Deformation Of Rod Research Articles

Design and PIC Simulation Studies of Millimeter-Wave-Tunable Gyrotron Using Metal PBG Cavity as its RF Interaction Circuit

In this article, a millimeter-wave gyrotron using a metal photonic band gap (PBG) cavity as its RF interaction circuit is studied for its tunability. A PBG cavity operating in a TE7,2-like mode is designed and analyzed for its mode selective property at ~260 GHz. Particle-in-cell (PIC) simulation of the PBG gyrotron predicted a continuous wave (CW) RF output of ~121 W in the desired TE7,2-like mode with an axial mode number, $q = 1$ . Furthermore, the tunability of a PBG gyrotron is studied by varying the magnetic field, which, in turn, varies with the axial mode number of the desired operating mode. A broad continuous tunable bandwidth of ~1.5 GHz is obtained for more than ~1.5 W of the output power. The designed PBG cavity is thermally analyzed to study the structural deformation of metal rods and its effect on the performance of the tunable gyrotron.

Numerical calculation of elements of thin-walled structures under alternating loading taking into account damage

The statement of the problem and the algorithms for calculating thin-walled rods of arbitrary section under spatially variable loading based on the theory of small elastoplastic deformations and the refined theory of rods are presented. Using the variational Lagrange principle, mathematical models are developed for the deformation and damage of thin-walled rods in a cylindrical coordinate system. A system of differential equilibrium equations for a rod with spatially variable loading in vector form is obtained. To solve the boundary-value problem, the central difference scheme of the second order of accuracy and the matrix sweep method are used. An example of calculation is given.

Hysteresis Losses during Loading-Unloading a Wheel with a Rod Protector

The problem of sequential loading-unloading a wheel with a deformable rod protector (tire tread) is considered. The presence of a slip zone in the contact zone with the road surface leads to different restoring forces during the loading-unloading process and to the energy losses due to dry friction. Two different approaches to finding the total normal reaction acting on the wheel from the road surface are proposed. The energy losses in the tire-road mechanical system are estimated on the loading-unloading cycle.

Taylor impact test revisited: Determination of plasticity parameters for metals at high strain rate

Taylor impact test is the simplest experimental approach for characterizing plastic behaviour of metals under high strain rate (up to 105 s−1). Herein, a cylindrical rod is impacted upon a rigid stationary anvil and the dynamic yield strength is estimated by comparing the experimentally obtained rod deformation with its theoretical counterpart. Despite being simple and potent concept, the lack of a comprehensive theoretical model (which relates the material constitutive with the deformation pattern of the rod) has so far restricted the use of the Taylor impact test in material characterization. In the present study the Taylor impact test is revisited and an attempt is made to formulate an inverse framework for efficient determination of constitutive parameters for metals. The inverse analysis is performed via the Extended Kalman Filter technique where the forward model is constituted based on the derivation given in Chakraborty et al. (2015). Unlike the common practice, for better estimation of material constants, the deformation time histories are also included in the present inverse formulation. For demonstration five different plasticity models viz Johnson–Cook model, Zerilli–Armstrong model, Steinberg–Cochran–Guinan–Lund model, Mechanical Threshold Stress model and Preston-Tonks-Wallace model are considered. The estimated parameters are found to be in good agreement with their reference values. It is shown that the most distinguished feature of the present attempt is that a single Taylor test is sufficient to determine the parameters with reasonable accuracy.

Comparative analysis of the fracture splitting deformation of the big end for C70S6, 36MnVS4 and 46MnVS5 connecting rods

During the fracture splitting process of the connecting rod, the plastic deformation, especially the plastic deformation before cracking, not only causes the big end hole of the connecting rod to be out of roundness, but also increases the residual stress, affecting the assembly precision and even the service life of the connecting rod. In this paper, the mechanical properties of microalloyed steel C70S6, 36MnVS4 and 46MnVS5 connecting rod were determined by tensile test. The displacement field, plastic strain and the deformation principle of the big end before the crack initiation of the fracture splitting of the connecting rod were numerically simulated. The results show that the yield strength, tensile strength and plasticity index of the new medium carbon microalloyed steels 46MnVS5 and 36MnVS4 are significantly higher than those of C70S6. However, the C70S6 connecting rod has a long loading time before crack initiation, and the plastic deformation area of the groove root front is large and the strain is high. The plastic deformation of 36MnVS4 and 46MnVS5 connecting rods is small and the area is concentrated. Among the three, the 46MnVS5 connecting rod has the smallest deformation and the C70S6 connecting rod has the largest deformation.

Deformation of a Three-Layer Rod with a Compressible Core in a Neutron Flow*

We studied the deformation of a three-layer elastoplastic rod with a compressible core in a neutron flow. To describe the kinematics of the sandwich asymmetric across the thickness, the broken line hypothesis are adopted: Bernoulli’s hypothesis for the thin face layers and Tymoshenko’s hypothesis with linear approximation of displacements over the thickness for the compressible core. The resistance of the core in the tangential direction is taken into account. The constitutive stress–strain relations correspond to the theory of small elastoplastic deformations. The system of differential equilibrium equations is derived using the variational method. The kinematic boundary conditions of the rod is free support of the ends by fixed rigid supports. The boundary-value problem is solved by determining four functions of deflections and longitudinal displacements of the midsurfaces of the face layers. The analytical solution is obtained on the basis of the method of elastic solutions. Its numerical analysis is carried out in the case of an evenly distributed load.

Calculation of turning rigidity of I-section reinforced concrete elements with normal cracks

The article provides a methodology for calculating the torsion of an I-beam element using its approximation in the form of a cross-rod system. The cross-sectional I-section is divided into a finite number of longitudinal rods of rectangular section. These rods focus on their axial, flexural and torsional stiffness. Longitudinal rods are connected by transverse vertical and horizontal rods. The transverse rods imitate the local deformation of the longitudinal rods at their contact with each other. In contrast to the previously proposed methodology, in order to reduce the number of unknowns for creating the basic scheme of a statically indeterminate system, it is proposed that not all transverse rods be cut, but only one step in the longitudinal direction. The forces in the longitudinal rods determined from this calculation are applied to the rods of the next step. The pitch of the transverse rods may be arbitrary. A method for determining the stiffness parameters of the rods of an approximating system is shown. The advantages of the proposed methodology are shown, which can significantly reduce the number of equations unknown in the system, calculate elements for bending with torsion, and also take into account the change in stiffness as a result of nonlinear work of materials and crack formation.

Analyzing trajectory tracking accuracy of a flexible multi-purpose deployer

Multi-purpose deployer (MPD), an articulated heavy load handling remote handling system, is considered as a potential RH system that can be used for a fusion reactor. In this study, dynamic equations of rigid–flexible coupling of the MPD were derived. A neural network adaptive sliding mode controller (NNASMC) was subsequently designed based on the complex nonlinearity and uncertainty of the dynamic MPD model to ensure accurate trajectory tracking of the MPD. The stability and robustness of the proposed method were analyzed based on the Lyapunov stability theory. The control performance of the NNASMC was simulated using ADAMS-MATLAB/Simulink. The position tracking accuracy of the MPD under the combined action of NNASMC, MPD’s rigid–flexible coupling model, model uncertainty, and flexible deformation errors was analyzed. Results show that the MPD tracking error occurs mainly due to the deformation of the connecting rods and joints. This finding provides a reference for the MPD controller design and improvement in its tracking accuracy.

Experimental Studies on the Effect of Different Field Shaper Geometries on Magnetic Pulse Crimping in Cylindrical Configuration

Copper-aluminum composite rods are a substitution for copper rods, result in both cost and weight reduction. The electromagnetic pulsed crimping technique, which is based on high-velocity impact, offers many advantages by utilizing a part of total stored energy on the capacitor bank to fabricate composite rods. The application of field shaper in electromagnetic pulsed crimping not only increases the effectiveness of the process but also increases the life or strength of the working coil. The effect of geometry of three types of field shaper on the plastic deformation of the composite rod was investigated to facilitate the field shaper design. The field shaper variation was done by changing the cross-section namely tapered, step-tapered, and stepped. It was found that the step-tapered field shaper results better in terms of uniformity in crimp quality, joint strength in compression, joint strength in tension, joint electrical resistance, joint leakage, and surface finish of the crimped sample among the three types of field shaper. This work will be of use for designing of field shaper for producing joint by electromagnetic pulsed crimping.

Finite Element Simulation of Temperature Field during Friction Surfacing of Al-5Mg Consumable Rod

A finite element model was developed to determine the temperature distribution in the preheating phase of the friction surfacing (FS) process. In the present study consumable rod was used as a tool. As a model of the heat source, a model applicable to the traditional friction stir welding (FSW) was used. The developed model has been validated by a full-scale experiment. Temperature fields were obtained for different modes of the FS process, where the variable parameters were the axial force and the speed of rotation of the consumable rod. The difference between calculated and experimental data is less than 10%. Influence of the axial force magnitude on the consumable rod and the rod rotation speed on the temperature field generated by friction and plastic deformation of the consumable rod was established.

Study of the hydraulic disturbance suppression of a vibrator under high-frequency vibration based on experiments and numerical simulations

Hydraulic disturbance of a vibrator is the main cause of distortion of the vibroseis geophysical exploration signal that is caused by high-frequency fluid vibration during servo valve cavity commutation. This disturbance is closely related to the structure, size, and arrangement of the hydraulic flow path of the vibrator reaction mass. In this work, a vibrator disturbance–suppression mechanism was examined, an experimental study was carried out on an improved design of the hydraulic flow channel, and the source of the hydraulic disturbance of the horizontal channel vibrator was determined. The vibrator hydraulic flow channel was changed to a vertical flow channel in the piston rod. In addition, the structure of the track was designed, and the angle of the oil inlet of the piston rod was tested at 0°, 45°, and 90°. Then, the fluid flow state and fluid–solid coupling analysis method were used to improve the vibration-suppression effect of the vibrator. The results showed that the optimal oil inlet angle is 90°, for which the turbulent intensity of the oil inlet is the smallest, the pressure drop loss is reduced, and the influence of the oil flow on the piston rod deformation is minimal. The vibration reaction mass test of the vibrator showed that the disturbance inhibition rate of the piston rod with a 90° inlet structure design reaches 64.087%; the hydraulic disturbance had the best suppression effect and effectively reduced the distortion of the seismic prospecting signals with this oil inlet angle, improving the quality and efficiency of oil and gas exploration.

Two-dimensional densely ordered packings of non-convex bending and assembled rods

The investigation of the problem of particle packing has provided basic insights into the structure, symmetry, and physical properties of condensed matter. Dense packings of non-spherical particles have many applications, both in research and industry. We report the two-dimensional dense packing patterns of bending and assembled rods, which are non-convexly deformed from simple objects and modeled as entangled particles. Monte Carlo simulations and further analytical constructions are carried out to explore possible densely packed structures. Two typical densely packed structures of C-bending rods are found, and their packing densities are identified as being functions of the aspect ratio and central angle. Six shapes of assembled rods, representing the combined deformations of rods, are employed in simulations with the packing structures classified into three types. The dense packing density of each packing pattern is derived as a function of different shape parameters. In contrast with the case of disordered packings, both the shape and order are verified to affect the packing density.

Synthesis and optical characterization of cerium doped MgWO4 phosphor

The synthesized pure MgWO4 phosphor has wolframite structure with pure monoclinic phase and the cerium doped MgWO4 phosphor has a secondary phase [WO6]6− with the formation of Ce2WO4 on sintered at 1000 °C for 4 h. FESEM shows that the grain sizes are in the range of 1–4 μm and also deformation of rod like morphology as on doping with cerium. Photoluminescence studies shows blue emission spectrum at 470 nm for pure, 1%, 3% and 5% of Cerium doped MgWO4 phosphor and its intensity is maximum for 3% of cerium doped MgWO4 phosphor.

SOLUTION OF THE MAIN DIFFERENTIAL EQUATION OF DEFORMATIONS OF THE CASING IN A CURVED WELL

In a curvilinear well, the casing functions as a long continuous rod. It is installed on the supports-centralizers and replicates the complex profile of the well, as a result of which it receives large deformations. To describe them, a system of differential equilibrium equations of internal and external forces and moments was composed, which was supplemented to a closed form with a differential equation of curvature. It is non-uniform, because it takes into account the own distributed weight of the rod. Two ways are proposed to solve the problem: by the method of mathematical compression of the system equations into a complex inhomogeneous differential equation or by projecting the equilibrium equations of forces on the global (vertical-horizontal) and on the local (tangent-normal) coordinate systems. It is shown that the first integral of the system can also be found from the equilibrium equations of a portion of a curved rod of finite length. This integral has the form of a second-order inhomogeneous differential equation with variable coefficients and is the main equation that describes the deformation of a long elastic rod under the action of the longitudinal and transverse components of the forces of distributed weight. The main requirement of the technology is the installation of a pipes column on the centering supports, the purpose of which is to ensure the coaxiality of the pipes and the borehole walls and the creation between them a cement ring of the same thickness and strength. Accounting for this requirement allowed us to linearize the main equation. Its solution is the clue to the formulas of deflections, angular slopes, internal bending moments and transverse forces in the rod with the arbitrary arrangement of supports and boundary conditions in their intersections. The solution of the main differential equation of angular deformations of a long bar is found in the form of a linear combination of Airy and Scorer’s functions and in the form of three linearly independent polynomial series in the sum with a partial solution. The obtained formulas of flexure and power parameters allow us to calculate stress and strain in the pipes column during the process of casing the borehole of an arbitrary profile which increases the reliability and durability of the well.

Generalized reciprocity theorems for infinitesimal deformations superimposed upon finite deformations of rods: the plane problem

The present paper is concerned with bending of extensible and shear-deformable rods, where we treat the case of plane deformations. Our emphasis is laid upon infinitesimal deformations superimposed upon finite deformations. In this framework, we focus on deriving generalized reciprocity theorems that must hold with respect to the superimposed infinitesimal deformations, when produced by different types of loadings. Besides imposed distributed and concentrated force and moment loadings, we consider the action of eigenstrains. Moreover, we also take into account the presence of jumps in kinematic entities, particularly concerning jumps of axial rod positions and of cross-sectional rotations. We first derive local and global universal reciprocity relations, which must hold for rods made of any material. The global universal relation then is specialized to the case of hyperelastic rods. From the latter relation, we prove that reciprocity theorems known from the linear theory, such as the theorems of Betti, Maxwell and Land, as well as Maysel’s formula, formally do hold for infinitesimal deformations superimposed upon finite deformations. As a formulation that appears to be novel also with respect to the purely linear theory, we present a combination of Maysel’s formula with the theory of Land, the former dealing with eigenstrains, the latter involving jumps in kinematic entities.

Shear deformable rod theories and fundamental principles of mechanics

We discuss the role of the principle of virtual work, of the objectivity and of the energy balance in the formulation of planar static rod theories, in a large deformations framework and consider the effects of transverse shear. According to these principles, we also discuss the differences of Haringx approach to equilibrium and buckling over Engesser approach, as well as the advantages of choosing the curvature strain measure as the derivative of the rotation of the cross section with respect to the reference, rather than current, arc length.

CALCULATION OF STRETCHING AND BENDING STRESS IN A CASING STRING INSTALLED IN A WELL WITH A COMPLEX PROFILE

The casing column in the curvilinear well is represented as a long solid elastic rod. It has a vertically actingweight, which is evenly distributed along the length and creates variable axial tensile forces in the column body. At the same time, it is influenced by the reaction forces of the borehole walls, which, together with the weight, bend the column of initially straight pipes. It is assumed that the casing axis replicates the axis of the bent borehole, and the walls reaction is continuously distributed along the length according to a certain law, which, together with the weight, bends the column of the initially straight pipes. A system of differential equilibrium equations of internal and external forces and moments was composed. This system was supplemented to a closed form with the differential equation of curvature. This system describes large deformations of a long elastic rod in one plane. The introduction of the distributed weight, wall reactions and resistance forces into the calculation makes it non-uniform. Its feature is the need to solve the inverse problem. In this case the external load and rod deformations defined by the well shape in the form of an inclinometric data table are known. The unknown internal forces and the function of the walls reaction which creates its predetermined shape must be determined. It is established that this function depends on the distribution of axial forces caused by weight and resistance forces. As a result the system was reduced to a linear inhomogeneous differential equation with variable coefficients of the first order as to the axialforce and its solution was obtained as a sum of integrals. It is shown that one of them can be found in quadratures only in the case of a constant radius of curvature of the well. This necessitated the use of numerical integration methods. Formulas for the distribution of axial forces and bending moments in the body of the column, as well as the reactions of the walls leading the column to the actual well profile are obtained from the solution of the basic equation. To calculate these force factors, a method for numerical integration of inclinometric measurements data and software for numerical analysis of a real well are developed. This technique allows to detect the areas of local increase of the curvature and difficult passage of the curvilinear wellbore and to calculate the main parameters of the stress-strain state of the casing column in it.

Post-implantation Deformation of Titanium Rod and Cobalt Chrome Rod in Adolescent Idiopathic Scoliosis.

Introduction: Post-implantation rod deformation is anticipated in scoliosis surgery but the difference in rod deformation between titanium and cobalt chrome rod has not been elucidated. This study aims to compare the difference in rod deformation between two groups.Materials and Methods: Twenty-one adolescent idiopathic scoliosis (AIS) patients were recruited from a single center. The over-contoured concave rods were traced prior to insertion. Post-operative sagittal rod shape was determined from lateral radiographs. Rod deformation was determined using maximal rod deflection and angle of the tangents to rod end points. The differences between pre- and post-operative rod contour were analysed statistically. Rod deformation and thoracic kyphosis between two types of implants were analysed.Results: Both rods exhibited significant change of rod angle and deflection post-operatively. Curvature of the titanium rod and cobalt chrome rod decreased from 60.5° to 37°, and 51° to 28° respectively. Deflection of titanium rod and cobalt chrome rod reduced from 28mm to 23.5mm and 30mm to 17mm respectively. There was no significant difference between titanium and cobalt chrome groups with regard to rod angle (p=0.173) and deflection (p=0.654). Thoracic kyphosis was increased from 20° to 26° in titanium group but a reduction from 25° to 23° was noticed in cobalt chrome group, but these findings were not statistically significant.Conclusion: There was no statistical difference in rod deformation between the two groups. Thus, the use of titanium rod in correction of sagittal profile is not inferior in outcome compared with cobalt chrome but with lower cost.

Experimental Study on Bearing Capacity of Reinforced Steel Tubular Scaffold under Uniform Loads

Five groups of tests were designed to analyze the influence of node types (fastener connection and mortise‐and‐tenon joint) and reinforcement modes of top horizontal cross rods (weak truss and stiffening truss) on the bearing capacity of the steel tubular scaffold under vertical uniform loads. Loading phenomenon, bearing capacity, failure mode, displacement at key positions, and strain development characteristics during tests were analyzed. The following conclusions were drawn: (1) The fastener scaffold reinforced by a top truss showed the highest bearing capacity and high material utilization. (2) The fastener scaffold reinforced by a top weak truss increased the bearing capacity and caused coordinated deformation of the top horizontal force rods. (3) The node displacement of the mortise‐and‐tenon scaffold was smaller than that of the fastener joint, whereas its bearing capacity was higher. (4) Vertical diagonal bracing can slightly increase the bearing capacity of the mortise‐and‐tenon scaffold but can also constrain the deformation of the vertical rods and change the failure mode.

Motion Planning for an Elastic Rod Using Contacts

The contribution of this article is to propose an approach that solves the motion planning problem for an extensible elastic rod using contacts with the environment. We first show how motion planning for a deformable rod can be done by coupling both quasi-static and dynamic rod models with sampling-based methods. Sampling directly in the submanifold of static equilibrium and contact-free configurations allows to take advantage of the dynamic model to improve the exploration of the state space. Then, thanks to the contact information (point, forces, direction, and the number of contacts), the exploration of the rapidly exploring random tree (RRT) approach can be improved. We present a new RRT-SLIDE algorithm, which guides the roadmap extension with a sliding contact mode based on some principles of human reasoning. We show that our approach is probabilistically complete. We also demonstrate the necessity of considering contacts on complex scenarios with several simulation experiments. Besides its performances, our algorithm does not require further tuning phase for a new scenario. Note to Practitioners —This article was done under the industrial project Flecto. It aims at solving the assembly/disassembly task for a rod while satisfying the elasticity parameters of its material in a digital mockup. For industrial applications, the resolution time is a critical point. On the one hand, probabilistic motion planning methods require to efficiently build a roadmap of valid rod configurations. On the other hand, accurate rod modeling implies the use of a simulator based on the finite-element method (FEM). Nevertheless, the very large size of the roadmap that leads to a high number of calls to the simulator is conflicting with the high computational cost of FEM simulation. To overcome this problem, one solution is to reduce the number of simulator calls. This can be achieved by sampling the free space with an efficient parameterization and by limiting the use of the simulator to roadmap extension in the free space or in the contact space. We introduce heuristics based on contact information returned by the simulator to significantly reduce the computational time. One of the main advantages of our algorithm is that it does not require any tuning phase for each scenario. Although we do not solve the more general gripper manipulation planning problem, this approach could be used as a first step before computing the grippers’ motion. In the framework of our project, we did not consider disassembling operations implying undoing rod knots. Consequently, we do not consider friction in our approach (friction simulation is necessary to handle knots).