Load-deflection Model Research Articles

Research on optimization of basic rail top bending prediction model

Since the basic rail of the switch needs to have a certain bending angle when the train changes direction, top bending is an important link in the production process of the basic rail. The three-point pressure top bending method is simple, flexible and widely used. In this study, the traditional three-point pressure bending is optimized, the influence of the pick width in the model is considered, a corresponding rebound model is established, and the model is applied to the pressure bending process of the basic rail. The bilinear strengthening model of the material was used to construct the bending moment expressions at different positions during the top bending process, and the relationship between the load and bending deflection in the elastic stage and elastic-plastic stage was obtained. The final top bending prediction model was obtained by combining the load-deflection model in the bending stage and the rebound stage. The correctness of the theoretical mathematical model was verified by establishing finite element simulations, and the theoretical calculation results were compared with the experimental results. The results showed that the top bend prediction optimization model established in this study had high feasibility and met the machining accuracy requirements.

Load-deflection model for T-section rail press straightening process under lateral loads

Straightening is an important process in the production route of a T-section rail. The three point reverse bending method has been utilized extensively for rail straightening process due to its apparent simplicity and good flexibility. Therefore, this paper studies the load-deflection model in the three point bending and its application for T-section rail press straightening process under lateral loads, considering the work-hardening materials. An elastic-plastic power-law hardening model of the material is adopted. The analytical formulas of the relationship between the loading force and the bending deflection is given in the elastic deformation stage and the elastic-plastic deformation stage during the bending process. The corresponding loading deflections for straightening certain initial deflections of a rail are also calculated according to the simple unloading law. The theoretical results are then compared with the experimental data of rails with different initial bending deflections. It is found that the load-deflection model and straightening model established in this study could achieve an allowable straightness error. The results of this subject can be provided as an analysis reference for the automatic control strategy of a rail straightening process.

Energy absorption in lattice structures in dynamics: Nonlinear FE simulations

An experimental study of the stress–strain behaviour of titanium alloy (Ti6Al4V) lattice structures across a range of loading rates has been reported in a previous paper [1]. The present work develops simple numerical models of re-entrant and diamond lattice structures, for the first time, to accurately reproduce quasi-static and Hopkinson Pressure Bar (HPB) test results presented in the previous paper. Following the development of lattice models using implicit and explicit non-linear finite element (FE) codes, the numerical models are first validated against the experimental results and then utilised to explore further the phenomena associated with impact, the failure modes and strain-rate sensitivity of these materials. We have found that experimental results can be captured with good accuracy by using relatively simple numerical models with beam elements. Numerical HPB simulations demonstrate that intrinsic strain rate dependence of Ti6Al4V is not sufficient to explain the emergent rate dependence of the re-entrant cube samples. There is also evidence that, whilst re-entrant cube specimens made up of multiple layers of unit cells are load rate sensitive, the mechanical properties of individual lattice structure cell layers are relatively insensitive to load rate. These results imply that a rate-independent load-deflection model of the unit cell layers could be used in a simple multi degree of freedom (MDoF) model to represent the impact behaviour of a multi-layer specimen and capture the microscopic rate dependence.

塑性率を損傷評価の指標とする機械設備の地震PRAにおける地震動強さの指標の検討

This study tries to evaluate the applicability of four candidate indices, those are JMA Instrumental Seismic Intensity, Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) and Standardized CAV, as Earthquake Hazard Index in the Seismic Probabilistic Risk Analysis (PRA) of mechanical components. As results of parametric elastoplastic earthquake response analyses of one-degree-of-freedom system with bi-linear load-deflection model against 60 near-field earthquake motions selected from NIED's K-NET and KiK-net observed earthquake motion data base in Japan, the correlation between those four indices and Ductility Factor (as Damage Assessment Index) reveals that the index AJMA, based on JMA Instrumental Seismic Intensity, has similar characteristics with PGV and suggests to be most promising one in the seismic capacity evaluations of mechanical features made by ductile materials.

Bilinear load-deflection model of fiber-reinforced polymer–concrete composite beam with interface slip

The design of fiber-reinforced polymer–concrete hybrid beam is usually governed by deformation. Due to the rigidity degradation caused by fiber-reinforced polymer–concrete slip, the load–slip and load–deflection curves demonstrate a bilinear characteristic. The originality of this article is to propose a bilinear analytical model and to determine two dominant parameters in this model, namely, initial bond stress and slip modulus of the interconnection. This model consists of two distinct linear stages. In Stage I, full composite action between fiber-reinforced polymer and concrete is obtained, and no slip exists; Stage II commences once interfacial bond force diminishes, when slip increases linearly versus load, and the overall beam rigidity drops compared with that in Stage I, indicating only partial composite action is realized. Finally, three large-scale specimens were tested to validate the proposed bilinear model and to calculate the two parameters.

Strain Evaluation and Fracture Properties of Hetero-Epitaxial Single Crystal 3C-SiC Squared Membrane

The following paper explores the development the bulge test technique combined with the micro-Raman analysis and a refined load-deflection model for high quality 3C-SiC squared-membranes. By the minimization of the total elastic energy, starting from the isotropic relation between the stress tensor and the strain tensor, it is possible to calculate the relationship between the maximum deflection and the applied pressure, in both regime of small and large deflection. From the measured breaking pressure through the refined model it is possible to evaluate the breaking strain of the membrane. Furthermore, the relationship between the measured shift of Raman Transverse Optical (TO) phonon modes and the total residual strain (Δa/a) within the epitaxial 3C-SiC layer was found.

Fracture property and quantitative strain evaluation of hetero-epitaxial single crystal 3C-SiC membrane

The following paper explores the development of a combined bulge test/micro-Raman analysis. This analysis, together with a refined load-deflection model (valid in both small and large deformation regimes, defined as the regimes in which the ratio between membrane deflection and width is smaller or larger than 1:10), allowed the determination of the elastic and optical properties of high quality single-crystal 3C-SiC squared membranes. Specifically we have evaluated the breaking strain of the membranes by measuring the breaking pressure for various membrane widths. The relation between the shift of the Raman Transverse Optical (TO) mode and the total residual strain (Δa/a) has been determined by measuring the TO shift for different membrane deflections. This relation, which allows determination of the residual strain by simply measuring the TO shift, was known only for thick samples (Olego et al) and high-oriented (100) thin films (Rohmfeld et al). Finally, we have calculated the TO stress-free value of high-quality thin single-crystal 3C-SiC/Si(100) films as 796.71 ± 0.04 cm−1.

Evaluation of Mechanical and Optical Properties of Hetero-Epitaxial Single Crystal 3C-SiC Squared-Membrane

The aim of this work is to develop the bulge test technique combined with the micro-Raman analysis and a refined load-deflection model for high quality 3C-SiC squared-membranes. By the minimization of the total elastic energy, starting from the isotropic relation between the stress tensor and the strain tensor, it is possible to calculate the relationship between the maximum deflection and the applied pressure, in both regime of small and large deflection. Furthermore, the relationship between the measured shift of Raman Transverse Optical (TO) phonon modes and the total residual strain (Δa/a) within the epitaxial 3C-SiC layer was found and in order to understand the stress distribution within the membrane, TO Raman shift maps were performed along the corner and the border of the membrane.

A Highly Accurate Closed-Form Model for Pull-in Voltage of Circular Diaphragms under Large Deflection

A simple easy to use highly accurate closed-form model to determine the pull-in voltage of electrostatically actuated circular diaphragms subject to large deflection has been developed. The model takes account of the nonlinear stretching of the diaphragm during large deflection, effects of residual stress, bending stress, and the effects of fringing field capacitances. At first a linearized uniform model of the nonlinear non-uniform electrostatic force has been derived that includes the effects of the fringing field capacitances. This model is then used in conjunction with the load-deflection model of a circular diaphragm subject to large deflection to derive the closed-form model for the pull-in voltage based on the condition that at unstable equilibrium, the electrostatic force is just balanced by elastic restoring force. The model has been verified by extensive 3-D electromechanical finite element analysis (FEA) using IntelliSuite. The model is in excellent agreement with 3-D electromechanical FEA with a maximum deviation of 1.6% for a wide range of residual stress and pull-in voltage values. The model leads to an integrated design strategy to optimize the electrical and mechanical design variables for MEMS-based capacitive type sensors having circular diaphragms. The model can be used to determine pull-in voltages of MEMS capacitive type pressure sensors, capacitive micromachined ultrasound transducers (CMUT) for medical diagnostic imaging, MEMS based microphones, touch mode pressure sensors, and other application areas where electrostatically actuated circular diaphragms are used. Keywords: MEMS, electrostatic, sensor, circular diaphragm, pull-in voltage

Analysis on the uniformly loaded rectangular cross-section cantilever by a modified load–deflection model

The load–deflection relationship of the uniformly loaded rectangular cross-section cantilever is analysed by a modified mechanical model, which exhibits its conformity to the physical situation by considering both the tangential and normal surface stresses. The analytical solution of the modelling equation is solved and presented in terms of the first and the second kinds of the Airy functions in association with Scorer's function. The resultant deflection profile contains an inflection point due to the restoring bending moment contributed by the critical surface loadings. The relationships of the tip deflection and the loading scenario are investigated, which reveal the fact that various loading scenarios can result in different deflection profiles, albeit with the same tip deflection. A numerical algorithm is given in the appendix to solve the loading scenario, by which the surface loadings can formally be determined for the designated applications for the devices utilizing the cantilever structure.

Bulge testing and fracture properties of plasma-enhanced chemical vapor deposited silicon nitride thin films

The mechanical properties and fracture behavior of silicon nitride (SiN x ) thin film fabricated by plasma-enhanced chemical vapor deposition is reported. Plane-strain moduli, prestresses, and fracture strengths of silicon nitride thin films deposited both on a bare Si substrate and on a thermally oxidized Si substrate were extracted using bulge testing combined with a refined load-deflection model of long rectangular membranes. The plane-strain moduli and prestresses of SiN x thin films have little dependence on the substrates, that is, for the bare Si substrate, they are 133 ± 19 GPa and 178 ± 22 MPa, respectively, while for the thermally oxidized substrate, they are 140 ± 26 GPa and 194 ± 34 MPa, respectively. However, the fracture strength values of SiN x films grown on the two substrates are quite different, i.e., 1.53 ± 0.33 GPa and 3.08 ± 0.79 GPa for the bare Si substrate and the oxidized Si substrate, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over the edge, surface, and volume of the specimens and fitted with the Weibull distribution function. For SiN x thin film produced on the bare Si substrate, the volume integration gave a significantly better agreement between data and model, implying that the volume flaws are the dominant fracture origin. For SiN x thin film grown on the oxidized Si substrate, the fit quality of surface and edge integration was significantly better than the volume integration, and the dominant surface and edge flaws could be caused by buffered HF attacking the SiN x layer during SiO 2 removal.

The exact solution of the load-deflection model of a uniformly loaded rectangular cross-section cantilever beam

This paper derives the exact solution of the model no. 3 proposed by Zhang et al for the rectangular cantilever beam. The model is solved by a reduced differential equation and the designated exact solution is formally presented in the integration form in terms of the Airy functions, Ai(X) and Bi(X). Both the deflection and curvature are presented as containing the constituents contributed by Ai(X) and Bi(X) and an additional portion attributed to the interaction between the Airy functions. The results show that the curvature at the fixed end is primarily determined by the contribution of Bi(X), while the dominant constituent for the deflection at the free end is dependent on the magnitude of the loading scenario. The relations for the directions of the constituent deflections and curvatures are deduced from the derived exact solution and by the properties of the Airy functions, which reveal that the contribution of Ai(X) results in forward deflection, and the curvature and the deflection are of the same sign. However, the curvature contributed by Bi(X) induces retrograde deflection, which means that the curvature and the deflection are of opposite sign. The results also suggest that the hardening effect of the present model can be represented by the contribution of Bi(X), with which the beam resists being deflected as if it were stiffened by Bi(X) under all loading scenarios. Nonetheless, there is no simple relation for the curvature and deflection attributed to the interaction of the Airy functions, which should be evaluated by direct integration and differentiation of the derived exact solution.

The exact solution of the load-deflection model of a uniformly loaded rectangular cross-section cantilever beam

This paper derives the exact solution of the model #3 proposed by Zhang et al for the rectangular cantilever beam. The model is solved by a reduced differential equation and the designated exact solution is formally presented in the integration form in terms of the Airy functions, Ai(X) and Bi(X). Both the deflection and curvature are presented as containing the constituents contributed by Ai(X) and Bi(X) and an additional portion attributed to the interaction between the Airy functions. The results show that the curvature at the fixed end is primarily determined by the contribution of Bi(X), while the dominant constituent for the deflection at the free end is dependent on the magnitude of the loading scenario. The relations for the directions of the constituent deflections and curvatures are deduced from the derived exact solution and by the properties of the Airy functions, which reveal that the contribution of Ai(X) results in forward deflection, and the curvature and the deflection are of the same sign. However, the curvature contributed by Bi(X) induces retrograde deflection, which means that the curvature and the deflection are of opposite sign. The results also suggest that the hardening effect of the present model can be represented by the contribution of Bi(X), with which the beam resists being deflected as if it were stiffened by Bi(X) under all loading scenarios. Nonetheless, there is no simple relation for the curvature and deflection attributed to the interaction of the Airy functions, which should be evaluated by direct integration and differentiation of the derived exact solution.

Fracture Properties of Silicon Carbide Thin Films by Bulge Test of Long Rectangular Membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mum were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 plusmn 47 and 201 plusmn 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 plusmn 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 plusmn 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 plusmn 0.88 and 3.16 plusmn 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mum-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mum-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws. [2007-0191].

Study on Calculation Method of Press Straightening Stroke Based on Straightening Process Model

It is difficult to determine straightening stroke precisely for automatic straightening machines. The existing calculation method of straightening stroke is based on straightening curvature equation. Because the initial curvature is obtained by curve fitting method, the method is inconvenient to use and its accuracy is not well. In this paper, a method to calculate straightening stroke based on straightening process model is put forward. So the mathematic load-deflection model of straightening process must be established at first. The straightening process model for shafts is developed according to the elastic-plastic mechanics theory. By using the model, the straightening stroke can be calculated directly according to the initial deflection of the bent part. It is advantageous to use and to decrease errors. Comparing with FEM results and experimental results, the calculation results by the model are exact and the errors are small. So the validity and the accuracy of the method are verified. It will be helpful to the development of automatic straightening machines.

Analysis of Inflated Conical Cantilever Beams in Bending

The bending behavior of straight inflated beams has been studied for several decades. A number of theoretical models exist that predict the load deflection behavior of the beams in bending. The various models approach the problem in different ways. This is especially the case by the way the wrinkling and collapse load are defined. A definition for the collapse load for straight cylindrical beams has been modified to suit single- and double-curved beams. The definition for the collapse load is used to derive a load deflection model for truncated conical beams. The effect of a beam being conical instead of straight is of extra significance for an inflated beam because it changes the prestress distribution introduced by the internal overpressure. Increasing the prestresses will result in an increased wrinkling and collapse load. The primary objective is to derive a load deflection model for inflated truncated conical beams. A secondary goal is to optimize the geometry to minimize the deflection using the same amount of skin material. The optimized geometry and the straight cylindrical beam made of polyphenylenesulphide foil will be analyzed and compared using finite element analysis.

On the Dynamics of Elastohydrodynamic Mixed Lubricated Ball Bearings. Part II: Non-Linear Structural Vibration

Equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange's equation considering the vibrational characteristics of the individual constituents such as inner race, outer race, cage, and balls, in order to investigate the structural vibration of the bearing. This article is the second part of the present study dealing with structural vibration, whereas in the first part, elastohydrodynamic mixed lubricated contact stiffness and damping coefficients are determined. Utilizing these stiffness and damping coefficients, a non-linear load-deflection contact model is developed. This is then used in the equations of motion. The equations of motion are solved using Runge-Kutta integration technique. This work differs from the previous studies in the sense that the model simulates the vibration, considering that both the lubricated contact stiffness and damping correspond to the conservative and dissipative energies, respectively. It is observed that under undamped conditions, all the elements of the bearing actively participate in energy sharing and oscillate periodically, containing more than one frequency. The system vibration, however, died down rapidly in the presence of damping.

A closed-form model for the pull-in voltage of electrostatically actuated cantilever beams

A simple computationally efficient closed-form model has been developed to determine the pull-in voltage of a cantilever beam actuated by electrostatic force. The approach is based on a linearized uniform approximate model of the nonlinear electrostatic pressure and the load deflection model of a cantilever beam under uniform pressure. The linearized electrostatic pressure includes the electrostatic pressure due to the fringing field capacitances and has been derived from Meijs and Fokkema's highly accurate empirical expression for the capacitance of a VLSI on-chip interconnect. The model has been verified by comparing the results with published experimentally verified 3D finite element analysis results and also with results from similar closed-form models. The new model can evaluate the pull-in voltage for a cantilever beam with a maximum deviation of ±2% from the finite element analysis results for wide beams, and a maximum deviation of ±1% for narrow beams (extreme fringing field).

Establishment and Application of Load-Deflection Model of Press Straightening

Establishment and Application of Load-Deflection Model of Press Straightening

Modeling, design and fabrication of a triple-layered capacitive pressure sensor

A novel triple-layered capacitive pressure sensor (TCPS) is presented. It consists of a polysilicon/nitride/polysilicon composite-membrane sandwich structure, and was fabricated by surface micromachining technology. The operation principle of TCPS is based on the combination of variations of the capacitor area and distance of electrodes with the applied pressure. A load-deflection model for the triple-layered composite-membrane is derived by the improved energy method for the analysis and design optimization of TCPS, which is in good agreement with finite element analysis performed by ANSYS™. Test results show the sensitivity of the device is about 40 fF/Torr (1 Torr = 133.32 Pa = 1 mm Hg) and the nonlinearity is about 0.32%. The pressure sensor described here has a full scale pressure range of 110 kPa. A sensor structure array with 10×10 cells was fabricated and the side length of each cell is 100 μm.