Modeling Machining Geometric Variation in a $N-2-1$ Fixturing Scheme

Fixtures are used to locate and constrain workpieces in machining. Fixture properties, such as accuracy and locator layout schemes, directly affect the resultant geometric variation on the machined workpiece surfaces. $N-2-1$ fixturing schemes $(N>3)$ are often used for large or compliant workpieces in machining. However, the impact of $N-2-1$ fixturing on product geometric variation is not well understood because of the uncertainty of contact under the overconstraint condition. This paper presents a modeling methodology to study the machining geometric variation in a 4-2-1 fixturing scheme. The model integrates the fixture-workpiece interactions resulted from the rigid-body variation in fixtures, workpieces, and machine tools, and the static deformation under external forces. The uncertainty of the fixture-workpiece contact condition due to the 4-2-1 constraint condition is modeled using the minimum potential energy theory. A numerical example of face milling is presented to demonstrate the methodology.