Do not worry about driver and power supply. Both are protected from overload. Power supply should be higher in amps than driver or/and motor.

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well, you can let it spin at desired load and speed and check it if overheats and how fast. I guess you can use the sensors in your fingers for a balpark initial estimate. The motors are damaged by overheating because high currents and/or limited cooling, long before a higher-than-rated voltage will do other kind of damage.

How do you detect that saturation point? If you have a scope and measure the current through one of the motor windings in full step mode, you should see a gradually increasing current per pulse. When you reach saturation, current will rise much much faster towards the end of the pulse and instead a sawtooth you will see a sawtooth with steep spikes at the end.

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The temperature will rise in a normal way, almost linearly with increasing current. Until you reach the point where the iron stator gets magnetically saturated. This is the real maximum that you might be able to use.

Also, I am using a 1A H-Bridge, but the power supply is 2A. Will this damage the H bridge, or does it regulate the current?

jremington: Look in the data sheet for the continuous output current instead. The data sheet also discusses what happens if that current is exceeded.

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So the 2A power supply is better than the 800mA one I was using before? And won't damage it? Also, how could I measure how long the motor can handle 7.5 volts at? Like I said, the project is almost due and can only provide the power necessary to turn the disk at 7.5 volts.

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Thats why at 5V your system did not work: not enough current was allowed due to the high L or too short dt. Suddenly, from 7.5V on there was enough current allowed to be able to spin. But if you want to be in the optimal region, you need to find a good relation between voltage (that will dictate current for a given on-pulse) and the load. The more load on the shaft of the stepper, the more current you will need, so the higher voltage you need to apply.

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Ok, what would be considered a long time? Like, if its running for three hours at a time? Or if it runs 15 minutes at a time two to four times a day?

Stepper motors are current driven devices. In order to overcome DC winding resistance but more important the impedance of the windings due to their inductance, you will have to put some suitable voltage over it. The amount of tension needed depends on basically two factors:

No way, the power supply rated current is the max it can give. It's normal (and required) to be higher than the load will draw. A car battery can provide hundreds of amps, that doesnt mean it will burn an arduino board that draws 100mA. If it is powered through the right pins of course. The current is limited by the motor's resistance, and as I mentioned above, it is high enough to keep both the H-bridge and power supply within safe limits.

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jremington: The motor can be damaged by overheating, if operated above the rated voltage for a long time. Depends on the H-bridge.

At 5 volts (not coming from the arduino BTW, external supply) It cannot spin the disk that is required. At 6 volts, it is inconsistant. At 7.5 volts, it works like a charm. My question however is this; Will I damage the motor by running it at this speed for extended periods of time?

At 5 volts (not coming from the arduino BTW, external supply) It cannot spin the disk that is required. At 6 volts, it is inconsistant. At 7.5 volts, it works like a charm. My question however is this; Will I damage the motor by running it at this speed for extended periods of time? Also, I am using a 1A H-Bridge, but the power supply is 2A. Will this damage the H bridge, or does it regulate the current?

Look in the data sheet for the continuous output current instead. The data sheet also discusses what happens if that current is exceeded.