Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Fu, Chao; Xu, Yuandong; Yang, Yue; Lu, Kuan; Gu, Fengshou; Ball, Andrew

doi:10.1016/j.jsv.2019.115047

Cited by 82 publications

(49 citation statements)

References 53 publications

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“…The temperature dependency of material properties given by Touloukian [41] can be expressed as a non-linear function of temperature, as shown in Equation (2). Although there are many other non-linear variations in the rotating systems [42,43], the non-linear gradation of material properties and non-linear temperature distribution are considered in the present work.…”

Section: Methodsmentioning

confidence: 99%

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

et al. 2020

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The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.

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Section: Methodsmentioning

confidence: 99%

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

et al. 2020

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“…As a comparison to other methods dealing with uncertainty models for instance combined hybrid uncertainty model proposed in [36] we have the following arguments. The approach in [36] is based on propagation of uncertainty (the sensitivity analysis) and mainly focuses on the classical interval arithmetic rather than providing direct (less/more conservative) solutions, see Equation (15) in [36]. Although, the Contamination model is another Hybrid or even called Mixed Model to contaminate non-probabilistic with probabilistic models via choosing proper tuning factor ( ).…”

Section: Comparisonmentioning

confidence: 99%

Day-Ahead Energy and Reserve Dispatch Problem under Non-Probabilistic Uncertainty

et al. 2021

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The current energy transition and the underlying growth in variable and uncertain renewable-based energy generation challenge the proper operation of power systems. Classical probabilistic uncertainty models, e.g., stochastic programming or robust optimisation, have been used widely to solve problems such as the day-ahead energy and reserve dispatch problem to enhance the day-ahead decisions with a probabilistic insight of renewable energy generation in real-time. By doing so, the scheduling of the power system becomes, production and consumption of electric power, more reliable (i.e., more robust because of potential deviations) while minimising the social costs given potential balancing actions. Nevertheless, these classical models are not valid when the uncertainty is imprecise, meaning that the system operator may not rely on a unique distribution function to describe the uncertainty. Given the Distributionally Robust Optimisation method, our approach can be implemented for any non-probabilistic, e.g., interval models rather than only sets of distribution functions (ambiguity set of probability distributions). In this paper, the aim is to apply two advanced non-probabilistic uncertainty models: Interval and ϵ-contamination, where the imprecision and in-determinism in the uncertainty (uncertain parameters) are considered. We propose two kinds of theoretical solutions under two decision criteria—Maximinity and Maximality. For an illustration of our solutions, we apply our proposed approach to a case study inspired by the 24-node IEEE reliability test system.

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“…Bit-induced vibrations originate from the bit-rock cutting process, while string-induced vibrations are caused by the contact between drilling tools and formation [5]. The bit rock interaction during drilling is a complex process with many uncertainties [6], which can be considered, in various ways, e.g., with hybrid uncertainties [7]. It has been shown that, for the torsional dynamic of the drill string, the energy input can be modeled using a nonlinear torque characteristic at the bit [8].…”

Section: Introductionmentioning

confidence: 99%

A Method for the Design and Optimization of Nonlinear Tuned Damping Concepts to Mitigate Self-Excited Drill String Vibrations Using Multiple Scales Lindstedt-Poincaré

et al. 2021

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In downhole drilling systems, self-excited torsional vibrations caused by the bit-rock interactions can affect the drilling process and lead to the premature failure of components. Especially self-excited oscillations of higher-order modes lead to critical dynamic loads. The slim drill string design and the naturally limited drilled borehole diameter limit the installation space, power supply and lead to numerous potentially critical self-excited torsional modes. Consequently, small and robust passive damping concepts are required. The variety of possible downhole boundary conditions and potential damper designs necessitates analytical solutions for effective damper design and optimization. In this paper, two nonlinear passive damper concepts are investigated regarding design and effectiveness to reduce self-excited high-frequency torsional oscillations in drill string dynamics. Based on a finite element model of a drill string, a suitable minimal model based on the identified critical mode is generated and solved analytically using the Multiple Scales Lindstedt-Poincaré (MSLP) method. The advantages of MSLP compared to conventional MS methods are shown for this example. On the basis of the analytical solution, parameter influences are determined, and design equations are derived. The analytical results are transferred to self-excited drill string vibrations and discussed using time domain simulations of the drill string model.

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Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Cited by 82 publications

References 53 publications

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

Day-Ahead Energy and Reserve Dispatch Problem under Non-Probabilistic Uncertainty

A Method for the Design and Optimization of Nonlinear Tuned Damping Concepts to Mitigate Self-Excited Drill String Vibrations Using Multiple Scales Lindstedt-Poincaré

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