Electric machine

An electric machine uses electromagnetism to transfer energy between electrical and mechanical forms, or between electrical circuits. An electric motor converts electrical input into mechanical output; an electrical generator converts mechanical input into electrical output. The wider machine category also includes the stationary electrical transformer. A rotating electric machine combines force on current-carrying conductors with electromagnetic induction; the same rotating conductors that develop torque can develop an opposing induced electric potential difference.^[ref]

For an original idealized direct current motor example, let $e=k_e\omega$, $\tau =k_{t}I$, and $V=e+IR$, where $e$ is the induced opposing electric potential difference, $\omega$ the angular velocity, $\tau$ the torque, and $R$ the winding electrical resistance. In coherent SI units, assume $k_e=k_t=0.1$, $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$, $I=2\mathrm{A}$, and $R=1\Omega$. Thenand the electromechanical conversion power balance isThe $20/24$ conversion fraction is about $83.3\%$ before friction and other losses. At rest the induced term vanishes, so applying the same $12\mathrm{V}$ gives $12\mathrm{A}$ in this simplified model. This makes the opposing induced electric potential difference experimentally visible: at fixed applied electric potential difference, a shaft-speed measurement and an electric current measurement distinguish a turning motor from its stalled state. Actual starting control and additional losses change the idealized numbers, not the need to balance electrical input, mechanical output, and heating.

Electromechanical conversion power balance applies conservation of energy to an electric machine's electrical and mechanical ports, internal storage and losses. In an electric motor sign convention, with electrical input positive and mechanical output positive,The internal term can include a changing magnetic field and rotational kinetic energy. Omitting it is justified only at the relevant steady operating point or after averaging over a cycle with no net storage change.

An original constant-field direct current motor model has winding electrical resistance $R$, inductance $L$, opposing induced electromotive force $e$, and current $i$:Multiplication by $i$ givesFor an ideal conversion coupling, $e=k_e\omega$ and electromagnetic torque ${\tau }_e=k_{t}i$ give $ei={\tau }_e\omega$ when the numerical constants agree in coherent SI units. The induced electrical term is converted power, not a resistive loss. DOE's motor analysis derives current from applied minus opposing induced electric potential difference and relates torque to field and armature current.^[ref]

Suppose $v=24\mathrm{V}$, $i=2\mathrm{A}$, $R=1\Omega$, $L=0.5\mathrm{H}$ and $di/dt=4\mathrm{A}{\mathrm{s}}^{-1}$. Then $e=20\mathrm{V}$ andThe terms are winding heating, increasing magnetic energy, and mechanical conversion. If $10\mathrm{W}$ is additionally going into rotational acceleration and mechanical losses are neglected, only $30\mathrm{W}$ reaches the shaft load at that instant. Calling all $40\mathrm{W}$ useful shaft output would omit a second storage term.

A proposed experiment records terminal electric potential difference, electric current, shaft speed and load torque during acceleration and after settling. The discrepancy between electrical input and load output can include storage as well as heating. For an electrical generator, reversing the port directions gives the corresponding mechanical-input balance; the physical energy accounting is unchanged.