Inertia is the resistance an object experiences to changes in velocity; the heavier or larger the object, the greater its inertia. In motion control or servo systems, both the motor and the load possess inertia, and the ratio of their moments of inertia affects the system's performance.
This ratio is one of the most important aspects of motor size adjustment, and also one of the most easily overlooked. Motor inertia is primarily driven by the size of the motor rotor. The load inertia is calculated by adding the inertia of all moving parts (belts, screws, racks and pinions, external loads, and couplings).
To enable a motor control system to effectively control the load during acceleration and deceleration, the inertia of the motor and the load should be as close to equal as possible; however, a 1:1 inertia match is difficult to achieve. Many factors influence the acceptable inertia ratio, but one of the most important is the system's compliance or termination. Mechanical components are not perfectly rigid, and the system becomes more compliant with the addition of more compliant components. System compliance is primarily driven by more flexible components such as belts and couplings; generally, the higher the compliance, the lower the inertia ratio should be.
There is no definitive formula for the ideal inertia, but most servo sizing guidelines aim for an inertia ratio of 10:1 or lower. A higher inertia ratio can cause the motor to work beyond its capacity when necessary and leads to increased settling time during vigorous motion, thus reducing efficiency, increasing operating costs, and cycle time. With an appropriate inertia ratio, if the ratio is very high (above 10:1), the motor may be completely uncontrollable by the system, even when stationary. This will result in the motor using excessive power to maintain load stability or requiring significant engineering time to bring the system to a steady state.
The motor manufacturing industry mostly uses four inertia estimation techniques to obtain accurate rotor inertia values in the actual physical structure of motors. The four methods are control compensation method, inertia comparison method, segment identification method and electrical comparison method.
Control compensation: In 1992, Robert D. Lorenz proposed a method for measuring the internal parameters of a motor, obtaining values including inertia, viscosity coefficient, and friction loss. The method is based on feedforward control theory to estimate the motor parameter values. This approach has been widely used in servo motors.
Inertia Comparison Method: Recently, MEA Testing Systems Ltd. in Israel has been using a technique of adding a flywheel with a known inertia value to observe the acceleration changes of the motor after the flywheel is added, and estimating the unknown inertia from the known inertia to obtain the rotor inertia value of the motor.
Segmented identification method: For permanent magnet DC brushed motors, system identification is performed by inputting multiple step voltages of the same magnitude and using mathematical matrix operations to obtain the motor's internal parameters, including inductance, resistance, back electromotive force constant (Back-EMF Constant), torque constant, rotor inertia, and viscosity coefficient.
Electrical Comparison Method: Given that an electric motor is a mechanism for converting electrical energy into kinetic energy, the motor system can be divided into two categories: electrical and mechanical. The electrical part refers to the input voltage, current, motor coil resistance, and inductance, while the mechanical part includes output torque, speed, motor inertia, and viscous hysteresis coefficient. As is known in automatic control, the electrical response speed is faster than the mechanical response speed. The method involves changing the motor's mechanical parameters to adjust its inertia, hence the longer measurement time. Changing the motor's electrical parameters and adjusting the motor's input power supply using a controller results in a shorter measurement time.
It is known that changing the motor's electrical parameters allows for a relatively short measurement time; however, the Lorentz method requires adjusting controller parameters, which is time-consuming, and the inertia estimation results have a large deviation, directly affecting the accuracy of the acceleration method. By utilizing the motor's electrical parameters, and considering the impact on inertia estimation, the testing efficiency of the motor measurement system can be improved to achieve rapid measurement. In conclusion, if the inertia ratio is too high, there are two ways to reduce it: increasing the gear ratio (the output distance of the motor per revolution) or using a larger motor. Due to the low mechanical advantage of pulleys, gearboxes are often required in belt drive systems. The inertia ratio of the system can also be significantly reduced because the gear ratio has an inverse square effect on the load's inertia. A second method to reduce the inertia ratio is to use a larger motor with higher inertia (sometimes moving to a medium-inertia motor). However, due to the required space and cost, a gearbox is the preferred solution.
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