A New Flatness Evaluation-Rotation Method Based on GA

Abstract

Flatness is one fundamental element of geometric forms, and the flatness evaluation is particularly important for ensuring the quality of industrial products. This paper presents a new flatness evaluation in the view of the minimum zone evaluation - rotation method based on genetic algorithm. This method determines the minimum zone through rotating measurement points in three dimensions coordinate. The points are firstly rotated about coordinate axes. Then they are projected in one axis, and the smallest projection length is the flatness value. The rotation angles are optimized by genetic algorithm to improve search efficiency. An exponential fitness function and the rotation angles range is designed on the basis of flatness characteristics. An adaptive mode of crossover and mutation probability is used to avoid local optimum. The results show this method can search the minimum zone and converge rapidly.

New Generation Geometrical Product Specification (GPS) Backed Flatness Error Estimation and Uncertainty Analysis

“…According to the above results and analysis, results of flatness error are in complete agreement with other methods [6,8], the difference of five calculations are 0.5μm for first data set and 0.7μm for second data set as shown in Tables 1 and 2, respectively. This difference is mainly caused by random error in each data set and different measurement positions.…”

“…To verify the authenticity of the EGA algorithms, flatness error results were compared to other methods [6,8]. Based on EGA, flatness error results were 0.00713mm and 0.02894mm for data points of [6,8] respectively, and results of EGA are in complete agreement with [6,8], this shows the authenticity of the EGA algorithms.…”

Novel on-machine measurement system and method for flatness of large annular plane

“…The value of δ 1 and δ 2 are substituted into equations (2. 19) and (2.20), and the value of ∆s (k + 2) which is the error of S (k + 2) can be obtained. Additionally, the final error separation formula is…”

“…For example, we can use a three-coordinate measurement machine or self-collimator to measure it directly. Similarly, there are many algorithms such as the minimum zone method [18], the rotation method based on genetic algorithm [19], the geometry searching approximation algorithm [20] and the modified artificial bee colony algorithm [21], which calculate the flatness indirectly. In addition, after expanding the EST method from line to plane, it is also widely used in measuring flatness [3,22,23], especially for the large-scale plane and onmachine conditions.…”