Motor constants

The constants K_M (motor size constant) and K_v (motor velocity constant, or the back EMF constant) are values used to describe characteristics of electrical motors.

Motor constant

K_M is the motor constant^[1] (sometimes, motor size constant). In SI units, the motor constant is expressed in (N⋅m/sqrt(W)):

K_{\mathrm {M} }={\frac {\tau }{\sqrt {P}}}

where

$\scriptstyle \tau$ is the motor torque (SI units, N·m)
$\scriptstyle P$ is the resistive power loss (SI units, W)

The motor constant is winding independent (as long as the same conductive material used for wires); e.g., winding a motor with 6 turns with 2 parallel wires instead of 12 turns single wire will double the velocity constant, K_v, but K_M remains unchanged. K_M can be used for selecting the size of a motor to use in an application. K_v can be used for selecting the winding to use in the motor.

Since the torque is current x Kt then Km becomes Kt / ( motor resistance)^0.5.

Motor velocity constant, back EMF constant

K_v is the motor velocity constant (= unloaded motor speed divided by applied voltage), measured in RPM per volt (not to be confused with kV, the abbreviation for kilovolt) or radians per volt-second (rad/V-s).^[2] The K_v rating of a brushless motor is the ratio of the motor's unloaded RPM to the peak (not RMS) voltage on the wires connected to the coils (the back EMF). For example, an unloaded motor of K_v, 5,700 rpm/V, supplied with 11.1 V, will run at a nominal 63,270 rpm (5,700 rpm/V × 11.1 V).

The terms K_e,^[3] K_b are also used,^[4] as are the terms back EMF constant.^[5]^[6] or the generic electrical constant.^[3] In contrast to K_V the value K_e is often expressed in SI units ${\frac {V\cdot s}{rad}}$ , thus it is an inverse measure of K_V.^[7] Sometimes it is expressed in non SI units krpm/V.^[8]

The field flux may also be integrated into the formula:^[9]

E_{b}=K_{\omega }\phi \omega

where

E_{b}

is back EMF,

K_{\omega }

is the constant,

\phi

is the flux, and

\omega

is the angular speed

An inverse measure is also sometimes used, which may be referred to as the speed constant.^[3]

By Lenz's law, a running motor generates a back-EMF proportional to the RPM. Once the motor's rotational velocity is such that the back-EMF is equal to the battery voltage (also called DC line voltage), the motor reaches its limit speed.

Motor Torque constant

K_T is the torque produced divided by armature current.^[10] It can be calculated from the motor velocity constant K_v.

K_{\mathrm {T} }={\frac {\tau }{I_{A}}}={\frac {60}{2\pi \cdot K_{V}}}

where $I_{A}$ is the armature current of the machine (SI units A ). K_T is primarily used to calculate the armature current for a given torque demand:

{I_{A}}={\frac {\tau }{K_{\mathrm {T} }}}

The SI units for the torque constant are newton-metres per ampere (N-m/A). Since N-m = J, and A = C/s, then N-m/A = J-s/C = V-s (same units as back EMF constant).

References

External links

DC Motors, Electric motor reference center
"Development of Electromotive Force" (PDF), biosystems.okstate.edu

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