If, in terms of vehicle bodies, the invention of the spoked wheel has made it possible to reduce the weight of wooden wheels, it is shrinking (since the 19e century), even more so than the embattage, already used since the end of the Middle Ages to reduce the wear of the wheels, which deserves attention, because the circle was then laid without effort, following thermal expansion, but above all because the rigidity of the whole wheel was considerably reinforced. However, it is in the field of artillery that the hooping technique will have been truly perfected, extreme precision being required to give a bi-bloc tube a much better hold than that of a one-piece tube of the same dimensions, except to auto-frette the latter. . Hooping has notoriously become synonymous with increased mechanical properties and, thus, possible lightening of a structure or lesser quantity of material required according to given stresses, this last aspect (preservation of resources) being relevant for the grip consideration of sustainable development in projects.
The method of assembly by shrinking has spread a lot, allowing for example to very quickly shrink and unshrink tools in their tool holder by induction or to transmit high powers with sprockets keyed on axles, practically supplanting the method of assembly which consisted of joining parts together using a key in a groove. Essentially for speed and lightening requirements, advances in mechanics, making it possible to work materials as close as possible to their limits, have led to the development of their study both at the theoretical and via fatigue tests in particular or numerical simulations.
This article details the various types of shrink-fitted assemblies joining together a pin and a ring, or any other part of revolution lending itself to a complete description (in terms of stresses, deformations and displacements) in polar coordinates. It incorporates multiple considerations: possibly different materials, hollow or solid shaft, bi-block or multi-block assembly, part of revolution cylindrical or not, ring and shaft of possibly different lengths, assembly possibly subjected to rotation. On the other hand, it only briefly addresses the case, dealt with in greater depth in the article [R 730]pressure equipment which is subject to specific regulations and for which a complete description in cylindrical coordinates is required.
The reader will find a glossary and a table of notations and symbols used at the end of the article.