How to understand the rigidity and inertia of servo motor?

To talk about rigidity, let's talk about stiffness.

Stiffness refers to the ability of a material or structure to resist elastic deformation when it is stressed, and is a representation of the difficulty of elastic deformation of a material or structure. The stiffness of a material is usually measured by the elastic modulus E. In the macroscopic elastic range, the stiffness is the proportional coefficient of the load of the part and the displacement, that is, the force required to cause the unit displacement, and its reciprocal is called the flexibility, that is, the displacement caused by the unit force. Stiffness can be divided into static stiffness and dynamic stiffness.

The stiffness (k) of a structure is the ability of an elastomer to resist deformation and tension. k=P/δ, where P is the constant force acting on the structure and δ is the deformation due to the force.

The rotational stiffness (k) of a rotating structure is: k=M/θ, where M is the applied torque and θ is the rotation Angle.

For example, we know that the steel pipe is relatively hard, the deformation of the general external force is small, and the rubber band is soft, and the deformation caused by the same force is relatively large, then we say that the rigidity of the steel pipe is strong, the rigidity of the rubber band is weak, or its flexibility is strong.

In the application of servo motor, the coupling to connect the motor and the load is a typical rigid connection; The use of a synchronous belt or 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 rigidity of the motor in the servo controller.

The mechanical stiffness of the servo motor is related to its response speed, the higher the general rigidity, the higher the response speed, but if the adjustment is too high, it is easy to make the motor produce mechanical resonance, so, in the general servo amplifier parameters have the option to manually adjust the response frequency, according to the mechanical resonance point to adjust, it takes time and experience (in fact, it is to adjust the gain parameters).

In the servo system position mode, apply force to deflect the motor, if the force is large and the deflection Angle is small, then it is considered that the servo system rigidity is strong, otherwise it is considered that the servo rigidity is weak. Notice the rigidity here, which is actually closer to the concept of speed of response. From the controller's point of view, rigidity is actually a parameter composed of the speed ring, the position ring and the time integral constant, and its size determines a response speed of the machine.

In fact, if you do not require fast positioning, as long as it is accurate, when the resistance is not large, the rigidity is low, you can also achieve accurate positioning, but the positioning time is long. Because the rigidity is low, the positioning is slow, and in the case of fast response and short positioning time, there will be an illusion of inaccurate positioning.

While the moment of inertia describes the inertia of an object's motion, the moment of inertia is a measure of the inertia of an object's rotation around an axis. The moment of inertia depends only on the radius of rotation and the mass of the object. The general load inertia is more than 10 times the inertia of the motor rotor, which can be considered as a large inertia.

The moment of inertia of guide rail and lead screw has a great influence on the rigidity of servo motor drive system. Under fixed gain, the greater the moment of inertia, the greater the rigidity, the easier to cause motor jitter; The smaller the moment of inertia, the smaller the rigidity, the more difficult the motor is to shake. The motor can not jitter by changing the smaller diameter guide rail and screw to reduce the moment of inertia and thus reduce the load inertia.

We know that usually in the selection of servo system, in addition to considering the torque and rated speed and other parameters of the motor, we also need to calculate the inertia of the mechanical system converted to the motor shaft, and then select the motor with the appropriate inertia size according to the actual action requirements of the machine and the quality requirements of the workpiece.

In the debugging (manual mode), the correct setting of inertia ratio parameters is the premise of giving full play to the best performance of the mechanical and servo system.

So what exactly is inertia matching?

In fact, it is not difficult to understand, according to the two laws of cow:

The required torque of the feed system = system moment of inertia J x angular acceleration θ

The angular acceleration θ affects the dynamic characteristics of the system. The smaller θ is, the longer the time from the command issued by the controller to the completion of the system execution, and the slower the system response. If θ changes, the system response will be fast and slow, affecting the processing accuracy.

The maximum output value of the servo motor is unchanged after selection, and if you want the change of θ to be small, J should be as small as possible.

And the above, the system moment of inertia J = the rotary inertia momentum of the servo motor JM + the load inertia momentum JL converted by the motor shaft.

The load inertia JL consists of the inertia of the table and the fixtures and workpieces mounted on it, the screw, the coupling and other linear and rotating moving parts converted to the inertia of the motor shaft. JM is the servo motor rotor inertia, the servo motor is selected, this value is a fixed value, and JL changes with the workpiece and other load changes. If you want the rate of change of J to be small, it is better to make the proportion of JL small.

This is the popular sense of "inertia matching".

Generally speaking, the motor with small inertia has good braking performance, the reaction of starting and accelerating to stop is fast, and the high-speed to the recovery is good, which is suitable for some light load and high-speed positioning occasions. Medium and large inertia motors are suitable for large loads and high stable requirements, such as some circular motion mechanisms and some machine tool industries.