Areal gear metrology with modified flanks
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Abstract
Gears are critical mechanical components in power transmission systems, used across a board spectrum of industries such as automobile, aerospace and renewable energy. Given the advancement of design and manufacture of gears in the past decades, the current gear inspection based on line oriented geometric description and tactile measuring technology has shown several deficiencies (lack of areal information, high cycle time etc.), when assessing complex geometries on gears flanks. Advanced sensing methods can capture dense point clouds on a complete gear body, but no evaluation method is available to extract areal information from these point clouds. This imposes a technical gap for gear manufacturers and users since no quantitative parameters characterize the gear’s deviations from its nominal geometry. An implicit equation, which analytically describes the complete gear geometry including both flanks on all teeth is obtained, as a new interpretation of the plumb line distance equation. No nominal points are needed to obtain an areal distance map, which contains gear modification and deviation information. A set of new areal parameters are defined as an extension of standardized line oriented parameters. A novel evaluation method based on the principle of orthogonal decomposition using 2D Chebyshev polynomials is proposed to extract areal gear characteristics from an areal distance map. Numerical simulations are carried out by three numerical integration algorithms on four types of spatial point distributions, to obtain the areal parameters from discrete areal distance maps. Experimental verification using a calibrated gear modification artifact compared the new areal parameters with the standardized line oriented parameters. A conformance of ± 1.5 μm between the evaluated areal parameters and the given certified line oriented parameter, obtained on four flank modifications and two pitch modifications, is achieved.This dissertation offers a foundation for a paradigm shift of gear metrology, particularly gear evaluation algorithms. The proposed method enables an improved evaluation of areal flank data, collected by various sensing principles: tactile, optical and even computed tomography. It can form the basis for further studies of microstructure and surface topography of gear flanks. Thus, the developed evaluation method can improve future gear manufacturing processes and provide a holistic quality assessment of gear products.