Symbol	Type	Description
$X_{\mathrm{in}}{Y}_{\mathrm{in}}{Z}_{\mathrm{in}}{O}_{\mathrm{in}}$	Coordinate system	Insert coordinate system
$P_{\mathrm{se}}$	Scalar	Point on the side cutting edge of the insert
$P_{\mathrm{be}}$	Scalar	Point on the bottom cutting edge of the insert
$P_{\mathrm{ce}}$	Scalar	Point on the corner cutting edge of the insert
$O_{\mathrm{in}}$	Scalar	The intersection point of the side and bottom cutting edge
$\kappa$	Scalar	The entering angle of the insert (in radian)
${\alpha }_{\mathrm{f}}$	Scalar	The clearance angle of the insert (in radian)
$X_{\mathrm{t}}{Y}_{\mathrm{t}}{Z}_{\mathrm{t}}{O}_{\mathrm{t}}$	Coordinate system	Tool coordinate system
${\theta }_{\mathrm{a}}$	Scalar	The axial rake angle (in radian)
${\theta }_{\mathrm{r}}$	Scalar	The radial rake angle (in radian)
$R_{\mathrm{t}}$	Scalar	The tool radius (in millimeters)
$L_{\mathrm{t}}$	Scalar	The tool length (in millimeters)
$R_{\mathrm{w}}$	Scalar	The cutting edge radius (in millimeters)
${\mathit{M}}_{\mathrm{in}}^{\mathrm{t}}$	Matrix	Homogeneous transformation matrix from $X_{\mathrm{in}}{Y}_{\mathrm{in}}{Z}_{\mathrm{in}}{O}_{\mathrm{in}}$ to $X_{\mathrm{t}}{Y}_{\mathrm{t}}{Z}_{\mathrm{t}}{O}_{\mathrm{t}}$
${\mathit{N}}_{\mathrm{rf}}^{\mathrm{in}}$	Vector	Unit normal vector of the rake face in the insertion coordinate system
${\mathit{N}}_{\mathrm{fse}}^{\mathrm{in}}$	Vector	Unit normal vector of the side edge flank face in the insertion coordinate system
${\mathit{N}}_{\mathrm{fbe}}^{\mathrm{in}}$	Vector	Unit normal vector of the bottom edge flank face in the insertion coordinate system
${\mathit{N}}_{\mathrm{rf}}^{\mathrm{t}}$	Vector	Unit normal vector of the rake face in the tool coordinate system
$F{S}_{\mathrm{se}}^{\mathrm{in}}$	Function	The flank face of the side edge in the insert coordinate system
$F{S}_{\mathrm{se}}^{\mathrm{t}}$	Function	The flank face of the side edge in the tool coordinate system
$h_{\mathrm{in}},d_{\mathrm{se}}$	Scalar	Height and width variable parameters (in millimeters)
$T{H}_{\mathrm{in}}$	Scalar	The thickness of the insert (in millimeters)
$r_{\mathrm{c}}$	Scalar	The radius of the corner edge (in millimeters)
$L_{\mathrm{se}}$	Scalar	The length of the side edge (in millimeters)
$a_{\mathrm{p}}$	Scalar	The axial depth of cut (in millimeters)
$a_{\mathrm{e}}$	Scalar	The radial width of cut (in millimeters)
$n_{\mathrm{s}}$	Scalar	The spindle speed (in r/min)
$f$	Scalar	The feed rate (in mm/min)
$P{L}_{\mathrm{se}}$	Scalar	The side edge flank wear plane
$P_{\mathrm{wse}}$	Scalar	The side edge wear point
$R_{\mathrm{wse}}$	Scalar	The radius of the cutting circle of the side edge (in millimeters)
$V{B}_{\mathrm{wse}}$	Scalar	The width of the wear land at side edge wear point $P_{\mathrm{wse}}$ (in millimeters)
$P_{\mathrm{sce}}$	Scalar	The tangent point of corner and side cutting edge
$P_{\mathrm{bce}}$	Scalar	The tangent point of corner and bottom cutting edge
$P_{\mathrm{ce}}^{\mathrm{in}}$	Function	The corner edge in the insert coordinate system
${\alpha }_{\mathrm{ce}}$	Scalar	Angle variable parameter (in radian)
$l_{\mathrm{ce}}$	Scalar	Length variable parameter (in millimeters)
${\mathit{V}}_{\mathrm{fce}}$	Vector	The direction of the intersection line between the flank face of the side and the bottom edge
$F{S}_{\mathrm{ce}}^{\mathrm{in}}$	Function	The flank face of the corner edge in the insert coordinate system
$F{S}_{\mathrm{ce}}^{\mathrm{t}}$	Function	The flank face of the corner edge in the tool coordinate system
$P_{\mathrm{wce}}$	Scalar	The corner edge wear point
$R_{\mathrm{wce}}$	Scalar	The radius of the cutting circle of the corner edge (in millimeters)
$V{B}_{\mathrm{wce}}$	Scalar	The width of the wear land at corner edge wear point $P_{\mathrm{wce}}$ (in millimeters)
$N_{\mathrm{t}}$	Scalar	Number of inserts
$M{L}_{\mathrm{i}}$	Scalar	The i-th length measurement point
$M{R}_{\mathrm{i}}$	Scalar	The i-th radius measurement point