Unbalance Force
Calculate the centrifugal force generated by an unbalanced rotor, F = m·e·ω², from the unbalanced mass m, the eccentricity e (distance from the centre of mass to the rotation axis) and the angular velocity ω (rad/s). The result, in newtons, is the rotating force that excites vibration in the bearings and structure — proportional to the square of speed, which is why unbalance becomes critical at high speeds. Quantifying it guides the balancing of rotors, fans, turbines and wheels, reducing vibration, noise and fatigue. Enter the unbalanced mass, the eccentricity and the angular velocity.
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Força de desbalanceamento
Nenhum rotor real é perfeitamente balanceado: sempre há uma pequena massa desbalanceada cujo centro de gravidade não coincide exatamente com o eixo de rotação. Ao girar, essa massa gera uma força centrífuga rotativa que sacode os mancais e a estrutura, sendo a principal causa de vibração em máquinas rotativas. A força é F = m·e·ω², onde m é a massa desbalanceada, e é a excentricidade (a distância entre o centro de massa e o eixo geométrico de rotação) e ω é a velocidade angular. O fator mais importante é o ω ao quadrado: a força de desbalanceamento cresce com o quadrado da rotação. Isso significa que um desbalanceamento minúsculo, inofensivo em baixa velocidade, pode gerar forças enormes em alta rotação — dobrar a rotação quadruplica a força. É por isso que rotores rápidos (turbinas, compressores, rebolos, rotores de motores elétricos, brocas de dentista) exigem balanceamento rigoroso, em que se mede a vibração e se adicionam ou removem pequenas massas de correção até reduzir e a níveis ínfimos. A norma ISO 1940 define classes de qualidade de balanceamento (G) conforme o produto e·ω admissível para cada tipo de máquina. Quantificar a força de desbalanceamento orienta esse balanceamento e o dimensionamento dos mancais e da fundação, que precisam suportar e amortecer essa excitação rotativa sem fadiga nem ressonância. Informe a massa desbalanceada, a excentricidade e a velocidade angular.
Related Tools
Shaft Critical Speed
Calculate the critical speed of a rotating shaft, ω_c = √(k ÷ m), from the shaft stiffness k and the rotor mass m. The result, in rad/s, is the rotational speed that coincides with the shaft's bending natural frequency — at it, any small unbalance causes large-amplitude resonant vibration that can damage the equipment. Shafts should run with a safe margin below the first critical speed (rigid rotors) or pass through it quickly to a range above (flexible rotors). It is an essential calculation in designing high-speed turbines, pumps and motors. Enter the stiffness and the mass.
Belt Centrifugal Tension
Calculate the centrifugal tension in a belt, T_c = m·v², from the mass per unit length m (kg/m) and the belt velocity v (m/s). When the belt wraps a pulley at high speed, its own mass, making the turn, generates a CENTRIFUGAL force tending to 'throw' the belt outward, LIFTING it off the pulley. This creates an additional tension throughout the belt (the centrifugal tension), the same at all points and not contributing to power transmission — it only 'steals' part of the belt's gripping capacity against the pulley. Centrifugal tension grows with the SQUARE of velocity, so it is negligible at low speeds but becomes important in fast belts. The effect is harmful: by lifting the belt off the pulley, centrifugal tension REDUCES the normal contact force and thus the friction available to transmit power — there is an OPTIMAL velocity above which increasing speed reduces transmissible power (the belt starts to 'float'). So belt speed has a practical limit (typically 25-30 m/s for conventional V-belts, more for special belts). Centrifugal tension must be added to the tensions to get the total tight- and slack-side tensions. Enter the mass per unit length and the velocity.
Hoist Rope Tension
Calculate the resultant force in an elevator's hoist rope, F = (Q + M_car − M_counterweight)·g, from the payload Q, the car mass and the counterweight mass (kg). The result, in newtons, is the unbalanced effort the steel ropes must transmit, already net of the counterweight's balancing effect. It is the basis for sizing the ropes (number, diameter and safety factor, typically ≥ 12 in elevator codes) and the traction sheave. When the load is such that car + load ≈ counterweight, the force tends to zero (balanced system). Enter the load, the car mass and the counterweight mass.
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