DC Motor Model Explorer

Derive a DC motor model from datasheet points and visualize classic curves. Adjust inputs and hit Recompute. Note: inertia affects transient behavior only; steady‑state efficiency is set by electrical constants and friction (no‑load current).

Reference datasheet: Pololu Micro Metal Gearmotors Rev 6.1 (PDF)

Resistance R

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Back-EMF Ke

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Torque const Kt

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Speed const

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Inertia J

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Peak Efficiency

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Formulas Used

Electrical model
$$ I(\omega) = \frac{V - K_e\,\omega}{R},\quad \tau = K_t\,(I - I_0) $$
Parameter fit
$$ R = \frac{V}{I_{\text{stall}}},\quad K_e = \frac{V - I_0 R}{\omega_{\text{nl}}},\quad K_t = \frac{\tau_{\text{stall}}}{I_{\text{stall}} - I_0} $$
Unit links
$$ K_v\,[\text{RPM/V}] = \frac{60}{2\pi K_e},\quad \omega\,[\text{rad/s}] = \frac{2\pi}{60}\,\text{RPM} $$
Power & efficiency
$$ P_{\text{mech}} = \tau\,\omega,\quad P_{\text{elec}} = V\,I,\quad \eta = \frac{P_{\text{mech}}}{P_{\text{elec}}} $$
Dynamics
$$ J\,\dot{\omega} + b\,\omega = \tau,\quad J = J_{\text{extra}} $$
V: supply voltage (V)
R: winding resistance (Ω)
K_e: back‑EMF constant (V·s/rad)
K_t: torque constant (N·m/A)
ω: angular speed (rad/s); ω = (2π/60)·RPM
ẇ = dω/dt: angular acceleration (rad/s²)
I: current (A)
I₀: no‑load current (A)
I_stall: stall current (A)
τ: torque (N·m)
τ_stall: stall torque (N·m)
rpm_nl: no‑load speed (RPM); ω_nl = (2π/60)·rpm_nl
K_v: speed constant (RPM/V) = 60/(2πK_e)
P_mech: mechanical power (W) = τ·ω
P_elec: electrical input power (W) = V·I
η: efficiency (%) = 100·P_mech/P_elec
J: total inertia (kg·m²) = J_extra in this model
b: viscous friction coefficient (N·m·s/rad)