Search Results (2)

This paper aims to obtain the best shape accuracy evaluation algorithm for silicon nitride ceramic balls after lapping, and to extract the initial signal of the ball surface to improve the accuracy and reliability of the algorithm. The research methods of this paper are as follows: Firstly, an analysis of the uniform envelope of the lapping trajectory of ceramic balls is carried out to verify whether the lapping trajectory after processing can achieve a consistent envelope on the balls’ surface. On this basis, it is found through experiments that the standard deviation SD between the roundness deviations of different contour sections is small. The value is maintained at approximately 0.03 μm, and the roundness deviation can approximately replace the spherical deviation. Then the different contour sections of the sphere are sampled by the Taylor roundness instrument. Considering the uncertainty, the sampling points of different contour sections are averaged and used as the original signal of the sphere surface. Then the EMD method is used to process the signal to be detected on the sphere surface. The initial signal of the sphere surface is extracted by judging whether the number of ripples Kc obtained by decomposition is greater than the critical value. Then the initial signal is used as the input value of the approximation algorithm. Through the roundness deviation approximation algorithm based on the least square method, the given minimum approximation domain range is finely processed. The divided fine points are used as the center of the circle to intersect with the initial signal. The maximum, minimum, and range of each circle are calculated to obtain the roundness error based on the minimum circumscribed circle, the maximum inscribed circle, and the minimum region method. Finally, the calculated values are compared with those obtained by the traditional algorithm. The experimental results of this paper show that the algorithm is consistent with the roundness error measured by the instrument, compared with the mainstream evaluation criteria. In summary, the conclusions can be drawn as follows: Through a large number of experimental cases and comparative experiments, the algorithm has high accuracy and reliability. The research results of this paper have essential reference significance for accurately evaluating the shape accuracy of ceramic balls in actual production. Full article

Ancient books on East Asian mathematics introduced to the Korean Peninsula enrich our understanding of the arithmetic notions that mold the creative thought processes of the ancients. They believed that all objects in the universe could be composed of circles and squares and all items could be expressed in terms of geometrical profiles. Through the combination of circles and squares, the ancient East Asians expressed the order of the world and unraveled it mathematically. These principles are evident in the construction principles of early Korean stone pagodas. In particular, the square root of 2 (√2) is a very important number in the delineation represented in the consolidation of inscribed and circumscribed circles with squares. Further, the square root of 2 is applied as a design principle in the construction of the stone pagodas at the temples Chŏngnimsa and Kamŭnsa. This article demonstrates that the ancients on the continuous impact of the Jiuzhang Suanshu and the Zhoubi Suanshu constructed the pagodas complying with design principles based on the arithmetic and geometric proportional systems of √2 times, which are intended to adjust compositional proportions and the gradual decrease in length to shape the tripartite partition of the foundation, the pagoda body, and the finial in stone pagodas. Full article