To talk about rigidity, we must first talk about stiffness.
Stiffness refers to the ability of a material or structure to resist elastic deformation under stress; it is a characterization of the ease with which a material or structure undergoes elastic deformation. The stiffness of a material is usually measured by its elastic modulus E. Within the macroscopic elastic range, stiffness is a proportionality coefficient that directly proportionalizes the load and displacement of a component, i.e., the force required to induce 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
Where M is the applied torque and θ is the rotation angle.
For example, we know that steel pipes are relatively rigid and generally deform less when subjected to external forces, while rubber bands are relatively soft and deform more when subjected to the same force. So we say that steel pipes are rigid and rubber bands are weak, or that they are flexible.
In servo motor applications, using a coupling to connect the motor and the load is a typical rigid connection; while using a synchronous belt or leather belt to connect the motor and the load is a typical flexible connection.
Motor rigidity is the ability of the motor shaft to resist external torque interference, and we can adjust the motor rigidity in the servo controller.
The mechanical stiffness of a servo motor is related to its response speed. Generally, the higher the stiffness, the faster the response speed. However, if the stiffness is set too high, it can easily cause mechanical resonance in the motor. Therefore, most servo amplifiers have an option to manually adjust the response frequency. This needs to be adjusted according to the mechanical resonance point, which requires time and experience (essentially adjusting the gain parameter).
In servo system position mode, a force is applied to deflect the motor. If the applied force is large and the deflection angle is small, the servo system is considered to have high rigidity; conversely, if the applied force is large and the deflection angle is small, the servo system is considered to have low rigidity. Note that the rigidity I'm referring to here is actually closer to the concept of response speed. From the controller's perspective, rigidity is actually a parameter composed of the speed loop, position loop, and time integral constant; its magnitude determines the mechanical response speed.
Brands like Panasonic and Mitsubishi servos have automatic gain control, which usually doesn't require special adjustment. Some domestically produced servos, however, can only be adjusted manually.
Actually, if you don't require fast positioning, as long as it's accurate, you can still achieve accurate positioning with low rigidity when the resistance is low, although the positioning time will be longer. Because low rigidity results in slow positioning, when a fast response and short positioning time are required, it can create the illusion of inaccurate positioning.
Inertia describes the inertia of an object's motion, while rotational inertia is a measure of an object's rotational inertia about an axis. Rotational inertia is only related to the radius of rotation and the object's mass. Generally, a load inertia exceeding 10 times the rotor inertia of a motor is considered to have a large inertia.
The moment of inertia of the guide rail and lead screw has a significant impact on the rigidity of the servo motor drive system. Under a fixed gain, the larger the moment of inertia, the greater the rigidity, and the more prone the motor is to vibration; conversely, the smaller the moment of inertia, the less rigid the motor is, and the less prone the motor is to vibration. Motor vibration can be prevented by reducing the moment of inertia through replacing the guide rail and lead screw with smaller diameter ones, thereby reducing the load inertia.
We know that when selecting a servo system, in addition to considering parameters such as motor torque and rated speed, we also need to calculate the moment of inertia of the mechanical system converted to the motor shaft, and then select a motor with a suitable moment of inertia based on the actual motion requirements of the machine and the quality requirements of the machined parts.
During debugging (in manual mode), correctly setting the inertia ratio parameter is a prerequisite for fully utilizing the optimal performance of mechanical and servo systems.
So what exactly is "inertia matching"?
It's not hard to understand, according to Newton's second law:
Torque required for the feed system = system moment of inertia J × angular acceleration θ
Angular acceleration θ affects the dynamic characteristics of the system. The smaller θ is, the longer the time from when the controller issues a command to when the system completes its execution, and the slower the system response. If θ changes, the system response will fluctuate, affecting machining accuracy.
Once the servo motor is selected, its maximum output value remains unchanged. If you want θ to change little, then J should be as small as possible.
The above is given by: System rotational inertia J = Rotational inertial momentum of the servo motor JM + Load inertial momentum converted from motor shaft JL.
The load inertia JL consists of the inertia of the worktable and the fixtures, workpieces, screws, couplings, and other linear and rotary moving parts, which are referred to the inertia on the motor shaft. JM is the rotor inertia of the servo motor, which is a fixed value once the servo motor is selected, while JL changes with the load, such as the workpiece. If a smaller rate of change of J is desired, it is best to make the proportion of JL smaller.
This is what is commonly known as "inertia matching".
Generally speaking, motors with low inertia have good braking performance, quick start-up, acceleration, and stopping response, and good high-speed reciprocating performance, making them suitable for light-load, high-speed positioning applications. Medium and large inertia motors are suitable for heavy-load applications with high stability requirements, such as some circular motion mechanisms and machine tool industries.
Therefore, if the servo motor's rigidity is too high or too low, the controller gain generally needs to be adjusted to change the system response. Excessive or insufficient inertia refers to a relative comparison between the load's inertia change and the servo motor's inertia.
