Brushless DC Motors: Low Inertia Advantages and Oscillation Causes

Thanks to the compact design of their permanent magnet rotors, brushless DC motors inherently possess the advantage of low inertia, making them the preferred choice for high-dynamic-response, high-precision servo drive systems.

Advantages of Low Inertia:

  • Extremely Fast Dynamic Response:​ Low inertia means the motor can start, stop, accelerate, and decelerate very rapidly, enabling easy high-speed forward and reverse operation. This is crucial for equipment requiring frequent speed changes and precise positioning, such as industrial robots, CNC machine tools, and drones.
  • High Control Precision:​ The system follows control commands better, allowing for more precise control of speed and position while reducing overshoot and oscillation.
  • Higher Efficiency:​ In applications with frequent acceleration/deceleration cycles, less energy is consumed to overcome the motor’s own inertia, resulting in higher overall energy efficiency.

However, precisely because of this fundamental physical characteristic of low inertia, these motors are extremely sensitive to load inertia and control parameters. Any slight command or disturbance can cause them to "overshoot" or "hunt," leading to oscillation.

Key Reasons for Oscillation Related to Low Inertia:

  • Load Inertia Mismatch (Core Cause):​ A servo system has an optimal inertia ratio​ (load inertia / motor rotor inertia). For low-inertia motors, this ratio needs to be smaller (e.g., <5:1, or even <3:1). If the actual load inertia is too large, the total system inertia increases. To keep up with commands, the controller outputs more torque, but due to the high inertia, the system is prone to overshoot. After overshooting, it corrects in the opposite direction, forming sustained oscillation (manifested as low-frequency shaking).
  • Insufficient Rigidity and Mechanical Resonance:​ Low-inertia motors respond very quickly, but their rapid torque changes are transmitted through couplings, ball screws, and other transmission components. If these components have backlash, elastic deformation, or insufficient rigidity, they act like springs, storing and releasing energy and causing mechanical resonance. The motor's slight vibrations are amplified by the mechanical structure, coupling with the motor's control frequency to produce high-frequency squealing or chatter—another very common source of oscillation.
  • Improper Control Parameter (PID Gain) Settings:​ Low-inertia motors naturally have low damping. The controller’s Proportional (P)​ and Integral (I)​ gains act as the system's "spring" and "damper." If the gains are set too high, the system response becomes too "aggressive," causing overshoot and oscillation. If set too low, the response is sluggish and may fail to suppress external disturbances. Tuning parameters for a low-inertia motor requires very fine adjustment within a narrow window.


Solutions and Recommendations

  • Precisely Calculate and Match Inertia:​ First, ensure the load inertia / motor inertia​ ratio is within the manufacturer’s recommended range (typically provided in manuals). If the load inertia is too large, a gearbox​ must be used to reduce the inertia reflected to the motor shaft.
  • Increase Mechanical Rigidity:​ Check and tighten all connections, use high-rigidity couplings, shorten the transmission chain, and avoid long shafts or flexible components.
  • Optimize Control Parameters:​ First, reduce the gains​ (especially P and I) to ensure system stability, then gradually and slowly increase them until the response is optimal.

Increasing the reduction ratio within allowable limits is the most direct and fundamental physical method to solve oscillation caused by excessive load inertia.

Core Principle:​ The square of the reduction ratio (i) multiplies the reduction of the load inertia reflected to the motor shaft.

The specific relationship is: The load inertia, when reflected to the motor shaft, is reduced to 1/(i²)​ of its original value (where i​ is the reduction ratio). Therefore:

Total Inertia Ratio = [Motor Inertia + Load Inertia / (i²)] / Motor Inertia

Increasing the reduction ratio i​ significantly reduces the reflected load inertia, making the total system inertia ratio smaller, which improves system response speed and stability.

Example:

Assume Motor Inertia Jm= 1 kg·cm², Load Inertia JL= 100 kg·cm².

  • When Reduction Ratio i=5: Reflected Load Inertia = 100 / (5²) = 4. Total Inertia Ratio ≈ (1 + 4) / 1 = 5.
  • When Reduction Ratio i=10: Reflected Load Inertia = 100 / (10²) = 1. Total Inertia Ratio ≈ (1 + 1) / 1 = 2.

As shown, increasing the reduction ratio from 5 to 10 lowers the total inertia ratio from 5 to 2, resulting in a faster and more stable system response.