Estun Servo Motor - Introduction to Servo Motor Inertia Knowledge

1. What is "inertia matching"?

1. According to Newton's second law: "The required moment T of the feed system = the transmission inertia of the system J×angular acceleration θ angle". The smaller the acceleration θ, the longer the time from the controller to the completion of the system's execution, and the slower the system response. If θ changes, the system reaction will be fast and slow, affecting the machining accuracy. Since the maximum output T value does not change after the motor is selected, if you want the change in θ to be small, J should be as small as possible.

2. The total inertia of the feed shaft "J = the rotational inertia momentum JM of the servo motor + the load inertia momentum JL converted by the motor shaft. The load inertia JL consists of the inertia of the worktable and the jigs installed on it, the workpiece, the screw, the coupling and other linear and rotary moving parts (taking the plane metal cutting machine as an example) and the inertia converted to the motor shaft. JM is the rotor inertia of the servo motor, and this value is fixed when the servo motor is selected, while JL changes with the change of load such as the workpiece. If you want the J rate of change to be smaller, it is better to make the proportion of JL smaller. This is known as "inertia matching" in the popular sense.

2. How to determine "inertia matching"?

The transmission 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 make the natural frequency of the system decrease, and it is easy to produce resonance, thus limiting the servo bandwidth, affecting the servo accuracy and response speed, and the appropriate increase of inertia is only beneficial when improving the low-speed crawl, therefore, the inertia should be reduced as much as possible under the condition that the mechanical design does not affect the stiffness of the system. When measuring the dynamic characteristics of a mechanical system, the smaller the inertia, the better the dynamic characteristics of the system respond. The larger the inertia, the greater the load on the motor, and 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 action and processing quality requirements have different requirements for 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 inertia matching needs to be determined according to the process characteristics of the machinery and the processing quality requirements. For basic metal cutting machine tools, 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, and some brands of motors with the same power are divided into light inertia, medium inertia, or large inertia. In fact, the load inertia is best calculated by formula. The common formula for calculating the inertia of form is readily available in the books I have learned in the past (you can check the mechanical design manual). We once did a test, in the shaft extension of a servo motor, plus a large inertia disc ready to do the test, the result is: the servo motor can not stop at low speed, shake the head and tail, and keep oscillating can not stop. Later, it was changed to: a coupling was installed on the shaft extension butt of the two servo motors, and one of the servo motors was energized, which was active as the power, and the other servo motor was used as the follower, that is, as a small load. It turns out that the servo motor that shakes its head and tail starts, moves, stops, and runs normally!

3. What is the work formula for the theoretical calculation of inertia?

There are formulas for inertia calculation, as for multiple loads, such as gears with gears, or turbine and worm transmission, as long as the inertia of each rotating part is calculated separately and then added to the system inertia, it is recommended to select different motors when selecting motors. The moment of inertia of the load must be calculated by calculation when designing, if there is no such value, the motor selection is definitely not so reasonable, or there will definitely be problems, which is one of the most important parameters of the servo. As for the motor inertia, it is marked on the motor sample manual. Of course, for some servos, the inertia of the load can be measured by adjusting the servo process, which can be used as a reference for calculations in theoretical design. After all, in the design stage, many parameters such as friction coefficient can only be guessed empirically and cannot be accurate. Formula for calculation in theoretical design: (FYI) The moment of inertia J is usually expressed as the flywheel moment GD2, and the relationship between them is

　　J=mp^2= GD^2/4g

where

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

D - radius and diameter of inertia (m);

g = 9.81m/s2 - gravitational acceleration flywheel inertia = velocity change rate * flywheel distance / 375

Of course, there will always be deviations between theory and practice, and in some regions (such as in Europe), the median value is generally obtained through practical testing. In this way, it is more accurate than our empirical formula. However, at present, it still needs to be calculated, and there are fixed formulas that can be checked in the mechanical design manual.

Fourth, about the coefficient of friction?

Regarding the coefficient of friction, the general motor selection only considers one coefficient added to the calculation process, and usually does not consider it when adjusting the motor. However, if this factor is very large, or to say, enough to affect the motor adjustment, some Japanese general servo, it is said that there is a parameter that is used for special testing, as for whether it is easy to use, I have not used it, it is estimated that it should be easy to use. Some netizens posted that someone had such a situation: the design copied foreign machines, the mechanical part was claimed to be the same, and the motor power was magnified by 50% of the selection, but the motor could not rotate. Because the machining and assembly accuracy of the prototype is too poor, the load inertia is about the same, and the frictional resistance is too different, and the specific working conditions are not well considered.

Of course, viscous damping and coefficient of friction are not the same thing. The coefficient of friction is a constant value, 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 actually unreasonable. Moreover, there is no design basis, this is best solved in the mechanical state, there is no good mechanical state, servo adjustment is completely empty words. In addition, viscous damping is related to mechanical structure design, processing, assembly, etc., which must be considered when selecting a model. And it is also closely related to the friction coefficient, it is precisely because the processing level is not enough that the friction coefficient is uncertain, the difference is large, and even the difference in the assembly level of skilled workers will lead to great differences, which must be considered in the selection of motors. In this way, there will be an insurance coefficient, of course, in the final analysis, it is a matter of motor power.

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

Some of you may think: it's too complicated! The actual situation is that a variety of parameters of a brand's products have been determined, under the conditions of satisfying power, torque, and speed, the product model has been determined, if the inertia is still not satisfied, can the power be increased by one gear to meet the requirements of inertia? The answer is: if the increase in power can lead to an increase in acceleration, it should be possible.

6. Servo motor selection

After selecting the mechanical transmission scheme, it is necessary to select and confirm the model and size of the servo motor.

(1) Selection conditions: In general, the selection of servo motor needs to meet the following conditions:

1. The maximum speed of the motor > the maximum moving speed required by the system.

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

3. Continuous load working torque≤ rated torque of the motor

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 rotation speed (speed at the load end, speed at the motor end) 3. Calculation of load torque (torque at continuous load, torque during acceleration.

The difference between low inertia and high inertia of servo motors

Moment of inertia = radius of rotation * mass

Low inertia means that the motor is relatively flat and long, and the spindle inertia is small, and when the motor does repeated movements with high frequency, the inertia is small and the heating is small. Therefore, the motor with low inertia is suitable for high-frequency reciprocating motion. However, the general moment is relatively smaller. The servo motor with high inertia is relatively coarse and has a large torque, which is suitable for occasions with high torque but not fast reciprocating motion. Because of the high-speed movement to the stop, the drive has to generate a large reverse driving voltage to stop this large inertia, and the heat generation is very large.

The moment of inertia is a measure of the inertia of the rigid body rotating around its axis, and the moment of inertia is a physical quantity that characterizes the magnitude of the rotational inertia of the rigid body. It is related to the mass of the rigid body and the distribution of the mass relative to the shaft. (Rigid body refers to an object that will not change in an ideal state), and the inertia of the motor when choosing is also an important indicator of the servo motor. It refers to the inertia of the servo motor rotor itself, which is quite important for the acceleration and deceleration of the motor. If the inertia cannot be well matched, the motor will be very unstable.

Generally speaking, the motor with small inertia has good braking performance, quick response to start, acceleration and stop, good high-speed reciprocation, and is suitable for some light load, high-speed positioning occasions, such as some linear high-speed positioning mechanisms. Medium and large inertia motors are suitable for occasions with large loads and high stability requirements, such as some circular motion mechanisms and some machine tool industries. If the load is relatively large or the acceleration characteristics are relatively large, and the motor with small inertia is selected, the damage to the motor shaft may be too great, and the selection should be selected according to the size of the load, the size of the acceleration, and so on.

The response control of the servo motor driver to the servo motor is optimally the ratio of the load inertia to the rotor inertia of the motor is one, and the maximum value shall not exceed five times. Through the design of the mechanical transmission device, the ratio of load inertia to the rotor inertia of the motor can be close to one or smaller. When the load inertia is really large, and it is impossible for the mechanical design to make the ratio of the load inertia to the rotor inertia of the motor less than five times, the motor with a large rotor inertia of the motor can be used, that is, the so-called large inertia motor. With a motor with a large inertia, the capacity of the drive should be larger to achieve a certain response.

Estun Servo Motor - Introduction to Servo Motor Inertia Knowledge

Estun Servo Motor - Introduction to Servo Motor Inertia Knowledge

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