Gravity Stiffness Research Articles

Deformation and force characteristics of double-cable suspension bridges

A double-cable suspension bridge has broad application prospects. As a kind of suspension bridge, it is a flexible structure with small overall stiffness, structural deformation induced by live loads is a major concern in the design of double-cable suspension bridges. Deformation and force characteristics of double-cable suspension bridges were studied in this paper, a theoretical analysis method is proposed for calculating the main cable’s horizontal force increment and vertical deformation under live load (concentrated and half-span uniform loads) of the double-cable system. Finite element models (FEMs) were established to verify the proposed formulas, and the comparison of formula solutions with FEM solutions revealed good agreement. The effects of key design parameters on the force and deformation were studied; and the deformation and force characteristics of double-cable suspension bridges were compared with those of traditional single-cable suspension bridges. Results showed that the ratio of the horizontal force increments of the two cables caused by the live load is mainly determined by the sag-to-span ratio of these cables. The sag-to-span ratio and the proportion of dead load distributed to the double cables affect the main cable deflection. Increasing the proportion of dead load borne by the top cable or reducing the sag-to-span ratio can increase the gravity stiffness of a double-cable system.

Improved curving performance using unconventional wheelset guidance design and wheel-rail interface – present and future solutions

The conventional railway wheelset benefits from its self-steering and self-centering ability. Because the wheelset has a simple structure and preferable dynamics, railway trucks with wheelsets have been widely used for nearly 200 years. In the design of a railway vehicle with wheelsets, compatibility between curving ability and hunting stability has been studied for many years. Based on past research, the vehicle design with conventional wheelsets has been well summarised. Today, the requirement for railway systems has dramatically changed. For example, high-speed trains are required to run over a 350 km/h cruising speed, while maintaining a high quality of ride comfort and light rail vehicles for urban transit, are required to achieve an excellent curving ability at intersections and turnouts, while maintaining a sufficient degree of safety against derailment. It is true to say that unconventional approaches are necessary for designing the next generation of railway systems. In this paper, the history of research on steering bogies, including conventional wheelsets, is explained. Examples of unconventional railway vehicle concepts are introduced. Furthermore, a new wheelset concept based on the reconsideration of the wheel-rail interface is mentioned. In the new wheelset concepts, gravity stiffness is potentially effective to realise high curving performance; therefore, the dynamics and practical application, including negative tread conicity in independently rotating wheelsets, are mentioned. Nowadays, active control of the wheelset is becoming a practical solution for guidance and is mentioned regarding its brief history and future possibility with unconventional bogie design.

A Study on Phase-Changing Materials for Controllable Stiffness in Robotic Joints

This paper studies the viability of using a class of phase-changing materials for the design of controlled variable stiffness robotic joints which enable the design of robots that can operate in confined spaces. In such environments, robots need to be able to navigate in proximity or while in contact with their environment to reach one or more manipulated target. Joints with controllable stiffness can substantially enhance functionality of this class of robots where relatively higher joint stiffness is required to support the robot weight against gravity and low stiffness is desired when operating in complex or delicate environments. The research work presented in this paper focuses on examining thermorheological fluids (TRF) to design and manufacture thermally controlled variable stiffness joints. Two phase-changing materials are considered in the study: low-melting-point solder and hot-melt adhesive. Both materials are embedded in a custom designed joint fabricated using 3D printing and silicone casting. Joint stiffness was investigated with both materials and reported here. The results shows that the proposed variable stiffness joints with TRF achieve wide ranges of load-deflection ratio varying between 0.05 N/mm (when thermally activated) to about 10 N/mm (in bonding state). On average, the joint can withstand 20 times its total weight when in the bonding state. Design challenges and durability of TRF-based joints are discussed.

Examination of the Blank Error on Mirror Accuracy of Lightweight SiC Mirror and a Compensation Method

Due to excellent characteristics of specific stiffness and thermal stability, silicon carbide-based (SiC) material is commonly selected to construct large-scale lightweight mirror. In general, the fabrication process of SiC mirror is similar to the casting process. The blank error of SiC mirror is 0~1 mm. Due to the high hardness of SiC, only the mirror surface and some positioning surface will be milled. The mirror surface accuracy will be degraded due to the fact that the blank error can cause significant changes in weight distribution. In this paper, Monte Carlo analysis is firstly performed to examine the blank error on gravity center, stiffness and mirror accuracy of a SiC mirror. It is found that according to the designed mount location, the amount of degradation is more than 2.5 nm of which the probability is 40.3%. It is known that the error of gravity center can be compensated by optimizing the axial mount location. Then inverse modeling and testing of gravity center for the SiC mirror is carried out in order to determine the optimal axial mount location. Based on the proposed method, the mirror degradation introduced by the blank error has been eliminated to the greatest extend.

Influence of the railway vehicle properties in the running safety against crosswinds

The aim of the present study consists of evaluating the influence of the most relevant geometric, mechanical and aerodynamic vehicle properties in the risk of derailment caused by crosswinds. To achieve this objective, a vehicle-structure interaction model is used to carry out non-linear dynamic analyses to assess the train-track coupling behaviour in the presence of winds. By computing the wheel-rail contact forces, the derailment risk is evaluated based on the unloading criterion, as suggested by the European Norm EN 14067–6 (2016), for several scenarios with different train and wind speeds. The wind is simulated with a stochastic model that allows the generation of turbulent wind time-histories based on power spectral density functions. The reference vehicle adopted in this work corresponds to the European InterCity Express 3 (ICE-3) train, whose original properties were parameterized in order to evaluate their influence in the vehicle's stability. The parametric study focused on several properties of the vehicle, namely the carbody mass, height of the gravity centre, aerodynamic coefficients, and stiffness and damping of the suspensions. Apart from the suspensions' properties, which prove to have a negligible influence in the vehicle's stability, the remaining parameters have a significant impact in the running safety against crosswinds.

Variation in Wood Properties of Hybrid Poplar Lumber by Radial and Vertical Position in Stem: A Case Study from Boardman, Oregon

Understanding of wood quality of hybrid poplar is critically important for manufacturers who want to know the suitability of the wood for specific products. To this end, lumber was milled from the merchantable stem of four hybrid poplar clones ages 10-11 yr., grown at single site near Boardman, OR. The vertical and radial position in the stem were recorded for each board and the boards were kiln dried, surfaced, and samples from each board tested to determine specific gravity (SG), dimensional stability, hardness, screw withdrawal, and bending strength and stiffness (modulus of rupture [MOR] and modulus of elasticity [MOE], respectively) from small clear specimens. Results show differences in wood properties relative to vertical and radial position in the stem. SG, hardness, screw withdrawal, and bending properties of lumber samples generally increased with height in tree. Tangential hardness, SG, and MOR varied significantly between different sides of the trees corresponding to predominant wind in the area. Boards milled from the center of the stem had lower MOE and MOR than boards milled from nearer the bark. The results of this study may be used to target specific stem locations for different end uses.

Gravity stiffness of a three-tower suspension bridge: Analytical solution via double-span bridge reduction to a single-span one with elastic constraints

Suspension bridge’s main cable under live load undergoes deformation depending on its gravity stiffness, i.e., work done against gravity under the initial dead load. In three-tower suspension bridges (3TSB), the middle tower's effect on the main cable's gravity stiffness is crucial but hard to assess. In this paper, the 3TSB model was simplified to the 2TSB with elastic constraints. The main cable shape was then calculated via the ratio between the simply supported beam's bending moment and the horizontal force component. The 2TSB model results were used to derive the 3TSB main cable's deflection using the middle tower's stiffness under vertical load. The analytical formula for gravity stiffness of 3TSB was derived by matching the latter with the simply supported beam's deflection formula. For a case-study 3TSB with main spans of 248 m + 1060 m + 1360 m + 380 m, analytical predictions were verified by FEM numerical results obtained via ANSYS. Linear relationships between live load and increments of the main cable's deflection and horizontal force component were derived. Besides, the main cable's deflection under live load can be reduced by increasing its sag-to-span ratio and cross-sectional area.

Impact of sleeping position, gravitational force & effective tissue stiffness on obstructive sleep apnoea

Accurate prediction of deformation and collapse of the upper airway during breathing is required for effective and personalised treatment of obstructive sleep apnoea (OSA). While numerical modelling techniques such as fluid–structure interaction (FSI) are promising, an outstanding challenge is to accurately predict the deformation of the airway during breathing and thus the occurrence of OSA. These difficulties arise because the effective stiffness of the soft tissue in the human upper airway varies due to neuromuscular effects on the stiffness of the underlying muscles. In addition, both the elasticity and anisotropy of the soft tissues along the upper airway are poorly characterised. Finally, gravitational effects on anatomic features are yet to be considered. In this study, a validated FSI technique is introduced that allows prediction of the extent and position of the major deformation in the upper airway. This technique is used to analyse the behaviour of the upper airway in the two most common sleeping positions and for a range of effective tissue stiffnesses. The results demonstrate that sleeping position, gravity and soft tissue stiffness (used here as a proxy for neuromuscular effects) are the main factors that affect upper airway collapse. Therefore, this study provides new insights into the mechanisms of OSA and a new methodology that significantly advances the patient-specific treatment of OSA.

Low-cost variable stiffness joint design using translational variable radius pulleys

Robot joints are expected to be safe, compliant, compact, simple and low-cost. Gravity compensation, zero backlash, energy efficiency and stiffness adjustability are some desired features in the robotic joints. The variable radius pulleys (VRPs) provide a simple, compact and low-cost solution to the stiffness adjustment problem. VRP mechanisms maintain a preconfigured nonlinear force-elongation curve utilizing off-the-shelf torsional spring and pulley profile. In this paper, three synthesis algorithms are presented for VRP mechanisms to obtain desired force-elongation curve. In addition, a feasibility condition is proposed to determine the torsional spring coefficient. Using the synthesis methods and the feasibility condition, a variable stiffness mechanism is designed and manufactured which uses two VRPs in an antagonistic cable driven structure. Afterwards, the outputs of three synthesis methods are compared to force-elongation characteristics in the tensile testing experiment. A custom testbed is manufactured to measure the pulley rotation, cable elongation and tensile force at the same time. Using the experiment as the baseline, the best algorithm achieved to reproduce the desired curve with a root-mean-square (RMS) error of 13.3%. Furthermore, VRP-VSJ is implemented with a linear controller to reveal the performance of the mechanism in terms of position accuracy and stiffness adjustability.

Analytical Solution for Horizontal Tension of Main Cable in Erection of Stiffening Girder

The horizontal tension of main cable is a key parameter to guarantee the safety of tower, form gravity stiffness and keep main cable shape correct during erection of stiffening girders. Instead of complicated Finite Element Modeling and iterative algorithms, simply analytical solutions of horizontal tension of main cable were deduced for two classical erection methods of stiffening girder based on the mathematical analogue and work-energy principle. Numerical method was also adopted to verify the analytical solutions on analysis of a single span suspension bridge. The results from analytical solution are found to be in good agreement with the numerical results. The theoretical results show that the presented analytical solutions can be easily applied in the calculation of the horizontal tension of main cable in any erection stage.

Impact on the number of floors of a reinforced concrete building subjected to sudden column removal

In recent decades, there have been many reports of buildings collapsing due to incidents such as gas explosions, terrorist attacks, and vehicle accidents. The goal of this paper is to present the findings of a study of the how the number of stories of a reinforced concrete (R.C.) structure impacts the building when a first-story column is removed instantaneously. Three R.C. buildings were studied, all of the same plan, but with varying numbers of floors (3, 5, and 7 floors). The criteria established for comparing the behavior of the buildings when sudden column removal occurs are (1) performance level of the beams, (2) gravity stiffness of the buildings, and (3) variations of applied axial forces to the columns. The Column Sensitivity Index (β) was utilized to compare the condition of neighboring columns before and after the column removal. The results of the study showed that the β increases when the number of floors increases, which means that the neighboring columns are more vulnerable to damage. On the other hand, when the number of floors increases, the performance level of the beams improves, and the number of created moment plastic hinges in the beams decreases. The Displacement Sensitivity Index (λ) was generated to compare the gravity stiffness of the structures at the top node of the removed column before and after column removal. The results showed that the reduction rate of the gravity stiffness decreased when the number of floors increased.

Shear-Rate-Independent Diffusion in Granular Flows.

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Parameters of static response of carbon fiber reinforced polymer (CFRP) suspension cables

The feasibility of longer spans relies on the successful implementation of new high-strength light weight materials such as carbon fiber reinforced polymer (CFRP). First, a dimensionless equilibrium equation and the corresponding compatibility equation are established to develop the cable force equation and cable displacement governing equation for suspension cables, respectively. Subsequently, the inextensible cable case is introduced. The formula of the Irvine parameter is considered and its physical interpretation as well as its relationship with the chord gravity stiffness is presented. The influences on the increment of cable force and displacement by λ 2 and load ratio p ′ are analyzed, respectively. Based on these assumptions and the analytical formulations, a 2000 m span suspension cable is utilized as an example to verify the proposed formulation and the responses of the relative increment of cable force and cable displacement under symmetrical and asymmetrical loads are studied and presented. In each case, the deflections resulting from elastic elongation or solely due to geometrical displacement are analyzed for the lower elastic modulus CFRP. Finally, in comparison with steel cables, the influences on the cable force equation and the governing displacement equation by span and rise span ratio are analyzed. Moreover, the influences on the static performance of suspension bridge by span and sag ratios are also analyzed. The substantive characteristics of the static performance of super span CFRP suspension bridges are clarified and the superiority and the characteristics of CFRP cable structure are demonstrated analytically.

Parametric Study of Cable Deflection and Gravity Stiffness of Cable-Stayed Suspension Bridge

The paper carries out the parameter analysis on the cable deflections and gravity stiffness of cable-stayed suspension bridge. Previous studies have given the formulas of cable deflections and gravity stiffness. According to these formulas, the three significant parameters were examined: rise-span ratio, concentrated load and the ratio of cable-stayed length to whole span. The result indicates when reasonable parameters are selected, the gravity stiffness of cable-stayed suspension bridge is improved greatly.

Quantifying Anti-Gravity Torques for the Design of a Powered Exoskeleton

Designing an upper extremity exoskeleton for people with arm weakness requires knowledge of the joint torques due to gravity and joint stiffness, as well as, active residual force capabilities of users. The objective of this research paper is to describe the characteristics of the upper limb of children with upper limb impairment. This paper describes the experimental measurements of the torque on the upper limb due to gravity and joint stiffness of three groups of subjects: able-bodied adults, able-bodied children, and children with neuromuscular disabilities. The experiment involves moving the arm to various positions in the sagittal plane and measuring the resultant force at the forearm. This force is then converted to torques at the elbow and shoulder. These data are compared to a two-link lumped mass model based on anthropomorphic data. Results show that the torques based on anthropometry deviate from experimentally measured torques as the arm goes through the range. Subjects with disabilities also maximally pushed and pulled against the force sensor to measure maximum strength as a function of arm orientation. For all subjects, the maximum voluntary applied torque at the shoulder and elbow in the sagittal plane was found to be lower than gravity torques throughout the disabled subjects' range of motion. This experiment informs designers of upper limb orthoses on the contribution of passive human joint torques due to gravity and joint stiffness and the strength capability of targeted users.

Seismic Response Analysis of Suspension Arch Bridge

This paper calculated the seismic response of suspension arch bridge witch subject the seismic loads in longitudinal, transverse, vertical or their combination based on the dynamic characteristics analysis. The results indicated that the earthquake-resistance capability of suspension arch bridge were under-estimated while not considering damping and were over-estimated while not considering gravity stiffness. The conclusions provided necessary reference for study and design of suspension arch bridge.

Cable Deflection and Gravity Stiffness of Cable-Stayed Suspension Bridge

The paper studye the cable deflections of cable-stayed suspension bridge subject to living load. in addition, an analytical formula of the gravity stiffness of the cable-stayed suspension bridge is derived. Duo to the dead load state in the cable-stayed part is more differ from that in the suspension part, the research aim at different parts of the cable in the cable-stayed suspension bridge. Using the energy relation principle associated with deformation of the cable, the cable deflections and gravity stiffness of cable-stayed suspension bridge are derived.

1103 操舵リンク系ジオメトリの非線形性を考慮した鉄道用自己操舵性独立回転車輪台車(OS2-1 交通・物流システムのダイナミクス(鉄道・エレベータ・荷役機械),OS2 交通・物流システムのダイナミクス,オーガナイズド・セッション)

Most of the bogies used for LRT have independently rotating wheels (IRW) so that the floor of the passenger compartment can be lower. IRW, however, do not have a sufficient ability to self-steer, and generate large lateral forces in curved sections of track. The EEF (a German acronym for Single-wheel Single-running-gear) bogie, on the other hand, has IRW that have the self-steering ability. The nonlinear profile of the wheels creates the gravity stiffness that gives them their self-steering ability. In this paper, a multibody dynamics model of the vehicle is developed, and a numerical simulation is conducted. Experiments with a 1/10 scale model vehicle has also been developed. From these results, a design method for the self-steering mechanism of a railway bogie, considering the nonlinear effects of linkage arrangement, is proposed.

Running performance of power-steering railway bogie with independently rotating wheels

This article proposes the concept of a steering bogie which utilizes self-steering ability while realizing further running performance with slight active control on a tight curve. An independently rotating wheel with EEF bogie naturally has self-steering ability, making use of gravity stiffness aroused by nonlinear tread gradient, but has oscillation in the wheel-steering motion. The proposed power-steering railway bogie consists of independently rotating wheels with a power-steering device and enables us to eliminate steering vibration while realizing ideal steering with slight power assist on curving. In this article, the theoretical investigation of the power-steering bogie and the control strategies is mentioned. Experimental results and numerical simulations with a scaled model vehicle show the effectiveness of the proposed bogie design and the proposed power-steering control.

Discussion of “ Gravity Stiffness of Classical Suspension Bridges ” by Alan Jennings (January, 1983)

Discussion of “ <i>Gravity Stiffness of Classical Suspension Bridges</i> ” by Alan Jennings (January, 1983)