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It may surprise design engineers that both Brushed DC and Brushless DC (BLDC) motors can operate as generators. A brushed DC motor is appropriate for generator applications requiring a DC voltage output, while a brushless DC motor is suitable for AC voltage applications. If using a BLDC for DC voltage output, a voltage rectification circuit is needed. If using a brushed DC motor for AC output, DC to AC electronics are needed.

This article examines the basic relations between speed, voltage, torque and current when using a brushed DC motor as a generator.

### INTRODUCTION

As a motor’s rotor rotates in a magnetic field, the electromotive
force induces a voltage on the rotor windings termed
the ‘back EMF’. The back EMF constant (K_{E}), given in mV/
rpm, is an indicated value on the motor specification sheet.
The back Emf (U_{i}) value is directly proportional to the angular
speed (ω) of the motor shaft rotation and is given as:

When operating the motor as a generator, the shaft is mechanically coupled and rotated by an external source, causing the coil segments in the rotor to rotate through a sinusoidally varying magnetic flux in the air gap. Each turn of the rotor winding is induced with sinusoidal voltage, with the speed of rotation and the magnetic flux linkage determining the voltage magnitude. For instance, if a rotor coil consists of one turn, the induced EMF is sinusoidal with a period equal to one electrical cycle.

By design, a brushed DC rotor is wound in an odd number of segments (3,5,7, … etc.) and supplies power to the coils through a pair of brushes. When the shaft is rotated in generation mode, the generated back-EMF voltage is measured at the output terminals. Based on the properties of the motor design (which includes the number of coil segments), a voltage ripple is typically present and generally represents less than 5% of the output voltage.

Since the output voltage is a function of shaft speed,
the back EMF constant (K_{E}) should be selected to satisfy
Eq. 1 when selecting a motor to be used as a generator.
Without considering the load, the back EMF constant of the
winding should be larger than . If the achievable shaft
speed does not reach a sufficient back EMF, a suitable gear
reduction can be added to increase the speed at motor
shaft, given that the motor’s maximum permissible speed
parameters are not exceeded.

### TERMINAL VOLTAGE, MAXIMUM CURRENT, AND LOAD RESISTANCE

Figure 1 shows that the voltage generated across the
terminal (U_{i}) of the motor is directly proportional to the
angular speed of the rotor when the load (R_{Load}) is not
connected across the terminals. In this condition, the current
through the motor is zero. When a load is connected across
the motor terminal, current flows and the voltage is reduced
depending on the total load resistance. The terminal voltage
(UT) when the load is connected and current (I_{Load}) is flowing
through the circuit is given as:

For a fixed angular speed of the motor shaft, as the load current increases, the terminal voltage reduces (Eq. 3). When the back EMF equals the resistive voltage drop across the terminals, the terminal voltage becomes zero.

Figure 2 shows the load current versus terminal voltage
graph of an ideal brushed DC motor for a generator. When
the motor terminals are not connected, U_{T} equals U_{i}, and
current does not flow through the rotor windings. When
the terminals are short-circuited, the maximum amount of
current would flow through the circuit and U_{T} becomes zero.

The maximum current through the circuit can be calculated as:

When all other parameters are constant, if the angular
speed on the motor shaft increases, the Fig. 2 graph
shifts towards right with same slope, increasing both U_{i}
and I_{Max}. In Eq. 5, the inherent resistance of the motor
windings (R_{Rotor}) is the limiting factor for maximum current
in generator mode. If R_{Rotor} is high, the sensitivity of the
generator system increases and the resulting voltage
variation with current drawn creates an unstable system.
A motor with a higher back EMF constant and lower
resistance will provide stable operation.

### DRIVING TORQUE AND POWER BALANCE

When a motor is driven in generator mode with open terminals, no current flows through the circuit and mechanical friction creates losses in the driving unit. This condition is similar to unloaded motor operation.

The torque (M) equation for a motor is given as

The generator must be driven with a torque that will generate
the required load current through the winding when the
terminals are closed across the load resistor (R_{Load}). Motor
selection is limited by the maximum amount of torque that
can be applied on the shaft in generator mode. The operation
of a brushed DC motor is limited by the maximum continuous
torque (thermal and mechanical) and maximum continuous
speed (mechanical and electrical) available. Selecting a
motor that can handle the generator torque on the shaft and
manage the maximum current through its circuit is similar to
the process of sizing a motor based on desired load points.

At steady state, the mechanical input power to the generator can be represented as:

The electrical output power at any load current and terminal voltage can be represented by the rectangular area under the slope as shown in Fig. 2.

The output power is maximum when UT is half of the Ui.
At this point, the load current ILoad is half of the maximum
current I_{Max}.

Therefore,

A motor used for generator purposes should not be chosen
solely on power considerations. Ideally, P_{Max} should always
be higher than the required electrical output power from
the generator. Depending on the load current value, the load
point on the Fig. 2 graph can move along the x-axis. Thus,
the actual power output (P_{Actual}), may be less than P_{Max}. While
selecting the right motor to be used as a generator, P_{Actual} should be taken into consideration and not P_{Max}. This may
require selecting a motor with a higher rating.

The efficiency of the generator can be determined as:

### SELECTING A MOTOR AS A GENERATOR

Example 1: This example reviews the selection of a Portescap Athlonix series DC brushed motor for a generator application. The back EMF constant of the Athlonix series 17 DCT with 209P coil is 1.17 mv/RPM. The motor’s characteristic curves are plotted in Fig. 3. If this motor is used as a generator at 5,000 RPM of shaft speed, the output back EMF would be 5.85 V. (Eq. 1)

The maximum load current through the circuit under shortcircuited condition would be

This value of I_{Max}. exceeds the maximum continuous
current of the motor (0.55 A). This may be acceptable for
intermittent operation, which is determined by the thermal
time constant of the motor and expected duty cycle. For
continuous generator operation, a load resistance (R_{Load}) is
recommended using the equation:

Where, I_{Cont} is the maximum continuous current of the motor.

So, if a load resistance of >3 Ω can be used in the generator, 209P coil is good for an input speed up to 5,000 RPM. If load resistance cannot be used due to mechanical or technical limitations, or if the input speed is higher than 5,000 RPM, another coil should be chosen. For example: the coil 211P may be a better choice to consider for this requirement.

Example 2: The back EMF of the Portescap 16C18 motor with 205P coil is 0.70 mV/RPM. At 10,000 RPM, the open circuit output voltage at the terminal is 7.0 V.

Under short-circuited condition, the maximum current that can flow through the windings is

which is less than the maximum continuous current (I_{Cont})
of the motor. Therefore, using this motor as a generator
at 10,000 RPM of shaft speed is acceptable without
considering an external resistance load.

The output characteristics for 16C18 at different shaft speed is plotted in Fig. 4.

The shaded box is the area of continuous operation. For intermittent operations, various factors such as maximum temperature rise, maximum shaft speed, mechanical limit of the motor, and generator life should be considered.

Figures 5 and 6 show that the efficiency of the 16C18is relatively higher at lower generator current. At maximum output power, the output efficiency is close to 50%. It is ideal to select a generator with working point close to the maximum efficiency. This ensures that losses in the system are minimized and reduced mechanical input power is needed to generate the desired output voltage-current characteristics.

### CONCLUSION

It is often misunderstood that a brushed DC motor running in generating mode is not as efficient as when functioning as a motor. However, reasonably high efficiency can be achieved with the proper selection of the motor, loads, and operating speed. The electrical and mechanical factors must always be considered when determining the operating points. Knowledgeable application engineers with extensive design experience are available for consultation to select the correct motor for a range of applications such as tachometer generators, mortar firing, and energy harvesters.