On micro flank geometric topography design for spiral bevel and hypoid gears.

• Macro tooth flank modeling, discretization and discrete point interpolation. • Determination of autocorrelation function from the actual measurement. • Fast Fourier transformation (FFT) based micro flank topography reconstruction. • Comprehensive effect considering both macro and micro flank. • Micro flank geometric topography reconstruction for spiral bevel and hypoid gears. Focusing on comprehensive effect of both macro and micro geometries, accurate flank geometric topography design in a micro scale is developed for spiral bevel and hypoid gears showing a complex flexural behaviors. Firstly, macro flank modeling is performed for determining sparse tooth surface by using the discrete point interpolation. For micro-scale and smooth flank points, the vector between the current point and the adjacent tooth surface point are used as the tangent vector, and the vector in normal direction is obtained by calculating vector product of tangent vector. Then, fast Fourier transform (FFT) method is employed for the micro flank geometric topography reconstruction considering comprehensive effect. While determining the height distribution parameters from the actual measurement, autocorrelation function (ACF) is established to obtain the reconstructed roughness height matrix, and these microscopic height data are added to the corresponding macroscopic smooth tooth surface points in the normal direction for accurate micro flank geometric topography generation. The proposed method is exercised with an example double helical grinding spiral bevel gear from an aerospace application to demonstrate the impact of reconstruction design on flank performance. [ABSTRACT FROM AUTHOR]