# Stepper motor current/torque model

• liquidFuzz
In summary, the conversation discusses setting up an expression for the current in a stepper motor coil, which resembles a trapezoid in the time domain. The speaker is trying to figure out how to model the torque behavior for different RPS, and their idea is to integrate over time to get the whole pulse. However, they are not interested in the charge, so they plan to divide the result with the pulse length to get an average current. The speaker also mentions that the current can be capped by altering the PWM ON cycle, and they want to find the PWM with the highest ON width. They then ask about the factors that determine the rise and fall time of the current pulse, as well as the limitations of the resistance and PWM.

#### liquidFuzz

TL;DR Summary
Is it possible to model torque based on current in coils?
I've set up an expression for the current in a stepper motor coil. Each current pulse resembles a trapezoid in the time domain. Now I'm trying to figure out how to best use this to model the torque behavior for different RPS. My ide was to integrate over time to get the whole pulse

$$\int_{t0}^{t1} i_1(t) dt + \int_{t1}^{t2} i_2(t) dt + \int_{t2}^{t3} i_3(t) dt$$

However I'm not interested in the charge, I*t. Thus I figured I could divide the result with pulse length of the longest pulse possible, i.e. a pulse at low RPS, thus getting a average current for a pulse at different RPS. Does this make any sense..?

Edit, one more thing, the current is capped by altering the pwm ON cycle in the duty cycle. This made me think I should try to find the pwm with the highest ON with of the pwm signal.

liquidFuzz said:
I've set up an expression for the current in a stepper motor coil. Each current pulse resembles a trapezoid in the time domain.
Does the voltage and inductance of the winding decide the rise and fall time of the current pulse ?
Does the resistance of the winding limit the current, or is that done only by PWM.

The motor torque is the product of the current and the magnetic field from the poles.
Is the permanent magnetic field of the rotor also a trapezoidal profile ?
How does the wound stator magnetic field profile react with the rotor PM pole profile ?

Does RPS mean Radians or Revolutions Per Second, or should it be poles/second ?