Analysis of servo motor inertia problem

When selecting and tuning a servo system, the issue of inertia often comes up. This typically involves calculating the inertia of the mechanical system as it's reflected to the motor shaft. In addition to factors like motor torque and rated speed, the inertia of the entire system must be considered. Choosing a motor with the right inertia is essential for meeting the motion requirements and processing quality of the machine. During commissioning, correctly setting the inertia ratio parameter is crucial for achieving optimal performance from both the mechanical system and the servo setup, especially in high-speed and high-precision applications where inertia matching becomes critical.

1. What is "inertia matching"?
According to Newton’s second law, the torque required for the feed system is equal to the system's drive inertia multiplied by the angular acceleration. The angular acceleration affects the dynamic behavior of the system. A smaller angular acceleration means a longer response time from the controller, resulting in a slower system reaction. If the angular acceleration fluctuates, the system may become sluggish, which can impact the precision of the process. Since the maximum torque output of the motor remains constant after selection, keeping the angular acceleration stable requires minimizing the inertia.

2. How to determine "inertia matching"?
The total inertia of the feed axis is the sum of the motor's rotational inertia and the load inertia converted to the motor shaft. Load inertia includes the inertia of moving parts such as tables, fixtures, screws, and couplings. Once the motor is selected, its inertia is fixed, while the load inertia changes depending on the workpiece. To keep the total inertia change minimal, it's better to have the load inertia as a small proportion of the motor's inertia—this is what is commonly referred to as "inertia matching."

Inertia matching plays a vital role in motor selection. Even for motors with the same power, different brands may have varying inertia values. Properly calculating the load inertia using formulas is essential for accurate motor selection. If this value is not calculated, the motor choice could be flawed or lead to operational issues. For basic metal-cutting machines, it's generally recommended that the load inertia be less than five times the motor's inertia.

3. Theoretical calculation of inertia?
Inertia calculations follow specific formulas. When multiple loads are involved, such as gears or worm drives, each rotating part’s inertia is calculated separately and then summed up. It's important to select a motor based on the calculated load inertia. Without this value, motor selection is likely to be inaccurate. In the design phase, parameters like friction coefficients are often estimated based on experience, making theoretical calculations an essential step. The formula for inertia is usually expressed in terms of the flywheel moment (GD²), with the relationship given by J = GD² / (4g).

4. On the friction coefficient?
Friction coefficient is usually accounted for in motor selection, but it's often not directly adjusted during tuning. However, if the coefficient is significant enough to affect performance, some servos offer special parameters for testing. Friction and viscous damping are different concepts—while friction is constant, viscous damping varies and can't be easily compensated by increasing motor power. These factors must be addressed during the mechanical design phase, as poor mechanical design can lead to serious control issues.

5. After theoretical calculation, fine-tuning adjustments
Some may find the process complex, but in practice, many parameters are already set for specific products. If inertia doesn’t meet requirements, increasing the motor power by one level might help. As long as the increased power can handle the acceleration, it should be acceptable.

6. Servo motor selection
After choosing the mechanical transmission scheme, the next step is to select and confirm the appropriate servo motor model and size. Key selection criteria include:

• Maximum motor speed > Maximum system speed
• Motor rotor inertia matches the load inertia
• Continuous load torque ≤ Motor rated torque
• Maximum motor torque > System’s peak torque (during acceleration)

These conditions ensure the motor can perform effectively under all operating scenarios.