I have a stepper motor and it is rated at 2 amps per phase. I also have a stepper driver which is rated at 750 miliamps per phase. To make matters worse I have a wall wart power supply rated as 9V @ 650miliamps. That power is converted by a voltage regulator PCB down to a usable 3.3 V at an unknown amperage.
My question is, what effect will underpowering the motor have?
Will it affect the speed of the motor or just holding torque?
Running a stepper motor at under its rated current will affect both its maximum speed and torque (both holding and dynamic), though depending on the driver type, it mostly affects the torque.
Firstly, The stepper motor driver you are linking requires power rails of 7-30V. Its logic interface is 5 or 3.3v.
Furthermore, your stepper motor is 3.6 ohms per winding, so even with 3.3V rails, your motors are going to pull ~900 ma, which will cause power rail brownouts.
Fortunately, in this context, the stepper motor controller IC provides chopped current limiting, which is a technique which limits the maximum amount of current it runs through the stepper motor. Therefore, you can run the stepper motor you have off the wall-wart you have, a the cost of reduced torque.
In a system which uses current chopping, the voltage largely determines the motors maximum speed, and the current the torque. There is interactions, but they are fairly small in effect size (assuming you are not at extremely low voltage or current), proportionate to the effect of changing the relevant characteristic directly.
I urge you to carefully study the A3967 datasheet (the A3967 is the stepper motor IC the linked driver uses).
Furthermore, the designer of that stepper motor driver provides a fairly decent introduction into the concepts of how the device works here, which, from your question, I don't think you have really read. You should carefully read it before you hook anything up, lest you damage one of your parts.
Additionally, the stepper motor driver you link already has a voltage regulator, so you do not even need the voltage regulator you included in your post (SFE sku: PRT-00114).
See the schematic for the Stepper Driver Here. The voltage regulator is IC2.
According to the product page, it uses an LM317, which has a output rated at 1.5A. Since your total power input is 9V * 0.65A, hopefully when it is regulated down to 3.3V you will get the maximum current.
Driving this stepper with 3.3v will definitely have an effect on your holding torque. I'd expect it to adversely affect the speed of the motor under load as well.
