Analysis of servo motor inertia problem

When selecting and tuning a servo system, the issue of inertia often arises. This refers to the rotational resistance that must be overcome by the motor during motion. In the selection process, factors such as motor torque and rated speed are considered, but it's equally important to calculate the mechanical system's inertia as seen from the motor shaft. Based on the machine’s movement requirements and part quality standards, an appropriate motor with matching inertia should be chosen. During commissioning, setting the correct inertia ratio is essential to ensure optimal performance of both the mechanical system and the servo. This is especially critical in high-speed and high-precision systems, where proper inertia matching is vital.

1. What is "Inertia Matching"?
According to Newton’s second law, the torque required for the feed system is T = J × α, where J is the system's moment of inertia and α is angular acceleration. A smaller α leads to a slower response, which can affect processing accuracy. Since the maximum output torque is fixed after motor selection, keeping J as small as possible ensures better dynamic performance. This principle underlies the concept of inertia matching.

2. How to Determine "Inertia Matching"?
The drive inertia affects the accuracy, stability, and dynamic response of the servo system. A larger inertia increases the system's time constant, reduces its natural frequency, and may cause resonance. While some inertia can help reduce low-speed crawling, the goal is to minimize it without compromising system stiffness. For most metal-cutting machines, the load inertia should ideally be less than five times the motor inertia. Proper inertia matching ensures smooth operation and precise control.

3. Theoretical Calculation of Inertia?
Inertia calculations involve summing the moments of inertia of all rotating components. The formula J = GD² / (4g) is commonly used, where G is the weight, D is the diameter, and g is gravity. Although theoretical calculations provide a baseline, real-world testing is crucial. Some manufacturers use intermediate values based on practical experience to refine their designs. In any case, accurate inertia calculation is essential for proper motor selection and system performance.

4. On the Friction Coefficient?
The friction coefficient plays a role in motor selection, though it's often accounted for in the calculation rather than directly adjusted. High friction can significantly impact motor performance, especially if not properly addressed. Some servos have built-in parameters for testing, but it's generally best to address friction at the mechanical design stage. Poor machining or assembly can lead to unpredictable variations in friction, making it difficult to achieve consistent performance.

5. After Theoretical Inertia Calculation, Fine Adjustment
Some might find the process complex, but many motor models come with pre-defined parameters. If inertia doesn't match, increasing power slightly can help. However, this should only be done if it improves acceleration capability. Ultimately, inertia matching is a key factor in achieving reliable and efficient servo system performance.

6. Servo Motor Selection
Once the mechanical transmission scheme is determined, the servo motor must be selected based on several criteria. These include:
1. Maximum motor speed > System's maximum speed requirement.
2. Motor rotor inertia should match the load inertia.
3. Continuous load torque ≤ Motor rated torque.
4. Motor's maximum torque > System's peak torque (during acceleration).

Calculations should also consider inertia ratio, speed, and torque requirements to ensure the motor meets all operational demands.