Simulation and analysis of grinding wheel based on Gaussian mixture model

Abstract

This article presents an application of numerical simulation technique for the generation and analysis of the grinding wheel surface topographies. The ZETA 20 imaging and metrology microscope is employed to measure the surface topographies. The Gaussian mixture model (GMM) is used to transform the measured non-Gaussian field to Gaussian fields, and the simulated topographies are generated. Some numerical examples are used to illustrate the viability of the method. It shows that the simulated grinding wheel topographies are similar with the measured and can be effective used to study the abrasive grains and grinding mechanism.

Key words： grinding wheel; 3D topographies measurement; Gaussian mixture model; simulation

Acknowledgements

This work was financially supported by National Science and Technology Key Project (2011ZX04003-022) and Shanghai Science Technology Commission (10DZ2292100).

Appendix

This set includes four 3D height parameters [9]:
S_q	The RMS value of the departures within the sampling area
S_z	The absolute height of the five highest peaks and the depths of the deepest valleys within the sampling area
S_{sk}	Asymmetry of surface deviations about the mean plane
S_{ku}	Peakness or sharpness of the surface height distribution
This set includes four 3D spatial parameters [9]:
S_{ds}	Number of summits of a unit sampling area
S_{tr}	Long crestness or uniform texture aspect
S_{td}	Pronounced direction of the surface texture
S_{al}	Shortest autocorrelation length that the areal autocorrelation function decays to 0.2
This set includes three 3D hybrid parameters [9]:
S_{\mathrm{\Delta }q}	RMS value of the surface slope within the sampling area
S_{sc}	Average of the principle curvatures of the summits within the sampling area
S_{dr}	Ratio of the increment of the interfacial area of a surface over the sampling area
This set includes six 3D functional parameters [9]:
S_{bi}	Ratio of the RMS deviation over the surface height at 5% bearing area
S_{ci}	Ratio of the void volume of the unit sampling area at the core zone over the RMS deviation
S_{vi}	Ratio of the void volume of the unit sampling area at the valley zone over the RMS deviation

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