Electronics Guide

Pole Pitch and Synchronous Velocity

The pole pitch, conventionally written as the Greek letter tau, is the distance along the track between adjacent magnetic poles. It plays the role that pole count plays in a rotary machine. A three-phase winding excited at frequency f produces a magnetic field that travels along the track at a synchronous velocity equal to twice the pole pitch times the frequency. A motor with a 24-millimeter pole pitch driven at 100 hertz therefore produces a field traveling at 4.8 meters per second. The relationship is exact and contains no gear ratio, which is why the drive's DC-link voltage translates so directly into a maximum usable velocity.

Force replaces torque as the output variable, and the thrust constant, expressed in newtons per ampere, replaces the torque constant. As in rotary machines, the thrust constant and the back-EMF constant are the same physical quantity in different units, a consequence of energy conservation. Sizing calculations that a rotary designer performs in torque and inertia are performed here in force and mass, and the moving mass includes the carriage, the payload, and any cable or hose the carriage drags with it.

Forcer, Track, and Travel

One part of the machine moves and the other stays fixed, and the designer chooses which. In a moving-coil arrangement the wound assembly, usually called the forcer, rides on the carriage while a passive magnet track lies along the machine base. The moving mass is low, which favors acceleration, but power, feedback signals, and often coolant must be routed to a moving part through a cable carrier whose flex life becomes a maintenance item. In a moving-magnet arrangement the windings are fixed and the carriage carries only magnets, so nothing flexes and nothing needs cooling on the carriage, at the cost of energizing a longer stator.

Length is the other choice. A short primary sliding along a long secondary is economical for long travel, because only the moving part contains the expensive active material. A long primary switched in segments costs far more per meter but permits many independently controlled carriages on one track, which is the basis of modern independent-cart transport systems. Track length in a short-primary design is limited only by the cost of extruded magnet sections and the accuracy with which they can be joined, since a discontinuity in magnet pitch at a joint appears to the controller as a commutation error.

End Effects

A rotary machine has no ends. A linear machine has two, and they matter. The magnetic circuit is interrupted where the iron of the forcer stops, so the flux distribution near the entry and exit edges differs from that in the middle. In induction machines this produces the longitudinal end effect: the secondary conductor entering the field must build its induced current from zero, and the current it carries at the exit edge must decay, both of which absorb energy and reduce thrust. The penalty grows with speed and is a principal reason that high-speed linear induction machines fall short of the efficiency their rotary counterparts achieve.

In permanent-magnet machines the finite length of the iron core produces an end-effect detent force, distinct from ordinary slot cogging, that varies with position at the pole pitch period. Designers attack it by shaping the end teeth, adding auxiliary teeth beyond the last wound slot, or choosing the overall core length so that the entry and exit contributions cancel. Finite element analysis is the standard tool for this optimization, as described under Finite Element Analysis for Power Electronics.

Linear Induction Motors

A linear induction motor drives a passive secondary, typically an aluminum or copper sheet backed by steel, called a reaction plate. The traveling field induces currents in the sheet, and the interaction produces thrust. As in a rotary induction machine, thrust requires slip, so the carriage always travels slower than the field. Single-sided designs place the winding on one side and rely on the steel backing to return the flux; double-sided designs sandwich the reaction plate between two windings, which cancels the normal force and improves coupling but requires access to both sides of the plate.

The defining virtue is the passive secondary. A reaction plate is cheap, needs no magnets, tolerates dirt and impact, and can be kilometers long. The defining weakness is the mechanical air gap, which in practical installations is several millimeters to more than a centimeter, far larger than the fraction of a millimeter a rotary machine enjoys. Magnetizing current rises accordingly, and efficiency and power factor both suffer. Linear induction machines therefore dominate applications where robustness and track cost outweigh efficiency: airport baggage handling and people movers, the linear-induction-propelled rapid transit fleets on the Vancouver SkyTrain, the Kelana Jaya line in Kuala Lumpur, the Beijing Capital Airport Express, and several Guangzhou metro lines, roller coaster launch tracks, and the Electromagnetic Aircraft Launch System, which replaced the steam catapult on the United States Navy's Gerald R. Ford class carriers. Toronto's Line 3, an early example of the same technology, ran from 1985 until its closure in 2023.

Permanent Magnet Linear Synchronous Motors

The permanent-magnet linear synchronous motor is the workhorse of precision motion. Rare-earth magnets alternate in polarity along the track, the forcer carries a three-phase winding, and the carriage moves in exact synchronism with the traveling field. There is no slip and no secondary conduction loss, so efficiency and force density exceed the induction alternative by a wide margin. Two construction styles divide the market.

Iron-core designs wind the coils on a laminated steel core. Force density is high because the iron concentrates flux across a small gap, and the thermal path from coil to mounting surface is short. The price is a large magnetic attraction between the core and the magnet track, commonly several times the rated thrust, which must be carried by the linear guides and the machine frame for the life of the machine. Iron also brings cogging, the position-dependent detent force produced by the interaction of slots and magnets.

Ironless designs, often built as a flat coil assembly running inside a U-shaped channel of opposing magnets, remove the core entirely. With no iron there is no cogging and no net attraction force, so the bearings carry only the payload and the motion is exceptionally smooth. The trade-off is lower force density, a poorer thermal path from the coils to any heat sink, and a low winding inductance that stresses the drive's current loop. Halbach magnet arrangements, which rotate the magnetization direction progressively so that the field reinforces on the working side and largely cancels on the other, recover part of the lost force density and are common in ironless and levitated designs.

Tubular Linear Motors

Wrapping the geometry around a single axis produces a tubular motor: a cylindrical magnet rod, usually a stainless tube containing stacked magnets, sliding through an annular coil assembly. Because the magnetic circuit is axially symmetric, the radial forces cancel and the bearings carry no net magnetic attraction at all. Flux linkage is efficient, and the winding is simple to manufacture. The limitation is inherent to the shape: the rod must be supported at its ends, so stroke is bounded by rod stiffness, and the design suits single-axis duty such as pressing, testing, and assembly rather than long transport.

Linear Stepper and Reluctance Machines

Linear stepper motors, descended from the planar Sawyer motor, move a toothed forcer across a toothed steel platen. Excitation shifts the forcer one tooth pitch at a time, and an air bearing supported by the platen surface carries the load. Two orthogonal forcer sets on one platen give planar motion over an area rather than along a line, without any stacked axis. Like their rotary relatives, these machines can run open loop, which suits inspection and handling equipment where cost matters more than dynamic stiffness. Switched reluctance variants dispense with magnets entirely and generate force by the tendency of the moving part to align with the excited pole, an approach attractive where magnet supply risk or high temperature rules out rare-earth material.

Voice Coil Actuators

For strokes of a few millimeters to a few centimeters, a voice coil actuator is usually the better answer than a commutated linear motor. A single coil moves in the radial field of a permanent magnet, and force is proportional to current over the working stroke with no commutation whatever. The drive is a simple bipolar current amplifier, the force is free of cogging and ripple, and the bandwidth is limited chiefly by moving mass. Voice coils position optical elements, drive the read-write head actuators in disk drives, provide the fine stage in coarse-fine positioning architectures, and supply the legs of fast steering mirrors and active vibration isolators. Related devices appear under Actuators and Final Control Elements.

Commutation From Linear Position

A rotary servo derives the electrical angle from a rotor-mounted encoder or resolver, and the mechanical-to-electrical mapping is fixed by the pole count. A linear motor has no rotor and no rotary sensor. The electrical angle is instead computed from the linear position: one electrical cycle corresponds to one pole pair, so the angle advances through a full 360 electrical degrees over twice the pole pitch. The linear encoder is thus doing two jobs at once, closing the position loop and supplying the commutation reference, and any encoder fault corrupts both.

This raises a problem that rotary drives largely avoid. At power-up with an incremental scale, the drive knows relative position but not the absolute electrical angle, and applying current at the wrong angle produces either no force or, worse, force in the wrong direction and a runaway. Several methods resolve it. Hall-effect sensors on the forcer give a coarse absolute angle immediately. An absolute linear scale removes the problem entirely, at higher cost. Where neither is available, drives perform a phase-finding routine at enable: the wake-and-shake method applies current at a series of trial angles and observes the resulting small motion, while saturation-based methods inject high-frequency or pulsed voltage and infer the angle from the anisotropy of the inductance without appreciable movement. Phase finding must be interlocked so that a failed or aborted routine cannot leave the axis enabled with an unknown angle, and vertical axes must be braked while it runs.

Current Loop, Inductance, and Bus Voltage

Ironless windings have very low inductance, because no iron core is present to raise the permeance the winding sees; the figure is a small fraction of that of a comparable iron-core machine. Low inductance is excellent for current-loop bandwidth but poor for ripple, because the current ripple produced by a given switching voltage is inversely proportional to inductance. Amplifiers intended for ironless motors therefore switch at tens of kilohertz rather than the few kilohertz a general-purpose industrial inverter uses, and installers sometimes add series inductors to keep ripple current, and the eddy-current heating it causes, within bounds. Iron-core motors present the opposite condition and behave much like a conventional permanent-magnet servo motor.

DC-link voltage sets the velocity ceiling. Back-EMF grows in proportion to velocity, and once it approaches the voltage the inverter can synthesize, no further current can be forced into the winding and thrust collapses. Because there is no gearbox to trade force for speed, the only remedies are a higher bus voltage, a motor wound with fewer turns, or field weakening, which in an iron-core machine buys a modest extension at the cost of additional loss. Sizing a linear axis therefore couples the mechanical profile and the electrical supply far more tightly than a geared axis does. The underlying hardware is covered under Power Stage Design, and the loop mathematics under Control Algorithms.

Thermal Limits Set the Continuous Force

A rotary motor spins, and the moving surface stirs air across its own housing. A linear forcer creeps along a track and does nothing of the kind. Its losses are almost entirely resistive heating in the coils, and its continuous force rating is whatever current the winding can carry indefinitely without exceeding its insulation and magnet temperature limits. Manufacturers accordingly publish separate ratings for natural convection, forced air, and liquid cooling of the same motor, and the liquid-cooled figure may be roughly double the unassisted one.

Heat matters beyond the motor itself. The forcer sits inside the machine's metrology loop, so the heat it injects expands the structure and the encoder scale, and thermal drift can exceed the positioning error the machine was built to achieve. Precision machines therefore route coolant through the forcer, insulate it from the structure, or use ironless motors whose losses are lower for a given force. Protection is by embedded thermistors or thermal switches wired to the drive, and correct sizing uses the root-mean-square force over the duty cycle rather than the peak, exactly as for rotary servo drive systems.

Sources

Ripple arises from several mechanisms with different spatial periods, and identifying which is present is the first diagnostic step. Cogging, or detent force, exists with no current flowing at all and comes from the interaction between the slotted iron core and the magnet track; its period follows the slot and magnet pitch. End-effect detent, described above, follows the pole pitch. Reluctance variation adds a component that depends on both position and current. Commutation ripple, by contrast, is produced by the electronics and the winding together: harmonics in the back-EMF waveform mean that sinusoidal current does not yield constant force, and offset or gain mismatch between the phase current sensors produces force variation at the first and second harmonics of the electrical cycle. Manufacturing tolerance in magnet placement and in the joints between magnet track sections adds an irregular component that repeats only over the full stroke.

Design Countermeasures

Machine designers attack ripple at the source. Skewing the magnets or the core teeth by roughly one slot pitch smears the cogging over position and reduces it substantially, at a small cost in thrust. Semi-closed or magnetically bridged slots reduce the permeance variation the magnets see. Fractional-slot concentrated windings raise the least common multiple of slot and pole numbers, which increases the cogging frequency and lowers its amplitude. Auxiliary teeth and optimized end-tooth geometry cancel the end-effect component. Where ripple must be eliminated rather than reduced, the ironless machine remains the definitive answer, because a coil assembly with no iron has no cogging mechanism at all.

Control Countermeasures

Whatever ripple survives the mechanical design must be handled by the controller, and its greatest weakness as a disturbance, its repeatability, is also the lever against it. Because cogging is a deterministic function of position, it can be measured once during commissioning and stored as a lookup table indexed by position or electrical angle, then injected as a feedforward current correction. Iterative learning control generalizes this for repeated motion profiles, refining a correction signal over successive passes until the tracking error converges. Repetitive control does the same for periodic operation by embedding a delay line in the loop that provides high gain at the disturbance frequency and its harmonics. Disturbance observers estimate the unmodeled force from the measured current and acceleration and cancel it in real time. Simply raising loop gain also suppresses ripple, but only until the first structural resonance limits the achievable bandwidth, which in a direct-drive axis arrives early.

Position Feedback

Linear encoders, optical or magnetic, provide the position signal. Optical scales offer the finest resolution and the lowest interpolation error but demand cleanliness; magnetic and inductive scales tolerate coolant, chips, and vibration at coarser resolution. Most scales output analog sine and cosine signals at a coarse grating period that the drive interpolates electronically, and the residual periodic error of that interpolation, sometimes called subdivision error, appears directly as velocity ripple. Distinguishing it from cogging is straightforward in practice, because the two have different spatial periods: interpolation error repeats at the scale grating period, cogging at the slot or magnet pitch.

Resolution also sets a noise floor. The velocity signal is obtained by differentiating position, so quantization steps become velocity noise that the velocity loop amplifies into audible current chatter. Absolute scales remove the homing and phase-finding sequence at power-up. Thermal expansion of the scale itself is a first-order error source in precision machines, which is why scales are mounted to expand from a defined fixed point and why the thermal expansion coefficient of the scale is matched to the machine structure or compensated in software. Feedback devices are treated in detail under Encoders and Position Sensors.

Bearings, Structure, and Reaction Forces

Linear guides carry the payload, the process force, and, for an iron-core motor, the constant magnetic attraction to the track. That attraction preloads the bearings continuously, which improves stiffness but consumes bearing life, and it makes assembly hazardous, since an unrestrained forcer will slam into its track. Air bearings eliminate friction and stiction entirely for the highest-precision stages, at the cost of a clean, dry air supply and of very low damping.

The machine frame absorbs the reaction to every acceleration, because Newton's third law is not negotiable and no gearbox is present to soften the impulse. High-acceleration stages therefore excite frame resonances that couple straight back into the encoder, and controller bandwidth is bounded by the lowest such mode. Countermeasures include notch and low-pass filters in the velocity loop, acceleration and jerk feedforward that reduce the error the feedback loop must correct, stiffer or better-damped structures, and, in the most demanding machines, a reaction mass that is allowed to recoil freely so that the disturbance never reaches the metrology frame.

Gantries and Multiple Forcers

Wide axes commonly use two forcers on parallel tracks driving a single crossbeam. Commanding them independently invites the beam to rack, so drives provide a gantry mode that closes a position loop on the average of the two encoders and a second, much stiffer loop on their difference, holding yaw near zero. A related arrangement places several forcers in series on one long track to multiply force, in which case the drive must be told the mechanical phase offset between them so that all contribute in the same electrical direction.

Segmented long-stator systems invert the usual arrangement. The track is divided into short, individually driven winding zones, and passive magnet carriers ride along it, each tracked by the controller and handed from one zone to the next as it travels. Because the carriers are independent, the track becomes a programmable conveyor on which spacing, velocity, and grouping change under software control. Commercial independent-cart systems built on this principle now serve packaging, filling, and assembly lines, an application discussed further under Material Handling and Conveyor Systems.

Attraction, Repulsion, and Stability

Two approaches dominate. Electromagnetic suspension attracts a ferromagnetic rail from below with controlled electromagnets, holding a small gap of a few millimeters. It works at zero speed and consumes little power, but Earnshaw's theorem guarantees that no arrangement of static fields can hold a ferromagnetic body in stable equilibrium, so the gap is inherently unstable and survives only through continuous feedback: a gap sensor, a controller running at kilohertz rates, and a current amplifier fast enough to correct before the body moves appreciably. Loss of control means contact, so the electronics are duplicated and touchdown surfaces are provided.

Electrodynamic suspension instead induces currents in a conductive track by relative motion, and the resulting repulsion is passively stable but requires speed to develop and produces magnetic drag. Diamagnetic and superconducting arrangements escape Earnshaw's restriction outright, which is why flux pinning in a high-temperature superconductor can hold a stable gap with no active control at all. These vehicle-scale mechanisms, including null-flux guidance and the superconducting maglev systems that use them, are covered under Maglev Transportation Systems.

Magnetic Bearings and Levitated Stages

Active magnetic bearings apply the electromagnetic suspension principle to rotating and sliding machinery. Position sensors measure the gap, a digital controller stabilizes the unstable plant, and power amplifiers drive the bias and control currents. The reward is operation with no contact, no lubricant, and no wear, in vacuum or in a corrosive process gas, at speeds no rolling bearing would survive.

The most demanding application is semiconductor lithography. Wafer and reticle stages in extreme-ultraviolet scanners operate in vacuum, where lubricated bearings would outgas and contaminate the optics, and they must position over a plane while settling to nanometer-scale accuracy in milliseconds. One answer is the magnetically levitated planar motor: a single moving body carrying magnets above a two-dimensional coil array, controlled in all six degrees of freedom at once, with no stacked axes and no bearings of any kind. The same coil array supplies both the long strokes in the plane and the fine correction in the remaining degrees of freedom, which removes the stacked coarse and fine stages earlier machines carried. Reticle stages, which must scan in synchronism with the wafer, use closely related levitated actuators. The manufacturing context appears under Semiconductor Wafer Fabrication.

Precision Manufacturing and Metrology

Wafer steppers, wire bonders, die attach equipment, flat-panel inspection systems, and coordinate measuring machines all depend on linear motors for the combination of nanometer resolution, high throughput, and freedom from wear particles. In these machines the motor is chosen for smoothness before force, which favors ironless and levitated designs, and the thermal budget of the drive is treated as a metrology parameter.

Machine Tools and Laser Processing

High-speed milling and laser cutting benefit from the acceleration a direct drive provides, because cycle time in contour work is dominated by how quickly the machine changes direction rather than by top speed. Linear motors also remove the ball screw's wear and thermal growth from the accuracy budget. The countervailing concerns are the absence of the screw's inherent self-locking on vertical axes, the need to keep ferrous chips away from an exposed magnet track by covers and seals, and the higher servo bandwidth required to keep a stiff axis stable. See Computer Numerical Control (CNC) Systems and Laser Processing Systems.

Packaging, Handling, and Automation

Independent-cart transport has changed the economics of flexible packaging lines. Because each carrier is addressed individually, a changeover that once required mechanical retooling becomes a software parameter, and product spacing can vary along a single track. Pick-and-place heads, gantry robots, and test handlers use linear axes for the same reason: throughput scales with acceleration, and acceleration scales with the removal of transmission mass. Related material appears under Industrial Robotics and Automation.

Transportation and Launch Systems

At the largest scale the same machines move vehicles. Linear induction motors propel rubber-tired and steel-wheeled transit vehicles where grade climbing or tunnel cross-section rules out adhesion drive, launch roller coasters, and accelerate aircraft from carrier decks. Linear synchronous motors, with magnets or coils on the vehicle and a segmented stator in the guideway, propel high-speed maglev vehicles and the most powerful ride launches. Conventional adhesion-based traction is covered under Railway Traction Systems.

When a Linear Motor Is the Right Choice

A direct drive is not always the economical answer. For long travel at modest speed and accuracy, a belt or a ball screw remains far cheaper, because the linear motor's cost grows with track length while the screw's cost grows only with the length of an extruded bar. Linear motors win where the requirement is high acceleration, sub-micrometer accuracy, very long stroke at high speed, extreme cleanliness, or freedom from maintenance in an inaccessible location. Sizing proceeds from the motion profile: compute the peak force from the required acceleration and the total moving mass, compute the root-mean-square force over the complete duty cycle including dwell, verify that the peak lies within the motor's intermittent envelope at the required velocity, and then confirm that the DC-link voltage supports the back-EMF at top speed.

Commissioning

Commissioning follows a fixed order, and skipping a step is the usual cause of trouble. Confirm that the encoder counts in the same direction that positive current drives the forcer, since a reversed sense turns the position loop into a positive feedback loop. Establish the commutation angle by Hall sensors, an absolute scale, or a phase-finding routine, and verify it by checking that force per ampere is maximized and symmetrical in both directions. Set current limits from the motor's thermal data rather than the amplifier's rating. Tune the current loop first, then velocity, then position, identifying resonances with a frequency response measurement and placing notch filters before raising gain. Finally, map and compensate cogging if the application requires smooth low-speed motion.

Common Faults

A runaway at enable almost always indicates a wrong commutation angle or a reversed feedback polarity, and a properly configured drive limits the damage through following-error and velocity-error trip thresholds. Overtemperature trips usually trace to duty-cycle underestimation, to a blocked or absent cooling path, or to an ambient temperature above the rating. Velocity ripple that appears only at low speed points to cogging or encoder interpolation error, separable by their spatial periods; ripple synchronized with the electrical cycle instead points to current-sensor offset or gain mismatch. Intermittent position faults on a moving-coil axis often begin as flex-life failures in the cable carrier, and the encoder cable is usually the first casualty. Loss of thrust after an overtemperature event suggests partial demagnetization, which is permanent. Above all, a vertical linear axis has no self-locking element: it requires a mechanical brake that engages on power loss, on emergency stop, and during any phase-finding routine.