Torsion Rod Research Articles

Energy harvesting of a heaving and forward pitching wing with a passively actuated trailing edge

This study experimentally investigates the energy harvesting capabilities of an oscillating wing with a passively actuated trailing edge. The oscillation kinematics are composed of a combined heaving and forward pitching motions, where the pitching axis is well behind the wing center of mass. Passive actuation is attained by connecting the trailing edge with the wing body using a torsion rod. The degree of flexibility of the trailing edge is represented by the Strouhal number based on the trailing edge natural frequency. The trailing edge passive response is studied for oscillation Strouhal numbers of 0.017, 0.025 and 0.033. Instantaneous aerodynamic forces are measured in a closed loop wind tunnel at a Reynolds number of 40000, based on the free stream velocity and the wing chord length. Measured results include the effective angle of attack induced by the trailing edge actuation as well as the lift and moment during the oscillation cycle. For the imposed kinematics in this study, the pitching motion has a positive contribution to the mean power output whereas the heaving motion has a relatively small but negative contribution. Additionally, by decreasing the natural frequency of the trailing edge closer to that of the imposed oscillation frequency, the magnitude of the lift and moment forces and hence the mean power output, increases. It is found that there exists a strong correlation between mean power output and the effective angle of attack, shown through the passive trailing edge response, resulting in an increase in energy harvesting potential.

Non-periodic homogenization of bending–torsion theory for inextensible rods from 3D elasticity

We derive, by means of \(\Gamma \)-convergence, the equations of homogenized bending rod starting from 3D nonlinear elasticity equations. The main assumption is that the energy behaves like \(h^2\) (after dividing by \(h^2\), the order of vanishing volume), where h is the thickness of the body. We do not presuppose any kind of periodicity and work in the general framework. The result shows that, on a subsequence, we always obtain the equations of the same type as in bending–torsion rod theory and identifies, in an abstract formulation, the limiting quadratic form connected with that model. This result is the generalization of periodic homogenization of bending–torsion rod theory already present in the literature.

Study on the Large Range Torque Transmitter Quickly Assembled Used for the Calibration of Hydraulic Tongs

For oil field, Square surface connection embedded in our torque transmitter are designed to connect 2 torsion rods instead of flanges, which can shorten the radial dimension of the large range torque transmitter, and realizes the rapid assembly in oil field. It is the chemical composition of elastomer that determines the mechanical properties of the elastomer; the paste process of strain gages will affect the parameters of the torque transmitter, such as linearity, measurement accuracy, hysteresis, repeatability etc.

State of the art review of knee-ankle-foot orthoses.

Knee-ankle-foot orthoses (KAFOs) are used to assist in ambulation. The purpose of this paper is to review existing KAFO designs which can be grouped into passive KAFOs, stance control (SC) KAFOs, and dynamic KAFOs. The conventional passive KAFOs do not provide any active control for knee motions. SCKAFOs lock the knee joint during the stance phase and allow free rotations during the swing phase. Some SCKAFOs switch between the stance and swing phases using body posture, while others use some kind of a control system to perform this switch. Finally, dynamic KAFOs control the knee joint during both stance and swing phases. Four dynamic systems are identified in the literature that use pneumatics, linear springs, hydraulics, and torsional rods made of superelastic alloys to control the knee joint during the gait cycle. However, only the two systems that use linear springs and torsional rods can reproduce the normal knee stiffness pattern which has two distinct characteristics: a soft stiffness during the swing phase and a hard stiffness during the stance phase. This review indicates that there is a need to conduct research regarding new KAFO designs that duplicate normal knee function during the whole gait cycle.

Resonant Frequency Change of Torsional Oscillator Induced by Solid 4He in Torsion Rod

The contribution of solid 4He contained in the torsion rod of a torsional oscillator to its resonant frequency is investigated using a modified torsional oscillator. The purpose of the present study is to discriminate between two possible contributions to the resonant frequency of the torsional oscillator, which abruptly increases below ∼0.2 K. The first possible contribution is the elastic property change of solid 4He in the torsion rod (i.e., shear modulus increase), and the second possible contribution is mass decoupling by the supersolid transition of solid 4He in the oscillating body (i.e., a decrease in the momentum inertia). A torsional oscillator that has no hollow space for solid 4He in the body was constructed, and its resonant frequency and Q-factor were compared to those of the conventional oscillator. The shear modulus contributions of solid 4He in the torsion rod were identical, but the momentum inertias of solid 4He in the oscillating body were quite different between the two oscillators. S...

The stability of thin, stretched and twisted elastic rods

The stability of thin elastic rods that have been stretched and twisted is considered. Two general stability criteria are proposed. The first is appropriate when both the axial stretch and the torsional twist are prescribed and it is based on the elegant method of Gent for the formulation of a knot in twisting. The second criterion is valid when the axial force and the moment about the axis of the rod are prescribed. Both criteria are valid for all thin elastic rods, being independent of the modelling approach adopted. The criteria are illustrated with specific examples of the phenomenological approach to the modelling of thin, elastic, incompressible rods in tension and torsion.

A nonstandard free boundary problem arising in the shape optimization of thin torsion rods

We study a 2 d -variational problem, in which the cost functional is an integral depending on the gradient through a convex but not strictly convex integrand, and the admissible functions have zero gradient on the complement of a given domain D . We are interested in establishing whether solutions exist whose gradient “avoids” the region of non-strict convexity. Actually, the answer to this question is related to establishing whether homogenization phenomena occur in optimal thin torsion rods. We provide some existence results for different geometries of D , and we study the nonstandard free boundary problem with a gradient obstacle, which is obtained through the optimality conditions.

Nanomechanical Torsional Resonators for Frequency-Shift Infrared Thermal Sensing

We investigate use of nanomechanical torsional resonators for frequency-shift-based infrared (IR) thermal sensing. Nanoscale torsion rods, ~1 μm long and 50-100 nm in diameter, provide both extraordinary thermal isolation and excellent angular displacement and torque sensitivities, of order ~10(-7) rad·Hz(-1/2) and ~10(-22) (N·m) Hz(-1/2), respectively. Furthermore, these nanorods act as linear torsional springs, yielding a maximum angular displacement of 3.6° and a dynamic range of over 100 dB; this exceeds the performance of flexural modes by as much as 5 orders of magnitude. These attributes lead to superior noise performance for torsional-mode sensing. We demonstrate the operational principles of torsional-mode IR detection, attaining an uncooled noise equivalent temperature difference (NETD) of 390 mK. By modeling the fundamental noise processes, we project that further reduction of device size can significantly improve thermal responsivity; a room-temperature NETD below 10 mK appears feasible.

Deflection of Structures using Principle of Quasi Work

A new methodology for obtaining deflections of structures is presented in this paper. It is based on Principle of Quasi Work, which connects two topologically similar systems thereby leading to a unique concept of standard elements for every category of structural problems. Using a priory known equation of deformation/deflection of elastic axis of these elements, solution for equation of deformed/ deflected elastic line of other structural members of similar category having different loading and boundary conditions is presented here. Th is methodology is easy to use as deflection of a given structure is obtained mostly by simple mu ltiplications and it also eliminates the use of internal force/bending mo ment expressions unlike conventional methods. Even though this methodology can be applied to any structure, its use is illustrated for one dimensional structural elements (viz. axial bars, torsion rods and beams) for the sake of conciseness and clarity. The concept of topologically similar system is exp lored for each category of elements as it lies at the heart of the principle of quasi work.

Frequency shift and dissipation of compound torsional oscillator at 10 mK

A compound torsion oscillator (TO), having two resonant mode frequencies (492 Hz and 1163 Hz) and high Q (0.5∼1 × 106), has become an important tool in studying the supersolid properties of 4He loaded into the main TO bob. By simultaneously exciting both modes of this TO, observations could be made on how changes in the drive amplitude of one mode affect the sample response measured by the other mode. In order to separate out the effects arising from the sample, “background” characteristics due to the unloaded TO itself were studied. The resonant frequency and response amplitude of both modes were measured at 10 mK as the drive amplitude of one mode was varied while the other was held fixed at a low drive amplitude. Unexpectedly, the resonant frequency and the response amplitude of the fixed mode decreased as the drive amplitude of the varied mode was increased. The two modes interact and affect each other. The decrease in frequency could be due to a decrease in the stiffness of the torsion rods, while the decrease in amplitude could indicate an increase in internal friction.

Thermal conductivity and torsional oscillations of solid 4He

Polycrystalline samples of hcp 4He of molar volume Vm = 19.5 cm3 with small amount of 3He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of 3He, x3, were studied: isotopically purified 4He with the estimated x3 < 10−10, commercial ‘well-grade’ helium with x3 ∼ 3·10−7 and a mixture with x3 = 2.5·10−6. Torsional oscillations at two frequencies, 132.5 and 853.6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the double-frequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and x3. The phonon mean free path increases with increasing x3. Annealing typically resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them.

Spectral finite element and nonlocal continuum mechanics based formulation for torsional wave propagation in nanorods

Because of future promising exploration of nanotechnology, focus is being put in the miniaturization of mechanical and electromechanical devices. Attention is sought toward the development of nanodevices and nanomachines. The length scales associated with nanostructures like are such that to apply any classical continuum techniques, we need to consider the small length scales such as lattice spacing between individual atoms, surface properties, grain size, etc. This makes a physically consistent classical continuum model formulation very challenging. So this work presents Eringen's nonlocal elasticity theory, that has been incorporated into classical torsional rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different torsional wave behaviors of nanorods from those of macroscopic rods. Nonlocal torsional rod model is developed for nanorods. Explicit expressions are derived for torsional wavenumbers and wave speeds of nanorods. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in torsional wave mode where no wave propagation occurs. This is manifested in the spectrum cures as the region where the wavenumber tends to infinite or wave speed tends to zero. Next, the Spectral Finite Element formulation of nanorods is performed. The exact frequency dependent shape functions and the dynamic stiffness matrix for the nanorod are obtained as a function of nonlocal scale parameter. It has been found that the nonlocal small scale has significant effect on the exact shape functions and the elements of the dynamic stiffness matrix. These effects are also captured in the present work. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

Derivation of the nonlinear bending–torsion model for a junction of elastic rods

We derive the one-dimensional bending–torsion equilibrium model for the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a union of thin, rod-like bodies. By taking the limit as the thickness of the three-dimensional rods tends to zero, and by using ideas from the theory of Γ-convergence, we find that the resulting model consists of the union of the usual one-dimensional nonlinear bending–torsion rod models which satisfy the following transmission conditions at the junction point: continuity of displacement and rotation of the cross-sections; balance of contact forces and contact couples.

Elastic effects in torsional oscillators containing solid helium

A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass---the signature of a ``supersolid'' phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.

Optimal stiffness of a pedicle-screw-based motion preservation implant for the lumbar spine

Pedicle-screw-based dynamic implants are intended to preserve intervertebral mobility while releasing certain spinal structures. The aim of the study was to determine the as yet unknown optimal stiffness value of the longitudinal rods that fulfils best these opposing tasks. A finite element model of the lumbar spine was used which includes the posterior implant at level L4/5. More than 250 variations of this model were generated by varying the diameter of the longitudinal rods between 6 and 12mm and their elastic modulus between 10MPa and 200MPa. The loading cases flexion, extension, lateral bending and axial rotation were simulated. Evaluated optimization criteria were the ranges of motion, forces in the facet joints, posterior bulgings of the intervertebral disc and the intradiscal pressures. Various objective functions were evaluated. The results show that the objective values depend more on the axial stiffness of the rods than on bending and torsional stiffness, rod diameter and elastic modulus. The optimal stiffness value for most of the investigated objective functions is approximately 50N/mm and is achieved, e.g. using a rod diameter of 6mm and an elastic modulus of 50MPa. The design with the least axial stiffness was the best one with regard to the mobility. The forces in the facet joints and the intradiscal pressures were reduced mostly by an implant with the highest axial stiffness. When minimal posterior disc bulging was the criterion, the optimal axial stiffness was also approximately 50N/mm. The optimal axial stiffness of a pedicle-screw-based motion preservation implant for the lumbar spine is approximately 50N/mm.

Investigation on Mechanical Behaviors of Shape Memory Alloy Torsion Rod

DSC test is carried out to determine the phase transformation temperatures of a NiTi SMA, which include martensitic starting temperature, martensitic finishing temperature, austenitic starting temperature and austenitic finishing temperature. The mechanical behaviors of shape memory alloy (SMA) torsion rod are investigated by using Zhou’s shear constitutive equation of SMA and the theorem of circular shaft in mechanics of materials. A critical torque equation is developed to describe the relationship between the martensitic phase transformation critical torque of SMA torsion rod and temperature.

A Device for Harvesting Energy From Rotational Vibrations

Abstract A new device designed to harvest rotational vibration energy is presented. The device is modeled as a spring-mass-damper system connected to a vibration source where a torsion rod is used as a spring element and a shearing electromagnetic induction circuit as the energy harvesting element. The device is inherently a resonant type harvester. A prototype device is tested using a purely sinusoidal vibration input and more realistic inputs consisting of wider bandwidths, multiple resonance peaks, and low amplitude noise. The performance of the prototype to realistic inputs verifies the ongoing challenge to vibration energy harvesting, namely, significant loss of performance when using broadband inputs with resonant based devices.

The optimal compliance problem for thin torsion rods: A 3D-1D analysis leading to Cheeger-type solutions

We consider the variational problem which consists in minimizing the compliance of a prescribed amount of isotropic elastic material placed into a given design region when it is subjected to a given load. We perform the asymptotics of this problem when the design region is a straight cylinder with infinitesimal cross section. The results presented in this Note concern the pure torsion regime and state the existence of optimal shapes for the limit problem. When the filling ratio tends in turn to zero, these optimal shapes concentrate on the boundary of the Cheeger set of the section of the design region.

A novel semi-inverse solution method for elastoplastic torsion of heat treated rods

Torsion rods are a primary component of many power transmission and other mechanical systems. The behavior of these rods under elastoplastic torsion is of major concern for designers. Different methods have so far been proposed which deal with the elastoplastic torsion of rods, most of which assume constant yield stress. This assumption produces rough and inaccurate results when the rods are heat treated, since in the process of heat treatment the form of yield stress distribution across the rod cross section changes. We propose a new method for calculating elastoplastic torsion of rods of simply connected cross section which is based on heat treatment observations. In our method the full plastic stress function is obtained by using the semi-inverse method. Elastoplastic stress function is obtained by generalizing the idea of the membrane analogy and using a piecewise continuous stress function. Since the proposed form of yield stress distribution can not be handled by the current Finite Element packages, we produce a computer package with a 3D graphical interface capable of calculating and displaying the 3D elastoplastic stress function, shear stress contours, and torque-angle of rotation per unit length. We show that our method produces excellent agreement for several known cross sections in comparison to methods which assume constant yield stress.

Observations on non-classical behavior of solid 4He with compound torsional oscillator

The response of oscillating hcp solid 4He samples was studied with a unique compound torsional oscillator a dummy mass and a sample (cylindrical or annular) container connected by two torsion rods. Identical solid sample could be probed within the same apparatus at two different frequencies (∼ 0.5 and 1.2 kHz) separately or simultaneously. The apparent onset of the non-classical rotational inertia (NCRI) occurred at a higher temperature in the higher frequency mode. The peak in dissipation of the higher mode also occurred at higher temperature. Surprisingly, the mechanical dissipation was significantly greater in the lower mode. When the lower mode was driven at high levels to induce "critical state" in the sample and the higher mode was simultaneously driven at a low level for probing, the critical state seen in the lower mode did not entirely appear. Conversely, if a critical state was induced by the higher mode, it also did not appear in the lower mode. These preliminary results are contrary to the simple expectation from identifying the critical state as indication of suppressed superfluid density.