Load-sharing Model Research Articles

A bivariate load-sharing model

The motivation of this work came from a data set obtained from an experiment performed on diabetic patients, with diabetic retinopathy disorder. The aim of this experiment is to test whether there is any significant difference between two different treatments which are being used for this disease. The two eyes can be considered as a two-component load-sharing system. In a two-component load-sharing system after the failure of one component, the surviving component has to shoulder extra load. Hence, it is prone to failure at an earlier time than what is expected under the original model. It may also happen sometimes that the failure of one component may release extra resources to the survivor, thus delaying the failure. In most of the existing literature, it has been assumed that at the beginning the lifetime distributions of the two components are independently distributed, which may not be very reasonable in this case. In this paper, we have introduced a new bivariate load-sharing model where the independence assumptions of the lifetime distributions of the two components at the beginning have been relaxed. In this present model, they may be dependent. Further, there is a positive probability that the two components may fail simultaneously. If the two components do not fail simultaneously, it is assumed that the lifetime of the surviving component changes based on the tampered failure rate assumption. The proposed bivariate distribution has a singular component. The likelihood inference of the unknown parameters has been provided. Simulation results and the analysis of the data set have been presented to show the effectiveness of the proposed model.

The geomechanical response of the Gulf of Mexico Green Canyon 955 reservoir to gas hydrate dissociation: A model based on sediment properties with and without gas hydrate

Gas hydrate is commonly found concentrated in sand- and silt-rich reservoirs and these are thought to have great potential as an energy resource. To evaluate this potential, it is critical to understand their in-situ stress state and their behavior during production. We explore the geomechanical behavior of sandy silt sediments from a hydrate reservoir at Green Canyon GC 955, deep-water Gulf of Mexico without hydrate and compare these results to previous work on the same sandy silty sediments with hydrate present. Previous results from hydrate-bearing sediments at GC 955 using intact specimens show that the ratio of lateral to axial effective stress under uniaxial strain (K0) is strongly time-dependent and over long timescales approaches 1 (isostatic stress state). New results from sediments without hydrate using reconstituted specimens reveal that K0 is 0.51 and independent of time and stress. The reservoir without hydrate is approximately three times more compressible than with hydrate. In addition, we find that hydrate-free sediments have a normalized creep rate of Cα/Cc of about 0.028 at all stress levels, whereas hydrate bearing sediments exhibit a decrease in Cα/Cc with stress. We use these observations to present a new geomechanical model that describes how stress and porosity evolve during production of the hydrate reservoir. The key insight in our proposed model is that the sediment skeleton and gas hydrate phases share any applied external load in proportion to their relative stiffnesses. The model results predict that hydrate-bearing sediments are stiffer than gas hydrate-free sediments and that K0 reduces dramatically after gas hydrate dissociation, as is observed. At GC 955, a 5 MPa depressurization is needed to cause gas hydrate dissociation. This change in pore pressure increases the vertical and horizontal effective stresses from 3.8 to 8.8 MPa and 3.8–4.4 MPa, respectively. The dramatic vertical effective stress increase will cause significant compaction (7%) and perturb stresses near the wellbore. These experimental observations and the load-sharing model presented have the potential to underpin a new generation of hydrate reservoir simulation models, which may drive more effective production approaches.

Simulations and predictions of future values in the time-homogeneous load-sharing model

Simulations and predictions of future values in the time-homogeneous load-sharing model

Multivariate conditional aging intensity functions and load-sharing models

The aging intensity functions analyze the aging property quantitatively, in the sense that the larger the aging intensity, the stronger the tendency of aging. They are useful tools to describe reliability properties of distributions. In the literature, the aging intensity functions have been studied in the univariate and bivariate case but without considering the possibility of observing a dynamic history. In this paper, the concept of aging intensity function is extended to the multivariate case by the use of the multivariate conditional hazard rate functions. Some properties of those functions are studied and a focus on the bivariate case is performed. Finally, the multivariate conditional aging intensity functions are studied for the order dependent version of the time-homogeneous load-sharing model and a study on the comparison among surviving components in a system is provided.

On the extended tooth contact and nonlinear dynamics for spur gears—An analytical model

In gear mesh, the extended tooth contact is a natural reaction stemming from the elasticity of solid bodies, which inevitably forces the theoretically separated teeth to engage and increases the actual contact ratio. Consequently, the changed mesh stiffness waveforms will further influence the dynamic response. A lot of works are devoted to mesh stiffness representation and dynamic modeling. However, the correlation between extended tooth contact and nonlinear dynamics still needs in-depth study. Motivated by a deeper understanding of the mesh mechanisms and dynamics, this paper proposed an analytical model attempting to combine the extended tooth contact and gear nonlinear dynamics. Starting from the gear elasticity, an analytical mesh stiffness model is proposed, which extended the application ranges of the popular fillet foundation polynomial formulas and covered both thin-walled and thick-walled gears. Moreover, A load-sharing model is developed, which explicitly represented the correlation between torques and intervals of extended tooth contact. Subsequently, the gear torsional dynamic model is extended to embody the extended tooth contact. A series of comparisons with FEM, existing theoretical models, and experiments demonstrated the acceptable accuracy of the present model.

Analytical approach to mesh stiffness modeling of high-speed spur gears

The centrifugal effect is a natural phenomenon in rotor dynamics, significantly changing the deformation responses in high-speed conditions. However, this phenomenon is generally unexplored in high-speed gears. This paper developed an analytical mesh stiffness model to bridge the kinematics and the centrifugal fields of spur gears. Starting from the elasticity of fillet-foundation, this model refined and extended the bi-dimensional formulas to consider gears in simultaneous rotating and meshing. The proposed load-sharing model additionally considered the extended tooth contact and centrifugal expansions, non-iteratively determining the complicated tooth engagement regions. Analytical formulas are further implemented with a fast numerical method, which removed restrictions of classical fillet-foundation formulas and covered both thick-walled and thin-walled gears. Quasi-static and dynamic solutions are compared with existing models, FEM, and experiments, showing the acceptable accuracy of this model and demonstrating noticeable centrifugal stiffening in high-speed conditions. To this end, sensitivities of centrifugal stiffening to multi-parameters are further investigated and characterized.

Effect of stiffness on load-sharing characteristics of twin rotors concentric face gear power-split transmission system

A twin rotors concentric face-gear power-split transmission system (TRCFGPSTS) applied to the core transmission mechanism of advanced aviation twin rotors helicopter was studied. The effects of torsional stiffness and support stiffness on the load-sharing characteristics of system were mainly studied. By comprehensively considering the factors such as manufacturing error and installation error, meshing stiffness, torsional stiffness, support stiffness and elastic deformation, and according to the power flow double closed-loop mechanical characteristics of this system, the static double closed-loop torsional angle elastic deformation coordination conditions are derived. The static load-sharing model was established by combining the moment balance equation of system. The load-sharing coefficient (LSC) and sensitivity parameters characterizing the load distribution of system were obtained. The effects of the torsional stiffness of the split-torsion shaft and the double-torsion shaft and the support stiffness of each gear on the load-sharing characteristics of the system were analyzed. The results show that the torsional stiffness of the split-torsion shaft and the double-torsion shaft has a great influence on LSC and sensitivity of the system, when its value is in the range of (1–1.6) × 105 N·m /rad and (2.4–4.3) ×105 N·m /rad, the system can meet the requirements of ± 5% of load-sharing characteristics under service conditions. Reducing the torsional stiffness of the split-torsion shaft can improve the load-sharing characteristics of the system, and the torsional stiffness of the right-branching double-shaft has little effect on the load-sharing characteristics of the left-branching of the system. The support stiffness of I-stage small cone angle face gear and Ⅲ-stage face gear is the most sensitive to LSC. With the increase of the support stiffness, the LSC first decreases and then gradually flattens, and the support stiffness of Ⅲ-stage face-gear has little effect on the I-stage LSC. The research results can provide a theoretical basis for the optimal design of load-sharing structure.

Experimental and numerical study on creep behaviors of 2D twill woven quartz fiber/silica matrix composites

This study investigates the creep deformation, damage, and rupture behaviors of 2D woven SiO2/SiO2 composites via experimental and numerical methods. In situ monotonic tensile tests and creep tests were conducted at 900 °C using a self-designed experimental system and digital image correlation. The tested specimens were characterized by X-ray computed tomography and scanning electron microscopy to conduct quantitative analyses and fracture observations. The obtained creep strain–time curves consist of primary and secondary stages, similar to the creep strain–time curves of most ceramic matrix composites. The matrix at the intersection of fiber bundles cracked under tensile loading. During subsequent creep loading, the propagation of matrix cracks, interfacial debonding, and fiber breakage in longitudinal fiber bundles were observed. At the mesoscale, the creep rupture entails a mechanism analogous to that observed in the monotonic tensile tests. Overall, the SiO2/SiO2 composites employed in this study exhibit excellent potential for long-term operation under mechanical loads at high temperatures. Next, a micromechanics-based creep model was proposed to simulate the creep behavior of the composites. In this model, the primary creep law and rule of mixtures were combined to describe the stress redistribution of various constituents and predict the deformation of the composites. In addition, the rupture life was predicted based on the global load-sharing model, two-parameter Weibull model, and shear lag model. The degradation of the matrix modulus and fiber strength was also considered to improve the accuracy of the simulation. The predicted results were in good agreement with the experimental data.

Study on dynamic load-sharing characteristics of face gear dual-power split transmission system with backlash, support and spline clearance

Abstract. The dynamic load-sharing characteristics of aircraft face gear dual-power split transmission system (FGDPSTS) are taken as the research object. Considering the factors of time-varying meshing stiffness, comprehensive error, backlash, support clearance, spline clearance, torsional stiffness, and support stiffness, the dynamic load-sharing model was constructed based on the lumped-parameter method. The loaded tooth contact analysis (LTCA) simulation method was used to calculate the time-varying meshing stiffness. The dynamic load-sharing coefficient (DLSC) is obtained by using Runge–Kutta method. The influences of errors, backlash, support clearance, spline clearance, torsional stiffness and support stiffness on DLSC were analyzed, and the biggest factors affecting dynamic load-sharing performance were found out. The results show that the influence of the backlash of the two-stage herringbone gear pair on the DLSC is more sensitive. The influence of support clearance on the DLSC is less. The load-sharing coefficient increases with the increase of the installation error and eccentricity error, and the influence of the error of the two-stage gears on the system load-sharing performance is the most sensitive. The torsional stiffness has little effect on the load-sharing coefficient of one stage but has great effect on the two-stage load-sharing coefficient. The influence of support stiffness on the DLSC of two-stage is stronger. It provided a theoretical basis for the dynamic stability optimization design of the system.

Study on the load-sharing characteristics of face-gear four-branching split-torque transmission system

In order to solve the load-sharing characteristics of face-gear four-branching split-torque transmission system (FGFBSTTS), the static load-sharing mechanical analysis model was established. In the model, the deformation coordination conditions of torsional angle and torque balance condition were considered. By using Loaded Tooth Contact Analysis (LTCA) technology of face gear and herringbone gear, the time-varying meshing stiffness was calculated. The influences of manufacturing errors, installation errors, I-stage pinion floating, II-stage pinion spline clearance floating, and radial limit ring clearance floating on the load-sharing characteristics are analyzed. The results show that the LTCA technology is more accurate to reflect the load-sharing characteristics of each meshing position. When the I-stage pinion and the II-stage pinion floated at the same time, the best load-sharing characteristics can be obtained. The load-sharing characteristics affected by manufacturing errors showed obvious periodic change. The radial limit ring plays a better auxiliary role in load-sharing characteristics. The theoretical results were compared with the experiments to verify the correctness of the theoretical analysis. The research results can provide a theoretical basis for the optimal design of the load-sharing structure, error control, and assembly of the face gear four branch transmission system.

Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

Analytical model for determining effective stiffness and mechanical behavior of polymer matrix composite laminates using continuum damage mechanics

The present paper proposes a new analytical model for predicting the effective stiffness of composite laminates with fiber breaks and transverse cracks. The model is based on continuum damage mechanics and the classical laminate theory. We derived damage variables describing stiffness reduction due to fiber breaks and its maximum value during ultimate tensile failure from the global load-sharing model. Furthermore, a simplified analytical model is presented for obtaining two damage variables for a cracked ply subjected to transverse tensile loading or in-plane shear loading. This model was developed assuming that the displacement field of the longitudinal direction can be expressed in the form of a quadric function by loosening the boundary condition for the governing differential equation. For verifying the developed model, the elastic constants of damaged composite laminates were predicted for cross-ply and angle-ply laminates and compared with the finite element analysis results. As for the appropriate expression of the effective elastic stiffness matrix of the damaged ply, we verified four types of effective compliance/stiffness matrices including the Murakami, Yoshimura, Li, and Maimí models. We found the Maimí model to be the most appropriate among these four models. Moreover, we successfully simplified the expressions for damage variables in the complicated infinite series obtained in our previous study. We also proved that this could contribute toward improving the accuracy of our analysis. After verifying the present model, the stress–strain response and failure strength of carbon- or glass-fiber-reinforced plastic cross-ply laminates were predicted using Maimí’s compliance model and the simplified damage variables.

Reliability Modelling and Evaluation for LTD System Based on Load-Sharing Model

Based on power adding technology, the linear transformer driver (LTD) scheme is widely used to generate high-energy pulsed outputs and adopts a hierarchical and modular structure. Although robust design and fault analysis for basic components have been conducted recently, there is still a lack of enough reliability analysis studies of the whole system. Taking an actual LTD system as an object, this paper presents a system reliability model based on a load-sharing mechanism. A unified load-sharing rule structure is established and four typical rules corresponding to equal, linear, exponential, and local-equal relationships are discussed in detail while evaluating the impact of the load-sharing mechanism. Subsequently, simulation experiments are performed to illustrate the effects of different load-sharing rules as well as analyzing the system reliability in which we simultaneously propose a self-adaptive Monte Carlo simulation flow to achieve the sampling probability adjustment according to the random failure sequence. The simulation results can serve as a suggestion for further improvement of the system reliability. Moreover, the model framework and the simulation analysis method described here are universal and can be applied to evaluate the reliability of other LTD-based systems with tiny modifications.

On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and non-informative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability ( $$C_{p}$$ ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.

A load share model for non-identical components of a k-out-of-m system

• A model for load sharing systems with non-identical components. • A new multivariate family of distributions for ordered random variables . • Inference procedure for the dependence parameter associated with load sharing effect. • Illustration of the proposed procedures on two component parallel system. We consider a k -out-of- m load sharing system when the lifetimes of the components are not necessarily identically distributed random variables. For such systems, a model for the load sharing phenomenon through the exponentiated conditional survival functions of ordered failure times is proposed. This model is more general than the load sharing model with identically distributed component lifetimes and leads to a different family of distributions for ordered random variables. A general expression for the reliability of the system is given. The computations of the reliability for a two component parallel load sharing system corresponding to the exponential and Weibull distributions are discussed. For illustrative purpose, we discuss the inference procedures for a two component parallel load sharing system corresponding to the exponential distributions . A simulation study is carried out to assess the proposed estimation and testing procedures. The applicability of the proposed load sharing model is shown through two data sets.

Research on the Load-Sharing Principle of a Novel Piezoelectric Dynamometer

The range of three-dimensional piezoelectric sensors in two tangential directions, depending on the maximum static friction force generated by axial preload, is usually only one-fifth of the axial preload, or even lower. It greatly limits the application of piezoelectric sensor in those situations where tangential measuring range is equal to or larger than axial measuring range. This article proposes a method that uses split cylindrical pins to realize load sharing only in tangential direction, and then establishes a load-sharing mathematical model based on the radius of cylindrical pin. Finally, Finite Element Method (FEM) is used to analyze load-sharing stability of 10 mm cylindrical pin and split pin. A load-sharing experiment based on a three-dimensional piezoelectric dynamometer with a tangential range of 1kN and an axial range of 5kN is designed. The experimental results indicate that the tangential load-sharing ratios are 21.4% and 23.0%, the axial load-sharing ratio is 81.0%, which is agree well with the results of FEM analysis. It proves that the static measurement accuracy of the piezoelectric dynamometer in axial direction is not affected. Great load-sharing performance in tangential direction but little load-sharing performance in axial direction can be realized by using split cylindrical pins.

Research on Dynamic Load-Sharing Characteristics of Two-Stage Asymmetric Star Gear System

It is well known that the asymmetric gears of the transmission system enhances the load carrying capacity of system, but there is no relevant conclusion about the dynamic load-sharing characteristics of the asymmetric gear transmission system. In order to analyze the dynamic performance of an asymmetric gear system, taking two-stage asymmetric helical gear star drive system as the research object, the load-sharing model of the two-stage asymmetrical helical star gear system is established by the centralized mass method and Newton's second law. The load sharing characteristic of the star gear is studied about the floating member and the tooth profile pressure angle. The influence of eccentricity error, load and input speed on the load sharing performance of the system is analyzed. Based on ADAMS virtual prototype model, through the simulation analysis of the dynamic meshing force of gears, the load sharing coefficient of each star gear is calculated, compare the results with the MATLAB solution to verify the correctness of the theory.

Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility

A load-sharing analysis methodology was proposed for the multiple-branch star gear transmission which is composed of a number of closed-loop power flows. The moment equilibrium and deformation compatibility equations for the two-stage star gearing were derived, which are clearly different from that used in planetary gear transmission. Then the load-sharing analysis model was established and employed to systematically study the load-sharing behavior of the two-stage three-branch star gearing, some untouched aspects were investigated. Results show that the most sensitive directions of the central and star gear assembly errors on load-sharing are along the meshing line. The effects of the size and direction of the central gear–manufacturing errors on load sharing are the same for each branch, the initial directions of the central or a certain star gear–manufacturing errors will have no effect on the load-sharing coefficient of the system, but the initial directions of the assembly errors will. The conditions in which the load distribution curves repeat the first track were also obtained. Finally, a numerical example of a three-branch star gear aviation reducer was adopted to verify the feasibility of this proposed method, and the calculation results show good agreement with a previously published and validated model.

Assessment of load sharing behavior for micropiled rafts installed with inclined condition

As a combined foundation, micropiled rafts under compressive loads show the load-sharing behavior between raft and micropiles. The load carrying and sharing behaviors of micropiled rafts installed with inclined condition would become further complicated as a result of the coupled influences of group and inclined configurations. In this study, the 3D finite element analyses were performed to investigate the load carrying and sharing behaviors of inclined micropiled rafts. Changes in foundation configurations, including micropile inclination angle and spacing, were considered in the analyses. The load carrying capacity of micropiled rafts varied with the inclination angle of micropiles and the proportion of load carried by inclined micropiles was larger than for vertically installed condition. The values of the load sharing ratio αp for the inclined condition were obtained and analyzed. The normalized load-sharing model for inclined micropiled rafts was proposed with the modified load capacity interaction factor and design equations as a function of micropile configuration and inclination angle. Case studies were selected from the literature and adopted to compare with the calculated results using the proposed method. The calculated results were in reasonable agreement with measured load sharing ratios.

MCMC Estimation of Multi-component Load-Sharing System Model and Its Application

In this study, we consider a multi-component load-sharing parallel system model and analyze the load-sharing tendency among the system’s components. The failure time distribution of each component is assumed as Modified Weibull. The maximum-likelihood estimators along with their standard errors of the load-share parameters are computed. The asymptotic and two bootstrap confidence intervals for the parameters are also constructed. Furthermore, Bayesian estimation is carried out by assuming gamma and non-informative priors of the unknown parameters. Markov chain Monte Carlo simulation techniques such as Gibbs sampler and Metropolis–Hasting algorithm have been implemented to obtain Bayes estimates and highest posterior density credible intervals. For highlighting the theoretical developments, a simulation study is conducted. The application of the proposed system model is illustrated by analyzing two real data sets exhibiting load-sharing tendencies.