Depth Analysis of Rigidity and Inertia Based on Servo Motor

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

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

The rotational stiffness (k) of the rotating structure is: k = M/ θ Where m is the applied moment, θ Is the rotation angle.

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

In the application of servo motor, coupling is a typical rigid connection; Using synchronous belt or belt to connect motor and load is a typical flexible connection.

The rigidity of the motor 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. Generally, the higher the stiffness, the higher the response speed. However, if it is adjusted too high, it is easy to cause mechanical resonance of the motor. Therefore, there is an option to manually adjust the response frequency in the general servo amplifier parameters. It needs time and experience to adjust according to the mechanical resonance point (actually adjusting 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, it is considered that the servo system is rigid, otherwise, it is considered that the servo rigidity is weak. Note that the rigidity I'm talking about here is actually closer to the concept of response speed. From the perspective of controller, rigidity is actually a parameter composed of speed loop, position loop and time integral constant. Its size determines a response speed of machinery.

Panasonic and Mitsubishi servo have automatic gain function. Usually no special adjustment is required. Some domestic servos can only be adjusted manually.

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

Inertia describes the inertia of an object's motion, and moment of inertia is the measurement of the inertia of an object's rotation around an axis. The moment of inertia is only related to the radius of rotation and the mass of the object. Generally, if the load inertia exceeds 10 times of the motor rotor inertia, it can be considered as 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, and the easier it is to cause motor jitter; The smaller the moment of inertia, the smaller the rigidity, and the less likely the motor is to shake. The motor does not shake by replacing the guide rail and screw rod with smaller diameter to reduce the moment of inertia, so as to reduce the load inertia.

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

During commissioning (manual mode), correctly setting inertia ratio parameters is the premise to give full play to the best efficiency of mechanical and servo system.

What exactly is "inertia matching"?

In fact, it is not difficult to understand. According to Niu Er's Law:

"Torque required for feeding system = system moment of inertia J" × angular acceleration θ

angular acceleration θ Affect the dynamic characteristics of the system, θ The smaller, the longer the time from the controller to the completion of system execution, and the slower the system response θ Change, the system response will be fast and slow, affecting the machining accuracy.

After the servo motor is selected, the maximum output value remains unchanged, if desired θ If the change of J is small, J should be as small as possible.

In the above, the system moment of inertia J = the rotational inertia momentum JM of the servo motor the load inertia momentum JL converted by the motor shaft.

The load inertia JL is composed of the inertia of the worktable, the fixture installed on it, the workpiece, the screw, the coupling and other linear and rotating parts converted into the inertia of the motor shaft. JM is the rotor inertia of the servo motor. After the servo motor is selected, this value is the fixed value, and JL changes with the change of the load such as the workpiece. If you want the change rate of J to be smaller, you'd better make the proportion of JL smaller.

This is "inertia matching" in the popular sense.

Generally speaking, motors with small inertia have good braking performance, fast response to start, acceleration and stop, and good high-speed reciprocating performance. They are suitable for some occasions with light load and high-speed positioning. Motors with medium and large inertia are suitable for occasions with high load and high stability requirements, such as some circular motion mechanisms and some machine tool industries.

Therefore, if the rigidity of the servo motor is too large and insufficient, it is generally necessary to adjust the controller gain to change the system response. If the inertia is too large and insufficient, it refers to a relative comparison between the inertia change of the load and the inertia of the servo motor.