OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 5 No. 2 2023 The equation of RPI cutting edge which determines the generating surface of the milling cuter under study is described in its own coordinate system (X1Y1Z1), as 1( ) [ 0 0 1] , r t t Τ = (1) where t is a length parameter of RPI cutting edge. The equation of RPI cutting edge (1) is sequentially converted into the coordinate system of the mill body (X4Y4Z4), taking into account the specified taper lead angle (fig. 3, position 1), the side rake angle (fig. 3, position 2) and the diameter of the cutter (fig. 3, position 3). ( ) { } { } { } 2 5 6 4 1 43 32 21 ( 2) ( ) ( 2 ) ( ) r t A d A A r t = l p − j ⋅ , (2) where { } 2 43 ( 2) A d is the matrix that determines the installation of RPI on a specified diameter of the cutter d in the coordinate system of the mill body(X4Y4Z4): { } 2 43 1 0 0 0 0 1 0 2 ( 2) 0 0 1 0 0 0 0 1 d A d = ; { } 5 32 ( ) A l is the matrix specifying the rotation of RPI relative to the axis OX3 of the coordinate system (X3Y3Z3) to provide a set side rake angle: { } 5 32 cos 0 sin 0 0 1 0 0 ( ) sin 0 cos 0 0 0 0 1 A l l l = − l l ; { } 6 21 ( 2 ) A p − j is the matrix that determines the rotation of RPI relative to the axis OX2 of the coordinate system 2 2 2 X Y Z to attain a set major cutting edge angle: { } 6 21 cos ( 2 ) sin ( 2 ) 0 0 sin ( 2 ) cos ( 2 ) 0 0 ( 2 ) 0 0 1 0 0 0 0 1 A p − j − p − j p − j p − j p − j = . By specifying the rotation of RPI cutting edge (2) relative to the tool axis, we obtain the equation of the generating surface of the milling cutter under consideration { } { } 5 4 4 5 54 ( , ) ( 2) ( ) ( ) f f r t A A r t q = p q (3) where q is the angular parameter of the milling cutter generating surface; { } 5 5( 2) f A p is the matrix specifying the rotation of the coordinate system of the working tool to align axis Zf with the axis of the milling cutter body: { } ( ) 5 5 cos( 2) 0 sin( 2) 0 0 1 0 0 2 sin( 2) 0 cos( 2) 0 0 0 0 1 f A p p p = − p p ; { } 4 54 ( ) A q is the matrix that specifies the rotation of RPI cutting edge profile 4( ) r t by the angle q.
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