The Panthers have won the NFC South the past two seasons, but only have one postseason victory to show for it.
Davis, an outside linebacker and the longest-tenured player on Carolina's roster, said Tillman can help change that given the experience and play-making ability he brings to the secondary.
''He is that piece that is missing on defense that can put us over the top,'' Davis said Monday as the team's offseason conditioning program got underway.
Carolina's secondary has been the defense's weak link since coach Ron Rivera's arrival in 2011.
Still, the Panthers finished in the top 10 on defense for the third straight year in 2014 despite allowing at least 28 points in seven of their first 12 games.
Tillman, who signed with Carolina as a free agent on April 9 following 12 seasons in Chicago, has started 152 career games and leads active defensive backs with 41 forced fumbles, is fourth in interceptions (36) and second with interception returns for touchdowns (eight). However, triceps injuries have limited him to 10 games the past two seasons.
''When you see what the guy has been able to do, not only making interceptions but to cause the fumbles that he has, it's unbelievable to know that a guy can do that. ... on a consistent level,'' Davis said.
Linebacker Luke Kuechly agrees with Davis' assessment of Tillman.
''Absolutely,'' Kuechly said, ''He brings experience and leadership. The guy has made a lot of plays and he's been around a while. He's seen everything.''
And he's familiar with the defense.
Tillman played for Rivera and current secondary coach Steve Wilks while with the Bears.
''He understands them and they understand him,'' Kuechly said. ''That will give him a leg up.''
He's one of several free agent pickups on defense.
The Panthers also signed linebacker Jason Trusnik, safety Kurt Coleman and cornerback Teddy Williams to low-risk contracts, in addition to re-signing veteran defensive tackles Colin Cole and Dwan Edwards.
''I think we had made some good additions,'' Kuechly said. ''I'm excited to meet all of these guys and see what we're all about.''
Said Davis: ''With this group, the sky is the limit.''
Hardy tied a franchise record with 15 sacks in 2013, but played only one game last season following his conviction on domestic abuse charges. Hardy appealed and the charges were dismissed in February when the accuser could not be located to testify.
The NFL is still investigating the matter and Hardy remains on the commissioner's exempt list.
''I hope he's not that good and it don't really work out for Dallas,'' Davis joked. ''But I know Hardy and I know what kind of player he is. He's going to go in and he's going to work his butt off. He's definitely going to make that defense better.''
Kuechly, the 2013 NFL Defensive MVP, and Davis are up for new contracts, and both expressed their desire to remain in Carolina on Monday.
However, both said their focus is on the season ahead and will let their agents handle the business side.
''I'm not worried about that,'' Kuechly said. ''I'm just excited to be here and run around and play football.''
Cam Newton, who is entering the final year of his contract, participated in offseason workouts on Monday, according to teammates. However, the fifth-year quarterback was not made available for interviews.
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