 • # 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. Traditional classification is as follows.

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 electromagnetic 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)

### 5.Electric potential, torque and energy equation

#### (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.) ### 7.Analysis of major parameters

#### (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.

• # Evaluation of motor

How to evaluate a motor? Typically industrial products can be evaluated with the following aspects. The most important characteristic of industrial products is low deviation.

#### (1) Full dimensions

The fundamental characteristics that customers require are assembling dimensions and outline dimensions.

The dimensional deviation of a good product should meet product standard requirement. (GB standard, industrial standard or enterprise standard)

#### (2) Basic performance

a. Rated voltage: known parameter (unit: V)

b. No load current: I0 (unit: A)

c. No load speed: n0 (unit: rpm)

d. Rated current: IL (unit: A)

e. Rated torque: TL (Unit: g.cm)

f. Rated speed: NL (Unit: rpm)

g. Current in stall: Ist (unit: A)

h. Torque in stall: Tst (unit: g.cm)

i. Other parameters such as efficiency, power, electric potential constant, torque constant etc. can be calculated from the above data.

#### (3) Special characteristics

a. Vibration: amplitude (unit: mm), vibration velocity (unit: mm/s), vibration acceleration (unit: mm/s2)

b. Noise: sound pressure LP (unit: dB(A) and acoustical power LW (unit: dB(A). They are both relative values.

c. EMC: This index is to evaluate the ability of the motor resisting the radio interference or the radio interference level that the motor generates.

d. Environment test: This is to judge the load capability of the motor under high and low temperature. Alternating temperature test is the common test. Alternating temperature and humidity test is more severe test. Magnetic field of ferrite magnet decreases by 5-7% under -80 ℃. The motor electric performance is therefore deviated.Mechanical shock, external alternating magnetic field, aging (long time) storage will also weaken the magnetic field.

e. Others: such as safety clearance, safety creepage distance, protection class, type of cooling etc.

### 9.Winding type and carbon brush placement principle

3-pole rotor/commutator winding graph (Figure 13)

a.Angel between slots of rotor and slots of commutator is 60°

b.Coil C is in the process of commutating. It is being shortcut by brush at negative terminal.

c.Brush locates at the centre line of the magnetic poles.  5-pole rotor/commutator winding graph(Figure 14)

a.Angle between slots of rotor and  slots of the commutator is 0°

b.Coil B is in the process of commutating. It is being shortcut by brush at positive terminal

c.Brush locates at the centre line of the magnetic poles.

#### ● Principle of carbon brush placement

a.Try to get maximum effective conductors. In other words, make the direction of current the same in as many conductors under the same pole as possible. In some cases (such as 12-pole rotor), we will sacrifice the number of effective conductors to improve commutation. Such cases will not be discussed here.

b.Minimize the electric potential of the commutating coil (the one that is shortcut). Typically the sides of that coil are placed at the edges of the magnetic poles or between the magnetic poles. So the carbon brushes are usually placed in the middle of the commutator bars that are connected to the coil.

c. Electric angle between positive and negative brushes is 180°.Conclusion: There is not a sole way to connect coil and commutator segments.

### 10.Typical application

According to the characteristics of our motor models, we hereby describe in details by means of types of power supply and motor load.

#### (1)Classified by input power supply

a.Dry battery, rechargeable battery, small capacity AC/DC adaptor.

The characteristic of such power supply is that they have large internalresistance, There is large voltage drop when the motor is applied with load.The output power of the motor is limited by the capacity of the power supply.When designing such motor, motor efficiency is not the only point to be considered.How to get the largest output power from the power supply is the most important. That is to say, try to get maximum value of P1=V*I.Practically, it is hard to achieve this target considering only the motor parameters. How to properly evaluate such motors is also a subject to us.

b.Input power supply from voltage divider as resistor or resisor/capacitor.

In such circuit, when the current changes, the output voltage changes. In actual application, AC input voltage is usually 120V-240V. Out of various reasons when the current increases, the resistor R1 or capacitor C will take more voltage drop.The output voltage is less. Motor speed is therefore lowered. Its operating point and characteristics will all deviate. The result will be different according to different application of the motors.Take the well-known hair dryer for example, if the above change happens, air flow decreases. The temperature of the resistor R1 rises. The resistor gets more voltage drop. The output voltage is lower, making the situation a vicious circle. The motor will lose its function quickly.

c. Regulated power supply

This is the ideal power supply. The input voltage doesn’t change with the environment or motor load. The motor’s characteristic is decided by the motor parameter itself. The motor performance data we provide to our customers are tested under such power supply. In practical application, high capacity accumulator battery and AC/DC adaptor (variation of V less than 5%) are deemed as regulated power supply.

#### (2)Classified by motor load

Startup of the motor with fan load is similar to the startup of the motor with no load. So there is no requirement to motor’s startup or stall torque. Sometimes we even need to restrict its torque from being too large. The most important feature of the motor with fan load is the stability and discreteness of its speed in mass production. The output power is in proportional with the motor speed. If the motor speed deviates a lot, the motor working characteristics will also deviate a lot. So the characteristic of the load at working point is the major point we look at.

Examples are cable retrieving devices for vacuum cleaners and tube retrieving fixtures for Irrigation machines.Similar to winching devices, the motor starts to work at its full load. The most important characteristic of such motor is its stall torque. The consistency of the stall torque is the key point during motor design and fabrication.Central door lock actuator also belongs to such winching load. Motors with such load usually work at short time working cycle.

Torque of such load is stable during work. The motor power increases linearly with the motor speed. It may reach its full load at startup. But in most cases it starts up with partial load. Usually it works under rated load for a very long time. We should consider various aspects including temperature rise in motor design. Reciprocating pump is the typical linear load.

There are still other loads like eccentric wheel, gearboxes that we are not going to discuss in this article.

• # Instruction for use

### Overload or Stall Condition

The motor temperature would rise gradually due to the internal energy conversion between the windings and iron core during running. The windings will not be burnt under rated load because of the balance between the produced and vented heat. But if it’s overloaded or stalled for a long time, the insulation film of copper wires might be dissolved due to high temperature. This will short-circuit the winding which causes high current even damages the motor and driving board. Besides, under overloaded condition, the strength of the gear or other parts attached on the shaft will be affected (tooth broken or wore out). So please make sure that motors are operated under rated working conditions.

### Motors Working at Lower Speed

For most of the dc motors, we use carbon brushes. When a motor runs, spark occurs in the contact area because of the friction between the brushes and commutator at the timing of the commutation. Carbon dust will accumulate in the commutator slots which might cause short circuit, burn the motor or the driving board if the motor runs at lower speed and the dust couldn’t be burned in time. Please kindly pay attention to this condition.

### Motors Working at Lower Speed

For most of the dc motors, we use carbon brushes. When a motor runs, spark occurs in the contact area because of the friction between the brushes and commutator at the timing of the commutation. Carbon dust will accumulate in the commutator slots which might cause short circuit, burn the motor or the driving board if the motor runs at lower speed and the dust couldn’t be burned in time. Please kindly pay attention to this condition.

### Remarks about PWM Controller

The lifetime of the brushes is shorter when the motor is powered with PWM controller not by rated voltage or constant voltage. And the carbon brushes might wear out easily under certain frequency of the PWM controller. Normally the frequency used for dc motors is 10～20KHZ. Heating might also occur because of sympathetic vibration if the frequency of the PWM switch is close to the motor components’. Besides, please be noted that the motor might not run if with integrated electrolytic capacitor under certain frequency. So we suggest motors with varistor inside if the motor is powered by PWM controller.

### About Inertia and Brake

It’s very common that after power off, the motor shaft will still rotate for a while because of the inertia. If instant brake needed, you can short-circuit the positive and negative poles then the power generated by the motor (reverse current) can stop it quickly. But this might increase the motor current and even shorten the lifetime.

A motor’s lifetime is related to the operating conditions such as the power supplier, duty cycle, and load conditions etc. The lifetime data on our spec is based on the rated testing conditions and motor running in one direction without any stop. It’s just for reference only. For actual products, please make full testing to ensure the lifetime is long enough.

### Assembly

There are screw holes designed for motor assembly. Please kindly refer to the outline and make sure the screw length is in the recommended range. As for the allowable torque, please kindly refer to the related technical standards. Over that range, it might slip the screw.

### Motor terminals

The motor terminal structures and inner parts might be broken when the soldering temperature is too high. The recommended operating way is using soldering iron 40W, 380℃, and less than 3 seconds. Besides, force on the terminals will also break the terminal structure.

### Axial Force

When you press gear or other parts on the output shaft, support for the other side shaft end will be needed. If it’s not possible to apply the support, the press force should be no more than the max allowable force.

### Shock and Drop

When you press gear or other parts on the output shaft, support for the other side shaft end will be needed. If it’s not possible to apply the support, the press force should be no more than the max allowable force.

### The Use of Binding Material

If binding material like glue is used during the assembly, please make sure it will not be added to the output shaft bearing. For some volatile glue, it might also stain the commuatator which affect the motor performance.

Please pay fully attention to the items mentioned above. If other issues during application, please kindly contact Kinmore for further information.