Correlation of the components of dimensional-chain elements

Abstract

The formation of errors in the components of dimensionalchain elements depends on the relevant conditions. In the design process, the tolerances on the components of elements in the corresponding dimen� sional chains (the dimensions of machine parts) are established. In assembly, the errors in the machine parts employed are due to their manufacture. For a techno� logical system, the errors in the components of dimen� sionalchain elements (the dimensions of the machine tool, tool, attachment, and blank) are determined by aspects of the technological error. These errors depend on various factors, such as the precision of blank instal� lation; the accuracy of machinetool adjustment; the rigidity of the system; the dimensional wear of the tool; and temperature deformation. In all the cases consid� ered, the factors that affect the error in the components of the elements are independent. This provides the basis for existing methods of determining the error of the closing element in dimensional chains (1-4). In operational dimensional chains whose elements are the dimensional parameters of the blank at differ� ent stages of a technological process, the formation of the error in the closing element is more complex. In such dimensional chains, the errors of some compo� nents of the elements (operational dimensions) are formed as a result of simultaneous and identical change in the given elements. This was attributed to the parallel linkage of the dimensional chain for a technological system in (5). This phenomenon was described as mutual error compensation by the com� ponents of the elements in (6, 7). However, it would be better to speak of mutual dependence or correlation of the components of the elements. The analysis of operational dimensional chains without taking account of the correlation between components of the elements leads to unfounded increase in the machining tolerances. This prevents complete dimensional analysis of technological pro� cess and establishment of the required precision with minimal consumption of material. The identification of operational dimensional chains with mutually dependent components of the elements is a challenge. The best approach is analysis of a dimensional dia� gram or graph of the dimensional links in the process. Thus complicates technological design and requires highly qualified staff. Automation of dimensional cal� culations in such conditions is problematic. Moreover, the quantitative characteristics of such correlations have not yet been established.