The electronic gear ratio of a servo motor is used to either increase or decrease the pulse frequency that the motor receives from the upper controller. This is typically defined by two parameters: the numerator and the denominator. If the numerator is greater than the denominator, the pulse frequency is increased; conversely, if the denominator is larger, the frequency is reduced. For example, if the upper computer sends a 100Hz signal and the electronic gear ratio is set to 1/2, the actual pulse frequency sent to the servo motor will be 50Hz. On the other hand, if the gear ratio is set to 2/1, the pulse frequency becomes 200Hz. The electronic gear ratio functions similarly to mechanical gearing, but it allows for shaftless transmission and offers more flexibility in adjusting speed and resolution.
**The Role of Electronic Gear Ratio**
Let’s take an example of a motor with a 17-bit encoder. In one full rotation, the encoder generates 131072 pulses, which are transmitted to the servo driver. If we want the motor to rotate at 20 revolutions per second (r/s), without any gear ratio adjustment, the controller would need to send 2,621,440 pulses per second, resulting in a pulse frequency of 2.62 MHz. However, most controllers, such as PLCs, have a maximum pulse output limit—typically 200 kHz or 500 kHz. To stay within these limits, the concept of an electronic gear ratio is introduced to reduce the pulse frequency sent to the servo motor.
**Servo Motor Electronic Gear Ratio Calculation Method**
**Motor Encoder Resolution**
Most servo motors come with encoders that generate a certain number of pulses per revolution. For example, a 2000-line encoder will produce 2000 pulses per revolution, and after quadrature processing, this becomes 8000 pulses per revolution. Similarly, a 2500-line encoder results in 10,000 pulses per revolution.
| Motor Model | Encoder Line Number | Motor Encoder Resolution |
|-------------|---------------------|---------------------------|
| Sanyo P2, P5 | 2000 | 8000 |
| Dahao Servo | 2500 | 10000 |
When the controller sends a pulse to the driver, the motor rotates by a specific angle. After secondary transmission, the movement of the frame is inversely proportional to the gear ratio. For instance, if the gear ratio is 1/4, the motor must rotate four times for the frame to move once.
Frame gears usually have angles of 0.36° or 0.45° for every 0.1 mm of movement. Most systems use the 0.36° gear.
In summary, the formula for calculating the electronic gear ratio is:
For screw mechanisms, the calculation differs slightly. If there is a 1:1 belt drive between the motor and the screw shaft, and the screw pitch is M mm per revolution, the formula becomes:
**Setting the Electronic Gear Ratio for Maximum Motor Speed**
When speed is the priority, it's essential to fully utilize the motor’s speed performance. For example, if the desired motor speed is 3000 RPM and the encoder has 8192 pulses per revolution, the required pulse frequency is calculated as follows:
$$
\text{Pulse Frequency} = \frac{8192 \times 3000}{60} = 409,600 \text{ Hz} = 409.6 \text{ kHz}
$$
If the controller can only output up to 100 kHz, the gear ratio must be adjusted. By setting the numerator (CMX) and denominator (CDV) to 1 initially, and then reducing the pulse frequency to 10 kHz, the actual motor speed becomes approximately 73 RPM. To reach the desired 300 RPM, the gear ratio should be adjusted accordingly.
$$
\frac{300}{73} \approx 4.11
$$
So, setting CMX to 300 and CDV to 73 will allow the motor to achieve the target speed.
**Setting the Electronic Gear Ratio for Mechanical Resolution**
In applications where precision is more important than speed, the electronic gear ratio should be set to match the system’s resolution. For example, if the motor is connected to a reduction mechanism with a 3:1 ratio and the lead screw has a 10 mm pitch, the resolution per pulse would be:
$$
\frac{10}{8192 \times 3} \approx 0.0004069 \text{ mm/pulse}
$$
To achieve a resolution of 1 μm/pulse, the number of pulses per revolution must be adjusted using the gear ratio. This ensures that the system meets the required accuracy while maintaining acceptable speed.
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