Unified method for typical gear failure modeling and stiffness calculation based on the matrix equation

The failure types in gear systems vary,with typical ones mainly including pitting,cracking,wear,and broken teeth.Different modeling and stiffness calculation methods have been developed for various gear failure types.A unified method for typical gear failure modeling and stiffness calculation is introduced in this study by considering the deviations in the time-varying meshing stiffness(TVMS)of faulty gears resulting from the use of different methods.Specifically,a gear tooth is discretized into a large number of microelements expressed with a matrix,and unified models of typical gear failures are built by adjusting the values of the matrix microelements.The values and positions of the microelements in the tooth failure model matrix have the same physical meaning as the parameter variables in the potential energy method(PEM),so the matrix-based failure model can be perfectly matched with PEM.Afterward,a unified method for TVMS is established.Modeling of healthy and faulty gears with pitting,wear,crack,and broken tooth is performed with the matrix equation,and the corresponding TVMS values are calculated by incorporating the matrix models with PEM.On the basis of the results,the mechanism of typical fault types that affect TVMS is analyzed,and the conclusions are verified through the finite element method.The developed unified method is a promising technique for studying the dynamic response characteristics of gear systems with different failure types because of its superiority in eliminating stiffness deviations.

The asymptotic behavior for a binary alloy in energy and material science:The unified method and its applications

The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958.This model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant.For instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down adequately.In this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive microstructure.Next,when the time scale is slower the microstructure becomes coarse.In this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the system.Finally,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model.The technique applied in this analysis is powerful and efficient,as evidenced by the computational work and results.This technique can also solve a large number of higher-order evolution equations.

Unified Solution Method of Rectangular Plate Elastic Bending

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Influence of High-Density Bedding Plane Characteristics on Hydraulic Fracture Propagation in Shale Oil Reservoir

The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.

THE INITIAL BOUNDARY VALUE PROBLEMS FOR A NONLINEAR INTEGRABLE EQUATION WITH 3×3 LAX PAIR ON THE FINITE INTERVAL

In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.

A Unified Dynamic Control Method for a Redundant Dual Arm Robot

Compared to single arm robot system, dual arm robot has the ability of performing human-like dexterity and cooperation. Dual arm cooperative operation has attracted more and more attention in industrial applications, such as in assembly of complex parts, manufacturing tasks and handling objects. A unified dynamic control method, which is divided into three modes, namely, independent mode, dependent mode, and half dependent mode, is proposed for a redundant dual arm robot with focus on the movement and force of the desired task being operated. Attention is devoted to develop a unified formulation of the above three modes. In addition, a closed form of inverse kinematic solution instead of numerical integration approach is proposed with the aim to guarantee position accuracy. Different from traditional dynamic controllers, where the independent redundancy resolution is obtained based on particular velocity or acceleration levels, here the two dynamic controllers are improved by combining a closed form of inverse kinematic solution with velocity and acceleration levels. Furthermore, the theoretical results of the proposed control method are validated by simulations and experiments.

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

The unified transform method to the high-order nonlinear Schrodinger equation with periodic initial condition

In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.

Unified Gas-Kinetic Wave-Particle Methods VI:Disperse Dilute Gas-Particle Multiphase Flow

A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is proposed.In the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes solution.The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen number.In the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)model.In the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)formulation.In the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly.The GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction.It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.

A unified solution method for free vibration analysis of functionally graded rotating type plates with elastic boundary condition

In this paper,a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate(FGRTP)of which the distribution of material is defined by four parameters is presented.It is assumed that the considered functionally graded materials(FGM)are distributed in the thickness direction according to four parameters.The displacement fields of any point on the FGRTP are determined by the first order shear deformation theory(FSDT),and all displacement functions are extended by ultraspherical polynomial.By applying the Ritz method to the energy function of the whole system,the constitutive equation of FGRTP is obtained and the natural frequencies are obtained by solving the eigenvalue problem.The boundary conditions are generalized to arbitrary boundary conditions by artificial elastic technique.The accuracy of the proposed method is verified by comparing with the previous literatures.The effects of different parameters on the free vibration characteristics of FGRTP are studied through some numerical examples.

FEA Versus IGA in a Two-Node Beam Element Based on Unified and Integrated Method

This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element.In this method,Timoshenko beam theory is unified and integrated in such a way that takes into account the effect of transverse shear and maintains the shear locking free condition at the same time to generate proper behavior in the analysis of thin to thick beams.The unified and integrated method is applied to finite element analysis(FEA)and isogeometric analysis(IGA)on two-node beam element.This method will be used to analyze uniformly loaded beams with various boundary conditions.A shear influence factor of f,which is a function of beam thickness ratio(L/h),is expressed explicitly as control of the transverse shear strain effect.The analysis gives interesting results showing that applying the unified and integrated method in FEA and IGA will yield exact values of DOF’s and displacement function even when using only a single element.Numerical examples demonstrate the validity and efficiency of the unified and integrated methods.

Generation and Application of A Standardized Load-Time History to Tubular T-joints in Offshore Platforms

Marine structures are mostly made of metals and always experience complex random loading during their service periods. The fatigue crack growth behaviors of metal materials have been proved from laboratory tests to be sensitive to the loading sequence encountered. In order to take account of the loading sequence effect, fatigue life prediction should be based on fatigue crack propagation（FCP） theory rather than the currently used cumulative fatigue damage（CFD） theory. A unified fatigue life prediction（UFLP） method for marine structures has been proposed by the authors＇ group. In order to apply the UFLP method for newly designed structures, authorities such as the classification societies should provide a standardized load-time history（SLH） such as the TWIST and FALSTAFF sequences for transport and fighter aircraft. This paper mainly aims at proposing a procedure to generate the SLHs for marine structures based on a short-term loading sample and to provide an illustration on how to use the presented SLH to a typical tubular T-joint in an offshore platform based on the UFLP method.

A Unified Fractional-Step,Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

This paper introduces a unified concept and algorithm for the fractionalstep(FS),artificial compressibility(AC)and pressure-projection(PP)methods for solving the incompressible Navier-Stokes equations.The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based(CB)Godunov-type treatment of convective terms with PP methods.Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP(split)methods,thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible.Therefore,the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a)overcome the numerical stiffness of the classical AC approach at(very)low and moderate Reynolds numbers,b)incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods,and c)further improve the stability and efficiency of the AC method for steady and unsteady flow problems.The FSAC-PP method has also been coupled with a non-linear,full-multigrid and fullapproximation storage(FMG-FAS)technique to further increase the efficiency of the solution.For validating the proposed FSAC-PP method,computational examples are presented for benchmark problems.The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

Over the past half century,a variety of computational fluid dynamics(CFD)methods and the direct simulation Monte Carlo(DSMC)method have been widely and successfully applied to the simulation of gas flows for the continuum and rarefied regime,respectively.However,they both encounter difficulties when dealing with multiscale gas flows in modern engineering problems,where the whole system is on the macroscopic scale but the nonequilibrium effects play an important role.In this paper,we review two particle-based strategies developed for the simulation of multiscale nonequilibrium gas flows,i.e.,DSMC-CFD hybrid methods and multiscale particle methods.The principles,advantages,disadvantages,and applications for each method are described.The latest progress in the modelling of multiscale gas flows including the unified multiscale particle method proposed by the authors is presented.

A Riemann–Hilbert Approach to Complex Sharma–Tasso–Olver Equation on Half Line

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.

Analyzing the general biased data by additive risk model

This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.

Multi-solitons of Thermophoretic Motion Equation Depicting the Wrinkle Propagation in Substrate-Supported Graphene Sheets

The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.

A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line

In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i？tu ＋ ？xxu-i｜u2｜？xu = 0 on the half line（-∞, 0] with decaying initial value. Assuming that the solution u（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit（x, t） dependence and is given in terms of the spectral functions{a（λ）, b（λ）}and{A（λ）, B（λ）}, which are obtained from the initial data u0（x） = u（x, 0） and the boundary data g0（t） = u（0, t）, g1（t） = ux（0, t）, respectively. The spectral functions are not independent,but satisfy a so-called global relation.

On controlled propagation of nonautonomous dispersive coupled Whitham-Broer-Kaup equation in shallow water

In this paper,the dispersive coupled Whitham-Broer-Kaup(DCWBK)equation with time-dependent coefficients describing the propagation of the shallow water waves are obtained.The propagation of solitons and elliptic(or chirped)waves can be manipulated by suitable variations of the dispersion coefficient.Here,controllable transmission of the surface waves for soliton similariton pairs with the snoidal backgrounds is considered.It is found that,when the dispersion coefficient is taken as increasing,the velocity is increasing with the dispersion coefficient increasing.While this holds vice versa for the height of propagation wave.