The lure of Microstepping a two-phase stepper motor is compelling. Visions of Microstepping a 1.8-degree hybrid stepper motor with 256 microsteps per full step flash in your mind. The resolution of 51,200 microsteps per revolution entices you. You’re glad you don’t own stock in high-resolution encoder companies.
Where’s the catch?
The real compromise is that as you increase the number of microsteps per full step the INCREMENTAL torque per microstep drops off drastically. Resolution increases but accuracy will actually suffer.
Few, if any, stepper motors have a pure sinusoidal torque vs. shaft position and all have higher order harmonics that in fact distort the curve and affect accuracy. And while microstepping drives have come a long way too, they still only approximate a true sine wave.
Significant too is that any load torque will result in a “magnetic backlash”, displacing the rotor from the intended position until sufficient torque is generated.
The actual expression for incremental torque for a single microstep is:
1. TINC = THFS x sin (90/µPFS)
The incremental torque for N microsteps is:
2. TN = THFS x sin ((90 x N)/µPFS))
||SYMBOLS and UNITS
Number of Microsteps per Full Step
Number of Microsteps taken
N Less than or equal to µPFS
||Holding Torque - Full Step
||Incremental Torque per Microstep
Incremental Torque for N Microsteps
N Less than or equal to µPFS
Table 1 dramatically quantifies the significant impact of the incremental torque per microstep as a function of the number of microsteps per full step.
A full step is considered 1 microstep per full step for Equations 1 and 2. A half step is 2 microsteps per full step.
Incremental Torque per Microstep
As the Number of Microsteps per Full Step Increase
Incremental Torque per Microstep Full Step
The consequence is that if the load torque plus the motor’s friction and detent torque is greater than the incremental torque of a microstep successive microsteps will have to be realized until the accumulated torque exceeds the load torque plus the motor’s friction and detent torque.
Simply stated, taking a microstep does not mean the motor will actually move! And if reversing direction is desired a whopping number of microsteps may be needed before movement occurs. That’s because the motor shaft torque must be decremented from whatever positive value it has to a negative value that will have sufficient torque to cause motion in the negative direction.
Accuracy vs. Resolution
“What if the motor is not loaded?” you ask? Thinking of using microstepping for some type of pointing or inertial positioning?
Well, the stepper motor still has friction torque due to its bearings and it has a detent torque, in addition to other harmonic distortions. You’ll have to “wind up” enough incremental torque to overcome the bearing friction. Even more disruptive than the bearing friction is the detent torque, which is typically 5 to 20% of the holding torque. Sometimes the detent torque is adding to the overall torque generation, sometimes it is subtracting from the powered torque generation. In any case it wrecks havoc with your overall accuracy.
Indeed, some manufacturers fabricate “microstepping” versions of their motors. Their efforts typically are to reduce the detent torque, usually at the expense of holding torque, to make the torque vs. rotor position closer to a sine wave, and to improve linearity of torque vs. current. These efforts reduce, but do not eliminate the compromises associated with microstepping in regards to accuracy.
How about using a lookup table to “correct” for the inaccuracies in the motor and microstepping drive? That too has been utilized. The problem is that if the load torque changes from when the lookup table was made the results can be worse than if you had not utilized a “calibrated” table at all!
Why Microstep Then?
There are still compelling reasons other than high resolution for microstepping. They include:
- Reduced Mechanical Noise.
Gentler Actuation Mechanically
Reduces Resonances Problems
In summary, although Microstepping gives the designer more resolution, improved accuracy is not realized. Reduction in mechanical and electromagnetically induced noise is, however, a real benefit. The mechanical transmission of torque will also be much gentler as will a reduction in resonance problems. This gives better confidence in maintaining synchronization of the open loop system and less wear and tear on the mechanical transmission system.
In fact, taking an infinite number of microsteps per full step results in two-phase synchronous permanent magnet ac motor operation, with speed a function of the frequency of the ac power supply. The rotor will lag behind the rotating magnetic field until sufficient torque is generated to accommodate the load.
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