When it comes to rigidity, let's first talk about stiffness.

Stiffness refers to the ability of a material or structure to resist elastic deformation under stress, and is a characterization of the difficulty of elastic deformation of a 

material or structure. The stiffness of materials is usually measured by the elastic modulus E. Within the macroscopic elastic range, stiffness is the proportional 

coefficient between the load and displacement of a component, that is, the force required to cause a unit displacement. Its reciprocal is called flexibility, which is the 

displacement caused by a unit force. Stiffness can be divided into static stiffness and dynamic stiffness.

The stiffness (k) of a structure refers to the ability of an elastic body to resist deformation and tension.

k=P/δ

P is the constant force acting on the structure, and δ is the deformation caused by the force.

The rotational stiffness (k) of the rotating structure is:

k=M/θ

Among them, M is the applied torque, and θ is the rotation angle.

For example, we know that steel pipes are relatively hard and generally deform less under external forces, while rubber bands are relatively soft and produce greater 

deformation under the same force. Therefore, we can say that steel pipes have stronger rigidity, rubber bands have weaker rigidity, or they have stronger flexibility.

In the application of servo motors, using couplings to connect the motor and load is a typical rigid connection; Using synchronous belts or belts to connect motors 

and loads is a typical flexible connection.

The rigidity of a motor refers to the ability of the motor shaft to resist external torque interference, and we can adjust the rigidity of the motor through a servo 

controller.

The mechanical stiffness of a servo motor is related to its response speed. Generally, the higher the rigidity, the faster the response speed. However, if the adjustment 

is too high, it is easy to cause mechanical resonance in the motor. So, in general servo amplifier parameters, there is an option to manually adjust the response 

frequency based on the mechanical resonance point, which requires time and experience (in fact, adjusting the gain parameter).

In the position mode of the servo system, apply force to deflect the motor. If the force is large and the deflection angle is small, it is considered that the servo system 

has strong rigidity. Otherwise, it is considered that the servo rigidity is weak. Note that what I mean by rigidity here is actually closer to the concept of response speed. 

From the perspective of a controller, rigidity is actually a parameter composed of velocity loop, position loop, and time integral constant, and its magnitude determines 

a response speed of the machine.

Both Panasonic and Mitsubishi servos have automatic gain function, which usually does not require special adjustment. Some domestic servos can only be manually 

adjusted.

In fact, if you don't require fast positioning, as long as you are accurate, you can also achieve accurate positioning when the resistance is not high and the rigidity is low, 

but the positioning time is long. Because low rigidity results in slow positioning, there may be an illusion of inaccurate positioning when quick response and short 

positioning time are required.

And inertia describes the inertia of an object's motion, while moment of inertia is a measure of the object's rotational inertia around its axis. The moment of inertia is 

only related to the radius of rotation and the mass of the object. Generally, if the inertia of the load exceeds 10 times the inertia of the motor rotor, it can be considered 

that the inertia is relatively large.

The rotational inertia of the guide rail and screw has a significant impact on the rigidity of the servo motor transmission system. Under a fixed gain, the greater the 

rotational inertia and rigidity, the more likely it is to cause motor vibration; The smaller the moment of inertia, the lower the rigidity, and the less likely the motor is to 

shake. The motor can be stabilized by reducing the moment of inertia of the load by replacing the guide rail and screw with a smaller diameter.

We know that when selecting a servo system, in addition to considering parameters such as motor torque and rated speed, we also need to first calculate the inertia 

of the mechanical system converted to the motor shaft, and then select the motor with the appropriate inertia size based on the actual action requirements of the 

machinery and the quality requirements of the machined parts.

Correctly setting the inertia ratio parameter during debugging (in manual mode) is a prerequisite for fully utilizing the optimal efficiency of mechanical and servo 

systems.

What exactly is' inertia matching '?

It's not difficult to understand, according to the Bull's Law:

The required torque for the feed system is equal to the system's moment of inertia J multiplied by the angular acceleration θ

The angular acceleration θ affects the dynamic characteristics of the system. The smaller the θ, the longer it takes for the controller to issue instructions and the 

system to complete execution, resulting in slower system response. If θ changes, the system response will fluctuate rapidly, affecting the machining accuracy.

After selecting the servo motor, the maximum output value remains unchanged. If you want the change in θ to be small, then J should be as small as possible.

And above, the system's moment of inertia J=the rotational inertia momentum JM of the servo motor+the load inertia momentum JL converted from the motor shaft.

The load inertia JL is composed of the inertia of the worktable, fixtures, workpieces, screws, couplings, and other linear and rotating moving parts converted to the 

inertia on the motor shaft. JM is the inertia of the servo motor rotor. Once the servo motor is selected, this value becomes a constant, while JL varies with changes in 

the load on the workpiece. If you want the rate of change of J to be smaller, it is best to make the proportion of JL smaller.

This is commonly known as' inertia matching '.

Generally speaking, motors with small inertia have good braking performance, fast response to starting, accelerating, and stopping, good high-speed reciprocating 

performance, and are suitable for situations with light loads and high-speed positioning. Motors with medium and high inertia are suitable for situations with high 

load and stability requirements, such as some circular motion mechanisms and some machine tool industries.

So if the rigidity of the servo motor is too high or too low, it is generally necessary to adjust the controller gain to change the system response. Excessive inertia and 

insufficient inertia refer to a relative comparison between the inertia changes of the load and the inertia of the servo motor.