Stochastic Analysis of the Wheel-Rail Contact Friction Using the Polynomial Chaos Theory

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
HyunWook Lee ◽  
Corina Sandu ◽  
Carvel Holton
Keyword(s):  
Chaos Theory ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Contact Friction ◽  
Accurate Estimation ◽  
Uncertain Parameters ◽  
Stochastic Variation ◽  
Rail System ◽  
The Coefficient Of Friction ◽  
Mass Spring

The coefficient of friction (CoF) is a very important factor for designing, operating, and maintaining the wheel-rail system. In the real world, accurate estimation of the CoF at the wheel-rail interface is difficult due to the effects of various uncertain parameters, e.g., wheel and rail materials, rail roughness, contact patch size, and so on. In this study, a stochastic analysis using polynomial chaos (poly-chaos) theory is performed with the newly developed 3D dry CoF model at the wheel-rail contact. The wheel-rail system is modeled as a mass-spring-damper system. Stochastic analyses with one uncertainty, combinations of two uncertainties, and a combination of three uncertainties are performed. The probability density function (PDF) results for stick CoF, slip CoF, and combined (total) CoF are presented. The stochastic analysis results show that the total CoF PDF before 1 s is dominantly affected by the stick phenomenon, whereas the slip dominantly influences the total CoF PDF after 1 s. The CoF PDFs obtained from simulations with combinations of two and three uncertain parameters have wider PDF ranges than those obtained for only one uncertain parameter. The current work demonstrates that the CoF is strongly affected by the stochastic variation of dynamic parameters. Thus, the PDF distribution of the CoF could play a very important role in the design of the wheel-rail system.

Wheel-Rail Dynamic Model and Stochastic Analysis of the Friction in the Contact Patch

2010 ◽  
Author(s):  
HyunWook Lee ◽  
Corina Sandu ◽  
Carvel Holton
Keyword(s):  
Stochastic Analysis ◽  
Lateral Displacement ◽  
Maximum Amplitude ◽  
Accurate Estimation ◽  
Uncertain Parameters ◽  
Dynamic Parameters ◽  
Stochastic Variation ◽  
The Coefficient Of Friction ◽  
Polynomial Chaos Theory ◽  
Probability Density Function Pdf

The coefficient of friction (CoF) is one of the most important parameters for characterizing the contact between the wheel and the rail. The assumption of a constant CoF is still used in most theoretical studies, although experimental work indicates that the CoF depends on material and dynamic parameters. In the real world, accurate estimation of the CoF is not simple due to various uncertainties. In this paper we present a new 3D nonlinear dry CoF model at the wheel-rail contact. In addition, a stochastic analysis using the polynomial chaos theory is performed with the CoF model. The maximum amplitude of rail roughness and the lateral displacement of the wheel are considered as uncertain parameters in this study. One of the novelties in this study is that our CoF model captures the maximum CoF value (an initial peak) when the wheel starts to move. The stochastic analysis results show that the CoF probability density function (PDF) of a combination of two uncertain parameters has wider PDF ranges than the PDF obtained for only one uncertain parameter. The current work demonstrates that the CoF is strongly affected by the stochastic variation of dynamic parameters. In reality, the CoF is critical to rail tractive performance and efficiency. Thus, the PDF distribution of the CoF must be accounted for in the design of the wheel-rail system.

Automating the Derivation of the Equations of Motion of a Multibody Dynamic System With Uncertainty Using Polynomial Chaos Theory and Variational Work

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Paul S. Ryan ◽  
Sarah C. Baxter ◽  
Philip A. Voglewede
Keyword(s):  
Chaos Theory ◽  
Polynomial Chaos ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Multibody Dynamic ◽  
Mass Spring ◽  
Polynomial Chaos Theory ◽  
Multibody Dynamic System ◽  
Crank Mechanism

Abstract Understanding how variation impacts a multibody dynamic (MBD) system's response is important to ensure the robustness of a system. However, how the variation propagates into the MBD system is complicated because MBD systems are typically governed by a system of large differential algebraic equations. This paper presents a novel process, variational work, along with the polynomial chaos multibody dynamics (PCMBoD) automation process for utilizing polynomial chaos theory (PCT) in the analysis of uncertainties in an MBD system. Variational work allows the complexity of the traditional PCT approach to be reduced. With variational work and the constrained Lagrangian formulation, the equations of motion of an MBD PCT system can be constructed using the PCMBoD automated process. To demonstrate the PCMBoD process, two examples, a mass-spring-damper and a two link slider–crank mechanism, are shown.

Uncertainty Quantification of Hot Gas Ingestion for a Gas Turbine Nozzle Using Polynomial Chaos

2015 ◽  
Author(s):  
Andrea Panizza ◽  
Alessio Bonini ◽  
Luca Innocenti
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Gas Turbine ◽  
Polynomial Chaos ◽  
Thermal Design ◽  
Efficient Estimation ◽  
Critical Parameters ◽  
Accurate Estimation ◽  
Stochastic Expansion ◽  
Hot Gas

One of the most critical parameters in the design process of cooled hot gas components, is the Back Flow Margin (BFM). This dimensionless parameter quantifies the margin to hot gas ingestion through a cooled component wall. A correct evaluation of this parameter is crucial in order to avoid component failure. In presence of combustion chambers that exhibit low pressure losses, BFM becomes one of the most restrictive requirements in the thermal design of cooled components. In this work, a conceptual BFM assessment of the first nozzle of an HP gas turbine is described. The component is subject to the highest thermal load; complex cooling systems are required to ensure an acceptable metal temperature and to match life time requirement. Due to manufacturing tolerances and fluid dynamic uncertainties, hot gas ingestion events are possible also for a nozzle that exhibits BFM higher than zero in nominal conditions, even if with a low probability. Here, the cooling scheme of the nozzle is modeled using an in-house fluid network tool that allows a quick and accurate computation of the equivalent cooling scheme and thus the occurrence of hot gas ingestion, corresponding to a negative flow rate in one of the cooling sub-models. However, as the probability of hot gas ingestion is rather small, an accurate estimation of this event based on the standard Monte Carlo method requires a huge number of runs. A more efficient estimation of this probability can be obtained using stochastic expansion methods, such as the Polynomial Chaos Expansion. Pseudospectral approximations based on either a tensor-product expansion or the Sparse Pseudospectral Approximation Method (SPAM) are used, in order to estimate the probability of hot gas ingestion and the sensitivity to random parameters. The results are compared with those coming from Monte Carlo method, showing the superior accuracy of the stochastic expansion methods.

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