Speed measurement of a general dc brushed motor based on sensorless method

1. Speed Measurement of a General DC Brushed Motor
Based on Sensorless Method
Chieh-Tsung, Chi
Department of Electrical Engineering,
Chienkuo Technology University
Changhua, Taiwan, R.O.C.
jih@ctu.edu.tw
Shih-An,Yin, member, IEEE
Department of Electrical Engineering,
Chienkuo Technology University
Changhua, Taiwan, R.O.C.
sayin@ctu.edu.tw
Abstract—DC brushed motor (abbreviated as DC motor later)
has some outstanding advantages for example cheap and control
easy compared to other types of motor. It has already been
widely used in industrial machines and household appliances. In
many applications of DC motor, the speed of the DC motor is
often a basic required to be measured parameter. To achieve this
purpose, a direct speed measuring method which a speed sensor
with suitable dimension or resolution needs to be coupled with
the axis of DC motor and leads to more complicated mechanical
structure and control circuit should be included in equipment.
Moreover, if the setup place of the speed sensor is insufficient, the
direct speed measuring method is then not allowed to be used.
The current parameter is one of the independent variables of DC
motor. Many important dynamic behaviors of the DC motor will
be characterized by this parameter. In this paper, we will
propose a new speed measurement of DC motor based on a
sensorless speed method. In order to verify the feasibility of our
proposed method, we test and compare the measured motor-
speed values of electric-spray pump by using the conventional
speed measuring method (couple a speed sensor with rotating
axis of DC motor) and the proposed sensorless speed measuring
method, respectively. The experimental measured results show
the method that the speed measurement of DC motor is read and
calculated based on the frequency of ripple component of the
motor current is actually feasible.
Keywords-component; DC brushed motor; speed measurement;
sensorless;ripple frequency; electric-sprayer pump
I. INTRODUCTION
DC motor is a device which is often used to convert the
electrical energy into the mechanical energy. The necessary
amount of DC motor in the world is still very large now. It is
often used in industrial and household application fields. A lot
of industrial equipments are required to be supplied with
kinetic energy for a linear or rotating motion requirement. In
these application fields, the DC motor is very suitable to be
selected for providing kinetic energy to drive the mechanical
load. In order to achieve the control purpose, many parameters
of system, such as the current, temperature, and speed, they
would be first sampled and feedback to the system controller
immediately. The close-loop control structure is formed.
In order to acquire the precise control of equipments which
is driven by a DC motor, such as a constant-torque control or
constant-speed control or position control, some types of sensor
like the speed and/or the current sensors will be integrated into
the system controller for dynamically conducting a close-loop
control purpose. In addition, in the motor characteristic testing
fields (includes performance tests and product mass-production
tests), DC motor is necessary to be tested regarding its speed
related performances under different loads’ condition. How to
quickly and precisely measure the speed data of DC motor is
one of the critical problems because it is a very important
performance evaluating index during the DC motor
characteristic test and production mass-production test. In the
regular performance test of DC motor, the speed measurement
is often carried out through coupling a real speed sensor with
the axis of DC motor. The measured speed data of DC motor
will be read, calculated, and displayed by the system controller.
This is generally called as a direct speed measuring method. If
the speed sensor is incorporated into the hardware circuits and
software algorithms well, the testing precision by using this
speed measurement method is very high. But there are some
disadvantages will be occurred and described as follows [1-3].
When the speed sensor is integrated into the application
equipment, the mechanical structure would become more
complex and the manufacturing cost of equipment would be
increased as well. The testing efficiency must become worse
because much more time will be required to change the speed
sensor;If the allowed installing space of the real speed sensor
has been critical limited, the direct speed measuring method
may be not suitable to be used here;When the direct speed
measuring method is applied to the measurement of torque-
speed characteristic curve for the measured DC motor, much
more time may be taken for adjusting the different load
condition.
Based on the basic working principle of DC motor, the
motor current is generally one of its important independent
parameters. The performance of DC motor can be directly
characterized by the current parameter. Especially, the DC
motors have their special mechanical structure. Many physical
electrical quantities can be obtained directly or calculated
indirectly from the dynamical current value of DC motor, for
example, power dissipation and speed. Especially, the motor
speed can also be obtained by using the dynamic current value.
This truth result is often and easily neglected by people. In
‹ ,((( ,3( 332

2. most application fields of DC motor, the current value of DC
motor is often a basic sampled parameter based on the
requirement of system control or circuit protection purposes.
The speed measurement of DC motor can certainly be obtained
without requirement of any speed sensor. Of course, the
application problems occurred as mentioned above would be
overcome there.
II. COMMUTATION PRINCIPLE OF DC MOTOR
In order to explain the speed calculation method of DC-
brushed motor from the sampled dynamic current value, the
first thing should be done is to review the basic commutating
principle of DC motor again. Fig. 1 shows part of mechanical
structure of a typical DC-brushed motor. It consists of some
commutators, brushes, and rotor windings [4,8]. The current
flowing into any one of the rotor windings before and after the
commutation process starts is assumed as i and i− ,
respectively. Firstly, because the flowing direction of winding
current would be dynamically changed when the DC motor is
normally working, an induced voltage would be occurred
across the commutated rotor winding at the same time.
Secondly, there is mutual induced voltage will be generated
due to the current variation or commutation process occurred
on the neighboring rotor windings. Thirdly, a rotation voltage
will be generated occurred on the commutated rotor winding
when the commutated rotor winding rotates through the
permanent magnet of DC-motor stator. Therefore, the total
voltage of commutated rotor winding is the sum of self induced
voltage, mutual voltage, and rotation voltage. As shown in Fig.
2, the rotating direction of DC-motor axis is assumed as
counterclockwise, the brush marked “+” is brush 1, and the
brush marked “-“ is brush 2. The branch circuit 1 is defined as
the flowing direction of current is from brush 1 to brush 2
along with clockwise direction. Comparatively, the branch
circuit 2 is defined as the flowing direction of current is from
brush 1 to brush 2 along with counterclockwise direction. The
flowing current and the resistance of all windings occurred on
the branch 1 is defined as 1i and 1r . Relatively, the same
parameter occurred on the branch 2 will be defined as
2i and 2r . The rotating induced voltage of windings a ,b , and
c are 1e , 2e , and 3e , respectively. Compared to the rotating
induced voltage of these armature windings, the values of self
induced voltage and mutual induced voltage are generally
lower than that of the rotating induced voltage. For simplifying
the analysis, the self and mutual induced voltages will not be
considered here. According to the Kirchhoff’s current law, the
current value of DC motor must copy with the
relationship 21 iii += .
As the time instant when the winding a is shorted by brush
happens, winding b and c is respectively formed as branch 1
and branch 2. The current flowing direction in branch 1 is
brush 1b’-b-brush 2. The voltage equation in branch 1 can
be expressed as
211 eriu +=
(1)
a
a’b
b’
c c’
+-
.
:,,,
windingsarmatureareThey
candcbbandaa ′′′
Commutator
Brush
Figure 1. The symbols’ definition of part of mechanism of DC-brushed
motor.
Fig. 2(a) shows that the branch 1 is composed of windings
a and b . The flowing direction of current branch 1 is brush 1-
a-a’-b-b’-brush 2. The branch voltage equation can be
expressed as
+-
a
a’b
c
b’
c’
(a)
+-
a
a’
b
c
b’
c’
(b)
+-
a
a’
b
c
b’
c’
(c)
Figure 2. Basic principle of cmmutating process in the armature windings of
DC brushed motor.
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3. 2111 eeriu ++=
(2)
The single winding c is formed as branch 2. The flowing
direction of current in branch 2 is brush 1 -c’-c-brush 2 and
the branch voltage equation of branch 2 is written as:
322 eriu += (3)
The voltage equation in branch 2 is kept invariant, as can be
seen in Equ. (2). Now, the winding b forms branch 1. The
voltage occurred in branch 1 will decreased when the winding
a is shortened by a brush. Because the supplying voltage
source across two brushes is always kept at a constant value,
the current value in branch 1 will be suddenly increased. At the
same time, the current flowing through the branch 2 is kept at a
constant value or none of change. Therefore, the total cuurent
flowing into the DC motor will be abruptly increased as well.
When the status of commutator is shown as Fig. 2(c), the
winding b is formed as the branch 1. The flowing direction of
current in branch 1 and equivalent voltage equation across the
brushes are the same as mentioned above. The amount of
current changing value is almost kept at constant value too. The
branch 2 is formed as by winding c and a . The flowing
direction of current in branch 2 is brush 1-a’-a-c’-c-
branch 2. The voltage equation can be written as follows:
3122 eeriu ++= (4)
Notice that the induced voltage across the branch 2 is the
sum of the induced voltages occurred in winding c and
winding a , respectively. The current value in branch 2 will be
suddenly decreased when the commutation process ends. There
is a very important conclusion can be obtained. The current of
DC motor appears a periodic waveform. It will generate six
ripples for every one revolution of DC motor because the DC
motor has two brushes and three commutators.
III. THE RELATIONSHIP BETWEEN CURRENT RIPPLE AND
SPEED
According to the basic commutating theory of DC motor,
the brush would slide between the two neighboring
commutators periodically. The neighboring armature windings
are connected and shortened. The total induced voltage value
by all armature windings is variable. The polarity of induced
voltage is always inversely to the applied external voltage
source of DC motor. Therefore, the current value of flowing
into the DC motor is variable too. In other words, the current of
DC motor is a DC current component is incorporated into a AC
ripple component of the current. The speed of DC motor is
closely with the ripple frequency of the current. For a general
DC-motor product, the number of commutators and pole of
pairs are fixed. The relationship between the speed of DC
motor and the frequency of ripple component of the motor
current is able to be written as follows [4]:
60
npkc
f
×××
= (5)
where
n : the speed of DC motor, the unit is ... mpr
f : the frequency of AC ripple component of the current,
the unit is Hz ;
k : the number of commutator of DC motor;
c : if the number of commutator k is even, then 1=c ;
comparatively, if k is odd, then 2=c .
As shown in Equ. (5), the speed of DC motor is
proportional to the frequency of the AC ripple component of
the current. Therefore, if we want to obtain the dynamical
speed value from the sampled current of DC motor, we should
have to successfully measure or get the AC ripple component
of the current from the DC-motor current.
IV. SPEED SENSOR BASED ON AN INFRARED DEVICE
A sensory circuit based on an infrared device is designed
and implemented for measuring the speed of DC motor, the
electrical structure is shown in Fig. 3. The primary side of
speed sensory circuit is driven by a constant current source,
therefore, there is an infrared light with constant intensity will
be injected into a reflecting plate which is installed on the
surface of the axis of DC motor. The distance between the
reflecting plate and the infrared device is always kept at
constant value. There is a tape with high reflectivity is attached
on the axis of DC motor. The action of tape, of course, will
follow the measured motor-axis rotation. Moreover, the
reflected light intensity which is received by the secondary side
of infrared device will be limited to be only affected by the
reflectivity of the reflecting plate.
(a)
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4. (b)
Figure 3. The fabricated speed sensory circuit of DC motor based on an
infrared device includes (a) circuit (b) devices arrangement.
As can be seen in Fig. 3(a), the resistor 1R is incorporated
into a zener diode 1D to form a simple voltage regulator. The
regulated voltage across the zener diode 1D , 1V , is used as the
bias voltage of transistor 1Q base. The transistor 1Q is designed
to work in linear operating area here. The relationship between
the emitter current EI and the collector current CI is given as
follows:
EC II
β+
β
=
1
(6)
where
β : the DC current gain of transistor 1Q ;
CI and EI : the current values flowing into the collector
and the emitter of 1Q , respectively;
Generally speaking, the DC current gain of transistor 1Q is
always much larger than one. The value of CI is almost
equivalent to that of EI . The current value flowing into the
collector of 1Q can be expressed as:
32
)( 1
RR
VV
I
QBEZ
C
+
−
≈ (7)
)( 1QBEV is the junction bias voltage between the collector
and the emitter of 1Q . As the infrared device 2Q is designed to
work within the safe operating region, the primary current
of 2Q can be controlled by adjusting the resistance of the
combined resistors ( 32 RR + ). In other words, the input-output
sensitivity of speed sensory circuit is also affected by the
resistance of ( 32 RR + ).
As the reflectivity of reflecting plate is different, the
secondary received light intensity of 2Q and the equivalent
resistance between the collector and the emitter is changeable
as well. The output voltage value of speed sensory circuit,
Vout, is inversely proportional to the received light intensity
of 2Q . As the received light intensity of 2Q is reduced, the
output voltage value Vout is a high logical level.
Comparatively, as the received light intensity of 2Q is
increased, the output voltage value Vout would be a low logical
level. In this paper, we will read the frequency value of Vout
and calculate the speed of DC motor.
V. EXPERIMENTS AND DISCUSSIONS
The sprayer has widely been applied in the agricultural and
the gardening industry. Especially, it is often used civil
application such as the sanitation of larger stock cultivation,
public place, and school. The output liquid pressure of the
employed electric sprayer, which is supplied an independent
rechargeable battery, is generally controlled by a step-down
buck converter. In experiments, the pump of electric sprayer is
driven by a DC (brushed) motor. The supplied voltage of DC
motor is regulated by the buck converter via a PWM
technology. Some protection circuits such as over-current,
over-temperature, and short circuit etc and friendly operating
interface are included in the system controller of electric
sprayer. Taken the working performance, manufacturing cost,
using safety, and operating reliability into consideration, an
electric sprayer with pressure- programmable capacity is then
successfully designed. The system controller design of DC-
motor is a close-loop control structure [6,7]. In addition, the
requirements of circuit protection or equipment, the current
value of DC motor will be necessary to be often dynamically
measured by a suitable current censor. We are hope to
furthermore improve the performance of electric sprayer and
free to increase the manufacturing cost. One new sensorless
speed measurement method based on the motor current will be
presented here. This method is mainly implemented by using
few of hardware devices.
In the experiments, the pump driven DC motor of electric
sprayer is applied to a direct voltage source 15 V, the speed of
DC motor is measured at a stable state. As shown in Fig. 4, ch1
is the output voltage waveform of the speed IR sensor which is
based on an infrared device. The one cycle of the voltage
waveform represents that the rotor axis of DC motor is turned
around one revolution. The ch2 is the measured motor current
waveform of the pump driven DC motor by using a hall-effect
current sensor. Fig. 4 shows the waveforms both the speed of
DC motor and the current of DC motor. Furthermore, the AC
ripple component of the motor current has a cyclic
characteristic and its period is equal to the time interval of
every one revolution of DC motor. On the one hand, Figs. 5
and 6 shows the different waveforms when the same measured
electric sprayer is supplied with different voltage sources, such
as 12 V and 15 V [9]. All the measured three waveforms have
the same time scale, namely 10 msec per division. On the other
hand, the spent time for the axis of DC motor to turn around
one revolution becomes longer when the applied voltage value
of DC motor is decreased. This phenomenon represents that the
speed of DC motor become slower when the applied voltage of
DC motor is decreased.
In order to verify the feasibility of the proposed sensoreless
speed method based on the AC ripple component of the motor
current, the comparison method will be used here. We shall
measure the speed of the pump driven DC motor by using the
335

5. speed sensory circuit based on the infrared device and the
ripple component of the motor current, respectively. The
electric sprayer will be applied to a direct voltage source 15 V,
12 V, and 10 V [5]. According to the working principle of DC
motor, the speed of DC motor is proportional to the applied
voltage value under the same mechanical load condition.
Therefore, the measured DC motor will be driven to work at
three different speeds.
Figure 4. Shows the speed of DC motor is measured by a non-contact speed
IR sensor.
Figure 5. The applied voltage is 15 V and enters into stable state. CH1 is the
measured speed waveform using infrared device; CH2 is the waveform of DC-
motor current.
Figure 6. The applied voltage is 12 V and enters into stable state. CH1 is the
measured speed waveform using infrared device; CH2 is the waveform of DC-
motor current.
When the pump driven DC motor is applied a direct voltage
source 15 V, the speed of DC motor is not measured until it
enters into stable state. As shown in Fig. 4, the speed of DC
motor is measured by the IR sensor and the sensorless method,
respectively. Fig. 5 shows that CH1 is the measured voltage
waveform based on the speed IR sensor. It represents that the
rotor axis of DC motor turns around one revolution for every
one cycle of square wave. The CH2 is the current waveform of
pump driven DC motor by using a hall-effect current sensor.
Fig. 5 indicates the waveforms both the speed of DC motor and
the current of DC motor. Furthermore, the AC ripple
component of the motor current has a cyclic characteristic and
its period is equal to the time interval when the axis of DC
motor is turned around one revolution. Figs. 6 and 7 show the
different experimental results when the electric sprayer is
driven to work by different voltage sources, such as 12 V, 10 V
and 15 V. These three measured waveforms or results mean
that the acquired frequency such as 62.5 Hz (15 V), 45.45 Hz
(12 V), and 38.46 Hz (10 V) are changed with the applied
voltage of DC motor. Refer to Equ. (5), these frequency of AC
ripple component of the motor current can be directly
converted into the equivalent speed value of DC motor are
3750 mpr .. (15 V), 2727 mpr .. (12 V), and 2308 mpr .. (10
V), respectively. The speed of DC motor becomes slower when
the applied voltage value of DC motor is decreased. This result
agrees well with the theoretical result of DC motor.
Figure 7. The applied voltage is 10 V and enters into stable state. CH1 is the
measured speed waveform using infrared device; CH2 is the waveform of DC-
motor current.
VI. CONCLUSIONS
In this study, there is a sensorless speed measurement in
DC motor is described. The proposed is based on the AC ripple
component of the motor current, which is used to detect the
ripple frequency because it is related to the speed of the motor.
The feasibility of the proposed speed measuring method is
evaluated in different applied voltage sources. The obtained
results with the same employed motor in different measuring
methods show that they are very similar. The manufacturing
cost and structure becomes higher, the allowable installed
space of speed sensor is limited and the measuring efficiency
may be then reduced. In fact, not all kind of sensors are always
allowed to be installed in the equipment. The speed
measurement of equipment like DC motor with a real speed
sensor is sometimes not suitable. Furthermore, the equipment
maybe hope to promote the operating performance and
required to be dynamically sampled the speed of equipment
where no free space exists. The proposed sensorless speed
336

6. measuring method designed for DC brushed motor is very
useful here.
ACKNOWLEDGMENT
This work was supported by the National Science Council
(Taiwan) under grant NSC 100-2622-E-270 -008 -CC3.
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