It's not that common for Western Bands to make it in Japan, even popular ones. Some of them did though. Here are 20 examples of those bands.
(Bands listed in alphabetical order. Under each band's picture, their most successful album and most successful single in Japanese charts, are listed.)
1) Asia
Alpha (1983) #4
No Data.
2) Bon Jovi
These Days (1995) #1
No Data. (Although Bon Jovi's singles sold very well in Japan)
3) Cheap Trick
Dream Police (1979) #4
I Want You To Want Me (1977) #1
4) Danger Danger
Screw It! (1991) #67
No Data.
5) Hanoi Rocks
I couldn’t find anything particular about charts, but the band is very popular in Japan, to the point they released albums/singles exclusively for Japan.
6) Helloween
Master Of The Rings (1994) #6
I Don't Wanna Cry Anymore (1993) #1 (Apart from it, they had seven other #1 hits in Japan)
7) Iron Maiden
The Final Frontier (2010) #5
No Data.
8. Journey
Frontiers (1983) #3
Who's Crying Now (1981) #4
9) Men At Work
Business As Usual (1981) #3
No Data.
10) Mr. Big
Hey Man (1996) #1
No Data. (It appears To Be With You didn’t chart, something that’s really bizarre because this band was really big in Japan.)
11) Mr. Mister
Welcome To The Real World (1985) #17
No Data.
12) Quiet Riot
Even though I couldn’t find something particular, the band had success in Japan, since their first two albums released there exclusively, and they did some live shows in Japan as well.
13) Rage
No info about charting positions, but the band was fairly popular in Japan during the 90s especially.
14) Rainbow
Down To Earth (1979) #90
No Data.
15) Scorpions
Crazy World (1990) #39
No Data.
16) Skid Row (US)
Slave To The Grind (1991) #3
No Data.
17) Supertramp
Breakfast In America (1979) #2
No Data.
18. Survivor
No Data.
Eye Of The Tiger (1982) #1
19) Toto
Isolation (1984) #2
2 Hearts (1992) #1
20) Whitesnake 
Whitesnake (1987) #19
No Data.
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