Abstract
With the rapid development of micromachining technology, sphericity errors have become an important factor that determines product quality; thus, it is critical to establish an algorithm to estimate sphericity errors effectively and accurately. In this paper, an asymptotic search method based on the minimum zone sphere (MZS) is proposed to estimate sphericity errors. A least square sphere center is used as the initial reference center through establishing a search sphere model to gradually approach the MZS center. Then, a quasi-MZS center is determined. According to the definition and geometric structure of the minimum zone sphere, five control points dominating the homocentric spheres are searched. As a result, the MZS center and the sphericity error are obtained. Both simulation experiments and data from the literature are utilized to verify the feasibility and performance. The results indicate that the proposed method is reliable and can estimate sphericity errors efficiently and accurately.
Highlights
In the field of precision machinery, instrumentation, and high-tech equipment, the form error of a high precision spherical surface is an important factor that determines the quality of components
The least square sphere (LSS) method is widely used for the merit of easy operation, but its sphericity error estimation is not critically accurate because it does not satisfy the minimum conditions of sphericity error estimation
If no points are located outside the outer sphere, the center O3 refers to the minimum zone sphere (MZS) center, and the sphericity error can be calculated
Summary
In the field of precision machinery, instrumentation, and high-tech equipment, the form error of a high precision spherical surface is an important factor that determines the quality of components. A simple, effective, and accurate method for estimating sphericity errors becomes very important. The common methods used for estimating sphericity errors include the least square sphere (LSS), minimum circumscribed sphere (MCS), maximum inscribed sphere (MIS), and minimum zone sphere (MZS) method. Several studies on the estimation of sphericity errors based on the MZS method have been reported. Wen proposed an immune evolutionary algorithm to estimate the minimum zone sphericity error.. Lei presented a geometry optimization searching algorithm for sphericity error estimation.. Kim used Voronoi diagrams to determine the concentric spheres to obtain sphericity errors.. Kim used Voronoi diagrams to determine the concentric spheres to obtain sphericity errors.11 Other methods, such as particle swarm optimization and genetic algorithms, are introduced for sphericity error estimation.. The MZS center is determined by employing this quasicenter as the reference center
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