Shoe Brake Torque
Calculate the braking torque of a simple shoe (or drum) brake, T = μ·F·r, from the friction coefficient μ, the normal force applied by the shoe F (N) and the drum radius r (m). The shoe brake presses a friction-lined shoe against the surface of a rotating drum (or cylinder); the friction between shoe and drum generates a tangential force (μ·F) which, acting at the drum radius, produces the braking torque. It is the principle of vehicle drum brakes, hoist and industrial drum brakes, and rotating-machine brakes. The torque is simply the friction force times the radius. An important effect in shoe brakes is SELF-ENERGIZING: depending on the shoe pivot geometry, friction itself can HELP press the shoe against the drum (leading shoe), raising the effective force and torque for a given actuation force — or HINDER it (trailing shoe). This amplifies braking (an advantage) but makes it sensitive to the friction coefficient (which varies with temperature and moisture), possibly causing unstable behavior. This basic formula gives the torque without the self-energizing factor, considered separately per geometry. Enter the friction coefficient, the normal force and the drum radius.
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Torque de freio de sapata
O torque de frenagem de um freio de sapata (ou de tambor) simples é T = μ·F·r, a partir do coeficiente de atrito μ, da força normal aplicada pela sapata F e do raio do tambor r. O freio de sapata pressiona uma sapata revestida de material de atrito contra a superfície de um tambor (ou cilindro) girante; o atrito entre a sapata e o tambor gera uma força tangencial (μ·F) que, atuando no raio do tambor, produz o torque de frenagem. É o princípio dos freios de tambor de veículos, de freios de guinchos e tambores industriais, e de freios de máquinas rotativas. O torque é simplesmente a força de atrito vezes o raio. Um efeito importante é a auto-energização (self-energizing): conforme a geometria de articulação da sapata, o próprio atrito pode ajudar a pressionar a sapata contra o tambor (sapata primária), aumentando a força efetiva e o torque para uma dada força de acionamento — ou atrapalhar (sapata secundária). Esse efeito amplifica a frenagem (vantagem) mas a torna sensível ao coeficiente de atrito (que varia com temperatura e umidade), o que pode causar comportamento instável. Esta fórmula básica dá o torque sem o fator de auto-energização, que é considerado à parte conforme a geometria. Informe o coeficiente de atrito, a força normal e o raio do tambor.
Related Tools
Disc Clutch Torque
Calculate the torque transmissible by a disc clutch (or brake), T = μ·F·N·r_m, from the friction coefficient μ, the axial clamping force F (N), the number of friction surfaces N and the mean friction radius r_m (m). A disc clutch transmits torque between two shafts by FRICTION between surfaces pressed together: an axial force F clamps the discs, and the friction at that interface, acting at the mean radius, generates the torque. The number of friction surfaces N multiplies the capacity — a single disc clutch has N=1 (one face) or N=2 (disc between two faces); MULTI-PLATE clutches (motorcycles, automatic transmissions) stack several discs with high N, transmitting large torque in compact space. The same principle applies to disc and clutch BRAKES: the braking (or transmitting) torque is μ·F·N·r_m. This is central in clutch and brake design: it sets the actuation force (pedal, spring, hydraulic actuator) needed to transmit/brake a given torque, and the area and number of discs. The design torque includes a service factor (1.2-3) over the nominal, to cover peaks and wear. Enter the friction coefficient, axial force, number of surfaces and mean radius.
Brake Contact Pressure
Calculate the contact pressure between the shoe/pad and the drum/disc of a brake, p = F ÷ A, from the normal force F (N) and the friction material contact area A (m²); the result is in kPa. Contact pressure is the normal force distributed over the friction surface area, and one of the most important parameters in a brake's or clutch's DURABILITY and PERFORMANCE. It must be below the friction material's ALLOWABLE pressure (linings, organic, semi-metallic, ceramic or sintered metallic pads — each with its limit). Pressures ABOVE the allowable lead to accelerated wear, overheating and friction loss (fading), reducing material life and impairing braking. Very LOW pressures underuse the material (a bigger, costlier brake than needed). Contact pressure also relates to the p·v product (pressure × velocity), the key indicator of the friction contact's thermal intensity — friction materials have a p·v limit above which they overheat, and that limit often governs design. This simple check — comparing contact pressure with the material's allowable — is essential in brake and clutch design and in choosing the right friction material for the application. Enter the normal force and the contact area.
Friction Torque
Calculate the friction torque in a shaft or bearing, T = μ·F·r, multiplying the friction coefficient μ by the normal force (load) F and the radius r where friction acts. The result, in N·m, is the moment friction opposes to rotation — the torque the motor must overcome just to turn the assembly, without doing useful work. Reducing friction torque (with lubrication, rolling bearings and good finishes) saves energy and lowers heating. Multiplied by the angular velocity, it gives the power dissipated by friction. Enter the friction coefficient, the force and the radius.
Brake Power Dissipated
Calculate the power dissipated by a brake under torque, P = T·(2π·n/60), from the braking torque T (N·m) and the rotation n (rpm). Dissipated power is the rate at which the brake converts mechanical energy to heat — the product of braking torque and angular velocity. It differs from total braking ENERGY: energy is the total heat generated (joules), while power is the INTENSITY of that heat generation (watts), and it determines the brake's steady-state temperature. A brake dissipating much energy but slowly (low power) heats little; one dissipating the same energy fast (high power) heats much more. Dissipated power is critical in brakes working CONTINUOUSLY or repetitively: retention brakes on long descents, industrial equipment brakes (hoists, cranes, conveyors holding load), and dynamometers (which measure engine power precisely by dissipating it in a brake). There, the steady-state dissipated power sets the COOLING capacity needed (ventilation, water cooling) to keep temperature stable. Equating dissipated power to cooling capacity gives the equilibrium temperature. Enter the braking torque and the rotation.
Rotational Braking Time
Calculate the time to brake (stop) a rotating system, t = (I·ω) ÷ T, from the moment of inertia I (kg·m²), the initial angular velocity ω (rad/s) and the braking torque T (N·m). When a brake applies a constant torque to a spinning system (a shaft, flywheel, machine rotor), it DECELERATES it to a stop. By Newton's second law for rotation (T = I·α, with α the angular deceleration), the stopping time is the initial angular momentum (I·ω) divided by the braking torque. This matters in several situations: EMERGENCY STOPPING of machines (safety codes require dangerous parts to stop within a maximum time after brake actuation — the shorter, the safer), sizing motor and shaft brakes, and clutches (the engagement time, where the clutch 'synchronizes' two shafts' speeds, follows the same physics). Systems with large moment of inertia (heavy flywheels, big rotors) take longer to stop with a given torque — so high-inertia machines need powerful brakes or more stopping time. The braking time, with the dissipated energy and power, completes a braking analysis. Enter the moment of inertia, the angular velocity and the braking torque.
Mean Friction Radius (Clutch)
Calculate the mean friction radius of a disc clutch or brake by uniform-wear theory, r_m = (D + d) ÷ 4, from the outer D and inner d diameters (m) of the friction annulus. The mean radius is the EFFECTIVE radius at which the resultant friction force is taken to act for torque calculation (T = μ·F·N·r_m). There are two classic assumptions for this radius: UNIFORM WEAR (assuming the disc has 'bedded in' and wears evenly, concentrating pressure at the inner radius; gives r_m = (D+d)/4, the simple mean of radii) and UNIFORM PRESSURE (new disc, constant pressure; gives r_m = (2/3)·(D³−d³)/(D²−d²), slightly larger). Uniform wear is most used in DESIGN, being conservative (slightly lower torque) and representing the run-in steady state. The mean radius shows an interesting design point: discs with a narrow friction annulus (D close to d, thin ring at large radius) have a high mean radius, transmitting more torque per unit force — so high-performance disc brakes use calipers acting near the disc edge (large radius). Enter the outer and inner diameters.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.