Solutions to Reduce Stepper Motor Resonance
| By: Zoe Li, Applications Engineer
Every stepper motor has a resonance point, and sometimes motor vibration can affect motor performance and motor life. It is important to know the possible solutions to eliminate motor vibration.
Stepper motors have discreet positions that the rotor can move to. Due to rotor inertia, when a stepper motor makes a step, it will overshoot its target slightly and oscillate before it gets the target point. When motor moves continuously, the oscillation of the rotor will come with a frequency. Once the frequency matches motor natural frequency, oscillation will become resonance and causes noise. When resonance overpowers the magnetic field between stators and rotors, motor will likely to lose synchronization. Motor resonance frequency can be models by the following equation:
Where K is torque stiffness, and J is inertia. By adjusting the parameter, we can reduce motor vibration. The following is a brief introduction of vibration reduction methods and how they cut resonance.
There are many ways to avoid resonance: simply by changing operation speed or micro-stepping. The following list is an overview of different methods of resonance reduction. Generally speaking, changing motor operation parameter would be the first choice to avoid resonance, because those methods are easy to implement.
- Try different operation speed
- Current change (If the customer can sacrifice motor torque output)
- Implement mechanical damper
- change load inertia
Motor Physical Parameter:
- Change motor inductance
- Change rotor inertia
- Change motor air gap
- Implement R winding, T connection
More detailed explanations of each method can be found as follows:
1. Avoid commutating close to or at resonant frequencies
Resonance usually happens at certain motor operation speed. When the operation speed matches resonance speed vibration will occur, as a result motor performance will be affected. The easiest way to avoid resonance could be simply changing operation speed, so the motor will not hit its resonance point.
2. Micro stepping at finer step sizes reduces oscillation
The coil in stepper motor will be energized in discretely, so rotor of the motor will tend to overshoot its position due to a rapid flux change. Micro-stepping can move the stator flux more smoothly by reducing excitation energy to the coils. This results in less vibration and less noise, and resonance will be eliminated.
Micro-stepping is not only a good way to reduce resonance, it can also be used to increase stepper motor positon accuracy.
3. Reducing current to reduce torque stiffness (dτ/dθ)
Motor will produce less torque with lower current input. As a result, less energy will be produced to move the rotor (i.e. lower dτ/dθ, torque stiffness). Many low speed applications will run smoother.
But, reducing current input to the motor will result in reduce of torque output. This method will work when the motor has enough torque margin.
4. Adjusting driver current decay parameters
Often times, fast current decay will reduce vibration and resonances. When driver switches current directions, current will decay in a transient manner, and residual current will interfere with current set to the other direction. Slow current decay will cause more torque ripple, therefore, more vibration will occur.
Fast current decay can eliminate interference between two current signals sent by motor driver, and reduce vibration during motor operation.
Figure 1. Current Signal from motor driver (Source: https://pdfs.semanticscholar.org/b7e7/19ca9630dfedf7362c46b2a3b099fe2bb6ee.pdf)
5. Increasing inductance will shift harmonics down in frequency
When motor is running, resonance will induce AC current into motor winding, and AC current will interfere with the DC current going through the winding. By increasing inductance, motor winding would be able to counteract the resonance, or shift resonance down in frequency.
6. Implementing R windings with two phases on
Figure 2. Phase diagram of the R-winding (taken from Patent US6969930 publication)
For hybrid stepper motors, stator has two phases. And winding coils are 90 ° apart from each other. For traditional stepper motor winding, the phase angles for each step is in increments of 45°: 0°, 45° 90°, 135°, 180°, 225°, 270°, 315°. When two phases are 45° from each other, both A and B phases are on. When two phases are 90° apart, only one phase will on. Since the current distribution of one phase on mode and two phase on mode are different, settling time of this two modes are different. Resonance will likely to occur due to uneven settling time during each step.
R windings can eliminate the 1-phase on position by placing new phase angle at: 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°. With two phases on all the time, driver will not supply 100 % current into one phase only. Having both phases on can make the settling time for each step identical, as a result, reducing resonance.
Figure 3. Winding setup of the R-winding (taken from Patent US6969930 publication)
R winding was invented by Ted Lin (U.S Patent No. 6969930). R-winding motor has two coils per pole, and each coil has different turns. Those two sets of wires are wound in series with each other, but the end of the first coil is connected to the end of the second coil. This design allows the motor phase to shift 22.5 degrees, and this results in reduced motor noise and vibration.
7. Implementing T-connection
Figure 4. Winding setup of the T-connection (taken from Patent US6597077B2 publication)
T-connection also forces the motor to always have two phases on. The result of T-connection is similar to R-winding: having both phases on can reduce vibration. Furthermore, inductance level of T-connection falls between a series and parallel connection. So the T-connection can provide performance level between series connection and parallel connection: higher torque at low speed compare to parallel connection, and higher torque output at high speed compare to series connection.
8. Increasing the number of phases
Motor with more phases will have smaller step angle, similar to micro-stepping, motor with more phases can reduce the excitation energy to rotate the rotor. As excitation energy being reduced, resonances will be eliminated.
2-phase motor has 8 magnetic poles, while 5-phase motor has 10 poles. 5 - phase motor has 2 poles per phase, so rotor will move 1/10 of a tooth pitch to line up with the next phase. As a result, 5-phase motor has 500 steps per revolution and 0.72° per step. Higher rotation resolution requires less excitation energy to rotate the rotor, therefore, less overshoot of the rotor.
If micro-stepping is implemented, 5-phase motor can operate with even finer resolution, and the vibration will be largely reduced.
1. Installing a mechanical damper
Figure 5. NEMA 23 Mechanical damper.
Mechanical damper on the shaft of the motor can add extra inertia on the shaft, and help to absorb the vibration and provides a stable damping effect. A flange mount can also absorb vibration.
2. Adjusting rotor inertia
The motor resonance can be determined by the relationship , where K torque stiffness, and J is inertia. The resonance range may change due to the damping effect of the load’s inertia. By Adjusting rotor inertia by changes materials, dimensions (eg. a longer rotor length), or designs (like a “car-wheel” hollow shaft design shown in figure 4), we can shift the resonance point to reduce vibration.
Figure 6. “Car-wheel” design.
3. Adjusting the air gap to increase or decrease torque stiffness
The air gap between rotor and stator tooth is related to the amount torque that the motor can generate. By changing the air gap distance, we can adjust the torque stiffness of the motor. As a result, we can shift resonance point to avoid vibration.
4. Changing load inertia
Inertia is the resistance of an object to accelerate or decelerate. If the motor has load on it, similar to mechanical damper, rotor inertia will be much greater and the oscillations will be reduced substantially.