To talk about rigidity, let's talk about rigidity first.
Stiffness refers to the ability of a material or structure to resist elastic deformation when subjected to force, and is a representation of the difficulty of elastic deformation of a material or structure. The stiffness of a material is usually measured by its modulus of elasticity, E. In the macroscopic elastic range, stiffness is a proportional coefficient proportional to the load of the part and the displacement, that is, the force required to cause unit displacement, and 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 is the ability of an elastomer to resist deformation and stretching. 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 the rotating structure is: k=M/θ where M is the applied moment and θ is the rotation angle.
For example, we know that the steel pipe is relatively hard, and generally deformed by external force, while the rubber band is softer, and the deformation caused by the same force is relatively large, then we say that the rigidity of the steel pipe is strong, and the rigidity of the rubber band is weak, or its Strong flexibility.
In the application of servo motors, the use of couplings to connect the motor and the load is a typical rigid connection; while the use of synchronous belts or belts to connect the motor and the 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 the motor to produce mechanical resonance. Therefore, there are manual adjustments in the general servo amplifier parameters. The option of the response frequency needs to be adjusted according to the resonance point of the machine, which requires time and experience (in fact, the gain parameter is adjusted).
In the servo system position mode, a force is applied to deflect the motor. If the force is large and the deflection angle is small, the rigidity of the servo system is considered to be strong, otherwise, the rigidity of the servo system is considered to be weak. Note that the rigidity here is actually closer to the concept of response speed. From the point of view of the controller, the stiffness is actually a parameter composed of the speed loop, the position loop and the time integral constant, and its size determines a response speed of the machine.
In fact, if the positioning is not required to be fast, as long as the positioning is accurate, when the resistance is not large, the rigidity is low, and the positioning can also be accurate, but the positioning time is long. Because the positioning is slow if the rigidity is low, there will be an illusion of inaccurate positioning when fast response and short positioning time are required.
Inertia describes the inertia of an object's motion, and rotational inertia is a measure 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, the inertia of the load exceeds 10 times of the inertia of the rotor of the motor, and the inertia can be considered to be large.
The rotational inertia of the guide rail and the lead screw has a great influence on the rigidity of the servo motor drive system. Under a fixed gain, the larger the rotational inertia, the greater the rigidity, and the easier it is to cause the motor to shake; the smaller the rotational inertia, the smaller the rigidity, and the less likely the motor to shake. . The moment of inertia can be reduced by replacing the guide rail and lead screw with a smaller diameter to reduce the inertia of the load so that the motor does not vibrate.
We know that when selecting a servo system, in addition to considering the parameters such as the torque and rated speed of the motor, we also need to first calculate the inertia of the mechanical system converted to the motor shaft, and then according to the actual action requirements of the machine and the quality of the workpiece. Requirements to specifically select a motor with a suitable inertia size.
During debugging (in manual mode), setting the inertia ratio parameter correctly is the premise to give 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 second law of cattle:
The torque required by the feeding system = system moment of inertia J × angular acceleration θ
The angular acceleration θ affects the dynamic characteristics of the system. The smaller the θ, the longer the time from the controller issuing the command to the completion of the system execution, and the slower the system response. If θ changes, the system response will be fast and slow, which will affect the machining accuracy.
After the servo motor is selected, the maximum output value does not change. If the change of θ is expected to be small, J should be as small as possible.
In the above, the system moment of inertia J = the rotational inertia moment of the servo motor JM + the load inertia moment JL converted from 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 rotary moving parts converted to the inertia of the motor shaft. JM is the rotor inertia of the servo motor. After the servo motor is selected, this value is a fixed value, while JL changes with the load of the workpiece. If you want the rate of change of J to be smaller, it is better to make the proportion of JL smaller.
This is the "inertia matching" in the popular sense.
Generally speaking, a motor with small inertia has good braking performance, quick response to start, acceleration and stop, and good high-speed reciprocation, which is suitable for some occasions with light load and high-speed positioning. Motors with medium and large inertia are suitable for occasions with large loads and high stability requirements, such as some circular motion mechanisms and some machine tool industries.