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Preliminary Concepts

Sources of Magnetic Fields

There are two sources of magnetic fields:

  • Permanent magnet: The magnetic field is generated by the internal structure of the material itself.

  • Electromagnet: The magnetic field is generated by the application of an electric current.

All magnets are dipoles, meaning that they have both a north and south pole. Like poles repel, opposite poles attract.

Magnetic Force

The magnetic force in a particle is equal to the charge of the particle times the cross product of its velocity and subjected magnetic field:

The magnitude of the force is thus:

Magnetic Field Lines

Magnetic field lines help to visualize the presence of a magnetic field. These lines form a closed path from the north to south pole of a magnet. The greater the density of lines, the stronger the field.

Magnetic Force on a Current Carrying Wire Subjected to an External Magnetic Field

The magnetic force of a wire carrying a current subjected to a uniform magnetic field is given by:

Note that the length vector points in the direction of the current’s conventional flow.

Ampere’s Right-Hand Rule

To find the direction of the magnetic field created by the current flowing through a wire, point your thumb in the direction of the current  and wrap your fingers around it. The wrapped direction of your fingers corresponds to the flow of the generated magnetic field. The direction of the magnetic field at a given point around the wire is its tangential path intersecting the point.

Electromagnetic Induction

Induced current and induced electromotive force (EMF) are two phenomena caused by a change in the amount of magnetic field passing through a coil. These quantities are governed by the rate at which the magnetic field changes.

  • Induced Current: The current produced in the coil by the changing magnetic field.

  • Induced Electromotive Force (EMF): The work done per unit charge to produce an induced current. The quantity is not actually a force, but a difference in electric potential (voltage drop).

  • Induction: The process of producing induced current and induced EMF.

Magnetic Flux

The magnetic flux quantifies the amount of magnetic field passing through a surface. The magnetic flux through a wire loop with an area A subjected to a magnetic field is given by:

Note that n-hat is the normal vector perpendicular to the area of the loop of wire.

Faraday’s Law

We can quantify electromagnetic induction by calculating the induced EMF using Faraday’s law:

Here N is the number of coils/loops of wire. We assume that the coils (or loops) of wire are closely spaced so that the flux through them is the same. The negative sign indicates that the EMF wants to oppose the change in the magnetic field.

Lenz’s Law

An induced current has a direction such that the magnetic field due to the induced current opposes the change in magnetic flux that induces it.

  • If an external magnetic field is increasing in a particular direction, its induced magnetic field will point in the opposite direction.

  • If an external magnetic field is decreasing in a particular direction, its induced magnetic field will point in the same direction.

To find the direction of the induced current, we can use our Right-Hand Rule: Point your thumb in the direction of the induced magnetic field with your palm faced at the center of the coil. The curled path of your fingers will point in the direction of the induced current.

Motional EMF

The movement of a conductor in a magnetic field induces an electromotive force. This is quantified by the following expression:

Fundamental Motor Concept

Motors convert electrical energy into mechanical energy using electromagnetic principles. The method of energy conversion is fundamentally the same in all electric motors.

BLDC Motors

Brushless DC (BLDC) motors are a type of synchronous motor, meaning that the magnetic field generated by both the stator and rotor rotate at the same frequency. Unlike brushed DC motors, the BLDC motor is electrically commutated using power switches instead of brushes.

Applications

Listed below are common applications which use BLDC motors:

  • Appliances

  • Automotive

  • Aerospace

  • Consumer

  • Medical

  • Automated Industrial Equipment

  • Instrumentation

BLDC Motor Components

Listed below are two types of motors which differ based on the implementation of the stator and rotor:

  • In-runner Motor: The stator is external and the rotor is internal. In-runner motors are more lightweight and can achieve greater rotational speeds due to their smaller rotating diameter.

  • Out-runner Motor: The stator is internal and the rotor is external. Out-runner motors can achieve greater torque due to their larger rotating diameter and generated BEMF.

Stator

The stator of a BLDC motor consists of stacked steel laminations with windings placed in slots that are axially cut along its inner periphery. The windings are created with many interconnected coils placed in the slots and are distributed evenly along the structure of the stator.

There are three classifications of the BLDC motor:

  • Single-phase

  • Two-phase

  • Three-phase

For our discussion, the numbers for each configuration correspond to the number of windings the stator has. The single-phase and three-phase motors are the most used out of all BLDC motors.

Single-Phase Motor

The figure below shows a diagram of a single-phase BLDC motor.

A single-phase motor has one stator winding, wound either clockwise or counter-clockwise along each arm of the stator, to create four magnetic poles as shown above.

Three-Phase Motor

The figure below shows a diagram of a three-phase BLDC motor.

A three-phase motor has three windings wound either in a star or Delta shape.

Stator Winding Types

There are two types of stator winding variants. The differentiation between the two variants is made based on the interconnection of coils in the stator windings to give different types of back electromotive force (BEMF) and phase currents.

  • Trapezoidal: BEMF and phase current is generated in a trapezoidal fashion.

  • Sinusoidal: BEMF and phase current is generated in a sinusoidal fashion. The torque output of a sinusoidal motor is smoother at the expense of greater copper usage for extra winding interconnections.

Shown below are figures demonstrating trapezoidal and sinusoidal BEMF respectively.

Rotor

The rotor of the BLDC motor consists of a shaft and a hub with permanent magnets that uniformly alternate in pole polarity (north and south). The number of pole pairs in a rotor typically range between two and eight. Three different rotor magnet arrangements are shown in the figure below:

Rotor Material

The magnetic field density of the rotor is governed by the type of magnetic material chosen to create it. Listed below are the two common types of materials used in rotors:

  • Ferrite magnets: Inexpensive and have low magnetic density per volume

  • Rare earth alloy magnets: Expensive and have high magnetic density per volume (Nd, SmCo, NdFeB, etc.)

The high magnetic density per volume characteristic of rare earth alloy magnets enables the rotor to compress further while achieving the same desired torque. This ultimately improves the size-to-weight ratio and allows for higher torque to be achieved for the same sized motor.

Rotor Position Sensing

The commutation of a BLDC motor is controlled electronically. The stator windings must be energized in a particular sequence to enable rotation. It is therefore crucial to know the position of the rotor in order to determine which winding must be energized.

Hall Effect Sensing

Hall Effect Theory

If a current carrying conductor is kept in a magnetic field, the field exerts a transverse force on the moving charge carriers. These charge carriers will typically be pushed to one side of the conductor. The buildup of charge at the opposing sides of the conductor will balance with this magnetic influence, producing a measurable voltage drop. The presence of this measurable transverse voltage is called the Hall effect.

Hall Effect Sensing Implementation

Most BLDC motors have three Hall effect sensors embedded into the stator of the motor to sense rotor position. Hall effect sensors output a high or low signal, corresponding to a north or south pole respectively, whenever the magnetic poles of the rotor pass by them. Shown below is an example placement of Hall effect sensors on the stator (sensors a, b, and c):

Based on the outputs of the Hall effect sensors, the required commutation sequence can be determined and executed.

Hall sensors require a power supply. The input voltage required may range from 4V-24V. The input current required may range from 5mA-15mA. The output of the Hall sensor is typically an open-collector type and so a pull-up or pull-down resistor may be required.

Hall Effect Sensing Drawbacks

Embedding Hall effect sensors into the stator is complex because any misalignments with respect to the rotor magnets could result in inaccurate rotor position sensing. To simplify the process of mounting Hall effect sensors, some motors may have the Hall effect sensors and Hall effect sensor magnets placed on the rotor. The result is that whenever the rotor rotates, the Hall effect sensor magnets give the same effect as the main rotor magnets. The Hall effect sensors are normally mounted on a PCB and fixed to the enclosure cap on the non-driving end. This allows for the Hall effect sensors to be adjusted easily to align with the rotor magnets.

Back EMF Theory

When a BLDC motor rotates, each winding generates a voltage known as back electromotive force (BEMF) that opposes the main voltage supplied to the windings according to Lenz’s Law. The polarity of the BEMF is in the opposite direction of the energized voltage. The BEMF depends on three primary factors:

  • Angular velocity of the rotor

  • Magnetic field generated by the rotor magnets

  • The number of turns in the stator windings

We can relate the BEMF to key characteristics by the following expression:

Here, we define the parameters:

  • N: The number of winding turns per phase

  • l: The length of the rotor

  • r: The internal radius of the rotor

  • B: The magnetic field density of the rotor

  • ω: The angular velocity of the motor

Notice that for a completely designed motor, all parameters of the above expression are constant except for the motor’s angular velocity. It is trivial to see that as the angular velocity (or speed) of the rotor increases, the BEMF also increases.

The potential difference across a winding can be calculated by subtracting the BEMF value from the supply voltage.

Motors are designed with a BEMF in such a way that when the motor is running at its rated speed, the potential difference between the BEMF and the supply voltage (voltage drop across the windings) will be sufficient for the motor to draw the rated current and deliver the rated torque. If the motor is driven beyond its rated speed, the BEMF may increase substantially, thus decreasing the potential difference across the winding, and reducing the current drawn. The effect is a droop in achievable torque.

When the supply voltage becomes equal to the BEMF and motor losses, the drawn current and achieved torque become zero.

Back EMF Sensing Implementation

BLDC motors can be commutated by monitoring the BEMF signals instead of Hall effect sensors. The relationship between Hall effect sensors and BEMF, with respect to phase voltage, is shown in the figure below:

As we may recall, every commutation sequence has one positively energized, one negatively energized, and one open-circuited winding. As shown in the figure above, the Hall effect sensor signal changes state when the voltage polarity of the BEMF changes from positive to negative or from negative to positive. Thus, the BEMF zero-crossings provides data necessary for commutation.

With this method of commutation, Hall effect sensors and Hall effect sensor magnets can be eliminated in motor construct, simplifying both design and cost. This is advantageous if the motor is to operate in environments where occasional cleaning of Hall effect sensors is required.

The figure below shows a block diagram for BEMF sensing control of a BLDC motor:

Back EMF Sensing Drawbacks

Ideally, the Hall effect sensor signal changes state when the BEMF crosses zero. In practical cases, there exists a delay due to the winding characteristics of the stator. This delay should be compensated by the MCU.

Recall that BEMF is proportional to the speed of rotation. At very low speeds, the BEMF would be of very low amplitude and it would be difficult to accurately detect zero-crossing behavior. With BEMF sensing, the motor has to be started in open loop. When sufficient BEMF is generated to detect zero-crossing accurately, the control should be shifted back to BEMF sensing. The minimum speed at which BEMF can be sensed is calculated from the BEMF constant of the motor.

Theory of Operation

Motor operation is based on the attraction or repulsion between magnetic poles. Consider the three-phase BLDC motor shown in the figure below:

The process begins when current flows through one of the three stator windings in a particular direction and generates a magnetic pole that attracts the closest permanent magnet of the opposite pole. The rotor will move if the current shifts to an adjacent winding. Sequentially charging each winding will cause the rotor to follow in a rotating field. To amplify rotation, another winding may be energized at the same time with current flowing in a particular direction to create a magnetic pole that repels the permanent magnet of the rotor in the desired direction.

For three-phase BLDC motors, each commutation sequence has one of the following:

  • A positively energized winding (current enters the winding)

  • A negatively energized winding (current exists the winding)

  • A non-energized winding

Torque is generated because of the interaction between the magnetic field generated by the stator coils and the permanent magnets of the rotor. Ideally, the peak torque occurs when these two fields are orthogonal or at a 90° angle to each other. In order to keep the motor running, the magnetic field produced by the windings should shift position as the rotor moves to catch up with the magnetic field of the stator. In general, torque is governed by the following factors:

  • Current amplitude

  • Number of turns on the stator windings

  • Strength and size of the permanent magnets

  • Air gap between the rotor and the windings

  • Length of the rotating arm

BLDC Motor Control

Switch Configuration and PWM

BLDC motors use electric switches to obtain current commutation in order to continuously rotate the motor. These switches are typically connected in an H-bridge structure for single-phase BLDC motors, and a three-phase bridge structure for three-phase BLDC motors. The figure shown below demonstrates the two circuit structures:

High-side switches are typically controlled with PWM, which converts a DC voltage into a modulated voltage that easily and efficiently limits the startup current, control speed, and torque. Raising the switching frequency typically increases PWM losses. Lowering the switching frequency limits the system’s bandwidth and can increase ripple current to destructive extents.

Commutation Sequence

Single-Phase BLDC Motor

The figure below shows the commutation sequence of a single-phase BLDC motor driver circuit.

Following the diagram carefully will provide the intuition necessary to grasp the commutation sequencing of single-phase BLDC motors.

The figure below shows an example of Hall sensor signals with respect to switch drive signals and armature current.

Three-Phase BLDC Motor

A three-phase BLDC motor requires three Hall sensors to detect the rotor’s position. Based on the physical position of the Hall sensors, there are two types of output: a 60° phase shift and a 120° phase shift. Combining these three Hall sensor signals can determine the exact commutation sequence.

The figure below shows the commutation sequence of a three-phase BLDC motor driver circuit for counter-clockwise rotation.

Three Hall effect sensors a, b, and c are mounted on the stator at 120° intervals, while the three phase windings are in a star formation. For every 60° rotation, a Hall effect sensor will change state. It takes six steps to complete an entire electrical cycle. In synchronous mode, the phase current switching updates every 60°.

Recall that the number of signal cycles needed to complete a mechanical rotation is equal to the number of rotor pole pairs. In the example, there are 2 rotor pole pairs. Thus, 2 signal cycles are required to complete a single mechanical revolution.

The figure below shows the timing diagrams where the phase windings U, V, and W are either energized or floated based on the Hall effect sensor signals. Remember that this is an example where the Hall effect sensor signals have a 120° phase shift with respect to each other where the motor rotates counter-clockwise.

Provided below is another example of three-phase BLDC motor commutation.

Torque and Speed Characteristics

The figure below shows an example of the torque and speed characteristics of a BLDC motor.

There are two parameters used to define a BLDC motor.

  • Rated Torque: During continuous operations, the motor can be loaded up to the rated torque. In a BLDC motor, the torque remains constant for a speed range up to the rated speed. The motor can run up to the maximum speed, which can be up to 150% of the rated speed. At this point, the torque will begin to drop.

  • Peak Torque: Applications which have frequent starts, stops, and reversal of rotation with load on the motor demand more torque than the rated torque. This requirement comes for a brief period, especially when the motor starts from a standstill and during acceleration. During this period, extra torque is needed to overcome the inertia of the load and rotor itself. The motor can deliver a higher torque, maximum up to peak torque, so long as it follows the speed torque curve.

BLDC Motor Selection

Selecting the proper type of motor for the given application and load characteristics crucial. Three parameters govern motor selection. They are:

  • Required peak torque

  • Required RMS torque

  • The operating speed range

Peak Torque

The peak torque required for an application can be calculated by taking the summation of the load torque, torque due to inertia, and the torque required to overcome friction. Other factors also contribute to overall peak torque requirements and can be compensated with a 20% safety margin as a rule of thumb.

The torque due to inertia is the torque required to accelerate the load from standstill or from a lower speed to a higher speed. This can be calculated by taking the product of load inertia, which includes rotor inertia, and load acceleration.

Note that JL+M is the sum of the load and rotor inertia, and a is the required acceleration. The mechanical system coupled to the motor shaft determines the load torque and the frictional torque.

RMS Torque

The RMS torque can be roughly translated to the average continuous torque required for the application. This value depends on many factors including:

  • Peak torque

  • Load torque

  • Torque due to inertia

  • Frictional torque

  • Acceleration and deacceleration

  • Run times

The RMS torque is quantified by the following equation:

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