Retirement benefits - Retirement Cost (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jun. 30, 2018	Jun. 30, 2017	Jun. 30, 2018	Jun. 30, 2017
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	$ 2.6	$ 2.8	$ 5.6	$ 5.7
Interest cost on projected benefit obligation	11.3	13.1	23.3	26.7
Return on assets – expected	(16.2)	(15.7)	(32.5)	(31.4)
Amortization of losses	7.9	7.4	16.3	15.0
Amortization of prior service cost	0.0	0.2	0.2	0.4
Settlement loss	0.5	0.5	1.0	0.8
Net periodic pension cost	6.1	8.3	13.9	17.2
Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	0.1	0.1	0.1	0.1
Interest cost on projected benefit obligation	5.1	5.5	10.3	10.6
Return on assets – expected	(4.2)	(4.1)	(8.4)	(8.3)
Amortization of losses	6.5	6.1	13.2	11.4
Amortization of prior service cost	(0.9)	(0.9)	(1.7)	(1.5)
Net periodic pension cost	6.6	6.7	13.5	12.3
U.S. Plans | Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	0.0	0.0	0.0	0.0
Interest cost on projected benefit obligation	8.0	8.8	16.0	17.6
Return on assets – expected	(13.4)	(13.3)	(26.8)	(26.6)
Amortization of losses	6.9	6.1	14.0	12.4
Amortization of prior service cost	0.0	0.0	0.0	0.0
Settlement loss	0.0	0.0	0.0	0.0
Net periodic pension cost	1.5	1.6	3.2	3.4
Non-U.S. Plans | Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	2.6	2.8	5.6	5.7
Interest cost on projected benefit obligation	3.3	4.3	7.3	9.1
Return on assets – expected	(2.8)	(2.4)	(5.7)	(4.8)
Amortization of losses	1.0	1.3	2.3	2.6
Amortization of prior service cost	0.0	0.2	0.2	0.4
Settlement loss	0.5	0.5	1.0	0.8
Net periodic pension cost	4.6	6.7	10.7	13.8
UMWA Plans | Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.0	0.0
Interest cost on projected benefit obligation	4.2	4.7	8.7	9.1
Return on assets – expected	(4.2)	(4.1)	(8.4)	(8.3)
Amortization of losses	5.0	5.0	10.5	9.4
Amortization of prior service cost	(1.2)	(1.2)	(2.3)	(2.3)
Net periodic pension cost	3.8	4.4	8.5	7.9
Black Lung and Other Plans | Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	0.1	0.1	0.1	0.1
Interest cost on projected benefit obligation	0.9	0.8	1.6	1.5
Return on assets – expected	0.0	0.0	0.0	0.0
Amortization of losses	1.5	1.1	2.7	2.0
Amortization of prior service cost	0.3	0.3	0.6	0.8
Net periodic pension cost	$ 2.8	$ 2.3	$ 5.0	$ 4.4