In the selection and debugging of the servo system, the inertia problem is often encountered. The specific performance is as follows: In the selection of the servo system, in addition to factors such as the torque and rated speed of the motor, we also need to calculate the inertia of the mechanical system converted to the motor shaft, and then according to the actual motion requirements and processing of the machine. The quality requirements of the part to select the motor with the appropriate inertia size; in the commissioning, the correct setting of the inertia ratio parameter is the premise to give full play to the best performance of the mechanical and servo system. This is particularly true on systems that require high speed and high precision, so that there is a problem of inertia matching.

1. What is “inertia matching”?

1. According to Newton’s second law: “The torque required for the feed system T = system transmission inertia J & times; angular acceleration θ angle”. The acceleration θ affects the dynamic characteristics of the system. The smaller the θ is, the longer the time from the controller to issue the command to the system is completed, and the slower the system response. If θ changes, the system reaction will be slow and slow, affecting the processing accuracy. Since the maximum output T value is unchanged after the motor is selected, if the change in θ is desired to be small, J should be as small as possible.

2. The total inertia of the feed axis “J=the rotational inertia momentum of the servo motor JM+the load inertia momentum JL converted by the motor shaft. The load inertia JL is (for example, a plane gold cutting machine) the workbench and the fixtures and workpieces mounted on it, The inertia of linear and rotary moving parts such as screws and couplings is converted to the inertia composition on the motor shaft. JM is the rotor inertia of the servo motor. After the servo motor is selected, this value is fixed, and JL changes with the load of the workpiece. And change. If you want J to change less, then it is better to make JL a smaller proportion. This is the “inertia match” in the popular sense.

Second, how to determine “inertia matching”?

The drive inertia has an impact on the accuracy, stability and dynamic response of the servo system. The inertia is large, the mechanical constant of the system is large, and the response is slow, which will reduce the natural frequency of the system and easily generate resonance. This limits the servo bandwidth and affects the servo accuracy and response speed. The proper increase of inertia is only beneficial when improving low-speed crawling. Therefore, the mechanical design should minimize the inertia without affecting the stiffness of the system. When measuring the dynamic characteristics of the mechanical system, the smaller the inertia, the better the dynamic response of the system; the larger the inertia, the larger the load of the motor, the more difficult it is to control, but the inertia of the mechanical system needs to match the motor inertia. Different institutions have different choices for the principle of inertia matching and have different performances. Different mechanism movements and processing quality requirements have different requirements on the relationship between JL and JM size, but most of them require the ratio of JL to JM to be less than ten. In a word, the determination of inertial matching needs to be determined according to the mechanical process characteristics and processing quality requirements. For basic metal cutting machines, for servo motors, the general load inertia is recommended to be less than 5 times the motor inertia.

Inertia matching is very important for motor selection. For motors of the same power, some brands have a light inertia, medium inertia, or large inertia. In fact, the load inertia is best calculated by the formula. The common form of body inertia calculation formula is readily available in previous books (you can check the mechanical design manual). We have done a test, in the extension of a servo motor shaft, plus a large inertia disk is ready to be used for testing, the result is: the servo motor can not stop at low speed, shaking his head and tail, and constantly oscillating how can not stop. Later changed to: the coupling of the two servo motors was added to the shaft, and one of the servo motors was energized, which was active as the power, and the other servo motor was driven as a small load. It turns out that the servo motor that shakes its head and tails starts, moves, stops, and everything works normally!

Third, the theoretical calculation of inertia?

Inertia calculation has a formula. As for multiple loads, such as gears with gears, or worm gears, it is only necessary to calculate the inertia of each rotating part and then add them to the system inertia. It is recommended to select different motors according to the motor selection. The moment of inertia of the load must be calculated by calculation. If there is no such value, the motor selection is definitely not reasonable, or there will definitely be problems. This is one of the most important parameters of the servo selection. . As for the motor inertia, the motor sample manual is marked. Of course, for some servos, the inertia of the load can be measured by adjusting the servo process as a reference for calculation in the theoretical design. After all, in the design phase, many parameters like the friction coefficient can only be guessed based on experience, and it is impossible to be accurate. The formula for calculation in theoretical design: (for reference only) The moment of inertia J is usually expressed by the flywheel moment GD2, and the relationship between them is

J=mp^2= GD^2/4g

In the middle

m and G-rotating part mass (kg) and weight (N);

g=9.81m/s2-gravity acceleration flywheel inertia=speed change rate*flying track/375

Of course, there will always be deviations between theory and practice. In some regions (such as in Europe), the intermediate values ​​are generally used to obtain actual tests. In this way, the formula is more accurate than our experience. However, there is still a need to calculate at present, there are fixed formulas to check the mechanical design manual.

Fourth, on the friction coefficient?

Regarding the friction coefficient, the general motor selection is only to consider a coefficient added to the calculation process, which is usually not considered in the motor adjustment. However, if this factor is large, or it is enough to affect the motor adjustment, some Japanese general-purpose servos, it is said that there is a parameter for special testing, as to whether it is easy to use, I have not used it, it is estimated to be easy to use. Some netizens posted that there have been cases like this: when designing a foreign machine, the mechanical part is said to be the same, the motor power is amplified by 50%, but the motor does not move. Because the precision of machining and assembly of the prototype is too poor, the load inertia is almost the same, and the frictional resistance is too different, and the specific working conditions are not considered well.

Of course, the viscous damping and friction coefficient are not the same problem. The friction coefficient is constant, which can be compensated by the motor power, but the viscous damping is a variable value, which can be alleviated by increasing the motor power, but it is unreasonable. Moreover, there is no design basis, this is best solved in the mechanical state, there is no good mechanical state, the servo adjustment is completely empty talk. Also, viscous damping is related to mechanical structure design, machining, assembly, etc., which must be considered when selecting a type. Moreover, it is closely related to the friction coefficient. It is precisely because the processing level is not enough that the friction coefficient is uncertain, the difference between the different points is large, and even the difference in the assembly level of the skilled workers will lead to great differences. These must be selected in the motor selection. considerate. In this way, there will be an insurance factor, of course, in the final analysis, the problem of motor power.

5. After the theoretical calculation of the inertia, the simplification of the fine adjustment correction

Some friends may think: too complicated! The actual situation is that a variety of parameters of a brand’s products have been determined. Under the conditions of power, torque and speed, the product model has been determined. If the inertia is still not met, can the power be increased by one gear to meet the inertia? Requirements? The answer is: If the power increase can drive the acceleration, it should be ok.

Sixth, servo motor selection

After selecting the mechanical transmission scheme, the model and size of the servo motor must be selected and confirmed.

(1) Selection conditions: Under normal circumstances, the following conditions must be met when selecting a servo motor:

1. Maximum motor speed > Maximum moving speed required by the system.

2. The rotor inertia of the motor matches the load inertia.

3 continuous load working torque ≤ motor rated torque

4. Maximum output torque of the motor> Maximum torque required by the system (torque during acceleration)

(2) Selection calculation:

1. Inertia matching calculation (JL/JM)

2. Calculation of swing speed (load end speed, motor end speed) 3. Load torque calculation (continuous load working torque, acceleration torque).

The difference between low inertia and high inertia of servo motor

Moment of inertia = radius of rotation * quality

The low inertia is that the motor is relatively flat and the spindle inertia is small. When the motor is repeatedly operated with high frequency, the inertia is small and the heat is small. Therefore, low inertia motors are suitable for high frequency reciprocating motion. But the general torque is relatively small. High inertia servo motors are relatively large and have large torques, which are suitable for high torque but not very fast reciprocating motion. Because of the high-speed motion to stop, the driver has to generate a large reverse drive voltage to stop this large inertia, and the heat is very large.

Inertia is a measure of the inertia of a rigid body rotating around an axis. The moment of inertia is a physical quantity that characterizes the rotational inertia of a rigid body. It is related to the mass and quality of the rigid body relative to the distribution of the shaft. (Rigid body refers to an object that does not change under ideal conditions). When it is selected, it encounters motor inertia, which is also an important indicator of servo motor. It refers to the inertia of the servo motor rotor itself, which is very important for the acceleration and deceleration of the motor. If the inertia is not well matched, the motor’s motion will be very unstable.

Generally speaking, the motor with small inertia has good braking performance, and the reaction of starting and accelerating stops is fast, and the high-speed reciprocating property is good. It is suitable for some light load and high-speed positioning occasions, such as some linear high-speed positioning mechanisms. Medium and large inertia motors are suitable for applications with high loads and high stability requirements, such as some circular motion mechanisms and some machine tool industries. If the load is large or the acceleration characteristics are relatively large, and the motor with small inertia is selected, the motor shaft may be damaged too much. The choice should be based on the size of the load, the magnitude of the acceleration, etc., in the general selection manual. There are related energy calculation formulas.

The servo motor driver responds to the servo motor. The optimum value is the ratio of the load inertia to the motor rotor inertia. The maximum can not exceed five times. Through the design of the mechanical transmission, the ratio of the load inertia to the motor rotor inertia can be made close to one or less. When the load inertia is really large and the mechanical design is impossible to make the ratio of the load inertia to the motor rotor inertia less than five times, a motor with a large rotor inertia of the motor, a so-called large inertia motor, can be used. To use a motor with a large inertia, the drive capacity should be larger to achieve a certain response.