# Good-bye, Guesswork!

##### By Jerry Leitz and John Sussmeier

Motion control engineers have long struggled with determining the correct wiring for phase and Hall sensor relationships between three-phase brushless DC (BLDC) motors and amplifiers. The problem becomes significant for development efforts on complex machines that require a plurality of different motors, amplifiers, and manufacturers to adequately satisfy motion requirements. To aggravate the problem further, motor and amplifier vendors lack a standard nomenclature between Hall and phase connections.

You can determine the correct phasing of a three-phase BLDC motor and amplifier without using trial and error.

Given three Hall wires, there are six possible connections between the motor and amplifier. Similarly, for three-phase wires, there are six possible connections between the motor and amplifier. The net result is 36 possible unique wiring combinations, of which only six are correct. However, once you've chosen any given combination for the Halls, the problem becomes determining which one of the six possible motor combinations is correct. (Alternatively, you can connect the motor first and then determine which of the six Hall combinations is valid.)

For correct motor phasing, the amplifier must apply current to each motor phase at the same instant that the back electromotive force (BEMF), measured as voltage, for that motor phase is at its peak. A mechanical analogy is firing a spark plug when the piston is at the top of its stroke.

Many phasing application notes describe a trial and error method in which the Halls are attached to the amplifier, and the correct motor wiring is then determined by finding the combination that seems to run the best. Of the six possible combinations for a single set of Hall connections, half will result in rotation that's the opposite of the Hall signal rotation pattern and thus won't work at all. Of the remaining three, one won't turn the motor (current flows through the windings but produces no torque), another will run the motor at reduced torque, and the third will be the correct connection. Trial and error methods are demonstrably subject to error, however, because it's sometimes difficult to determine which combination is best without using a dynamometer. In many cases, two of the six possible phase wiring combinations will appear to run the motor satisfactorily, but only one is right.

Here's a case in point. During the recent development of a high-speed inserting machine that contains 62 BLDC servomotors, engineers incorrectly phased several motor applications. Consequently, several months of improper commutation resulted in not only elevated motor temperatures but also occasional software-initiated motor stoppages, due to excessive position error.

For one application in particular, the stoppages were attributed incorrectly to intermittent encoder failures because under observation, the encoder value would intermittently remain unchanged when the motor was commanded to aggressively accelerate. Investigation determined, however, that the encoder wasn't at fault, as rotor stall took place at an angular position where a commutation switch point occurred. Incorrect commutation led to reduced generated torque at that particular rotor position, which was insufficient to overcome the sum of the motor's cogging torque and friction load torque—thus, rotor stall.

You can determine proper phase wiring without using trial and error techniques if you know both the BEMF waveforms and Hall output relationships for the motor, and the phase current waveforms and sensor input relationships for the amplifier. Figures 1 and 2 illustrate actual amplifier and motor waveforms, supplied by their respective vendors. Please note that these figures show relationships for a motor with 120º (electrical) Hall spacing and an amplifier configured for this spacing. Motors with 60º Hall spacing are commercially available but generally less common. For either case, however, the commutation angle remains constant at 60º for six-step commutation, and the method described herein works for both 60º and 120º spacing.

If the motor vendor doesn't provide this information, you can determine the BEMF and Hall relationships by mechanically back driving the motor and capturing the waveforms for each of the three phases and Hall sensors on an oscilloscope. Back driving the motor provides another benefit: It confirms that the motor phase windings are properly phased with the Hall sensors (i.e., the BEMF waveforms' zero crossings should line up with the rising and falling Hall sensor outputs). For example, during the motor selection process for the above-mentioned inserting machine, engineers identified several motors from numerous vendors that had gross errors between their BEMF waveforms and their respective Hall sensor outputs. Accordingly, rated output torque was significantly reduced from that which the vendors advertised in their data sheets.

## Determining Correct Phasing

Referring to the figures, the basic commutation method can be described as follows:

1) Connect the three Hall signals between the motor and amplifier in any order.

2) For the first Hall, determine which two motor phases (Figure 2) produce a BEMF peak in the middle of the Hall signal. The polarity isn't important; a negative peak is just as good as a positive. From Figure 1, determine which two amplifier pins are providing current (again, the polarity doesn't matter). We know we need to connect the two motor phases to these two amplifier pins, but we don't know which is which. However, regardless of the polarity, we do know that the unused motor phase must be connected to the unused amplifier pin.

3) Repeat for the second Hall. Again, two motor phases on the graph will line up with the middle of the second Hall, but we don't know which is which. Two amplifier pins will also provide current during the middle of this second Hall. Connect the now-unused motor phase to the now-unused amplifier pin. Now there's only one phase each left for the motor and amplifier, and they must be connected to each other (it wouldn't hurt to repeat the process in the middle of the third Hall as a check).

Throughout this method, we've talked about always using the middle of the Hall signals when, in fact, any identifiable point on the graphs would have sufficed. Using the middle of a Hall signal greatly simplifies the process, however, because a unique BEMF peak always coincides with the middle of unique Hall signal. Furthermore, if you need to determine which phases are active with an oscilloscope, the middle of any Hall will always look the same, regardless of the direction of rotation chosen (a rising Hall in one direction looks like a falling Hall if the motor is spun the other way). There's never a need to look at two Halls on the scope at the same time. If you look at the middle of the Hall, one at a time is always enough, as we'll now demonstrate.

## An Example

We've now determined the correct phase wiring for the amplifier/motor combination that uses the vendor-provided information found in Figures 1 and 2. To minimize confusion, it's preferable but not necessary to connect the motor and amplifier Halls in the same order, starting from the lowest logical label (regardless of the label names).

For example, H1, H2, and H3 correspond to U, V, and W, which correspond to A, B, and C, which correspond to whatever other labels motor and amplifier vendors decide to designate their Hall sensors. In actual practice, you can connect the three Halls in five other ways, resulting in six possible unique, correct, phase-winding connections.

The phase current output and Hall sensor input relationships (Figure 1) originate from an amplifier manufacturer's application notes. The physical relationship between sensor inputs and phase current outputs is valid for all six-step commutating amplifiers configured for 120º Hall spacing; however, amplifier vendor labels for sensor inputs and phase current outputs all vary, and they aren't necessarily in logical order.

Note the amplifier phase current relationships at the center of each of the Hall sensor signal period states. For H1, between 60º and 120º, output phase current flows from A to C. Similarly, for H2, between 180º and 240º, output phase current flows from B to A. Likewise, for H3, between 300º and 360º, output phase current flows from C to B. You'll see this information tabulated in lines 1 and 3 of Table 1.

Now we must characterize the motor. Figure 2 shows the motor's BEMF waveforms and Hall outputs. We'll note peak voltage relationships, located in the center of each of the Hall sensor signal period states. "Peak" can correspond to either positive or negative voltage peaks and is immaterial when using this method. For H1, between 300º and 360º, the peak voltage is on phase M3-M1. In the same way, for H2, between 180º and 240º, the peak voltage is on phase M2-M3. Finally, for H3, between 60º and 120º, the peak voltage is on phase M1-M2, as shown in lines 2 and 4 of Table 1.

## Tabulating

Because A-C pairs with M3-M1, by process of elimination amplifier B connects to motor M2. Again, because B-A pairs with M2-M3, amplifier C connects to motor M1. We are left with C-B paired with M1-M2 and conclude that amplifier A must connect to motor M3. We use the process of elimination instead of a direct substitution method because it advantageously permits both the polarity of the BEMF peaks and the direction of current flow in the windings to be irrelevant for the procedure.

Therefore, for phasing:

 Amplifier pin A connects to motor pin M3 Amplifier pin B connects to motor pin M2 Amplifier pin A connects to motor pin M1

Of course, these connections are valid only when the amplifier Halls H1, H2, and H3 are connected to motor Halls H1, H2, and H3, respectively. We could have connected the three Halls five other, different ways, but using this methodology for any combination allows us to easily achieve the correct results. MC

#### Make Contact!

Jerry Leitz owns Automation Consultants Inc. and provides motion control software for Pitney Bowes, Document Messaging Technologies. His 22 years of work include expertise in motion control, vision systems, and hard real-time software for machine control. He holds a B.S. in electrical engineering.

John Sussmeier, P.E., is an Engineering Fellow for Pitney Bowes, Document Messaging Technologies. His 18 years of work include expertise in motion control, precision mechanics, optical design and scanning, and paper handling. He holds both a B.S. and an M.S. in mechanical engineering.