Calculation Of Mechanical Stresses Research Articles

Hierarchical rank-one sequence convexification for the relaxation of variational problems with microstructures

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative information essential for the calculation of mechanical stresses and the computational minimisation of discretised energies. For materials, whose microstructure can be well approximated in terms of laminates and where each laminate stage achieves energetic optimality with respect to the current stage, the approximate envelope coincides with the rank-one convex envelope. Although the proposed method provides only an upper bound for the rank-one convex hull, a careful examination of the resulting constraints shows a decent applicability in mechanical problems. Various aspects of the algorithm are discussed, including the restoration of rotational invariance, microstructure reconstruction, comparisons with other semi-convexification algorithms, and mesh independency. Overall, this paper demonstrates the efficiency of the algorithm for both, well-established mathematical benchmark problems as well as nonconvex isotropic finite-strain continuum damage models in two and three dimensions. Thereby, for the first time, a feasible concurrent numerical relaxation is established for an incremental, dissipative large-strain model with relevant applications in engineering problems.

The Influence of Mechanical Deformation Consideration on the Results of the Calculation of the Vacuum Circuit Breaker Drive Shaft

One of the important directions of theoretical, computational and experimental research related to the improvement and development of new design elements of modern electrical devices, primarily medium voltage circuit breakers and contactors, is the study of not only electromagnetic, but also mechanical processes in these electrical devices. The paper is devoted to the creation and use of computational models for calculating mechanical forces and deformations of an absolutely rigid and real drive shaft of a medium voltage vacuum circuit breaker in static mode with the aim of quantitative comparison of the obtained numerical results. Calculation studies are performed using the finite element method. A comparative analysis of the calculation of mechanical stresses in the drive shaft of a vacuum circuit breaker in a static mode for an absolutely rigid and real shafts is carried out in this paper on the basis of the developed models. The obtained results of computer modeling are given in detail in tabular and graphic forms, including the shape of the deflection of the medium voltage vacuum circuit breaker shaft at the maximum stroke of the actuator of the electrical device under study. It has been demonstrated that the mechanical deformation of the shaft causes a decrease in contact drop and contact pressure forces, but with a correctly selected cross-section, these values are not critical and have little effect on the circuit breaker operation (about 20% and 7%, respectively). It is shown that as a result of shaft bending, additional axial forces appear in the supports, which significantly affect the choice of bearings according to the equivalent static load.

Investigation of a Radial Turbine Design for a Utility-Scale Supercritical CO2 Power Cycle

This paper presents the design procedure and analysis of a radial turbine design for a mid-scale supercritical CO 2 power cycle. Firstly, thermodynamic analysis of a mid-range utility-scale cycle, similar to that proposed by NET Power, is established while lowering the turbine inlet temperature to 900 ∘ C in order to remove cooling complexities within the radial turbine passages. The cycle conditions are then considered for the design of a 100 MW t h power scale turbine by using lower and higher fidelity methods. A 510 mm diameter radial turbine, running at 21,409 rpm, capable of operating within a 5% range of the required cycle conditions, is designed and presented. Results from computational fluid dynamics simulations indicate the loss mechanisms responsible for the low-end value of the turbine total-to-total efficiency which is 69.87%. Those include shock losses at stator outlet, incidence losses at rotor inlet, and various mixing zones within the passage. Mechanical stress calculations show that the current blade design flow path of the rotor experiences tolerable stress values, however a more detailed re-visitation of disc design is necessitated to ensure an adequate safety margin for given materials. A discussion of the enabling technologies needed for the adoption of a mid-size radial turbine is given based on current advancements in seals, bearings, and materials for supercritical CO 2 cycles.

Peculiarities of Designing of Suspensions for Stators of High Power Turbogenerators

The analysis of existing designs of the stator fastening of Turbogenerators of various design versions is carried out. It is shown that the application of a spring suspension is the integral part of the design of Turbogenerators rated 100 MW and higher. The detailed calculation of the complex stressed state of the stators suspension of Turbogenerators manufactured at SE "PLANT "ELECTROTYAZHMASH" rated 200 MW and 250 MW with hydrogen and hydrogen-water cooling is submitted in the scientific work, taking into account the uneven thermal distribution along the horizontal axis of the aggregate for some number of electrical-sheet steels. The various types of the stator deformation caused by a number of forces are considered. It is proposed to carry out the calculation of mechanical stresses by iterative execution of mechanical and thermal calculations coordinated with electrical stresses. As limiting conditions for taking in to account of forces caused by temperature changes, the limiting conditions of the first kind were considered. At that, in the mechanical calculation, it is necessary to take into account the design peculiarities for each row of springs, taking into consideration the correction for temperature. The key factor is the difference between the calculated vibrations for a stand separately core and its installation in to the casing with suspension, depending up on the modulus of elasticity of the stacked up laminated core for electrical-sheet steels 3413, 3414 GOST21427.1-83, M270-50A. The possibility of changing of steel 38Х2Н2ВА to steel 34CrNiMo6 and steel 40NiCrMo7 is shown, provided that the GOST8479-70 complies with the same strength group.

Mechanical Calculation of Flexible Wires of Overhead Lines with Barrage Balls

Aerial barrage balls serve for marking high-voltage wires in order to visually warn pilots of civil and military aviation about the presence of overhead lines. The present article deals with the mechanical calculation of flexible overhead wires of overhead lines, in which aerial warning barrage balls are installed. The wire is considered as a homogeneous flexible thread having the outline of a parabola and a chain line. The load from the aerial barrage balls must not be substituted with a distributed one by simple division of the total load into the span length, since it can cause incorrect results. The formulas for determining the sag are given for a different number of aerial barrage balls as a function of their number and the coefficient of concentrated forces. The acceptable accuracy of mechanical calculation is demonstrated when using the model of wire in the form of a parabola adopted in the design practice, provided that the components of concentrated forces are correctly determined. The equation of state is recorded, taking into account the weight and wind loads on the wire, as well as load coefficients in two planes, depending on the number of barrage balls. The performed calculations demonstrate an acceptable accuracy of the determination of the stress at various loadings of the span. For more accurate calculation of mechanical stresses and sag arrows, a vector-parametric method for calculating the flexible wires of overhead lines is suggested, where the calculated model of wires in the form of a flexible elastic thread is put taking into account of the spatial arrangement of all structural elements. The results of mechanical calculation according to the program that had been developed and to the existing methods for a different number of aerial barrier balls moved along the span are presented.

Dynamic stresses in a Francis model turbine at deep part load

A comparison between numerically obtained dynamic stresses in a Francis model turbine at deep part load with experimental ones is presented. Due to the change in the electrical power mix to more content of new renewable energy sources, Francis turbines are forced to operate at deep part load in order to compensate stochastic nature of wind and solar power and to ensure grid stability. For the extension of the operating range towards deep part load improved understanding of the harsh flow conditions and their impact on material fatigue of hydraulic components is required in order to ensure long life time of the power unit.In this paper pressure loads on a model turbine runner from unsteady two-phase computational fluid dynamics simulation at deep part load are used for calculation of mechanical stresses by finite element analysis. Therewith, stress distribution over time is determined. Since only few runner rotations are simulated due to enormous numerical cost, more effort has to be spent to evaluation procedure in order to obtain objective results.By comparing the numerical results with measured strains accuracy of the whole simulation procedure is verified.

Mechanical Stress Reduction of Rotor Core of Interior Permanent Magnet Synchronous Motor

In this paper, the bridge shape of interior permanent magnet synchronous motor (IPMSM) is designed for integrated starter and generator (ISG) which is applied in hybrid electric vehicle (HEV). Mechanical stress of rotor core which is caused by centrifugal force is the main issue when IPMSM is operated at high speed. The bridge is thin area in rotor core where is mechanically weak point and the shape of bridge significantly affects leakage flux and electromagnetic performance. Therefore, bridge should be designed considering both mechanic and electromagnetic characteristics. In the design process, we firstly find a shape of bridge has low leakage flux and mechanical stress. Next, the calculation of mechanical stress and the electromagnetic characteristics are performed by finite element analysis (FEA). The mechanical stress in rotor core is not maximized in steady high speed but dynamical high momentum. Therefore, transient FEA is necessary to consider the dynamic speed changing in real speed profile for durability experiment. Before the verification test, fatigue characteristic is investigated by using S-N curve of rotor core material. Lastly, the burst test of rotor is performed and the deformation of rotor core is compared between prototype and designed model to verify the design method.

Mechanische Zuverlässigkeit von keramischen Kaltleiterbauelementen – Möglichkeiten zur Verbesserung

Abstract In service, PTC-components have to withstand large temperature changes, which result from their electric working conditions. These temperature changes cause large temperature differences due to heat transport and inhomogeneously distributed heat sources. As a result, thermo-mechanical stresses occur, which my cause the failing of the component. A physical model is presented which makes the calculation of mechanical stresses in PTC components in dependence on the electrical loading possible, if the relevant material parameters are known. The interaction between the electric field equations and the equation of the thermal diffusion is taken into account, and the electric and the temperature field in dependence of the position in the PTC is calculated. Then the mechanical stress field and the failure rate is determined. This model is then used to reduce temperature differences (thermal management) and – in consequence – mechanical stresses in PTC components by selection of more suitable PTC material...

Development of an in vivo method for determining material properties of passive myocardium

Calculation of mechanical stresses and strains in the left ventricular (LV) myocardium by the finite element (FE) method relies on adequate knowledge of the material properties of myocardial tissue. In this paper, we present a model-based estimation procedure to characterize the stress-strain relationship in passive LV myocardium. A 3D FE model of the LV myocardium was used, which included morphological fiber and sheet structure and a nonlinear orthotropic constitutive law with different stiffness in the fiber, sheet, and sheet-normal directions. The estimation method was based on measured wall strains. We analyzed the method's ability to estimate the material parameters by generating a set of synthetic strain data by simulating the LV inflation phase with known material parameters. In this way we were able to verify the correctness of the solution and to analyze the effects of measurement and model error on the solution accuracy and stability. A sensitivity analysis was performed to investigate the observability of the material parameters and to determine which parameters to estimate. The results showed a high degree of coupling between the parameters governing the stiffness in each direction. Thus, only one parameter in each of the three directions was estimated. For the tested magnitudes of added noise and introduced model errors, the resulting estimated stress-strain characteristics in the fiber and sheet directions converged with good accuracy to the known relationship. The sheet-normal stress-strain relationship had a higher degree of uncertainty as more noise was added and model error was introduced.

Development of an in vivo method for determining material properties of passive myocardium

Calculation of mechanical stresses and strains in the left ventricular (LV) myocardium by the finite element (FE) method relies on adequate knowledge of the material properties of myocardial tissue. In this paper, we present a model-based estimation procedure to characterize the stress–strain relationship in passive LV myocardium. A 3D FE model of the LV myocardium was used, which included morphological fiber and sheet structure and a nonlinear orthotropic constitutive law with different stiffness in the fiber, sheet, and sheet-normal directions. The estimation method was based on measured wall strains. We analyzed the method's ability to estimate the material parameters by generating a set of synthetic strain data by simulating the LV inflation phase with known material parameters. In this way we were able to verify the correctness of the solution and to analyze the effects of measurement and model error on the solution accuracy and stability. A sensitivity analysis was performed to investigate the observability of the material parameters and to determine which parameters to estimate. The results showed a high degree of coupling between the parameters governing the stiffness in each direction. Thus, only one parameter in each of the three directions was estimated. For the tested magnitudes of added noise and introduced model errors, the resulting estimated stress–strain characteristics in the fiber and sheet directions converged with good accuracy to the known relationship. The sheet-normal stress–strain relationship had a higher degree of uncertainty as more noise was added and model error was introduced.

Evaluating Calculation of Mechanical Stresses due to Metal in Absorption of a Laser Pulse

The results of evaluating calculation of mechanical stresses generated in a metal target heated by a several tens nanosecond laser pulse are given. The thermoelastic, hydrodynamic, and evaporating mechanisms of the stress generation are considered.

The effect of droplet sprinkling on the oxidation kinetics of zirconium cladding in steam

The influence of oxide layer cracking on the acceleration of Zr cladding oxidation in steam was investigated. Cracking occurs due to temperature gradients, which arise during cooling of the cladding surface by droplet jets. Experimental results on characteristics of heat removal and the temperature gradients induced are presented for different regimes of sprinkling. A model for the calculation of mechanical stresses under the experimental conditions was developed in frame of the theory of envelopes. It was shown that the stresses are sufficiently high to induce cracking of the outer oxide layer. Experimental investigations of oxidation kinetics of Zr-1%Nb cladding were carried out under the conditions of surface cooling by droplet jets. The results of these experiments confirmed that the reaction of oxidation can be strongly accelerated by sprinkling.

Rotor Torque Distribution in Electrical Machines via Maxwell's Stresses

The calculation of mechanical stresses at the rotor surface is shown to be a simple procedure for the common types of electrical machine in which armature current can be represented as a rotor surface current sheet. Use of this technique can lead to a better appreciation of the mechanics of torque production in electromagnetic machines than alternative energy methods.

Magnetostatic Design of 85KG Superconducting Dipoles

Extension of the present Tevatron dipole to 85kG has been considered by Wilson.1 An accelerator utilizing such dipoles has been designated as the Pentevac since it would permit 5 TeV protons to circulate within the boundaries of the Fermilab site. The present note contains results of magnetic field, force, and mechanical stress calculations for one possible Pentevac dipole.

Maximum attainable toroidal magnetic fields for tokamaks

A calculation method of determining the maximum permissible magnetic field values for superconducting toroidal magnet systems in tokamak reactors is described. Simple scalings for the maximum magnetic field values B max are found. The results of mechanical stress calculations by the element method are introduced into the formulas for calculating B max , yielding considerable changes compared to the B max values calculated without the finite element correction.

Experimental determination of short-circuit currents in electric power networks

No means has yet been discovered whereby the abnormal rise of current occurring during short circuits is avoided. Protection against its destructive effects remains, therefore, a subject of major importance. Among the problems requiring short-circuit current determinations, the following are the chief ones: (1) Selection of oil circuit breakers of the required interrupting capacity. (2). Determination of the size of current-limiting reactors. (3) Determination of relay settings in relay systems depending on selective action from over-current and directional relays. (4) Calculation of mechanical stresses in the structural elements of apparatus subject to short-circuit electromagnetic forces. Each of these problems requires the knowledge of the magnitude of short-circuit currents; relay problems frequently require, in addition, the relative phases of currents and voltages at different points of the system during short circuits; in item (4) above the wave-form of the short-circuit current sometimes has to be considered. The available information on the latter subjects, i. e. on phase relations and on wave form during short circuits is relatively meager, probably because it has been required in special cases only. Nevertheless, the demands for these data are increasing — on account of both the tendency towards increased sensitiveness of protective devices and the rapid increase in the magnitude of the short-circuit currents to be handled — and it will be worth while, therefore, if this added information is obtained. This paper is confined to the problems of the determination of the magnitude of short-circuit currents. The magnitude of short-circuit currents depends on a multiplicity of factors which have been enumerated and dealt with in other publications. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> When the impedances of all the circuit elements affected by the short-circuit are known together with the current-time decrement characteristics of all machinery capable of supplying current to the short circuit, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> the problem of short-circuit-current determination resolves itself into one of current division in a given network of electrical conductors under given electromotive forces. In the following paper, the comparative merits of three methods — calculation, a-c. test, and d-c. test — of determining short-circuit currents in networks are briefly discussed. Two d-c. experimental methods applicable to the “short-circuit calculating table” are analyzed in detail. The accuracy of its results, by both methods, is obtained for a variety of circuit conditions. The proper field of use of the short-circuit calculating table, and the best method of its application are determined.

Experimental Determination of Short-Circuit Currents in Electric Power Networks

No means has yet been discovered whereby the abnormal rise of current occurring during short circuits is avoided. Protection against its destructive effects remains, therefore, a subject of major importance. Among the problems requiring short-circuit current determinations, the following are the chief ones: (1) Selection of oil circuit breakers of the required interrupting capacity. (2). Determination of the size of current-limiting reactors. (3) Determination of relay settings in relay systems depending on selective action from over-current and directional relays. (4) Calculation of mechanical stresses in the structural elements of apparatus subject to short-circuit electromagnetic forces. Each of these problems requires the knowledge of the magnitude of short-circuit currents; relay problems frequently require, in addition, the relative phases of currents and voltages at different points of the system during short circuits; in item (4) above the wave-form of the short-circuit current sometimes has to be considered. The available information on the latter subjects, i. e. on phase relations and on wave form during short circuits is relatively meager, probably because it has been required in special cases only. Nevertheless, the demands for these data are increasing — on account of both the tendency towards increased sensitiveness of protective devices and the rapid increase in the magnitude of the short-circuit currents to be handled — and it will be worth while, therefore, if this added information is obtained. This paper is confined to the problems of the determination of the magnitude of short-circuit currents. The magnitude of short-circuit currents depends on a multiplicity of factors which have been enumerated and dealt with in other publications.1 When the impedances of all the circuit elements affected by the short-circuit are known together with the current-time decrement characteristics of all machinery capable of supplying current to the short circuit,2 the problem of short-circuit-current determination resolves itself into one of current division in a given network of electrical conductors under given electromotive forces. In the following paper, the comparative merits of three methods — calculation, a-c. test, and d-c. test — of determining short-circuit currents in networks are briefly discussed. Two d-c. experimental methods applicable to the “short-circuit calculating table” are analyzed in detail. The accuracy of its results, by both methods, is obtained for a variety of circuit conditions. The proper field of use of the short-circuit calculating table, and the best method of its application are determined.