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Abstract
Geometrical tolerancing was developed to improve the weakness of previous tolerance systems to handle imperfect form and ambiguous references and was primarily developed for assembly of components. Although there have been recent modifications to increase tolerance zone's utility, it is still basically a go/nogo system with components being in or out of tolerance. The use of tolerance zones is causing real industrial problems in the specification of high valued precision products. For example: in healthcare, the specification of the geometrical shape of the cup in total hipjoint replacements by a simple tolerance zone is allowing some cups to fail, by dislocating out of position, prematurely. A new design of nonspherical head is beginning to appear and the market requires improved specification. Further mathematical decomposition for the specification of the tolerancing zone is required to distinguish between good and failing functional geometries [1, 2]. The connection with filtration is explored. In particular the definitions for 'primary mapping' contained in ISO 166101 [3] is developed to include the foundations of decomposition in terms of structures called 'complete lattices'. One very useful property of complete lattices is the existence of a smallest subset of lattice elements (called lattice generators) that can reconstruct the whole of the lattice using just joint (or alternatively meet) operations. These lattice generators constitute a basis (or frame) of the lattice and form a measurement scale for the nesting index of the associated decomposition/filter. This definition of decomposition, given here, is universal and goes beyond just decomposition of geometrical products. Examples will be given to illustrate the utility of the definition to other aspects of smart manufacturing, including: formal concept analysis [4] for smart information systems.
Original language  English 

Article number  034011 
Number of pages  5 
Journal  Surface Topography: Metrology and Properties 
Volume  6 
Issue number  3 
Early online date  11 Jun 2018 
DOIs  
Publication status  Published  1 Sep 2018 
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Paul Scott
 Department of Engineering  Professor
 School of Computing and Engineering
 Centre for Precision Technologies  Research Director
Person: Academic
Projects
 1 Finished

EPSRC Fellowship in Manufacturing: Controlling Geometrical Variability of Products for Manufacturing
1/09/13 → 31/12/18
Project: Research