The rigidity and inertia of the servo motor are two very important performance parameters, which respectively reflect the characteristics of the servo motor in response to the control signal. Here are the definitions and explanations of these two concepts:

1. Rigidity
    Rigidity usually refers to the ability of the servo motor to resist position deviation or deformation when subjected to external loads or internal disturbances. The rigidity of the servo motor reflects the speed at which the system responds to input signals and the adaptability to load changes.
    • Position rigidity: usually related to the feedback control ability of the servo system and the driving torque of the motor. The high rigidity means that when the load changes, the servo system can quickly return to the set position, avoiding excessive errors.
    • The relationship between rigidity and the system: In servo motor systems, rigidity is usually closely related to the matching of the motor, transmission device (such as reducer) and feedback system. Highly rigid systems can respond quickly to control signals and have high resistance to load changes (such as load inertia, friction, etc.).
    The greater the rigidity of the servo motor, the smaller the position error of the system in the face of external disturbances (such as load fluctuations), and the higher the control accuracy of the system.

2. Inertia

    Inertia refers to the resistance of an object to rotating motion, and is usually used to describe the moment of inertia of the servo motor drive shaft or the entire system. In a servo system, the magnitude of inertia determines how fast the motor responds and its ability to accelerate and decelerate.
    • Definition of inertia: Inertia is a physical quantity related to the mass distribution of an object and the distance of an object around the axis of rotation. Usually the larger the inertia, the more force an object needs to change its state of motion (accelerate or decelerate) as it rotates. In servo motor systems, inertia represents the degree to which the motor and the load it drives respond to acceleration and deceleration.
    Mathematically, the inertia J can be calculated by the following formula:
    J=∑mi ri2
    Where mi is the mass of each small mass and ri is the distance from that small mass to the axis of rotation.
       • Load inertia and motor inertia matching: servo system inertia matching is very important. If the inertia of the motor does not match that of the load, the system may experience excessive response delays or instability. Generally speaking, too large or too small load inertia will affect the response speed and accuracy of the system, resulting in difficult control.
            •For example, if the load inertia is large, the motor needs to provide more torque to change the rotation speed of the load, which affects the speed of acceleration and deceleration.
            •If the motor inertia is too large, it will also make the system overreact under a small load, resulting in unstable control system.

Relation between rigidity and inertia
    There is a relationship between rigidity and inertia, which together determine the dynamic performance of the servo motor system.
    • The greater the inertia, the lower the rigidity usually: if the load inertia is too large, the rigidity of the system will be reduced. Because the larger load inertia makes the motor take longer time to respond to the control signal, the response speed of the system is slow, and the position error is large.
    • The higher the rigidity, the smaller the inertia: for the same motor, the higher rigidity usually means that the system can respond quickly to the control signal, reducing the error. Smaller inertia can improve the response speed, so it is necessary to choose the appropriate motor and load inertia to achieve the control effect.