Multidimensional entropy evaluation of non-uniform distribution of assembly features in precision instruments

Abstract

The non-uniform distribution of assembly features such as form error and stress has a significant influence on the accuracy and stability of precision instruments. Therefore, to improve assembly precision, non-uniformly distributed assembly features must be evaluated in terms of value non-uniformity as well as location non-uniformity. However, the current effective non-uniformity evaluation methods for assembly features only consider the value non-uniformity without considering the influence of the data location. This study proposes a multidimensional entropy evaluation method (MDEEM) and establishes multidimensional entropy evaluation indexes (MDEEIs) to evaluate the non-uniformity of assembly features in a plane region considering both their value and location. First, the mathematical model and MDEEIs for non-uniform data in a one-dimensional (1D) geometric space were developed and verified, wherein the concept of control distance was introduced and the information entropy theory was adopted. Then, the MDEEIs for non-uniform data in a two-dimensional (2D) geometric space were established and verified based on those in the 1D space. Subsequently, the MDEEM was proposed to demonstrate the non-uniformity evaluation process for assembly features in a 2D plane region. Finally, the proposed MDEEM was applied to reveal the distribution characteristics of two types of assembly features that mainly affect the assembly quality, namely form error and stress. This study provides an evaluation method for the non-uniform distribution of various assembly factors in a plane region and aids in the optimization of precision assembly processes.