The Deep Influence of Gearbox Reduction Ratio Selection on the Stability of the Cutting Machine Servo System

1、 Core mechanism: How to improve inertia matching through reduction ratio

The stability of a servo system depends on the ratio of the motor rotor inertia to the load inertia (i.e. inertia ratio). Excessive inertia ratio can lead to slow system response, positioning jitter, and even step loss; If the inertia ratio is too small, it may cause system oscillation.

The reducer plays a key role as an inertia matching device here. According to physical principles, the equivalent inertia of the load converted to the motor shaft is inversely proportional to the square of the reduction ratio. The calculation formula is:

Converted to the load inertia of the motor shaft=actual load inertia/(reduction ratio) ²

This means that the improvement in deceleration ratio to inertia ratio is on the order of squares. For example, a gearbox with a reduction ratio of 10:1 can reduce the inertia of the load converted to the motor shaft to 1/100 of its original value. This has transformed the previously incompatible "small horse pulling big car" system into a responsive and stable matching state by selecting the appropriate reduction ratio.

2、 The specific impact of improper selection of reduction ratio on stability

1. Too small reduction ratio: too large inertia ratio, system instability

Phenomenon: The servo motor exhibits significant shaking, inaccurate positioning, large tracking errors, and even frequent alarms during start stop or acceleration/deceleration.

Reason: Insufficient reduction ratio, resulting in the load inertia converted to the motor shaft still being too large. Servo drives cannot effectively control such a large inertia, PID parameter tuning is difficult, and system rigidity cannot be improved. For equipment such as cutting machines that require frequent start stop and precise positioning, this can directly lead to problems such as decreased cutting accuracy and tool vibration.

2. Excessive reduction ratio: dynamic response deteriorates, efficiency decreases

Phenomenon: Although the system is stable, the acceleration and deceleration process is slow, and the equipment rhythm cannot meet the requirements. Meanwhile, the motor may operate in a low efficiency range for a long time, resulting in increased heat generation.

Reason: Although the excessive reduction ratio makes the inertia ratio extremely small, it also excessively amplifies the motor speed, resulting in a low output speed. In order to achieve the target speed, the motor needs to run at high speed for a long time, deviating from the high-efficiency zone. In addition, multi-stage reducers may cause additional transmission clearances and efficiency losses, which may affect the final positioning accuracy.

3、 Practical suggestions for selecting the reduction ratio of the cutting machine

For equipment such as cutting machines that require both dynamic response and positioning accuracy, the selection of reduction ratio should follow the following principles:

1. The primary goal is to match inertia: do not calculate the reduction ratio solely based on experience or speed/torque. The load inertia should be calculated or measured first, and combined with the rotor inertia of the selected servo motor, the target inertia ratio should be controlled within a reasonable range. For the cutting machine, it is usually recommended to control the inertia ratio between 5:1 and 10:1 to balance response speed and stability.

2. Comprehensive verification of speed and torque: On the premise of meeting inertia matching, verify whether the output speed and torque after deceleration meet the process requirements of the cutting machine. Ensure that the rated torque of the motor multiplied by the reduction ratio and transmission efficiency is still greater than the required torque of the load, with a safety factor of 1.2-2.0 times.