sizzling is right. Need to know make and model to be sure.
With that said, your CPU is an 84w part, your other components will prob draw only 100-120w and the 1070 will draw about 150w at full pelt, unless you overclock. So your talking about 350-400w max.
Sizzling is saying that if it's a poor quality unit (PSU) then it's prob not providing the power it's rated for, and if it's an old PSU it will lose some of it's efficiency and may cause issues.
An additional point though, the 1070 is a bit too powerful for your CPU. The CPU will bottleneck a little I suspect. What res are you gaming on? 1080p @60hz? If so, save some money, get a GTX1060 or an RX580 and get an extra 8gbs of memory. That will serve you better than the 1070, which won't reach it's full potential with the low-ish clocks of the I5 4460. Just a thought to consider.
If you're going to get a high end GPU like the 1070, then you want to have a decent PSU. I wouldn't want to be risking expensive parts with a PSU thats gonna crap out.