Cogging Torque

Cogging Torque

Cogging torque describes the interaction of rotor magnets acting on stator poles

Spin motor shaft with hand pulsation felt during the process is called cogging torque

When magnet in the motor passes stator teeth reluctance experienced by magnet under slot opening causes varying reluctance which contributes to cogging torque

Narrow the slot opening means smaller the cogging torque, if there is no slot opening, cogging torque will be zero

As a thumb rule slot opening must be at least two to three times the covered diameter of the wires

Radial dimension of pole shoe also plays a role in cogging torque

If radial shoe dimension is too small, shoe tip become saturated and added to reluctance which contributes to cogging torque

Each magnet in rotor contributes to cogging torque therefore relation between number of stator slot and magnet pole influences the cogging torque.

Permanent Magnets

Permanent Magnets

There are different type of magnets available

1. Alnoco
2. Ferrite (Ceramic)
3. Samarium Cobalt
4. Neodium Iron Boron

Selection of magnet plays a major role in performance and cost. Ferrite magnets are most popular and is inexpensive.

Samarium cobalt and Neodium magnet are high performance. Neodium is popular in high performance application and cheaper than samarium cobalt.

Magnets are made in two types bonded and sintered

Bonded magnets are made by suspending powdered magnet material in non conductive non magnetic resin. Magnet formed in this way are not suitable for high performance application since substantial fraction of magnet is made by non magnetic material

Sintered magnets are made by sintering process allows magnet to be formed without bonding agent

Permanent magnets are magnetic material with large hysteresis loop

The hysteresis loop is formed by applying large possible field intensity to an unmagnetized material and shutting it off. This allows material to recoil and is called demagnetization curve

If two ends of magnets are shirted by infinite permeable material and material recoils and attain a final point at H=0. The flux density leaving the magnet at this point is equal to remanence or residual flux density Br

Remanence is the maximum flux density that the magnet can produce by itself

If permeability surrounding the magnet is zero, no flux will flow-out of magnet, final point attained is B=0 at this point magnetic fled intensity across the magnet is equal to negative of coercivity or coercive force Hc

For permeance value between zero and infinitive operating point of magnet lies in second quadrant

Between remanence and coerecivity.

The magnitude of slope in second quadrant is known as permeance coefficient Pc

When Pc =0, magnet is operating at coerecivity B=0 , H = -Hc

Pc = infinity B=Br and H=0

Samarium cobalt and Neodium magnet have straight demagnetising curve throughout the second quadrant at room temperature

At higher temperature demagnetizing curve shrinks towards origin.

As demagnetizing curve shrinks towards origin, flux available from orgin drops however this effect is reversible

The maximum energy product BHmax is the maximum product of flux density and field intensity

BHmax is usually mentioned in Million of Gauss-Oer-steds MGOe

Magnetic Materials

Magnetic Material

Flux density B density of magnetic field flowing through a given area of material

Flux intensity H Intensity of magnetic field due to interaction of B

Ferromagnetic material – electrical steel which is usually used for motor construction

Ferromagnetic material

Hysteresis loop is formed by applying sinusoidal excitation of different amplitude and plotting B versus H

For common electrical steel hard saturation reaches at flux density between 1.7 to 2.3T

Core losses

When ferromagnetic material are excited with any time varying field, energy is dissipated due to hysteresis and eddy current losses

Hysteresis loss results because energy lost in every time a hysteresis loop traversed

Loss is directly proportional to size of the loop.

Eddy current loss is caused by electric current induced within ferromagnetic material under time varying excitation. This induced ferromagnetic material circulated within material and dissipate as heat.

Eddy current loss can be minimized by increasing resistivity of material. Electrical steel contains small amount of silicon, which increases resistivity of material. Another way is to use laminated sheet to increase resistivity. Thin lamination is required to reduce eddy current losses.

PMSM - Sizing

Motor Sizing

For high torque motor its better to use higher diameter which gives more room for magnet around the rotor

As motor dimension is fixed, air gap flux density and ampere turns are responsible for maximising the torque output

Low cost motor airgap shear stress varies from 0.5 to 2

High cost motor airgap shear stress varies from 1.5 to 3

Very high-performance motor airgap shear stress varies from 2 to 10

Large liquid cooled machines airgap shear stress varies from 10 to 20

Fundamental Implication

Power is directly proportional to torque

Volume, mass, inertia is few constrains we need to consider while designing

The volume of the motor increases with square of radius or diameter

The ratio of output power to volume cannot be increases by increasing motor diameter

Once diameter is chosen there are two ways to increase power developed. First is by increasing the operating speed. If speed is dictated by application, we need to use some form of speed reduction to increase torque

Other way to increase power output is by increasing magnetic and electrical loading.

Magnetic loading can be increased by using high performance magnet

Surface mount machines and Interior permanent magnet machines

Surface mount machines – low speed operation, less complexity

IPM used for three reasons

1. Flux concentration
2. Rotor structural strength increases – high speed
3. Drive over wide speed range – field weakening mode

Introduction - Permanent Magnet Synchronous Motor Design

Introduction

Brushless DC motors are typically classified by having trapezoidal back emf and are typically driven by rectangular pulse current

PM synchronous motor differed from BLDC motor by having sinusoidal back emf and driven by sinusoidal current

Motors are usually designed for inside rotor and outside rotor. In this magnetic field travels in radial direction which are usually called as radial flux motor

If magnetic field travels between stator and rotor in axial direction, called axial motor

All electrical motor is constructed with winding on stator and permanent magnet on rotor

Magnet poles and Motor phases

It is possible to build PMSM with any even number of magnet pole and any number of phases greater than or equal to one

Usually most of the PMSM motor are designed for 3 phases

The choice of magnet depends on application and space available for magnet

For high speed motor it’s better to choose low number of pole count and for high torque motor its better to choose high pole number.

For high speed motor D:L ration will be 1:1 or less and for high torque motor forms pan cake like structure since it can accombadate more magnets

Stator

Stator usually has teeth that protrude towards magnet on the rotor from outer ring of steel called stator back iron. In between teeth are called slots where electrical winding is placed

Electrical and Mechanical measures

Mechanical speed – rotor shaft makes one complete revolution it travels 360 deg mechanical

Electrical speed – movement of rotor which puts back the rotor in same identical magnetic orientation

Fe is the fundamental electrical frequency, which determines the speed at which the commutation must occur to run at given speed. Inverse of the frequency is commutation time period which determines the time over which to energize the phase completely. 

Fe determines the design of power electronics to keep the motor running

It is Common to use fewer magnet poles for high speed motor. Higher the magnet poles increase, torque production efficiency decreases

Inrush Current Limiter

Inrush Current Limiter

The problem is for higher current at startup is due to charging of output cap C1 which is usually called as inrush current. This inrush current will last longer till the output cap charges to input voltage level. Once output reaches input voltage level diode blocks it.

This type of problem will exist in "Hot plugging" system like battery.

Inrush can be approximately calculate by

Ipeak = Vin * sqrt(Cout/L)

approximate pulse time can be calculated by

Tpulse = Pi * sqrt(L * Cout)

There are two ways to solve this problem practically

1) Passive inrush current limiter

2) Active inrush current limiter

Passive inrush current limiter

This system includes Resistor (approx around 10 to 20 Ohm depends on practical application)



Resistor uses is of Thermistor (Resistance will drop due to rise of temperature which is due to current) type. This has its own disadvantage, resistor will get heat up lot since whole load current will pass through R1 & R2
 
Active Current Limiter

This includes Switch S1 in addition to R1&R2. S1 may be mechanical relay or any power electronics switch like Mosfet, SSR along with its control circuit.



This will serve the purpose but will include additional cost and complexity.

If there is any control over input voltage from previous stage can be solved. For simulation purpose try programmable input voltage source.

Capacitive Power Supply Design

Calculation of a capacitive power supply

Schematic uses single pulse rectification



For the function of a Zener diode: During the positive half-wave, D1 operates as a voltage-limiting component. The required output voltage can be acheived by adjusting the zerner diode value, in your case its 57V, Since zener is before D2 we need to consider voltage drop across D2 (0.7V), You should choose 57+0.7V zener diode D1.

During negative half cycle of input large amount of current flow through D1, it should be limited which can be done by R1.

R1 = Peak input voltage / max current through D1

Peak input voltage = 1.414 * 230V
Max current through D1 can be tacken from datasheet say 1A

R1 = 325.22 ohm.

Choose some nearest value say 330 Ohm

Since load current pass through R1,we should consider power dissipation.

Form factor of single pulse rectifier 2.2,
Actual load current 20mA *2.2 = 44mA
P = I*I*R
p = 44*44*330 = 0.6388W
This component will get heated up need to consider derating wrt temperature, lifetimne etc consider 2x

Power ratingof R1 = 1W

Voltage drop across resistor at full load

Vr1 = 0.6388/44mA = 14.5V

Now its time to calculate capacitor value

Capacitive reactance = 230V-23-14.5-57.7/44mA = 3063.63 Ohm

Capacitance C1 = 1/2Pi*f*XC = 1/(2*3.14*50*3063.63) = 1.03uF

C1 voltage rating should be higher than ac input, select x rated cap usually called as box cap or film cap.

D2 can be any diode 1N4001 commonly used.

C1 smothering of rectified AC.

Time period of 50Hz 20ms

During negative half cycle output should be tack care by C1, Hals cycle time period 10 mS

Ripple voltage can be considered based on application requirement and available size, economical factor, say 2% of output voltage ~ 1V

Load resistance = Voltage/ load current = 57/20mA = 2850 Ohm

C1 = -10ms / (2850 * ln(56/57)) ~ 200uF, nearest 220uF, 100V

Add some 0.1uF or lesser for noise elimination parallel to C1

Add fuse for protection

Note: This circuit doesn't provide any galvanic isolation