Brushless DC Motor

A brushless motor is a type of electrical motor which does not use a commutator or brushes to switch the direction of current in the electromagnet in the motor. Instead it uses a sophisticated control system to turn on the coils in sequence to keep the rotor turning. Removing the brushes increases the efficiency and top speeds of this motor compared when compared to a traditional Brushed DC Motor.

It is often used for the spinner of a robot as it can achieve higher speeds and torques than a brushed motor.

## Operation

They use typically 3 coils which are turned on in sequence, the magnetic fields these generate interact with permanent magnets on the rotor. This sequence is analogous to a donkey chasing a carrot. The coils are turned on according to the rotor position so that the permanent magnets try and reach the north/south poles generated by the coil. As the rotor nears these poles the next set of coils are turned on and hence the rotor again turns/chases the new north and south poles. In order to turn on the right coils at the right time the shaft position needs to be determined. This can be done using sensors such as hall effect sensors or encoders. It can also be done by measuring the back-emf produced by the permanent magnets passing past a coil. This latter method is known as “sensor-less” brushless DC control and is common in brushless motors available for RC hobbyists. You can tell the type of method being used by the number of leads, if only three are present then there are no connections for the sensors, more than this and there are sensors present.

When a brushless motor is being controlled by an “simple” controller (ie. one which simply performs the coil switching and voltage is constant) it follows a similar characteristic curve to a brushed motor. However, with brushless motors an ESC also controls the speed of the motor by varying the applied voltage essentially creating multiple performance curves the motor can be on depending on the input throttle. The speeds and torques reached can also depend on the programming of the ESC. Many ESCs have a “soft-start” function which will limit the ESC’s responses to sudden increases in throttle. Hence when starting from standstill the full battery voltage will not be applied to the coils immediately and will be increased over a small time period. This means the motor will start spinning up at a lower voltage drawing less stall current than the maximum stall current. It also avoids applying the maximum torque immediately which could strip teeth off gears. However this does mean the theoretical stall torque is not applied and the minimum time taken to reach max speed is affect.

## Uses

### Rotary Weapons

Brushless motors are generally used in fighting robots for rotary weapon systems. This is due to a couple of reasons. Brushless motors have a much better power/weight ratio than brushed motors because of their higher efficiency meaning simply for the same size of motor you get more power in a brushless motor. Furthermore they won’t wear out at high speeds (a common problem with brushed motors).

Rotary weapons inflict damage by rotating and so obtain rotational kinetic energy. Then they hit something and dissipating this energy into whatever is hit. The amount of damage done depends on the amount of energy and how well it is transferred. The rotational energy can be increased by spinning the weapon faster or making the weapon heavier. Weapon design is a trade off between making the weapon as heavy and as fast as possible and being able to withstand the forces it will generate when it hits something (not all of the energy will the transferred into the thing you hit). But how does weapon design affect the motor you choose to drive it? It comes down to the same characteristics as before, speed a torque.

When something spins it has rotational mass (moment of inertia). Heavier and larger weapons will have larger moments of inertia and hence require larger torques in order to accelerate them. You want to have enough torque in order accelerate quickly for two reasons. Firstly from a tactical point of view having a weapon operating at top speed quickly is important in maximising the damage it can do. Secondly if the weapon does not accelerate quickly it will cause the motor to operate near the stall torque area of the graph. This means you will be using large currents for longer which can overheat the motor.

Using a belt drive with rotational weapons is a recommended as it helps isolate the motor from the effects of the weapon hitting something. When the weapon hits something it will  cause a large counter torque which could damage the motor. Using different sized pulleys in the belt drive system can act as gearing to increase the torque applied to the weapon.

The maximum speed of the motor is also important to ensure the weapon reaches sufficient speeds to inflict damage. However, most motors will spin fast enough to make a formidable weapon and so the main care needs to be made in ensuring the motor provides sufficient torque. Furthermore spinning a weapon too fast could actually limit the effectiveness of the weapon as faster weapons have less bite and introduce gyroscopic effects which could interfere with driving the robot.

## Selection

When choosing a brushless DC motor for a rotary weapon you need to consider the weapon you are driving. Choosing a brushless isn’t quite as simple as simply choosing one that is able to provide a satisfactory maximum speed and torque mainly because they are often not directly specified. Two values can give you an idea of the top speed and available torque when choosing a brushless motor.

The Kv rating of a motor gives you an idea of the maximum speed the motor can achieve when used with a suitable ESC and a battery of particular voltage. The kv rating is a constant representing the ratio between the maximum RPM of the motor and the voltage across its terminals.

Kv  = RPM/V
(V = battery voltage,  ω = rad/s)

Hence
RPM = Kv\*V

So a motor with a Kv rating of 2200 when connected to a battery of 1V will rotate at 2200 RPM when there is nothing attached to the motor shaft (no load). The same motor will rotate at 4400 RPM when connected to a 2V battery. As soon as the motor is loaded the achieved RPM of the motor will be lower.

The other important factor when choosing a motor is Torque. In brushless motors the torque produced is proportional to the magnetic field present in the coils in the motor. This can be increased by either using more coils (larger motor) or using more current. The torque is also affected by the Kv rating as this indicates how the motor is constructed.

A lower Kv motor will result in more torque when comparing motors of a similar size. This means a motor with a lower Kv will produce more torque for the same amount of current compared to a high Kv motor. Lower Kv motors are designed to spin larger propellers on quadcopters. Transferring this knowledge to our application it follows that lower Kv motors can turn heavier weapons. Low Kv motors are often used with larger batteries (4s li-pos). This means for the same input power the current will be lower than using a smaller battery (P = VI) which is important as because low Kv motors use thinner wire to achieve the larger number of coils and so have a lower current handling capability.

Another significant indicator of a motor’s torque is the power of the motor and its size. Larger motors will be able to fit more coils of wire within them. More coils equals stronger magnetic fields and hence more torque.

However, neither of these methods give you a numerical value for the torque a motor. If we assume the linear characteristic of the “simple” controller we can find a theoretical value. Torque of the motor is given by: T = 9.55\*(I-I0)/Kv Where T is the output torque (Nm) I is the current (A), I0 is the no load current and Kv is the Kv rating in RPM/V (the 9.55 converts this into (rad/s)/V). If we want to find the maximum torque we can set the current through the coils I to the stall current, however the Soft Start functionality of the ESC may mean this full torque is never applied. The angular acceleration of the weapon is given by a (rad/s^2) = T/I where I (kgm^2) is the weapon’s moment of inertia and T is the applied torque. The time taken to reach a particular speed (w in rad/s)  from standstill is given by t = w/a where t is in seconds.

Because of the large number of assumption made in these equations it may be better to use the Team Runamok Spinner calculator found here.

If you want to avoid calculation the most successful weapons in this competition have gone for the mantra: bigger is better. So generally as big as possible for your price range. The last bit is particularly important as don’t forget more powerful motors will require higher rated ESCs and even larger batteries and this cost can quickly add up.