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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:

Is = U/R

Ms = Is·k

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

Figure 2.

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):


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:

Figure 3.

Power output P is the product of angular speed ω and torque M (P = M · ω); for a given voltage it reaches its maximum Pmax at half the stall torque Ms, 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 = Pm / Pel). Maximum efficiency ηmax 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:

Figure 4.

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

Figure 4.

Where Tmax is the maximum tolerated armature temperature, Tamb is the ambient temperature, Rmax is the rotor resistance at temperature Tmax and Rth 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.

Figure 5.