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The purpose of this paper is to analyze the time-dependent reliability of harmonic drive.

The transient finite element analysis (FEA) of harmonic drive is established to calculate the stress under different loads. Combined with the residual strength model and random variables, the time-dependent reliability model of harmonic drive is deduced by the stochastic perturbation method and Edgeworth series. Based on accelerated life tests, the degradation parameters are estimated by maximizing likelihood function. Under variable load, the key stress from transient FEA is transformed into probability density function by kernel density estimation, and the residual strength model is modified by adding adjustment factors to deal with strength degradation under different loads.

The critical position of stress concentration from transient FEA is consistent with the fatigue fracture position at the accelerated life test sample. Compared with the time-dependent reliability method with equivalent circular-shell static stress or empirical degradation parameters, the proposed method has the smallest prediction error of failure life. Under variable load, the state function should be expanded to second-order series for avoiding error items relevant to variance. The failure life expectation under random variable load is smaller than that under constant load.

The time-dependent reliability method of harmonic drive is firstly proposed under constant and variable load. The transient FEA of harmonic drive is established to calculate the stress for strength analysis. The accelerated life test of harmonic drive is conducted for degradation parameters estimation. The adjustment factor is added to the residual strength model for strength degradation under different loads.

Sand production is a challenging issue during hydrocarbon production in the oil and gas industry. This paper aims to investigate one sand production process, i.e. transient sand production, using a novel bonded particle lattice Boltzmann method. This mesoscopic technique provides a unique insight into complicated sand erosion process during oil exploitation.

The mesoscopic fluid-particle coupling is directly approached by the immersed moving boundary method in the framework of lattice Boltzmann method. Bonded particle method is used for resolving the deformation of solid. The onset of grain erosion of rocks, which are modelled by a bonded particle model, is realised by breaking the bonds simulating cementation when the tension or tangential force exceeds critical values.

It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. It is found that when the drawdown happens at the wellbore cavity, the tensile failure area appears at the edge of the cavity. Then, the tensile failure area gradually propagates inward, and the solid particles at the tensile failure area become fluidised because of large drag forces. Subsequently, some eroded particles are washed out. This numerical investigation is demonstrated through comparison with the experimental results. In addition, through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

A novel bonded particle lattice Boltzmann method is used to investigate the sand production problem at the grain level. It is proved that the complex fluid–solid interaction occurring at the pore/grain level can be well captured by the immersed moving boundary scheme in the framework of the lattice Boltzmann method. Through breaking the cementation, which is simulated by bond models, between bonded particles, the transient particle erosion process is successfully captured.

The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head.

An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other.

The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes.

The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis.

This paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation.

Firstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin’s method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given.

The FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs’ code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs.

The FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant.

The aim of this work is to reveal the temperature rise characteristics of the new designed disc during a braking process. In underground coal mines, the highest temperature of the disc brake used for inclined downward belt conveyors should be < 150 to prevent gas explosion during a braking process. To meet the requirements, a new type of disc was designed.

By using ANSYS software, the disc surface and interior temperature rise variations, effect of braking time and running speed on temperature rise are analyzed numerically.

The results show that the new designed disc can meet the coal mines’ requirements well, during the braking process the disc surface temperature increases at first and then decreases, there is an obvious temperature gradient in the axial direction; when running speed increases to two times of the rated one, the highest temperature nearly reaches 150; and a prolonged braking time can decrease the highest temperature effectively.

It indicates that the disc brake should act as earlier as possible to slow down the belt conveyor when overspeed occurs; and when the running speed increases to two times of the rated one, the braking time must be prolonged to prevent gas explosion.

Research findings of this paper provides theoretical basis for the practical applications of the disc brake used for inclined downward belt conveyor.

This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations.

This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations.

The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result.

This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.

During running-in, the change in the honed cylinder liner surface alters the performance and efficiency of the piston ring-pack system. The present paper, thus, aims to investigate the surface topography and wear and friction evolution of a cylinder liner surface during the running-in tests on a reciprocating ring–liner tribometer under a mixed lubrication regime. After an initial period of rapid wear termed “running-in wear”, a relatively long-term steady-state surface topography can emerge. A numerical model is developed to predict the frictional performance of a piston ring-pack system at the initial and steady-state stages.

The liner surfaces are produced by slide honing (SH) and plateau honing (PH). The bearing area parameter (Rk family), commonly used in the automotive industry, is used to quantitatively characterize the surface topography change during the running-in process. A wear volume-sensitive surface roughness parameter, Rktot, is used to show the wear evolution.

The experimental results show that a slide-honed surface leads to reduced wear, and it reduces the costly running-in period compared to the plateau-honed surface. The simulation results show that running-in is a beneficial wear process that leads to a reduced friction mean effective pressure at the steady-state.

To simulate the mixed lubrication performance of a ring–liner system with non-Gaussian roughness, a one-dimensional homogenized mixed lubrication model was established. The real surface topography instead of its statistical properties is taken into account.

In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time.

The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach.

The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits.

The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

This paper studies the nonlinear dynamics of membrane structure considering wrinkling effect. The coupling between wrinkles and vibration is investigated elaborately, and new insight on the dynamics of wrinkled membrane is unveiled.

Based on the stability theory of plates and shells, the wrinkling model of the membrane structure is established. Considering the effects of wrinkling and nonlinearity, the dynamic response is calculated with NewMark method.

Wrinkling will impact the dynamics of the membrane structure significantly for asymmetrical tension loading cases, dynamic response of the wrinkled membrane structure can be classified into three categories: when the vibration is small, the dynamics of the wrinkled membrane structure will behave linearly, and the wrinkles will only affect the dynamic properties as initial conditions; when the vibration is relatively large, the wrinkles will interact with the vibration during the dynamic process, and the dynamics of the structure shows very complex features; when the vibration is large enough, the dynamics will be dominated by the geometric nonlinearity of large-amplitude vibration.

In the previous works on dynamics of wrinkled membrane structure, only the vibration modes have been studied, which means all those investigations are confined with linear vibration; little research has been conducted on the nonlinear dynamics of wrinkled membrane structure. In view of this, this paper presents an investigation of dynamic properties of membrane structure considering the wrinkling and geometric nonlinear effects. This research work presents some novel discoveries on the nonlinear dynamics of wrinkled membrane.

This paper aims to develop an assembly behaviour dynamic model of reheat stop valve assembly under run‐time situations and combined (assembly error, friction, fluid dynamics and thermal load behaviour) and to carry out assembly process evaluation and optimisation.

The fluid dynamic behaviour analysis is carried out for the dynamic torque characteristics of reheat stop valve and for the thermal load distribution of the valve shaft‐bush subassembly, which is used for evaluating the thermal deformation of valve shaft by using of finite elements method. The assembly behaviour dynamic model is developed by multibody dynamics theory, which is as the basis of developing virtual prototyping platform for analysing and evaluating the current assembly process.

It is revealed that the deformation (ε) of valve shaft due to the thermal load, and the assembly coaxial error (e) can change the motion clearance remarkably, which lead the dynamic properties and performance of reheat stop valve changed greatly. The current assembly behaviour variable are not optimum and the initial design clearance between valve shaft and bush 4# can be optimised by the developed virtual prototyping platform on the basis of ADAMS® API. The results of evaluation for the assembly behaviour reveal the well dynamic characteristics of reheat stop valve with the optimum assembly behaviour variable. This will be useful for improving the current assembly process of reheat stop valve.

The present assembly behaviour dynamic model based on virtual prototyping for optimum assembly process design uses only single objective optimisation (the most important clearance between valve shaft and bush 4#). For a complete optimum assembly process design has to be carried out with other three clearance variables (the clearance between valve shaft and bush 1#, bush 2# and bush 3#) together.

The present analysis provides some benchmarks for improving the current assembly process. In practice, the assembly coaxial tolerance of valve shaft‐bush subassembly and the initial design clearances must be limited strictly.

This paper provides a methodology for analysis and evaluation of reheat stop valve assembly behaviour with the consideration of combined environmental behaviours. Based on this methodology, it is possible to develop an assembly behaviour dynamic model, and further, to develop a virtual prototyping platform for analysing and evaluating the assembly process which will offer help to designers for improving the reheat stop valve assembly process.