Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Static-to-kinematic modeling and experimental validation of tendon-driven quasi continuum manipulators with nonconstant subsegment stiffness

Continuum robots with high flexibility and compliance have the capability to operate in confined and cluttered environments. To enhance the load capacity while maintaining robot dexterity, we propose a novel non-constant subsegment stiffness structure for tendon-driven quasi continuum robots(TDQCRs) comprising rigid-flexible coupling subsegments.Aiming at real-time control applications, we present a novel static-to-kinematic modeling approach to gain a comprehensive understanding of the TDQCR model. The analytical subsegment-based kinematics for the multisection manipulator is derived based on screw theory and product of exponentials formula, and the static model considering gravity loading,actuation loading, and robot constitutive laws is established. Additionally, the effect of tension attenuation caused by routing channel friction is considered in the robot statics, resulting in improved model accuracy. The root-mean-square error between the outputs of the static model and the experimental system is less than 1.63% of the arm length(0.5 m). By employing the proposed static model, a mapping of bending angles between the configuration space and the subsegment space is established. Furthermore, motion control experiments are conducted on our TDQCR system, and the results demonstrate the effectiveness of the static-to-kinematic model.

Stiffness Characteristics of a Basic Nonlinear Air Spring Model

This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

Improved Stiffness Modeling for An Exechon‑Like Parallel Kinematic Machine(PKM)and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.

Dynamic Characteristics of Double-Helical Planetary Gear Sets Under Time-Varying Mesh Stiffness

Internal and external meshes are two of primary excitation sources which induce vibration while double-helical planetary gear sets are in transmission. Based on the analysis of tooth movement principle,three cases of mesh stiffness are derived via investigating the length of action lines,and catalogued in terms of β < β0,β = β0and β > β_0. The simulation demonstrates mesh stiffness between gear pairs performs as a trapezoid waveform( TW) and changes along with the line of action simultaneously,total mesh stiffness comes from the superposition of each engaged gear. While governing equations of motion contained 16 DOFs( degree of freedom) are constructed and effectively solved through the combination of numerical approaches. Comparing with sinusoidal waveform mesh stiffness( SW),the results show that dynamical factors and perturbation under the excitation of TW( β < β_0) are greater and remarkable than that from SW,with respect to the mean dynamic factors about 1. 51 and 1. 28,respectively. The fluctuation response between ring- planet( R- P) is stronger than sun-planet( S-P) which is also validated by both approach studies,frequency spectra analyses identifies larger distinct rotational resonance and more frequencies under TW excitation.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

Performance of composite foundations with different load transfer platforms and substratum stiffness over silty clay

The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress distribution across the embankment width and the behaviour of unreinforced foundations.Thus,five centrifuge tests were conducted to examine the bearing and deformation behaviours of NPRS(Non-Connected Piled Raft Systems)and GRPS(GeosyntheticReinforced Pile-Supported systems)with varying substratum stiffness,then a comparative analysis was conducted on embankment settlement,pressures underneath the embankments,and axial forces along the piles.The results indicated that greater substratum stiffness correlates with reduced settlement and deformation at various depths.Deformation occurring 5 meters from the embankment toe includes settlement in NPRS and upward movement in GRPS.The potential sliding surface is primarily located within the embankment in NPRS,whereas it may extend through both the embankment and foundation in GRPS.The pile-soil stress ratio and efficiency in NPRS are higher than in GRPS across the embankment.The axial force borne by end-bearing piles is significantly greater than that by floating piles.As the buried depth increases,the axial force in GRPS initially rises then declines,whereas in NPRS,it remains relatively constant within a certain range before decreasing.This study aids in assessing the applicability of composite foundations in complex railway environments and provides a reference for procedural measures under similar conditions.

A Fatigue Damage Model for FRP Composite Laminate Systems Based on Stiffness Reduction

This paper introduces a stiffness reduction based model developed by the authors to characterize accumulative fatigue damage in unidirectional plies and(0/θ/0)composite laminates in fiber reinforced polymer(FRP)composite laminates.The proposed damage detection model is developed based on a damage evolution mechanism,including crack initiation and crack damage progress in matrix,matrix-fiber interface and fibers.Research result demonstrates that the corresponding stiffness of unidirectional composite laminates is reduced as the number of loading cycles progresses.First,three common models in literatures are presented and compared.Tensile viscosity,Young’s modulus and ultimate tensile stress of composites are incorporated as key factors in this model and are modified in accordance with temperature.Four types of FRP composite property parameters,including Carbon Fiber Reinforced Polymer(CFRP),Aramid Fiber Reinforced Polymer(AFRP),Glass Fiber Reinforced Polymer(GFRP),and Basalt Fiber Reinforced Polymer(BFRP),are considered in this research,and a comparative parameter study of FRP unidirectional composite laminates with different off-angle plies using control variate method are discussed.It is concluded that the relationship between the drop in stiffness and the number of cycles also shows three different regions,following the mechanism of damage of FRP composites and the matrix is the dominant factor determined by temperature,while fiber strength is the dominant factor that determine the reliability of composite.

Non-invasive model for predicting high-risk esophageal varices based on liver and spleen stiffness

BACKGROUND Acute bleeding due to esophageal varices(EVs)is a life-threatening complication in patients with cirrhosis.The diagnosis of EVs is mainly through upper gastrointestinal endoscopy,but the discomfort,contraindications and complications of gastrointestinal endoscopic screening reduce patient compliance.According to the bleeding risk of EVs,the Baveno VI consensus divides varices into high bleeding risk EVs(HEVs)and low bleeding risk EVs(LEVs).We sought to identify a non-invasive prediction model based on spleen stiffness measurement(SSM)and liver stiffness measurement(LSM)as an alternative to EVs screening.AIM To develop a safe,simple and non-invasive model to predict HEVs in patients with viral cirrhosis and identify patients who can be exempted from upper gastrointestinal endoscopy.METHODS Data from 200 patients with viral cirrhosis were included in this study,with 140 patients as the modelling group and 60 patients as the external validation group,and the EVs types of patients were determined by upper gastrointestinal endoscopy and the Baveno Ⅵ consensus.Those patients were divided into the HEVs group(66 patients)and the LEVs group(74 patients).The effect of each parameter on HEVs was analyzed by univariate and multivariate analyses,and a noninvasive prediction model was established.Finally,the discrimination ability,calibration ability and clinical efficacy of the new model were verified in the modelling group and the external validation group.RESULTS Univariate and multivariate analyses showed that SSM and LSM were associated with the occurrence of HEVs in patients with viral cirrhosis.On this basis,logistic regression analysis was used to construct a prediction model:Ln[P/(1-P)]=-8.184-0.228×SSM+0.642×LSM.The area under the curve of the new model was 0.965.When the cut-off value was 0.27,the sensitivity,specificity,positive predictive value and negative predictive value of the model for predicting HEVs were 100.00%,82.43%,83.52%,and 100%,respectively.Compared with the four prediction models of liver stiffness-spleen diameter to platelet ratio score,variceal risk index,aspartate aminotransferase to alanine aminotransferase ratio,and Baveno VI,the established model can better predict HEVs in patients with viral cirrhosis.CONCLUSION Based on the SSM and LSM measured by transient elastography,we established a non-invasive prediction model for HEVs.The new model is reliable in predicting HEVs and can be used as an alternative to routine upper gastrointestinal endoscopy screening,which is helpful for clinical decision making.

Clinical value of predictive models based on liver stiffness measurement in predicting liver reserve function of compensated chronic liver disease

BACKGROUND Assessment of liver reserve function(LRF)is essential for predicting the prognosis of patients with chronic liver disease(CLD)and determines the extent of liver resection in patients with hepatocellular carcinoma.AIM To establish noninvasive models for LRF assessment based on liver stiffness measurement(LSM)and to evaluate their clinical performance.METHODS A total of 360 patients with compensated CLD were retrospectively analyzed as the training cohort.The new predictive models were established through logistic regression analysis and were validated internally in a prospective cohort(132 patients).RESULTS Our study defined indocyanine green retention rate at 15 min(ICGR15)≥10%as mildly impaired LRF and ICGR15≥20%as severely impaired LRF.We constructed predictive models of LRF,named the mLPaM and sLPaM,which involved only LSM,prothrombin time international normalized ratio to albumin ratio(PTAR),age and model for end-stage liver disease(MELD).The area under the curve of the mLPaM model(0.855,0.872,respectively)and sLPaM model(0.869,0.876,respectively)were higher than that of the methods for MELD,albumin bilirubin grade and PTAR in the two cohorts,and their sensitivity and negative predictive value were the highest among these methods in the training cohort.In addition,the new models showed good sensitivity and accuracy for the diagnosis of LRF impairment in the validation cohort.CONCLUSION The new models had a good predictive performance for LRF and could replace the indocyanine green(ICG)clearance test,especially in patients who are unable to undergo ICG testing.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

Letter to editor‘Non-invasive model for predicting high-risk esophageal varices based on liver and spleen stiffness’

predicting high-risk esophageal varices based on liver and spleen stiffness".Acute bleeding caused by esophageal varices is a life-threatening complication in patients with liver cirrhosis.Due to the discomfort,contraindications,and associated complications of upper gastrointestinal endoscopy screening,it is crucial to identify an imaging-based non-invasive model for predicting high-risk esophageal varices in patients with cirrhosis.

Importance of Sand Grading on the Compressive Strength and Stiffness of Lime Mortar in Small Scale Model Studies

Mortars provide the continuity required for the stability and exclusion of weather elements in masonry assemblies. But because of the heterogeneity of the mortar, its mechanism of behaviour under different load effects is dependent on the properties of the constituents of the mortar. The aim of paper is to determine the effect sand grading for various cement-sand-lime mortar designations (BS) and strength classes (EC) on the compressive strength and stiffness of mortar. Two silica sands;HST 95 and HST60 were used to make mortars in three strength classes: M2, M4 and M6, corresponding to mortar designations iv, iii and ii respectively. The results show that mortar made with the HST60 sand (coarser grading) usually resulted in mortar with a higher compressive strength and stiffness. The One Way ANOVA analysis of both compressive strength and stiffness at a significance level of 5% on the effect of sand grading on the two parameters also shows that they are both significant. There is also strong evidence of a linear correlation between the stiffness and compressive strength. The results indicate that in order to replicate full scale behaviour of masonry at model scales, the grading of fine aggregate in the models should be similar so as to properly model full scale behavior.

Stiffness Degradation Modeling for Composite Wind Turbine Blades Based on Full-Scale Fatigue Testing

In order to provide more insights into the damage propagation composite wind turbine blades(blade)under cyclic fatigue loading,a stiffness degradation model for blade is proposed based on the full-scale fatigue testing of a blade.A novel non-linear fatigue damage accumulation model is proposed using the damage assessment theories of composite laminates for the first time.Then,a stiffness degradation model is established based on the correlation of fatigue damage and residual stiffness of the composite laminates.Finally,a stiffness degradation model for the blade is presented based on the full-scale fatigue testing.The scientific rationale of the proposed stiffness model of blade is verified by using full-scale fatigue test data of blade with a total length of 52.5 m.The results indicate that the proposed stiffness degradation model of the blade agrees well with the fatigue testing results of this blade.This work provides a basis for evaluating the fatigue damage and lifetime of blade under cyclic fatigue loading.