Will this exhaust fan still work fine?

Hi, my exhaust fan keeps making loud noise for about 2 weeks and i tried to get the fan out but the small cover in the middle is broken and i think that makes the exhaust fan noises. Will this still work fine without the cover?? Or should i just buy a new one? Help me pls :((

Hi, my exhaust fan keeps making loud noise for about 2 weeks and i tried to get the fan out but the small cover in the middle is broken and i think that makes the exhaust fan noises. Will this still work fine without the cover?? Or should i just buy a new one? Help me pls :((