Since the 1970s, linear motors have directly driven high-speed motion systems. Their operation is similar to that of their cylindrical cousins, as they physically resemble flattened rotary motors, split open along the axis of rotation. But linear motors convert electrical power directly into translational movement — eliminating the mechanical transducers such as ballscrews and belts that complicate accurate positioning.

All linear motors make smooth strokes, but the steppers are unique in that they use pulses of excitation current for precisely defined linear position increments. Input is not dc or ac; it is pulsed current that flows to motor phases for metered steps of motion. Even with this basic open-loop control using simple controller electronics, linear steppers position with high resolution — to 5 mm and better.

Linear steppers fall into two categories: Variable reluctance and hybrid types. Mechanically, the two are similar, consisting of a primary (or forcer) and secondary or platen. Their platens are identical, made of low-cost ferromagnetic steel plate. Force-producing magnetic flux travels in transverse yoking paths, consisting of alternating teeth and slots. However, as we'll soon explore, the forcers of linear variable reluctance and hybrid steppers differ in both construction and electromagnetic operation.

Variable reluctance types

Variable reluctance is the original linear motor design. The forcer consists of phases (with teeth) and laminated stacks with no permanent magnets. The phase coils are nestled into the slots; a phase is associated with one or more teeth. To boost electromagnetic coupling between the forcer and platen (and minimize core losses) the stack material is made of laminated, low-carbon magnetic silicon steel. It's cut in either a U or E profile. The platen consists of photochemically etched teeth on a steel bar, filled with epoxy and ground smooth.

How do variable reluctance linear motors work? Without permanent magnets, the only control on variable reluctance types is input current. It's fed into the motor in different phases as pulses of current. Input current switches on and off at angles to different motor phases to generate thrust force by electromagnetic reluctance. The forcer is constantly moving from positions of high to minimum reluctance. The latter positions occur where the tooth of the forcer aligns with the tooth of the platen. In variable reluctance linear steppers, the physical distance between phases must be:

Where M = Number of motor phases

τt = Tooth pitch

n = Integral number

The fluxes generated by a two-phase reluctance motor in phase A and B are:

Where ΛA, ΛB = constant component of magnetic permeance in the relative poles of phases A and B

ΛA1, ΛB1 = fundamental component of magnetic permeance in the relative pole of phases A and B, respectively.

Reluctance force generated by a pole in the motor is:

Where mmf = magnetomotive force required by the motor

Λδ = airgap permeance

Then, the thrust reluctance force generated by the pole 1 in phase A is:

The reluctance force generated by the other poles can calculated in the same way. To enhance the force density of these motors, airgap permeance is increased; this maximizes the difference between maximum and minimum permeances of the motor's flux loops.

Note that the maximum value of reluctance force is proportional to the square of magnetomotive force, which is phase current multiplied by the number of turns in a coil: Fm = (Im N)2 and airgap permeance. However, this is limited by thermal motor loading — which restricts the phase current and mmf into to the motor.

Because phase current is limited, so too is motor force — so linear variable reluctance steppers are medium step-angle electromechanical devices usually used for high speed applications and coarse positioning, with low to medium load requirements.

Hybrid linear operation

Linear hybrid stepper forcers include permanent magnets. The forcer stack is similar to those of variable reluctance types, but between the two poles of the U-shaped stack there must be a distance:

Where τ = tooth pitch

ts = tooth width

n = integral number

This ensures that the electrical offset between phases is correct for proper motor operation.

In hybrid linear steppers, energy (and the relative magnetic fluxes generated) is derived from the current into forcer phase coils and the permanent magnets. Again, as in variable reluctance types, thrust force is related to the variation of magnetic loop electromagnetic reluctance. However, in hybrids this force is accompanied by rare-earth permanent magnet forces, which help generate flux and thrust force for higher force density.

If high harmonics are ignored, the flux generated by permanent magnets in each pole or tooth for a phase are:

Where ΨP = average flux generated by the permanent magnet in a pole

ΨP1 = fundamental flux generated by permanent magnet in a pole.

Interestingly, the thrust force generated by the linear hybrid stepper is proportional to ΨP1, and mmf: NP IA.

Stepper motor drivers

For simplicity, we just analyzed motors in which only one phase is excited at a time. In practice, this kind of excitation has limitations: For starters, it has low thrust-force density and makes for sluggish motion. Too, in hybrid linear steppers there is a force from permanent magnets that resists motion. But exciting multiple phases so that one phase has current enough to generate thrust and the second phase has current sufficient in the opposite direction to minimize and even eliminate this resistant force.

Once phase current rotates with an electric cycle, the motor moves with a tooth pitch τt. This makes the flux in pole 4 increase gradually from Φm/2 to Φm and the flux in pole 3 decrease gradually from Φm/2 to zero. At the same moment, the flux in pole 1 decreases gradually with the slow reduction of current in phase A. When this phase A current equals that of phase B, the forcer moves with τt/8. The other stages are similar.

Often, linear stepper systems must reduce move times by accelerating and traveling quickly. Maximum acceleration is the fastest a series of high-frequency phase current pulses can bring motor movement to the rated velocity without loosing step positions. (Maximum deceleration is defined similarly, but for slowing.) Friction always makes maximum acceleration slightly lower than maximum deceleration. Both, however, are highly dependent on the electromagnetic coupling between forcer and platen, preload, and movable-mass payload.

In driving and controlling a stepper motor system, the maximum driving frequency (either for supply voltage or current input) is determined and limited by the maximum acceleration/deceleration.

Closed-loop stepping

In applications necessitating high speed, closed-loop control prevents losing steps. A position verification sensor (PVS) or sensing devices verify position and detect stalls to increase running stability, especially at high speed. A PVS confirms that moves match the number of steps commanded. It operates as an incremental encoder to recognize lost steps and allows the controller to move the forcer to a desired position and hold the forcer in a commanded stop position with holding force.

For the ultimate linear machine, this closed-loop control can be combined with microstepping. Microstep control is the use of many very small, consistently wide pulses of excitation to form sinusoidal or cosinusoidal waveforms for phase current. Input current can go to one, two, or more phases at a time. Microstepping for linear motors is widely available, thanks to motor electronics and drivers supported by microprocessors, digital signal processor (DSPs) and other electronic devices. This technique is useful in applications necessitating 5, 1, 0.5, and even 0.1 µm accuracy.

Assuming the motor moves one tooth pitch width τt by Nm current signals, motor resolution RE ∞ τt/Nm. Therefore, for high motor resolution tooth pitch must be reduced and the number of microstepping signals Nm increased with controls.

Welcome to flatland

Hybrid steppers generate more force density than variable reluctance types, so they're most common. Most are single-axis units, used in wire-bonding machines, die bonders, wafer probes, and PCB drillers for their linear accuracy and acceleration capabilities. Single-axis linear stepper motors are usually used in open-loop positioning.

Hybrid technology lends itself to planar stages as well. Dual-axis hybrid steppers consist of four forcer assemblies that allow sliding in any direction on a plane. Each has two coil assemblies for phases A and B for eight coil assemblies in total. For electromagnetic and mechanical balance, the two forcer assemblies used for the X axis are mounted in an alternating pattern. (This provides balanced thrust for X-axis movement.) Similarly, the Y-axis forcer assemblies are mounted orthogonally to the first two. (In contrast, single-axis coil assemblies for the axes are usually mounted adjacently for mechanical balance.) Air bearings float the forcer above the platen, and the forcer surface is lapped for flatness, to help the air bearings operate properly. The inherent attractive force (from the magnets) between forcer and platen serves to preload these bearings.

The motors accelerate up to 2gs with repeatability to 5 µm, and resolution to 5 µm for two-phase motors — and 2.5 µm for four-phase motors.

Dual-axis linear steppers are most commonly used in numerical machine tools and robotics that require multi-axis motion.

Dr. Lin is a Senior Member of IEEE. For more information on linear step motors, visit baldor.com.

Variable reluctance: Straight up

Let's consider a two-phase linear variable reluctance motor and see how it makes one move. This is accomplished in four steps. Its phase A has two poles (1 and 2) as does phase B: 3 and 4. Each phase's coils are nestled in the slots between the phase's poles. Each pole has two teeth respectively.

During step one, phase A has current in the positive direction. Reluctance force generated makes the two teeth of pole 1 align fully with the relative teeth on the platen, while the two teeth of pole 2 fully misalign with the platen teeth near them. At that moment, phase B has no current and all four of its teeth are in various degrees of partial misalignment with the platen teeth.

During step two, phase B has positive current. The flux its current generates is directionally the same as that going through pole 4 — so the reluctance force generated makes the two teeth of pole 4 fully align and the two teeth of pole 3 fully misalign with their relative platen teeth. Because phase A doesn't have current and its four teeth are in various degrees of partial misalignment, it makes the forcer move backward by ¼ the tooth pitch.

During step three, phase A has current in the negative direction and phase B has no current at all. The main fluxes generated are the same directionally as that going through pole 2. Here, the four teeth of phase B are all partially misaligned with platen teeth, so it makes the forcer move backward by another 1/4 tooth pitch.

During step four, the phase B has negative current in direction and phase A has none. The main fluxes generated by current in phase B are the same as through pole 3. Phase A teeth (in various degrees of misalignment) make the forcer move backward with another 1/4 tooth pitch. Then the cycle returns to the situation in step one, and repeats.