DC Brushed Motors Theory

Reference to the chart reveals useful performance information valid for all MCP DC brushed servomotors.It shows speed n, current I, output power P and efficiency η plotted against torque M for a given supply voltage U.

Principles of Operation

Torque M is a function of the current I and the torque constant k (expressed in Nm/A). The motor develops its maximum torque Ms at stall (n=0), when the current is maximum and determined only by the supply voltage U and the rotor resistance R:

I_s = U/R

M_s = I_s·k

With increasing speed, an increasing back EMF E is induced in the armature which tends to reduce the current:

The value of E is the product of angular speed ω (expressed in rad/s) and the torque constant (expressed in V/rad/s=Vs=Nm/A):

E=kω

Thus the supply voltage splits into two parts: RI, necessary to establish the current I in the armature, which generates the torque M, and kω to overcome the induced voltage, in order to generate the speed ω:

U = RI + kω

No-load speed n₀ is a function of the supply voltage and is reached when E becomes almost equal to U; no-load current I₀ is a function of friction torque:

With increasing speed, an increasing back EMF E is induced in the armature which tends to reduce the current:

Power output P is the product of angular speed ω and torque M (P = M · ω); for a given voltage it reaches its maximum P_max at half the stall torque M_s, where efficiency is close to 50%. The maximum continuous output power is defined by an hyperbola delimiting the continuous and intermittent operation ranges.

Efficiency η is the mechanical to electrical power ratio (η = P_m / P_el). Maximum efficiency η_max occurs at relatively high speed. Its value depends upon the ratio of stall torque and friction torque and thus is a function of the supply voltage:

The maximum continuous torque depends upon dissipated power (I²R), its maximum value is determined by:

Where T_max is the maximum tolerated armature temperature, T_amb is the ambient temperature, R_maxis the rotor resistance at temperature T_max and R_th is the total thermal resistance (rotor-body-ambient).

At a given torque M, increasing or decreasing the supply voltage will increase or decrease the speed. The speed-torque function varies proportionally to the supply voltage U.