Torque

207  Transfer Torque and Efficiency Analysis of Magnetic Gear 
Module: DP 
20151225 
Gears are used to transfer power. Velocity and torque are transformed depending on the gear ratio. Originally, mechanical gears using conventional wheels had issues with noise due to the meshing of wheels, and its maintenance requiring lubricating oil. As a gear to solve these issues, there is the magnetic gear. Magnetic gears are coupled with the magnetism of things like permanent magnets, and can transfer power without contact, as well as reducing noise and maintenance costs.
When prioritizing the size of the transfer torque, rare earth sintered magnets with high energy product are selected for permanent magnets used in magnetic gear. However, since rare earth sintered magnets have high electric conductivity (not as strong as metals such as copper though), eddy current will occur in the permanent magnet and become the cause for decrease in transfer efficiency of magnetic gear. Eddy current of permanent magnets will occur due to variations in magnetic flux density of the gap; however, due to the principle of magnetic gears using pole pieces, the magnetic flux density distribution of gaps have various harmonics components, and for this reason, magnetic field analysis is effective in accurately estimating eddy current.
In this example, the transfer torque and transfer efficiency are obtained with magnetic field analysis for the flux modulated type magnetic gear using permanent magnets for the inner and outer rotor and positioning a pole piece between the magnets. In addition, how transfer torque and transfer coefficient are affected due to revolution speed is researched.


205  Analysis of IPM Motor Characteristics using Thermal Equivalent Circuit Updated 
Module: DP 
20160627 
To realize high output and efficiency in a motor, it will be important to understand temperature increase in each part of the motor. This is because coil resistance and magnet characteristics change with increase in temperature, and this may cause a large impact in the motor characteristics. It is insufficient with a magnetic field analysis of constant temperature, and it will become clear that magnetic field analysis accounting for temperature increase will become necessary.
As a method to account for temperature increase, there is a method of running a coupled analysis of magnetic field and thermal analysis. With this coupled analysis, detailed predictions such as evaluating temperature is possible, but apart from magnetic field analysis, it will become necessary to create a thermal analysis model, and this results in extra work.
On the other hand, a magnetic field analysis using heat equivalent circuit can add a heat equivalent circuit to the circuit of magnetic field analysis, and easily run analysis accounting for temperature increase. This method does not create a complex 3D thermal analysis model and it easily and quickly obtains results. Here, we confirm a situation where temperature increases due to eddy current of the iron loss and magnet, which causes demagnetization of the magnet and torque reduction.


201  Iron Loss Analysis of an SR Motor 
Module:DP 
20141215 
With the skyrocketing prices of rare earth magnets, expectations have been rising for SR (switched reluctance) motors because they have a motor format that does not use permanent magnets. SR motors have a simple structure that can achieve solid performance at a low price. However, since they do not use permanent magnets, it is difficult to obtain the same efficiency as a permanent magnet motor, and efficiency increase is becoming an issue. Reduction of iron loss that occurs during drive is said to be a possible solution to this problem. This is where it becomes important to accurately obtain iron loss of SR motors.
The magnetic flux density waveform in each part of the SR motor is in a state where direct current magnetic flux is superimposed on the alternating current magnetic flux. Direct current bias magnetism, like in this case, has confirmed that the iron loss analysis method using the conventional Steinmetz empirical law produces underestimated evaluations of loss.
This example, to accurately capture iron loss that occurs in the SR motor, we will introduce hysteresis loss accounting for the hysteresis loop of the materials and the iron loss analysis methods accounting for eddy current loss on the inside of the lamination cross section.


200  Iron Loss Analysis of IPM Motor using Hysteresis Model 
Module:DP, LS 
20141215 
Recently, PM motors are being applied in home appliances and electric automobiles, and the demand for compactness and high power is increasing. On the other hand, small and highpower motors tend to be affected by highfrequency components due to magnetic saturation and high rotations, which results in increased loss in the motor, therefore, they are also expected to have increased efficiency. In the realization of highlyefficient motors, it will become increasingly important to accurately estimate loss.
In the drive circuit of a PM motor, there are times when current vector control using PWM control (pulse width modulation) is run. Current waveform that is being supplied by PWM control have carrier harmonic current superimposed on the basic wave control, and with this carrier harmonic current, highfrequency of the magnetic field is applied to the motor core and iron loss occurs. With harmonic components and magnetic saturation of the iron core due to permanent magnets, it will be necessary to evaluate iron loss with magnetic flux density waveform that is different from the conventional sinusoidal alternating current. Also, in a high rotation PM motor, the variable frequency of magnetic flux density becomes increasingly high and the eddy current distribution of the depth direction of the laminated steel due to skin effect becomes difficult to ignore. With these conditions, evaluation using the highlyaccurate iron loss calculation function becomes required.
Therefore, in this case study, a hysteresis model accounting for minor loops of the direct current bias magnetism and the lamination analysis function accounting for eddy current distribution in the lamination direction are run simultaneously to evaluate iron loss due to high carrier harmonic components in the IPM motor.


195  Torque characteristics analysis of threephase induction motors using 3D correction function 
Module:DP, TR 
20141215 
An induction motor is a motor in which the rotating magnetic field of the stator winding causes induced current to flow in an secondary conductor, which exerts force on the rotor in the rotational direction and causes it to spin.
In an induction motor, magnetic flux in the axis direction, such as leakage flux in the coil end, can have a large effect on motor characteristics. However, transient phenomena are strong in the inductance motor, and analysis time is needed in order to achieve a steady state solution. Due to this, being able to evaluate characteristics in a 2D analysis is desirable, but 3D effects such as leakage flux in the coil ends are ignored in a 2D analysis, and there are cases when an accurate analysis cannot be obtained. In JMAG, highly accurate results can be quickly obtained by performing corrections on 3D effects.
This document introduces introduces a case study which obtains inductance correction values, and then obtains NT characteristics (revolution speedtorque characteristics) using the 3D correction function.


194  Analysis of HighSpeed Rotation Motors Accounting for Eddy Current 
Module:DP, LS 
20141215 
PM synchronous motors are used in HEV drives, air conditioner compressors, and various other industries. Especially in case of PM synchronous motors for HEV drives, highspeed rotation is advancing faster than ever to achieve a small size with high output density. The iron core of a PM synchronous motor is composed of magnetic steel sheets, and the iron loss generated in the magnetic steel sheets have generally been evaluated in the post processing of a magnetic field analysis, In this case, the effects of iron loss on the magnetic field analysis were not accounted for. However, the effects of iron loss on the magnetic field can no longer be ignored as rotation speeds are further increased, which causes the risk of not being able to accurately analyze the torque output by the motor when evaluating iron loss in postprocessing.
Here we discuss the steps for accounting for eddy current loss occurring in the magnetic steel sheets during a magnetic field analysis, and then analyze the effects on torque.


193  Calculation of Equivalent Circuit Parameters of SinglePhase Induction Motors 
Module:FQ 
20141215 
Since single phase induction motors can be used with singlephase AC, which is common in general household power supply, it is widely used for electrical home and office appliances such as washers and fans as small power motors. However, unlike threephase AC, single phase AC cannot independently create a rotational magnetic field, and since it cannot run a motor at this state, there is a need to develop a rotational magnetic field somehow and make it run.
Characteristics of single phase induction motors are affected by factors such as the secondary side and leakage inductance. These are called equivalent circuit parameters and they are important because they characterize the device's properties. Equivalent circuit parameters are greatly affected by current distribution induced by secondary conductors and magnetic saturation near the gap, and accurately understanding these characteristics using finite element analysis will be required.
We will be obtaining the secondary resistance, leakage inductance and excitation inductance of main coil winding of capacitatorstart singlephase induction motor that has auxiliary winding


191  Torque Analysis of ThreePhase Induction Motors Accounting for the Skew Using the Multislice Method 
Module:DP 
20141215 
An induction motor can utilize skew easily because the cage is constructed by metallic casting such as die casting. When skew is applied, it arranges the variations in the magnetic flux that links to the cage in a sinusoidal wave. This makes it possible to eliminate the harmonic components from the induction current that cause negative torque and constrain things like the torque variations caused by influence from the slots.
Generally when skew is applied, magnetic flux also flows in the axis direction, and this requires that a 3D analysis is performed in order to thoroughly evaluate skew effect. However, 3D analyses tend to cause an inordinate amount of calculation costs. The multislice method, representing skew approximately with a 2D crosssection superimposition, is effective.
In this document, the multislice method is used to compare torque waveforms of a cage threephase induction motor with and without skew, and is then used to verify the effects of using skew to reduce torque variations.


188  Thermal Demagnetization Analysis of IPM Motors Accounting for Coercive Force Distribution of Magnets 
Module:DP 
20140619 
The purpose of this Application Note is to help JMAG users understand the
steps and settings used in a JMAG analysis. It is intended to help those
who are working with a new analysis target better understand the analysis
steps and the setting contents.
The actual JMAG model described in this Application Note is available for
download from the JMAG Application Catalog. This model will allow you to
view the model, settings and results. You can also create a template from
the model to use as a starting point when analyzing your own geometry.
They can be downloaded using the same method as the analysis model data.
Please refer to the JMAG manual for more information on templates.
This example presents whether or not the demagnetization region can be
smaller by assigning distribution to the coercive force of permanent magnets.


181  Analysis of SR Motor Drive Characteristics 
Module:DP, LS 
20150604 
With the skyrocketing prices of rare earth magnets,
expectations have been rising for SR (switched reluctance) motors because they have a motor format that does not use permanent magnets.
SR motors have a simple structure that can achieve solid performance at a low price.
However, torque generation depends only upon the saliency between the stator and rotor, so torque variations are extremely large and cause vibration and noise,
meaning that the use applications are limited. On the other hand, because of the skyrocketing prices of rare earth metals, the improvement in current control technology,
the possibility of optimized designs thanks to magnetic field analysis,
and the rising ability to reduce challenges, SR motors are being reexamined.
SR motors sometimes drive while changing switch timing in accordance with rotation speed so it is useful to understand properties such as torque,
current and iron loss in accordance with revolution speed.
This example presents how to confirm drive characteristics such as torque,
loss, and efficiency in a motor when its switch timing changes for each rotation speed.


180  Analysis of SR Motor Dynamic Characteristics 
Module:DP 
20140425 
With the skyrocketing prices of rare earth magnets, expectations have been
rising for SR (switched reluctance) motors because they have a motor format
that does not use permanent magnets. SR motors have a simple structure
that can achieve solid performance at a low price. However, torque generation
depends only upon the saliency between the stator and rotor, so torque
variations are extremely large and cause vibration and noise, meaning that
the use applications are limited. On the other hand, because of the skyrocketing
prices of rare earth metals, the improvement in current control technology,
the possibility of optimized designs thanks to magnetic field analysis,
and the rising ability to reduce challenges, SR motors are being reexamined.
SR motors create their excitation state by alternating between opening
and closing switches in accordance with the position of the rotor's rotation,
however the timing of the alternating causes major changes in the torque
properties. Also, it is important not only to increase the torque average
and torque constant, but also to consider the optimum switch timing to
control vibration and noise.
This example presents how to carry out an analysis with different switch
timings to evaluate torque and current in SR motors.


179  Analysis of SR Motor Static Characteristics 
Module:DP 
20130123 
With the skyrocketing prices of rare earth magnets, expectations have been
rising for SR (switched reluctance) motors because they have a motor format
that does not use permanent magnets. SR motors have a simple structure
that can achieve solid performance at a low price. However, torque generation
depends only upon the saliency between the stator and rotor, so torque
variations are extremely large and cause vibration and noise, meaning that
the use applications are limited. On the other hand, because of the skyrocketing
prices of rare earth metals, the improvement in current control technology,
the possibility of optimized designs thanks to magnetic field analysis,
and the rising ability to reduce challenges, SR motors are being reexamined.
SR motors operate using the nonlinear region of a magnetic steel sheet,
so because the inductance displays nonlinear behavior, it is impossible
to carry out advanced projections that are accurate with calculation methods
that follow linear formulas. Consequently, it becomes necessary to use
the finite element method (FEM), which can handle nonlinear magnetic properties
in material and minute geometry.
This example presents an evaluation for each rotor position of the effect
on flux linkage (shown as IPsi characteristics below) when excitation
current is changed.


177  Torque Characteristic Analysis of a Three Phase Induction Motor 
Module:DP,LS 
20120831 
An induction motor is a motor in which the rotating magnetic field of the
stator coils causes induced current to flow in an auxiliary conductor,
which exerts force on the rotor in the rotational direction and causes
it to spin. Induction motors are widely used in everything from industrial
machines to home appliances because they have a simple construction and
are small, light, affordable, and maintenancefree.
It is possible to drive an induction motor so that its slip is constant
by adjusting the voltage or current against load variations. When this
happens, each characteristic changes with influence from magnetic saturation
and leakage flux because of the excitation variations in a specific slip.
This Application Note explains how to obtain the torque characteristics
in an induction motor when the current amplitude has been changed in a
specific slip.


176  Drive Characteristic Analysis of a ThreePhase Induction Motor 
Module:DP,LS 
20120831 
An induction motor is a motor in which the rotating magnetic field of the
stator coils causes induced current to flow in an auxiliary conductor,
which exerts force on the rotor in the rotational direction and causes
it to spin. Induction motors are widely used in everything from industrial
machines to home appliances because they have a simple construction and
are small, light, affordable, and maintenancefree.
In an induction motor, the current induced by the auxiliary conductor exerts
a large influence on its characteristics. It also causes strong magnetic
saturation in the vicinity of the gap, in particular. This is why a magnetic
field analysis based on the finite element method (FEM) is useful when
investigating the motor's characteristics for a design study.
This Application Note explains how to confirm drive characteristics such
as torque, loss, and efficiency in an induction motor when its rotation
speed changes.


173  Basic Characteristic Analysis of an IPM Motor 
Module:DP,LS 
20120608 
Demand for higher efficiency and smaller size in motors has grown from
the need to accommodate devices that incorporate miniaturization and energy
efficiency in their designs. In order to meet this demand, motors have
to improve their output density and reduce their losses. One type of loss
commonly found in motors is iron loss, which increases drastically at high
rotation speeds and high magnetic flux densities. This increase can lead
to a rise in temperature and a reduction in efficiency. Consequently, it
is growing more important to predict iron loss at the motor design stage.
Unfortunately, it is not possible to obtain iron losses accurately in studies
that use the magnetic circuit method or rules of thumb. In order to obtain
them accurately, one needs to find the distribution and time variations
of the magnetic flux density in each part of the motor after accounting
for a fine geometry and the material's nonlinear magnetic properties. Using
the finite element method (FEM) is essential in order to carry out this
kind of a detailed analysis.
This Application Note demonstrates an analysis in which an IPM motor's
cogging torque, torque, magnetic flux density distribution, and iron loss
in the stator core are obtained.


167  Iron Loss Analysis of a Three Phase Induction Motor 
Module:DP,LS 
20130627 
An induction motor is a motor in which the rotating magnetic field of the
stator coils causes induced current to flow in an auxiliary conductor,
which produces force in the rotational direction.
Induction motors are widely used in everything from industrial machines
to home appliances because they have a simple construction without parts
that experience wear from abrasion, and can be used simply by connecting
them to a power source.
Improved efficiency in induction motors is an important theme. Iron loss,
a cause of lower efficiency along with primary and secondary copper loss,
must be reduced in order to improve efficiency. The relative importance
of iron loss tends to grow especially with higher rotations due to the
inverter drive, so it is helpful to estimate the complex iron loss distribution
inside the core.
This Application Note presents an example of how to find the iron loss
in the stator core and rotor core at a rotation speed of 3,300 r/min.


166  Line Start Simulation of an Induction Machine Using a Control Simulator and the JMAGRT 
Module:FQ,LS,RT 
20151225 
Collaborative design is difficult because the controls and motor are designed independently. However, it has become necessary to resolve challenges through highaccuracy simulations at the beginning of the development process in order meet demands for more advanced motors. An effective way of achieving this is for the simulations to be performed while collaborating on the motor design circuit/control designs.
An induction motor's characteristics are influenced by leakage reactance and resistance, including resistance on the secondary side. The resistance on the secondary side is affected by the skin effect, so the finite element method (FEM) needs to be used to obtain the distribution of the secondary induced current. With JMAG, it is possible to use a magnetic field analysis to obtain the resistance and leakage reactance, and to create a model of an induction motor, as well. Incorporating this motor model, called a "JMAGRT model," to a circuit/control simulator makes it possible to use JMAGRT to run a linked simulation with it.
This Application Note explains how to use the JMAGRT to create a JMAGRT model of an induction motor, import it to a circuit/control simulator, and run an induction motor line start simulation.


165  Creating an Efficiency Map for an IPM Motor 
Module:DP,LS,RT 
20120731 
IPM motors use rare earth sintered permanent magnets because they have
strong magnetic energy. They can use the magnetic torque from the magnet's
field and the rotating magnetic field in addition to the reluctance torque
that originates from the difference in inductance between the daxis and
qaxis, so they have a wide drive range and are highly efficient.
Their efficiency changes with their rotation speed and their load, so it
is beneficial to create an efficiency map when designing the motor and
its controls. However, the calculations required to create an efficiency
map are typically huge, so it takes time to organize the results as well.
Though is possible to estimate the efficiency by using the motor's voltage
equation and torque formula to calculate the torque, voltage, and current,
one cannot use this method to estimate the iron loss or account for the
effects of the nonlinear magnetic properties of the motor's iron core.
The main problem is the difficulty of correctly calculating the efficiency.
To help with this problem, an efficiency map that accounts for influence
from iron loss and nonlinear magnetic properties can be easily obtained
by creating a JMAGRT model of the target and using JMAGRT Viewer's efficiency
map calculation function.
This Application Note presents the use of the JMAGRT Viewer to create
an efficiency map for an IPM motor.

 163  TorqueCurrent Curve Analysis of an SPM Motor
 Module:DP  20130617  One of the fundamental properties of a permanent magnet synchronous motor is the relationship between its current and torque (torquecurrent curve). The torque generated at each current value is uniform with increases in current up to a certain point, so the torque increases in a linear fashion. However, magnetic saturation effects occur with further current increases, and the torque generated with each increase in current begins to drop off. Because a permanent magnet synchronous motor's torquecurrent curve is highly susceptible to saturation effects in the motor's magnetic circuit, it is helpful to obtain the torquecurrent curve with a magnetic field analysis taking saturation into account in order to evaluate the motor's design and drive characteristics. This Application Note presents how to obtain the torquecurrent curve as a basic property of one type of permanent magnet synchronous motor, the surface permanent magnet synchronous (SPM) motor.

 162  Drive Simulation of an SR Motor using a Control Simulator and the JMAGRT  Module:DP,RT  20150424  SR motors are gaining attention as motors that do not use permanent magnets. However, torque pulsation is greater in SR motors because of the way their torque is generated, so it is seen as important to suppress torque pulsation not only with detailed design of magnetic circuits, but also using SR motor control. In order to evaluate suppression of torque pulsation with control simulation, it is necessary to have an SR motor model that shows behavior conforming to a real motor. With JMAG, it is possible to create a detailed model that conforms to a real machine and accounts for the torque's dependency on rotor angle and the magnetic saturation characteristics of the magnetic circuit in an SR motor. Importing this motor model, a "JMAGRT model," to a control/circuit simulator makes it possible to carry out a linked simulation that accounts for an SR motor's detailed characteristics as well as a motor drive's control characteristics. This kind of operation makes control simulation to suppress an SR motor's torque pulsation possible. In this Application Note, after using JMAGRT to obtain an SR motor's torque and inductance characteristics, the JMAGRT model is imported into a circuit/control simulator, voltage is applied to drive the SR motor, and the torque pulsation is analyzed. By evaluating the obtained torque pulsation in detail, investigations can be carried out to reduce the torque pulsation (this Application Note does not incorporate actual attempts to reduce torque pulsation).

 161  Line Start Analysis of a Threephase Induction Machine
 Module:DP  20120831  The simplest method for starting an induction motor is a line start that connects the motor to a direct power supply. For a line start, the static impedance is small compared to impedance during rated operation, so a large current flows during the initial startup. The large current flowing through both the primary and secondary sides during startup causes intense magnetic saturation near the induction motor's gap. This magnetic saturation results in reduced impedance, so the starting current grows even larger. The size of the starting current affects the voltage source capacity connected to the induction motor, as well as both the electromagnetic force and heat capacity that operate on the motor's coils. This is why it is beneficial to investigate the starting performance of an induction motor with the finite element method (FEM), which can account for local magnetic saturation. This Application Note presents an analysis that simulates the line start of an induction motor and obtains the starting performance of its rotation speed variations.

 159  Sensitivity Analysis of Dimensional Tolerance in an SPM Motor
 Module:DP  20131028  The corners of magnets used in surface permanent magnet (SPM) motors can be filleted, chamfered, etc. However, it is difficult to maintain exactly the same production in the manufacturing process, and some variation among finished products will occur. Dimensional tolerance is set so as to eliminate the effects of these variations on motor performance. There are tradeoffs between dimensional tolerance, performance, and cost, so it is important to investigate these at the design stage. With numerical analysis using the finite element method (FEM), it is possible to evaluate the sensitivity of motor performance, such as torque, by simply changing the dimensions. This Application Note presents how to assume a dimensional tolerance of ±0.4 mm for a chamfer, and find out whether changing dimensions within the tolerance range has an effect on motor performance by comparing cogging torque and induced voltage.


157  Analysis of Eddy Currents in an IPM Motor Using the Gap Flux Boundary 
Module:DP,FQ 
20141027 
It is becoming increasingly common for permanent magnet motors to use rare
earth magnets in order to achieve higher output density because they have
a high energy product. Neodymium rare earth magnets have a high electric
conductivity because they contain a great deal of iron, so when a varying
magnetic field is applied to them they produce joule loss from eddy currents.
IPM structure adoption and field weakening controls have become prevalent
in recent years in order to allow faster rotation. This has led to an increase
in the frequencies and fluctuation ranges of the varying fields applied
to magnets, resulting in a corresponding increase in joule losses. By dividing
the magnet like one would a laminated core to control eddy currents, one
can obtain a method of raising the apparent electric conductivity while
lowering the eddy currents. Armature reactions in the stator occur before
the eddy currents produced in the magnet, so the eddy currents are determined
by: The slot geometry of the stator core, the geometry of the rotor, the
nonlinear magnetic properties of the core material, and the current waveform
that flows through the coil.
In order to examine these kinds of magnet eddy currents ahead of time,
one has to be precise when accounting for things like these various geometries
and material properties. This is why a magnetic field simulation using
the finite element method (FEM), which can account for them, would be the
most effective.
This Application Note explains how to use the gap flux boundary condition
to evaluate the eddy current loss in the magnet by changing the number
of magnet divisions. This will make it possible to obtain effective results
in a shorter period of time than with a normal transient response analysis.

 156  Segregation Analysis of Torque Components for an IPM Motor
 Module:DP  20120731  IPM motors are often used as high performance motors because they are highly efficient and their structure makes it possible to achieve a wide range of operation. They are able to achieve high efficiency because they obtain maximum total torque by using their controls to adjust their magnet and reluctance torques. For this reason, it is important to find out the distribution of both of these torques during operation when the IPM motor is being designed. The motor's detailed geometry and the material's nonlinear magnetic properties need to be taken into account to obtain the torque characteristics, and it is even more difficult to segregate the torque into two components by using manual calculations. In order to proceed with the design while looking into how much each one contributes, it needs to be studied with an electromagnetic field analysis that uses the finite element method (FEM). In this Application Note, the torque components are separated and the magnetic flux density distributions created by each magnetomotive force are confirmed.

 124  Cogging Torque Analysis of an SPM Motor Accounting for Uneven Stator Diameter
 Module:DP,DS  20130627  When a motor is assembled, the inner diameter of the stator can become uneven because of fabrication errors, shrink fitting, press fitting, etc. Cogging torque increases due to this unevenness, causing vibration and noise. When a frame is pressed onto a stator core, and when the frame thickness is not uniform in the circumferential direction, the fitting pressure has a distribution in the circumferential direction, and the inner diameter of the stator can become uneven. In order to deal with vibration and noise, it is necessary to accurately grasp the amount of unevenness and evaluate the cogging torque in relation to this unevenness. The stator's innerdiameter unevenness due to press fitting depends on the frame's geometry, so it can be accurately grasped using the finite element method (FEM). This Application Note presents how to obtain the cogging torque with and without uneven displacement in the stator teeth, based on the displacement obtained in an analysis of stress from press fitting.


120  Thermal Demagnetization Analysis of an SPM Motor 
Module:DP 
20140826 
Exactly how to resolve the problem of rising temperatures is a vital issue
when trying to achieve an improvement in a motor's efficiency and output.
Among the materials used in a motor, the magnet experiences the greatest
variations in properties in relation to temperature. In the case of rareearth
magnets, demagnetization can occur within tens of degrees above 100 deg
C. Whether they demagnetize or not depends on the reverse magnetic field
applied and the temperature. They still have some resistance if either
the temperature is raised only or if a reverse magnetic field is applied
only, but the combination of the two causes a great reduction in resistance.
A large current flows in the coils when the motor is overloaded and is
producing a lot of torque, which leads to a large reverse magnetic field
and heat, increasing the possibility of demagnetization. Solutions to this
problem include heatresistant magnets and increased motor size, but these
lead to tradeoff issues during the design stage because of the larger
size and higher cost.
In order to carry out a precise evaluation of demagnetization, it is necessary
to get a definite grasp of areas where a reverse magnetic field occurs
and the materials' demagnetization properties. With magnetic field analysis
simulation using the finite analysis method (FEM), it is possible to calculate
the reverse magnetic field and determine whether magnets and other parts
demagnetize due to reverse magnetic field, taking material demagnetization
properties into account.
This Application Note presents how to change the temperature of permanent
magnets in an analysis, and then evaluate the effects on the torque waveform,
magnetic flux density distribution, etc.


119  Torque Characteristic Analysis of a Three Phase Wound Rotor Induction Motor 
Module:DP 
20150604 
A woundrotor induction motor is a motor that causes induced current to flow in the secondary coil using a rotating magnetic field in the statorcoil,
and thus produces turning force through the interaction of the current and the rotating magnetic field. Because induced current flows through the coil,
electric power can be extracted and regenerated via slip rings.
In an induction motor, the current induced by the secondary conductor exerts a large influence on its characteristics. It also causes strong magnetic saturation in the vicinity of the gap, in particular.
For these reasons, analysis based on the finite element method (FEM) can accurately handle induced current and magnetic saturation, and is useful for understanding detailed characteristics in advance.
This Application Note shows how to obtain the current density distribution and sliptorque curve.

 115  Eccentricity Analysis of an SPM Motor
 Module:DP  20130426  Motors have many parts, which must be assembled correctly for a usable product. Even if each part is made within acceptable limits for manufacturing errors, when various parts with small errors are put together, the errors can have a cumulative effect. In particular, if eccentricity (deviation, deflection) occurs in the cylindrical axis of the rotor and stator, the magnetic flux density distribution and electromagnetic force can become unbalanced, causing vibration and noise. Ideally, parts would be manufactured without any errors, but in reality, error reduction requires precise mechanical manufacturing, which means a huge increase in costs. This is why it is necessary to figure out the tolerance zone of tradeoff between settings and performance for each part at the design stage. In order to grasp these at the design stage, highly precise evaluation sensitive to parts' manufacturing errors is needed, so electromagnetic field analysis using the finite element method (FEM) is effective. This Application Note presents how to evaluate the cogging torque waveform and effects on the electromagnetic force acting on the stator in an SPM motor with and without eccentricity.


111  Starting Performance Analysis of a Universal Motor 
Module:DP 
20151225 
A universal motor is a motor that rotates on both direct and alternating currents. A universal motor is used in home appliances and industrial machines because these motors are robust, compact, light, and fast with a simple construction, and have a large starting torque. However, problems such as vibration and a reduction in starting torque caused by the cogging torque occur as the size of the motor becomes smaller. Evaluating the starting performance of a universal motor at the design stage is necessary to resolve these problems.
This document introduces the use of a magnetic field analysis to obtain the speed versus time graph, the current waveform, and the torque versus time graph for a universal motor.

 109  Operating Time Analysis of an Electromagnetic Relay Accounting for Eddy Currents
 Module:TR  20131028  Electromagnetic relays are devices that use an electromagnet to physically connect and disconnect contact points. Magnetic flux is generated from the magnetomotive force, which is expressed as the product of the number of turns in the coil and the current that is applied to the coil. This flux produces an attraction force in the movable core, making the relay close. To put it simply, the attractive force is determined from the area of the gap between the movable core and the stator core and the size of the magnetic flux density produced in said gap. With a relay whose movable core does not move linearly, however, it is a difficult problem to predict the magnetic flux density in the gap because it does not become parallel. The nonlinear magnetic properties of the iron core and yoke also affect the magnetic flux density in the gap. With a JMAG magnetic field analysis, it is possible to obtain the attraction force of the movable core while accounting for these factors. One of the reasons that the response is delayed in electromagnetic relays is eddy currents, which are produced when the magnetic flux generated by current flow undergoes time variations. The eddy currents are generated in a direction that inhibits changes in the magnetic flux, causing a delay in the initial rise of the attraction force when the current begins to flow. This reduces the injector's responsiveness. JMAG makes it possible to account for the effects from eddy currents and obtain an electromagnetic relay's responsiveness by running a transient response analysis. This Application Note presents the use of the motion equation function to evaluate the operating time of an electromagnetic relay with DC voltage drive. Eddy currents generated in the core are considered for this purpose.

 106  Iron Loss Analysis of a Brush Motor
 Module:DP,LS  20130627  Brush motors are used in many devices, particularly smallersized ones. With demands for energysaving in recent years, higher efficiency is desired not only in high performance and largescale motors used in HEVs and large appliances, but also in smallscale brush motors. To respond to these demands, it is important to reduce loss. Loss reduces efficiency directly, and also causes further reductions by increasing a device's temperature through heat generation, so it is necessary to know the amount and distribution of loss in order to create improved designs that suppress this loss. Motor loss is dominated by copper loss and iron loss, and copper loss can be more or less known from the current flowing in the coils. Iron loss, however, depends on material properties, drive conditions, and geometry, and is therefore difficult to evaluate through desktop calculation. Magnetic analysis using the finite element method (FEM) is useful at the design stage because it can consider all electromagnetic behavior and motor geometry, and therefore makes estimation of the distribution and total amount of iron loss possible. This note presents how to obtain the iron loss in the stator core and rotor core of a brush motor.

 103  Efficiency Analysis of a Permanent Magnet Synchronous Motor
 Module:DP,LS  20130426  A permanent magnet synchronous motor rotates by converting electric energy to mechanical energy. The important thing when converting energy is efficiency indicated by the power factor for the amount of current effectively used, as well as the percentage of output versus input. Evaluating the power factor and input/output characteristics that account for efficiency is necessary to design a highly efficient motor. This example presents the use of a magnetic field analysis to evaluate the efficiency of a permanent magnet synchronous motor.


95  Analysis of a Universal Motor

Module:DP 
20130627 
Motors in electrical industrial equipment are often used for cutting and
machining, so it is desirable for them to be usable at high rotation speeds.
Induction motors cannot achieve high rotation speeds with commercial power
supplies because their rotation speed is determined by alternating current
frequency. DC brush motors can achieve high rotation speeds, but it is
necessary to provide DC power for them, so they cannot be used with commercial
power supplies. Universal motors, on the other hand, are designed to be
connected to commercial power supplies, and because they can rotate at
high rotation speeds with either direct or alternating current, they can
fulfill purposes needing thousands of r/min, such as electric drills. Because
of their high degree of versatility, they are widely used in everydaylife
applications. Users of industrial tools often hold them in their hands,
making reduced weight desirable in addition to low vibration and noise
levels. Development to solve these issues is being carried out in universal
motor design.
The basic structure is the same as in a brush motor, but when the supplied
power is alternating current, the output itself varies periodically. Further,
they are used under difficult conditions such as when inrush current occurs
when a commercial power supply is directly connected from a stopped state.
Therefore, electromagnetic field analysis using the finite element method
(FEM), which can account for nonlinear magnetization properties of the
materials, is useful in order to evaluate magnetic saturation during overload.
This note presents how the characteristics of a universal motor can be
obtained, including torque versus current (TI), torque versus speed (TN),
and magnetic flux density distribution.


94  Analysis of Detent Torque of a PM Stepper Motor

Module:TR 
20130228 
PM stepper motors are commonly used for positioning of moving parts in
small devices such as printers and video equipment. In order for its drive
to function with an open loop, the most important characteristics for a
stepper motor are controllability and holding torque, and not the motor's
output. Therefore, the desired characteristics are detent torque, which
is a nonexcitation holding torque, and stiffness torque, which is an excitation
holding torque.
A PM stepper motor is made up of a multipole magnetized rotor and offset
inductors for each phase. In order to reduce their size and number of parts,
claw pole inductors are made from folded steel sheet. Because of this,
the flow of magnetic flux is three dimensional, so it is necessary to carry
out a 3D electromagnetic field analysis using the finite element method
(FEM) to proceed with an accurate preliminary study.
This Application Note describes how the detent torque can be calculated
for a PM stepper motor.


93  Cogging Torque Analysis of a Motor with 8 Poles and 9 Slots Accounting
for Eccentricity

Module:DP 
20100831 
Eccentricity can occur on the center axis or the rotation axis of a motor.
It is advantageous to evaluate the effects of eccentricity because it can
cause vibrations and noise and break the symmetry of the magnetic flux
density distribution and the electromagnetic force.
This example presents the use of a magnetic field analysis to obtain the
cogging torque and electromagnetic force with and without eccentricity.


89  Stiffness Torque Analysis of a PM Stepper Motor

Module:TR 
20131028 
PM stepper motors are commonly used for positioning of moving parts in
small devices such as printers and video equipment. In order for its drive
to function with an open loop, the most important characteristics for a
stepper motor are controllability and holding torque, and not the motor's
output. Therefore, the desired characteristics are detent torque, which
is a nonexcitation holding torque, and stiffness torque, which is an excitation
holding torque.
A PM stepper motor is made up of a multipole magnetized rotor and offset
inductors for each phase. In order to reduce their size and number of parts,
claw pole inductors are made from folded steel sheet. Because of this,
the flow of magnetic flux is three dimensional, so it is necessary to carry
out a 3D electromagnetic field analysis using the finite element method
(FEM) to proceed with an accurate preliminary study.
This Application Note describes how the stiffness torque at 0.5 A of current
can be calculated for a PM stepper motor.


82  Analysis of a Synchronous Reluctance Motor

Module:DP 
20130627 
Skyrocketing prices of rare earth magnets have led to rising expectations for synchronous reluctance motors (referred to below as SynRMs), which do not use permanent magnets. SynRMs have a simple structure that can achieve solid performance at a low price. However, torque is generated only by the rotor's saliency and the coil's magnetomotive force, so raising the torque density depends greatly on the core's nonlinear magnetic properties and the rotor geometry. This is why they have a different format than a typical motor. On the other hand, the aforementioned rising prices of rare earth magnets, improvements in current control technology, and the ability of optimization designs using magnetic field analysis have raised the possibility of lowering these barriers, giving SynRMs the chance to be reexamined.
SynRMs operate using the nonlinear region of a magnetic steel sheet, so the inductance expresses nonlinear behavior as well. This behavior distorts the excitation current waveform a great deal, making it impossible to run advanced projections that are accurate with calculation methods that follow linear formulas. Consequently, it becomes necessary to use the finite element method (FEM), which can handle nonlinear magnetic properties in material, detailed motor geometry, and transient currents.
This Application Note presents an evaluation of torque variations that occur when the phase of a sinusoidal wave current is changed.


80  Cogging Torque Analysis of an SPM Motor with Skewed Magnetization

Module:TR 
20130627 
Reductions in vibration and noise are being sought after because they are a cause of torque variations in motors, and demands for reduction are particularly strong with motors that are used in machine tools and power steering. Cogging torque, which is a torque variation that is produced when there is no current, is generated because the electromagnetic force produced in the gap changes according to the rotor's rotation. This makes it necessary to apply skew to the stator and rotor and come up with innovative geometry for the magnet and stator in order to reduce torque variations by limiting variations in the electromagnetic force. Applying skew reduces the cogging torque, but it also brings disadvantages such as producing force in the thrust direction and generating eddy currents from the magnetic flux that links in the lamination direction.
Consequently, in order to accurately evaluate a motor that has skew applied, one needs a magnetic field analysis simulation that uses the finite element method (FEM), which can account for a detailed 3D geometry, instead of studies that use the magnetic circuit method or a 2D magnetic field analysis.
This Application Note presents the use of a magnetic field analysis to obtain the flux density distribution, cogging torque, and induced voltage of an SPM motor that has skewed magnetization applied to its magnet.


74  Speed Versus Torque Analysis of a SinglePhase Induction Motor

Module:DP 
20131217 
Singlephase induction motors are widely used as small output motors for
the drives in household electrical appliances and office machinery, like
fans and washing machines, because they can use singlephase AC, the typical
power source for home electronics. Unlike threephase AC, however, singlephase
AC cannot create a rotating magnetic field by itself, meaning that it cannot
start a motor. For this reason, it needs to use an alternate method to
generate a rotating magnetic field to start the motor.
The induced current flowing in the secondary conductor largely affect the
performance of the motor because the motor rotates by using the interaction
between this current and the magnetic field of the stator coils. Strong
magnetic saturation distribution is also generated near the gap, so the
nonlinear characteristics of the magnetic properties have a big influence
on performance, as well. At the step before the design phase, it is helpful
to run an analysis and evaluation using the finite element method (FEM)
to understand a singlephase induction motor's characteristics by accounting
for induced current and magnetic saturation characteristics.
This Application Note explains how to obtain the current density distribution
and SpeedTorque curve created by auxiliary winding that uses a capacitor.

 71  Basic Characteristic Analysis of a Motor with 2 Brushes, 6 Poles, and 19 Slots
 Module:DP  20131028  Small brush motors generally have a structure containing 2 poles and 3 slots, but there are times when a multipole structure is adopted in order to produce higher torque. The reason for this is because achieving a higher torque makes it possible to omit deceleration systems. Brush motors have a construction where the number of poles and number of slots are not divisible, with the objective of raising the rectification effect or limiting torque variations. In exchange for reducing torque variations, however, there is a drawback when it comes to torque output. This is why selecting the number of poles and slots have become a design theme, especially when it comes to small motors, which have a small number of slots. This makes the selection process difficult because the difference in distribution becomes large. The model for this analysis has 6 poles and 19 slots, so there are 3.16 slots per pole. They cannot be divided into decimals however, so there have to be either 3 or 4 slots for each magnetic pole. As a result, the induced voltage in each coil and the torque generated are unbalanced. These evaluations need to be able to account for an accurate circuit geometry, and the current flowing through coil connected via a commutator needs to be handled accurately, as well. This is why an electromagnetic field analysis using the finite element method (FEM) is necessary to account for everything. This Application Note presents an analysis to obtain the speed versus torque and torque versus current for a motor that has 2 brushes, 6 poles, and 19 slots.


69  Iron Loss Analysis of an IPM Motor

Module:DP,LS 
20131028 
Demand for higher efficiency and smaller size in motors has grown from
the need to accommodate devices that incorporate miniaturization and energy
efficiency in their designs. In order to meet this demand, motors have
to improve their output density and reduce their losses. One type of loss
commonly found in motors is iron loss, which increases drastically at high
rotation speeds and high magnetic flux densities. This increase can lead
to a rise in temperature and a reduction in efficiency. Consequently, it
is growing more important to predict iron loss levels at the motor design
stage.
Unfortunately, it is not possible to obtain iron losses accurately in studies
that use the magnetic circuit method or rules of thumb. In order to obtain
them accurately, one needs to find the distribution and time variations
of the magnetic flux density in each part of the motor after accounting
for a fine geometry and the material's nonlinear magnetic properties. Using
the finite element method (FEM) is essential in order to carry out this
kind of a detailed analysis.
This Application Note explains a case example that obtains the iron loss
and its distribution in a permanent magnet motor.


68  Speed Versus Torque Characteristic Analysis of a ThreePhase Induction
Motor

Module:DP 
20131028 
An induction motor is a motor in which a rotating magnetic field in the
stator coils causes induced current to flow in an auxiliary conductor.
This current and magnetic field exert force on the auxiliary conductor
in the rotation direction and cause the motor's rotor to rotate. Induction
motors are widely used in everything from industrial machines to home appliances
because they have a simple construction and are small, light, affordable,
and maintenancefree.
In an induction motor, the current induced by the auxiliary conductor exerts
a large influence on its characteristics. It also causes strong magnetic
saturation in the vicinity of the gap, in particular. This is why a magnetic
field analysis based on the finite element method (FEM) is useful when
investigating the motor's characteristics for a design study.
This Application Note explains an analysis that confirms the SpeedTorque
curve and current density distribution of an induction motor.


63  Analysis of Torque Characteristics of a Cage Induction Motor 
Module:FQ 
20130228 
Induction motors have been widely used for a long time in general industries
because they have a simple structure, and are affordable, robust and highly
efficient. When an induction motor rotates at synchronous speed, no torque
is produced. However, when proper slip is caused, the maximum torque can
be obtained. Losses are generated in a cage induction motor when current
flows through the cage, so the pros and cons of continuous rotation depending
on the amount of the heat generated need to be studied.
In an induction motor, the current induced by the auxiliary conductor exerts
a large influence on its characteristics. It also causes strong magnetic
saturation in the vicinity of the gap, in particular. This is why a magnetic
field analysis based on the finite element method (FEM) is useful when
investigating the motor's characteristics for a design study.
This Application Note introduces a case example that obtains the SlipTorque
curve, TorqueCurrent curve, CurrentVoltage curve at maximum torque, and
the CurrentJoule Loss curve for the cage. 

59  Iron Loss Analysis of an IPM Motor Accounting for a PWM Direct Link 
Module:DP,LS 
20151225 
Vector controls using a PWM (Pulse Width Modulation) control are commonly included in the drive circuits of high efficiency motors. A PWM control makes it possible to adjust the phase or amplitude of a current according to load and rotation speed, so they can achieve high efficiency in a wide operation range. The control frequency of a PWM is called a carrier frequency. Carrier frequencies are often used up to almost 20 kHz. To form the current waveform supplied by the PWM control, the carrier harmonic current is superimposed on the basic wave current. This carrier harmonic current applies a highfrequency magnetic field to each part of the motor. As a result, core iron loss and magnet eddy current loss are generated.
The total amount of these losses is not a dominant factor, but they can be a hindrance when trying to raise efficiency, so they need to be eliminated in the design process. In order to study these problems, both the motor's electromagnetic behavior and what kinds of controls the drive circuit performs have to be investigated.
In order to run an advance study of these phenomena in CAE, a high fidelity motor model and inverter model need to be coupled. There are three ways of accomplishing this: Directly linking with a circuit/control simulator, entering a current waveform obtained by using a JMAGRT motor model and a circuit/control simulator, and entering actual current measurements.
In this analysis, the iron losses of the IPM motor that accounts for the carrier harmonic are obtained by directly linking to a circuit/control simulator.


58  Efficiency Analysis of an IPM Motor

Module:DP,LS 
20131028 
An IPM motor's features are in its rotor geometry, where its magnets are
embedded. When the stator's rotating magnetic field is applied in a direction
that runs perpendicular to the rotor magnets (the qaxis) the motor operates
like a normal SPM motor. When the current phase is displaced and the daxis
component is applied, however, the motor operates so that the magnetic
fields in the rotor magnets are weakened. This is called field weakening.
In an SPM motor the daxis current operates enough to weaken the magnetic
field, so the rotation speed increases but the torque decreases. However,
the rotor geometry in an IPM motor is created so that there is a difference
in inductance between the daxis and qaxis, so it is possible to generate
torque with the daxis current, which weakens the magnets. This makes it
possible to recover the part weakened by the flux. Consequently, an IPM
motor achieves a greater range of operation by incorporating field weakening
controls.
For this reason an IPM motor's characteristics depend greatly on its rotor
geometry, so studies using the magnetic circuit method are difficult. In
order to perform an advance design study accurately, an electromagnetic
field analysis using the finite element method is necessary.
This Application Note presents the use of magnetic field analysis to obtain
the efficiency of an IPM motor in each current phase with a rotation speed
of 1800 rpm and the current amplitude of 4.0 A when the motor is driven
by sinusoidal wave current.


56  Torque Characteristics Analysis of a Self Starting Type Permanent
Magnet Motor

Module:DP 
20131028 
A self starting permanent magnet motor combines the characteristics of
an induction motor and a permanent magnet motor, so it has higher efficiency
than an induction motor even without a control device like an inverter.
It behaves as an induction motor when it starts, generating torque when
the rotor cage first slips against the rotating magnetic field created
by the stator and then produces a secondary current. Consequently, this
kind of motor has superior starting ability because there is no need to
account for the rotor's startup position or rotation speed. When the rotation
speed increases and the motor synchronizes, the permanent magnet begins
to generate the magnetomotive force and produce torque instead of the secondary
current, so there is no secondary iron loss. This kind of motor has a weak
point, however: The torque falls a great deal when the motor deviates from
its synchronicity, and it gets out of step as a magnet motor so the torque
variations are large. This is why self starting permanent magnet motors
can achieve fullvoltage starting with household current and are very efficient
while in a synchronous state, but have drawbacks like relatively low starting
torque and recovery once they have lost synchronization.
These factors make it so that a magnetic field analysis simulation based
on the finite element method is necessary to investigate whether the motor's
characteristics meet the requirements ahead of time.
This Application Note shows how to obtain the current density distribution
and slip versus torque curve.


55  Integrated Magnetization Analysis of an IPM Motor

Module:DP,ST 
20131028 
Interior permanent magnet (IPM) motors often use strong rare earth magnets.
They have poor workability, however, because the magnets are inserted into
the rotor's small gaps during the assembly process. After the magnets have
been inserted the rotor generates a strong magnetic field, which means
that the workability when embedding it into the stator gets worse, as well.
This is why in some cases they assemble the magnets while still in an unmagnetized
state and magnetize them after they have been assembled. This construction
method is called integrated magnetization. Using this means of construction
can improve the assembly process a great deal, but there is also the possibility
that the magnets will not be completely magnetized.
Consequently, first one needs to confirm whether or not integrated magnetization
is even possible, and then from there to estimate the electrical power
that the equipment needs for magnetization.
Using a magnetic field analysis simulation with the finite element method
(FEM) provides the ability to change the making current amount and yoke
geometry as magnetization conditions, as well as to account for magnetic
saturation and evaluate whether or not the magnets are completely magnetized.
This Application Note explains how to determine the changes that occur
in a magnetizing field if the making current is changed during magnetization,
as well as how to obtain the induced voltage and cogging torque in the
motor using the aforementioned magnets.


46  Sensitivity Analysis of the Magnetization Pattern of an SPM Motor

Module:DP,ST 
20130426 
The magnet in a surface permanent magnet (SPM) motor is arranged on the
rotor's surface, facing the stator. The motor produces torque from the
interaction between the magnetic field produced by the magnet and the magnetic
field produced from the excitation coil. Cogging torque, which is generated
during noload rotation, depends largely on the magnet's magnetizing state.
Adjusting the magnet's magnetization pattern makes it possible to reduce
the cogging torque, which lowers efficiency and causes vibration and noise.
In order to control the magnetization pattern in the magnet of an actual
machine precisely, a great number of magnetization devices is required.
This makes a real machine hard to control, but with a magnetic field analysis
simulation that uses the finite element method (FEM), it is possible to
estimate how the cogging torque in the physical phenomenon will change
by simply setting the magnetization pattern. Once the optimum magnetization
pattern has been found, studying the magnetization method can lead to a
reduction in development cost.
This Application Note presents the use of a magnetic field analysis to
obtain the surface flux density for radial pattern, parallel anisotropic
pattern, and polar anisotropy pattern magnets. It also displays the changes
in induced voltage and cogging torque caused by differences in the magnetization
patterns.


43  Torque Analysis of a Coreless Motor 
Module:TR 
20160225 
As their name implies, coreless motors have a rotor that lacks a core and is made of only a coil. For this reason, there is no core to produce iron loss in the rotor, and its moment of inertia is small. They can be controlled easily because their characteristics are linear and they have small torque ripples, but they are not versatile enough to produce a large amount of torque. This is why they are often used in small precision equipment that requires high rotation speeds and good responsiveness. The rotor coil is hard to construct because it is made of only a coil. It is important to design the coil's twist angle to be able to produce torque. The model needs to be made precisely because coreless motors are used in compact equipment and because the detailed geometry of the parts can affect the characteristics.
In order to carry out these evaluations, the coil's twist needs to be accounted for accurately in three dimensions. An electromagnetic field analysis using the finite element method (FEM) is necessary to accomplish this because it can evaluate the distribution of the electromagnetic force produced in the magnetic circuit in detail.
This Application Note presents an evaluation of the torque waveform of a coreless motor when current is running.


40  Cogging Torque Analysis of an SPM Motor

Module:DP 
20131028 
The rotor's rotation in a permanent magnet motor can generate positive
and negative torque, even when there is no current flow. This torque is
called "cogging torque." While output torque a center of focus
in motors used in precision equipment, cogging torque reduction must be
taken into account as well. Skew and fractional slots are means of reducing
this cogging torque. Skew is a widely used technique that attempts to cancel
out cogging torque by applying an appropriate amount of twist to the stator
or rotor. This generates electromagnetic force in the thrust direction,
however, which presents challenges such as a decrease in performance and
an increase in manufacturing cost. Fractional slots do not have the drawbacks
found in skew, but the winding pattern is different from that found with
integer slots. This means that the torque generation becomes difficult
to evaluate because the teeth geometry and the magnet's magnetization distribution
are hard to design accurately.
In order to carry out these evaluations, an electromagnetic field analysis
using the finite element method (FEM) needs to be carried out because it
can perform detailed evaluations of the electromagnetic force distribution
produced in the magnetic circuit.
This Application Note presents the use of magnetic field analysis to obtain
the cogging torque of an 8pole, 9slot SPM motor, which has relatively
small period.


39  Torque Analysis of a Three Phase Induction Motor Accounting for the
Skew

Module:DP,TR 
20120731 
An induction motor can utilize skew easily because the cage is constructed
by metallic casting such as die casting. When skew is applied, it arranges
the variations in the magnetic flux that links to the cage in a sinusoidal
wave. This makes it possible to eliminate the harmonic components from
the induction current that cause negative torque and contain things like
the torque variations caused by influence from the slots.
Applying skew generally affects the flow of magnetic flux in the axial
direction, making it complex. This is why an analysis that can correctly
verify the three dimensional magnetic flux flow is necessary to obtain
an advance evaluation of the skew's effects.
This Application Note presents a comparison of the torque waveforms of
three phase squirrel cage induction motors with and without torque, and
introduces the effects of using skew to reduce torque variations. Changes
in the higher components caused by skew are also displayed by separating
the frequencies of the secondary current, which causes the torque variations.


38  Starting Performance Analysis of a Single Phase Induction Motor

Module:DP 
20130228 
Single phase induction motors are widely used as small output motors for
the drives in household electrical appliances and office machinery, like
fans and washing machines, because they can use single phase AC, the typical
power source for home electronics. Unlike three phase AC, however, single
phase AC cannot create a rotating magnetic field by itself, meaning that
it cannot start a motor. For this reason, it needs to use an alternate
method to generate a rotating magnetic field to start the motor.
It is important to verify whether or not torque is generated in the intended
direction and continues to rotate stably ahead of time in the design phase.
In order to carry out this verification, the conditions where the rotor
follows the equation of motion according to the electromagnetic force mechanism
and starts up need to be analyzed correctly.
The purpose of this Application Note is to introduce an example of a single
phase induction motor that uses a capacitor to set up an auxiliary winding
and show its rotation speed versus time, torque versus time, and the magnetic
flux density distribution and current density distribution in the bar just
after the motor starts.


37  Vector Control Analysis of an IPM Motor Using Control Simulator and
the JMAGRT 
Module:DP,RT 
20150424 
Traditionally, the design of a motor's controls and the design of the motor
itself were often performed independently because coordinated designs were
difficult to carry out. Motor control designs have been getting more advanced,
however, so there has been an increasing demand for simulations that use
detailed motor models that exhibit behavior that conforms to that of an
actual machine.
With JMAG, it is possible to create a detailed model that conforms to a
real machine and accounts for spatial harmonics and magnetic saturation
characteristics that are included in a motor. Importing this motor model,
a "JMAGRT model," to a control/circuit simulator makes it possible
to carry out a linked simulation that accounts for a motor's magnetic saturation
and spatial harmonics as well as a motor drive's control characteristics.
The purpose of this Application Note is to demonstrate how to import a
JMAGRT model to a control/circuit simulator after using the JMAGRT to
obtain the inductance spatial harmonics of the torque and coil. The model
is then used to run an analysis that controls the speed of an IPM motor
to its target value.


36  Operating Time Analysis of an Electromagnetic Relay 
Module:TR 
20160225 
Electromagnetic relays are devices that use an electromagnet to physically connect and disconnect contact points. Magnetic flux is generated from the magnetomotive force, which is expressed as the product of the number of turns in the coil and the current that is applied to the coil. This flux produces an attraction force in the movable core, making the relay close.
To put it simply, the attractive force is determined from the area of the gap between the movable core and the stator core and the size of the magnetic flux density produced in said gap. With a relay whose movable core does not move linearly, however, it is hard to predict the magnetic flux density in the gap because it does not become parallel. The nonlinear magnetic properties of the iron core and yoke also affect the magnetic flux density in the gap. With a JMAG magnetic field analysis, it is possible to obtain the attraction force of the movable core while accounting for these factors.
This Application Note presents the use of the motion equation function to evaluate the operating time of an electromagnetic relay that uses a DC voltage drive.


26  Braking Torque Analysis of an Electromagnetic Brake

Module:TR 
20131028 
An electromagnetic brake is an auxiliary brake device for largescale vehicles
like trucks and buses. It is fit onto the propeller shaft and applies a
braking force. There are both hydraulic and electromagnetic types. With
an electromagnetic brake, a magnetic field is produced in the stator coil,
making eddy currents occur because of time variations in the magnetic flux
density linking to the rotor. This, in turn, produces a braking torque.
The range in which eddy currents occur in the rotor and the braking torque
can vary a great deal according to the current flowing to the stator coil
and the rotor's rotation speed.
In order to estimate the electromagnetic brake's performance accurately
at the design stage, it is best to carry out an electromagnetic field analysis
simulation using the finite element method (FEM) because it can approximate
the material's nonlinear magnetic properties and can approximate the skin
effect caused by current distribution, as well.
This Application Note shows how to obtain the braking torque of an electromagnetic
brake during drive.


24  Cogging Torque Analysis of an SPM Motor with a Skewed Stator

Module:TR 
20130627 
Reductions in vibration and noise are being sought after because they are
a cause of torque variations in motors, and demands for reduction are particularly
strong with motors that are used in machine tools and power steering. Cogging
torque, which is a torque variation that is produced when there is no current,
is generated because the electromagnetic force, which is produced in the
gap, changes in relation to the rotor's rotation, making it necessary to
apply skew to the stator and rotor and improvise with the magnet and stator's
geometry in order to limit said variations in electromagnetic force as
a countermeasure for reducing the torque variations. When applying skew,
force in the thrust direction is produced in exchange for a reduction in
the cogging torque, meaning that there is the disadvantage of producing
eddy currents from the magnetic flux that links in the lamination direction.
Consequently, in order to accurately evaluate a motor that has skew applied,
one needs a magnetic field analysis simulation that uses the finite element
method (FEM), which can account for a detailed 3D geometry, instead of
studies that use the magnetic circuit method or a 2D magnetic field analysis.
This note presents the use of magnetic field analysis to evaluate the cogging
torque of an SPM motor with a skewed stator.


23  Eccentricity Analysis of an IPM Motor 
Module:DP 
20151225 
Rotor eccentricity is one cause of vibration and noise in motors. It is well known that motor torque is produced by electromagnetic attraction and repulsion between the stator and rotor, but not much attention is paid to the fact that electromagnetic attraction acts in the radial direction between the rotor and stator. This is because it seems that this electromagnetic force is canceled out and therefore not produced because the rotor and stator are normally arranged concentrically. However, if there are dimensional errors in the parts that support the shaft or stator and concentricity is not maintained, in other words if there is eccentricity, the electromagnetic force in the radial direction is not canceled out. In this case, friction increases due to the constant action of the radial load on the shaft bearings, causing vibration and noise.
A certain amount of error from processing has to be expected. Processing error itself is not so large that the parts cannot be put together, but even assembly error can cause a minute eccentricity of around 1/10 mm. Analysis that can handle this level of precision is needed to evaluate this kind of minute geometry difference, and electromagnetic field analysis using the Finite Element Method (FEM) is useful because it has the sensitivity for detailed geometry differences.
This Application Note presents how to obtain variations in electromagnetic force according to changes in the amount of rotor eccentricity.


18  Thermal Analysis of an IPM Motor

Module:HT,LS,TR 
20131028 
Exactly how to resolve the problem of rising temperatures is a critical
issue when trying to achieve an improvement in a motor's efficiency and
output. In order to solve this problem it is important to investigate a
magnetic design that reduces the losses themselves because they are a source
of heat, but it is also important to study a thermal design that improves
heat dissipation and does not let the temperature rise. Copper loss in
the coils and iron loss in the core are the dominant heat sources, so this
analysis mainly evaluates the effects of this heat. Changes in the magnet's
properties due to temperature are large and its heat resistance is low,
so it is necessary to design while paying careful attention to rising temperatures
during operation. During operation, rated evaluations with a continuously
operated constant load are run until a thermal balanced state has been
reached. In addition to these rated evaluations, however, thermal transient
evaluations that add a thermal cycle with an intermittently operated electrical
overload are performed, as well.
In order to carry out an accurate thermal design, it is necessary to first
correctly understand the heat generation amount and location, so it would
be advantageous to calculate the losses in a magnetic field analysis simulation
using the finite element method, and from there to carry out a thermal
analysis using the resulting loss distribution.
This Application Note explains how to evaluate a motor's temperature distribution
by creating a thermal analysis model that can investigate the loss analysis
and temperature distribution in order to obtain the motor's total loss
distribution, and then analyzing the elevated temperature process.


16  Analysis of a Hybrid Stepper Motor 
Module:TR 
20160225 
Hybrid stepper motors are used as actuators for equipment where position detection accuracy is required, such as the joints of robots or rotary tables for machine tools. The rotor has a construction that sandwiches a magnet that is magnetized in the axial direction between two rotor cores that have serrated teeth to create salient poles, and the tips of the stator core's teeth are shaped like gears as well. Because the rotation resolution is determined by the number of rotor teeth and the number of phases for the drive coil, the design uses large number of teeth, such as 50 or 100, so the angle resolution can be increased .The most important characteristics for a stepper motor are the controllability, the detent torque, which is a nonexcitation holding torque, and the stiffness torque, which is an excitation holding torque, and not the motor's output.
The twoplated rotor core of a stepper motor has an N pole on one side and an S pole on the other, so a multipole magnet is achieved by deviating the saliency of the gear condition by 1/2 pitch. Consequently, the magnetic circuit is 3D. There are also times when the division pitch geometry of the teeth is complicated, so it is necessary to carry out a 3D electromagnetic field analysis using the finite element method (FEM) to proceed with an accurate preliminary study.
This document introduces how the detent torque and stiffness torque can be calculated for a hybrid stepper motor.


15  Cogging Torque Analysis of an SPM Motor with a Step Skewed Magnet Updated 
Module:TR 
20160627 
Reductions in vibration and noise are being sought after because they are a cause of torque variations in motors, and demands for reduction are particularly strong with motors that are used in machine tools and power steering. Cogging torque, which is a torque variation that is produced when there is no current, is generated because the electromagnetic force, which is produced in the gap, changes in relation to the rotor's rotation, making it necessary to apply skew to the stator and rotor and improvise with the magnet and stator's geometry in order to limit said variations in electromagnetic force as a countermeasure for reducing the torque variations. When applying skew, force in the thrust direction is produced in exchange for a reduction in the cogging torque, meaning that there is the disadvantage of producing eddy currents from the magnetic flux that links in the lamination direction.
Consequently, in order to accurately evaluate a motor that has skew applied, one needs a magnetic field analysis simulation that uses the finite element method (FEM), which can account for a detailed 3D geometry, instead of studies that use the magnetic circuit method or a 2D magnetic field analysis.
This Application Note presents the use of magnetic field analysis to evaluate the magnetic flux density distribution and cogging torque in each part of an SPM motor with a step skewed magnet.


11  Pullin/pullout Analysis of a PM Stepper Motor Using a Control Simulator and the JMAGRT 
Module:RT,TR 
20150826 
Stepper motors are commonly used for positioning in printers and digital
cameras. With a PM stepper motor, there are excitation types such as one
phase excitation, two phase excitation, and onetwo phase excitation for
the excitation system, and the accuracy for stepper motor positioning changes
depending on which system is used. Pullin and pullout torques are important
indicators that show the transient characteristics of a stepper motor,
so it is vital to understand and study them in advance.
To measure them, begin to gradually reduce the load on the stepper motor
from a stationary state, measure the pullin torque when it begins to rotate,
begin to gradually increase the load in sync with the pulses from a rotating
state, and measure the pullout torque when it loses synchronism. It is
necessary to carry out transient analysis while changing the load in order
to solve this phenomenon in magnetic field analysis. While it is possible
to calculate it using an equation of motion with JMAG's 3D transient response
analysis, such calculations take too much time. With JMAG, it is possible
to create a motor model that is detailed and conforms to a real machine,
and that accounts for spatial harmonics and magnetic saturation characteristics
that are included in a stepper motor. By importing this motor model, a
"JMAGRT model," to the control/circuit simulator, it is possible
to derive the stepper motor's pullin and pullout torques quickly and
accurately because it accounts for the motor's magnetic saturation characteristics
and spatial harmonics.
This note presents how JMAGRT can be used to calculate holding torque
and coil inductance that varies with current. The result is the JMAGRT
motor model used as a reference for a circuit / control simulator that
runs a transient analysis to obtain pullin and pullout torques of the
stepper motor. By also using a single JMAGRT motor model and changing
the circuit on the circuit/control simulator, it is possible to obtain
the characteristics of two types of drives: a bifilar winding with a unipolar
drive, and a monofilament winding with a bipolar drive. Other parameters
are the same for both analyses.


8  Analysis of an Axial Gap Motor 
Module:TR 
20141215 
Unlike typical cylindrical motors such as radial gap motors, axial gap
motors have a structure in which the stator and the rotor, which is arranged
on a disk, face each other and produce rotation. For that reason, because
it is possible to arrange thinner parts than with a radial gap motor, they
can respond to demands for miniaturization of equipment.
With axial gap motors, evaluations using the magnetic circuit method and
empirical data are difficult because the magnetic flux that passes through
the rotor and stator, which face each other, becomes a 3D magnetic circuit,
meaning that a 3D electromagnetic field simulation using the finite element
method (FEM) is necessary because it can carry out an accurate analysis.
This Application Note shows how to use JMAG's 3D magnetic field analysis
to carry out a load analysis of an axial gap motor, and then obtain the
SpeedTorque curve and the TorqueCurrent curve.


7  Analysis of a Spindle Motor

Module:TR 
20130228 
Spindle motors are often used as drive motors where limited space is an
issue, as is the case with storage media like hard disks. They employ an
outer rotor structure in order to obtain a large torque, but to do so they
have to use a great deal of permanent magnets while remaining thin and
compact. In order to reduce the number of parts used in their composition,
the rotor core has functions that both bear the magnet's flux path and
transfer the generated torque, which supports the magnet, to the shaft.
For this reason the rotor core is composed of materials that are easy to
produce, meaning that there is a possibility that its efficiency as a magnetic
circuit will decrease. As motors get smaller, they require a design that
accounts for flux leakage because it begins to affect the disc in the rotor.
For this reason, spindle motors need electromagnetic field simulations
that use the finite element method (FEM), which can account for detailed
3D geometry and magnetic saturation in materials, in order to carry out
an accurate evaluation.
This Application Note shows how the SpeedTorque curve, the TorqueCurrent
curve and the magnetic flux density distribution of a spindle motor can
be obtained.


6  Analysis of the SR Motor Torque Ripple 
Module:DP 
20120410 
With the skyrocketing prices of rare earth magnets, expectations have been
rising for SR (switched reluctance) motors because they have a motor format
that does not use permanent magnets. SR motors have a simple structure
that can achieve solid performance at a low price. However, torque generation
depends only upon the saliency between the stator and rotor, so torque
variations are extremely large and cause vibration and noise, meaning that
the use applications are limited. On the other hand, because of the skyrocketing
prices of rare earth metals, the improvement in current control technology,
the possibility of optimized designs thanks to magnetic field analysis,
and the rising ability to reduce challenges, SR motors are being reexamined.
SR motors operate using the nonlinear region of a magnetic steel sheet,
so the inductance displays nonlinear behavior that distorts the excitation
current waveform a great deal, making it impossible to carry out advanced
projections that are accurate with calculation methods that follow linear
formulas. Consequently, it becomes necessary to use the finite element
method (FEM), which can handle nonlinear magnetic properties in material
and minute geometry as well as transient currents.
This Application Note explains how to carry out a torque analysis that
changes the switch conversion timing and evaluate both the torque ripples
and average torque in an SR motor.


3  Analysis of a Permanent Magnet Brush Motor 
Module:DP 
20160425 
A brush motor generates torque through the electromagnetic attraction and
repulsion between its rotor and stator. They do not have many parts and
do not require drive circuits, so they are widely used as a power source
for compact equipment. A brush motor is composed of a magnetic circuit
part, which actually generates torque via electromagnetic phenomena, and
the brush/commutator part, which corresponds to the drive circuit. In order
to aim at improving the performance of a brush motor, it is necessary to
raise the usage efficiency of the magnetic circuit in each part and expertly
utilize the nonlinear material characteristics. Proper placement of the
brush/commutator that correspond to the drive circuit is also vital.
In order to evaluate the usage efficiency of the magnetic circuit, torque
variations, current waveforms, etc. at the design stage, it is best to
first do a detailed calculation of the magnetic flux density in each part,
and then perform an electromagnetic field simulation using the finite element
method (FEM), which can evaluate torque with high accuracy.
This note presents how the characteristics of the brushtype PM motor can
be obtained, including torque versus current (TI), torque versus speed
(TN), and magnetic flux density distribution.


1  Torque Characteristic Analysis of a Three Phase Induction Motor 
Module:DP 
20120410 
An induction motor is a motor in which the rotating magnetic field of the stator coils causes induced current to flow in an auxiliary conductor, exerting force on the rotor in the rotational direction and causing it to spin.
Induction motors are widely used in everything from industrial machines to home appliances because they have a simple construction and are small, light, affordable, and maintenancefree.
In an induction motor, the current induced by the auxiliary conductor exerts a large influence on its characteristics.
It also causes strong magnetic saturation in the vicinity of the gap, in particular.
With Finite Element Analysis (FEA), it is possible to investigate the characteristics that accurately evaluate the features listed above, so preliminary design evaluations are effective.
This Application Note introduces a case example of how to obtain the current density distribution of an auxiliary conductor and its rotation speed versus torque characteristics.

