Cubic spline fitting using data dependent triangulations

In order to solve the hobbing machining data calculation and hobbing simulation of non-circular gear with various shapes, the piecewise cubic spline fit method has been adopted to unify the polar coordinate expression of non-circular pitch curve. The method to generate hobbing machining data was deduced based on hobbing linkage mathematical model, and the machining data error caused by piecewise cubic spline fitting method was analyzed. The three-dimension software has been used as simulation tool to make secondary development, and then non-circular gear hobbing simulation was realized based on machining data, which can verify the validity of machining data and the relevant design drawbacks of non-circular gear. The work of this paper lay a good foundation for design parameters optimization and hobbing of non-circular gear.

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Influence of curve fitting techniques on hydrostatic characteristics of ship

Journal of Mechanical Engineering ◽

10.3329/jme.v39i2.1853 ◽

1970 ◽

Vol 39 (2) ◽

pp. 100-112

Author(s):

Md Mashud Karim ◽

Md Ashim Ali ◽

Kho. Sahriar Iqbal

Keyword(s):

Curve Fitting ◽

Mechanical Engineering ◽

Cubic Spline ◽

Ship Hull ◽

Least Square ◽

Ship Stability ◽

Hull Form ◽

B Spline ◽

Using Data ◽

Table Data

This paper presents influence of curve fitting techniques on hydrostatic characteristics of marine vessels.Â Three vessels having lengths of 32.16m, 70.0m and 25.6m are selected for this study. The hull geometries of these vessels are represented by three curve fitting techniques such as least square, cubic spline and B-spline methods. At first, hydrostatic characteristics of the vessels are calculated using data only available in offset table and then using more data generated by curve fitting techniques. Finally, results obtained by offset table data are compared to those by fitted data. It is seen that there are some influences of curve fitting technique on the hydrostatic characteristics of ship especially at lightly loaded condition. Keywords: Curve fitting technique, ship hull form, offset table, hydrostatic characteristics, ship stability, cross curve. doi:10.3329/jme.v39i2.1853 Journal of Mechanical Engineering, Vol. ME39, No. 2, Dec. 2008 100-112

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Fourier Transformation of X-Ray Rocking Curves from Interferometer Structures

Advances in X-ray Analysis ◽

10.1154/s0376030800015615 ◽

1993 ◽

Vol 37 ◽

pp. 135-144

Author(s):

J. M. Hudson ◽

B. K. Tanner ◽

R. Blunt

Keyword(s):

Layer Thickness ◽

Bragg Peak ◽

Noisy Data ◽

X Ray Diffraction ◽

Interference Structure ◽

X Ray ◽

Auto Correlation ◽

Interference Fringes ◽

Spline Fitting ◽

Cubic Spline Fitting

AbstractWe discuss the use of Fourier transform techniques to extract layer thickness from the interference fringes observed in high resolution X-ray diffraction rocking curves of pseudomorphic HEMT structures. The interference structure is extracted by cubic spline fitting to the extrema of the data, thereby obtaining a background envelope which is used to normalise the data. The resulting constant background is subtracted from the data and the residual Fourier transformed. Auto correlation of the residual significantly improves the result from noisy data. Satisfactory results are obtained only when the Bragg peak from the substrate is windowed out. With a limited dynamic and angular range, there is often insufficient data to separate the two closely spaced periods arising from the total layer thickness and that excluding the quantum well. The result then corresponds to the average of these two thicknesses.

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