Time-varying Contact Research Articles

Endemic-epidemic modelling of school closure to prevent spread of COVID-19 in Switzerland

The goal of this work was to quantify the effect of school closure during the first year of coronavirus disease 2019 (COVID-19) pandemic in Switzerland. This allowed us to determine the usefulness of school closures as a pandemic countermeasure for emerging coronaviruses in the absence of pharmaceutical interventions. The use of multivariate endemic-epidemic modelling enabled us to analyse disease spread between age groups which we believe is a necessary inclusion in any model seeking to achieve our goal. Sophisticated time-varying contact matrices encapsulating four different contact settings were included in our complex statistical modelling approach to reflect the amount of school closure in place on a given day. Using the model, we projected case counts under various transmission scenarios (driven by implemented social distancing policies). We compared these counterfactual scenarios against the true levels of social distancing policies implemented, where schools closed in the spring and reopened in the autumn. We found that if schools had been kept open, the vast majority of additional cases would be expected among primary school-aged children with a small fraction of cases filtering into other age groups following the contact matrix structure. Under this scenario where schools were kept open, the cases were highly concentrated among the youngest age group. In the scenario where schools had remained closed, most reduction would also be expected in the lowest age group with less effects seen in other groups.

Optimization of cycloid wheel shaping based on thermal mixed lubrication and wear characteristics

The cycloid pinwheel mechanism plays a key role in the function of RV reducers, making the lubrication and wear characteristics of the cycloid tooth profile vital areas of research. This study uses the RV-20E reducer as a case study to analyze the time-varying contact force and relative velocity between the cycloid wheel and the pinwheel, factoring in the system's dynamic properties. A transient contact model for thermal mixed lubrication of the cycloid tooth profile was developed, incorporating friction and temperature rise, and was based on a rough surface model of the dynamic bonding interface. This model enabled the calculation of oil film thickness, contact stress, and wear volume at the interface between the cycloid wheel and the pinwheel. Additionally, the study assessed the impact of traditional shaping methods on wear characteristics and derived a fitted cycloid tooth profile for the profile grinding process. These findings provide valuable insights into improving the lifespan of RV reducers.

Study on the wear characteristics of cylindrical needle bearings on the crankshaft of RV decelerator

PurposeThe purpose of this study is to systematically analyze the wear of cylindrical needle bearings in rotary vector reducers under temperature rise and identify the influencing factors.Design/methodology/approachBased on the dynamic characteristics of the RV-20E reducer, the time-varying contact force of the cylindrical needle bearing and the entrainment speed of the inner and outer raceways were calculated. A mixed elastohydrodynamic lubrication model of the needle bearing, considering friction and temperature rise, was established using a dynamic rough tooth surface model. The model solved for the oil film thickness, contact stress and wear conditions of the bearing raceway contact area. The effects of the number of rolling needles, the diameter of rolling needles and surface strength on the wear characteristics were analyzed.FindingsThe results of this study show that the oil film thickness, oil film pressure and surface scratches of cylindrical needle bearings exhibit an uneven, patchy distribution under the combined effects of friction and temperature rise. When the radius of the rolling needle is less than 1.44 mm, inner ring wear is less than outer ring wear. Conversely, when the radius exceeds 1.44 mm, inner ring wear is greater. The optimal rolling needle radius is 1.6 mm. Increasing the number of rolling needles and enhancing the yield strength of the contact surface significantly extend bearing life.Originality/valueThis study provides valuable recommendations for optimizing bearing structural parameters and material characteristics in the design of rotary vector reducers.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0242/

Dynamic modeling considering time-varying contact pairs and parameterized defects of deep groove ball bearings for its vibration characteristic analysis

Dynamic modeling considering time-varying contact pairs and parameterized defects of deep groove ball bearings for its vibration characteristic analysis

Mathematical analysis and prediction of future outbreak of dengue on time-varying contact rate using machine learning approach

This article introduces a novel mathematical model analyzing the dynamics of Dengue in the recent past, specifically focusing on the 2023 outbreak of this disease. The model explores the patterns and behaviors of dengue fever in Bangladesh. Incorporating a sinusoidal function reveals significant mid-May to Late October outbreak predictions, aligning with the government's exposed data in our simulation. For different amplitudes (A) within a sequence of values (A = 0.1 to 0.5), the highest number of infected mosquitoes occurs in July. However, simulations project that when βM = 0.5 and A = 0.1, the peak of human infections occurs in late September. Not only the next-generation matrix approach along with the stability of disease-free and endemic equilibrium points are observed, but also a cutting-edge Machine learning (ML) approach such as the Prophet model is explored for forecasting future Dengue outbreaks in Bangladesh. Remarkably, we have fitted our solution curve of infection with the reported data by the government of Bangladesh. We can predict the outcome of 2024 based on the ML Prophet model situation of Dengue will be detrimental and proliferate 25 % compared to 2023. Finally, the study marks a significant milestone in understanding and managing Dengue outbreaks in Bangladesh.

Analysis of the thermal lubrication characteristics of cycloid pinwheel transmission mechanisms in RV reducers

In this paper, the cycloidal pin wheel drive mechanism of the secondary drive component of the rotary vector (RV) reducer is studied. Under the condition of grease lubrication, considering tooth profile modifications and machining errors, we established a three-dimensional load-bearing contact analysis model of a cycloid pinwheel transmission mechanism. We studied the time-varying contact characteristics of the gear teeth and dynamic joint surfaces of the inner and outer races of a crankshaft bearing. Considering the thermal effects, we proposed an analysis model of the lubrication characteristics of cycloid pinwheel transmission mechanisms. We also studied the thermal lubrication properties, such as load de-formation, lubrication film thickness, contact pressure and temperature increase at the lubrication contact area. The accuracy of the model was verified by temperature experiments on the inner raceway of an RV reducer bearing and the evolution law of the dynamic thermal lubrication characteristics of the inner and outer races of the crankshaft bearing, the meshing gear tooth pair and the whole process of single pin tooth meshing were revealed. This study provides an effective method for analyzing the temperature increases of the key joints of RV reducers.

Influence of idler misalignment fault on contact and dynamic characteristics of helical gear

Due to the advantages of stable helical gear transmission, it is widely used in industry, agriculture, and national defense. Shaft misalignment has a great influence on the vibration, bearing capacity, and life of gear transmission. Based on the idler wheel drive system as the research object, according to the principle of gear meshing, the helical gear time-varying contact wire length model was deduced. The dynamic model of the gear transmission system with faults is established considering the faults of the idler's center distance error and angle error, and the influence law of idler misalignment fault on the vibration of the idler transmission system is revealed. On this basis, the finite element model under angle error is established to analyze the contact stress of the tooth surface under different faults and reveal the contact stress distribution law of the tooth surface. The results show that the misalignment fault will change the length of the helical gear contact line. When the gear shaft misaligns, it will increase the axial force of the gear and increase the axial vibration of the gear. Moreover, the angle error will cause uneven load distribution on the tooth surface of the helical gear, which will reduce the contact area of the gear and increase the contact stress. The phenomenon of off-load of gear accelerates the wear of the gear tooth surface and shortens the life of the gear. The study of idler misalignment fault is of great significance for prolonging the life of gear and providing the basis for gear fault diagnosis.

Mathematical modeling of the infectious spread and outbreak dynamics of avian influenza with seasonality transmission for chicken farms

A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for R0>1. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

Dynamic Investigations on the Wear Behavior of a 3D Revolute Joint Considering Time-Varying Contact Stiffness: Simulation and Experiment

The existence of the relative radial and axial movements of a revolute joint’s journal and bearing is widely known. The three-dimensional (3D) revolute joint model considers relative radial and axial clearances; therefore, the freedoms of motion and contact scenarios are more realistic than those of the two-dimensional model. This paper proposes a wear model that integrates the modeling of a 3D revolute clearance joint and the contact force and wear depth calculations. Time-varying contact stiffness is first considered in the contact force model. Also, a cycle-update wear depth calculation strategy is presented. A digital image correlation (DIC) non-contact measurement and a cylindricity test are conducted. The measurement results are compared with the numerical simulation, and the proposed model’s correctness and the wear depth calculation strategy are verified. The results show that the wear amount distribution on the bearing’s inner surface is uneven in the axial and radial directions due to the journal’s stochastic oscillations. The maximum wear depth locates where at the bearing’s edges the motion direction of the follower shifts. These findings help to seek the revolute joints’ wear-prone parts and enhance their durability and reliability through improved design.

Analysis of contact behaviours and vibrations in a defective deep groove ball bearing

Rolling element bearings are vital parts for rotating machinery. When a defect occurs on the surface of the bearing raceway or rolling element, giving rise to the abnormal vibration of the bearing and even the rotating machine. Thus, it is of great significance to understand the vibration characteristics of the bearing for fault diagnosis and machine condition monitoring. In recent decades, researches on defect-induced bearing vibration in machine condition monitoring have attracted increasing attention. Model-based investigation is a highly useful method for enhancing our understanding of defect-induced vibration and fault excitation mechanism of the bearing. It also serves as a basis for establishing the theory of bearing failure. With this in mind, a novel dynamic model of deep groove ball bearing (DGBB) with a localized outer race defect is proposed in this paper. In this model, the additional displacement excitation which is modelled as a piecewise function based on kinematics is considered, and the angle-based contact force is developed and modelled as a piecewise function taking into account the angular position, collision velocity, and impact force. In addition, an analytical formulation of the angle-varying effective stiffness matrix of the DGBB with a localized raceway defect of varying size is established. The proposed dynamic model is used to study the influences of different defect scenarios (i.e. angular positions and widths) on the time-varying contact stiffness, contact force, spectral characteristics, and bearing vibrations. The comparisons between the simulations and the experiments show that the proposed model is effective.

On epidemic spreading in metapopulation networks with time-varying contact patterns.

Considering that people may change their face-to-face communication patterns with others depending on the season, we propose an epidemic model that incorporates a time-varying contact rate on a metapopulation network and its second-neighbor network. To describe the time-varying contact mode, we utilize a switched system and define two forms of the basic reproduction number corresponding to two different restrictions. We provide the theoretical proof for the stability of the disease-free equilibrium and confirm periodic stability conditions using simulations. The simulation results reveal that as the period of the switched system lengthens, the amplitude of the final infected density increases; however, the peak infected density within a specific period remains relatively unchanged. Interestingly, as the basic reproduction number grows, the amplitude of the final infected density within a period gradually rises to its maximum and then declines. Moreover, the contact rate that occupies a longer duration within a single period has a more significant influence on epidemic spreading. As the values of different contact rates progressively increase, the recovery rate, natural birth rate, and natural death rate all decrease, leading to a larger final infection density.

Nonlinear dynamic behaviors of angular contact ball bearing with waviness based on a synthetical multi-degree-of-freedom mathematical modelling

This paper proposes a synthetical multi-degree-of-freedom mathematical modelling for analyzing the dynamic characteristics of angular contact ball bearing with waviness subjected to the external load working conditions. The above multi-degree-of-freedom mathematical modelling is established based on nonlinear elastic Hertz contact theory and inner raceway control theory by employing improved Newton–Raphson iteration method; the validation of the established mathematical modelling is verified by comparing the presented results with the existing literature results. The above mathematical modelling has considered raceway waviness, ball waviness, bearing clearance, centrifugal force, gyroscopic moment, external loads, and rotating speed comprehensively. Firstly, the effects of waviness order and waviness amplitude on time-varying contact and stiffness characteristics of angular contact ball bearing are investigated systematically. Then, the influences of bearing clearance, rotating speed, axial force, radial force, and torque on the dynamic contact and stiffness characteristics of angular contact ball bearing with waviness are analyzed thoroughly. The main results show that the solution results of mathematical modelling have converged, respectively, when raceway waviness order increases to 25 and ball waviness order increases to 5; The variation tendencies of time-varying contact angle, contact force, and stiffness of angular contact ball bearing with waviness are aperiodic; The amplitudes of time-varying contact angle, contact force, and stiffness of angular contact ball bearing increase evidently with waviness amplitude increased; The bearing clearance has important influence on the contact angle and contact force of outer raceway and inner raceway, respectively; The effects of radial force and torque on contact and stiffness characteristics are consistent basically in the corresponding direction; The influences of axial force and rotating speed on the contact and stiffness characteristics are more remarkable compared with other factors. The investigations of contact and stiffness characteristics of angular contact ball bearing with waviness are helpful for the designation and manufacture of high precision angular contact ball bearing.

The influence of race waviness on skidding characteristics of rolling bearings

Waviness is the main shape deviation generated in the processing of rolling bearings. The existence of race waviness directly alters displacement excitation and contact stiffness between the ball and the wavy race simultaneously, which will greatly affect the dynamic performance of rolling bearings. Most of the current work studying bearing dynamics with race waviness ignored the influence of waviness on contact stiffness. In addition, the influence of race waviness on bearing skidding problems was rarely investigated. To fill the research gap, a skidding dynamic model of race waviness bearing coupled with the time-varying displacement excitation and time-varying contact stiffness excitation is established by considering the nonlinear factors including internal nonlinear contact, non-continuous collision contact between ball and cage, lubrication friction, clearance and pocket gap. The validity of the dynamic model is verified by previously published results and analytical results of a static model. The influence of waviness amplitude and order on the contact and skidding characteristics are analyzed. The results indicate that the contact stiffness and contact force between the ball and race increase with the waviness amplitude and order. In addition, the waviness also causes fluctuations in the contact force. The increase in waviness amplitude and order restrains the skidding of the ball in the unloaded area. The waviness amplitude causes significant fluctuations in skidding, and the waviness order increases the number of skidding fluctuations. The results provide a theoretical basis for the surface quality assessment of rolling bearings via dynamic studies.

The role of 3D contact geometry in modeling dynamic wheel-rail interaction at short-wave irregularities on rail surface

Modelling wheel-rail interaction at short-wave irregularities is an important issue under the context of vehicle-track system dynamics for analyzing and preventing severe impact. The present paper broadens the applicability of vehicle-track dynamics model to account for 3D short-wave irregularities on rail surface. The key is developing a meshing grid approach combined with the accurate conjugate gradient (CG) method for contact mechanics under arbitrary 3D contact geometry. Therefore, both the global dynamics and local contact solutions can be provided. In this study, short-pitch rail corrugation is employed for investigating the role of 3D contact geometry in modelling dynamic wheel-rail interaction. The traditional vehicle-track coupled dynamics model using Hertzian spring is used for comparison. The results show short-pitch rail corrugation contributes two different aspects, i.e., wheel center trajectory and time-varying contact stiffness. These two aspects are found to be the root causes for explaining the influence of the varying 3D geometry irregularity size on dynamic wheel-rail contact force.

Digital visualization of time-varying local bearing contact recognition for non-orthogonal aviation spiral bevel gears

Focusing on the time-varying meshing performance assessment and recognition, a new computer aided design/ computer aided manufacturing/ computer aided engineering (CAD/CAM/CAE) integration-based digital visualization of local bearing contact recognition is developed for non-orthogonal aviation spiral bevel gears. At first, universal tooth flank modeling and its CAD/CAM software development are developed to get a closed-form solution to the whole tooth flank points. Then, with applications of an improved digital kinematics arrangements, digital virtual assembly in CAD software is proposed for time-varying meshing simulation. To distinguish with the conventional loaded tooth contact analysis (LTCA), a digital deformation layering method is developed to show local bearing contact at each time-varying deformation layer. Where, accurate search for the loaded meshing points is developed by using the improved dichotomy iteration method. Moreover, instantaneous contact ellipse in software development is determined by chord intercept method. CAD/CAM/CAE integration-based digital visualization is performed by correlating with sensitive assembly error driven virtual simulation. Finally, the given numerical instance can verify the proposed method.

A dynamic model considering the time-varying friction moment of a flexible rotor system

PurposeBearing friction moments are important factors that affect the vibrations of rotor systems. The bearing friction moments are related to the dimension parameters, lubrication conditions and manufacturing errors of support bearings. This work studies the effects of the bearing friction moments on the vibrations of rotor systems.Design/methodology/approachThe rotor is separated into several shaft elements for formulating a flexible rotor. The time-varying friction moment (TFM) is affected by the time-varying contact loads. The vibrations of FRS from the TFM and Palmgren's friction moment (PFM) calculation methods are compared. Moreover, the effects of the rotor offset and radial clearance on the frequency-amplitude characteristics of FRS are studied.FindingsThe TFM method is more consistent with the actual operation mechanisms. The rotor offset and radial clearance can significantly affect the nonlinear vibrations of FRS. This work provides a new reference and research method for the vibration analysis of rotor systems considering the friction effects.Originality/valueThe elastohydrodynamic lubrication (EHL), elastic hysteresis and differential sliding are considered. A flexible rotor system (FRS) dynamic model considering the TFM is proposed. The vibrations of FRS from the TFM calculation method and empirical calculation formula are compared. The effects of the rotor offset and radial clearance on the frequency–amplitude characteristics of FRS are studied.

Epidemic threshold influenced by non-pharmaceutical interventions in residential university environments

The control of highly contagious disease spreading in campuses is a critical challenge. In residential universities, students attend classes according to a curriculum schedule, and mainly pack into classrooms, dining halls and dorms. They move from one place to another. To simulate such environments, we propose an agent-based susceptible–infected–recovered model with time-varying heterogeneous contact networks. In close environments, maintaining physical distancing is the most widely recommended and encouraged non-pharmaceutical intervention. It can be easily realized by using larger classrooms, adopting staggered dining hours, decreasing the number of students per dorm and so on. Their real-world influence remains uncertain. With numerical simulations, we obtain epidemic thresholds. The effect of such countermeasures on reducing the number of disease cases is also quantitatively evaluated.

Time-Varying Tool-Chip Contact in the Cutting Mechanics of Shear Localization

Abstract Shear localization is the dominant chip formation mechanism in machining of high performance metallic components, such as those made of titanium and nickel-based alloys. This paper presents an analytical thermo-mechanical model considering a new tool-chip contact mechanism due to shear localization. First, it is experimentally shown that the sticking and sliding contact lengths fluctuate with the frequency of shear localization. Second, a cutting mechanics model is developed considering the shear band formation, its rolling on the tool’s rake face, and the time-varying tool-chip contact length with experimental validation. Finally, the transient temperature at the tool-chip interface is predicted by taking the rolling phenomenon and the time-varying heat sources at the tool-chip interface into account. The proposed model shows that at the beginning of each segmentation cycle, the entire tool-chip contact length is dominated by sliding condition with negligible sticking length. When the tool advances, new workpiece material piles up in its front with an increase in the sticking length. Meanwhile, the sliding length decreases due to the drop in the load-bearing capacity of the shear band. When enough material piles up in front of the tool, a new shear band forms, and the entire contact length returns to the sliding condition. This process repeats each time a shear band occurs, causing the cyclic formation of shear bands and time-varying nature of the tool-chip contact length, therefore influencing the temperature and stress evolution at the tool-chip interface.

Effect of clearance on the dynamic characteristics of high-speed rolling bearings with multiple defects

Clearance is a pivotal factor in determining the fatigue life of high-speed rolling bearings (HSRBs). As HSRBs naturally experience various defects, their clearance levels tend to rise. However, a clear understanding of the vibration caused by clearance is still lacking. To address this gap, a five-degree-of-freedom dynamics model for HSRBs is proposed. This model accounts for centrifugal force, gyroscopic moment, and time-varying contact angle. In addition, the proposed model incorporates asymptotic theory to describe the defect process and the time-varying contact force derived from the Hertzian point contact theory between rolling elements and raceways. Furthermore, the model considers the variations in load zone and rolling element velocity that arise due to clearance. Applying this model, the dynamic response of HSRBs with different level clearances is calculated. The model's correctness is verified by comparing the dynamic response with the finite element model results and data measured using a test rig built for aero-engine spindle bearing. The results demonstrate that the extent of the load zone shrinks as the clearance increases, although the reduction rate gradually slows down. Since the bearing is loaded only in the load zone, aggravated clearance causes rolling elements to slip in the non-load zone. The effect of clearance on contact force is significantly weaker pronounced than that of defects. These research findings provide a theoretical foundation for the analysis and performance prediction of HSRBs and have important reference values for their optimal design.

A Nonlinear Repeated Impact Model of Auxetic Honeycomb Structures Considering Geometric Nonlinearity and Tensile/Compressive Deformation

Abstract This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson’s ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin–Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge–Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.