DC Motor No-Load Speed
Calculate the no-load speed of a DC motor, ω = V ÷ K_e, from the applied voltage V and the back-EMF constant K_e (V·s/rad). The result, in rad/s, is the speed the motor reaches with no load, when the generated back-EMF nearly equals the applied voltage and the current drops to a minimum. It is the upper speed limit of the motor for a given voltage, the basis of the torque-speed curve (running from stall torque at zero speed to no-load speed at zero torque). It lets you estimate the operating range of servos and DC motors. Enter the voltage and the constant K_e.
Result
—
Velocidade sem carga de motor CC
Quando um motor de corrente contínua gira, ele não é só um motor — é também um gerador: ao girar, o rotor gera uma tensão que se opõe à tensão aplicada, chamada força contraeletromotriz (FCEM, ou back-EMF). Essa tensão é proporcional à velocidade: V_fcem = K_e·ω, onde K_e é a constante de velocidade (ou de FCEM) do motor. À medida que o motor acelera, a FCEM cresce, reduzindo a diferença de tensão que impulsiona a corrente — e, portanto, reduzindo a corrente e o torque. O motor atinge a velocidade sem carga (no-load speed) quando, sem nenhuma carga mecânica para vencer (só o atrito interno mínimo), a FCEM quase iguala a tensão aplicada, a corrente cai ao mínimo e a velocidade se estabiliza: ω ≈ V ÷ K_e. Essa é a velocidade máxima que o motor atinge para uma dada tensão — qualquer carga aplicada o desacelera. A velocidade sem carga é um dos dois pontos que definem a curva torque-velocidade de um motor CC, que é uma reta decrescente: no extremo de velocidade zero (eixo travado), o torque é máximo (torque de bloqueio) e a corrente é máxima (corrente de bloqueio = V/R); no extremo de torque zero (sem carga), a velocidade é máxima (esta velocidade sem carga). Entre os dois, o motor opera, e o ponto de máxima potência fica no meio (metade da velocidade sem carga), enquanto a máxima eficiência fica perto da velocidade sem carga. Conhecer ω sem carga permite estimar a faixa de operação do motor e escolher a tensão adequada para a velocidade desejada — e, combinada com o torque de bloqueio, caracteriza completamente o desempenho do motor. Em unidades SI, K_e é numericamente igual à constante de torque K_t. Informe a tensão aplicada e a constante K_e.
Related Tools
Stepper Motor Speed
Calculate the rotation speed of a stepper motor, RPM = (pps × 60 × step angle) ÷ 360, from the pulse frequency pps (steps per second) and the motor's step angle (degrees per step). The result, in revolutions per minute, relates the command frequency sent to the driver with the actual shaft speed. Stepper motors lose torque at high speeds, so there is a practical maximum rotation. It is essential for programming axis speeds in 3D printers, CNC and automation. Enter the pulse frequency and the step angle.
Motor Torque from Current
Calculate the torque produced by a DC motor, T = K_t·I, from the torque constant K_t (N·m/A) and the armature current I. The result, in N·m, shows a DC motor's torque is directly proportional to current — which is why measuring current is the simplest way to estimate (and limit) torque and detect overloads. The torque constant K_t is a motor characteristic (numerically equal to the back-EMF constant K_e in SI units). It is the basis of torque control in servomotors and robotics. Enter the torque constant and the current.
Torque from Force and Distance
Calculates torque τ=F·d·sin(θ) in N·m from applied force, lever arm and angle.
Gear Dynamic Load
Calculate the effective dynamic load on gear teeth, F_d = F_t·K_v, from the nominal tangential force F_t (N) and the dynamic factor K_v. The dynamic load is the REAL tangential force the teeth bear in operation, larger than the nominal force (simply torque over radius) because of the dynamic effects of meshing at speed. These effects — vibrations, contact impacts, tooth deflections under load and manufacturing errors — make the instantaneous tooth load fluctuate and peak above the average, especially at high pitch-line velocities. The dynamic factor K_v (from Barth or other formulas) quantifies this amplification. The dynamic load is then used in strength checks: in Lewis bending stress (risk of tooth breakage at the root) and Hertzian contact stress (risk of surface fatigue and pitting). Using the nominal load without amplifying by the dynamic factor would underestimate the demands and lead to undersized gears that fail prematurely by fatigue. It is an essential, classic step in gear design. Enter the nominal tangential force and the dynamic factor.
Gear Torque
Calculate the torque transmitted by a gear, T = (F_t·d) ÷ 2000, from the tangential force F_t (N) and the pitch diameter d (mm); the result is in N·m (the 2000 converts d/2 from mm to m). Torque is the moment the gear transmits about its axis, and the tangential force F_t acts at the pitch radius (d/2), creating that moment. This relation is the bridge between the POWER/torque side (what the shaft transmits) and the TOOTH-FORCE side (what sizes the strength): from shaft torque, the tooth tangential force (F_t = 2T/d) is obtained, which then feeds the bending (Lewis) and contact (Hertz) calculations. Conversely, given the tangential force, the torque is obtained. In a gear train, torque CHANGES at each stage by the gear ratio (a reduction that multiplies speed by 1/i multiplies torque by i, conserving power minus losses), while power stays roughly constant. So a reducer's last stage (low speed) transmits the HIGHEST torque and needs the most robust gears. Knowing the torque at each gear is essential to size teeth, shafts, keys and bearings. Enter the tangential force and the pitch diameter.
DC Motor Stall Current
Calculate the stall current of a DC motor, I = V ÷ R, from the applied voltage V and the armature resistance R. The result, in amperes, is the maximum current the motor draws when the shaft is locked (zero speed, no back-EMF) — far higher than normal operating current. It is the most dangerous current: it can burn the motor and driver if sustained, so systems include stall protection. It also corresponds to the maximum (stall) torque point on the torque-speed curve. It is essential for sizing fuses, drivers and power supplies. Enter the voltage and the armature resistance.
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.