Subsidiary Guarantors of the Public Bonds (Consolidated Condensed Statements of Cash Flow) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2016	Jan. 03, 2015	Dec. 28, 2013
Condensed Cash Flow Statements, Captions [Line Items]
Net cash provided by (used in) operating activities	$ 215.5	$ 314.6	$ 202.3
INVESTING ACTIVITIES
Additions to property, plant and equipment	(46.4)	(30.0)	(41.7)
Proceeds from sales of property, plant and equipment	0.0	0.0	2.8
Investments in joint ventures	0.0	(1.1)	(2.5)
Other	(3.6)	(3.7)	(3.3)
Net cash used in investing activities	(50.0)	(34.8)	(44.7)
FINANCING ACTIVITIES
Borrowings of long-term debt	450.0	0.0	775.0
Payments on long-term debt	(530.9)	(249.8)	(875.0)
Payments of debt issuance costs	(2.4)	0.0	(2.3)
Cash dividends paid	(24.4)	(24.0)	(23.7)
Purchase of common stock for treasury	(92.6)	0.0	0.0
Purchases of shares under employee stock plans	(7.7)	(10.5)	(0.8)
Proceeds from the exercise of stock options	13.3	7.3	8.6
Excess tax benefits from stock-based compensation	4.9	5.6	3.4
Contributions from noncontrolling interest	2.5	1.0	2.0
Net cash (used in) provided by in financing activities	(187.3)	(270.4)	(112.8)
Effect of foreign exchange rate changes	(7.9)	0.2	(2.0)
Increase (decrease) in cash and cash equivalents	(29.7)	9.6	42.8
Cash and cash equivalents at beginning of the year	223.8	214.2	171.4
Cash and cash equivalents at end of the year	194.1	223.8	214.2
Parent [Member]
Condensed Cash Flow Statements, Captions [Line Items]
Net cash provided by (used in) operating activities	221.2	274.1	127.1
INVESTING ACTIVITIES
Additions to property, plant and equipment	(15.9)	(7.7)	(11.9)
Other	0.3	(2.4)	(2.9)
Net cash used in investing activities	(15.6)	(10.1)	(14.8)
FINANCING ACTIVITIES
Borrowings of long-term debt	450.0		775.0
Payments on long-term debt	(530.9)	(249.8)	(875.0)
Payments of debt issuance costs	(2.4)		(2.3)
Cash dividends paid	(24.4)	(24.0)	(23.7)
Purchase of common stock for treasury	(92.6)
Purchases of shares under employee stock plans	(7.7)	(10.5)	(0.8)
Proceeds from the exercise of stock options	13.3	7.3	8.6
Excess tax benefits from stock-based compensation	4.9	5.6	3.4
Contributions from noncontrolling interest	0.0	0.0	0.0
Net cash (used in) provided by in financing activities	(189.8)	(271.4)	(114.8)
Effect of foreign exchange rate changes			0.0
Increase (decrease) in cash and cash equivalents	15.8	(7.4)	(2.5)
Cash and cash equivalents at beginning of the year	11.4	18.8	21.3
Cash and cash equivalents at end of the year	27.2	11.4	18.8
Subsidiary Guarantors [Member]
Condensed Cash Flow Statements, Captions [Line Items]
Net cash provided by (used in) operating activities	24.3	9.1	(10.0)
INVESTING ACTIVITIES
Additions to property, plant and equipment	(21.1)	(19.6)	(25.0)
Proceeds from sales of property, plant and equipment			2.8
Other	(3.9)	(1.2)	(1.3)
Net cash used in investing activities	(25.0)	(20.8)	(23.5)
FINANCING ACTIVITIES
Borrowings of long-term debt	0.0		0.0
Payments of debt issuance costs	0.0		0.0
Purchase of common stock for treasury	0.0
Contributions from noncontrolling interest	0.0	0.0	0.0
Net cash (used in) provided by in financing activities	0.0	0.0	0.0
Effect of foreign exchange rate changes			0.0
Increase (decrease) in cash and cash equivalents	(0.7)	(11.7)	(33.5)
Cash and cash equivalents at beginning of the year	3.3	15.0	48.5
Cash and cash equivalents at end of the year	2.6	3.3	15.0
Non-Guarantor Subsidiaries [Member]
Condensed Cash Flow Statements, Captions [Line Items]
Net cash provided by (used in) operating activities	(30.0)	31.4	85.2
INVESTING ACTIVITIES
Additions to property, plant and equipment	(9.4)	(2.7)	(4.8)
Investments in joint ventures		(1.1)	(2.5)
Other		(0.1)	0.9
Net cash used in investing activities	(9.4)	(3.9)	(6.4)
FINANCING ACTIVITIES
Borrowings of long-term debt	0.0		0.0
Payments of debt issuance costs	0.0		0.0
Purchase of common stock for treasury	0.0
Contributions from noncontrolling interest	2.5	1.0	2.0
Net cash (used in) provided by in financing activities	2.5	1.0	2.0
Effect of foreign exchange rate changes	(7.9)	0.2	(2.0)
Increase (decrease) in cash and cash equivalents	(44.8)	28.7	78.8
Cash and cash equivalents at beginning of the year	209.1	180.4	101.6
Cash and cash equivalents at end of the year	164.3	209.1	180.4
Eliminations [Member]
Condensed Cash Flow Statements, Captions [Line Items]
Net cash provided by (used in) operating activities			0.0
INVESTING ACTIVITIES
Proceeds from sales of property, plant and equipment			0.0
Net cash used in investing activities			0.0
FINANCING ACTIVITIES
Net cash (used in) provided by in financing activities			0.0
Effect of foreign exchange rate changes			0.0
Increase (decrease) in cash and cash equivalents			0.0
Cash and cash equivalents at beginning of the year	0.0	0.0	0.0
Cash and cash equivalents at end of the year	$ 0.0	$ 0.0	$ 0.0