Question

A motor with a maximum running speed of 1000rpm and with a torque-speed characteristic given by Tm​=200−0.76ωₘ​Nm(ωₘ​ in rads⁻²) is directly connected to a load with a torque-speed characteristic given by TL​=0.02ω2/L​Nₘ. Determine the steady state running speed. If TL​=2ω2/L​Nm determine the steady state running (load) speed if a 5:1 reduction gearbox is used. What value of gear ratio would be required if the motor was to be used to drive a load given by TL​=ω2/L​Nₘ at a (load) speed of 210rpm?

Answer 1

To determine the steady state running speed and load speed when a motor is directly connected to a load, we set the torque-speed characteristics of the motor and load equal to each other and solve for the speed. When a 5:1 reduction gearbox is used, the load speed can be found by dividing the motor speed by 5. To drive a load with a specific torque-speed characteristic and speed, the gear ratio needed can be determined by rearranging the load torque equation.

Step-by-step explanation:

To determine the steady state running speed when a motor is directly connected to a load, we need to find the point at which the torque-speed characteristics of the motor and load intersect.

Setting Tm (motor torque) equal to TL (load torque), we have:

200 - 0.76ωₘ = 0.02ω²/L

Simplifying the equation, we get:

0.02ω² + 0.76ωₘ - 200/L = 0

This equation is quadratic in form. To solve it, we can use the quadratic formula or graphical methods.

For the second part of the question, when a 5:1 reduction gearbox is used, we can take the motor speed and divide it by 5 to get the load speed.

For the third part of the question, we need to find the gear ratio that allows the motor to drive a load with a given torque-speed characteristic and speed. By rearranging the load torque equation, we can determine the gear ratio needed.