Concentrated Torque Research Articles

Redundant Parallel Beam Multiaxis Force Sensor—Stress Correlation Coefficient

The stress nonuniformity on the loading neck is an important factor that leads to the local force error of an individual multiaxis force sensor (MAFS) in a distributed multiaxis force sensing system (DMAFSS). The stress correlation coefficient is used to characterize the stress nonuniformity. The stress correlation coefficient decreases with the increase of the loading offset. A full-constrained high-relative-stiffness-ratio structure is important for an MAFS to obtain a good stress correlation coefficient on its loading neck under various external loads. An individual MAFS with two loading necks is employed in the sensing system to increase the relative stiffness ratio. A thin loading neck, a long loading neck distance, and a high stiffness loading frame are important for the high-relative-stiffness-ratio structure. A local high-relative-stiffness-ratio structure is valuable for a large-scale DMAFSS. The mechanical hinge on the loading neck is useful to realize a large-scale lightweight DMAFSS. The extreme load including the load outside the reference loading zone and the concentrated torque affects the stress correlation coefficient apparently which should be specified in future standards.

An object-oriented method for fully coupled analysis of floating offshore wind turbines through mapping of aerodynamic coefficients

This work presents a novel object-oriented approach to model the fully-coupled dynamic response of floating offshore wind turbines (FOWTs). The key features offered by the method are the following: 1) its structure naturally allows for easy implementation of arbitrary platform geometries and platform/rotor configurations, 2) the analysis time is significantly faster than that of standard codes and results are accurate in situations where rotor dynamic contribution is negligible, and 3) an extremely flexible modeling environment is offered by the object-oriented nature of Modelica. Moreover, the current modeling facility used for the code development is open source and is naturally suitable for code sharing. In the present method, the aerodynamic model computes the aerodynamic loads through the mapping of steady-state aerodynamic coefficients. This modeling approach can be placed at the intersection between simplified aerodynamic methods, such as TDHMill, and full beam element/momentum-based aerodynamic methods. Aerodynamic loads obtained from the coefficients mapping are composed of a concentrated thrust and a concentrated torque. The thrust acts at the hub, while the torque is applied at the rotor low-speed shaft of a simplified rigid rotor equation of motion (EoM) used to emulate the rotor response. The aerodynamic coefficients are computed in FAST for a baseline 5 MW wind turbine. A standard rotor-collective blade-pitch control model is implemented. The system is assumed to be rigid. Linear hydrodynamics is employed to compute hydrodynamic loads. The industry-standard numerical-panel code Sesam-Wadam (DNV-GL) is used to preprocess the frequency-domain hydrodynamic problem. Validation of the code considers a standard spar-buoy platform, based on the Offshore Code Comparison Collaboration (OC3-Hywind). The dynamic response is tested in terms of free-decay response, Response Amplitude Operator (RAO), and the time histories and power spectral densities (PSDs) of several load cases including irregular waves and turbulent wind. The resulting model is benchmarked against well-known code-to-code comparisons and a good agreement is obtained.

The Influence of Symmetrical Boundary Conditions on the Structural Behaviour of Sandwich Panels Subjected to Torsion

The paper discusses the influence of load and support conditions on the behaviour of sandwich panels subjected to torsion. 3-D numerical models are presented, in which various boundary conditions have been defined. The case of the load causing the concentrated torque in the span is analyzed, and the load definition affects the structural response. The numerical results were compared with the results obtained for the analytical beam model, which included both free torsion and secondary warping torsion. The conditions under which the models achieve a high agreement between the results were determined, but the significant sensitivity of the solution was also indicated. In each case of the considered load and boundary conditions, the structural response shows appropriate symmetry.

On the post-buckling analysis of a circular column with cylindrical constraint under concentrated torque loading

With the hypotheses of small deformation and Bernoulli-Euler beam, a gap element is introduced to describe the contact between the circular column and the external cylinder. The dynamic relaxation method is used to calculate the static equilibrium of the twisted column constrained by the cylinder. The post-buckling modes of a torsional column in a cylinder are investigated for the deformation configurations of one-point, two-point, three-point, and point-line-point contact. It is found that the end constraint has an effect on the length of the two suspended sections of helical buckling mode, but has no effect on the length of the continuous contact section in the middle. The relations have been derived among critical torque, post-buckling modes, lengths of each section, and loads (including shear, bending moment, and contact force). Finally, the torsional buckling has been investigated for sucker rods and drill pipes with lengths of 1 km. It is found that the helical buckling of multiple pitches occurs. The results of the current study provide theoretical guidance for the design of centralizer spacing in oil and gas engineering applications.

Research on Biomimetic Models and Nanomechanical Behaviour of Membranous Wings of Chinese Bee Apis cerana cerana Fabricius.

The structures combining the veins and membranes of membranous wings of the Chinese bee Apis cerana cerana Fabricius into a whole have excellent load-resisting capacity. The membranous wings of Chinese bees were taken as research objects and the mechanical properties of a biomimetic model of membranous wings as targets. In order to understand and learn from the biosystem and then make technical innovation, the membranous wings of Chinese bees were simulated and analysed with reverse engineering and finite element method. The deformations and stress states of the finite element model of membranous wings were researched under the concentrated force, uniform load, and torque. It was found that the whole model deforms evenly and there are no unusual deformations arising. The displacements and deformations are small and transform uniformly. It was indicated that the veins and membranes combine well into a whole to transmit loads effectively, which illustrates the membranous wings of Chinese bees having excellent integral mechanical behaviour and structure stiffness. The realization of structure models of the membranous wings of Chinese bees and analysis of the relativity of structures and performances or functions will provide an inspiration for designing biomimetic thin-film materials with superior load-bearing capacity.

Twisting statics of functionally graded nanotubes using Eringen’s nonlocal integral model

In this contribution, a nonlocal integral model is formulated to investigate the twisting static behaviors of through-radius functionally graded (FG) nanotubes based on Eringen’s nonlocal integral elasticity. In comparison to the widely-used nonlocal differential model in the literature, the nonlocal integral model developed herein is self-consistent and well-posed. Closed-form solutions of rotational angle are derived for both clamped–clamped and clamped-free FG nanotubes. It is shown that the nonlocal parameter has a stiffness-softening effect on both clamped–clamped and clamped-free tubes, and the scaling effect is more sensitive to the former than the latter. The serious unresolved paradox that the torsional angle of a clamped-free FG nanotube with a concentrated torque at free end, when being modeled using the nonlocal differential model, is found to be identical with the classical result can now be well resolved based on the developed nonlocal integral model. The illustrative examples show that the maximum torsional angle can be prescribed by tailoring the through-radius microstructures of the nanotubes, and the increment of the nonlocal parameter and the applied torques can increase the torsional angle, while the increment of the effective shear rigidity can decrease the torsional angle.

A New Dynamic Performance Model of Motor Stalling and FIDVR for Smart Grid Monitoring/Planning

The stalling of highly concentrated constant torque induction motor loads due to system faults may result in fault induced delayed voltage recovery. This state can cause significantly depressed local voltage for several seconds after the fault is cleared and can also lead to widely cascaded system failure. Though there is extensive study conducted within the modeling of motor loads, the dynamic connection between the aggregated induction motor loads and the grid still needs further investigation. In this paper, a dynamic performance model is developed for motor stalling and over heat thermal tripping. Specifically, this dynamic model can be constructed with an energy-like Lyapunov function, and can be incorporated as part of power system dynamic cascading model. The simulation examples are carried out in an enhanced version of the IEEE 57 bus test system, as demonstration for feasibility. This model may be beneficial for smart grid monitoring and planning, as well as energy analysis for power system cascading failure.

Interaction Mechanics Model for Rigid Driving Wheels of Planetary Rovers Moving on Sandy Terrain with Consideration of Multiple Physical Effects

Predicting wheel‐terrain interaction with semiempirical models is of substantial importance for developing planetary wheeled mobile robots (rovers). Primarily geared toward the design of manned terrestrial vehicles, conventional terramechanics models do not provide the sufficient fidelity required for application on autonomous planetary rovers. To develop a high‐fidelity interaction mechanics model, in this study the physical effects of wheel lug, slip sinkage, wheel dimension, and load are analyzed based on experimental results, including wheel sinkage, drawbar pull, normal force, and moment, which are measured on a single‐wheel test bed. The mechanism of lug‐terrain interaction is investigated systematically to clarify the principle of increasing shear stress, conditions of forming successive shearing among adjacent lugs, and the influence on shear displacement of soil. A mathematical model for predicting the concentrated forces and torque of rigid wheels with lugs for planetary rovers moving on sandy terrain is derived by integrating the improved models of normal and shearing stress distributions. In addition to the wheel parameters, terrain parameters, and motion state variables, wheel‐terrain interaction parameters, such as the linear varying sinkage exponent, the soil displacement radius, and load effect parameters, were proposed and explicitly included in the model. In the single‐wheel experiments, the slip ratio was increased approximately from 0.05 to 0.6, and the relative errors of the predicted results using the proposed model are less than 10% for all the wheels when compared with the experimental data. The proposed model has been used in the simulation of a four‐wheeled rover, and its effectiveness is evaluated by comparing the simulation results with experimental results.

Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end

The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated constant vertical load, to a concentrated constant horizontal load and to a concentrated constant bending torque at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler–Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper.

Out-Plane Stability of Derrick of Inclined Drilling Rig

K-type derrick of inclined drilling rig that is top driving is usually loaded by axial compression, lateral force and concentrated torque simultaneously, and is more prone to out-plane instability due to its poor torsional rigidity. Here the upper segment of derrick was simplified as cantilever beam-column with laced-bar lattice structure. Stability model was established by energy method, and Ritz method was employed to obtain deformation curves for lateral deflection and torsion. Effects of dip angle of derrick and position of top drive on deformation were analyzed. At last the out-plane instability process of derrick is presented by increasing longitudinal compressive force gradually. For ultimate loads of well drilling condition, out-plane stability requirement of derrick is met.

Accurate Simulation Solutions of Euler Angular Velocity/Acceleration and Statics of Parallel Manipulators by CAD Variation Geometry

A CAD variation geometry approach is proposed for accurately solving the Euler angles, Euler angular velocity/acceleration, and the active forces due to a concentrated torque of limited-DOF parallel manipulators (PMs). First, a simulation mechanism of PM with Euler angles, a simulation mechanism of PM with Euler angular velocity/acceleration, and a simulation mechanism of PM with Euler angular torques are created and combined into one simulation mechanism. Second, when modifying the driving dimension of the active legs, the simulation mechanism of PM is varied correspondingly, and the Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved automatically and visualized dynamically. Third, a 3DOF PM and a 5DOF PM are illustrated, and their Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved accurately by CAD variation geometry and are verified by the analytic solutions.

Stress properties at the tip of a conical notch

The singular behavior of a three-dimensional conical notch under torsional or torsionless loading was analyzed using the Papkovich-Neuber displacement potential method. Based on the analysis of the Legendre polynomial with complex index λn (Thompson, T. R. and Little, R. W. (1970). End effects in a truncated semi-infinite cone, Quart. J. Mech. Appl. Math. 23, 185–196), transcendental equations to the stress order λn of a torsional or torsionless notch at the cone tip are given for various notch angles. Analytical solutions for stress distributions around the cone tip under a concentrated torque T, and around the line notch tip under an expansion source E, are derived using the Legendre polynomial expression. These solutions can be applied for the study of penetration or perforation, where a penetrator is simulated as a concentrated force and as an expansion source. Curves of the first order eigenvalues show that there exist very weak singular stresses at the three-dimensional conical notch. According to the evidence observed in the conical notch experiment (Williams, M. L. (1966). Stress singular, adhesion, and fracture. In Proc. 5th Nat. Congress for Appl. Mech. pp. 451–464), when the base of a cone is loaded, fracture occurs along its side instead of at its tip. This observation suggests that there may exist a comparatively weak singularity at the cone tip.

On the solution of a concentrated torque on an orthotropic half-space

The exact expressions of displacement and stresses in an orthotropic half-space subjected to a concentrated torque are obtained by means of Hankel transform.

Solution of the problem of a concentrated torque on a semi-space by similarity transformations

Similarity transformations are constructed and used to obtain an exact solution for the axisymmetric boundary value problem of a homogeneous isotropic elastic semi-space subjected to a concentrated torque normal to its surface.

Box beams subject to torsion

Stress analysis is carried out for the case where a cantilever box beam is subjected to distributed torque and concentrated torque at the tip. Direct stress σ x acting in a cover plate is assumed to be in the form of ∑ n σ n(x)y n where n is an odd integer and the fundamental equation governing a box beam is introduced, using variational method. The accuracy can be investigated by comparing the values of strain energy by each obtained solution. Since this calculation is very complicated, strain energy formula is simplified by the new device. From the results of theoretical analysis, it became evident that, for the case where approximation improves, there is no necessity for the empirical formula proposed by Kuhn to be used, and that the range affected by the clamped end is about within the breadth of a box beam from the clamped end.

Torsion of structural cores on deformable foundations

An approximate method is presented for assessing the influence of foundation deformations on the warping stresses of a shear core subject to torsional loading. The core is assumed supported on elastic foundations such that the vertical displacements are proportional to the imposed forces. Solutions have been derived for two general forms of loading, a concentrated torque at any level, and a distributed twisting moment whose intensity is defined as any polynomial in the height coordinate. A numerical example is given to illustrate the reduction in warping stresses which can occur as a result of relative foundation deformations.

Analysis of core wall structure subjected to applied torque

An approximate theory to analyze the torsional deformation of symmetrical core wall structures subjected to applied torque is presented. Explicit solutions are obtained for the case of a concentrated torque at the top and the case of uniformly distributed torques. An experiment is carried out to verify the accuracy of the theoretical calculations. An example is worked out to show the importance of warping stress due to torsion. Finally, design curves are presented for the case of uniformly distributed torque to facilitate design calculations.

Response of a semi-infinite elastic solid to an arbitrary torque along the axis

The response of an otherwise stress-free elastic half space to an arbitrarily distributed static torque along the axis of symmetry is obtained. As an example, numerical results are found for the stress and displacement fields due to the special case of a concentrated torque acting at a finite distance from the free surface.

TORSION OF A SEMI-INFINITE BODY AND A LARGE THICK PLATE

Michell derived the equation for torsion of bars of varying circular cross-section. Using this equation, and by means of Fourier-Beesel series, Purser analysed the local effect near the ends of the bar due to an arbitrary distribution of torsional shearing forces over its terminal sections. A similar analysis is given in this paper for the torsional problem of a semi-infinite body and a large thick plate, which are essentially bars having very large radii. The Fourier-Bessel series is replaced by a Fourier-Bessel integral. Stress and displacement components for the general cases are expressed in integral forms. These are then used to solve particular problems. In the first problem the torsional shearing force is distributed linearly within a circular area at the boundary of a semi-infinite body. The second problem consists of a semi-infinite body subjected to a concentrated torque at its boundary, which is considered as the limiting case of uniform shearing forces distributed over a finite circular area of the boundary. The similar problem for a large thick plate subjected to two equal and opposite concentrated torques on its surfaces is also discussed. Numerical results are given.