[Episode 7] This Is Just the Beginning! Ichinose and Friends’ Motor Driver Dojo

From here, I’ll be explaining pulsation of the output torque, which greatly affects the quietness of a motor, as well as sinusoidal driving, in which pulsation is minimal. I’ll divide this material into the ten topics shown below. We begin with a discussion of motor torque pulsation.

Contents of Episode 7

• ・What Is Torque Pulsation?
• ・Sinusoidal Conduction
• ・Waveforms in Sinusoidal Driving
• ・Synchronous Rectification
• ・Power Supply Currents in Sinusoidal Driving
• ・Torque Pulsation in Sinusoidal Driving
• ・Sinusoidal Current Timing
• ・Sinusoidal Current Phase Changes
• ・Advance Angle Control of a Brushless Motor
• ・Sinusoidal Driving Waveforms

What is Torque Pulsation?

In articles up to this point, I have talked about the output torque of a motor. This term “output torque” actually has two meanings. One is the average torque that occurs when the motor rotates a load; the other meaning is the instantaneous torque. The average torque is used when we are studying the range of loads that a motor can rotate, or the efficiency of a motor (see the article on S-T Characteristics). The instantaneous torque is used when studying motor vibrations and noise.

As the equations above indicate, the instantaneous torque is the product of sinθ and the magnitude of the electromagnet magnetic force. And so when these are not constant, the torque changes in a pulsating manner. This is called torque pulsation. Pulsation of the torque greatly affects the amount of motor noise. I’ll explain torque pulsation for the case of 120 degree conduction.

The output torque of the first equation above is called the total torque. The electromagnet magnetic force in the total torque represents the vector sum (composite) of the magnetic forces generated by the windings of the three phases. Earlier, I said that the output torque is created by two magnetic forces, which are this composite magnetic force of the electromagnet and the magnetic force of a permanent magnet, but as another way of looking at this, we can say that the total torque is what you get when you calculate the torques for each of the three phases before combining them, and then taking the vector sum.

The relationships between the phase torques and the total torque are the same, but the electromagnet magnetic forces are calculated only for specific phases. The phase torques in 120 degree conduction are as shown below. The direction of the phase magnetic force for a winding is fixed in the direction of the coil, and the magnitude changes according to the current waveform. The magnetic force direction is constant, and so we’ll consider only the angle of the rotor, which is θ, as the angle with the permanent magnet magnetic force (for total torque, the relative difference between the angles of the composite magnetic force and of the rotor must be θ). From this angle θ and the current magnitude (= electromagnet magnetic force), the phase torque waveform is the waveform for the (U phase) torque shown below.

We perform these calculations for each of the three phases, U, V, and W, and combine them to obtain the total torque. As you can see from the upper waveform for the (total) torque, in 120 degree conduction, large pulsations occur six times within one electrical cycle.

120 degree conduction is widely used owing to the simple algorithms and excellent motor efficiency, but when it comes to motor noise, as these torque pulsations indicate, it is the worst conduction method for three-phase brushless motors. And so in applications where quietness is required, other conduction methods have been proposed. Next, I will explain such conduction methods.

Sinusoidal Conduction

In order to understand conduction methods resulting in minimal torque pulsation, let me again explain the occurrence of torque pulsation.

In the case of 120 degree conduction, the magnitude of the composite magnetic field of the electromagnet formed by the windings pulsates, and the angular velocity of the field also pulsates. For example, in the region of Fig. A, winding magnetic fields are generated only by the U and V phases, and so the angular velocity is zero. The current value changes, and so the magnetic field strength changes. In region B, the V phase magnetic field diminishes, while the W phase magnetic field increases. At this time, the magnetic field is rotating rapidly, and the strength is somewhat small. In region C the angular velocity is again zero, and the field strength changes. In this way, both the velocity and the strength of the electromagnet field pulsate while changing, and so the total torque pulsates.

Well then, what should we do to suppress such torque pulsation? The answer is, we should hold constant the strength and the angular velocity of the electromagnet magnetic field. If the angular velocity is constant, the angular relation with the rotor is constant, and sinθ is a constant value (assuming that the rotor rotates at constant speed). Such a magnetic field can be achieved by using sinusoidal winding currents. When sinusoidal currents shifted by 120 degrees each are passed in the coils of the U, V, and W phases, we obtain a rotating magnetic field of constant size and angular velocity as the field of the electromagnet composite magnetic force (see the figure below).

In order to cause sinusoidal currents to flow in the windings, the applied voltages must also be sinusoidal. A motor driver uses PWM control to achieve such sinusoidal voltages. In the previous article on Applied Voltage Pulses, I explained that PWM control is performed to change the magnitude of the applied voltage, and by changing the duty value at each prescribed angle in one electrical cycle, a sinusoidal waveform can be generated. A conduction method in which the conduction waveform is sinusoidal is called sinusoidal conduction or sinusoidal driving.

Waveforms in Sinusoidal Driving

PWM control is used to apply a voltage with a sinusoidal waveform. PWM control differs in some respects from 120 degree conduction, so I’ll explain it using the following diagram.

In 120 degree conduction, the PWM pulse width is constant in accordance with the applied voltage value. For example, if the specified duty is 60%, then the PWM pulse is 60% over the entire region.

Whereas in sinusoidal driving, the sine wave value reflects the electrical angle. However, there are many different conduction waveforms used in sinusoidal driving, so I’ll explain things using one example.

For example, if the specified duty is 60%, then the amplitude of the sine wave is 30%. The figure shows a waveform in which, with the maximum duty at 80% and the minimum duty at 20%, the width between maximum and minimum is 60%. If, from this, the specified duty value is decreased, then the upper and lower sides approach a duty of 50%. Written as an expression, we obtain specified duty/2xsinθ+50 (%). Although not shown in the figure, in some cases the minimum duty is fixed at 0% to shape the waveform; the expression would then be specified duty/2x(sinθ+1) (%).
When such PWM pulses are applied and the behavior is viewed using an oscilloscope, the following waveform is observed.

These waveforms differ in the following two respects from 120 degree conduction (see Actual Signal Waveforms in Brushless Motor Driving).

• ・UL also consists of PWM pulses, and its waveform is the inversion of UH.
• ・The peak values of the power supply voltage appear to be a series of crests one atop another. Upon zooming in, the power supply current is uneven.

Let me explain the reasons for this.

The two meanings of the term “duty”

The word “duty” has appeared pretty frequently in this series of articles, but broadly speaking, it has two meanings. One of these is the duty specified for an applied voltage input from an external device. This indicates the magnitude of the applied voltage, from a minimum of 0% to a maximum of 100%. The other meaning is the duty of an actual PWM pulse. In 120 degree conduction, these two concepts of “duty” have nearly the same meaning, but in sinusoidal conduction, they do not mean the same thing. You need to understand that they have different meanings.

Synchronous Rectification

In motor drivers, the lower-side signals may be switched between high and low to complement the low and high (on/off) levels of the gate signals of the upper-side transistors, as with the “UL consisting of PWM pulses that are the inversion of UH signals” that I just mentioned. This is an important operation for fixing winding terminal potentials at high or at low level.

When I explained 120 degree conduction, I didn’t explicitly mention this fixing of the potentials of the winding terminals. That was because, for reasons I’ll explain later, in 120 degree conduction it is often the case that complementary PWM pulse operation is not performed. However, in sinusoidal driving it is important that the winding terminal voltages are as set by the controller (it is important that potentials can be fixed), and so complementary operation is a necessity.

In order to clarify the effects of complementary PWM operation, I’ll use the images below (for single-side PWM) to explain a case in which a winding terminal voltage is initially adjusted solely through on/off switching of an upper-side transistor, rather than by complementary operation. When the upper-side transistor is turned on as in the figure on the left, the winding terminal voltage goes high. Let’s focus on the direction of the winding current at this time. As I explained before, even when in this state, in sinusoidal driving either a positive-direction or a negative-direction winding current is possible.

Suppose that the upper transistor is then turned off. At this time, if the winding current is in the positive direction, then the winding terminal voltage goes low via the lower-side diode, and so the potential is as intended. But if the current is in the negative direction, then the winding terminal voltage remains high, and a shift from the pulse width (duty value) of the PWM signal output by the controller occurs. This means that disorder occurs in the sinusoidal waveform of the sinusoidal driving.

In order to eliminate the cause of this disruption of the waveform, complementary PWM operation is used. As shown in the figures below, when the upper-side transistor is turned off, if the lower-side transistor is turned on, the winding terminal goes low regardless of the current direction. Using this complementary PWM operation, the winding terminal voltage will go high when it needs to go high, and will go low when low is needed, so that the voltage intended by the controller can be applied. This PWM control method is called synchronous rectification, complementary PWM, or high/low PWM.

There are also harmful effects caused by fixing the potential at winding terminals while using synchronous rectification of PWM pulses. In 120 degree conduction, the current flows in the positive direction when the upper transistor is turned on, so that the intended voltage can more or less be applied, and when this is weighed against the harmful effects, there are cases in which single-side PWM is advantageous. It is important to choose a PWM method that is suited to the application.

Also, an interval is provided such that both the upper-side and the lower-side gate signals are low at the time of high/low switching, so that actual gate signals are not completely complementary. This low interval is called the dead time; its purpose is to prevent punch-through currents that may occur when both the upper and the lower transistors are in the on-state simultaneously.

Power Supply Currents in Sinusoidal Driving

In the article on “Power Supply Currents” I explained that power supply currents flow according to the on or off states of the power transistors. In sinusoidal driving, these on/off states are more complicated than in 120 degree conduction, as you can see from the waveforms below.

The PWM waveforms of these diagrams are enlargements of those at point A (in the left-hand diagram) in one electrical cycle.

First, at ① the U voltage is high and the V and W voltages are low, and so the current passing through the winding flows in the paths shown below. The current flowing from the power supply passes through the U phase windings, and after being divided between the V and W phases, the currents are combined and return to the power supply. From this, the waveform that appears as the power supply current at ① is the same as that of the U phase current.

Next, at ② the V phase voltage changes to high, so that the U and V voltages are high while the W voltage is low. In contrast with ①, the V phase current flows through the upper-side transistor, and so the current flowing in the power supply is equal to the W phase current. However, you should not that the polarities are opposite. From this we see that the waveform of what appears as the power supply current at is the waveform of the W phase current, but with the polarity inverted. At both ① and ② the winding current waveforms are seen, so that the waveform of the power supply current has the shape of overlapping crests.

Changes in the waveform of a power supply current resulting from transistor on/off switching have various applications, so you need to understand them.

In the case of 120 degree conduction, PWM was used for just one phase, but in sinusoidal driving, PWM is used for all three of the phases, U, V, and W (but depending on the conduction waveform, there may be only two phases). Here the positional relationships between the PWM pulses are the quantities to be controlled. More specifically, there are PWM pulses that are all moved to the right with the turn-off timings aligned, as in the first diagram below. And, there are PWM pulses that have the centers of their high and low intervals aligned. These kinds of PWM pulses are called sawtooth wave comparison or triangular wave comparison PWM signals (see below).

Next page: Torque Pulsation in Sinusoidal Driving, Sinusoidal Current Timing and Phase Changes, Advance Angle Control, and Sinusoidal Driving Waveforms