Geometric model in Rc (cutter + spindle)

Known motion of Rc in Rg

PREPARATION: CUTTER

Create a FE model in Rc (cutter+spindle) Mesh Mc

qc(t)

PREPARATION: WORKPIECE

INTERACTION

Known matrices in eq. 1b

FE Interpolation

Known motion of Rs in Rg Create a FE model in Rs (workpiece + supports)

Known motion of Rc in Rs

mesh Ms contains only T10 elements inside mB

Known matrices in eq. 1a

Create Box mB in Rm(tI)

True

Choose FE Reduction

deformed shape of the cutter

Matrix Pc

Discretize the active parts of the cutter

Known matrices in eq. 5b

Known matrices in eq. 5a

Matrix Ps

Expand

Expand rhs of 5 yc(t)

Calculate YsT and YcW (eq. 7)

Pattern of M

cutting forces at t Use cutting force model

Matrices Hc Pc

Use Hc Pc yc(t - Dt)

Discretize the workpiece into T10

Mesh Ms

mesh inside mB (T10 elements)

FE Interpolation

Subdivide into T4

Deformed shape of the workpiece

Mesh Mm

qs(t)

False

Mesh the outside of Mm inside mB

Link vertices of MS to yc (eq. 16) Build the pattern of M

Box mB

Choose FE Reduction

Solve eq. 5 mesh MS: refined description of elementary tools, (T3 elem., BREP)

Geometric model in Rs (workpiece + supports)

Boolean chip

Deformed shape of MS at t (rake faces, and clearance faces)

Use Hc Pc Deformed shape of MS at t - DT

ys(t)

Mesh M+, in Rm (T4 elements)

Machined surface SM(t)

Link the vertices of M+m (T4 mesh) to ys

Extraction

Matrices Hs Ps

Use Hs Ps Boolean intersection Update D

BREP description M of the swept domain in Rm

D, dexel model of the workpiece in Rm

Place M in Rm INTERACTION: step by step solution of eq. 5, time step = DT

initialization at t=tI F+(t) is defined by ys(t) for any point inside mB

D(tI), Initial dexel model of the workpiece, in Rm