General principles for selection of gear ratios in servo systems - Solutions - China Power

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In the servo system, the reducer is an important component, and its performance has a significant impact on the system, the first of which is the choice of the total gear ratio.

General principles for gear ratio selection:

(1) Minimize the moment of inertia of the reducer (converted to the motor shaft).

(2) Minimize the transmission gap or minimize the transmission error caused by the reducer.

(3) The motor drives the load to produce the maximum acceleration. For the steering gear that manipulates the missile's rudder surface, rapidity is the most important indicator, so the transmission ratio should generally be selected according to the principle of maximum acceleration.

Select the gear ratio according to the principle of maximum load acceleration:

The pure inertia load is set to pure inertia, the moment of inertia is JL, and has a certain frictional moment Mf. If the motor rotor moment of inertia is Jm and the gearbox transmission ratio is i, then the torque balance equation converted to the load shaft is iMm-Mf=(i2Jm+JL). ωL(1) where Mm—the torque output by the motor ;ωL———load angular acceleration. From (1), ωL=iMm-Mfi2Jm+JL(2) is used to find the derivative .ωL/i for (2), and let it be zero, and then i=MfMm+(MfMm)2+JLJm(3) The optimum gear ratio to meet the maximum acceleration conditions.

If the load friction torque Mf=0, then i=JLJm(4) is the commonly used formula for selecting the optimal gear ratio. The practical meaning is that after the gear ratio is selected according to this formula, the rotor inertia of the motor is converted to the load shaft. The value is equal to the load moment of inertia. That is, if i2Jm=JL(5) meets the transmission ratio of this condition, the load can have the maximum acceleration. Secondly, it can be seen from equation (3) that the friction torque or constant load torque will increase the transmission ratio. The significance is also obvious, because Mm is certain, when the load torque is increased, only by increasing the transmission ratio, the torque for pushing the load can be increased.

Therefore, in the design, the gear ratio should be appropriately increased according to the actual load situation. The effect of the load on the optimum gear ratio is further analyzed below. When the initial speed is not zero, the optimal gear ratio is selected. When the missile is maneuvering, the steering gear is subjected to two kinds of control signals. The first type is the command signal from the seeker, which is a signal with a low frequency and a large amplitude; The second type is the signal from the autopilot to control the attitude of the missile. It is a high-frequency small-amplitude signal that requires the servo to respond quickly. The latter signal is superimposed on the previous signal, at which time the load speed is not zero and there is a hinge moment. In the reducer, the planetary reducer is much more precise than the general reduction ratio. It can be equipped with stepper motor and servo motor.

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