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In the mechanical motion control, the precision gear reducer is a mechanical energy conversion link, the torque of the motor after the precision gear reducer can be amplified, the speed can be reduced, on the contrary, the load of inertia by the precision gear reducer coupling to the motor, can be reduced. Its action is shown in Figure B-1

Fig. B-1

As we know, the ideal case is that the power of the transmission process is conserved, but in reality there is always loss. Let the efficiency of the transmission process beη，then：/η=

And because of the deceleration ratioi=/ =/ i（B-1）

so=iη（B-2）

——The motor torque（NM），——Load moment（NM），

，——Motor, angular velocity of load（radian/s）

Let's take a look at the action of gear reducer on the moment of inertia. According to the basic principle of energy indestructibility, in the transmission chain, the stored energy at the same time is equal:

Thus, it can be concluded:

（B-3）

J_{em}-——Equivalent moment of inertia converted to the motor shaft（kgm^{2}）

J_{L}——The moment of inertia of the load（kgm^{2}）

It can be seen from the above deduction that the usual formulas we are familiar with about the gearbox are all derived from the conservation of energy law of physics.

The above（1）—（3）Represents the three basic functions of the reducer:

1. Reduce servo motor speed（ =/ i）

The limit power of servo motor is generally reflected between 1000rpm and 6000rpm, or even as high as 10000rpm. In the actual use process, such a high speed is rarely used. Meanwhile, in order to make full use of the rated power of the motor, it is necessary to obtain the required working speed through a reducer with appropriate reduction ratio.

2. Torque amplification（=iη）

When the motor input power to the reducer is fixed, the output torque of the reducer is bound to be larger because the output speed of the reducer is reduced. In many cases, this is also an important reason to choose a reducer.

3. Matching load moment of inertia（）

The moment of inertia of the servo motor is relatively small, generally equivalent to the servo motor load moment of inertia of no more than four times that of servo motor itself inertia (different brand servo motor design has a very specific data), and there are many kinds of load in practical application, if the moment of inertia of load and moment of inertia of the motor can accept differ too far, can greatly reduce the response speed of the servo motor, Thus affect the production efficiency and increase the dynamic error. And the reducer can play a key role in matching the inertia.