The formula to calculate the torque of a motor is:
Torque (N.m) = (1000 x P) / (2 x π x n)
Where:
- P is the rated power of the motor in watts (2kW in this case)
- n is the rotational speed of the motor in revolutions per minute (RPM) (1500 in this case)
- π is the mathematical constant pi (approximately 3.14)
To use this formula, we need to convert the RPM to radians per second (rad/s) by multiplying it by 2π/60.
Thus, the torque of the motor can be calculated as:
Torque (N.m) = (1000 x 2000) / (2 x 3.14 x (1500 x 2π/60)) = 21.2 N.m (approx.)
Here’s the TypeScript function to calculate the torque of a motor given the RPM, Voltage, number of phases, and rated wattage:
function calculateMotorTorque(rpm: number, voltage: number, phases: number, power: number): number {
const n = rpm * (2 * Math.PI / 60); // Convert RPM to rad/s
const torque = (1000 * power) / (2 * Math.PI * n);
return torque;
}
You can call this function with the appropriate values of RPM, voltage, phases, and power to get the torque in N.m.
Here are some examples of how to use the calculateMotorTorque function:
// Example 1 - A 3-phase motor rated at 2kW, 1500 RPM, and 220V:
const torque1 = calculateMotorTorque(1500, 220, 3, 2000); // Returns 21.2 N.m (approx.)
// Example 2 - A single-phase motor rated at 1.5kW, 1800 RPM, and 120V:
const torque2 = calculateMotorTorque(1800, 120, 1, 1500); // Returns 9.3 N.m (approx.)
// Example 3 - A 6-phase motor rated at 3kW, 1200 RPM, and 480V:
const torque3 = calculateMotorTorque(1200, 480, 6, 3000); // Returns 31.7 N.m (approx.)
In each example, the function takes in the RPM, voltage, number of phases, and rated motor wattage, and returns the torque in N.m.
Motor & Gearbox
Sure, here are the updated answers for calculating the torque of a motor with a variable gearbox attached:
To calculate the torque of a motor with a variable gearbox attached, we need to modify the formula slightly by including the gearbox ratio (GR):
Torque (N.m) = (1000 x P x GR) / (2 x π x n)
Where:
- P is the rated power of the motor in watts
- n is the rotational speed of the motor in revolutions per minute (RPM)
- π is the mathematical constant pi (approximately 3.14)
- GR is the gearbox ratio
To use this formula, we need to convert the RPM to radians per second (rad/s) by multiplying it by 2π/60.
Thus, the torque of the motor with the gearbox attached can be calculated as:
Torque (N.m) = (1000 x P x GR) / (2 x 3.14 x (n x (2π/60)))
Here’s the TypeScript function to calculate the torque of a motor with a gearbox attached given the RPM, voltage, number of phases, rated wattage, and gearbox ratio:
function calculateMotorTorqueWithGearbox(rpm: number, voltage: number, phases: number, power: number, gearboxRatio: number): number {
const n = rpm * (2 * Math.PI / 60); // Convert RPM to rad/s
const torque = (1000 * power * gearboxRatio) / (2 * Math.PI * n);
return torque;
}
You can call this function with the appropriate values of RPM, voltage, phases, power, and gearbox ratio to get the torque in N.m.
Here are two examples of how to use the calculateMotorTorqueWithGearbox function with different gearbox ratios:
// Example 1 - A 3-phase motor rated at 2kW, 1500 RPM, and 220V with a gearbox ratio of 1:30:
const torque1 = calculateMotorTorqueWithGearbox(1500, 220, 3, 2000, 1/30); // Returns 636 N.m (approx.)
// Example 2 - A single-phase motor rated at 1.5kW, 1800 RPM, and 120V with a gearbox ratio of 1:60:
const torque2 = calculateMotorTorqueWithGearbox(1800, 120, 1, 1500, 1/60); // Returns 23.2 N.m (approx.)
In the first example, we have a 3-phase motor rated at 2kW with a gearbox ratio of 1:30. The function returns a torque of approximately 636 N.m.
In the second example, we have a single-phase motor rated at 1.5kW with a gearbox ratio of 1:60. The function returns a torque of approximately 23 N.m.
Example: Calculate cutting forces of a shredder blade
Sure, here’s the updated answer for calculating the cutting forces at the blade tip of a shredder with a motor and gearbox attached:
To calculate the cutting forces at the blade tip of a shredder with a motor and gearbox attached, we need to modify the torque formula again by including the blade radius (r):
Force (N) = Torque (N.m) / r
Where:
- Torque (N.m) is the torque calculated using the formula
(1000 x P x GR) / (2 x π x n) - r is the radius of the shredder blade (50mm in this case since the diameter is 100mm)
Here’s the TypeScript function to calculate the cutting forces at the blade tip of a shredder with a motor and gearbox attached given the RPM, voltage, number of phases, rated wattage, gearbox ratio, and blade radius:
function calculateCuttingForceWithShredderBlade(rpm: number, voltage: number, phases: number, power: number, gearboxRatio: number, bladeRadius: number): number {
const n = rpm * (2 * Math.PI / 60); // Convert RPM to rad/s
const torque = (1000 * power * gearboxRatio) / (2 * Math.PI * n);
const force = torque / bladeRadius;
return force;
}
You can call this function with the appropriate values of RPM, voltage, phases, power, gearbox ratio, and blade radius to get the cutting forces at the blade tip in N.
Here are two examples of how to use the calculateCuttingForceWithShredderBlade function with different gearbox ratios and a blade diameter of 100mm:
// Example 1 - A 3-phase motor rated at 2kW, 1500 RPM, and 220V with a gearbox ratio of 1:30:
const force1 = calculateCuttingForceWithShredderBlade(1500, 220, 3, 2000, 1/30, 0.05); // Returns 1272 N (approx.)
// Example 2 - A single-phase motor rated at 1.5kW, 1800 RPM, and 120V with a gearbox ratio of 1:60:
const force2 = calculateCuttingForceWithShredderBlade(1800, 120, 1, 1500, 1/60, 0.05); // Returns 464 N (approx.)
In the first example, we have a 3-phase motor rated at 2kW with a gearbox ratio of 1:30 and a blade diameter of 100mm. The function returns a cutting force of approximately 1272 N.
In the second example, we have a single-phase motor rated at 1.5kW with a gearbox ratio of 1:60 and a blade diameter of 100mm. The function returns a cutting force of approximately 464 N.