In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micr...In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.展开更多
The existing leakage models,which include smooth plane leakage model,rough and waveform surface leakage model,and tapered-face leakage model,can not be applied to describing the active state of contacting mechanical s...The existing leakage models,which include smooth plane leakage model,rough and waveform surface leakage model,and tapered-face leakage model,can not be applied to describing the active state of contacting mechanical seal.In these models,only prime microscopic surface topography and constant leakage rate are taken into consideration.Based on fractal geometry theory,a leakage model was established with consideration of the change of microscopic surface topography and time-correlation of leakage rate.The relationship between leakage rate,the change of microscopic surface topography of seal surface and leaking channel under operation conditions was described quantitatively by fractal parameter with unattached dimension.There existed an optimum fractal parameter during the mechanical seal running,which corresponded to the lowest leakage rate.The research results helped to ascertain the roughness and waviness of seal surface,and to select machining methods of sealing members.According to the leakage model presented in this paper,the leakage rate of contacting mechanical seal can be forecasted,which may be used as reference in the maintenance and operation of mechanical seals.展开更多
基金Projects(50975092,50805052,U0834002) supported by the National Natural Science Foundation of ChinaProject(9151030101000007) supported by the Natural Science Foundation of Guangdong Province,ChinaProject(2009ZZ0041) supported by the Fundamental Research Funds for the Central Universities in China
文摘In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.
文摘The existing leakage models,which include smooth plane leakage model,rough and waveform surface leakage model,and tapered-face leakage model,can not be applied to describing the active state of contacting mechanical seal.In these models,only prime microscopic surface topography and constant leakage rate are taken into consideration.Based on fractal geometry theory,a leakage model was established with consideration of the change of microscopic surface topography and time-correlation of leakage rate.The relationship between leakage rate,the change of microscopic surface topography of seal surface and leaking channel under operation conditions was described quantitatively by fractal parameter with unattached dimension.There existed an optimum fractal parameter during the mechanical seal running,which corresponded to the lowest leakage rate.The research results helped to ascertain the roughness and waviness of seal surface,and to select machining methods of sealing members.According to the leakage model presented in this paper,the leakage rate of contacting mechanical seal can be forecasted,which may be used as reference in the maintenance and operation of mechanical seals.
