Gray Chaos Evaluation Model for Prediction of Rolling Bearing Friction Torque

2010 ◽  
Vol 38 (3) ◽  
pp. 102623 ◽  
Author(s):  
M. R. Mitchell ◽  
R. E. Link ◽  
Xia Xintao ◽  
Lv Taomei ◽  
Meng Fannian
Keyword(s):  
Evaluation Model ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Bearing Friction

Poor Information Analysis of Rolling Bearing Friction Torque Characteristic Parameter Based on Phase Space

2011 ◽  
Vol 382 ◽  
pp. 167-171
Author(s):  
Lei Lei Gao ◽  
Xin Tao Xia
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Characteristic Parameter ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Point Estimation ◽  
Experimental Result ◽  
Bayesian Probability ◽  
Characteristic Parameters ◽  
Bearing Friction

The friction torque of rolling bearings belongs to an information poor system with unknown probability distributions and trends. This counteracts dynamical assessment for the characteristics of the rolling bearing friction torque as a time series. For this reason, the chaos theory is employed to recover the original dynamic characteristics of a friction torque time series by means of the phase space reconstruction theory. The dynamical Bayesian probability density function of the characteristic parameters of the friction torque is constructed by the information poor theory based on the phase space. The method for point estimation, interval estimation, and trend estimation of the characteristic parameters is proposed in this paper. The investigation shows that the error between the calculated result and the experimental result is very small.

Chaotic Characteristic and Nonlinear Dynamic Performance of Rolling Bearing Friction Torque

2010 ◽  
Vol 26-28 ◽  
pp. 88-92 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv ◽  
Fan Nian Meng
Keyword(s):  
Time Series ◽  
Nonlinear Dynamic ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Box Dimension ◽  
Rolling Bearings ◽  
Chaotic Characteristic ◽  
Chaotic Theory ◽  
Bearing Friction

Based on the chaotic theory, the methods of the Lyapunov exponent and the box dimension were applied to evaluate the chaotic characteristic and the nonlinear dynamic performance of the rolling bearing friction torque. The time series were obtained via the experimental investigation on the friction torque of the rolling bearings under the condition of different rotational speeds. It is found that the rolling bearing friction torque is of a chaotic system because the maximum of Lyapunov exponents of its time series is greater than zero according to the chaotic theory. And the result shows that the mean of the box dimension of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a time series.

Chaos Prediction of Rolling Bearing Friction Torque

2010 ◽  
Vol 26-28 ◽  
pp. 190-193 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Time Series ◽  
Experimental Investigation ◽  
Chaos Theory ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Local Region ◽  
Space Applications ◽  
Region Method ◽  
Weight One ◽  
Bearing Friction

Based on the chaos theory, the adding-weight one-rank local-region method was applied to predict the time series of the rolling bearing friction torque. The experimental investigation on the rolling bearing for space applications shows that the method is able to predict effectively the rolling bearing friction torque, only with very small predicted error.

Dynamic Prediction Model for Rolling Bearing Friction Torque Using Grey Bootstrap Fusion Method and Chaos Theory

2012 ◽  
Vol 443-444 ◽  
pp. 87-96 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Probability Distributions ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Local Region ◽  
Fusion Method ◽  
Dynamic Prediction ◽  
Region Method ◽  
True Value ◽  
Weight One ◽  
Bearing Friction

Synthesizing the grey bootstrap fusion method and the five chaos forecasting methods (viz., the adding-weight zero-rank local-region method, the one-rank local-region method, the adding-weight one-rank local-region method, the improved adding-weight one-rank local-region method, and the maximum Lyapunov exponent method), a dynamic prediction model is proposed to calculate the predicted true value and the predicted interval of a chaotic time series under the condition of unknown probability distributions and trends. At the same time, the five forecasting values are acquired with the help of the five chaos forecasting methods, respectively, and the five forecasting values are fused to deduce the predicted true value and the predicted interval by means of the grey bootstrap fusion method. As time goes on, a series of the predicted true value and the predicted interval is obtained dynamically. Experimental investigation of the rolling bearing friction torque shows that using the grey bootstrap fusion method, the predicted true value and the measured values have an identical trend only with a small error, the predicted interval is acquired along with a high reliability, and the dynamic prediction of the rolling bearing friction torque as a chaotic time series is made without any prior knowledge of probability distributions and trends.

Information Entropy of Rolling Bearing Friction Torque as Data Series

2010 ◽  
Vol 44-47 ◽  
pp. 1115-1119 ◽  
Author(s):  
Xin Tao Xia ◽  
Long Chen ◽  
Fan Nian Meng
Keyword(s):  
Experimental Investigation ◽  
Information Entropy ◽  
Rotational Speed ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Data Series ◽  
Entropy Theory ◽  
Rolling Bearings ◽  
Bearing Friction

The information entropy theory is applied to evaluate the uncertainty of the rolling bearing friction torque. The data series are obtained via the experimental investigation on the friction torque of the rolling bearings under the condition of different rotational speeds. And the result shows that the information entropy of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a data series.

Dynamic Prediction of Rolling Bearing Friction Torque Using Lyapunov Exponent Method

2010 ◽  
Vol 44-47 ◽  
pp. 1120-1124 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Small Data ◽  
Data Sets ◽  
Dynamic Prediction ◽  
Information Method ◽  
Small Data Sets ◽  
Bearing Friction

Based on the chaos theory, the Lyapunov exponent method is employed to predict dynamically the time series of the rolling bearing friction torque. First, the embedding dimension and the delay time for the phase space reconstruction are estimated with the Cao method and the mutual information method, respectively. Second, the maximum of the Lyapunov exponents is calculated by small data sets. Lastly, the nearest neighboring point is sought via the Euclidean distance. The experimental investigation shows that the method proposed in this paper is able to forecast effectively the rolling bearing friction torque as a time series, only with very small predicted error.

Uncertainty of Rolling Bearing Friction Torque as Data Series Using Grey Bootstrap Method

2010 ◽  
Vol 44-47 ◽  
pp. 1125-1129
Author(s):  
Xin Tao Xia ◽  
Long Chen ◽  
Fan Nian Meng
Keyword(s):  
System Theory ◽  
Experimental Investigation ◽  
Bootstrap Method ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Data Series ◽  
Rolling Bearings ◽  
The Mean ◽  
Bearing Friction

Based on the information poor system theory, the grey bootstrap method is employed to estimate the uncertainty of the rolling bearing friction torque. The data series are obtained via the experimental investigation of the friction torque of the rolling bearings under the condition of different rotational speeds. And the results show that the mean of the dynamic fluctuant range (MDFR) of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a data series.

scholarly journals Bearing friction effect on cup anemometer performance modelling

2021 ◽  
Vol 2090 (1) ◽  
pp. 012101
Author(s):  
D Alfonso-Corcuera ◽  
S. Pindado ◽  
M Ogueta-Gutiérrez ◽  
A Sanz-Andrés
Keyword(s):  
Rotation Rate ◽  
Aerodynamic Drag ◽  
Aerodynamic Characteristics ◽  
Friction Torque ◽  
Performance Modelling ◽  
Friction Forces ◽  
Aerodynamic Drag Coefficient ◽  
Yaw Angle ◽  
Cup Anemometer ◽  
Bearing Friction

Abstract In the present work, the effect of the friction forces at bearings on cup anemometer performance is studied. The study is based on the classical analytical approach to cup anemometer performance (2-cup model), used in the analysis by Schrenk (1929) and Wyngaard (1981). The friction torque dependence on temperature was modelled using exponential functions fitted to the experimental results from RISØ report #1348 by Pedersen (2003). Results indicate a logical poorer performance (in terms of a lower rotation speed at the same wind velocity), with an increase of the friction. However, this decrease of the performance is affected by the aerodynamic characteristics of the cups. More precisely, results indicate that the effect of the friction is modified depending on the ratio between the maximum value of the aerodynamic drag coefficient (at 0° yaw angle) and the minimum one (at 180° yaw angle). This reveals as a possible way to increase the efficiency of the cup anemometer rotors. Besides, if the friction torque is included in the equations, a noticeable deviation of the rotation rate (0.5-1% with regard to the expected rotation rate without considering friction) is found for low temperatures.

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