scholarly journals Stress-Based Weibull Method to Select a Ball Bearing and Determine Its Actual Reliability

2020 ◽  
Vol 10 (22) ◽  
pp. 8100
Author(s):  
Baldomero Villa-Covarrubias ◽  
Manuel R. Piña-Monarrez ◽  
Jesús M. Barraza-Contreras ◽  
Manuel Baro-Tijerina
Keyword(s):  
Weibull Distribution ◽  
Standard Method ◽  
Ball Bearing ◽  
Contact Stresses ◽  
New Method ◽  
Hertz Contact ◽  
Outer Race ◽  
Two Parameters

Since the designed bearing’s reliability of 90% was determined in a lab environment, it does not represent the actual used environment. In this paper, a new methodology to determine the actual reliability that corresponds to the use conditions is offered. This new method is based on the standard method used to select the ball bearing. The proposed method is based on the two parameters of Weibull distribution, where the shape (β) and scale (η) parameters are both determined from the Hertz contact stresses values, which are generated under the surface of the motionless outer race, and by the forces transmitted between the ball and the outer race. Therefore, the derived reliability is different from the 90% index offered by manufacturers.

An improved model for investigating the vibration characteristics of ball bearing owing to outer race waviness under high speed

2021 ◽  
Vol 69 (2) ◽  
pp. 89-101
Author(s):  
Pingping Hou ◽  
Liqin Wang ◽  
Zhijie Xie ◽  
Qiuyang Peng
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Vibration Measurement ◽  
Vibration Frequencies ◽  
Outer Race ◽  
Response Characteristics ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Initial Clearance ◽  
Improved Model

In this study, an improved model for a ball bearing is established to investigate the vibration response characteristics owing to outer race waviness under an axial load and high speed. The mathematical ball bearing model involves the motions of the inner ring, outer ring, and rolling elements in the radial XY plane and axial z direction. The 2Nb + 5 nonlinear differential governing equations of the ball bearing are derived from Lagrange's equation. The influence of rotational speed and outer race waviness is considered. The outer race waviness is modeled as a superposition of sinusoidal function and affects both the contact deformation between the outer raceway and rolling elements and initial clearance. The MATLAB stiff solver ODE is utilized to solve the differential equations. The simulated results show that the axial vibration frequency occurred at l fc and the radial vibration frequencies appeared at l fc fc when the outer race waviness of the order (l) was the multiple of the number of rolling elements (k Nb) and that the principal vibration frequencies were observed at l fc fc in the radial x direction when the outer race waviness of the order (l) was one higher or one lower than the multiple of the number of rolling elements (k Nb 1). At last, the validity of the proposed ball bearing model was verified by the high-speed vibration measurement tests of ball bearings.

New method for measuring ball-bearing raceway radii

1964 ◽  
Vol 7 (3) ◽  
pp. 208-210
Author(s):  
D. I. Kolpakov ◽  
V. V. Matveev
Keyword(s):  
Ball Bearing ◽  
New Method ◽  
Bearing Raceway

scholarly journals The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 48-76
Author(s):  
Freddy Hernández ◽  
Viviana Giampaoli
Keyword(s):  
Weibull Distribution ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Mixed Model ◽  
Random Effect ◽  
Estimation Procedure ◽  
Weibull Regression ◽  
Two Parameters ◽  
The Impact

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

Multi-objective optimization of the manufacture of face-milled hypoid gears on numerical controlled machine tool

2020 ◽  
pp. 095440542097803
Author(s):  
Vilmos V Simon
Keyword(s):  
Machine Tool ◽  
Angular Displacement ◽  
Contact Stresses ◽  
Machining Process ◽  
New Method ◽  
Energy Losses ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Gear Manufacture

A new method is presented for advanced manufacture of hypoid gears on numerical controlled machine tool. The tool geometry and machine tool settings are determined to introduce the optimal tooth modifications into the teeth of hypoid gears. The goal is to reduce the maximum tooth contact stresses, angular displacement error of the driven gear, and energy losses in the oil film existing between tooth surfaces. The calculation is based on the optimal variation of machine tool settings on the classical machine tool for hypoid gear manufacture. The novelty of the method is that during the machining process of teeth surfaces, the variation of machine tool settings on the cradle-type hypoid generator is conducted by polynomial functions of fifth-order. By an algorithm, this variation of machine tool settings is transferred to the numerical controlled machine tool for hypoid gear manufacture (hypoid generator). The obtained results have shown that by applying the optimal manufacture process, considerable reductions in tooth contact stresses and angular displacement errors of the driven gear, and a moderate reduction in energy losses were obtained. Therefore, by applying this new method in practice, advanced manufacture of hypoid gears on CNC hypoid generator is made possible, resulting improved operating characteristics of the hypoid gear pair.

EEMD-Based Speaker Emotional Analysis for Speech Signal

2011 ◽  
Vol 121-126 ◽  
pp. 815-819 ◽  
Author(s):  
Yu Qiang Qin ◽  
Xue Ying Zhang
Keyword(s):  
Emotion Recognition ◽  
Empirical Mode Decomposition ◽  
Speech Signal ◽  
Ensemble Empirical Mode Decomposition ◽  
New Method ◽  
Speech Signals ◽  
Emotional Speech ◽  
Mode Decomposition ◽  
Two Parameters ◽  
Mode Mixing

Ensemble empirical mode decomposition(EEMD) is a newly developed method aimed at eliminating mode mixing present in the original empirical mode decomposition (EMD). To evaluate the performance of this new method, this paper investigates the effect of two parameters pertinent to EEMD: the emotional envelop and the number of emotional ensemble trials. At the same time, the proposed technique has been utilized for four kinds of emotional(angry、happy、sad and neutral) speech signals, and compute the number of each emotional ensemble trials. We obtain an emotional envelope by transforming the IMFe of emotional speech signals, and obtain a new method of emotion recognition according to different emotional envelop and emotional ensemble trials.

Analysis of Contact Stress on Coating Based upon Hertz Theory

2012 ◽  
Vol 155-156 ◽  
pp. 133-137
Author(s):  
Li Ping Wang ◽  
Hao Dong Luo ◽  
Yan Mei Cui
Keyword(s):  
Finite Element Method ◽  
Coating Thickness ◽  
Contact Stresses ◽  
Contact Theory ◽  
Hard Coating ◽  
Thin Coating ◽  
The Finite Element Method ◽  
Hertz Contact ◽  
Hertz Theory ◽  
Mechanics Performance

It is necessary to study the mechanics performance of thin coating, which composite the prerequisite of coating’s application. The contact stresses are important factors for the design of hard coating/substrate because the failure of the hard coating is usually caused by these stresses. The finite element method is applied to simulate the stress of coating with contact load based on Hertz contact theory. The accuracy of model was initially tested in systems without a film. The contact stresses have been calculated based on various coating/substrate modulus ratios and the coating thickness. Results show that coating thickness changes from 1.5um to 3um, the effects of coating/substrate combination is perfect. The research has important guiding significance for the application of coating.

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