Loading Geometry Research Articles

Transient mixed thermal elastohydrodynamic lubrication analysis of aero ball bearing under non-steady state conditions

A transient mixed thermal elastohydrodynamic lubrication model of bearing considering the thermal effect and the changes in velocity, load, and contact geometry is proposed. Based on the bearing dynamic and lubrication analysis, the effects of bearing rotational speed and start-stop conditions on the dynamic behavior and lubrication performance are studied. Results show that when the bearing rotational speed exceeds a certain critical value, the increasing speed will reduce the film thickness, especially the outer raceway. The increasing bearing acceleration can cause a higher slide-roll ratio and film temperature at the initial start-up process. Compared with the start-up process, the lubrication change in the shut-down process has a similar opposite trend, but the overall lubrication performance is better.

Free vibration and transient response of initially compressed CNT-reinforced composite plates

This paper investigates the linear free vibration and nonlinear transient response of carbon nanotube (CNT)-reinforced composite plates subjected to pre-existent compressive load in thermal environments. CNTs are reinforced into matrix according to uniform and functionally graded distributions. The properties of constitutive materials are assumed to be temperature-dependent while the effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations are established within the framework of classical plate theory incorporating von Kármán nonlinearity and initial geometrical imperfection. Analytical solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain a time differential equation including both quadratic and cubic nonlinear terms. Fourth-order Runge–Kutta numerical integration scheme is employed to determine dynamical deflection-time response of nanocomposite plates. Numerical analyses are presented to consider the influences of CNT volume fraction, CNT distribution, initial compressive load, geometrical imperfection, elevated temperature and plate geometry on the natural frequencies and nonlinear dynamical response of nanocomposite plates. The study reveals that the natural frequency and dynamical deflection are strongly decreased and increased when initial compressive load is increased, respectively. Numerical results also find that the natural frequencies are enhanced and dynamical deflection is dropped as a result of increase in volume percentage of CNTs, respectively.

Improved Similarity Law for Scaling Dynamic Responses of Stiffened Plates with Distorted Stiffener Configurations

Experimental analysis on small-scale models is widely used to predict the dynamic responses of full-scale structures subjected to impact loads. However, due to manufacturing constraints, achieving a perfectly scaled model under a large scaling factor is challenging, leading to the use of distorted scaled models as a compromise. This paper introduces an improved similarity law that ensures distorted scaled models accurately replicate the dynamic responses of prototype stiffened plates under impact loads. The proposed similarity law meticulously considers both the distorted attached plate thickness and variations in stiffener configuration. Double input parameters involving the load case and geometry are formulated to govern the dynamic responses of integrated stiffeners. Additionally, an approximate method rooted in elastic–plastic theory is developed to assess the dominant behaviors of stiffened plates during impact. Consequently, the distorted stiffener configuration of scaled models is designed through a methodology primarily centered on capturing dominant behaviors. Comprehensive numerical simulations are conducted to evaluate the behavior of stiffened plates subjected to impact loads. The results compellingly demonstrate that the proposed similarity law adeptly compensates for geometric distortions, ensuring reliable predictions of dynamic responses in distorted scaled models.

Анализ контакта конических зубьев шестерен на основе машинного обучения

In this paper, we study the analysis of the contact of bevel gear teeth based on machine learning methods. Bevel gear teeth are widely used in various industrial and mechanical systems to transmit rotational motion with high precision and reliability. Traditional methods of gear contact analysis are based on mathematical models and empirical formulas, which may be limited in accuracy and applicability. In recent years, machine learning has become a powerful tool in the field of engineering and mechanics to more accurately model and predict the contact behavior of bevel gear teeth. The paper proposes the use of machine learning methods, such as neural networks or deep learning algorithms, to train models capable of analyzing the contact of bevel gear teeth. Wear, load, and gear geometry data can be used to train models, which can then predict contact parameters and evaluate contact performance.

MODELING OF THREE-LAYER FLOWS WITH NON-UNIFORM EVAPORATION BASED ON THE EXACT SOLUTION OF CONVECTION EQUATIONS

Mathematical modeling of three-layer convective flows of two liquids and a gas-vapor mixture in a horizontal channel is based on the exact solution of the Navier-Stokes equations in the Boussinesq approximation. Thermocapillary interfaces are assumed to be non-deformable. The inhomogeneous mass transfer of the light liquid to the upper layer is considered. The Soret and Dufour effects are taken into account in the upper layer, and the gas flow rate is given. The influence of thermal load and flow geometry on the main characteristics of the flow was studied using the example of the water–benzine–air system. It is shown that the Soret effect has an impact on the nature of the flow. The influence of the effect of thermodiffusion, changes in the longitudinal temperature gradients, and thicknesses of the layers of the system on the dew point is revealed.

The relevance of analytical formulations predicting stiffener tripping

In search for the governing failure mode of externally pressurized ring-stiffened cylinders the focus is, due to its loading and slender geometry, drawn to elastic buckling. However, the hydrostatic pressure loading and imperfections cause nonlinear behaviour, and excessive deformation results in plastic failure, denoted by collapse. This implies that a true bifurcation point is often hardly observed, and this raises the question whether it is worthwhile to spend much effort to determine the elastic buckling pressures other than to ensure they are well above the collapse pressure? This paper focuses on the elastic buckling of ring frames, generally referred to as frame tripping. Some latest attempts in improving the accuracy of the analytical formulations will be questioned. Firstly, this study will compare non-linear buckling with linear-elastic material behaviour to elastic buckling by means of finite element analysis. Secondly, the non-linear elastic-plastic effects will be included too. Doing so, the effect of the geometrical non-linearity and material elastic-plastic non-linearity will be visible separately and will give an indication of the relevance of frame tripping results predicted by analytical elastic buckling formulations. Literature offers a variety on analytical formulations, each with an underlying idea to remove undesired assumptions that impair results. Even recently comprehensive formulations are published to establish an accurate value of the elastic tripping pressures. This paper shows whether those methods are still relevant in modern pressure hull design or not.

In vivo strain measurements in the human buttock during sitting using MR-based digital volume correlation

Advancements in systems for prevention and management of pressure ulcers require a more detailed understanding of the complex response of soft tissues to compressive loads. This study aimed at quantifying the progressive deformation of the buttock based on 3D measurements of soft tissue displacements from MR scans of 10 healthy subjects in a semi-recumbent position. Measurements were obtained using digital volume correlation (DVC) and released as a public dataset. A first parametric optimisation of the global registration step aimed at aligning skeletal elements showed acceptable values of Dice coefficient (around 80%). A second parametric optimisation on the deformable registration method showed errors of 0.99mm and 1.78mm against two simulated fields with magnitude 7.30±3.15mm and 19.37±9.58mm, respectively, generated with a finite element model of the buttock under sitting loads. Measurements allowed the quantification of the slide of the gluteus maximus away from the ischial tuberosity (IT, average 13.74 mm) that was only qualitatively identified in the literature, highlighting the importance of the ischial bursa in allowing sliding. Spatial evolution of the maximus shear strain on a path from the IT to the seating interface showed a peak of compression in the fat, close to the interface with the muscle. Obtained peak values were above the proposed damage threshold in the literature. Results in the study showed the complexity of the deformation of the soft tissues in the buttock and the need for further investigations aimed at isolating factors such as tissue geometry, duration and extent of load, sitting posture and tissue properties.

A Novel Design of Centrifugal Pump Impeller for Hydropower Station Management Based on Multi-Objective Inverse Optimization

The impeller, regarded as the central component of a centrifugal pump, plays a pivotal role in dictating overall performance. Overcoming challenges arising from the complexity of design parameters and the time-intensive nature of the design process has been a persistent obstacle to widespread adoption. In this study, we integrated ANSYS-CFX 2023 software with innovative inverse design techniques to optimize the impeller design within a centrifugal pump system. Our investigation reveals groundbreaking insights, highlighting the significant influence of both blade load and shaft surface geometry on impeller performance. Notably, through load optimization, substantial enhancements in centrifugal pump efficiency were achieved, demonstrating improvements of 1.8% and 1.7% under flow conditions of 1.0 Q and 0.8 Q, respectively. Further, the efficiency gains of 0.44% and 0.36% were achieved in their corresponding flow conditions. The optimization of blade load and shaft surface configuration notably facilitated a more homogenized internal flow pattern within the impeller. These novel findings contribute substantively to the theoretical foundations underpinning centrifugal pump impeller design, offering engineers a valuable reference to elevate their performance. Our utilization of ANSYS-CFX software in conjunction with inverse design methodologies showcases a promising avenue for advancing impeller design, ultimately culminating in superior efficiency and performance for centrifugal pumps.

Overload and variable amplitude load effects on the fatigue strength of welded joints

Different load spectra and individual load peaks might substantially relax high residual stresses as well as induce compressive residual stresses in welded components and, consequently, affect the fatigue performance of these joints. Consideration of peak loads and resulting relaxation of residual stresses in fatigue analyses can substantially enhance the accuracy of life prediction. The aim of the current study is to experimentally investigate the fatigue strength of welded joints subjected to different levels of overloads and variable amplitude (VA) loads and to develop local fatigue assessment method to account for the relaxation of residual stresses via a mean stress correction using the 4R method. The 4R method applies a local stress ratio for the mean stress correction considering material strength, residual stresses, applied stress ratio of external loading and local weld geometry in elastic–plastic material behaviour. Fatigue tests were carried out on fillet-welded longitudinal gusset joints made of S700 high-strength steels under applied stress ratio R = 0–0.1. A mild strength steel (S355) and ultra-high-strength steel (S1100) were selected as reference steel grades for the fatigue testing to study the material strength effects. Numerical analyses were conducted to evaluate the fatigue notch factors using the effective notch stress concept with the reference radius of rref = 1.0 mm and theory of critical distance (TCD) using the point method. The experimental results indicated that a substantial improvement in the fatigue strength capacity can be claimed in the joints subjected to tensile overloads, particularly in the studied S700 and S1100 steels. The higher-level overload (0.8fy), corresponding to the nominal cross-sectional area, improved the mean fatigue strength of the welded joints manufactured of high-strength S700 steel by approximately 60%, while the lower overload (0.6fy) improved the mean fatigue strength by 20%. In addition, a use of equivalent nominal stresses for the joints subjected to VA loads resulted in conservative assessments when employing S–N curves obtained for the CA loading. The 4R method, via the local mean stress correction for individual cycles, provided higher accuracy for the fatigue assessments.

Dynamics analysis of a crane with consideration of a load geometry and a rope sling system

In the paper, the authors present a general mathematical model of an open-loop kinematic chain with auxiliary sub-chains in application to the dynamics analysis of an exemplary boom crane. The developed model takes into account the influence of the load geometry (with particular attention to all its inertial moments), the rope sling system, and the flexibility of the drives and the selected link of the crane on the dynamic response of the crane and the load. The dynamics equations are derived using a formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations of the second kind. The mathematical model has been successfully validated using the commercial MSC.Adams program and the ANSYS-MSC.Adams program interface and then the influence of the aforementioned factors on the behavior of the load and the crane drives is assessed using the kinetic energy, positioning, and RMS indicators.

Semi-analytical model for predicting mechanical properties of metals using flat truncated cone indenter and its application

Based on the energy density equivalence method, a semi-analytical model describing the relationship between the material parameters of Hollomon’s law, load, displacement, and indenter geometry under flat truncated cone indentation (FTCI) was proposed. For a specific indenter, the model parameters were determined by presetting a small volume of material in finite element analysis (FEA). An FTCI test method to obtain the strain hardening coefficient and strain hardening exponent of the material from the load–displacement curve was proposed, and a damage factor (β) model was developed to predict the elastic modulus of the material by using multi-stage loading and unloading tests. Indentation tests were conducted on ten types of steel material using two types of flat truncated cone indenters with 15° and 30° angles. The results showed that the errors between the Young’s modulus measured via the indentation and uniaxial tensile tests were less than 5%; the relative errors between the indentation tensile strength and yield strength by the 30° flat truncated cone indenter and the uniaxial tensile test were less than 6%. For the 30° flat truncated cone indenter, the goodness-of-fit between the stress–strain relationship measured via the indentation and the uniaxial tensile tests was more than 0.95, and 80% of the goodness-of-fit was more than 0.97.

Analytical computation of stress intensity factor for active material particles of lithium ion batteries

The stress intensity factor is a widely used parameter in linear elastic fracture mechanics to assess the stress field near the crack tip, and it is usually defined as the product between the remote stress, the square root of the crack length, and a geometric factor depending on the geometry of the test specimen, the size and location of the crack. However, this well-established expression cannot be used in case of non-constant stress distribution on crack surfaces, typically resulting from diffusive field. This work presents an analytical procedure to compute the stress intensity factor due to any kind of stress distribution that can be expressed as a polynomial. Firstly, the non-constant stress distribution is expressed as a polynomial. Then, the stress intensity factor is computed according to the principle of superposition of effects, as the sum of the stress components of each single polynomial grade and the corresponding geometric factors. The geometric factors for sphere with central and superficial cracks are determined using a finite element model, and closed-form expressions for these geometric factors are provided as functions of a normalized geometric parameter. These functions can be used in case of any stress loading and spherical geometry. The analytical procedure is specifically applied to assess the stress intensity factor caused by stress resulting from lithium diffusion in active material particles of lithium ions batteries electrodes. The results are compared with those obtained using a multiphysics finite element fracture model, showing good agreement and demonstrating the accuracy of the proposed analytical procedure. Then, the procedure presented in this work enables avoiding expensive multiphysics simulations and can be used to develop fast, accurate, and computationally efficient lithium ion batteries degradation models for the online estimation of the capacity decay with charge/discharge cycles.

Phase field modeling on fracture behaviors of elastomers considering deformation-dependent and damage-dependent material viscosity

Elastomers have attracted great research interests owing to their high compliance and large deformation capacity. However, with inevitable flaws, elastomers are susceptible to rupture, leading to reduction in stretchability and loss of functionality. Though phase field model (PFM) provides a feasible tool in fracture simulation on brittle elastic materials, numerical study on the fracture of elastomers is still at a tentative stage with challenges stemming from the extremely large deformation and the nonlinear material properties. In addition, recent experimental observations on the insensitivity of the onset of rupture to loading rates suggest another knowledge gap in revealing the role of the rate-dependent viscoelasticity in fracture. To capture such phenomenon and fill the research gap, this work will propose a finite element (FE) framework by incorporating the polymer dynamics into the PFM. For the first time, the driving force to the fracture of viscoelastic elastomers is identified and the micro-mechanism of the material viscosity is further elucidated with the consideration of polymer chain breakage. The disentanglement of polymer chains in the fracture process is considered in the model to release the constraints on polymer chain reptation from nearby chains, capturing the inherent damage-dependent as well as the deformation-dependent material viscosity. The simulation results demonstrate good agreement with existing experimental data in both loading rate sensitivity tests and geometry sensitivity tests. With the variation of loading rates, obvious differences in stress responses are observed, while the critical fracture stretches almost keep constant. This work provides a deeper understanding on the fracture mechanisms of viscoelastic materials and is expected to provide guidance for the better design and full potential applications of elastomer-based devices.

Contact feedback helps snake robots better use vertical bending to propel through uneven terrain.

Snakes can bend their elongate bodies in various forms to traverse various environments. We understand well how snakes use lateral body bending to push against asperities on flat ground for propulsion, and snake robots can do so effectively. However, snakes can also use vertical bending to push against uneven terrain of large height variation for propulsion, and they can adjust this bending to adapt to novel terrain presumably using mechano-sensing feedback control. Although some snake robots can traverse uneven terrain, few have used vertical bending for propulsion, and how to control this process in novel environments is poorly understood. Here we systematically studied a snake robot with force sensors pushing against large bumps using vertical bending to understand the role of sensory feedback control. We compared a feedforward controller and four feedback controllers that use different sensory information and generate distinct bending patterns and body-terrain interaction. We challenged the robot with increasing backward load and novel terrain geometry that break its contact with the terrain. We further varied how much the feedback control modulated body bending to conform to or push against the terrain to test their effects. Feedforward propagation of vertical bending generated large propulsion when the bending shape matched terrain geometry. However, when perturbations caused loss of contact, the robot easily lost propulsion or had motor overload. Contact feedback control resolved these issues by helping the robot regain contact. Yet excessive conformation interrupted shape propagation and excessive pushing stalled motors frequently. Unlike that using lateral bending, for propulsion generation using vertical bending, body weight that can help maintain contact with the environment but may also overload motors. Our results will help snake robots better traverse uneven terrain with large height variation and can inform how snakes use sensory feedback to control vertical body bending for propulsion.

Effects of Internal Boundary Layers and Sensitivity on Frequency Response of Shells of Revolution

New applications introduced capsule designs with features that have not been fully analysed in the literature. In this study, thin shells of revolution are used to model drug delivery capsules both with closed and open designs including perforations. The effects of internal boundary layers and sensitivity on frequency response are discussed in the special case with symmetric concentrated load. The simulations are carried out using high-order finite element method and the frequency response is computed with a very accurate low-rank approximation. Due to the propagation of the singularities induced by the concentrated loads, the most energetic responses do not necessarily include a pinch-through at the point of action. In sensitive configurations, the presence of regions with elliptic curvature leads to strong oscillations at lower frequencies. The amplitudes of these oscillations decay as the frequencies increase. For efficient and reliable analysis of such structures, it is necessary to understand the intricate interplay of loading types and geometry, including the effects of the chosen shell models.

Mechanistic Code for Asphalt Pavements Loaded by Farming Vehicles

Farming vehicles are relatively heavy and slow-moving machines, typically equipped with rubber tracks or flotation tires (or both). The objective of this study was to develop, validate, and openly share a new mechanistic code for calculating asphalt pavement responses under the loading conditions of such vehicles. For a given farming vehicle, the loading geometry was modeled by exploiting symmetry considerations and representing tread contact areas as groups of rotated rectangular patches. For the purpose of calculating responses, the pavement system was modeled as a layered elastic half-space, loaded vertically by many small identical circular areas—collectively approximating the patches. Computational efficiency was sought by solving the layered model for one circular area and executing a series of coordinate transformations, interpolations, and translations, to represent the entire vehicle loading. The new code is named LynFarm; it was validated through its ability to reproduce mechanical responses generated by farming vehicles as they were driven over an instrumented asphalt pavement section. LynFarm is openly shared on GitHub for further verification, validation, and improvement by the pavement engineering community.

K-shell radiation and bright spot characteristics of high-energy-density Fe-Cr-Ni plasmas influenced by X-pinch load geometry

K-shell radiation is diagnostically advantageous for the study of high-energy-density plasmas. The current work investigates the influence of load geometry on K-shell x-rays in Z-pinch plasmas produced on the 1-MA Zebra generator. Stainless steel (Fe: 69%, Cr: 20%, Ni: 9%) X-pinch wire loads are fielded with an interwire angle of 31° (small-angle) or 62.5° (large-angle), respectively and studied using various x-ray diode, imaging, and spectroscopic diagnostics. The large-angle geometry produced large, individual x-ray-emitting bright spots (> 3 keV) at the wire cross-point averaging areas ≥ 1 mm2, with noteworthy soft x-ray (> 0.75 keV) bursts and radiation yields ≤ 14.6 kJ. The small-angle geometry produced multiple x-ray-emitting bright spots extending the pinch axis with smaller average sizes (≤ 0.5 mm2), consistent with stronger current, increased radiation yield (≥ 15.5 kJ), and notable hard x-ray (> 9 keV) bursts, which peak with largest cumulative bright spot size. Spectroscopic analysis is performed with non-LTE collisional-radiative modeling, indicating a cold, nonthermal plasma region radiating from neutral to Ne-like ions, a hot, thermal region radiating from Fe and Cr He- and Li-like ions, and an intermediate region radiating Kα satellites from Li-like to O-like ions. Modeling of the nonthermal and satellite features imply a fractional hot electron abundance ∼0.1% and ∼0.5% for large- and small-angle geometries, respectively. Relative intensity analysis is performed on Heα and Kα lines, revealing intensity ratios that deviate from the original wire composition. Optical depth estimates allude to optically thick, thermal K-shell plasmas with densities consistent with non-LTE modeling.

The Impact of Nano-TiO2 Particles on the Moisture Susceptibility and Fracture Toughness of HMA under Mixed-Mode I/II Loading and Various Crack Geometry and Temperatures

In recent decades, some of the main goals of pavement engineers have been to increase bearing capacity, enhance tensile strength, and improve the moisture susceptibility of asphalt mixtures. Because moisture and frost intensify the damage caused by traffic loads on pavements in cold climates, the life and safety of asphalt pavements in this climate are reduced. Finally, cracking at low temperatures and moisture damage leads to a decrease in the serviceability of asphalt pavement in cold climates relative to temperate climates. Hence, a comprehensive and accurate program is necessary to estimate the fracture toughness and moisture susceptibility of asphalt mixtures in cold climates. In recent years, nanotechnology has become very popular due to its unique features in enhancing the operation of bitumen and asphalt mixtures. For this purpose, in this study, the impact of nano-TiO2 on pavement performance against cracking and moisture susceptibility is investigated. To achieve this objective, SCB specimens were fabricated with different ratios of nano-TiO2 (0.0% and 0.9%) and studied at the three temperatures of −5°C, −15°C, and −25°C under pure mode I, pure mode II, and four distinct mixed-mode (I/II) loading (Me=0.2, Me=0.4, Me=0.6, Me=0.8) for various crack geometry, including vertical and angular cracks for which the crack angle is 45° in samples with angular cracks. In addition, the indirect tensile strength (ITS) test was employed to estimate the moisture susceptibility. The results indicated that modifying the asphalt mixture properties with 0.9% nano-TiO2 had a significant impact on the fracture behavior of the samples in both vertical and angular cracks under all temperatures. Additionally, with the application of nano-TiO2 and decreasing temperature, the fracture toughness of the samples increased. Furthermore, the findings displayed that the employment of 0.9% nano-TiO2 reduced the moisture susceptibility of asphalt mixtures by approximately 6%.

Effect of material distribution on bending and buckling response of a bidirectional FG beam exposed to a combined transverses and variable axially loads

This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton’s principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam.

Structural and thermal investigations of rolling tires in a flat road

Rubber is an essential component of a pneumatic tire. In general, the tire, or the rubber part, is heated by the hysteresis effects caused by the deformation of the rubber part during the operation. Besides, the tire temperature depends on many factors, such as inflation pressure, vehicle loading, car speed, road tire, environment condition, and tire geometry, etc. This study focuses on the finite element approach to compute by simulating the temperature distributions of a steady-state rolling tire. For simplicity, the tire is assumed to be composed of rubber, body-ply, wire, and rim only. The nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model, while the other parts are assumed to be a linear elastic material. The coupled effects of the inflation pressure and vehicle loading are investigated. Hysteresis energy loss is used as a bridge to link the strain energy density to the heat source in rolling tires. The steady-state thermal analysis may obtain the temperature distribution of rolling tires. On the other hand, an efficient computational process is being introduced to decrease the time for coupled 3D dynamic rolling simulation of the tire. The simulation results show that loading is the main factor in determining the temperature field