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Linear motor

A linear motor is an designed to produce linear force and motion directly, rather than rotational , by unrolling the active components of a conventional rotary motor into a linear configuration. This results in a device where the and (or equivalent primary and secondary elements) are arranged along a straight path, enabling thrust generation through electromagnetic interaction without the need for mechanical conversion mechanisms like or belts. Linear motors operate on fundamental electromagnetic principles, such as the in DC variants (where force F = BIL, with B as magnetic flux density, I as , and L as length in the field) or and synchronous effects in AC types. Key types include DC linear motors, which use and permanent magnets or electromagnets for precise ; linear motors (LIMs), which employ a traveling from polyphase AC to induce in a conductive secondary for asynchronous operation; and linear synchronous motors (LSMs), which synchronize a moving with persistent poles on the secondary for higher . These designs offer advantages like high , accuracy, and elimination of backlash, making them suitable for demanding environments. Historically, concepts for linear motors date back to the , with early proposals in the , and a significant advancements in the and 1960s driven by researchers like E.R. Laithwaite, leading to practical implementations in transportation. Applications span high-speed ground transport systems like trains achieving test speeds exceeding 600 km/h (373 mph) and operational speeds up to 431 km/h (268 mph) as of 2025, including China's 600 km/h prototype unveiled in July 2025, industrial automation including conveyors and , precision machining, launch assists, and even pumps for liquid metals. Efficiencies often exceed 85-97% in optimized designs, with power densities supporting applications from small actuators to large-scale propulsion.

Fundamentals

Definition and basic principles

A linear motor is an electric motor that produces linear force or motion directly, rather than rotational torque, by converting electrical energy into linear mechanical work. This configuration eliminates the need for mechanical linkages like belts or screws, enabling direct drive in applications requiring precise linear displacement. The fundamental operating principle relies on electromagnetic interaction between a fixed part, known as the stator, and a moving part, often called the translator or rotor. When electric current flows through conductors in the presence of a magnetic field, it generates a force according to the Lorentz force law. This force propels the translator linearly along the stator. The magnitude of the force is described by the equation \vec{F} = I \vec{L} \times \vec{B}, where \vec{F} is the force vector, I is the current in the conductor, \vec{L} is the length vector of the conductor, and \vec{B} is the magnetic field vector. Key components include the primary part (typically the stator with energized windings or permanent magnets) and the secondary part (the translator, which reacts to the field). A small air gap separates these parts to allow motion without contact, influencing the magnetic flux density and overall efficiency. End effects, arising from fringing magnetic fields at the open ends of the motor, reduce thrust and efficiency compared to idealized infinite-length models by causing uneven field distribution. Conceptually, a linear motor can be visualized as an unrolled rotary motor, where the cylindrical becomes a flat track and the slides along it instead of rotating.

Comparison to rotary motors

Linear motors can be conceptualized as rotary motors that have been "unrolled" along their circumference, transforming rotational into direct linear force without intermediate mechanical linkages. This conceptual equivalence relates the linear force F_{\text{linear}} to the rotary torque \tau_{\text{rotary}} via the effective r of the unrolled structure, given by the equation: F_{\text{linear}} = \frac{\tau_{\text{rotary}}}{r} where r represents the distance from the center of rotation in the original rotary design. Structurally, linear motors differ from rotary motors by eliminating the need for rotary-to-linear conversion mechanisms such as belts, gears, screws, or crankshafts, which simplifies the overall system design and removes sources of mechanical backlash, friction, and wear. This direct-drive approach reduces component count and maintenance requirements, enabling cleaner and more compact assemblies, particularly in precision applications. Operationally, linear motors enable direct production of , achieving higher peak speeds of up to 10 m/s or more and accelerations reaching 10g (approximately 98 m/s²), surpassing the capabilities of most rotary motor systems constrained by conversion inefficiencies. However, their open-ended geometry introduces end effects—non-uniform distributions at the stator's edges due to finite length—which reduce efficiency, particularly at high speeds, and necessitate longer stators to support extended travel distances without performance degradation. In terms of performance trade-offs, linear motors offer higher in short-stroke operations where mechanical conversions would otherwise introduce losses, but they are prone to cogging (or ) forces from magnetic attraction between iron cores and permanent magnets, leading to force ripple that manifests as variations. Additionally, while rotary motors typically provide higher power-to-weight ratios for continuous operation, linear motors exhibit lower over long strokes due to the extended mass required, making them less favorable for applications demanding sustained high power in elongated paths.

Types

Linear induction motors

Linear induction motors (LIMs) feature a primary section composed of polyphase windings, typically three-phase, mounted on a laminated iron to generate a traveling magnetic wave when supplied with . The secondary consists of a solid conductive sheet, usually aluminum or , which may be backed by ferromagnetic backiron to concentrate the and improve performance. This construction enables a large air gap, often 15–30 mm, compared to the smaller gaps in rotary motors, accommodating misalignments and debris. Single-sided LIMs place the primary on one side of the secondary for simpler setups, while double-sided variants position primaries on both sides to produce balanced and minimize lateral forces. In operation, the polyphase currents in the primary create a synchronous traveling at speed v_s = 2 \tau f, where \tau is the pole pitch and f is the supply frequency, inducing eddy currents in the stationary secondary. These currents generate a secondary that interacts with the primary via the principle, producing a net force on the secondary. The motor operates asynchronously, with the secondary velocity v_r lagging behind v_s by a slip s = \frac{v_s - v_r}{v_s}; maximum occurs at slips around 0.1–0.2, and the thrust-velocity curve mirrors the torque-speed characteristic of rotary induction motors. End effects, arising from the finite length of the primary, cause a reduction in effective and at higher speeds. Key characteristics of LIMs include self-starting capability without additional controls, low due to the robust secondary design, and high to contaminants like or , which suits them for rugged environments where precise positioning is secondary. Operating speeds typically range from 1 to 5 m/s in standard designs, though \eta = \frac{P_{out}}{P_{out} + P_{losses}} is moderate (often 70–85%), limited by Joule losses in the secondary conductors (I_2^2 R_2) and losses in the backiron, exacerbated by the large air gap and end effects that increase with . The power factor is generally low (0.6–0.8) owing to high magnetizing requirements and leakage . Variants of LIMs address specific performance needs; the short primary/long secondary configuration energizes a compact primary while using an extended passive secondary, ideal for low-speed, high-thrust scenarios like , as it minimizes length and reduces end-effect losses during . In contrast, the double-sided enhances and force uniformity by symmetrically inducing currents, often used where vertical or lateral stability is important.

Linear synchronous motors

Linear synchronous motors (LSMs) feature a construction where the primary component consists of polyphase windings arranged to generate a traveling , while the secondary component incorporates permanent magnets or DC-excited electromagnetic poles that establish a stationary field with alternating north and south poles along its length. This design necessitates precise alignment between the primary and secondary to minimize losses and ensure effective magnetic interaction. The absence of mechanical transmission elements allows for direct , distinguishing LSMs from rotary-to-linear conversion systems. In operation, LSMs achieve motion at synchronous speed given by v = 2 f \tau, where f is the electrical and \tau is the pitch, resulting in no slip between the traveling field from the primary and the fixed field from the secondary. Thrust is produced through the arising from the interaction of these , enabling high —up to 95% at constant speeds—due to the elimination of slip-related losses. Control is typically managed using variable frequency drives to adjust speed and by varying the input frequency, while end effects at the finite length of the motor can slightly reduce performance near the edges. Key characteristics of LSMs include high in positioning and , attributed to their synchronous , and zero in ideal configurations without ferromagnetic saliency. However, they are sensitive to load variations, as excessive load can cause the motor to lose synchronism and stall. The generated forces comprise a tangential component responsible for and a normal component causing attraction between primary and secondary, which must be managed to prevent excessive wear or misalignment. Among variants, the permanent magnet linear (PMLSM) employs rare-earth permanent magnets in the secondary for high , often exceeding that of iron-core designs, making it suitable for applications requiring compact, powerful actuation. Ironless LSMs, which omit ferromagnetic cores in the primary, reduce force ripple and eliminate cogging by avoiding magnetic and reluctance variations, though at the cost of lower .

Brushed and brushless linear motors

Brushed linear motors operate on principles similar to traditional DC motors but adapted for linear motion, featuring a voice coil-like design where direct current flows through coils positioned in a magnetic field to generate force. The force produced follows the Lorentz force equation F = B I L, where B is the magnetic flux density, I is the current, and L is the effective length of the conductor in the field. Mechanical commutation is achieved using brushes that contact a commutator or linear bar, switching current direction to maintain motion as the forcer moves along the rail. This design is simple and cost-effective for short-stroke applications, providing high force density in compact forms. However, brush wear from friction limits operational speeds and lifespan, often to around 10^6 cycles, while generating sparks and dust that restrict use in clean or hazardous environments. Brushless linear motors, in contrast, employ electronic commutation to eliminate mechanical contacts, using sensors or back (back-EMF) detection to determine the position of the permanent translator relative to the stator windings. These motors typically feature three-phase windings in the stator and a permanent array in the moving forcer, enabling sinusoidal or trapezoidal current control for smoother operation. This configuration supports higher speeds, up to 20 m/s, with accelerations exceeding 20 g in optimized designs, and requires no maintenance due to the absence of brushes. Both types exhibit high force density suitable for short-stroke precision tasks, but brushed variants suffer from sparking, reduced efficiency below 80%, and shorter operational life due to component wear. Brushless designs achieve efficiencies over 90% through minimized losses, though they demand more complex drive electronics for commutation and control. In automation settings, brushless linear motors are preferred for their , extended , and reliability in demanding environments.

Specialized types

Homopolar linear motors utilize a single-turn placed within a direct current (DC) to generate pulsed high forces, operating without alternating magnetic fields. This configuration enables extreme accelerations, making them suitable for applications such as , where projectiles are launched with potential for hypervelocities up to 10 km/s or more in theoretical designs, though practical achievements are typically 2-3 km/s as of 2025. The force on the rails or armature arises from magnetic pressure, expressed as F = \frac{1}{2} \frac{B^2 A}{\mu_0}, where B is the strength, A is the cross-sectional area, and \mu_0 is the permeability of free space; this derives from the self-induced compressing the rails inward. Tubular linear motors feature a cylindrical in which a moving coil is housed inside a tubular permanent arrangement, providing a compact with high force density in constrained spaces. This geometry minimizes end effects—unwanted variations in at the motor's extremities—resulting in smoother operation and improved efficiency compared to flat linear motors. Such motors are applied in micro-robotics and systems, where their enclosed structure supports reliable performance in limited volumes. Piezoelectric linear motors leverage the deformation of piezoelectric materials under applied voltage to create ultrasonic vibrations that drive a slider via or stick-slip mechanisms. In the friction-based ultrasonic variant, resonant vibrations at frequencies above 20 kHz propel through intermittent contact, while stick-slip types use quasi-static cycles of sticking and slipping for precise positioning. These motors achieve nano-scale precision with resolutions below 1 μm and operate at low speeds under 1 m/s, rendering them ideal for environments requiring contamination-free, high-accuracy motion in applications like and handling. Recent advancements as of 2025 include arc-linear motors, a variant derived from linear motors offering high torque density and compact structure for direct-drive applications in and machinery, and U-shaped linear motors, which enhance efficiency and integration in automation systems through their unique geometry. These specialized types highlight distinct advantages: homopolar motors excel in extreme scenarios, designs offer compactness for enclosed settings, and piezoelectric variants provide unparalleled in sensitive precision tasks.

History

Early developments and low-acceleration designs

The concept of the linear motor emerged in the early with Wheatstone's 1841 for an electromagnetic , which represented one of the first models demonstrating through electromagnetic forces. This design laid foundational principles for converting directly into linear , though it remained experimental and focused on basic electromagnetic interactions rather than practical implementation. A significant advancement came in 1905 when Alfred Zehden patented the first feasible (US Patent 782,312), intended for driving elevators and trains through asynchronous . This patent described a primary winding creating a traveling to induce motion in a secondary conductor, emphasizing simplicity in low-speed applications like vertical lifts. From the to the , low-acceleration linear induction motors (LIMs) gained traction in settings, particularly for conveyors and cranes, where their asynchronous operation allowed reliable, low-speed without mechanical linkages. These designs prioritized robustness over high performance, using basic wound primaries to produce modest forces suitable for horizontal or overhead transport in factories and ports. Following , linear motors saw initial applications in , such as shuttles for weaving and basic handling equipment, though challenges like low efficiency—typically 30-50% due to large air gaps and material limitations—necessitated improvements in core laminations and windings. By the , the first practical LIMs emerged for baggage handling in airports and warehouses, leveraging their simplicity for asynchronous, low-acceleration transport of loads over short distances. These systems highlighted the motors' advantages in non-contact propulsion, despite ongoing efficiency constraints addressed through better insulation and magnetic materials.

High-acceleration and modern advancements

In the 1960s, Eric Laithwaite advanced concepts for high-performance applications, including early prototypes. Concurrently, pioneering work on linear synchronous motors (LSMs) in and laid the groundwork for variants with permanent magnets for improved density. Herbert Weh contributed to synchronous machine theory, influencing later permanent magnet linear synchronous motor (PMLSM) architectures that enabled higher accelerations. These early efforts transitioned to high-acceleration capabilities in the 1980s through the adoption of neodymium-iron-boron (NdFeB) rare-earth magnets, which provided superior magnetic flux density and allowed accelerations of 5-10 g in compact PMLSM configurations. The 1970s saw accelerated adoption of linear synchronous motors (LSM) driven by maglev research, particularly in and , where prototypes like the ML-500 achieved speeds over 500 km/h using LSM propulsion, spurring refinements in high-speed, high-acceleration designs. By the , advancements in digital controls, including servo feedback loops, enhanced precision positioning in linear motors, enabling sub-micrometer accuracy through real-time error correction and adaptive algorithms. Key modern advancements include the integration of insulated gate bipolar transistors (IGBTs) in , facilitating high-frequency switching up to several kHz for smoother operation and reduced ripple in linear motor drives. This has contributed to efficiency gains exceeding 95% in optimized PMLSM systems, minimizing losses in high-acceleration applications. Miniaturization efforts have also produced piezo variants of linear motors, leveraging piezoelectric stacks for compact, high-precision actuation in sub-millimeter scales with forces up to 1200 N. In the , tubular linear motors gained prominence in , offering integrated designs with moving coils or magnets for direct-drive precision and reduced cogging, supporting accelerations over 10 in lightweight payloads. As of 2025, ongoing in superconducting linear motors utilizes high-temperature superconductors for zero electrical resistance, with demonstrating speeds up to 600 km/h (167 m/s) in test tracks while maintaining persistent currents for efficient propulsion; for example, China's developed a superconducting prototype capable of 600 km/h.

Applications

Industrial and manufacturing uses

Linear motors play a pivotal role in factory automation, particularly in pick-and-place robots where brushless variants enable high-speed positioning with cycle times under one second. These brushless linear motors, which eliminate mechanical contacts like brushes for smoother operation, facilitate rapid acceleration and precise placement in repetitive assembly tasks. Multi-axis systems, often powered by such motors, coordinate synchronized movements across large workspaces, enhancing throughput in assembly lines. In machine tools, linear motors drive direct-drive spindles and slides in computer (CNC) machines, providing backlash-free motion essential for high-precision . Permanent magnet linear synchronous motors (PMLSM), a common type in these applications, deliver speeds exceeding 25 meters per minute while maintaining sub-micron accuracy without intermediary transmission elements. This direct-drive approach ensures reliable positioning in operations like milling and grinding, where even minor inaccuracies can compromise part quality. Compared to traditional systems, linear motors offer reduced maintenance due to the absence of mechanical wear components, requiring only periodic for support bearings. In semiconductor wafer handling, for instance, linear motors enable contactless of delicate wafers to processing stations, minimizing contamination risks and supporting vacuum-compatible environments with ironless designs. Adoption of linear motors in surged during the as initial costs declined through improved techniques and broader by companies like . In repetitive tasks, these motors achieve energy savings of 20-30% over conventional drives by optimizing power delivery and eliminating transmission losses.

Transportation systems

Linear motors play a pivotal role in modern propulsion systems, enabling efficient and high-speed transportation. Linear induction motors (LIMs) have been employed in conventional urban applications, such as the , which opened in 1987 and uses two LIMs per car to propel steel-wheeled vehicles along a 2.9-mile elevated loop in . In contrast, linear synchronous motors (LSMs) power advanced systems, including Japan's , which achieved a world-record speed of 603 km/h during a 2015 test run on the Yamanashi test track. Monorail and often utilize short-stator configurations, where the is mounted on the and interacts with a long reaction plate on the guideway, providing precise for rubber-tired vehicles. These systems excel in navigating challenging , offering grade-climbing capabilities up to 15% under normal operations, which reduces the need for extensive earthworks and tunneling. Some systems rely on (), which employs onboard superconducting magnets cooled to near-absolute zero to generate powerful that levitate the train above the guideway, minimizing and enabling ultra-high speeds. The LSM propulsion in EDS-based systems achieves efficiencies exceeding 85% at speeds above 500 km/h, primarily due to the synchronous interaction between the vehicle's magnets and the guideway's traveling . The Shanghai Maglev, the world's first commercial high-speed maglev line using (), began passenger operations in January 2003, connecting Pudong to the city center over 30 km in about 8 minutes at speeds up to 431 km/h. As of 2025, concepts continue to explore LSM-based for pod systems targeting speeds over 1,000 km/h in low-pressure tubes, with ongoing prototypes emphasizing energy-efficient and acceleration.

Aerospace and defense applications

Linear motors play a critical role in applications, particularly in launching systems where high-force electromagnetic is essential for carrier-based operations. The (EMALS), developed by for the U.S. Navy, utilizes linear synchronous motors to accelerate along the , replacing conventional catapults with electronically controlled launches. This system delivers stored through solid-state , enabling precise profiles tailored to various weights and types, from lightweight unmanned vehicles to heavy fighters. EMALS has been operational aboard the (CVN-78) since 2017, supporting enhanced sortie generation rates and reduced mechanical wear. In flight simulation for training, linear motors serve as actuators in six-degrees-of-freedom (6-DOF) motion platforms, providing immersive and realistic replication of maneuvers. These brushless linear actuators generate high-fidelity force feedback by translating electrical signals into smooth across surge, sway, heave, roll, , and yaw axes, allowing pilots to experience accurate vestibular cues during simulated flights. Such systems improve training efficacy by minimizing latency and maximizing bandwidth in motion cuing, essential for high-stakes scenarios. Within defense applications, enable advanced weaponry and guidance technologies requiring extreme and . Railguns, functioning as homopolar linear motors, propel projectiles using Lorentz forces generated by high-current pulses, achieving muzzle velocities exceeding 7 (over 2.4 km/s) without explosive propellants. U.S. prototypes have demonstrated this capability for extended-range naval strikes, leveraging systems to deliver megajoule-level energy in milliseconds. Additionally, compact linear actuators control fins and control surfaces in guidance systems, enabling rapid, precise adjustments for intercepting threats in air roles. Ongoing defense research emphasizes technologies to enhance linear motor performance in directed energy systems, including railguns and high-energy lasers, by improving and discharge efficiency for sustained high-power operations. These advancements support integrated weapon platforms on , focusing on reliability under extreme conditions.

Emerging and research applications

Linear synchronous motors (LSMs) have found innovative use in amusement rides, particularly for high-speed launches in roller coasters. For instance, at amusement park employs an LSM launch system to accelerate its train, reaching speeds up to 193 km/h through a series of three launches. Research into superconducting linear synchronous motors (LSMs) aims to enhance train efficiency by leveraging high-temperature superconductors for stronger magnetic fields and reduced energy loss. A study proposes an energy-economical superconducting linear thrusting system for ultra-high-speed , estimating energy consumption per passenger-kilometer at about 20% of conventional designs through improved and stability. This research aligns with efforts to advance sustainable . Proposed integrations of linear motors in electric vehicles include wheel-in-wheel drive systems, where the motor directly propels the wheel without traditional drivetrains, potentially improving efficiency and space utilization. A 2014 patent describes a linear motor mounted on the wheel carrier to generate linear force for wheel rotation, addressing delivery challenges in compact designs; post-2020 has explored scaling this for production EVs to enable independent wheel control and . In (VR) applications, piezoelectric linear actuators enable precise haptic feedback by converting electrical signals into micro-vibrations that simulate textures and forces. A 2023 IEEE paper introduces a piezo-based motor technology for (XR) devices, offering realistic tactile sensations with response times under 1 ms and low power consumption, expanding immersion beyond visual and auditory cues. Nanoscale linear motors are emerging in microelectromechanical systems (MEMS) for nanopositioning tasks, such as in . A 2021 study details a piezoelectric MEMS linear motor achieving bidirectional motion with 10 nm resolution and forces up to 1 mN, fabricated using silicon-on-insulator processes for integration into compact sensors. Similarly, Berkeley Lab's 2014 synthetic nanomotor delivers piconewton forces over nanometer distances via electrostatic actuation, advancing bio-mimetic devices for . Advancements in for linear stators, reported in 2024 reviews, explore to eliminate physical connections in moving systems, potentially reducing maintenance in dynamic applications like automated guided vehicles. However, high-density linear motor designs face thermal management challenges, including buildup from eddy currents that can degrade and reduce lifespan; strategies like advanced cooling channels have shown up to 30% temperature reduction in prototypes. Recent piezoelectric research incorporates nanoscale enhancements, such as vortex structures in thin films, to boost response coefficients by over 50% for linear actuation in quantum sensing applications.