Nonlinear behavior for periodically excited brushless motor

2019 ◽  
Vol 38 (2) ◽  
pp. 522-535
Author(s):  
Jianzhe Huang ◽  
Xingzhong Xiong
Keyword(s):  
Working Condition ◽  
Analytic Solution ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Strong Nonlinearity ◽  
Periodic Motions ◽  
Content Type ◽  
Strongly Nonlinear ◽  
Brushless Motor ◽  
Analytic Expressions

Purpose Due to the coupling between the direct-axis current, quadrature-axis current and rotor speed, the dynamic response could be strongly nonlinear. Besides, if the working condition is severe, the loading is no longer constant and multiple harmonics could be introduced. In this paper, the periodic motions for brushless motor will be solved, and accurate analytic solution will be obtained through the proposed method. The purpose of this study is to provide accurate analytic solution of periodic motions for brushless motor with fluctuated loading, which is a dynamic system with strong nonlinearity. Design/methodology/approach A newly developed semi-analytic algorithm called discrete implicit maps is used to give analytic solutions for both stable and unstable motions for such a motor. Findings The accurate analytic expressions for stable and unstable periodic motions have been obtained. For unstable motion, it can stay on the unstable orbit for many periods without any controller. Through bifurcation analysis, the parameter sensitivity has been obtained which can be a suggestion for design and operation. Originality/value This paper provides all possible analytical solutions for period-1 motion as well as the unstable motions in a range of system parameters. It offers a chance to control the unstable motion for such a motor.

scholarly journals A new analytic solution of complex Langevin differential equations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rabha Ibrahim
Keyword(s):  
Differential Equations ◽  
Analytic Solution ◽  
Function Theory ◽  
Special Functions ◽  
Analytic Solutions ◽  
Geometric Function Theory ◽  
Content Type ◽  
Complex Differential Equation ◽  
Geometric Function ◽  
Carathéodory Functions

PurposeIn this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.Design/methodology/approachThe methodology is based on the geometric function theory.FindingsThe authors present a new analytic function for a class of complex LDEs.Originality/valueThe authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

Exact and approximate analytic solutions of the thin film flow of fourth-grade fluids by the modified Adomian decomposition method

2016 ◽  
Vol 26 (8) ◽  
pp. 2432-2440 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Jun-Sheng Duan ◽  
Randolph Rach
Keyword(s):  
Thin Film ◽  
Analytic Solution ◽  
Adomian Decomposition Method ◽  
Fluid Flows ◽  
Fourth Grade ◽  
Analytic Solutions ◽  
Exact Analytic Solution ◽  
Content Type ◽  
Adomian Decomposition ◽  
Film Flows

Purpose The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications. Design/methodology/approach The approach to calculating a new form of the exact analytic solution of thin film fluid flows rests upon a sequence of transformations including the modification of the classic technique due to Scipione del Ferro and Niccolò Fontana Tartaglia. Next the authors establish a lemma that justifies the new expression of the exact analytic solution for thin film fluid flows of fourth-grade fluids. Second, the authors apply a modification of the systematic ADM to quickly and easily calculate the sequence of analytic approximate solutions for this strongly nonlinear model of thin film flow of fourth-grade fluids. The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific and engineering applications. Herein, the authors seek to establish the relative merits of the ADM in the context of the thin film flows of fourth-grade fluids. Findings The ADM is shown to closely agree with the new expression of the exact analytic solution. The authors have calculated the error remainder functions and the maximal error remainder parameters in the error analysis to corroborate the solutions. The error analysis demonstrates the rapid rate of convergence and that we can approximate the exact solution as closely as we please; furthermore the rate of convergence is shown to be approximately exponential, and thus only a low-stage approximation will be adequate for engineering simulations as previously documented in the literature. Originality/value This paper presents an accurate work for solving thin film flows of fourth-grade fluids. The authors have compared the approximate analytic solutions by the ADM with the new expression of the exact analytic solution for this strongly nonlinear model. The authors commend this technique for more complex thin film fluid flow models.

Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ming-Xian Lin ◽  
Chia-Hsiang Tseng ◽  
Chao Kuang Chen
Keyword(s):  
Decomposition Method ◽  
Large Deflection ◽  
Adomian Decomposition Method ◽  
Nonlinear Behavior ◽  
Bernoulli Beam ◽  
Rapid Convergence ◽  
Content Type ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam ◽  
Better Than

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

A study on diesel engine crankshaft bearing failure analysis with consideration of bearing lubrication

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qi Liu ◽  
Baiqi Huo ◽  
Yunsheng Liu ◽  
Junchao Zhu
Keyword(s):  
Diesel Engine ◽  
Failure Mechanism ◽  
Working Condition ◽  
Mixed Lubrication ◽  
Bearing Failure ◽  
Content Type ◽  
Lubrication Performance ◽  
Lubrication Characteristics ◽  
The Relationship ◽  
Engine Crankshaft

Purpose The edge of diesel engine crankshaft main bearing is more likely to fail in its real working condition. This paper aims to study the bearing failure mechanism by finding the relationship between bearing lubrication characteristics and its working condition. Design/methodology/approach This work builds the mixed lubrication model of crankshaft bearing to analyze the cause of bearing abnormal wear, and the finite difference method was used to solving the average Reynolds equation. During the analysis, journal misaligned angle, external load and roughness are considered. Findings The result shows that the wear of the diesel engine crankshaft bearing happens in engine startup phase and the bottom of the bearing are more prone to be excessively worn. Under the influence of journal misalignment, bearing asperity contact load and speed range of mixed lubrication will increase markedly. The edge of the bearing will be excessively worn. The effect of misalignment on bearing lubrication performance varies under different shaft rotation speed. Originality/value The former research studies on crankshaft bearing either just focused on its lubrication characteristics or interested in its failure types (wear, adhere, cavitation). This paper studies the relationship between bearing failure mechanism and lubrication performance.

scholarly journals Dynamic Characteristics of Deeply Buried Spherical Biogas Digesters in Viscoelastic Soils

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hongwei Hou ◽  
Shihu Gao ◽  
Qianqian Guo ◽  
Long Chen ◽  
Bing Wu ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Fractional Derivative ◽  
Elastic Medium ◽  
Shell Structure ◽  
Fractional Derivatives ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Dynamic Responses ◽  
Significant Difference ◽  
The Continuum

The harmonic vibration characteristics of a deeply buried spherical methane tank in viscoelastic soil subjected to cyclic loading in the frequency domain are investigated. The dynamic behavior of the soil is described based on the theory of fractional derivatives. By introducing potential functions, the closed-form expressions for the displacement and the stress of the viscoelastic soil surrounding the deeply buried spherical methane tank are obtained. Two die structures are considered: a homogeneous elastic medium and a shell structure. Based on the theory of elastic motion and the Flügge theory, analytic solutions for the dynamic responses of the spherical methane tank in a fractional-derivative viscoelastic soil are derived explicitly. Analytic solution expressions of the undetermined coefficients are determined by using the continuum boundary conditions. The system dynamic responses to the homogeneous elastic medium and the shell structure and the influences of the parameters of the fractional derivative, soil, and die on the dynamic characteristic of the system are compared and analyzed. The results indicate a significant difference between the dynamic responses of the die structures for the two models.

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
Aysenur Toptan ◽  
Nathan W. Porter ◽  
Jason D. Hales ◽  
Benjamin W. Spencer ◽  
Martin Pilch ◽  
...  
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Simulation Tool ◽  
Code Verification ◽  
Simulation Tools ◽  
Steady State Heat ◽  
The One ◽  
Selection Of

Abstract When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. Here, we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

scholarly journals Modeling nonlinear compressional waves in marine sediments

2009 ◽  
Vol 16 (1) ◽  
pp. 151-157 ◽  
Author(s):  
B. E. McDonald
Keyword(s):  
Marine Sediments ◽  
Plane Waves ◽  
High Stress ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Compressional Waves ◽  
Series Of Experiments ◽  
Model Equations ◽  
The Time Domain ◽  
Water Saturated

Abstract. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.

Wave-Based Control of a Nonlinear Flexible System

2006 ◽  
Author(s):  
William J. O’Connor ◽  
Francisco Ramos ◽  
Vicente Feliu
Keyword(s):  
Control Strategies ◽  
System Modeling ◽  
Nonlinear Behavior ◽  
Effective Control ◽  
Space Structures ◽  
Large Space ◽  
Flexible System ◽  
Strongly Nonlinear ◽  
Mechanical Waves ◽  
Actuator System

The motivation for this work is the control of flexible mechanical systems, such as long, light robot arms, gantry cranes, and large space structures, with an actuator at one end and a free boundary at the other. Very effective control strategies have recently been developed which are based on interpreting the actuator motion as launching mechanical “waves” (propagating motion) into the flexible system while absorbing returning “waves”. These control systems are robust to system changes and to actuator limitations. They are generic, require very little system modeling, need only local sensing, and are computationally light and easy to implement. In a flexible arm, when elastic deflections are large, frequently there is strongly nonlinear behavior. This paper investigates how such nonlinearities affect the wave-based control strategy. In summary, the news is good. It is found that errors arise only when trajectories are very demanding, and even then the errors are small. Some strategies for correcting these errors are explained: addition of a linear element at the actuator-system interface, error correction by second manoeuver, and redefinition of the waves in a less-than-optimal way. The paper presents these ideas and illustrates them with numerical simulations.

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