【TOYO MOTOR】Solutions to Reduce Stepper Motor Resonance

Each stepper motor has a resonance point, and sometimes motor vibration can affect motor performance and service life. It is very important to understand the possible solutions to eliminate motor vibration.

Stepper motors have hidden positions where the rotor can move. Due to rotor inertia, when a stepper motor takes a step, it will slightly overshoot the target and oscillate before reaching the target position. When the motor is running continuously, the oscillation of the rotor will have a certain frequency. Once this frequency matches the natural frequency of the motor, the oscillation will turn into resonance and generate noise. When the resonance exceeds the magnetic field between the stator and the rotor, the motor may lose synchronization. The motor resonance frequency can be modeled by the following equation:

Here, K is the torsional stiffness and J is the inertia. By adjusting parameters, we can reduce motor vibration. The following is a brief introduction to vibration reduction methods and how they eliminate resonance.

There are many ways to avoid resonance: simply change the operating speed or use micro-stepping. The following list outlines different resonance reduction methods. In general, changing the motor operating parameters is the first choice to avoid resonance because these methods are easy to implement.

Motor operation:

Try different operating speeds

Micro-stepping

Current change (if the customer can sacrifice the motor torque output)

Implement mechanical dampers

Change the load inertia

Motor physical parameters:

Change the motor inductance

Change the rotor inertia

Change the motor air gap

Implement R windings, T connection

A more detailed description of each method is as follows:

Electrical settings

Resonance usually occurs at a certain motor operating speed. When the operating speed matches the resonant speed, vibration occurs, which affects the motor performance. The simplest way to avoid resonance is to simply change the operating speed so that the motor does not reach the resonance point.

The coils in a stepper motor will be energized discretely, so the rotor of the motor tends to overshoot due to the rapid change of magnetic flux. By reducing the excitation energy of the coil, micro-stepping can move the stator flux more smoothly. This can reduce vibration and noise, and eliminate resonance.

Micro-stepping is not only a good way to reduce resonance, but also can be used to improve the positioning accuracy of stepper motors.

The motor will generate less torque with a lower current input. Therefore, less energy will be generated to move the rotor (i.e., lower dτ/dθ, torsional stiffness). Many low-speed applications will run more smoothly.

However, reducing the current input to the motor will result in a reduction in torque output. This method will work when the motor has sufficient torque margin.

Many times, fast current decay can reduce vibration and resonance. When the driver switches the current direction, the current decays transiently, and the residual current will interfere with the current set to the other direction. Slow current decay will lead to greater torque ripple, thus more vibration will occur.

Fast current decay can eliminate the interference between the two current signals from the motor driver and reduce the vibration during motor operation.

Figure 1. Current signal from motor driver (Source: https://pdfs.semanticscholar.org/b7e7/19ca9630dfedf7362c46b2a3b099fe2bb6ee.pdf)

When the motor is running, resonance will induce alternating current in the motor windings, and the alternating current will interfere with the direct current flowing through the windings. By increasing the inductance, the motor windings will be able to counteract the resonance or reduce the resonance frequency.

Figure 2. Phase diagram of the R winding (taken from patent publication US6969930)

For a hybrid stepper motor, the stator has two phases. And the winding coils are 90° apart from each other. For traditional stepper motor windings, the phase angle of each step increments by 45°: 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°. When the phase angle between the two phases is 45°, both phase A and phase B are conducting. When the two phases are 90° apart, only one phase is turned on. Due to the different current distributions between the one-phase on mode and the two-phase on mode, the establishment times of these two modes are different. Resonance may occur because the settling time of each step is uneven.

The R winding can eliminate the 1-phase conduction positions by placing the new phase angles at the following positions: 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°. With both phases always on, the driver does not supply 100% current to only one phase. Turning on both phases can make the settling time of each step the same, thereby reducing resonance.

Figure 3. Winding configuration of the R winding (taken from US Patent No. 6969930 publication)

The R winding was invented by Ted Lin (US Patent No. 6969930). The R-winding motor has two coils per pole, with each coil having a different number of turns. These 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 to have a phase shift of 22.5 degrees, thereby reducing motor noise and vibration.

Figure 4. Winding configuration of T-connection (taken from patent publication US6597077B2)

The T-connection also forces the motor to always have two phases on. The result of the T-connection is similar to that of the R-type winding: having both phases on can reduce vibration. In addition, the inductance level of the T-connection is between that of series and parallel connections. Therefore, the T-connection can provide a performance level between series and parallel connections: higher low-speed torque compared to parallel connection, and higher high-speed torque output compared to series connection.

Motors with more phases have smaller step angles, similar to micro-stepping. Motors with more phases can reduce the excitation energy required to rotate the rotor. As the excitation energy decreases, resonance will be eliminated.

A 2-phase motor has 8 poles, while a 5-phase motor has 10 poles. A 5-phase motor has 2 poles per phase, so the rotor will move 1/10 of a tooth pitch to align with the next phase. Therefore, a 5-phase motor has 500 steps per revolution, with each step being 0.72°. Higher rotational resolution requires less excitation energy to rotate the rotor, thus resulting in less overshoot of the rotor.

If micro-stepping is implemented, a 5-phase motor can operate with finer resolution, and vibration will be significantly reduced.

Mechanical damping

Figure 5. NEMA 23 mechanical damper.

A mechanical damper on the motor shaft can add extra inertia to the shaft, helping to absorb vibrations and provide a stable damping effect. Flange mounting can also absorb vibrations.

Motor resonance can be determined by the following relationship, where K is the torsional stiffness and J is the inertia. The resonance range may change due to the damping effect of the load inertia. By adjusting the rotor inertia through changing materials, dimensions (such as a longer rotor length), or design (like the "wheel" hollow shaft design shown in Figure 4), we can shift the resonance point to reduce vibrations.

Figure 6. "Wheel" design.

The air gap between the rotor and stator teeth is related to the amount of torque that the motor can generate. By changing the air gap distance, we can adjust the torque stiffness of the motor. Therefore, we can shift the resonance point to avoid vibrations.

Inertia is the resistance of an object to acceleration or deceleration. If there is a load on the motor, similar to a mechanical damper, the rotor inertia will be much larger, and the oscillation will be significantly reduced.

Author of this article: Zoe Li, Application Engineer