* Federer improves to 7-0 against Kohlschreiber
* Swiss chases sixth Cincinnati title
* Ferrer battles to three-set win over Harrison (Adds late matches)
CINCINNATI, Aug 13 (Reuters) - Roger Federer got his delayed hardcourt season off to a positive start with straightforward 6-3 7-6 (7) win over Germany's Phillip Kohlschreiber to ease into the third round of the Western and Southern Open on Tuesday.
Struggling with a sore back, Federer did not play last week's event in Montreal and has not tested himself on the North American hardcourt since Indian Wells in March.
But the former-world number one signaled that he is ready to challenge for an unprecedented sixth Cincinnati title and then perhaps a sixth U.S. Open to add to his grand slam collection.
"It was important to play a clean match," Federer told reporters. "I had a few tough weeks, months behind me, I was happy to play a clean match.
"I told myself I was not going to come back until I felt no pain in my back. Eventually I started to workout very hard
"It is a tournament I have always played in lead up to the U.S. Open, I like it here. I love the calmness of this place."
It has been far from a vintage season for Federer, who has seen his world ranking dip to number five and haul of titles stuck at one.
Federer arrives in the United States off a particular rough patch of form, losing in the second round at Wimbledon and then dropping his opening match at his home tournament in Gstaad.
However, the Swiss maestro was all business on an unusually chilly Ohio night, running his record against Kohlschreiber to 7-0.
Milos Raonic, who became the first Canadian to crack the top 10 of the world rankings after reaching the final in Montreal, struggled at first to adjust to his new status before storming back to take a 3-6 6-4 6-3 victory over American Jack Sock.
Earlier, third seeded Spaniard David Ferrer was forced to work for his spot in the last 16, grinding out a 7-6 (5) 3-6 6-4 win over plucky American wildcard Ryan Harrison.
Harrison, who learned before the match that he had been given a wild card entry into the U.S. Open, almost celebrated his trip to Flushing Meadows with an upset, battling the feisty Ferrer for two hours and 42 minutes on a blustery centre court.
Ferrer would have been prepared for a fight, having needed five sets to stop Harrison in the second round of Wimbledon in 2011 and the young American did not disappoint the home crowd, forcing the first set to a tiebreak before falling 7-5.
"Just wish I would have served a little better," Harrison lamented. "Obviously, I had some chances.
"I feel like my game is obviously right there on the brink of playing those top guys. That's kind of where you want it.
"Obviously, it would have been great to get a win today but I know that going in, if I compete the way I can and play the way I'm capable of, I'm going to be able to challenge just about anybody."
Ninth seed Swiss Stanislas Wawrinka enjoyed a smooth passage into the second round with a 6-3 6-4 win over Italy's Andreas Seppi, while evergreen German 11th seed Tommy Haas advanced with a no-fuss 6-4 6-4 decision over South African Kevin Anderson.
Spain's Feliciano Lopez upset Japanese 10th seed Kei Nishikori 6-4 7-6 (4) and 15th seed Gilles Simon of France retired with a hip strain while trailing Canadian Vasek Pospisil 6-3 1-1. (Editing by John O'Brien)