According to the laws of electromagnetism, when a magnetic field changes, a nearby conductor will generate an induced electromotive force (EMF). The direction of this EMF conforms to Faraday's law and Lenz's law, and is exactly opposite to the voltage originally applied across the coil. This voltage is called the back EMF. In a permanent magnet synchronous servo motor , as long as the motor rotates, a coil will inevitably cut magnetic lines of force, thus generating a back EMF. The back EMF is denoted by E1, and its effective value is calculated as follows:
in:
KE — is the proportionality constant;
FN — the frequency of the stator current;
NL—Number of turns per phase stator winding;
ф——Amplitude of the main magnetic flux.
I. Factors Determining Back Electromotive Force
◆Rotor angular velocity
◆Magnetic field generated by the rotor magnet
◆Number of turns in stator winding
Once the motor design is complete, the rotor magnetic field and the number of turns in the stator windings are fixed. Therefore, the only factor that determines the back electromotive force is the rotor angular velocity, or rotor speed. As the rotor speed increases, the back electromotive force also increases.
II. Back EMF Test Method
According to the general technical specifications for permanent magnet AC servo motors, we typically use the back electromotive force (EMF) constant to evaluate permanent magnet synchronous motors. The back EMF constant is a crucial technical parameter for permanent magnet synchronous motors, as it relates to motor performance and controller design. Therefore, this parameter must be precisely tested during the production of permanent magnet synchronous servo motors, and standard testing methods must be used to verify whether the designed product meets the technical requirements.
GB/T50349 General Technical Conditions for Permanent Magnet AC Servo Motors stipulates that the motor under test should first be driven to a certain speed n specified in the technical conditions, and then its waveform should be observed with an oscilloscope. The back electromotive force constant (Ke) is calculated through voltage and speed, and Ke is required to meet the technical conditions for permanent magnet synchronous servo motors.
Figure 1: Back EMF testing platform
The above figure shows the back EMF test platform for a permanent magnet synchronous servo motor. According to the test standard requirements, the test motor is driven to run at an electric speed of n under no-load. The speed is measured by a speed sensor, and the back EMF U of the test motor is measured by a WP4000 frequency converter power analyzer.
During the test, the back electromotive force U of the motor at no-load speed n was measured, and the back electromotive force constant was calculated using the following formula to verify whether it meets the technical requirements.
In the formula:
Ke – Back electromotive force constant, with units of volts per radian negative first second (V/rad*-1^s);
U—Back electromotive force of the motor line, in volts (V). The effective value of the back electromotive force of the line for a sine wave driven motor and the amplitude of the back electromotive force of the line for a square wave driven motor.
N – Rotational speed at the measured point, in revolutions per minute (r/min).
This solution utilizes the WP4000 frequency converter power analyzer to perform back electromotive force (EMF) and speed tests, employing effective synchronization methods to ensure simultaneous testing of electrical and non-point parameters. Furthermore, the WP4000 power analyzer has an open raw data port, allowing the front-end to directly share raw waveform data with the host computer via Ethernet, completely replacing the need for an oscilloscope. Custom analysis software can directly perform back EMF constant testing, meeting the automated testing requirements of servo motor testing systems.
