The magnitude of the rotor's moment of inertia directly affects the starting and braking performance of the motor , and should be measured when necessary. There are no specific national standards specifying the magnitude of the rotor's moment of inertia; it is generally agreed upon by the user and the manufacturer based on actual needs.
The moment of inertia is represented by the symbol J, with the unit kg · m², and is a standard physical quantity in Chinese and international standards. However, in engineering, it is customary to use GD². The relationship between the two is shown in equation (1).
There are two methods for determining the rotor's moment of inertia: calculation and measurement. Measurement methods include the single-wire method, the double-wire method, the auxiliary pendulum method, and the inertial rotation method. Today, Ms. [Name] will briefly analyze how to determine the rotor's moment of inertia using the calculation method and the single-wire method . Other methods are similar; you can use these analogies, derivations, and inferences to apply them.
Calculation method for determining rotor moment of inertia
Although the motor rotor is a nearly regular cylinder, it is difficult to perform accurate calculations because it is made of at least three different materials that intersect with each other. When the requirements are not high, the rotor can be regarded as a cylinder with uniform density. After weighing its mass m, the moment of inertia of a cylinder can be calculated using the formula (2) for calculating the moment of inertia of a cylinder.
In formula (2):
J—Moment of inertia (kg·m2);
m — rotor mass (kg);
r — rotor radius (m).
Moment of inertia of a single wire rotor
The single-wire measurement method is further divided into two different methods: the single-wire measurement method assisted by a dummy rotor and the single-wire measurement method with an additional auxiliary torsional pendulum.
The experimental method of single steel wire assisted by dummy rotor
This method is suitable for small motors with a rotor mass not exceeding 50kg. However, it is costly and time-consuming to test because a dummy rotor needs to be fabricated.
● Requirements for manufacturing dummy rotors
(1) The material density is uniform, and rolled round steel is preferred.
(2) The outer circle is round and the end face is flat.
(3) Try to make its mass and shape the same as the rotor being tested.
After the fabrication is completed, its external dimensions are accurately measured, and its moment of inertia Ja (kg·m2) is calculated using formula (2).
●Testing Steps
(1) Reliably suspend the dummy rotor under the steel wire. The other end of the steel wire is securely tied to a bracket. It should be noted that the steel wire must be tied to the center of the diameter of the dummy rotor so that its axis is vertical when it hangs naturally. The length of the steel wire is about 2m, and its cross-sectional diameter depends on the mass of the dummy rotor. That is, after the dummy rotor is suspended, it should not have obvious elongation deformation, but it should not be too thick, otherwise it will affect the test swing and cause a large error due to the straightness of the steel wire itself.
(2) During the test, rotate the dummy rotor 30°-45°, then release it, allowing it to rotate freely back and forth due to the torque of the steel wire. Use a stopwatch to record the time taken for the dummy rotor to complete one rotation cycle (from the original stationary position to the maximum angle on the left, back to the original stationary position, then to the maximum angle on the right and back to the original stationary position, this constitutes one oscillation cycle). To ensure accurate timing, do not time the first 1-2 cycles, then record the time of several cycles and take the average as the time Ta (s) taken for one rotation cycle of the dummy rotor. The starting and ending points of the timing should be at the position with the maximum oscillation speed, i.e., the center of the oscillation.
(3) Replace the above dummy rotor with the test rotor that has been dynamically balanced, and use the same method to find the oscillation period T (s) of the real rotor being tested.
(4) Calculate the moment of inertia of the test rotor using formula (3) (kg·m2).
Experimental method of single wire measurement with auxiliary torsional pendulum
●Machining requirements for the auxiliary torsional pendulum
The auxiliary torsional pendulum is cylindrical, with a through hole in its central axis slightly larger in diameter than the steel wire. Its outer diameter should be approximately the same as that of the rotor under test, and its mass should be 10% to 15% of that of the rotor under test. The material should have uniform density, preferably rolled round steel.
After the fabrication is completed, its external dimensions are accurately measured and its moment of inertia Ja (kg·m2) is calculated using formula (2).
●Testing Steps
(1) The test rotor is reliably suspended under a steel wire. The other end of the steel wire is securely tied to a support. The rotational oscillation period T (s) of the test rotor is obtained using the same method as in the single-wire test with dummy rotor assistance.
(2) Attach the auxiliary torsional pendulum to the steel wire rope suspending the test rotor. Then, conduct the test using the same method as above and calculate the rotational oscillation period Tf (s).
(3) Calculate the moment of inertia J (kg·m2) of the test rotor using equation (4).
