Stiffness and rigidity:
Stiffness refers to the ability of material or structure to resist elastic deformation when subjected to force, and is a characterization of the difficulty of elastic deformation of a material or structure. The stiffness of a material is usually measured by the modulus of elasticity E. In the macro elastic range, the stiffness is the proportional coefficient of the part load and displacement, which is the force required to cause the unit displacement. Its reciprocal is called flexibility, the displacement caused by a unit force. The stiffness can be divided into static stiffness and dynamic stiffness.
The stiffness (k) of a structure refers to the elastic body’s ability to resist deformation and tension.
k=P/δ
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 as follows:
k=M/θ
M is the moment and θ is the angle of rotation.
For example, the steel pipe is relatively hard, 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 is rigid, and the rubber band is weak and flexible.
In the application of servo motor, it is a typical rigid connection to connect the motor and the load by coupling, while the typical flexible connection is to connect the motor and load with synchronous belt or belt.
Motor rigidity is the ability of motor shaft to resist external torque interference. We can adjust the rigidity of motor in servo driver.
The mechanical stiffness of servo motor is related to its response speed. Generally, the higher the rigidity, the higher the response speed, but if it is adjusted too high, the motor will produce mechanical resonance. Therefore, in general AC servo drive parameters, there are options to manually adjust the response frequency. To adjust the response frequency according to the resonance point of the machine, it requires the debugging personnel’s time and experience (in fact, adjusting the gain parameters).
In the servo system position mode, the motor is deflected by applying force. If the force is large and the deflection angle is small, then the servo system is considered to be rigid, otherwise, the servo system is considered to be weak. This rigidity is closer to the concept of response speed. From the controller’s point of view, rigidity is actually a parameter composed of speed loop, position loop and time integral constant. Its size determines a response speed of the machine.
But if you don’t need fast positioning and only need accuracy, then when the resistance is small, the rigidity is low, and you can achieve accurate positioning, but the positioning time is long. Because the positioning is slow when the rigidity is low, the illusion of inaccurate positioning will exist in the case of fast response and short positioning time.
The moment of inertia describes the inertia of the motion of the object, and the moment of inertia is the measurement of the inertia of the object around the 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 is more than 10 times of the rotor inertia of the motor.
The moment of inertia of guide rail and lead screw has great influence on the rigidity of servo motor drive system. Under fixed gain, the greater the moment of inertia is, the greater the rigidity is, the easier it is to cause motor shaking; the smaller the moment of inertia, the smaller the rigidity, the less likely the motor is to shake. It can reduce the moment of inertia by replacing the guide rail and screw rod with smaller diameter, so as to reduce the load inertia to achieve no shaking of the motor.
Generally, in the selection of servo system, in addition to considering the parameters such as torque and rated speed of the motor, we also need to calculate the inertia converted from the mechanical system to the motor shaft, and then select the motor with appropriate inertia size according to the actual mechanical action requirements and the quality requirements of the machined parts.
In debugging (manual mode), setting the inertia ratio parameters correctly is the premise of giving full play to the best efficiency of mechanical and servo systems.
What is inertia matching?
According to Niu Er’s Law:
The required torque of feeding system = system moment of inertia J × angular acceleration θ
The smaller the angular acceleration θ, the longer the time from the controller to the end of the system execution, and the slower the system response. If θ changes, the system response will change quickly and slowly, which will affect the machining accuracy.
After the servo motor is selected, the maximum output value remains unchanged. If you want the change of θ to be small, then J should be as small as possible.
The system moment of inertia J = servo motor rotation inertia momentum JM + motor shaft conversion load inertia momentum JL.
The load inertia JL is composed of the inertia of the worktable, fixture, workpiece, screw, coupling and other linear and rotary moving parts converted to the inertia of the motor shaft. JM is the inertia of the servo motor rotor. After the servo motor is selected, this value is a fixed value, while JL changes with the change of the workpiece load. If you want the rate of change of J to be smaller, it is better to make the proportion of JL smaller. Generally speaking, the motor with small inertia has good braking performance, fast response to start, acceleration and stop, and good high-speed reciprocating performance, which is suitable for some light load and high-speed positioning occasions. Medium and large inertia motors are suitable for large load and high stability requirements, such as some circular motion mechanisms and some machine tool industries.
So the rigidity of AC servo motor is too big and the rigidity is not enough. Generally, the gain of AC servo driver should be adjusted to change the system response. The inertia is too big and the inertia is insufficient. It is a relative comparison between the inertia change of the load and the inertia of the AC servo motor.
In addition, the influence of the reducer on the rigid load should be considered: the gearbox can change the inertia matching. Generally, when the inertia ratio of the load to the motor is more than 5, the reducer is considered to improve the inertia matching. The inertia ratio is inversely proportional to the square of the deceleration ratio.
Post time: Sep-02-2020