There are two universal concepts in motors that will always be true. The first is that Back EMF is directly proportional to angular velocity (or armature speed). The second is that motor torque is directly proportional to motor current.
BEMF vs. angular velocity
The back EMF equations illustrate the relationship between angular velocity and BEMF quite clearly:
Notice that N, B, and A are all constants specific to the motor construction. They never change, unless there is some dramatic entropy going on! At that point BEMF detection is the least of your concerns!
Aside from the sinusoidal nature of the signal, BEMF (bemf) is directly proportional to motor speed (ω) and nothing else.
Current vs. torque
The next universal concept is the relationship between motor torque and motor current. Again, the equations describe this clearly:
Note again that current (I) and torque (T) are directly proportional to each other. Yes, there are other factors that affect current like voltage and the temperature dependence on resistivity of copper. These things can increase or decrease the motor current capability which will affect the total available torque. However, they will not change the torque-to-current relationship.
Let’s think for a moment. A stepper motor is typically a fixed current system. That is, the controller feeds a fixed set of currents into two phases at a rotational velocity that ends up being directly reflected by the rotor. If a fixed current into a motor produces a fixed torque how can a stepper motor have a fixed current and rotate at a fixed speed for a wide range of loads or torques? The answer is in the phase shifting, automatically, of the BEMF with respect to the drive current.
The phase current will generate the torque based on the aforementioned equations. What direction that torque will be applied will depend on the load. A lightly loaded stepper motor will have a small portion of the torque actually driving the load. A remaining portion of the motor torque is used to slow
the motor down. To never go above the commanded rotational speed the current is first driving the motor to go faster and then braking
it to go slower. The overall torque coming out the output shaft is zero
for an unloaded motor.
The following graphs estimate BEMF and motor current. BEMF also is a good representation of rotor position as the moving magnets in the rotor induce BEMF in the stator. It is not as pretty as I have drawn it but it is a reasonable illustration of the point. The rotor magnetic field is fixed to the rotor and rotates with it. The stator field is related to the current in the stator. A “positive” current in the stator creates a “positive” field and vice versa.
With magnetics (and some people), opposites attract. Looking at Figure 6 above when the polarity in the stator is the opposite of the rotor there is attraction and thus acceleration. When the polarity is the same in both the rotor and stator, braking occurs. In an unloaded motor we get an almost perfect distribution of acceleration and braking. As the stepper motor is loaded, the BEMF shifts to convert more of the torque to forward motion and less to braking.
In Figure 7, which illustrates a partially loaded stepper motor, the back EMF has shifted to increase the percentage of driving torque over the braking torque. This shift will continue as external loading is increased until the loading exceeds the potential torque capability.
In a fully loaded stepper motor, the moment that the torque demand causes the back EMF to shift any further the output torque decreases. Then it is all over. The motor stops rotating. “YOU EAT NOW!” has no effect. All the yelling in the world is not going to get this thing moving again.
Part 2 of this series looks at the effects of torque on back EMF and BEMF detection circuitry.
David Swanson is principal engineer and Radek Stejskal is application support senior engineer
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