A Surface Pitting Life Model for Spur Gears: Part II—Failure Probability Prediction

1991 ◽  
Vol 113 (4) ◽  
pp. 719-724 ◽  
Author(s):  
J. W. Blake ◽  
H. S. Cheng
Keyword(s):  
Size Distribution ◽  
Failure Probability ◽  
Spur Gear ◽  
Crack Size ◽  
Initial Crack ◽  
Spur Gears ◽  
Probability Estimates ◽  
Probability Prediction ◽  
Life Model ◽  
Service Behavior

A predictive pitting model for estimating failure probabilities and service lives has been developed. This paper presents the failure probability analysis and a discussion of the model’s application to spur gears. Probability estimates are based on an initial crack size distribution and on possible interaction between cracks and inclusions. Plots of the fraction of components experiencing pitting (percent) versus life show less spread than would be expected. However, trends predicted based on parametric variation are consistent with service behavior. The model is applied by linking the pitting model with a spur gear performance code. Results are compared with AGMA standards.

A Surface Pitting Life Model for Spur Gears: Part I—Life Prediction

1991 ◽  
Vol 113 (4) ◽  
pp. 712-718 ◽  
Author(s):  
J. W. Blake ◽  
H. S. Cheng
Keyword(s):  
Life Prediction ◽  
Spur Gears ◽  
Empirical Methods ◽  
Contact Conditions ◽  
Gear Design ◽  
Metallic Inclusions ◽  
Life Model ◽  
Service Behavior ◽  
Semi Empirical ◽  
Surface Breaking Crack

Surface pitting is a major failure mode for gears. Estimation of failure probability and service life are important in gear design. Current techniques give only a pass/fail rating based on semi-empirical methods. A predictive model for estimating service lives and failure probabilities has been developed. This paper discusses the life prediction analysis, which is based on propagation of a surface breaking crack under rolling/sliding contact conditions. The effects of both surface roughness and non-metallic inclusions can be included. While predicted lives are lower than expected, trends observed through parametric variation are consistent with service behavior.

A Probabilistic Environmentally Assisted Cracking Model for Steam Generator Tubes

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Tae Hyun Lee ◽  
Jae Young Yoon ◽  
Hyo On Nam ◽  
Il Soon Hwang
Keyword(s):  
Bayesian Inference ◽  
Stress Distribution ◽  
Size Distribution ◽  
Steam Generator ◽  
Crack Size ◽  
Initial Crack ◽  
Probability Of Detection ◽  
Alloy 600 ◽  
Pressurized Water ◽  
Environmentally Assisted Cracking

A probabilistic environmentally assisted cracking (PEAC) model was developed to describe the propagation of primary water stress corrosion cracking for Alloy 600 in roll-transition region of steam generator (SG), a severe environmentally assisted cracking problem in pressurized water reactors (PWRs). In the PEAC model, crack growth rate (CGR) and probability of failure (POF) were obtained by adopting a Bayesian inference that decreases the uncertainties of unknown parameters and their distributions in theoretical equations. The CGR is mainly dependent on three factors: probability of detection (POD), initial crack size distribution, and stress distribution. The POD, which is a logistic link was updated with Bayesian inference based on SG inspection data. The crack size distribution, which is relative to initiation time expressed by a Weibull function, was also updated with Bayesian inference using POD. The stress distribution caused by mechanical rolling is considered to be a major contributing factor along the SG tube. It based on finite element analysis is deterministic model unlike POD and initial crack distribution. According to this model, the uncertainty of hyperparameters in the CGR which are parameters of a prior distribution was reduced, and the appropriate level of confidence was achieved by utilizing the available data. Moreover, a benchmark study for the SG tube was performed to evaluate reliability of Alloy 600 SG components in nuclear power plants. The POF was estimated from the developed PEAC model and failure criteria by taking into account the effects of inspection and repair of defective tubes. The results from this study are applied to demonstrate risk reduction in PWRs by adopting risk-informed in-service inspection.

A Practical Method to Predict Total Fatigue Life of Welded Joints Structures

2015 ◽  
Author(s):  
Huiying Gao ◽  
Shun-Peng Zhu ◽  
Zhiqiang Lv ◽  
Fang-Jun Zuo ◽  
Hong-Zhong Huang
Keyword(s):  
Fatigue Life ◽  
Crack Initiation ◽  
Welded Joints ◽  
Practical Method ◽  
Crack Size ◽  
Initial Crack ◽  
Practical Procedure ◽  
Life Model ◽  
Crack Initiation Life ◽  
Life Predictions

Welded joints are usually the weakest link for welded structures due to the existence of stress concentration caused from welding. Fracture mechanics-based approach is a main method used to predict fatigue life for welded joints structures. In engineering, there are two main problems in fatigue life prediction, one is whether crack initiation life can be ignored or not, and the other one is to determine the crack size starting to propagate. Based on this research, a practical procedure is proposed to predict fatigue life of welded joints structures using an initial crack life model and Paris law. Emphasis is put on the discussion about crack initiation life and how to choose an appropriate method to determine the initial crack size. Noted that the proposed method in this paper does not need any tests to determine crack initiation life when crack size reaches a specified value, which depends on experience and is considered as crack size starting to propagate, thus human factors and uncertainty can be minished. Through comparison analysis, fatigue life predictions based on the proposed method are in a good agreement with experimental data.

FORWARD APPORTIONMENT OF CENSORED COUNTS FOR DISCRETE NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF FAILURE PROBABILITIES

2009 ◽  
Vol 16 (03) ◽  
pp. 213-234
Author(s):  
MINNIE H. PATEL ◽  
H.-S. JACOB TSAO
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Closed Form ◽  
Failure Probability ◽  
Likelihood Estimation ◽  
Lifetime Distribution ◽  
Nonparametric Maximum Likelihood ◽  
Kaplan Meier ◽  
Probability Estimates ◽  
Failure Probabilities

Empirical cumulative lifetime distribution function is often required for selecting lifetime distribution. When some test items are censored from testing before failure, this function needs to be estimated, often via the approach of discrete nonparametric maximum likelihood estimation (DN-MLE). In this approach, this empirical function is expressed as a discrete set of failure-probability estimates. Kaplan and Meier used this approach and obtained a product-limit estimate for the survivor function, in terms exclusively of the hazard probabilities, and the equivalent failure-probability estimates. They cleverly expressed the likelihood function as the product of terms each of which involves only one hazard probability ease of derivation, but the estimates for failure probabilities are complex functions of hazard probabilities. Because there are no closed-form expressions for the failure probabilities, the estimates have been calculated numerically. More importantly, it has been difficult to study the behavior of the failure probability estimates, e.g., the standard errors, particularly when the sample size is not very large. This paper first derives closed-form expressions for the failure probabilities. For the special case of no censoring, the DN-MLE estimates for the failure probabilities are in closed forms and have an obvious, intuitive interpretation. However, the Kaplan–Meier failure-probability estimates for cases involving censored data defy interpretation and intuition. This paper then develops a simple algorithm that not only produces these estimates but also provides a clear, intuitive justification for the estimates. We prove that the algorithm indeed produces the DN-MLE estimates and demonstrate numerically their equivalence to the Kaplan–Meier-based estimates. We also provide an alternative algorithm.

The Compliance of Solid, Wide-Faced Spur Gears

1990 ◽  
Vol 112 (4) ◽  
pp. 590-595 ◽  
Author(s):  
J. H. Steward
Keyword(s):  
Experimental Data ◽  
Contact Line ◽  
Load Distribution ◽  
3D Model ◽  
Spur Gear ◽  
Point Load ◽  
Spur Gears ◽  
Line Load ◽  
Gear Teeth ◽  
Theoretical Results

In this paper, the requirements for an accurate 3D model of the tooth contact-line load distribution in real spur gears are summarized. The theoretical results (obtained by F.E.M.) for the point load compliance of wide-faced spur gear teeth are set out. These values compare well with experimental data obtained from tests on a large spur gear (18 mm module, 18 teeth).

scholarly journals A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions

2006 ◽  
Vol 43 (4) ◽  
pp. 916-926 ◽  
Author(s):  
Ayalvadi Ganesh ◽  
Giovanni Luca Torrisi
Keyword(s):  
Size Distribution ◽  
Ruin Probability ◽  
Heavy Tail ◽  
Claim Size ◽  
Probability Estimates ◽  
Claim Size Distribution ◽  
Risk Processes

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under heavy tail conditions on the claim size distribution.

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