This is the resistance of the electrical path between the two motor terminals. Because R is usually small, a common Ohmmeter is not suitable. So we use Ohm’s Law instead.

While holding the motor shaft fixed (using fingers is OK for small motors), ramp up the power supply to send a moderate current through the motor. For a Speed-400 motor, 2–3 Amps is appropriate, and will require about 1 Volt.

Simultaneously read off the actual current i and voltage v. Compute the resistance:

R = v/i

The readings will vary somewhat as the motor shaft is held in different rotation positions, so take several readings and average the resulting R’s.

The no load current of a brushless motor is defined as the current the motor draws, with no load applied, at a specific voltage. The no load current is measured in Amps and denoted “Io.”  The key point here is that the current is measured at a specific voltage. 

This is the ratio of motor speed Ω to the back-EMF v_m. It controls the dependence of the motor’s zero-load speed Ω_o on the applied voltage v:

                 Ω_o  = v_mK_v = (v − i_oR) K_v

The torque constant, Kt, of a motor is a very useful parameter for sizing and controlling motors showing a linear speed / torque relationship. Both DC brush type and Brushless motors exhibit this linear performance curve relationship.

Kt is simply the slope of the torque / current curve of a motor. The units of the constant are found in torque units per amp. (e.g. N-m/amp, oz-in/amp, etc.) Kt can be useful in both design and application. Looking at the current in the system the designer or control system can calculate the actual torque output of the motor during operation. This can be used in a variety of ways. It allows the designer to understand the actual load that is seen in the application and understand if the optimal motor for the application is being used. On the control side, a control can be set up with a current limit to ensure that the mechanical system is not over loaded or it can be used to assure that the motor does not overheat during use. Additionally, Kt is used in torque mode applications to maintain a controlled amount of torque to meet the application needs.

To measure the K_e of the motor, put the motor shaft in a lathe and rotate the shaft at some speed [rpm] such as 1000rpm. With a dc motor, use a dc voltmeter to measure the armature voltage. The K_e is then the voltage you read divided by the speed in rad/sec. Convert rpm to rad/sec as-

With a BLDC motor use an ac voltmeter to measure the voltage between any 2 wires of the 3 motor wires and then convert the line-to-line voltage to the phase voltage value by dividing the line-to-line voltage by 1.73

The basic purpose of DC motor is to convert electrical energy into mechanical energy. DC motor's working is based on the principle: "When a current carrying conductor is placed in the magnetic field, the conductor experiences magnetic force." The direction of this force can be given by Fleming's left hand rule.

Referring to the image; F is Force, B is the Magnetic Field, I is the Current.

The magnitude of the force can be given as; F=BIL

Armature winding is connected to the DC supply to set up the electric current in the winding. Magnetic field can be provided by the field winding or by the permanent magnets. Armature winding experiences force due to magnetic field generated by energized field winding or permanent magnets. 

Commutator is made segmented to achieve undirectional torque. Otherwise, direction of the force would have reversed everytime when the direction of the movement of the conductor is reversed in the magnetic field.

Armature Winding is the windings, in which voltage induced. The Field Winding is the winding in which the main field flux is produced when the current through the winding is passed. 

Turn: A turn consists of two conductors connected to one end by an end connector.

Coil: A coil is formed by connecting several turns in the series.

Winding: A winding is formed by connecting several coils in series.

The figure of the turn:

The figure of the Coil:

The figure of the Winding:

The angular distance between the centers of two adjacent poles on a machine is known as pole pitch or pole span.

The pole pitch is always 180 degrees electrical regardless of the number of poles in a machine.

The stator is the stationary outside part of a motor. The stator of a permanent magnet dc motor is composed of two or more permanent magnet pole pieces. The magnetic field can alternatively be created by an electromagnet. In this case, a DC coil (field winding) is wound around a magnetic material that forms part of the stator.

The rotor is the inner part which rotates. The rotor is composed of windings (called armature windings) which are connected to the external circuit through a mechanical commutator. Both stator and rotor are made of ferromagnetic materials. The two are separated by air-gap.

The schematic diagram for a DC motor is shown below. A DC motor has two distinct circuits: Field circuit and armature circuit. The input is electrical power and the output is mechanical power. In this equivalent circuit, the field winding is supplied from a separate DC voltage source of voltage Vf. Rf and Lf represent the resistance and inductance of the field winding. The current If produced in the winding establishes the magnetic field necessary for motor operation. In the armature (rotor) circuit, VT is the voltage applied across the motor terminals, Ia is the current flowing in the armature circuit, Ra is the resistance of the armature winding, and Eb is the total voltage induced in the armature.

When a BLDC motor rotates, each winding generates a voltage known as back Electromotive Force or back EMF, which opposes the main voltage supplied to the windings according to Lenz’s Law. The polarity of this back EMF is in opposite direction of the energized voltage. Back EMF depends mainly on three factors:

• Angular velocity of the rotor

 • Magnetic field generated by rotor magnets

• The number of turns in the stator windings

EQUATION 1: Back EMF = (E) ∝ NlrBω where: N is the number of winding turns per phase, l is the length of the rotor, r is the internal radius of the rotor, B is the rotor magnetic field density and ω is the motor’s angular velocity

Inertia is an object's resistance to a change in speed. To determine the inertia of an object, its mass is multiplied by the square of its distance from the axis of rotation. ... The ratio of the load inertia to the motor inertia is one of the most important aspects of servo motor sizing.

Why is rotor inertia important to know? 

A motor cannot be selected for replacement by the power rating or the torque speed curve alone without knowing how the rotor inertia has affected the continuous torque required in the application.

Motor rotor inertia can be measured by making an experiment. The inertia can be calculated from the equation-

Acceleration torque(lb – in) = Inertia (lb -  in -  sec^2)  x acceleration (rad/ sec^2)

Also (rearranging the terms)

Inertia = (Acceleration torque/ Acceleration) (lb -  in -  sec^2) 

Inductance of a Coil. Inductance is the name given to the property of a component that opposes the change of current flowing through it and even a straight piece of wire will have some inductance. Inductors do this by generating a self-induced emf within itself as a result of their changing magnetic field.

Inductance is measured by applying a sinusoidal signal and then measuring the phase difference between the voltage wave form and current wave form. Connect the motor to a function generator or the such. Place a resistor in series between the motor and the function generator on the negative side

For A BLDC Motor, the Inductance = Reactance/ 2π x Frequency