29 ms·

You're assuming that torque remains constant at higher angular velocities, which is not true in most electric motor-drives.

• Gravityloss 12y ago
  It doesn't stay constant. I didn't assume it stays constant either. Your maximum torque can be extracted by the right gear from the maximum _power_ peak. That means even with diminishing torque with angular velocity, if it diminishes only slowly, it's still worth going to higher angular velocities. Example: Say if you have a motor that has 100 Nm of torque at 100 radians/s, which is 10 kW of power, and 80 Nm of torque at 200 radians/s, which is 16 kW of power. And further, you specify that you need to have the maximum torque in the wheels at 10 radians/s. With a 10:1 gear ratio, when your wheels run at 10 radians/s, your engine runs at 100 radians/s and provides 10 kW. Thus the torque at the wheels is 10000W / 10 radians/s = 1000 Nm. With a 20:1 your engine runs at 200 radians/s and 16 kW and wheel torque is: 16000 W / 10 radians/s = 1800 Nm. More torque at the wheels with less torque at the engine! Of course, with a fixed ratio, the latter vehicle would be limited to a lower top speed. That's why we have gearboxes and variators etc. With an electric motor though that has better torque at lower speed, you can often try to design for a compromise so that you don't need a gearbox and might not even need a gear ratio at all. I used SI units since you get extraneous confusing factors otherwise. Here's an example of a brushless motor power vs rpm. You can get maximum torque for your selected angular velocity by operating at the max motor power and using the right gearing. http://www.mcpappyracing.com/images/dyno/chart_power.jpg http://www.mcpappyracing.com/images/dyno/chart_power.jpg