Acquisitions - 2021 Acquisition Additional Information (Details)		3 Months Ended		4 Months Ended	6 Months Ended	12 Months Ended
	Aug. 23, 2021 USD ($)	Jan. 01, 2022 USD ($)	Oct. 02, 2021 USD ($) facility	Jan. 01, 2022 USD ($)	Jan. 01, 2022 USD ($)	Jan. 01, 2022 USD ($)	Jan. 02, 2021 USD ($)	Dec. 28, 2019 USD ($)
Business Acquisition [Line Items]
Goodwill		$ 396,887,000		$ 396,887,000	$ 396,887,000	$ 396,887,000	$ 351,753,000	$ 336,032,000
Acquisition related costs						3,655,000	485,000	843,000
Payments to acquire businesses, net of cash acquired						143,981,000	$ 7,095,000	$ 177,798,000
Clouth
Business Acquisition [Line Items]
Consideration transferred			$ 92,864,000
Goodwill			25,806,000
Goodwill, expected tax deductible amount			6,836,000
Intangible assets other than goodwill acquired			34,467,000
Intangible assets other than goodwill, expected tax deductible amount			$ 5,326,000
Revenue from the date of acquisition					23,221,000
Operating income (loss) from date of acquisition					(4,068,000)
Amortization expense					3,481,000
Acquisition related costs					2,710,000
Clouth | Germany
Business Acquisition [Line Items]
Number of manufacturing facilities | facility			3
Clouth | Poland
Business Acquisition [Line Items]
Number of manufacturing facilities | facility			1
Balemaster
Business Acquisition [Line Items]
Goodwill	$ 26,836,000
Goodwill, expected tax deductible amount	0
Intangible assets other than goodwill acquired	28,060,000
Intangible assets other than goodwill, expected tax deductible amount	0
Revenue from the date of acquisition				9,038,000
Operating income (loss) from date of acquisition				(641,000)
Amortization expense				2,042,000
Acquisition related costs				782,000
Payments to acquire businesses, net of cash acquired	$ 53,747,000
Other
Business Acquisition [Line Items]
Goodwill		27,951,000		$ 27,951,000	$ 27,951,000	$ 27,951,000
Other | Industrial Processing | India
Business Acquisition [Line Items]
Consideration transferred		$ 2,882,000