My DC brushed motor is rated 4.5V-15V. My application requires the motor to spin with different speeds so I am using PWM to regulated the it. I will be supplying the motor with a 12V battery and using Arduino and a motor driver to regulate the motor. I am not sure what does this voltage range in the specification of the motor mean. Does this mean that regardless of the duty cycle it will be OK since I am using 12V battery? Or does that mean that the average voltage (e.g. 25% duty cycle, that means average 3V) needs to be inside 4.5V-15V? I think that since the battery is 12V, its ok because the voltage on the motor is going to be 12V(when ON) and 0V (when OFF), but I am not 100% sure and I need to be :) And one more thing. Is the PWM from the Arduino (490Hz) that controls the motor driver the same as the PWM frequency of the motor driver that controls the motor? (490Hz seems kind of low to me)
Motors have so many "characteristics" the boilerplate values are very vague.
Min voltage is usually required to get it going.
Max voltage is the max you should apply to a starting or locked rotor motor to keep it from burning out. (Though the latter is not always true.)
However, that's just the numbers they have to give you. They are almost always based on the simple "Apply voltage and go" control model.
The truth is, when properly controlled you can use MUCH larger and smaller voltages assuming...
You do not apply a voltage large enough to break through the insulation and or arc out.
You do not supply enough current to demagnetize or magnetize the motor or burn out any internal wires or insulation.
You do not overheat the motor.
Having said that, Over-rating a motor will void it's warranty, and may significantly decrease the life of the motor. The latter is especially true with brushed motors.
In your particular application the max you can ever supply to the motor is 12V which is well inside the motor rating so you are good to go.