#### Background knowledge

• ##### 1.Basic concepts

Motor is an energy conversion device that converts electric energy into mechanical energy or mechanical energy into electric energy, using magnetic field as media.
PMDC motor is an energy conversion device that converts electric energy into mechanical energy, usingpermanent magnetic field as media provided by permenant magnets like ferrite magnets and neodymium magnets.
Every motor needs two basic conditions to function: magnetic field and current.

• ##### 2.Classification of motor

There are many ways to classify the motors.
The motors Kinmore makes belong to brush type
strontium ferrite permanent magnet DC motor. • ##### 3.Basic theories

Research to the motors is based on the following five scientific laws. In order to have a preliminary acquaintance to motor principles, we need to known these laws first. ##### (1) Law of electromagnetic induction (Faraday 1831)

Conductors (of finite dimensions) moving through a uniform magnetic field
will have currents induced within them.
The direction of the current is judged by right hand rule and follows the
equation: E=B*L*V
E: Electromotive force (Unit: V)
B: Magnetic flux density of magnetic field (1 Tesla=104 Gauss)
L: Effective length of conductor (Unit: m)
V: Velocity of the conductor (Unit: m/s)
See figure 1 to the right, if we connect a lead wire to the conductor,induced
current will be generated.

• ##### (2) Biot-Savart Law

Conductors with current within them will generate electro
magnetic force in a magnetic field. The direction is judged
by left hand rule, (see figure 2) and follows the equation:
F=B*I*L
F: Electromagnetic force (Unit: N)
I: Current in the inductor (Unit: A)
B: Magnetic flux density of the magnetic field (Unit: Tesla)
L: Effective length of the conductor (Unit: m)
Left hand rule is also called as motor rule.
Right hand rule isalso called as generator rule. • ##### (3) Kirchhoff's circuit laws (See figure 3)

KCL ΣI=0: At any node (junction) in an electrical circuit, the sum of
currents flowing into that node is equal to the sum of currents flowing
out of that node
KVL ΣU=0: The directed sum of the electrical potential differences
(voltage) around any closed network is zero.

• ##### (4) Law of conservation of energy

The total amount of energy in an isolated system
remains constant over time.

##### (5) Ampère's circuital law

In short, conductors with current within them generate magnetic
field around them. The direction of the magnetic filed is judged by
right hand thrumb rule and follows the equation. (See figure 4)
∮H×dL=∑I=IA+IB+IC+…
H: magnetic field intensity (Unit: A/M)
L: Length of conductor (Unit: M)
I: Current (Unit: A) • ##### 4.Basic principles 2-pole PMDC motor
2-bar commutator
2-conductors (1-loop coil) simple armature.
According to Biot-Savart Law and left-hand rule,armature
runs in CCW direction.
It is a simple but unpractical motor.(Figure 5)

##### (1) Electric potential (Figure 6)

From V=E+2△U+I*r we get E=V-2△U-I*r
Meanwhile E=KE*Φ*n(armature back EMF)
V: power supply voltage (Unit: V)
2△U: brush voltage drop (Unit: V)
I: armature current (Unit: A)
R: rotor resistance (Unit: Ω)
KE: EMF constant = Z/60 (for a 2-pole motor.
Z: number of conductors)
Φ: magnetic flux (Unit: Weber) = average magnetic
flux density B * width of magnetic pole *effective
length of rotor
N: speed (Unit: rpm)

##### (2) Torque

TE=KTΦ*I（electromagnetic torque: N.M）
KT: torque constant = Z/2π
Φ: magnetic flux (unit: Weber)
I: armature current (unit: A)

##### (3) Relationship between power and torque：

P=T*n/97500 P: power（unit: W）
T: torque (unit: g.cm)
n: speed (unit: rpm)
When the unit of T is “N?m”, P=T*n/9.55（unit: W） • ##### (4) Energy equation(Figure 7)

P1=2△U*I+I2r+PE
PE=P2+PFe+Pmec
PE: electromagnetic power P2: output power
Pmec: mechanical loss PFe: iron loss
P2=P1-2△U*I-I2r-PFe-Pmec (unit: W)
Efficiency: η=P2/P1*100%
PFe+Pmec is also called no load power
P0=PFe+Pmec
PE=P2+P0 and TE=T2+T0

• ##### (5) Energy transmission graph: (Figure 8) • ##### 6.Performance characteristic (Figure 9)

n=f(T2) relationship between speed & torque.
I=f(T2) relationship between current & output power
η=f(T2) relationship between efficiency & torque
P2=f(T2) relationship between output power & torque • ##### (1) I=f(T2)

I=TE/KT*Φ=(T0+T2)/KT*Φ=T0/KT*Φ+T2/KT*Φ=I0+[1/KT*Φ]*T2 (liner equation)
I0: no load current Φ: constant
At stall, n=0, E=0, according to Figure 6, current Ist=(U-2△U)/r

##### (2) n=f(T2)

E=V-2△U-I*r=KEΦ*n
n=(V-2△U-I*r)/KE*Φ={U-2△U-[(I0+T2)/KT*Φ]*r}/KE*Φ
=(U-2△U-I0*r)/KE*Φ-r/KE*KT*Φ2*T2
= n0-[r/KE*KT*Φ2]*T2（equation of lines）

##### (3) P2=f(T2)

P2=T2*n/9.55=[n0-(V/KE*KT*Φ2)*T2]/9.55=[n0*T2-(r/KE*KT*Φ2)*(T2)2]/9.55

P2 is a second-degree parabola (Figure 10)

• (5) Energy transmission graph: (Figure 8)
(Equation iscomplicated thus is omitted here.) ##### (1) Turns of coil and magnet wire diameter (other parameters remain unchanged)

We know from 5.1 that the potential constant KE increases when the turns of coil increase. Motor speed n is therefore lowered. On the contrary, when the turns of coil decrease, the motor speed increases. When the diameter of the magnet wire increases, the rotor resistance r reduces. Back EMF of the rotor increases (E=V-2△U-I*r). The motor speed n therefore increases. On the contrary, when the diameter of the magnet wire decreases, the motor speed n decreases. The current at stall is in inverse proportion to the resistance r.Turns of the coil and diameter of the magnet wire restrict each other under the space limit of the lamination slot. We should clearly understand such relationship when we try to adjust the motor parameters.

##### (2) Magnetic flux (other parameters remain unchanged)

Magnets with higher magnetic flux density and longer lamination sheets will both increase the magnetic flux Φ. From 5.1 and 6.2 we know that speed n decreases. At the same time, load (T2) has less influence over speed n. The characteristic of the motor is thus called hard. On the contrary, if we use magnets with lower magnetic flux density and shorter lamination sheets, the characteristic of the motor is called soft.

##### (3) Air gap

See figure 12, the magnetization curve of the air gap
Φδ=-μ0*(Sδ/δ)*Fδ
Φδ: Air gap flux
Sδ: Air gap area
Δ: Air gap length
Fδ: Air gap magnetomotive force(magnetic EMF)
Permeance angle: α=tg-1[μ0*(Sδ/δ)].
We can see that when δ is longer, α is smaller, air gap flux Φδ is smaller. Motor speed will increase if the other parameters remain unchanged. On the contrary, when δ is shorter, α is larger, air gap flux Φδ is larger. Motor speed will decrease. We will see the same result as we see in 7.2. We usually pursue the maximum possible value of (Φδ*Fδ) in motor design.

##### (4) Effective volume D2*L

Motor torque is proportional to D2*L.
[D: diameter of the rotor L: length of the rotor]
Motor power is proportional to D2*L *n.