Avoiding Resonance with Stepper Motors
Stepper motors are electrical brushless motors, usually with a high number of poles. They are typically used as an easy and cost-effective positioning solution, as they can be driven step by step without needing a rotor position feedback system (such as an encoder or integrated hall sensor). This way of driving a motor without feedback is also called “open loop” control. However, the design of these motors and the way they are driven can lead to trouble in certain conditions. In this paper, we will review different ways to avoid these issues and ensure a proper motion.
GENERALITY ABOUT STEPPER MOTORS
Stepper motor phases are commutated sequentially by an external electronic driver which will subsequently move the rotor (typically carrying a permanent magnet) from one stable position to the next one. The motor chosen must offer a sufficient torque to move the rotor and load to the next step after each commutation. If the torque is not sufficient or if the speed is too high, there is a risk of losing synchronism between the driver and the actual rotor position. This can cause a loss of steps, possible changes in direction of rotation and a general erratic motion.
Figure 1 shows the concept of a very simple 2-phase stepper motor with one pole pair. The electronically driven commutation sequence (A, B, -A, -B) will create a full rotor revolution over four steps (90° per step).
OSCILLATION AROUND STABLE POSITION
At each step, the rotor tends to align its poles with the stator’s poles. As long as one phase is energized continuously (without switching to the next phase), the rotor holds a stable position.
Figure 2 shows that if the rotor moves ahead of the target position, the motor will develop a negative torque that will tend to pull the rotor back to the target position. On the other hand, when the rotor is before the target position (left hand side), a positive torque will push the rotor forward in the direction of the target position. In these conditions, it appears that an oscillation phenomenon can easily occur, as the rotor inertia (including the inertia of the load, if any) will prevent the rotor from stopping exactly on the stable position. Whenever the rotor moves from a stable position to the next stable position (one step further), the angular position will usually overshoot the rotor’s target position due to its kinetic energy as it approaches. It will then start oscillating around the position as soon as the negative torque calls the rotor back to the target position. The natural frequency of this periodic oscillation can be calculated as follows:
However, this oscillation will reduce in magnitude over time, thanks to the system’s losses. This amplitude reduction is usually referred to as “damping” and depends on several factors. Eventually the damping will always bring the rotor to a still position if only one phase is energized, but in some cases, it makes sense to optimize the damping when the phases are energized sequentially (commutation).
At high speed, the commutation period becomes shorter, and if the oscillation is not over before the next step is commanded there is a risk of resonance (the tendency of the mechanical system to respond at a greater amplitude). This will likely happen if the commutation frequency is close to the system’s natural frequency as seen in figure 3.
Resonance can lead to erratic operation of the motor, losing steps and changing the direction of rotation randomly. Therefore, it is important to take preventive measures to avoid any resonance to occur to ensure proper synchronism between the command and the actual rotor position.
WAYS TO AVOID RESONANCE
Avoid Natural Frequency
Resonance typically occurs when the commutation frequency is close to the mechanical system’s natural frequency of vibration. Consequently, the most basic way to prevent the occurrence of resonance is to keep the commutation frequency away from the system’s natural frequency using the parameters described. However changing the commutation frequency is not always possible as it sometimes requires other changes to compensate the speed change.
Shift Natural Frequency
Instead of changing the commutation frequency, it is better to shift the natural frequency to a higher or a lower frequency in order to prevent the commutation frequency from matching it. This is typically done by working on the two parameters that influence the natural frequency: the holding torque and the total inertia of the system.
Usually, a motor is sized to be used at its rated current which defines the holding torque. Using a higher current (to increase the holding torque) is not possible for a continuous operation as the higher joule losses would result in an excessive coil temperature. However, it is possible to use a lower current (to achieve a lower holding torque and shift the natural frequency down) if the lower torque is sufficient for the application’s needs.
The mechanical system’s moment of inertia is the sum of the motor’s rotor inertia plus the load inertia. The motor developer can change the rotor’s inertia by implementing design changes. The natural resonance frequency of a motor without load is generally provided in the motor’s specifications. Otherwise, the user can work on the load inertia (completely independent from the motor). Increasing the inertia will shift the overall system’s natural frequency down, and vice-versa. Changing the system’s inertia can also affect the motor’s performance in the application and should be confirmed with the motor provider to ensure a proper operation.
Prevent Resonance with Microstepping
The higher the energy brought into the mechanical system, the higher the risk to trigger a resonance phenomenon. To prevent this, microstepping can be a good solution instead of driving a stepper motor with full steps. Each microstep (half step, ¼ step, etc.) has a smaller step angle and requires less energy to move from one stable position to the next one. Target position overshoot is smaller and so is the magnitude of the oscillation, which is often an effective way to avoid resonance.
In addition, microstepping generally offers lower noise, less vibration and a smoother operation. Stepper motors are often driven in microsteps.
Prevent Resonance with Damping
There are various types of damping factors:
|•||Load Friction and Motor Bearing Friction
Friction provides a breaking torque (opposed to the instant direction of rotation) that is constant, regardless of motor speed. While it helps dampen the oscillation and prevents resonance, one should keep in mind that friction also adds to the load applied on the motor at any speed. So, it is important to ensure the motor’s performance is sufficient when adding friction to prevent resonance.
Viscous friction also provides a breaking torque, but its magnitude depends on the motor speed. The higher the speed, the stronger the viscous damping. This is usually the preferred way of damping an oscillating motion. It provides strong breaking while the oscillation amplitude is great (higher speed at the beginning) and only very light breaking once the oscillation is smaller (unlike dry friction which provides the same breaking magnitude even at very low speed). As a consequence, viscous friction is a good way to dampen oscillation within a very short time, and without adding too much load onto the motor.
There are different phenomena that can bring viscous friction to a system:
|»||Eddy-current generated in iron of the stator (iron losses), acting as a braking torque. These losses are higher when speed is higher, and do not exist in the absence of motion, so can be considered as viscous friction. Depending on the motor design and technology, iron losses can be different from one motor to another. Disk magnet motors usually have limited iron losses which enable them to reach relatively high speeds. Therefore, one should not rely only on iron losses to dampen the oscillation of a disk magnet motor and may want to consider another way of preventing resonance with such a motor.|
|»||Back-EMF (voltage) induced in the coil, resulting in a current and a breaking torque that will dampen the oscillation. This current is typically allowed when the unenergized phase is short-circuited, and since it is proportional to the motor speed (the higher the speed, the stronger the breaking torque), it can also be considered as a viscous friction. Chopper drivers (constant current) typically don’t enable this type of damping since the current is kept constant despite Back-EMF variations.|
|»||Electronic damping solutions can be applied by driving the motor in a particular way without changing any mechanical parameter in the system.|
|»||An external mechanical damper can also be added in the application or onto the motor to absorb some of the vibration energy by viscous friction to prevent resonance.|
The step-by-step, sequential operation of stepper motors can lead to resonance issues whenever favorable conditions for resonance are simultaneously met. Sometimes, acting on just one of these conditions can be sufficient to eliminate resonance. One should also keep in mind that depending on the motor technology and design, there can be additional frequency ranges that are likely to trigger resonance, apart from the natural oscillation frequency. Among them is, for example, mid-frequency resonance. Motor providers can help you determine what frequency ranges are likely to trigger a resonance and how to prevent its occurrence.