Calculating gearbox power involves understanding the power input from the motor and the gearbox's efficiency.
Based on the provided reference snippet, p is the motor rated power in kilowatts, which is the primary input power to the gearbox.
A gearbox transmits power from an input source (like a motor) to an output load. It doesn't generate power itself; rather, it modifies the torque and speed while accounting for some power losses due to friction and other factors.
Understanding Gearbox Power
When discussing "gearbox power," people are typically referring to:
- Input Power: This is the power supplied to the gearbox, usually from the motor or engine.
- Output Power: This is the power delivered by the gearbox to the load. It is always less than or equal to the input power due to efficiency losses.
The power transmitted remains largely constant (minus losses) while the gearbox changes the relationship between torque and speed according to its ratio.
Input Power Calculation
As mentioned in the reference:
- p is the motor rated power in kilowatts.
This motor power (P_input) serves as the input power to the gearbox. You can also calculate the input power if you know the input torque (T_input) and input speed (N_input) using the formula:
$P{input} (kW) = \frac{T{input} (Nm) \times N_{input} (RPM)}{9549}$
The reference also mentions "And as the motor rated speed in RPM or revolution per" (N_input). This speed, along with the motor power (p), could be used to calculate the motor's output torque (T_input), which is the input torque to the gearbox.
Output Power Calculation
The output power (Poutput) of the gearbox is calculated by taking the input power and multiplying it by the gearbox's efficiency ($\eta{GB}$).
$P{output} = P{input} \times \eta_{GB}$
Where:
- $P_{output}$ is the output power (usually in kW or Watts).
- $P_{input}$ is the input power (motor power, p).
- $\eta_{GB}$ is the gearbox efficiency (a value between 0 and 1).
Gearbox efficiency varies depending on the type of gearbox (e.g., spur, helical, worm), the number of stages, lubrication, and operating conditions. Typical efficiencies range from 90% to 99% for common types like helical gears, but can be much lower for worm gears (e.g., 50% to 90%).
Calculating Output Torque (Mentioned in Reference Context)
While the question is about power, the reference snippet focuses on calculating output torque (T2) using motor power (p), motor speed (N), and gearbox ratio (GB). The formula for output torque is related to power, speed, and the gearbox ratio and efficiency.
In an ideal scenario (100% efficiency):
$P{input} = P{output}$
$T{input} \times N{input} = T{output} \times N{output}$
Since $N{output} = N{input} / GB$, we get:
$T{output} = T{input} \times GB$
Using the power formula $P{input} = \frac{T{input} \times N{input}}{9549}$:
$T{input} = \frac{P{input} \times 9549}{N{input}}$
Substituting $T{input}$ into the ideal $T{output}$ formula:
$T{output} = \frac{P{input} \times 9549}{N_{input}} \times GB$ (Ideal Output Torque)
Considering efficiency:
$T{output} = \frac{P{input} \times 9549}{N{input}} \times GB \times \eta{GB}$ (Actual Output Torque)
The reference refers to T2 as gearbox output torque, p as motor power, GB as gearbox ratio, and N as motor speed. It likely uses a formula similar to the one above (or its rearranged form) to calculate T2.
Summary of Key Terms from Reference
| Term | Symbol (from reference context) | Description | Unit (from reference context) |
|---|---|---|---|
| Motor Rated Power | p | Input power to the gearbox | Kilowatts (kW) |
| Motor Rated Speed | N | Input speed to the gearbox | RPM |
| Gearbox Ratio | GB | Ratio of input speed to output speed | Unitless or e.g., X:1 |
| Gearbox Output Torque | T2 | Output torque from the gearbox | Newton meter (Nm) |
Practical Calculation Steps
To calculate the gearbox output power:
- Identify Input Power: Determine the power supplied to the gearbox. As per the reference, this is often the motor's rated power (p in kW).
- Find Gearbox Efficiency: Obtain the efficiency ($\eta_{GB}$) of the specific gearbox. This information is usually provided by the manufacturer. If not available, typical values for the gearbox type can be estimated, but manufacturer data is best.
- Calculate Output Power: Multiply the input power by the efficiency.
$P{output} (kW) = p (kW) \times \eta{GB}$
Example:
If a motor rated at 5 kW (p = 5 kW) drives a gearbox with an efficiency ($\eta_{GB}$) of 95% (0.95), the output power would be:
$P_{output} = 5 kW \times 0.95 = 4.75 kW$
This 4.75 kW is the power the gearbox delivers to the connected load. The remaining 0.25 kW is lost as heat within the gearbox.
