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Stall torque

Stall torque is the torque produced by a mechanical device whose output rotational speed is zero. The concept applies to electric motors, internal combustion engines, and fluid transmissions. For example, in an electric motor such as a DC motor, it refers to the maximum torque when its rotor is prevented from rotating.^[1] This condition occurs when the applied load equals or exceeds the motor's capability to initiate motion, often during startup or when holding a position against resistance.^[2] In DC motors, stall torque is achieved because the absence of rotation eliminates back electromotive force (back EMF), allowing the full supply voltage to drive the maximum current through the windings, limited primarily by the armature resistance.^[1] The torque itself is directly proportional to this stall current, calculated as the torque constant multiplied by the current drawn.^[1] On the characteristic speed-torque curve of a DC motor, stall torque marks the point at zero speed, with torque decreasing linearly to zero at the no-load speed.^[2] Stall torque is a critical parameter in motor selection and design, as it determines the motor's ability to overcome initial inertia, friction, or static loads in applications like robotics, aerospace systems, and electric vehicles.^[3]^[4] However, prolonged operation at stall draws excessive current, leading to rapid overheating, insulation degradation, and potential motor failure if not managed with appropriate current limiting or thermal protection.^[5] Engineers must ensure power supplies can handle peak stall currents—often several times the rated value—while sizing motors to avoid sustained stall conditions in duty cycles.^[6]

Fundamentals

Definition

Stall torque is the maximum torque that a device, such as an electric motor or internal combustion engine, can produce when its output shaft is prevented from rotating, resulting in zero rotational speed.^[7]^[8] This condition occurs when the load torque equals or exceeds the device's capability to generate rotational motion, causing the rotor or crankshaft to remain stationary despite full input power.^[7] Torque itself is the measure of rotational force, mathematically defined as the cross product \vec{\tau} = \vec{r} \times \vec{F}, where \vec{r} is the position vector from the axis of rotation to the point of force application, and \vec{F} is the applied force vector.^[9] In the stall condition, the device's input energy—whether electrical or chemical—is directed entirely toward generating this maximum torque, with no mechanical work performed at the output since angular velocity is zero, leading to all input power being dissipated as heat.^[10] Stall torque is typically expressed in units of newton-meters (Nm) in the International System of Units or pound-feet (lb-ft) in imperial units, with the standard notation \tau_\text{stall} used in engineering analyses.^[7]^[11]

Significance and Applications

Stall torque plays a pivotal role in engineering design by determining the capacity of motors and engines to manage startup loads, provide overload protection, and establish efficiency ratings. Engineers rely on stall torque specifications to size components appropriately, ensuring systems can initiate motion against high resistance without failure. Exceeding stall torque can lead to severe damage, including overheating from excessive current draw or mechanical stress resulting in component breakdown.^[12]^[13] In performance curves, stall torque represents the maximum output at zero rotational speed, serving as the y-intercept of the torque-speed characteristic, with torque decreasing to zero at the no-load speed. This parameter contrasts sharply with no-load speed, highlighting the trade-off between torque and velocity in device operation. Understanding this curve is essential for predicting system behavior under varying loads.^[14] Stall torque finds broad applications across engineering domains, such as robotics for maintaining positional holding against gravitational or external forces, automotive systems for enabling hill starts where initial torque overcomes incline resistance, and industrial machinery for rapid acceleration of heavy loads. In design practices, safety factors are incorporated by selecting components with stall torque capacities 1.5 to 2.25 times the anticipated peak demand to account for thermal limits and variability.^[12]^[15]^[14] However, stall torque is inherently transient, intended for short-duration events; prolonged exposure risks thermal runaway due to sustained high currents, accelerated wear on bearings and windings, or complete system failure. Designers must therefore limit stall conditions to brief intervals, integrating protective mechanisms like current limiters to mitigate these hazards.^[12]^[13]

Electric Motors

DC Motors

In brushed DC motors, stall torque represents the maximum output torque produced when the rotor is prevented from rotating, resulting in zero speed and maximum armature current. This condition arises because the back electromotive force (EMF) is absent, allowing the full supply voltage to drive current through the armature resistance. The stall current is given by I_{\text{stall}} = \frac{V}{R_a}, where V is the supply voltage and R_a is the armature resistance, enabling the strongest interaction between the armature's magnetic field and the stator's field.^[1] The stall torque \tau_{\text{stall}} is calculated as \tau_{\text{stall}} = K_t \cdot I_{\text{stall}}, where K_t is the torque constant in Nm/A. This relationship stems from the Lorentz force acting on the current-carrying conductors in the armature windings within the magnetic field: the force on each conductor is \mathbf{F} = I \mathbf{L} \times \mathbf{B}, where I is current, \mathbf{L} is the length vector of the conductor, and \mathbf{B} is the magnetic flux density; the resulting torque is the sum of moments \tau = r F \sin \theta across all windings, proportional to current via the torque constant K_t.^[16]^[17] Stall torque is typically 5 to 10 times the rated torque in permanent magnet DC motors, providing high starting capability but limited by excessive current draw that leads to rapid I²R heating in the windings. At stall, motor efficiency drops to zero since mechanical power output is torque times speed, and speed is zero. Armature reaction, caused by the armature flux distorting the main field, and brush-commutator friction further reduce effective stall torque by introducing losses, with armature reaction becoming prominent at high currents and friction contributing mechanical drag.^[18]^[16]^[19]^[20] In practical applications, such as early electric vehicles, DC motors deliver instant stall torque at standstill for quick acceleration, exemplified by permanent magnet DC motors producing up to 10-12 times full-load torque momentarily. For a typical small hobby DC motor operating at 12 V, stall torque values range from 0.1 to 1 Nm, depending on size and design, though prolonged stall operation must be avoided to prevent thermal damage.^[18]^[21]

AC and Other Motors

In AC motors, particularly three-phase induction motors, stall torque—also known as locked-rotor torque—refers to the maximum torque produced at zero rotor speed, where the slip s = 1. This torque arises from the interaction between the stator's rotating magnetic field and the induced currents in the stationary rotor, enabling the motor to start under load. Unlike DC motors, which rely on direct voltage-current relationships for linear torque production, induction motor stall torque is influenced by the alternating current's frequency and the rotor's slip, with the breakdown torque (maximum torque during acceleration) often exceeding stall torque by 20-50% depending on design.^[22] The torque in a three-phase induction motor is given by the equation:

T = \frac{3}{2\pi n_s} \cdot \frac{s E_2^2 R_2}{R_2^2 + (s X_2)^2}

At stall (s = 1), this simplifies to the starting torque:

T_\text{stall} = \frac{3}{2\pi n_s} \cdot \frac{E_2^2 R_2}{R_2^2 + X_2^2}

Here, n_s is the synchronous speed in revolutions per second, E_2 is the rotor induced EMF per phase at standstill (proportional to stator voltage), R_2 is the rotor resistance per phase, and X_2 is the rotor reactance per phase at standstill. These parameters highlight how increasing rotor resistance boosts stall torque at the cost of efficiency, a key design consideration for high-starting-torque applications.^[22] Typically, stall torque in induction motors ranges from 150% to 300% of the rated full-load torque, varying by NEMA design class; for example, Design B motors, common in general industrial use, provide a minimum of 200% locked-rotor torque to ensure reliable starting.^[23]^[24] In practical applications like industrial pumps and fans, this allows the motor to overcome initial inertia without excessive current draw, though prolonged stall risks overheating due to high locked-rotor currents (600-700% of rated).^[25] Synchronous motors differ markedly, as their rotor locks to the stator field at synchronous speed; stall torque at zero speed is minimal without auxiliary starting mechanisms like damper windings, which enable induction-like behavior during startup. Once synchronized, the maximum sustainable torque equals the pull-out torque, typically 150-200% of rated, beyond which the motor stalls by losing synchronism.^[26] For other motor types, such as stepper motors used in precise positioning systems like CNC machines, stall torque corresponds to the holding torque when the rotor is energized but stationary. This is calculated as T_\text{stall} = K_t \cdot I, where K_t is the motor's torque constant (in Nm/A) and I is the phase current; the holding torque typically exceeds the maximum dynamic torque, with dynamic torque often around 60-70% of holding torque at low speeds. This enables detent torque without power in unenergized states but requires current for active holding. NEMA standards for stepper motors emphasize this holding capability for step accuracy, with typical ratings from 0.5 to 10 Nm depending on frame size.^[27]^[28]^[29]

Internal Combustion Engines

In the context of internal combustion engines, stall torque refers to the torque required to initiate rotation from standstill (cranking torque), analogous to the starting load overcome by the starter motor.

Spark-Ignition Engines

In spark-ignition engines, stall torque, commonly termed the cranking torque requirement, denotes the torque essential to initiate crankshaft rotation at zero RPM, countering the resistance from air-fuel mixture compression within the cylinders and frictional losses in components such as bearings and piston rings. This torque is supplied by the starter motor engaging the flywheel gear, enabling the pistons to cycle through compression and ignition until the combustion process generates self-sustaining rotation. The principles stem from the force exerted by expanding combustion gases on the piston crown post-ignition, transmitted via the connecting rod to produce piston force on the crankshaft, with peak resistance occurring during the compression stroke absent combustion.^[30] The primary factor governing stall torque demand is the compression ratio, as higher ratios amplify the peak cylinder pressure during compression—governed by the polytropic process where pressure scales with the ratio raised to the polytropic exponent—necessitating greater input torque to overcome the resultant gas forces. For a typical automotive spark-ignition engine with a 10:1 compression ratio, this elevates the cranking resistance substantially compared to lower ratios (e.g., 8:1), by a factor of approximately 1.3-1.5 times due to the nonlinear pressure rise.^[30] Stall torque characteristics in these engines are inherently transient, surging to a peak during the initial cranking cycles before stabilizing as speed builds to 200-300 RPM for reliable ignition. In automotive V8 configurations, this peak typically ranges from 180-400 Nm at the crankshaft, constrained by starter motor output (often 1.5-3 kW) and battery capacity. The torque profile fluctuates per cylinder cycle, with inertial effects from reciprocating masses adding oscillatory components that the flywheel dampens. Stall torque is measured using an engine dynamometer in motoring mode, where the crankshaft is initially locked to quantify static compression resistance before dynamic cranking tests assess peak loads across cycles. Cold starts exacerbate demands, as elevated lubricant viscosity heightens hydrodynamic friction in bearings and rings, potentially increasing required torque by 50% or more relative to warm conditions (e.g., from -30°C oil thickening). In practical automotive contexts, insufficient stall torque capability—such as from undersized starters or weak batteries—results in prolonged cranking or outright failure to start, particularly in high-compression designs, underscoring the need for matched components in vehicle engineering. Historically, early 20th-century spark-ignition engines (circa 1900s) depended on manual cranking via a hand lever, exposing operators to severe risks like arm fractures or fatalities from backfire-induced kickback, which spurred safety advancements including the 1912 electric self-starter invention by Charles F. Kettering for Cadillac.^[31]

Compression-Ignition Engines

In compression-ignition engines, commonly known as diesel engines, stall torque refers to the maximum rotational force required to crank the engine from a standstill, primarily to overcome the high resistance during the compression stroke. These engines operate on higher compression ratios, typically ranging from 14:1 to 25:1, compared to spark-ignition engines, which increases the cylinder pressure and thus demands substantially greater cranking torque for reliable starting.^[32] The diesel cycle relies on fuel injection occurring after the air compression phase, where the elevated temperatures from compression ignite the injected fuel, but during cranking, the starter must generate sufficient torque to achieve these pressures without combustion occurring.^[33] Key factors influencing stall torque in diesel engines include the mean effective pressure (MEP) during cranking and the engine's displacement volume. The torque T can be approximated by the relation T = \frac{p_{me} \times V_d}{4\pi}, where p_{me} is the mean effective pressure and V_d is the displacement, derived from the work done over the engine cycle for a four-stroke configuration.^[34] Peak compression pressures in diesel engines often reach 25-40 bar during cranking, resulting in higher MEP values (typically 5-10 bar) that elevate torque requirements compared to spark-ignition engines.^[35] Glow plugs, which preheat the combustion chamber, significantly aid cold starts by reducing the compression resistance and overall cranking load, enabling easier ignition of the fuel-air mixture.^[36] Diesel engines exhibit stall torque demands that are typically 1.5 to 2 times higher than those of comparable spark-ignition engines due to the elevated compression pressures, though they often crank at slower speeds of 100-250 RPM versus around 200 RPM for gasoline engines, reflecting the need for robust starters to handle the load.^[37] Turbochargers, common in modern diesels, have minimal impact on stall torque since no exhaust flow is present during cranking to generate boost, though they enhance full-load torque once running.^[38] Stall torque is measured using locked-crank tests, where the crankshaft is restrained, and torque is applied incrementally to simulate starting conditions, following standards like SAE J1253 for determining cranking load requirements. In practical applications, heavy-duty trucks with large diesel engines often require starters delivering 500-1000 Nm of torque to overcome these loads reliably. Early diesel engines from the 1920s faced significant hand-cranking challenges due to high compression, leading to the development of electric starters and aids like glow plugs to mitigate starting difficulties.^[39]^[40]^[41]

Fluid Couplings and Transmissions

Hydrodynamic Couplings

Hydrodynamic couplings, also known as fluid couplings, transmit stall torque through the hydrodynamic action of fluid shear between the rotating impeller (pump) and the stationary runner (turbine) within sealed, fluid-filled chambers, enabling power transfer without direct mechanical contact. At stall conditions, where the output shaft is at zero speed, the relative motion creates viscous drag in the fluid, allowing the coupling to transmit up to 100% of the input torque, limited by the slip and design parameters such as fluid fill level. This principle originated from early 20th-century innovations, with Hermann Föttinger's patents in the 1900s laying the groundwork, and Voith producing the first practical hydrodynamic couplings by 1929 based on this Föttinger principle.^[42]^[43] Key characteristics of stall torque in these couplings include full transmission at standstill (100% slip), where the impeller accelerates the fluid to impart momentum to the runner, but efficiency decreases as output speed increases due to persistent slip, typically 2-6% under normal operating conditions. The fluid fill level significantly influences performance; typical fillings of 40-80%, with higher levels within this range (up to 80%) maximizing stall torque capacity, while lower levels reduce it, resulting in softer starts, higher slip, and increased temperatures. For instance, in industrial conveyor systems, such as belt conveyors spanning up to 2 km, hydrodynamic couplings provide smooth acceleration by gradually building torque from zero, preventing abrupt loads on the drive system. Representative industrial sizes can transmit stall torques ranging from 1000 to 5000 Nm, depending on the coupling diameter and application.^[43]^[44] A simplified model for stall torque in basic hydrodynamic couplings approximates the viscous shear contribution as \tau_{stall} = \mu A \frac{r^2}{h} \Delta \omega, where \mu is the fluid viscosity, A is the effective surface area, r is the mean radius, h is the gap between impeller and runner, and \Delta \omega is the relative angular velocity (equal to the input speed at stall). However, actual transmission also involves fluid density and geometry factors, with torque generally proportional to the square of the impeller speed. Limitations include significant heat generation from fluid shearing during prolonged stall, which can overheat the coupling in seconds to minutes; thus, designs incorporate fusible safety plugs to release fluid and prevent damage, restricting continuous stall operation to brief periods. These couplings are particularly valuable in applications like conveyors driven by internal combustion engines, where they mitigate engine stall risks by limiting torque peaks.^[45]^[43]

Torque Converters

A torque converter in an automatic transmission utilizes a three-element hydrodynamic design comprising a pump (impeller), turbine, and stator to achieve torque multiplication, particularly at low output speeds. The pump, directly connected to the engine's crankshaft, rotates and imparts kinetic energy to the transmission fluid, directing it toward the turbine blades to generate rotational force that drives the vehicle's transmission input shaft. The stator, mounted between the pump and turbine on a one-way clutch, redirects the fluid exiting the turbine back toward the pump in the direction of rotation, creating additional reaction torque that amplifies the input. This process is most effective during stall conditions, where the turbine remains stationary while the pump spins, such as when the vehicle is held stationary with the brakes applied and the transmission in drive.^[46]^[47]^[48] The stall torque multiplication arises from the conservation of angular momentum in the fluid flow across the elements, influenced by the stator's blade angle, with energy principles derived from Bernoulli's equation applied to model pressure and velocity changes in the fluid. The key metric is the multiplication ratio K = \frac{\tau_{\text{stall}}}{\tau_{\text{input}}}, which typically ranges from 2 to 2.5 in standard automotive designs, though optimized configurations can reach up to 3. This ratio diminishes as turbine speed increases, approaching 1:1 in the coupling phase. For instance, an engine producing 1000 Nm of torque at stall might deliver 1800–3000 Nm to the transmission, enhancing low-speed acceleration without mechanical linkage slip.^[48]^[47]^[49] To mitigate efficiency losses from fluid slip at cruising speeds, modern torque converters incorporate a lock-up clutch that engages above a certain speed ratio, mechanically bypassing the hydrodynamic elements for direct drive and achieving near 100% torque transfer. Stall torque and speed are quantified through dynamometer testing, where the turbine is mechanically locked to replicate the stalled state, measuring input versus output torque and the RPM at which balance occurs. Development of torque converters traces to the early 20th century, with General Motors' first mass-produced automotive application in the Buick Dynaflow transmission of 1948, evolving into widespread use in systems like the Turbo-Hydramatic by the 1960s.^[50] In racing, high-stall converters (e.g., 3000–5000 RPM) enable launch control by allowing engines to rev to peak torque bands from standstill, optimizing drag strip acceleration.^[51]^[52]^[53]^[54]

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