When discussing gearbox power, the focus is often on the power input from the motor or the power transmitted through the gearbox to the output shaft. Based on the provided reference, the formula explicitly given for calculating the Motor power (which serves as the input power to the gearbox) is detailed below.
The reference also provides a formula for the Gear Reducer Torque (output torque), which is related to the motor power, input speed, gear ratio, and efficiency.
Formula for Motor Power (Input Power)
According to the reference, the formula for Motor power is:
Motor power = torque ÷ 9550 × Rated power's motor input speed /Ratio /service factor
This formula can be written more clearly as:
Pin = (T / 9550) × (Nin / Ratio / Service Factor)
or
Pin = (T × Nin) / (9550 × Ratio × Service Factor)
Where:
- Pin is the Motor power (Input Power to the gearbox), typically in kilowatts (kW).
- T is the torque. Based on the context provided in the reference (which also gives a torque output formula), this 'torque' in the power formula likely refers to the required output torque, potentially including considerations like the service factor.
- 9550 is a constant used to convert units when torque is in Newton-meters (Nm) and speed is in revolutions per minute (rpm) to power in kilowatts (kW). (Power (kW) = Torque (Nm) × Speed (rpm) / 9550).
- Nin (Rated power's motor input speed) is the input speed to the gearbox, typically the motor's rated speed, in revolutions per minute (rpm).
- Ratio is the gear ratio of the reducer (Input Speed / Output Speed).
- Service Factor is a factor used in design to account for external load conditions, operating hours, and reliability requirements, influencing the required capacity.
This formula allows for calculating the required motor power based on the necessary torque, input speed, gear ratio, and service factor.
Related Formula: Gear Reducer Torque (Output Torque)
The reference also provides the formula for calculating the output torque of the gear reducer, which involves the motor power and other parameters:
Gear Reducer Torque = 9550 * Motor power / Rated Power motor's input revolution*Ratio* gear reducer efficiency
This formula can be written as:
Tout = (9550 × Pin / Nin) × Ratio × Efficiency
or
Tout = (9550 × Pin × Ratio × Efficiency) / Nin
Where:
- Tout (Gear Reducer Torque) is the output torque of the gearbox, typically in Newton-meters (Nm).
- 9550 is the unit conversion constant.
- Pin (Motor power) is the input power to the gearbox in kW.
- Nin (Rated Power motor's input revolution) is the input speed in rpm.
- Ratio is the gear ratio.
- Efficiency (gear reducer efficiency) is the mechanical efficiency of the gearbox, typically expressed as a decimal (e.g., 0.95 for 95% efficiency).
This torque formula demonstrates how the output torque is produced from the input power, speed reduction through the ratio, and accounting for efficiency losses. It shows that, according to standard principles and this reference, input power is directly proportional to output torque when considering efficiency, ratio, and speed.
Understanding these formulas is crucial for selecting the appropriate motor for a given gearbox application and for determining the capabilities of a gearbox based on the input power available.
