**DC Brush Motor**

**Principles of operation**

Reference to the chart reveals useful performance information valid for all fulling servomotors.

It shows speed n, current I, output power P and efficiency ¦Ç plotted against torque M for a given supply voltage U. 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:

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 ¦Ø (expressed in rad/s) and the torque constant (expressed in V/rad/s=Vs=Nm/A):

E = k¦Ø

Thus, the supply voltage splits into two parts: RI, necessary to establish the current I in the armature, which generates the torque

M, and k¦Ø to overcome the induced voltage, in order to generate the speed¦Ø:

U = RI + k¦Ø

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

Power output P is the product of angular speed¦Ø and torque M (P = M.¦Ø); 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¦Çis the mechanical to electrical power ratio (¦Ç= Pm / Pel). Maximum efficiency¦Çmax 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 (I^{2}R), its maximum value is determined by:

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.

**Small Brushless DC Motor**

**Principles of operation**

The differences between a DC motor having a mechanical commutation system and a BLDC motor are mainly found in :

- the product concept

- the commutation of phase currents.

From the user's point of view, brushless DC motors follow the same equations as those with brushes: torque is proportional to current, speed depends on the voltage and the load torque.

**The commutation of brushless motors**

In the conventional DC motor commutation takes place mechanically through the commutator-and-brush system. In a BLDC motor, commutation is done by electronic means. In that case the instantaneous rotor position must be known in order to determine the phases to be energized.

The angular rotor position can be known by:

- using a position sensor (Hall sensor, optical encoder, resolver)

- electronically analyzing the back-EMF of a non-energised winding. This is called sensorless commutation.

**Use of Hall sensors**

In general, BLDC motor have three phase windings. The easiest way is to power two of them at a time, using Hall sensors to know the rotor position. A simple logic allows for optimal energizing of the phases as a function of rotor position, just like the commutator and brushes are doing in the conventional DC motor.

**Use of an encoder or resolver**

The rotor position may also be known by use of an encoder or resolver. Commutation may be done very simply, similar to the procedure with Hall sensors, or it may be more complex by modulating sinusoidal currents in the three phases. This is called vector control, and its advantage is to provide a torque ripple of theoretically zero, as well as a high resolution for precise positioning.

**Use of Back-EMF analysis**

A third option requiring no position sensor is the use of a particular electronic circuit. The motor has only three hook-up wires, the three phase windings are connected in either triangle or star. In the latter case, resistors must be used to generate a zero reference voltage. With this solution the motor includes no sensors or electronic components and it is therefore highly insensitive to hostile environments. For applications such as hand-held tools, where the cable is constantly moved, the fact of just three wires is another advantage.

The functioning of a sensorless motor is easy to understand. In all motors, the relation of back-EMF and torque versus rotor position is the same. Zero crossing of the voltage induced in the non-energised winding corresponds to the position of maximum torque generated by the two energized phases. This point of zero crossing therefore allows to determine the moment when the following commutation should take place depending on motor speed. This time interval is in fact equivalent to the time the motor takes to move from the position of the preceding commutation to the back-EMF zero crossing position. Electronic circuits designed for this commutation function allow for easy operation of sensorless motors.

**Small Brushless DC Motor**

As the back-EMF information is necessary to know the rotor position, sensorless commutation doesn't work with the motor at stall. The only way of starting is to pilot it at low speed like a stepper in open loop.

**Remember:**

- for commutation, position sensors are necessary when operating in incremental mode

- sensorless commutation is recommended only for applications running at constant speed and load.

**Operating principle of BLDC motors:**

It follows the same equations as the DC motor using mechanical commutation except that parameters like iron losses and losses in the drive circuit are no longer negligible in applications where efficiency is of prime importance.

**Iron losses**

They depend on speed and, in the torque formula, may be introduced as viscous friction. The equation for useful motor torque becomes:

**Losses in the electronics**

The current and votage required by the motor and the drive circuit to operated at the desired speed and torque depend also on the drive circuit.

As an example, a driver bridge in bipolar technique will reduce the voltage available at the motor terminals by about 1.7V, and the total current must include the consumption of the circuitry.