# Stepper motor control limits

One of the fundamental questions that arose during the control and testing of the SCARA arm was what is the maximum speed achievable and the torque available at that speed.

Some digging around in the world-wide-web revealed the following:

• The speed is limited by the torque availability from the stepper to rotate. For steppers, as the torque drops exponentially with speed, that places an upper limit on the speed we can run it at for a given load torque.
• Typical stepper pullout torque curve:

• Stepper motors are used for precise, open-loop positioning. The maximum speed is limited by the time it takes for the stepper coils to energize to its maximum holding current, and then de-energize as the polarity flips. (Reference from http://www.daycounter.com/Calculators/Stepper-Motor-Calculator.phtml)
• Current through the coil (I) is proportional to the time (T), the voltage has been applied (V) and inversely proportional to the inductance (L):$latex I= \frac{V*T}{L}$
• For one step the current must go from 0 to latex Imax and back to 0, or alternatively from -Imax to +Imax:

$latex I= 2*I_{max}$

$latex T= \frac{L*I_{max}*2}{V}$

where, T is the number of seconds for a single step.

• To compute maximum revolutions per second – divide seconds per step by steps per revolution.$latex \frac{rev}{sec} = \frac{V}{(\frac{L*2*Imax}{steps/rev})}$$latex P_{max}=2*I_{max}*V$
• Pmax does not occur when the motor is going max speed because the current is a triangle wave. Instead, it occurs when the slope of the current is small compared to the on holding time of the step pulse.
• This combined with the fact that as the number of micro-steps increases, the amount of torque available decreases exponentially, places an upper limit on how fast the motor can rotate.
• Some other references:
• If we try to push the input frequency higher, with the hope to rotate faster, once it goes beyond the limit it can handle, the motor stops rotating and “sings” (generates high frequency, harmonics which are audible)