Roundness Modelling by Fractal Interpolation

프랙탈 보간에 의한 진원도 모델링

  • Published : 2006.06.01

Abstract

There are many modelling methods using theoretical and experimental data. Recently, fractal interpolation methods have been widely used to estimate and analyze various data. Due to the chaotic nature of dynamic roundness profile data in roundness some desirable method must be used for the analysis which is natural to time series data. Fractal analysis used in this paper is within the scope of the fractal interpolation and fractal dimension. Also, two methods for computing the fractal dimension has been introduced which can obtain the dimension of typical dynamic roundness profile data according to the number of data points in which the fixed data are generally lower than 200 data points. This fractal analysis result shows a possible prediction of roundness profile that has some different roundness profile in round shape operation.

Keywords

References

  1. Chin, D. H., Yoon, M. C. and Sim, S. B., 2005, 'Roundness modeling in BTA deep hole drilling,' Precision Engineering, Vol. 29, pp. 176-188 https://doi.org/10.1016/j.precisioneng.2004.06.003
  2. Kang, M. C., Kim, J. S. and Kim, K. H., 2005, 'Fractal dimension analysis of machined surface depending on coated tool wear,' Surface & coating technology, Vol. 193, pp. 259-265 https://doi.org/10.1016/j.surfcoat.2004.07.020
  3. Barnsley, M. F., 1993, Fractals everywhere, Academic Press Inc
  4. Marvasti, M. A. and Strahle, W. C., 1995, 'Fractal geometry analysis of turbulent data,' Signal processing, Vol. 41, pp. 191-201 https://doi.org/10.1016/0165-1684(94)00100-E
  5. Shah, E. N., Reddy, N. P. and Rothschild, B. M., 2005, 'Fractal analysis of acceleration signals from patients with CPPD, rheumatoid arthritis, and spondyloarthroparthy of the finger joint,' Computer methods and programs in biomedicine, Vol. 77, pp. 233-239 https://doi.org/10.1016/j.cmpb.2004.10.004
  6. Yoon, M. C., Cho, H. D., Kim, S. K. and Kim, J. S., 2000, 'A Study on the Characteristics of Machined Profile Modeling in Cylindrical Shape Machining,' KSMTE, Vol. 9, No. 3, pp. 55-61
  7. Hadjileontiadis, L. J., Douka, E. and Trochidis, A., 2005, 'Fractal dimension analysis for crack identification in beam structures,' MSSP, Vol. 19, pp. 659-674
  8. Jeong, J. S., Chin, D. H. and Yoon, M. C., 2006, 'End milling Force Estimation by Fractal Interpolation,' J. of KSMPE, Vol. 5, No. 1, pp. 7-12
  9. Mistakidis, E. S., 1997, 'Fractal geometry in structural analysis problems: A variational formulation for fractured bodies with non-monotone interface conditions,' Chaios, solutions & fractals, Vol. 8, No. 2, pp. 269-285 https://doi.org/10.1016/S0960-0779(96)00052-5