Electronic – Stepper motor torque constant and electrical constant

If speed and acceleration aren't a problem, then there are two other mechanical performance issues you need to get right. One is the torque. You should measure the amount of torque required to turn the dials on your lathe while making its deepest cut into steel. You're a mechanical engineer, I'll leave you to think of a way to measure it.

Take a look at the datasheets for the stepper motors you are considering, and they should have a speed / torque graph:

You can see that this motor's torque just about peaks at 0.8Nm. But at this torque, it can barely move. Obviously you wouldn't use this motor for any torque duty above about 0.5Nm. Select a motor which has plenty of torque.

The other issue is the resolution you need. Again, it's up to you to decide what resolution you need, and what your lathe is really cable of. Stepper motors are typically 200 or 400 steps per revolution.

If 1" takes 8s, and the motor is rotating at 0.8RPS, then one revolution gives 0.156" travel (is this a metric lathe?). For a 200 step motor, each step gives 0.78 thou travel. That's pretty good actually. If you used a microstepping motor driver, that will essentially increase the resolution. You should do this anyway, even if you don't want the extra resolution. The microstepping will prevent the motor suffering from the resonance that happens at certain speeds.

You don't say it, but your problem may be that you're trying to start the stepper at full speed. If so, there is a maximum speed (which varies somewhat with load) beyond which a stepper will not accelerate, and this speed is normally well below what you can reach with a gradual increase in speed. Google on "stepper motor torque curve".

The problem is that, with a 4-phase stepper such as you are using, if the shaft angle lags more than 2 step angles behind the commanded angle, the torque reverses and the motor sits and vibrates and makes horrible noises. This is not, technically speaking, a stall condition, where the shaft does not move at all.

The torque-speed curve for your motor can be found at http://www.kelinginc.net/KL34H2120-42-8AT.pdf and indicates that the motor can be run at 5000 steps/second, which suggests that your problem is your attempt at fast start.

If, on the other hand, you've already tried a slowly increasing step rate while running, then you probably do need a heftier motor. However, my calculations for a .144 hp motor at 10 rps gives about 2 Nm torque, and the linked torque curve for your stepper is about the same, so I wouldn't expect a problem. Unless, of course, you've modified your mechanical setup somehow.