Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters

2005 ◽  
Author(s):  
Shao Wang ◽  
Wai Kin Chan
Keyword(s):  
Silicon Wafer ◽  
Roughness Parameter ◽  
Hard Disk ◽  
Spectral Density Function ◽  
Power Spectral ◽  
Fractal Parameters ◽  
Asperity Contacts ◽  
Fractal Roughness ◽  
Magnetic Hard Disk ◽  
Wafer Surfaces

To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnetic hard disk and silicon wafer surfaces. A novel scheme involving a variable transformation was developed to extract fractal parameters. This scheme was validated by accurate recovery of fractal parameters from simulated surfaces. The fractal dimension, the fractal roughness parameter and the fractal domain length were found for magnetic hard disk and silicon wafer surfaces.

scholarly journals Study on Gear Contact Stiffness and Backlash of Harmonic Drive Based on Fractal Theory

2021 ◽  
Author(s):  
Tao Zhang ◽  
Zhifeng Liu ◽  
Congbin Yang ◽  
Yang Wang ◽  
Qianqian Liu
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Fractal Theory ◽  
Roughness Parameter ◽  
Tooth Surface ◽  
Gear Backlash ◽  
Fractal Parameters ◽  
Fractal Roughness ◽  
Gear Contact ◽  
Tooth Pair

Abstract Contact stiffness and backlash model of harmonic reducer is related to robot’s positioning accuracy and vibration characteristics. Harmonic reducer tooth pair height is typically less than 1 mm. Thus, backlash and contact stiffness measurement and modeling are relatively complex. In this paper, contact stiffness and backlash model is proposed by establishing a relationship between fractal parameters and tooth contact load. Non-contact optical profiler and RMS method are combined to obtain fractal roughness parameters of real machined tooth surface. Finally, the effect of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash is studied. The results indicate that surface topography parameters and contact force have significant effects on contact stiffness and backlash. By increasing the fractal dimension, a decrease of gear backlash and contact stiffness is observed. However, the opposite is true for the fractal roughness parameter. Lastly, an increase in contact force improves the contact stiffness.

scholarly journals Interval estimation for contact stiffness of bolted joint with uncertain parameters

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988370 ◽  
Author(s):  
Yongsheng Zhao ◽  
Hongchao Wu ◽  
Congbin Yang ◽  
Zhifeng Liu ◽  
Qiang Cheng
Keyword(s):  
Fractal Dimension ◽  
Contact Surface ◽  
Contact Stiffness ◽  
Interval Estimation ◽  
Roughness Parameter ◽  
Normal Pressure ◽  
Bolted Joints ◽  
Uncertain Parameters ◽  
Fractal Parameters ◽  
Fractal Roughness

Bolted joints are elements used to create resistant assemblies in the mechanical system, whose overall performance is greatly affected by joints’ contact stiffness. Most of the researches on contact stiffness are based on certainty theory whereas in real applications the uncertainty characterizes the parameters such as fractal dimension D and fractal roughness parameter G. This article presents an interval estimation theory to obtain the stiffness of bolted joints affected by uncertain parameters. Topography of the contact surface is fractal featured and determined by fractal parameters. Joint stiffness model is built based on the fractal geometry theory and contact mechanics. Topography of the contact surface of bolted joints is measured to obtain the interval of uncertain fractal parameters. Equations with interval parameters are solved to acquire the interval of contact stiffness using the Chebyshev interval method. The relationship between the interval of contact stiffness and the uncertain parameters, that is, fractal dimension D, fractal roughness parameter G, and normal pressure, can be obtained. The presented model can be used to estimate the interval of stiffness for bolted joints in the mechanical systems. The results can provide theoretical reference for the reliability design of bolted joints.

Identification of the State of a Magneto-Fluidized Bed by Pressure Fluctuations

2006 ◽  
Vol 4 (1) ◽  
Author(s):  
Sachin Dahikar ◽  
Ram Sonolikar
Keyword(s):  
Fluidized Bed ◽  
Autocorrelation Function ◽  
Pressure Fluctuations ◽  
Spectral Density Function ◽  
Functional Relationships ◽  
Power Spectral ◽  
Data Points ◽  
Instantaneous Pressure ◽  
Conventional Signal ◽  
Mutual Information Function

Local instantaneous pressure signals obtained through a magneto-fluidized bed have been analyzed using both classical and advanced signal analysis methods, which can deliver the necessary information about the presence of the bubbling and turbulent flow pattern. The conventional signal processing tool such as autocorrelation and cross correlation were used as preliminary tools to analyze the data. Evaluation of the dominant bubble frequency was completed using the autocorrelation function and power spectral density function. Mutual information function was used to identify the periodicity and the predictability of the local instantaneous pressure signals. Since it does not demand any particular functional relationships between the data points, it is a better method (compared to autocorrelation function) for measuring the predictability of nonlinear systems.

Analog Frontend for Tribo-Current-Based Fly-Height Sensor for Magnetic Hard Disk Drive

2018 ◽  
Vol 65 (2) ◽  
pp. 556-566
Author(s):  
Arup Polley ◽  
Pankaj Pandey ◽  
Bryan E. Bloodworth ◽  
Costin Cazana
Keyword(s):  
Hard Disk Drive ◽  
Hard Disk ◽  
Disk Drive ◽  
Magnetic Hard Disk ◽  
Fly Height

High Sensitivity Optical Detection of Oriented Microdefects on Silicon Wafer Surfaces Using Annular Illumination

CIRP Annals ◽  
2001 ◽  
Vol 50 (1) ◽  
pp. 389-392 ◽  
Author(s):  
Takashi Miyoshi ◽  
Satoru Takahashi ◽  
Yasuhiro Takaya ◽  
Shoichi Shimada
Keyword(s):  
Silicon Wafer ◽  
Optical Detection ◽  
High Sensitivity ◽  
Wafer Surfaces
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