Arduino and tm1637 voltage

Hello ive got a problem and im losing my patience if i connect arduino to 9v battery after 1 or 2min tm1637 stops working properly if connect it to 4.5v battery back tm1637 doesnt even turn on what to do?

The clear blunder is not comprehending what the "Vin" or "RAW" terminal is. The regulator on the Arduino UNO/ Nano/ Pro Mini/ Mega2560/ Leonardo/ Pro Micro has very little heatsink, so will not pass very much current (depending on the input voltage and thus, how much voltage it has to drop) before it overheats and (hopefully reversibly) shuts down. It is essentially a novelty provided in the very beginning of the Arduino project when "9V" power packs were common and this was a practical way to power a lone Arduino board for initial demonstration purposes. And even then it was limited because an unloaded 9 V transformer-rectifier-capacitor supply would generally provide over 12 V which the regulator could barely handle.

Nowadays, 5 V regulated switchmode packs are arguably the most readily available in the form of "Phone chargers" and switchmode "buck" regulators are cheap on eBay so these can be fed into the USB connector or 5 V pin to provide adequate power for most applications. Unfortunately, many tutorials or "instructables" are seriously outdated or misleading and have not been updated to reflect the contemporary situation.

If powering from batteries, as long as the battery pack cannot exceed 5.5 V, this must be connected to the 5 V pin.

I have both 10 and 12 volt wall warts that I use to power my Arduino, and when embedding them I use about 7.5 to 8.5 volts on the Vin terminal. Reason for this is it gives me additional protection, does wonders with A/D stability, additional filtering, over load protection, etc. I have seen the 5V chargers go up to about 6.5 volts and some are not well regulated. If I supply the 5V directly and something glitches on the board the possibility of blasting the processor is there. I normally do not power from the arduino especially if using the A/D. This response is to help you get started in solving your problem, not solve it for you.
Good Luck & Have Fun!
Gil