INDEBTEDNESS - Senior Credit Facilities (Details)			1 Months Ended	3 Months Ended		9 Months Ended		12 Months Ended
	Aug. 15, 2022	Aug. 12, 2022 USD ($)	Aug. 31, 2022 USD ($)	Oct. 01, 2022 USD ($)	Oct. 02, 2021 USD ($)	Oct. 01, 2022 USD ($)	Oct. 02, 2021 USD ($)	Dec. 31, 2021 USD ($)
Line of Credit Facility [Line Items]
Write off of deferred debt issuance cost				$ 1,100,000	$ 0	$ 1,100,000	$ 200,000
Senior Credit Facilities
Line of Credit Facility [Line Items]
Loss on extinguishment of debt			$ 1,100,000					$ 200,000
Write off of deferred debt issuance cost			700,000
Unamortized debt issuance costs			400,000
Fees paid			1,500,000
Senior Credit Facilities | Term loan | Fed Funds Effective Rate Overnight Index Swap Rate
Line of Credit Facility [Line Items]
Basis spread on variable rate (as a percent)	0.50%
Senior Credit Facilities | Term loan | London Interbank Offered Rate (LIBOR), Period One
Line of Credit Facility [Line Items]
Basis spread on variable rate (as a percent)	1.00%
Interest period which may be elected, shortest (months)	1 month
Senior Credit Facilities | Term loan | London Interbank Offered Rate (LIBOR), Period Three
Line of Credit Facility [Line Items]
Interest period which may be elected, shortest (months)	3 months
Senior Credit Facilities | Term loan | Term Secured Overnight Financing Rate (“SOFR”) Loans/Alternative Currency Loans
Line of Credit Facility [Line Items]
Basis spread on variable rate (as a percent)	0.10%
Senior Credit Facilities | Term loan | London Interbank Offered Rate (LIBOR), Period Four
Line of Credit Facility [Line Items]
Interest period which may be elected, shortest (months)	6 months
Line of Credit | Senior Credit Facilities
Line of Credit Facility [Line Items]
Fronting fees percentage		0.125%
Maximum period within which net proceeds should be reinvested		360 days
Period after end of 360 day period if committed to be reinvested		180 days
Percentage of capital stock		100.00%
Percentage of capital stock of material first tier foreign subsidiaries		65.00%
Non-voting capital stock percentage		100.00%
Consolidated leverage ratio to repurchase capital stock and pay cash dividends		2.75
Aggregate amount of repurchases and dividend declarations		$ 100,000,000.0
Additional amount for all such repurchases and dividend declarations after effective date		$ 100,000,000.0
Percentage of cumulative consolidated net income		50.00%
Percentage of cumulative consolidated net deficit		100.00%
Weighted-average interest rate of senior credit facilities (as a percent)				4.50%		4.50%
Line of Credit | Senior Credit Facilities | Four Fiscal Quarters After Certain Permitted Acquisitions
Line of Credit Facility [Line Items]
Consolidated coverage ratio		4.00
Line of Credit | Senior Credit Facilities | Last Day Of Any Fiscal Quarter | Minimum
Line of Credit Facility [Line Items]
Consolidated interest coverage ratio		3.00
Line of Credit | Senior Credit Facilities | Last Day Of Any Fiscal Quarter | Maximum
Line of Credit Facility [Line Items]
Consolidated coverage ratio		3.75
Line of Credit | Senior Credit Facilities | Four Fiscal Quarters After Certain Permitted Acquisitions Financed By Unsecured Debt
Line of Credit Facility [Line Items]
Consolidated coverage ratio		4.25
Line of Credit | Senior Credit Facilities | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		$ 770,000,000.0
Line of Credit | Bilateral Foreign Credit Instrument Facility | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		25,000,000.0
Term loan | Senior Credit Facilities
Line of Credit Facility [Line Items]
Fees paid			300,000
Term loan | Bilateral Foreign Credit Instrument Facility | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		$ 200,000,000.0
EBITDA consolidated coverage ratio most recently		2.75
Term loan | Current SPX Term Loan Facilities
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		$ 245,000,000.0
Unamortized debt issuance costs				$ 700,000		$ 700,000		$ 1,000,000.0
Financial Letter of Credit Fee | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		500,000,000.0
Financial Letter of Credit Fee | Financial Letters of credit | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		200,000,000.0
Financial Letter of Credit Fee | Non -Financial Letters of Credit | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		50,000,000.0
Financial Letter of Credit Fee | Non-U.S. Exposure | Revolving loans
Line of Credit Facility [Line Items]
Maximum borrowing capacity under financing arrangement		$ 150,000,000.0
Domestic Line of Credit
Line of Credit Facility [Line Items]
Amount of available borrowing capacity				489,000,000.0		489,000,000.0
Letters of credit issued, amount outstanding				11,000,000.0		11,000,000.0
Foreign credit instrument facility
Line of Credit Facility [Line Items]
Amount of available borrowing capacity				12,200,000		12,200,000
Letters of credit issued, amount outstanding				$ 12,800,000		$ 12,800,000
Foreign credit instrument facility | Senior Credit Facilities
Line of Credit Facility [Line Items]
Fronting fees percentage		0.25%
Revolving loans | Senior Credit Facilities
Line of Credit Facility [Line Items]
Fees paid			$ 1,200,000