuming ωL is much smaller than R and position feedback keeps V and E (and hence I) in phase, the voltage equation can be simplified in algebraic form as V = E + RI. Substituting relations of E~wr and T~I we obtain:



The strengths of brushless dc motors can be fully leveraged in small systems that require delicate motion and the highest of accuracies. For example, in laser printers, a polygon mirror is coupled directly to the motor shaft and its speed controlled very accurately between 5,000 to 40,000 rpm. When an intensity-modulated laser beam strikes the revolving mirror, the reflected beam travels according to the position of the rotor at that moment. Therefore, this reflected beam can be used for scanning. How is an image is produced? The drum has a photoconductive layer on its surface, with its photosensitivity tuned to the laser wavelength. The latent image of the information to be printed is formed on the drum surface by the laser, and then attracts toner. The developed image is then transferred to paper and fixed using heat and pressure.

Another brushless dc motor application is on flexible flying probe systems, in which probes are moved to test pads for testing of electronic circuits. (These are replacing conventional needle-bed adapters, because high packing density in conjunction with increasingly short product life cycles often make it impossible to recoup the initial investment in adapter-specific setups.) They're suitable for automatic prototype testing, small-scale or varied production, or again, where needle-bed adapters are too costly.

Brushless dc servomotors contribute to the continued development of flying probes. One company, Scorpion Technologies, Hamburg, makes these testers to include dc motors for testing circuits with hundreds of connectors or components. On the X and Y axis the accuracy is ±10 µm, while on the Z it's ±100 µm. One of their multifunctional backplane testing systems even allows automatic testing of large backplanes using CAD data.

First, planar drives position moving joystick probes over test pads. With the help of a sophisticated three-axis positioning system, test needles or cups are moved freely along all axes to exact, definable angles. The relevant test coordinates can be calculated on the basis of the CAD data and utilized for positioning. Reliable contact can even be made with DIN connectors, VHDM or HMZD connectors, and DIP connectors.

This operation calls for lightweight but powerful drives — as flying probes are designed for up to 12 tests per sec. Here, brushless dc servodrives with rare-earth rotors and skewed winding make for especially high dynamic response and power for rotary speeds to 40,000 rpm, and output power of 11 W. Service life is only restricted by the life of ball bearings and electronics — to 10,000 operating hours. A spindle directly attached to the drive provides the speed reduction required.

Another dc motor application is in hard drives. The aluminum surface of a disk drive is coated with a magnetic film. Data is read and written by a magnetic head floating about 0.5 mm from the disk surface, suspended by airflow from the rotating disk. Because this airflow maintains the constant gap, the head can touch the disk and cause damage to the magnetic film when the disk is stopped or slowed down. To prevent this, spindle motors must satisfy strict conditions when decelerating. As the main secondary memory device of the computer, hard disks provide great information storage capacity and short access time. In fact, small brushless dc motors have largely replaced ac synchronous motors as disk-drive spindle motors as well, and have contributed to miniaturization and increased computer memory capacity. And although brushless dc motors are more complicated structurally (because of Hall elements, ICs on the stator, circuitry, and the like) they stay cooler and don't require amplifiers for operation.

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Equivalent circuit equations

Shown here is a per-phase equivalent circuit, where λm is the flux linkage of stator winding per phase due to the permanent magnet.

For steady-state conditions (assuming v and e are sinusoidal at frequency ω) our equivalent circuit includes values:

X = ωL and

V, I, E, and λm = Phasors with rms amplitudes. The steady state circuit equation is:

V = E + (R + jωL)I

For a maximum mechanical power at a given speed, I and E are in phase. This also gives maximum torque/ampere — minimum current/Nm. A brushless dc motor with position feedback (from the rotor) via Hall devices, optical devices, or encoders maintains a particular angle between V and E. E is in phase with rotor position, and V is determined by the inverter supply to the motor. Assuming that ωL is much smaller than R, when λ is in phase with E, V is also in phase with E. Thus the circuit can be analyzed using magnitudes of E, V, and λ as a dc circuit.

One caveat: When E and λ are in phase, the motor mechanical power output (before friction, windage, and iron losses) is:

where m is the number of phases, |E|, |I|, and |λm| are the amplitudes of phasors E, I, and λm, and electromagnetic torque is:

where ωr = 2ω/p = Rotor speed in rad/sec, and

p = Number of poles. Then:

The actual shaft output torque is Tload = Tem - Tlosses, where Tlosses = Total torque due to friction, windage, and iron losses. Dropping the amplitude (modulus) signs, we have:

and in terms of rotor speed, E = p/2ωrλm.

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