Full-factor matrix model of accuracy of dimensions performed on CNC multipurpose machines

OBRABOTKAMETALLOV Том 23 № 4 2021 TECHNOLOGY against each other, a change in depths of cut ∆ t 1 and ∆ t 2 can lead to a change in the balance of forces. As a result, the scattering intervals of the performed dimensions are of three different orders [6, 27]. By combining all 3 variants of the location of the scattering fi elds, it is possible to form a single model of the scattering fi eld, taking into account not only the plane-parallel displacements of technological subsystems of the performed dimensions on the longitudinal carriage of double-carriage opposite adjustments, but also the angular displacements around the base points. Below is a full-factor matrix model of the performed diametrical dimension on the longitudinal carriage: ( ) ( ) 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 2 1 2 1 1 0 0 1 01 1 0 2 01 1 0 2 1 0 1 O O O 0 0 2 1 1 0 0 1 0 0 2 0 2 1 0 1 0 2 O O O O O O 1 2 1 1 0 01 1 0 2 1O O O 1 if t t t t t O t t t O O t t e t p e t p e t p e t p a a a a t p a a t p a a a a t p a a t p e t p e t p a a a w                    é ù é ù é - + + + - + + ê ú ê ú ê ë û ë û êë ù é ù + + - + + ú ê ú ú ê ú û ë û - + - + = ( ) ( ) ( ) ) ( ) ( ) 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 2 0 1 0 2 O O O 1 1 0 0 1 0 0 2 1 2 1 0 1 0 2 O O O O O 01 1 0 2 1 2 1 1 0 0 1 0 0 2 01 1 0 2 1 0 1 0 2 O O O O O O 1 2 01 1 0 2 , 2 2 where 0; 1 2 t t t t O t t t t t t t t a t p a a t p a a a a t p a a t p e t p e t p e t p e t p a a a a t p a a t p e t p e t p                   + ³ + + + ³ + - + - + + æ ö é÷ ç + + ÷ ç ÷ çè ø ë  ( ) ( ) ( ) ( ) ( ) ( ) 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 O O O O 0 0 2 0 2 O O 1 1 0 0 1 0 0 2 1 2 1 0 1 0 2 O O O O O O 01 1 0 2 1 2 1 1 0 0 1 0 01 1 0 2 1 0 1 O O O O O 1 2 if 2 2 t t t t t t t t t a a a a t p a a t p a a a a t p a a t p e t p e t p e t p e t p a a a a t p a                       æ ö é ù ÷ ç+ + + + ê÷ ê ú ç ÷ ç ê ú ê è ø û ë ù + ú úû + + + - - - + - + +   ( ) ( ) 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 2 0 2O 1 1 0 0 1 0 0 2 1 2 1 0 1 0 2 O O O O O O 01 1 0 2 1 2 1 2 1 1 0 0 1 01 1 0 2 01 1 0 2 1 0 1 O O O O 0 0 2 1 0 2 1 O O O O ; 2 2 t t t t t t t t t t t a t p a a a a t p a a t p e t p e t p e t p e t p e t p e t p a a a a t p a a t p a a                      + + + + é ù é ù é - - + + - - + + ê ú ê ú ê ê ú ê ú ê ë û ë û ë ù + + - ú úû  ( ) ( ) ( ) ( ) 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 2 0 1 0 2 O O O O 1 2 1 1 0 0 1 0 0 2 01 1 0 2 1 0 1 0 2 O O O O O O 1 1 0 0 1 0 0 2 1 2 1 0 1 0 2 O O O O O O 01 1 0 2 1 01 1 0 2 if , 2 2 where t t t t t t t t t t t a a t p a a t p e t p e t p a a a a t p a a t p a a a a t p a a t p e t p e t p e t p e t p                     é ù + + ê ú ê ú ë û - + - + + £ + + + £ - - - ( ) ( ) 1 1 0 0 0 0 2 1 1 0 0 1 0 0 2 1 0 1 0 2 O O O O O O 0; t t t a a a a t p a a t p    ìïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïíïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïïï + - + + ïïïïî  (1)