Axial Pretension Research Articles

Characterization of the Mechanical Properties of Low Stiffness Marine Power Cables through Tension, Bending, Torsion, and Fatigue Testing

The exploitation and harnessing of offshore marine renewable energy have led to an increased demand for reliable marine power cables with long service lives. These cables constitute a considerable share of the total installation cost of offshore renewable energy facilities and have high maintenance and repair costs. The critical characteristics of these power cables must be determined to reduce the risk of exceeding their ultimate strength or fatigue life, which can result in unwanted and unexpected failures. This study investigates dynamic marine power cables that are suitable for application in devices that harness energy from ocean currents, waves, and tides. Tension, bending, torsion, and fatigue tests were conducted on three dynamic power cables (1 kV, 3.6 kV, and 24 kV) that have high flexibility, i.e., low mechanical stiffness. The specimen lengths and axial pretension force were varied during the tests. The results are discussed in terms of the mechanical fatigue degradation and ultimate design load, and the key observations and lessons learned from the tests are clarified. The study’s main contribution is the results from physical component testing of the dynamic marine power cables without metallic armors, which can be used to calibrate numerical models of this type of dynamic marine power cable in the initial design of, e.g., inter-array cables between floating wave energy converters. The benefits offered by this type of cable and the importance of the results for creating reliable numerical simulation models in the future are highlighted.

The role of axial pre-tension in reducing energy dissipation of micro/nano-mechanical resonators

Pre-tension is usually applied to raise the frequency of resonators. Theoretical studies revealed that tensile stress could inhibit thermoelastic damping of the resonators and thus increase the quality factor when thermoelastic damping is dominant. Up to now, there is little theoretical investigation for its impacts on other energy dissipation mechanisms, especially support loss. In this paper, a concise formula for the support loss of doubly clamped beam resonators with pre-tension is derived. Then theoretical analyses are carried out, revealing that the pre-tension decreases thermoelastic damping but increases support loss of micro-beam resonators. Making a trade-off between two competing influences of the pre-tension on support loss and thermoelastic damping by tuning pre-tension, an optimal quality factor can be achieved when these two dissipation mechanisms are dominant. Theoretical results of effects of pre-tension on thermoelastic damping and support loss are verified by finite element simulation, and the theoretical prediction of the quality factor associated with these two energy dissipation mechanisms also has the similar trend to the experimental data of reported researches. As a result, the quality factor can be improved by tuning the axial pre-tension in the case that thermoelastic damping greatly surpasses support loss of the resonator. Application of axial pre-tension is further demonstrated to be an effective approach to improving the quality factor of most polymer-based beam resonators. Hopefully, this work will provide theoretical basis and practical guidelines to the design and development of high-performance micro/nano resonators.

Simultaneous determination of the mass and position of attached particles using a micro-beam resonant mass sensor with axial pre-tension

Simultaneous determination of the mass and position of attached particles using a micro-beam resonant mass sensor with axial pre-tension

Modeling of Thermal Contact Resistance of Ball Screws Considering the Load Distribution of Balls

Abstract A new analytical method for the modeling of the thermal contact resistance of ball screws considering the load distribution of balls is proposed in this research. The load on balls is analyzed by the force analysis of ball screws, and then, the thermal contact resistance is obtained by the minimum excess principle and Majumdar–Bhushan (MB) fractal theory. The proposed method is validated by experimental results. The comparison with experimental and former results indicates that it is an effective method to evaluate the thermal contact resistance of ball screws. On that basis, effects of axial load, axial pretension, and geometry error of balls are discussed. It is concluded that the thermal contact resistance of ball screws increases along with axial load increase. The load on balls all decreases with axial pretension increase, and the thermal contact resistance of ball screws decreases with the axial pretension increase as well. When the axial load is applied on the nut in an axial-pretension ball screw, the load distribution in Nut A or B becomes less homogenized when the nut moves from nut position parameter ξ = 0 to 1. When the nut moves to ξ = 0.25, the thermal contact resistance will reach a minimum value, and it gets a maximum value at the nut position ξ = 1. The interval range of load and thermal contact resistance are obtained via uncertain analysis. It is concluded that the geometry error has much greater effects on the balls far away from the spacer.

Dynamic Modeling of a Ball-Screw Drive and Identification of Its Installation Parameters

Abstract Parametric expressions of equivalent stiffnesses of a ball-screw shaft are obtained by derivation of its geometric parameters, the finite element method (FEM), and data fitting based on a modified probability density function of log-normal distribution. A dynamic model of a ball-screw drive that considers effects of bearing stiffnesses, the mass of the nut, and the axial pretension is established based on equivalent stiffnesses of its shaft. With the dynamic model and modal experimental results obtained by Bayesian operational modal analysis (BOMA), installation parameters of the ball-screw drive are identified by a genetic algorithm (GA) with a new comprehensive objective function that considers natural frequencies, mode shapes, and flexibility of the ball-screw drive. The effectiveness of the methodology is experimentally validated.

Collagen peptide simulated bending after applied axial deformation

Structural proteins in the extracellular matrix are subjected to a range of mechanical loading conditions, including varied directions of force application. Molecular modeling suggests that these mechanical forces directly affect collagen's conformation and the subsequent mechanical response at the molecular level is complex. For example, tensile forces in the axial direction result in collagen triple helix elongation and unwinding, while perpendicular forces can cause local triple helix disruption. However, the effects of more complicated mechanical loading, such as the effect of axial pretension on collagen bending and triple helix microunfolding are unknown. In this study we used steered molecular dynamics to first model a collagen peptide under axial tension and then apply a perpendicular bending force. Axial tension causes molecular elongation and increased the subsequent perpendicular bending stiffness, but surprisingly did not increase the predicted collagen triple helix microunfolding threshold. We believe these results elucidate a key potential mechanism by which microscale mechanical loads translate from cellular and micro scales down to the nano and atomistic. Further, these data predict that cryptic force-induced collagen triple helix unwinding is axial-deformation independent, supporting the possibility that cell traction forces could be a key molecular mechanism to alter the cellular matrix microenvironment to facilitate collagen enzymatic degradation and subsequent cellular migration, such as in tumor extravasation.

Evaluation of thermoelastic damping in micromechanical resonators with axial pretension: An analytical model accounting for two-dimensional thermal conduction

It has been reported that application of tensile axial stress can simultaneously increase quality factor and resonant frequency for micromechanical resonators. In this study, we formulate an analytical model for evaluating thermoelastic damping in micromechanical resonators based on the thermal energy method, in which thermal conductions in both thickness direction and axial direction are considered. An explicit expression for thermoelastic damping in the form of infinite series has been obtained. The proposed analytical model is further validated by finite element analysis. Results of the present study demonstrate that the 2D model needs to be adopted in order to accurately evaluate thermoelastic damping of micromechanical resonators with axial pretension. In addition, the 2D model proposed in the present study eliminates the inherent inconsistency entailed in the 1D model.

Cross-Flow Vortex-Induced Vibration (VIV) Responses and Hydrodynamic Forces of a Long Flexible and Low Mass Ratio Pipe

Laboratory tests were carried out to investigate the cross-flow (CF) dynamic responses and hydrodynamic forces of a flexible pipe that subjected to vortex-induced vibration (VIV). The pipe had a critical mass ratio of 0.54 and an aspect ratio of 181.8. The uniform flow environment was realized by towing the pipe along a towing tank. The towing velocity ranged from 0.1–1.0 m/s with an interval of 0.05 m/s. Two axial pre-tension cases (200 N and 300 N) were enforced. The structural strains were measured at seven positions evenly distributed along the pipe. Then a modal analysis method was applied to reconstruct the displacement responses. It is revealed that the maximum CF displacement amplitude reached up to 2.18 pipe diameter and the strain response exhibited higher harmonic components. The CF dominant frequency gradually rises with the increase of reduced velocity and up to a three-order vibration mode can be observed. In addition, mean drag coefficient, lift force coefficient and added mass coefficient were also calculated to further investigate the fluid force feature of a low mass flexible pipe undergoing VIV.

Vibrations in 3D space of a spinning supported pipe exposed to internal and external annular flows

This paper conducts a dynamical analysis of drill-string-like pipes based on the ground-breaking contribution of Païdoussis et al. (2008), in which the stability of a tubular cantilever conveying internal and external annular flows without spin is investigated. The innovations of this paper are generalized as follows: i) A spinning three-dimensional (3D) model is developed to simulate working drill strings; ii) Supported pipes instead of cantilevers are considered due to the stabilizers and heavy loads encountered at the free end (the drill bit); iii) Hamiltonian, instead of Newtonian, derivation is performed to achieve the governing equations of such system with gyroscopic effects induced by spinning motion and fluid–structure interaction (FSI), namely a doubly gyroscopic system; iv) 3D motions, involving in-plane and out-of-plane transverse motions, are studied; v) The frequencies, energy, mode shapes and time-domain responses to the initial conditions are comprehensively investigated to display the dynamical characteristics of the system. The results obtained reveal that the viscous external fluid, flow velocity, spinning speed as well as the gravity and axial pretension all have significant effects on the dynamical behaviors of the pipe. The dynamics of the present system has been demonstrated rather different from that of cantilevered structures without spin.

Study on vibration and stability of an axially translating viscoelastic Timoshenko beam: Non-transforming spectral element analysis

• Derive equations of motion for the translating viscoelastic Timoshenko beam. • Present non-transforming spectral element modeling for translating beam problem. • Highlight the superiorities by comparing its results with those of other methods. • Process both wave and time domain analyzes for translating viscoelastic beam. • Study roles of beam velocity, axial loads and viscoelasticity on dynamic response. Engineering systems, such as rolled steel beams, chain and belt drives and high-speed paper, can be modeled as axially translating beams. This article scrutinizes vibration and stability of an axially translating viscoelastic Timoshenko beam constrained by simple supports and subjected to axial pretension. The viscoelastic form of general rheological model is adopted to constitute the material of the beam. The partial differential equations governing transverse motion of the beam are derived from the extended form of Hamilton's principle. The non-transforming spectral element method (NTSEM) is applied to transform the governing equations into a set of ordinary differential equations. The formulation is similar to conventional FFT-based spectral element model except that Daubechies wavelet basis functions are used for temporal discretization. Influences of translating velocities, axial tensile force, viscoelastic parameter, shear deformation, beam model and boundary condition types are investigated on the underlying dynamic response and stability via the NTSEM and demonstrated via numerical simulations.

A New Equation for the Shear Strength of Cable Bolts Incorporating the Energy Balance Theory

The application of cable bolts as a secondary support system is an increasing trend in underground coal mines worldwide. The performances of cable bolts have been evaluated under both axial and shear loading conditions. Two methods of testing cables for shear, single and double shear, have been recognised. This paper examines the shear behaviour of a variety of cable bolts under different pre-tension loads by double shear testing. Plain, spiral and the combination of both cable types were used in this study. The initial axial load and the type of cable bolts are the main factors affecting their shear strength. By increasing the axial pre-tension load, the peak shear load occurs at lower shear displacement. The failure angle due to cable bending across the joint at different pre-tension loads varied between 41° and 49°. This demonstrates that the ratio of axial and perpendicular displacements is almost constant and on average the failure occurs at about 45°. A novel analytical model is proposed to evaluate the shear behaviour of pre-tensioned fully grouted cable bolts subjected to double shearing. Energy and Fourier Series methods were incorporated in the model to simulate the shear behaviour of cable bolts. The comparison of the experimental results with the proposed model shows a good agreement.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Experimental research regarding static rigidity in transversal direction of “normal“ module

The paper presents some experimental results regarding the total deformation of ”normal” modules found in the structure of modular sets. The study presents the main aspect regarding the experimental methodology used for the determination of static rigidity in the transversal direction, the measuring scheme and test stand used. Modules deformations were analysed, under the action of transversal static force, in the presence of axial pretension force, using advanced equipment. The research conducted showed that modules with symmetric structure present increased stiffness compared to the asymmetric modules and T cross channels.

Effect of mass ratio on hydrodynamic response of a flexible cylinder

The effect of the mass ratio on the flow-induced vibration (FIV) of a flexible circular cylinder is experimentally investigated in a towing tank. A Tygon tube with outer and inner diameters of 7.9 mm and 4.8 mm, respectively, was employed for the study. The tube was connected to a carriage and towed from rest to a steady speed up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water. Reynolds number based on the cylinder’s outer diameter was 800–13,000, and the reduced velocity (velocity normalized by the cylinder’s natural frequency and outer diameter) spanned from 2 to 25. When connected, the cylinder was elongated from 420 mm to 460 mm under an axial pre-tension of 11 N. Based on the cylinder’s elongated length, the aspect ratio (ratio of the cylinder’s length to outer diameter) was calculated as 58. Three mass ratios (ratio of the cylinder’s structural mass to displaced fluid mass, m*) of 0.7, 1.0, and 3.4 were determined by filling the cylinder’s interior with air, water, and alloy powder (nickel-chromium-boron matrix alloy), respectively. An optical method was adopted for response measurements. Multi-frequency vibrations were observed in both in-line (IL) and cross-flow (CF) responses; at high Reynolds number, vibration modes up to the 3rd one were identified in the CF response. The mode transition was found to occur at a lower reduced velocity for the highest tested mass ratio. The vibration amplitude and frequency were quantified and expressed with respect to the reduced velocity. A significant reduced vibration amplitude was found in the IL response with increasing mass ratios, and only initial and upper branches existed in the IL and CF response amplitudes. The normalized response frequencies were revealed to linearly increase with respect to the reduced velocity, and slopes for linear relations were found to be identical for the three cases tested.

Upheaval buckling solution for submarine pipelines by segmented ditching and hot water flushing

An upheaval buckling solution is proposed using a preheating method combined with constraints from two segmented ditching constructions, which are scheduled before and after preheating. In this solution, some selected pipe segments along the route were curve-laid and preserved resting on the seabed in the first ditching construction, while other straight segments were trenched. The subsequent hot water flushing operation induced the curve-laid segments to buckle on the seabed, and then these prebuckles were laterally constrained by the second ditching operation carried out during preheating. After preheating, the cooling rebound of these prebuckles was constrained by the new trenches, and axial pretension was induced in the pipe wall to offset the axial compression in service and upgrade the thermal stability of the entire pipeline. A detailed design approach is provided in this paper, and corresponding Finite Element Model (FEM) verification is given for an example pipeline.

One-year stress relaxation of timber joints assembled with pretensioned bolts

In our previous study, great increases of hysteretic damping and initial slip resistance of timber joints were attained by applying axial pretension to the steel fasteners. To evaluate the effectiveness of this method, 1-year stress-relaxation measurement was carried out. Nine prestressed joints were prepared and three of them were restressed after 3 and then 6 months after the initial prestressing. All joints were exposed to indoor conditions, and relaxation of the pretension was regularly measured from time-dependent decreases of axial strain of the bolts. After measurement, the joints were subjected to cyclic and monotonic loading tests until failure. The average ratio of residual stress to the initial prestress after 1 year was about 0.23 and 0.66, respectively, for joints without restressing and those with restressing. A simulated stress-relaxation curve developed from the four-element relaxation model predicted 3% of the initial stress after 5 years. Without a regular restressing program, the initial prestressing effect therefore must be considered negligible. However, about 20% of the pre-stress level can be reasonably assumed if restressing is carried out annually. This small residual stress was found to introduce suffi cient frictional damping to signifi cantly increase the equivalent viscous damping ratio of the joints.

Optimum Design of Thick-Walled Multi-Layered CFRP Pipes to Reduce Process-Induced Residual Stresses

Process-induced residual stresses may cause cracking in thick-walled multi-layered CFRP pipes during the curing of the pipes, significantly affecting the ultimate structural performance. Several factors influence the amount of the residual stresses, such as thermal and elastic properties of CFRP, and stacking sequences and dimensions of pipes. This paper deals with the optimum design of thick-walled multi-layered CFRP pipes by minimising the process-induced residual stresses under some constraints of structural stiffnesses. An analytic model based on quasi-static thermoelasticity is adopted for the calculation of the residual stresses in the multi-layered CFRP pipes. The numerical results of optimisation show that, in the case of cross-ply pipes, the residual stresses can be reduced to a certain level by controlling ply thicknesses. However, in real process conditions, the optimised pipes are susceptible to cracking because the transverse residual stress is still large in a strength-based sense. To further suppress the residual stresses, the effects of stacking sequence, wall thickness and axial pre-tension on the optimum solutions are carefully examined.