On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters

2021 ◽  
Vol 105 (0) ◽  
pp. 151-169
Author(s):  
A. Ivanov ◽  
I. Savych
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Random Noise ◽  
Least Squares Estimator ◽  
Textured Surface ◽  
Textured Surfaces ◽  
Bivariate Model ◽  
Content Type ◽  
Trigonometric Regression ◽  
Trigonometric Model

A multivariate trigonometric regression model is considered. Various discrete modifications of the similar bivariate model received serious attention in the literature on signal and image processing due to multiple applications in the analysis of symmetric textured surfaces. In the paper asymptotic normality of the least squares estimator for amplitudes and angular frequencies is obtained in multivariate trigonometric model assuming that the random noise is a homogeneous or homogeneous and isotropic Gaussian, in particular, strongly dependent random field on  R M , M > 2. \mathbb {R}^M,\,\, M>2.

Experimental study on friction coefficient and temperature rise of heavy-load grease-lubricated spherical plain bearings with surface texture

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jinlong Shen ◽  
Tong Zhang ◽  
Jimin Xu ◽  
Xiaojun LIU ◽  
Kun Liu
Keyword(s):  
Friction Coefficient ◽  
Temperature Rise ◽  
Surface Texture ◽  
Tribological Performance ◽  
Textured Surface ◽  
Textured Surfaces ◽  
Roughness Parameters ◽  
Heavy Load ◽  
Friction Coefficients ◽  
Content Type

Purpose This paper aims to improve the tribological performance of grease-lubricated spherical plain bearings (SPBs) under heavy load, dimple-type textures were prepared by laser on the outer surface of the inner ring. The influence of roughness parameters of a textured surface on reducing friction coefficient and temperature rise was also explored. Design/methodology/approach This study adopts a laser processing method to fabricate dimple-type textures. Three-dimensional roughness parameters were used to characterize the textured surfaces. The friction coefficients of five SPBs with surface texture and one original commercially available SPB without surface texture under different nominal loads were measured on a self-established test rig. The data of temperature rise were obtained by nine embedded thermal couples. Findings The results indicate that SPBs with textures generally exhibit lower friction coefficients than the original SPB without textures. The dimple depth has a significant influence on improving the tribological performance, which coincides with the analysis by surface roughness parameters. A textured surface with negative Ssk and high Vvc has the minimum temperature rise. Originality/value As it is too difficult to arrange sensors into heavy-load SPBs, there are few reports about the temperature characteristics. Through nine embedded thermal couples, the distribution of temperature rise on the inner ring of SPBs was given in this study. The positive effect of surface texture on reducing temperature rise and friction coefficient was verified, which is beneficial for the design of heavy-load SPBs.

Comparisons of tribological properties between laser and drilled dimple textured surfaces of medium carbon steel

2017 ◽  
Vol 69 (4) ◽  
pp. 516-526 ◽  
Author(s):  
Chenchun Shi ◽  
Aibing Yu ◽  
Jianzhao Wu ◽  
Weiyang Niu ◽  
Yanlin Wang
Keyword(s):  
Tribological Properties ◽  
Wear Debris ◽  
Surface Texturing ◽  
Laser Surface Texturing ◽  
Heat Affect Zone ◽  
Textured Surface ◽  
Textured Surfaces ◽  
Wear Properties ◽  
Content Type ◽  
Worn Surfaces

Purpose The study aims to compare tribological properties between laser dimple textured surface and drilled dimple textured surface, and to analyze the influence of dimple hardened edges and ability of trapping wear debris on wear properties of dimple textured surfaces. Design/methodology/approach Circular textured dimples were produced on AISI 1,045 specimen surfaces using laser surface texturing (LST) and drilled surface texturing (DST) methods. Tribological behaviors of LST, DST and non-textured specimens were studied using ball-on-disc tribo-tester. Metallographic structures, dimples and worn surface morphologies were observed using a three-dimensional digital microscope. Hardnesses of substrate and dimple edges were measured. Findings There was no obvious difference in wear and friction coefficients between LST and DST specimens. Hardnesses of laser dimple edges were much higher than that of drilled dimple edges and specimen substrate. The hardened materials of laser dimple edge included recast zone and heat affect zone. Laser dimple was cone-shaped and drilled dimple was cylinder-shaped. Drilled dimple had a better ability of trapping wear debris than laser dimple. Non-uniform wear phenomenon occurred on worn surfaces of LST dimple specimens. Originality/value The ability of textured dimples to trap wear debris is affected by single dimple volume. Hardened edges of dimples cause non-uniform wear on worn surfaces of LST specimens.

scholarly journals Asymptotic normality of the least squares estimate in trigonometric regression with strongly dependent noise

2019 ◽  
pp. 24-41
Author(s):  
T. O. Drabyk ◽  
O. V. Ivanov
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Least Squares ◽  
Regression Function ◽  
Least Squares Estimator ◽  
Stationary Time Series ◽  
Model Parameters ◽  
Local Transformation ◽  
Stationary Time ◽  
Trigonometric Regression

The least squares estimator asymptotic properties of the parameters of trigonometric regression model with strongly dependent noise are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise under which the least squares estimator of regression model parameters are asymptotically normal. Trigonometric regression model with discrete observation time and open convex parametric set is research object. Asymptotic normality of trigonometric regression model parameters the least squares estimator is research subject. For obtaining the thesis results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev-Hermite polynomials of the transformed Gaussian time series values and it’s covariances, central limit theorem for weighted vector sums of the values of such a local transformation and Brouwer fixed point theorem.

Tribological performance and self-lubricating mechanism of the laser-textured surface filled with solid lubricant in rolling friction pair

2018 ◽  
Vol 70 (2) ◽  
pp. 371-384 ◽  
Author(s):  
Xijun Hua ◽  
Xuan Xie ◽  
Bifeng Yin ◽  
Peiyun Zhang ◽  
Jinghu Ji ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Solid Lubricant ◽  
Friction Pair ◽  
Rolling Friction ◽  
Textured Surface ◽  
Textured Surfaces ◽  
Content Type ◽  
Texture Density ◽  
Composite Solid ◽  
Lubricating Mechanism

Purpose This paper aims to find out the tribological performance and self-lubricating mechanism of the laser-textured surface filled with solid lubricant in rolling friction pair. Design/methodology/approach The textures on the surfaces of GCr15 bearing steel were produced by acousto-optic Q diode-pumped yttrium aluminum garnet laser with the technology of “single pulse one time, repeating at intervals” and filled with composite solid lubricant. The tribology tests were conducted on the MMW-1A universal friction and wear testing machine. Findings It was found that the solid-lubricated micro-textured surface can reduce the friction coefficient effectively. The MoS2/PI composite solid lubricant works better than the single MoS2 solid lubricant, and the ratio of PI/MoS2 + PI at 20 per cent is the best recipe. The friction coefficient of the sample surfaces decreases first and then increases with the increase in texture densities, and a texture density of 19.6 per cent has the best effect on friction reduction. The friction coefficient of the textured surfaces gradually decreases with the increase in both rational speed and load. For the same texture density, the friction coefficient of textured surfaces decreases slightly with the increase in diameter. Furthermore, the mechanism of “rolling-extrusion-accumulation” occurred on the textured surface can collect the solid lubricant, thereby, improve the effect of lubricating and anti-friction. Originality/value The results of the experimental studies demonstrated the application prospect of laser surfaces texturing combined with solid lubricant in rolling friction pair.

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