The motor body of the brushless DC motor is similar in structure to the permanent magnet synchronous motor, except that there is no cage winding and its starting device. Its stator winding can be simple single-phase or more than three-phase structure. The connection methods of armature windings mainly include star and delta connection. Electronic commutation circuits generally have bridge and non-bridge types. , they can be composed of many variations. The following is a simple analysis of the working principle of the most common two-two-three-phase star six-state permanent magnet brushless DC motor.
The structure of the three-phase two-pole brushless DC motor
A, B, and C are three-phase stator windings, which are respectively connected with the power switching devices V1, V2, V3 in the electronic switch circuit, and the tracking rotor of the position sensor is placed on the rotating shaft of the motor. VP1, VP2 and VP3 are evenly distributed at one end of the brushless DC motor with a difference of 120 degrees in the spatial quotient. Through the action of the rotating shading plate on the motor shaft, the position of the rotor magnetic pole is determined according to whether a certain optoelectronic device is illuminated by light.
If the A phase of the stator winding is energized at a certain moment, the current interacts with the main magnetic field generated by the permanent magnet on the rotor to generate electromagnetic torque, so that the rotor rotates, and the position of the rotor magnet becomes an electrical signal through the position sensor. , and then control the electronic switch circuit, so that each phase winding of the stator will be turned on in turn, and the stator phase current will change phases in a certain order with the change of the rotor position. In this way, the conduction sequence of the electronic switch circuit can be synchronized with the rotation angle of the rotor to achieve the effect of mechanical commutation.
Mathematical Model of Brushless DC Motor
Three-phase two-pole brushless DC motor, inner rotor structure, star-shaped connection of stator windings, and three Hall elements are evenly distributed with a difference of 120 degrees in space. At the same time, it is assumed that the motor has the following characteristics:
(1) The magnetic circuit of the motor is not saturated, and the eddy current effect, hysteresis loss and armature reaction are ignored;
(2) Less than the influence of cogging torque;
(3) The power devices in the control circuit are all ideal switching devices.
Torque Equation
When the DC motor is in normal working state, the electromagnetic torque refers to the torque generated by the interaction between the conductor and the permanent magnet after the armature winding is energized. When the motor is working normally, two phases of the winding are kept on at the same time, so the electromagnetic power Pm is:
Pm=2EpIp
Disregarding the influence of current commutation, the electromagnetic torque Te of the motor is:
Te= Pm/Wi/Np =2npEpIp/W1=2npψp Ip
In the formula, Ep is the peak value of the electromotive force of the brushless DC motor;
Ip is the current peak value of the motor
Ψp is the peak value of the electromagnetic flux linkage of the motor
It can be seen from the formula that the electromagnetic torque of the motor is proportional to the peak current
equation of motion
In general, the equation of motion of the system is
Te – TL – Zw=J*dw/dt
In the formula, Te and TL are the electromagnetic torque and load torque of the motor
W is the angular velocity of the motor;
Z is the viscous friction coefficient
J is the moment of inertia of the motor rotor
Characteristic Analysis of Brushless DC Motor
Starting characteristics
At start, since the back EMF is zero, the armature current is:
I=Ud -2△U/2R
In the formula, Ud is the line voltage of the two-phase windings turned on by the motor;
△ U is the power drop in the control circuit;
R is the internal resistance of the motor stator winding
Due to the small internal resistance, the armature current increases rapidly when starting, so the starting electromagnetic torque is large, which can be started quickly, and can also be started directly under load. When the speed increases, the armature repulsion makes the induced electromotive force increase, the torque of the motor decreases, and the acceleration speed also decreases, and finally enters the normal working state, and the speed and armature current are stable at this time.
When the motor is started with no load, the curve of the speed and armature current with time is shown in the figure
Mechanical properties
The mechanical characteristics refer to the relationship between the speed of the motor and the torque of the electromagnetic when the DC voltage Ud is constant. The mechanical characteristics equation of the brushless DC motor is:
n=15/ BlπR′Wфsquare(U-RI-L dI/dt)
After finishing, you can get:
n=30/π* Kt Ud – 2RTe/Ke Kt
In the formula, Kt is the torque coefficient of the motor
Ke is the induced electromotive force coefficient of the motor
Ud is the line voltage
It can be seen that there is a linear relationship between rotational speed and electromagnetic torque. However, in the actual operation process, when the electromagnetic torque becomes larger, the armature reaction will produce a certain demagnetization effect. At the same time, considering the nonlinearity of the power device driving the control circuit, the end of the mechanical characteristic curve of the motor will bend downward. .
The mechanical characteristic curve of the brushless DC motor is shown in the figure
Adjustment characteristics
The regulation characteristic refers to the changing relationship between the speed of the motor and the applied voltage when the electromagnetic torque of the motor is constant. When the brushless DC motor is in a stable state, ignoring the loss of the power device driving the control circuit, there is the following relationship
Ud=raI +π/30*Ken
KTI-TL=π/30Zn
Then the relationship between speed and voltage is
N=30/30 KTKe+πraZ*(KT Ud –ra –TL)
Thus, the curve of the speed of the brushless DC motor changing with Ud under different electromagnetic torque Te can be obtained, Te1<Te21<Te3<Te4
The brushless DC motor has good control performance, but when Ud is small, the electromagnetic torque is also small, the electromagnetic torque is also small, the load torque cannot be restrained, and the motor cannot be started, so the speed of the motor is zero, and when Ud increases When it exceeds the gate line voltage, the motor starts to start and gradually runs to a steady state. When the Ud is larger, the speed is also larger. At the same time, due to the existence of friction, the adjustment characteristic does not pass through the origin.
