Roundness Modeling Using Fractal Interpolation


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There are many modelling methods using theoretical and experimental data. Recently, fractal interpolation methods have been widely used to estimate and analyse various data. Due to the chaotic nature of dynamic roundness profile data in roundness, some desirable method must be used for the analysis of data which is natural to sequential 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 have been introduced, which can calculate the fractal dimension of typical dynamic roundness profile data according to the number of data points in which the fixed data are generally lower than 120 data points. This fractal analysis shows a possible prediction and analysis of roundness profile that has some different roundness profile in round shape operation such as cylindrical grinding, turning, drilling and boring.



Edited by:

Dongming Guo, Tsunemoto Kuriyagawa, Jun Wang and Jun’ichi Tamaki




M. C. Yoon and D. H. Chin, "Roundness Modeling Using Fractal Interpolation ", Key Engineering Materials, Vol. 329, pp. 521-526, 2007

Online since:

January 2007




[1] M.F. Barnsley, Fractals everywhere, Academic Press Inc, (1993).

[2] E.N. Shah, N. P. Reddy, B.M. Rothschild, 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 (2005), p.233�239.


[3] D.H. Chin, M.C. Yoon, S.B. Sim, Roundness modelling in BTA deep hole drilling, Precision Engineering, Vol. 29 (2005), p.176~188.


[4] M.C. Yoon, H.D. Cho, S.K. Kim, J.S. Kim, A Study on the Characteristics of Machined Profile Modelling in Cylindrical Shape Machining, KSMTE, Vol. 9, No. 3 (2000), p.55�61.

[5] M.C. Kang, J.S. Kim, K.H. Kim, Fractal dimension analysis of machined surface depending on coated tool wear, Surface & coating technology, Vol. 193 (2005), p.259�265.


[6] M.A. Marvasti, W.C. Strahle, Fractal geometry analysis of turbulent data, Signal processing, Vol. 41 (1995), p.191~201.


[7] L.J. Hadjileontiadis, E. Douka, A. Trochidis, Fractal dimension analysis for crack identification in beam structures, MSSP, Vol. 19 (2005), p.659�674.


[8] E.S. Mistakidis, Fractal geometry in structural analysis problems: A variational formulation for fractured bodies with non-monotone interface conditions, Chaios, solutions & fractals, Vol. 8, No. 2 (1997), p.269�289��.