Guarantor Financial Information (Condensed Consolidating Statements of Cash Flows) (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2018	Sep. 30, 2017	Dec. 31, 2017	Dec. 31, 2016
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	$ 946.4	$ 890.8
Net cash provided by (used in) discontinued operating activities	(49.0)	(17.6)
Net Cash Provided by (Used in) Operating Activities	897.4	873.2
Cash flows from investing activities:
Capital expenditures	(251.2)	(149.9)
Acquisitions and equity method investments, net of cash acquired	(281.5)	(60.3)
Proceeds from sale of property, plant and equipment		3.8
Proceeds from Equity Method Investment, Distribution	(12.1)
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0	0.0
Net cash provided by (used in) continuing investing activities	(520.6)	(206.4)
Cash flows from financing activities:
Net proceeds (repayments) in debt	(17.7)	11.6
Debt issuance costs	(12.0)	(0.2)
DividendsPaid	351.2	318.0
Dividends paid to noncontrolling interests	(41.1)	(15.5)
Payments to Noncontrolling Interests	0.0	(6.8)
Repurchase of ordinary shares	(514.1)	(911.1)
Other, net	31.8	40.7
Net proceeds (repayments) from debt	0.0	0.0
Net cash provided by (used in) continuing financing activities	(868.9)	(1,222.5)
Effect of exchange rate changes on cash and cash equivalents	(34.8)	100.0
Net increase (decrease) in cash and cash equivalents	(526.9)	(455.7)
Cash and cash equivalents	1,022.5	1,259.0	$ 1,549.4	$ 1,714.7
IR Ireland [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	97.2	82.7
Net cash provided by (used in) discontinued operating activities	0.0	0.0
Net Cash Provided by (Used in) Operating Activities	97.2	82.7
Cash flows from investing activities:
Capital expenditures	0.0	0.0
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	889.7	0.0
Net cash provided by (used in) continuing investing activities	889.7	0.0
Cash flows from financing activities:
Net proceeds (repayments) in debt	0.0	0.0
Debt issuance costs	0.0	0.0
DividendsPaid	351.2	318.0
Dividends paid to noncontrolling interests	0.0	0.0
Repurchase of ordinary shares	(514.1)	(911.1)
Other, net	36.3	41.9
Net proceeds (repayments) from debt	(157.9)	1,104.5
Net cash provided by (used in) continuing financing activities	(986.9)	(82.7)
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 International [Member]
Cash flows from investing activities:
Proceeds from Equity Method Investment, Distribution	0.0
IR Irish Holdings [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	(2.7)	0.0
Net cash provided by (used in) discontinued operating activities	0.0	0.0
Net Cash Provided by (Used in) Operating Activities	(2.7)	0.0
Cash flows from investing activities:
Capital expenditures	0.0	0.0
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	(648.3)	0.0
Net cash provided by (used in) continuing investing activities	(648.3)	0.0
Cash flows from financing activities:
Net proceeds (repayments) in debt	0.0	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) from debt	651.0	0.0
Net cash provided by (used in) continuing financing activities	651.0	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	17.5	(17.5)
Net cash provided by (used in) discontinued operating activities	0.0	0.0
Net Cash Provided by (Used in) Operating Activities	17.5	(17.5)
Cash flows from investing activities:
Capital expenditures	0.0	0.0
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	(4.0)
Payments for (Proceeds from) Businesses and Interest in Affiliates	501.0	1,170.9
Net cash provided by (used in) continuing investing activities	497.0	1,170.9
Cash flows from financing activities:
Net proceeds (repayments) in debt	0.0	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) from debt	(474.8)	(1,153.4)
Net cash provided by (used in) continuing financing activities	(474.8)	(1,153.4)
Effect of exchange rate changes on cash and cash equivalents	0.0	0.0
Net increase (decrease) in cash and cash equivalents	39.7	0.0
Cash and cash equivalents	40.3	0.0	0.6	0.0
IR Global [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	(116.4)	(214.2)
Net cash provided by (used in) discontinued operating activities	0.0	0.0
Net Cash Provided by (Used in) Operating Activities	(116.4)	(214.2)
Cash flows from investing activities:
Capital expenditures	0.0	0.0
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0	270.1
Net cash provided by (used in) continuing investing activities	0.0	270.1
Cash flows from financing activities:
Net proceeds (repayments) in debt	(31.6)	0.0
Debt issuance costs	(12.0)	(0.2)
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) from debt	96.8	(55.5)
Net cash provided by (used in) continuing financing activities	116.4	(55.7)
Effect of exchange rate changes on cash and cash equivalents	0.0	0.0
Net increase (decrease) in cash and cash equivalents	0.0	0.2
Cash and cash equivalents	0.0	0.2	0.0	0.0
IR New Jersey [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	791.7	228.1
Net cash provided by (used in) discontinued operating activities	(51.0)	(15.5)
Net Cash Provided by (Used in) Operating Activities	740.7	212.6
Cash flows from investing activities:
Capital expenditures	(69.0)	(59.8)
Acquisitions and equity method investments, net of cash acquired	0.0	(2.7)
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	(3.0)
Payments for (Proceeds from) Businesses and Interest in Affiliates	(1,205.7)	(347.0)
Net cash provided by (used in) continuing investing activities	(1,271.7)	(409.5)
Cash flows from financing activities:
Net proceeds (repayments) in debt	7.5	7.5
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	(1.2)	(1.2)
Net proceeds (repayments) from debt	434.9	35.8
Net cash provided by (used in) continuing financing activities	426.2	27.1
Effect of exchange rate changes on cash and cash equivalents	0.0	0.0
Net increase (decrease) in cash and cash equivalents	(104.8)	(169.8)
Cash and cash equivalents	254.5	464.8	359.3	634.6
IR Lux Finance [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	(24.7)	(23.9)
Net cash provided by (used in) discontinued operating activities	0.0	0.0
Net Cash Provided by (Used in) Operating Activities	(24.7)	(23.9)
Cash flows from investing activities:
Capital expenditures	0.0	0.0
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	0.0	11.7
Net cash provided by (used in) continuing investing activities	0.0	11.7
Cash flows from financing activities:
Net proceeds (repayments) in debt	0.0	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) from debt	24.7	12.2
Net cash provided by (used in) continuing financing activities	24.7	12.2
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
Other Subsidiaries [Member]
Condensed Financial Statements, Captions [Line Items]
Net cash provided by (used in) continuing operating activities	183.8	835.6
Net cash provided by (used in) discontinued operating activities	2.0	(2.1)
Net Cash Provided by (Used in) Operating Activities	185.8	833.5
Cash flows from investing activities:
Capital expenditures	(182.2)	(90.1)
Acquisitions and equity method investments, net of cash acquired	(281.5)	(57.6)
Proceeds from sale of property, plant and equipment		3.8
Proceeds from Equity Method Investment, Distribution	(13.1)
Payments for (Proceeds from) Businesses and Interest in Affiliates	636.4	56.2
Net cash provided by (used in) continuing investing activities	185.8	(87.7)
Cash flows from financing activities:
Net proceeds (repayments) in debt	6.4	4.1
Debt issuance costs	0.0	0.0
DividendsPaid	0.0	0.0
Dividends paid to noncontrolling interests	(41.1)	(15.5)
Repurchase of ordinary shares	0.0	0.0
Other, net	(3.3)	0.0
Net proceeds (repayments) from debt	(747.8)	(1,105.5)
Net cash provided by (used in) continuing financing activities	(798.6)	(1,131.9)
Effect of exchange rate changes on cash and cash equivalents	(34.8)	100.0
Net increase (decrease) in cash and cash equivalents	(461.8)	(286.1)
Cash and cash equivalents	727.7	794.0	1,189.5	1,080.1
Consolidation, Eliminations [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
Acquisitions and equity method investments, net of cash acquired	0.0	0.0
Proceeds from sale of property, plant and equipment		0.0
Proceeds from Equity Method Investment, Distribution	0.0
Payments for (Proceeds from) Businesses and Interest in Affiliates	(173.1)	(1,161.9)
Net cash provided by (used in) continuing investing activities	(173.1)	(1,161.9)
Cash flows from financing activities:
Net proceeds (repayments) in debt	0.0	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) from debt	173.1	1,161.9
Net cash provided by (used in) continuing financing activities	173.1	1,161.9
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