Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2017	Jun. 30, 2016	Mar. 31, 2016	Dec. 31, 2016	Dec. 31, 2015
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	$ (33.3)		$ (0.9)
Net cash provided by (used in) discontinued operating activities	(10.1)		(6.7)
Net Cash Provided by (Used in) Operating Activities	(43.4)		(7.6)
Cash flows from investing activities:
Capital expenditures	(35.2)		(40.1)
Acquisition of businesses, net of cash acquired	(9.8)		0.0
Proceeds from sale of property, plant and equipment	0.4		0.0
Proceeds from Sale of Equity Method Investments		$ 423.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0		0.0
Net cash provided by (used in) continuing investing activities	(44.6)		(40.1)
Cash flows from financing activities:
Net proceeds (repayments) in debt			(254.0)
Debt issuance costs	(0.2)		(2.1)
DividendsPaid	102.7		82.2
Dividends paid to noncontrolling interests	(6.9)		(6.7)
Repurchase of ordinary shares	(250.1)		(250.1)
Other, net	18.4		(11.1)
Net proceeds (repayments) in debt	0.0		0.0
Net cash provided by (used in) continuing financing activities	(341.5)		(98.2)
Effect of exchange rate changes on cash and cash equivalents	37.3		22.0
Net increase (decrease) in cash and cash equivalents	(392.2)		(123.9)
Cash and cash equivalents	1,322.5		612.9	$ 1,714.7	$ 736.8
IR Ireland [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	21.6		17.3
Net cash provided by (used in) discontinued operating activities	0.0		0.0
Net Cash Provided by (Used in) Operating Activities	21.6		17.3
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0		0.0
Net cash provided by (used in) continuing investing activities	0.0		0.0
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	102.7		82.2
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	(250.1)		(250.1)
Other, net	16.6		(11.1)
Net proceeds (repayments) in debt	314.7		326.1
Net cash provided by (used in) continuing financing activities	(21.5)		(17.3)
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.1		0.0
Cash and cash equivalents	0.1		0.0	0.0	0.0
IR Irish Holdings [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	0.0		0.0
Net cash provided by (used in) discontinued operating activities	0.0		0.0
Net Cash Provided by (Used in) Operating Activities	0.0		0.0
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0		0.0
Net cash provided by (used in) continuing investing activities	0.0		0.0
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	0.0		0.0
Net cash provided by (used in) continuing financing activities	0.0		0.0
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.0		0.0
Cash and cash equivalents	0.0		0.0	0.0	0.0
IR Lux International [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	0.0		(0.1)
Net cash provided by (used in) discontinued operating activities	0.0		0.0
Net Cash Provided by (Used in) Operating Activities	0.0		(0.1)
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	1,153.2		(3.3)
Net cash provided by (used in) continuing investing activities	1,153.2		(3.3)
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	(1,153.2)		3.4
Net cash provided by (used in) continuing financing activities	(1,153.2)		3.4
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.0		0.0
Cash and cash equivalents	0.0		0.0	0.0	0.0
IR Global [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	(72.6)		(67.6)
Net cash provided by (used in) discontinued operating activities	0.0		0.0
Net Cash Provided by (Used in) Operating Activities	(72.6)		(67.6)
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	72.8		(381.5)
Net cash provided by (used in) continuing investing activities	72.8		(381.5)
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	(0.2)		(2.1)
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	0.0		440.2
Net cash provided by (used in) continuing financing activities	(0.2)		438.1
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.0		(11.0)
Cash and cash equivalents	0.0		0.4	0.0	11.4
IR New Jersey [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	27.3		(11.7)
Net cash provided by (used in) discontinued operating activities	(17.8)		(4.7)
Net Cash Provided by (Used in) Operating Activities	9.5		(16.4)
Cash flows from investing activities:
Capital expenditures	(10.5)		(18.2)
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0		65.7
Net cash provided by (used in) continuing investing activities	(10.5)		47.5
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	(69.7)		(31.1)
Net cash provided by (used in) continuing financing activities	(69.7)		(31.1)
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	(70.7)		0.0
Cash and cash equivalents	563.9		0.0	634.6	0.0
IR Lux Finance [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	0.0		(1.0)
Net cash provided by (used in) discontinued operating activities	0.0		0.0
Net Cash Provided by (Used in) Operating Activities	0.0		(1.0)
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	11.6		0.0
Net cash provided by (used in) continuing investing activities	11.6		0.0
Cash flows from financing activities:
Net proceeds (repayments) in debt			(254.0)
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	(11.6)		(253.0)
Net cash provided by (used in) continuing financing activities	(11.6)		1.0
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.0		0.0
Cash and cash equivalents	0.0		0.1	0.0	0.1
Other Subsidiaries [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	(9.6)		60.3
Net cash provided by (used in) discontinued operating activities	7.7		0.0
Net Cash Provided by (Used in) Operating Activities	(1.9)		60.3
Cash flows from investing activities:
Capital expenditures	(24.7)		(21.9)
Acquisition of businesses, net of cash acquired	(9.8)
Proceeds from sale of property, plant and equipment	0.4
Payments for (Proceeds from) Businesses and Interest in Affiliates	919.7		(485.6)
Net cash provided by (used in) continuing investing activities	885.6		(507.5)
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	(6.9)		(6.7)
Repurchase of ordinary shares	0.0		0.0
Other, net	1.8		0.0
Net proceeds (repayments) in debt	(1,237.5)		319.0
Net cash provided by (used in) continuing financing activities	(1,242.6)		312.3
Effect of exchange rate changes on cash and cash equivalents	37.3		22.0
Net increase (decrease) in cash and cash equivalents	(321.6)		(112.9)
Cash and cash equivalents	758.5		612.4	1,080.1	725.3
Consolidation, Eliminations [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	0.0		1.9
Net cash provided by (used in) discontinued operating activities	0.0		(2.0)
Net Cash Provided by (Used in) Operating Activities	0.0		(0.1)
Cash flows from investing activities:
Capital expenditures	0.0		0.0
Acquisition of businesses, net of cash acquired	0.0
Proceeds from sale of property, plant and equipment	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	(2,157.3)		804.7
Net cash provided by (used in) continuing investing activities	(2,157.3)		804.7
Cash flows from financing activities:
Net proceeds (repayments) in debt			0.0
Debt issuance costs	0.0		0.0
DividendsPaid	0.0		0.0
Dividends paid to noncontrolling interests	0.0		0.0
Repurchase of ordinary shares	0.0		0.0
Other, net	0.0		0.0
Net proceeds (repayments) in debt	2,157.3		(804.6)
Net cash provided by (used in) continuing financing activities	2,157.3		(804.6)
Effect of exchange rate changes on cash and cash equivalents	0.0		0.0
Net increase (decrease) in cash and cash equivalents	0.0		0.0
Cash and cash equivalents	$ 0.0		$ 0.0	$ 0.0	$ 0.0