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Noncommercial-Share Alike 2.0 Licence UK: England & Wales

https://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Extrusion with Sliding on Die Face

A hodograph can be constructed for a simple form of extrusion
used for non-ferrous metals. Here, we assume a smooth square die with
sliding on die faces and plane strain conditions.

Extrusion with Sliding on Die Face

Rule 1:

Look for symmetry and reduce the geometry accordingly.

Look for symmetry and reduce the geometry accordingly.

Extrusion with Sliding on Die Face

Rule 2:

Label regions of the model which move relative to each other.

Label regions of the model which move relative to each other.

A particle will travel a path as shown. It is sheared
when meeting line AB to move parallel to AC, then sheared at BC to move
parallel to CD.

Extrusion with Sliding on Die Face

Rule 3:

Define an origin of the hodograph, O, corresponding to a stationary component of the system.

Define an origin of the hodograph, O, corresponding to a stationary component of the system.

Extrusion with Sliding on Die Face

Rule 4:

Draw the velocity vector of the unknown force Q, i.e. unit length (Oq), on the hodograph.

Draw the velocity vector of the unknown force Q, i.e. unit length (Oq), on the hodograph.

Extrusion with Sliding on Die Face

Rule 5:

Draw vectors in the known directions of the moving components (Or and Os), relative to the origin O and to each other (qr and rs) on the hodograph.

Draw vectors in the known directions of the moving components (Or and Os), relative to the origin O and to each other (qr and rs) on the hodograph.

Extrusion with Sliding on Die Face

Rule 6:

Each vertex where these vectors intersect represents one (or more) of the labelled regions of the model.

Each vertex where these vectors intersect represents one (or more) of the labelled regions of the model.

Oq
defines motion of particles in region Q .

Extrusion with Sliding on Die Face

Rule 7:

Velocity vectors must be oriented parallel to slip planes due to conservation of matter.

Velocity vectors must be oriented parallel to slip planes due to conservation of matter.