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# How to Reduce Geometrical Variation in Assembled Products

Doktorsavhandling
Författare Johan S Carlson 91-7197-928-x Chalmers University of Technology Göteborg 2000 Institutionen för matematik, Matematisk statistik en assembled products, body-in-white (BIW), dimensional variation, geometrical variation, fixtures, fixture diagnosis, locating schemes, multivariate analysis, rigid body motion, robust design, root cause, quality Algebra och geometri, Matematisk statistik, Konstruktionsteknik, Mekanisk tillverkningsteknik

## Sammanfattning

Vehicle problems, such as wind noise, water leakage and door closing effort are examples of quality and functionality defects that are controlled by the dimensional accuracy of the structural frame of an auto body.

The aim of this thesis is towards methods for reducing geometrical variation in assembled products in the automotiv other industries. A general approach to these problems, based on the general idea for how rigidly parts are located in their final position using locating schemes, is developed. In particular, a positioning function which relates locating scheme errors to the corresponding displacement of parts is derived.

The positioning function is used to quantify the degree of coupling in a design concept and the geometrical stability provided by a locating scheme. In this way, designers are alerted, during early design phases, to geometrically sensitive and coupled design concepts that are difficult to manufacture and assembly to a proper quality level.

However, even for well designed products and assembly processes, the assembly tools such as positioning fixtures may become worn or broken and cause dimensional variation. Fixtures are high precision tools used to position parts for assembly and measurement. The positioning function is combined with methods from multivariate analysis to diagnose fixture errors from routine measurements on parts and products, rather than from special measurements on fixtures. One reason for fixtures being at the centre of interest is that experience from the automotive industry suggests fixture failures as a major reason for dimensional variation in the structural frame of an auto body.