One of the major causes of step motor stalling is a phenomenon called resonance. As motors accelerate and decelerate their shafts typically oscillate, causing variations in shaft speed and position, Figure 1. These variations require additional motor torque to quell, thus reducing the available torque for the commanded move. Though at first glance, oscillation torque may seem insignificant, a closer look shows otherwise. In many cases oscillations can sap as much torque as that required for the move. As a result, engineers who follow the rule of thumb and specify a motor with two times the required torque may still be surprised.

What is resonance?

Designers liken step motors to mass-spring systems, Figure 2. The reason is that the magnetic field between rotor and stator behaves like a spring, often producing a resonant response.

Resonance can be defined by two variables: natural resonant frequency fn and the damping ratio ζ. The natural frequency is determined by spring stiffness K and inertia J as follows:

The damping ratio is a dimensionless number that reflects how rapidly transient oscillations decay. The amplitude of a decaying oscillation changes from one cycle to the next by a factor of:

For ζ = 0, the decay factor is 1, and there is no cycle-to-cycle decay. In other words, the system rings endlessly. For ζ between 0 and 1, the decay factor becomes progressively smaller, approaching 0 as ζ approaches 1. When ζ = 1, the decay factor is undefined, and there is no oscillation. Here, the shaft settles to its commanded position without any ringing. For ζ between 0 and 21, the decay factor is greater than 1. This means the ringing increases, and the system is unstable.

In an ordinary step-motor-and-drive system, the viscous coefficients of friction, b₁, b₂, and b₃, are very small, Figure 2.

Furthermore, at medium speed, b₁ may become negative, forcing the damping ratio to values near 0 or a negative number. This is the motor’s midrange instability. It is the speed range where the drive provides less than the commanded current, and there is enough oscillation to cause a loss of synchronism in the motor. Designers attempt to solve the problem by increasing the coefficient of friction, b₃.

Damping methods

Elastomeric couplings. One way to damp resonance is to insert an elastomer coupling between the rotor and load. If the system starts to oscillate, the coupling b₃ will remove energy as the other members of the system oscillate. For good damping, the stiffness of the coupling K₂ must be well below that of the motor K₁.

The drawback, however, is that the system will be very poor at maintaining position, and the load will be easily disturbed by outside forces. Also, many elastomer couplings become “set” with time and loading, causing the load to change position with respect to the rotor.

Fluid-filled motors. Another damping method is to increase b₂ by filling the motor with a viscous ferrofluid. The ferrofluid is magnetic and held in place by the rotor’s permanent magnets. Though this method provides good damping, it comes at the expense of torque at high velocities. Such systems will move smoothly at low speeds, but won’t perform at high velocities.

Viscous dampers. This method uses a comparatively large seismic mass coupled to the rotor via a viscous fluid or elastic solid. The main load remains firmly attached to the rotor, viscous dampers do not sacrifice stiffness. When the load starts to ring, however, the inertia of the solid causes the load to respond sluggishly.

The drawback to viscous dampers appears during rapid acceleration. Typically, machines will run well at high speed, but won’t respond well in accel and decel modes. Also, inertial or viscous dampers are expensive, sometimes costing as much as the motor itself. They require double-shafted rotors and take up significant space.

Active damping. The objective of active damping is to raise the value of ζ by controlling the coefficient b₁. To illustate the process, it helps to look at a block diagram, which shows the motor as a selfcontained position loop, Figure 3.

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