Mechanical transmission mechanisms play a crucial role in equipment operation and control systems. Whether it's speed reduction, torque increase, inertia matching, or cost-effectiveness optimization, all are achieved through the speed reduction ratio of the transmission mechanism. So, what kind of transmission ratio is more suitable? How do we evaluate and select the mechanical transmission ratio of an operation and control system? Today, we'll briefly analyze the reduction ratio.
We generally assume that, within the allowable range of motor speed output, for the same load torque requirement, a larger transmission reduction ratio results in a smaller required motor torque. In principle, this is not problematic, because as mentioned earlier, the system output torque is inversely proportional to the transmission reduction ratio; the reduction in speed through the transmission mechanism increases the system torque output.
However, we must say that this is the ideal situation when the output torque is fully (100%) applied to the load inertia. In reality, this is not entirely the case because the motor itself, as the power source, also has inertia. That is to say, the torque output by the motor needs to be distributed simultaneously to the load inertia and its own inertia. The transmission mechanism (such as a gearbox) merely amplifies and increases the torque output from the motor to the load. Before the motor outputs torque to the gearbox, it must first overcome the acceleration caused by its own inertia. This portion of torque acts directly on the motor itself and cannot be "save effort" through the gearbox.
When the transmission reduction ratio increases, the torque demand on the load side is indeed reduced through the reduction mechanism. However, the required motor speed also increases. To meet the dynamic response within the same time period, the motor needs to reach a higher speed in the same amount of time. In other words, while reducing the torque output requirement for the motor to overcome load inertia, the requirement for motor acceleration increases. Since acceleration is related to torque, this actually increases the torque requirement for the motor to generate acceleration. So, does this combination of increase and decrease ultimately increase or decrease the torque?
Let's try to deduce the underlying principles using the following simple transmission model.
The acceleration torque required by the load is:
Iload·β
Therefore, the acceleration torque that the motor needs to apply to the load is...
Iload·β÷X
The next step is to calculate the torque that the motor needs to exert to meet the load acceleration requirements.
The acceleration of the motor is
β·X
The torque acting on the motor is then...
Imotor·β·X
Therefore, we conclude that the total torque required to be output by the motor is...
We found that the relationship between total torque and speed ratio is a superposition of a direct proportional curve and an inverse proportional curve. The trend of this curve depends on the inertia relationship between the motor and the load (note that this is not the same as the load inertia ratio).
This is exactly what we said before:
Firstly, as the speed ratio increases, the speed ratio and load inertia become inversely proportional, making it easier for the motor to drive the load, and the required torque naturally decreases.
On the other hand, due to the increase in speed ratio, the motor's own speed requirement increases, which means it needs higher acceleration to meet the operating speed of the load, and the increase in acceleration leads to an increase in torque requirement.
The key question is, within the motor's speed range, which of the two torque change trends is dominant? This depends on the motor's inertia.
Next, let's look at how the torque demand changes with the speed ratio at different levels of motor inertia.
In the following trend chart
The principal coordinate (left side) represents the torque.
The secondary coordinate (right side) represents the inertia ratio of the transmission system after incorporating the reduction mechanism.
The horizontal axis represents the transmission reduction ratio.
If the motor inertia is very small, only 1%-5% of the load, then the trend is as follows.
If the motor inertia continues to increase, we will see the lowest point of torque gradually approach a smaller speed ratio.
From the trends above, we can understand that:
Properly adjusting the gear ratio can reduce the demand on motor torque. Within a certain speed ratio range, increasing the speed ratio can help reduce the demand on motor torque output. However, outside this range, increasing the gear ratio will actually increase the torque demand. From an economic (or energy-saving and environmental protection) perspective, the critical value of this range is precisely the lowest point of the torque curve. At this speed ratio, the required motor torque is minimized, which can be considered the "optimal."
The "range" or "optimal point" mentioned above is related to the inertia of the motor itself. The smaller the motor's inertia, the larger the adjustable range of the speed ratio; the larger the motor's inertia, the smaller the adjustable range of the speed ratio.
Because of the relationship between motor inertia and speed ratio, different motors have different optimal transmission ratios. Therefore, when selecting and designing a motor, it is necessary to reconsider the optimal speed ratio each time a motor is replaced. The trend curves mentioned above can be listed according to the application requirements, and then the best combination of "motor" and "speed ratio" can be found.
It's important to note that, with a constant load, increasing the motor's inertia also increases the torque demand—meaning a larger motor needs to be selected. Looking at the curve analysis above, when the motor's inertia increases tenfold, the torque demand also increases several times over. While with low-inertia motors, we can improve the load-inertia ratio by adjusting the gear ratio, the adjustment space for high-inertia motors is very small. Therefore, we do not actually recommend using medium- or high-inertia motors.
There are a few other points I'd like to mention.
Motors from different manufacturers and different series have different torque and speed characteristics, and therefore require different transmission mechanisms . In other words, when changing motor brands and series, we strongly recommend reassessing the motor characteristics and transmission ratio.
Adjusting the reduction ratio can effectively optimize and match mechanical and electrical systems, and the cost-effectiveness of such adjustments is often extremely high. For example, reducers with speed ratios of 1:3, 1:5, 1:7, and 1:9 have very similar (or identical) costs within a certain range, but they can greatly optimize motor matching, thereby reducing the overall cost.
While torque is a crucial parameter for motor selection, other factors need to be considered, such as temperature rise, bus voltage, and current. Furthermore, given the complexity of mechanical systems, these factors are not addressed or analyzed in detail here. Specific application selection requires further calculation and analysis based on actual conditions.
