Non-constant Cross-section Research Articles

Flexures for Kibble balances: minimizing the effects of anelastic relaxation

We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e. bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields 1.2×10−4 . This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure’s internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.

Kinetostatics-based stiffness analysis of continuum manipulators considering non-constant cross sections

Continuum manipulators are widely used for their compliant and dexterous nature, but their design and modeling are simplified by keeping the cross-section constant. Inspired by biological structures like elephant trunks and octopus tentacles, previous studies have proposed continuum manipulators featuring non-constant cross sections, but few of them study how the cross sections affect the manipulator’s properties, such as stiffness. In this paper, a general kinetostatic model and a stiffness model are presented for continuum manipulators with non-constant cross sections and experimental validations are conducted under various actuating and loading conditions. Moreover, comparative stiffness analysis is performed among manipulator designs with different non-constant cross sections. The results indicate a significant impact of cross-section-varying rates on the system stiffness along different directions. This approach and analysis are significant for the structure design and stiffness optimization of continuum manipulators, particularly in applications where stiffness is a primary objective.

Linear Source Approximation in MPACT for Efficient and Robust Multiphysics Whole-Core Simulations

This work seeks to improve upon an existing formulation of the Method of Characteristics (MOC) with a Linear Source Approximation (LSA) for problems that use nonconstant cross sections like multiphysics feedback and the two-dimensional/one-dimensional (2D/1D) formulation. The previous LSA formulation for lattice physics calculations uses precomputed coefficients that are dependent on the multigroup total or transport cross sections, and the method can be demonstrated to lack robustness when there are negative sources. In this paper, the method is reformulated to eliminate the cross-section dependence of the precomputed coefficients without adding additional operations, and a more robust formulation is also developed to prevent the calculation of negative sources. Thus, the method has increased efficiency and robustness in multiphysics and 2D/1D simulations. The new method is implemented in the MPACT code and tested on several light water reactor problems. The numerical results show that with the new Linear Source formulation, the number of mesh elements can be significantly reduced while maintaining accuracy, resulting in reduced run time and memory usage. Furthermore, our results demonstrate improved efficiency for cases with depletion, thermal-hydraulic feedback, and in three-dimensional (2D/1D) calculations without any robustness issues.

A novel approach to reduce fan rotor blades stress in case of resonance due to inlet flow distortion by means of piezoelectric actuators

Resonant vibration condition involves a drop in the life-cycle of the components and is one of the main causes of high cycle fatigue failure (HCF) in turbomachinery blades. As a consequence vibration damping techniques play a key role for turbomachinery designers. Even though resonant vibration conditions can be identified by means of the Singh’s Advanced Frequency Evaluation (SAFE) diagram at the design level, not all resonant conditions can be avoided. Among these methods, systems of piezoelectric (PZT) actuators can be tuned to actively damp the vibrations caused by resonant excitations. In this work, an analytical model was developed to identify the optimal voltage distribution that maximises the reduction in blade stress. The model considers the flexural–torsional–extensional deformations coupling due to the pre-twisting, non-constant cross-section and inertial loads of the rotating blades. A typical case was examined to demonstrate the effectiveness of the proposed method, which involved vibration induced by inlet flow distortion in an axial fan stage coupled with a three-strut front frame. A decoupled approach based on Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) simulations was used to evaluate the aerodynamic loads and to numerically validate the optimal voltage distribution on the PZT actuator pairs. The results show that the proposed method alleviates the effects of the resonant response to an inlet flow distortion on a fan integrally bladed disc (blisk) and the optimal voltage distribution predicted by the model is the one that achieves the highest blade stress mitigation.

LES/DNS fluid-structure interaction simulation of non-linear slender structures in Nektar++ framework

Nektar++ is a spectral/hp element open-source framework written in C++ for the construction of classical low-order h-type as well as higher-order p-type finite element solvers. It seeks to overcome the implementation challenges of the complex data structures associated with high-order finite element methods; hence, providing an efficient, flexible and HPC scalable platform for the development of solvers for partial differential equations using the spectral/hp element method. In the present work, capabilities of Nektar++ is leveraged for development of two fluid-structure interaction (FSI) solvers for simulations of highly deformable nonlinear slender structures. The FSI solver uses the incompressible Navier-Stokes (NS) solvers of Nektar++ for fluid flow while the structural dynamics is modelled using Geometrically-Exact Composite Beams (GECB). The open-source SHARPy framework is linked to Nektar++ and used for structural simulation. Aiming at high-fidelity (LES/DNS) FSI simulations, the thick-strip approach is used to reduce computational costs. In this approach, the full 3D fluid domain is represented with series of smaller 3D domains normal to the local axis of the structure and having a finite thickness in the spanwise direction where periodicity is also assumed. Hence, while reducing the computational costs by avoiding the discretization of equations over the entire slender structure, the strip thickness allows capturing the local 3D turbulent wake and accurately predict the fluid forces on the structure. Two approaches are adopted to avoid the dynamic remeshing due to the large and non-linear deformation of the structure. In the first approach, the transformed the NS equations are solved in the non-inertial body-fitted coordinates while in the second approach the NS equations are formulated in the moving frame of reference and solved with the spectral/hp element method. A hybrid parallelisation approach of Nektar++ is extended for the thick-strip method which allows having non-constant cross-section along the structural span as well as efficient and flexible use of computational resources, and excellent HPC performance for the FSI simulations. The capability of the FSI solver is demonstrated via several examples.

A practical thermoelectric leg for TECs with optimal current improvement

The maximum temperature difference, which is corresponding to the optimal current, is important for evaluating the performance of thermoelectric coolers (TECs). As a representative of the thermoelectric leg with non-constant cross-section, the pyramidal thermoelectric leg has more advantages than the traditional cuboidal thermoelectric leg due to the large temperature gradient. However, the fabrication is much complex. In this work, a new shaped thermoelectric leg for TECs with almost the same property with the pyramidal legs is proposed and a simple practical approach for fabrication by taking one-side cut from the cuboidal leg is presented. Optimal current improvement is demonstrated by the theoretical calculation and the finite element simulation as well as the test results.

Detailed micro-modeling of partially grouted reinforced masonry shear walls: extended validation and parametric study

Partially grouted reinforced masonry (PG-RM) shear walls have been widely used as structural elements in low- and medium-rise earthquake-resistant buildings. Nonetheless, assessing its shear strength represents a complex task mainly because the partial grouting provides a non-constant cross section, which results in heterogeneous stress–strain patterns. Consequently, refined modeling techniques are needed to reproduce local failure mechanisms taking place in these walls, which significantly influence the global response. In response to this issue, a detailed micro-modeling approach based on the finite element method was proposed in previous studies by the authors. Although the numerical strategy provided accurate results, further validation is required. Therefore, in this study, the experimental results of seven PG-RM shear walls of multi-perforated clay bricks with bed-joint reinforcement are employed as validation cases. These seven walls presented variations in five design parameters. The validated numerical model was then employed to perform a parametric study to assess the influence of the wall aspect ratio, axial pre-compression stress, and horizontal reinforcement ratio on the in-plane lateral behavior of PG-RM shear walls. The obtained results show that the three studied design parameters modified the crack patterns of the walls. Besides, increasing the axial pre-compression stress or reducing the aspect ratio resulted in higher walls’ shear strength. Additionally, decreasing the horizontal reinforcement ratio or increasing the aspect ratio generated a higher story-drift ratio at maximum lateral force. Finally, it was corroborated that the positive effect of the axial pre-compression stress on the walls’ shear strength decreases inversely proportional to the aspect ratio.

Simplified micro-modeling of partially-grouted reinforced masonry shear walls with bed-joint reinforcement: Implementation and validation

Partially grouted reinforced masonry (PG-RM) shear walls of hollow concrete blocks (HCB) have been an object of study during the last years. The non-constant cross-section of this type of structural element and the presence of reinforcement set a challenging scenario when assessing their lateral resistance. This scenario makes simple approaches (e.g., design expressions) lacking accuracy. Besides, the most accurate existent analysis methodologies rely on user-defined sub-routines that are not available for commercial use. Therefore, proper analysis methodologies are still a need. In this regard, this research aims at reproducing the behavior of PG-RM shear walls with bed-joint reinforcement with a simple but also accurate approach. In this line, the in-plane behavior of PG-RM shear walls was reproduced by implementing 2D micro-models in a multi-purpose commercial FE code without requiring excessive work, advanced programming skills, and unaffordable hardware. The model approach was validated by reproducing two identical full-scale PG-RM shear walls. Although the model was not able to reproduce cyclic loading as in the tests, the model captured the experimental failure mode and lateral resistance with an acceptable degree of accuracy. Moreover, the distribution of cracks and deformations in horizontal reinforcement elements were appropriately reproduced at the lateral resistance, indicating the most demanded reinforcement portions. Additionally, the proposed modeling approach was compared with two alternative approaches: a 2D model that reproduced tensile failure employing interfaces and a smeared crack model and a 3D model that reproduced tensile failure utilizing a smeared crack model. The benchmark results pointed out the advantages of the reference model over the alternative modeling approaches. The first alternative model reproduced an excessive displacement capacity, and the second alternative model simulated an inaccurate crack pattern and was associated with a heavy computational burden.

Modal Velocity-Based Multiaxial Fatigue Damage Evaluation Using Simplified Finite Element Models

Abstract This work proposes a new method for the fatigue damage evaluation of vibrational loads, based on preceding investigations on the relationship between stresses and modal velocities. As a first step, the influence of the geometry on the particular relationship is studied. Therefore, an analytic expression for Euler Bernoulli beams with a non-constant cross section is derived. Afterward, a general method for obtaining geometric factors from finite element (FE) models is proposed. In order to ensure a fast fatigue damage evaluation, strongly simplified FE-models are used for the determination of both factors and measurement locations. The entire method is demonstrated on three mechanical structures and indicates a better compromise between effort and accuracy than existing methods. For all examples, the usage of velocities and geometric factors obtained from simplified FE models enables a sufficient fatigue damage calculation.

Comprehensive modeling for optimized design of a thermoelectric cooler with non-constant cross-section: Theoretical considerations

With the popularization of electric vehicles, a thermoelectric cooler can be a promising battery thermal-management device that achieves the heat dissipation and uniform heating of a battery pack to improve its performance. In this study, a three-dimensional numerical model was established in order to qualitatively and quantitatively analyze the factors affecting the cooling performance for a thermoelectric cooler with a non-constant cross-section via the finite element method, and a one-dimensional mathematical model was constructed in order to explain the working mechanism of the influencing factors. The optimization included the geometric structure, temperature difference, leg geometry, and contact layers. The results show that compared with a thermoelectric cooler with a constant cross-section, the cooling capacity and the coefficient of performance of an optimized thermoelectric cooler with a non-constant cross-section were improved by 35.73% and 21.59%, respectively. Compared with the thermoelectric cooler with a non-constant cross-section before optimization, the cooling capacity and the coefficient of performance after optimization increased by 20.98% and 20.52%, respectively.

Polynomial relations for cylindrical wheel stiffness characterization for use in a rolling noise prediction model

In vehicle tire/road contact modeling, dynamic models are typically used which incorporate the vehicle’s suspension in their estimation: thus relying on a known stiffness to determine the movement of the wheel in response to roughness excitation. For the case of a wheeled device rolling on a floor (such as a delivery trolley moving merchandise around inside a commercial building), there is often no suspension, yet the wheel is still too soft to able to be considered mechanically rigid (as is the case in train/rail contact). A model which is aimed at incorporating the dynamic effects of the trolley in predicting the sound generated by rolling needs to provide a robust way of estimating the wheel’s effective stiffness. This work presents an original technique for estimating the stiffness of a solid cylindrical wheel. A parametric study was conducted in order to identify the dependence of the wheel stiffness on each of the relevant variables: including the wheel’s radius, axle size, width, applied load, and material properties. The methodology may be used to estimate the stiffness of new wheel types (i.e. different geometries and materials) without needing to solve a finite element model each time. Such a methodology has application beyond the field of acoustics, as the characterization of shapes with non-constant cross sections may be useful in the wider field of materials science.

Series solution of beams with variable cross-section

In structural engineering beams with non-constant cross-section or beams with variable cross-section represent a class of slender bodies, aim of practitioners’ interest due to the possibility of optimizing their geometry with respect to specific needs. Despite the advantages that engineers can obtain from their applications, non-trivial difficulties occurring in the non-prismatic beam modeling often lead to inaccurate predictions that vanish the gain of the optimization process. As a consequence, an effective non-prismatic beam modeling still represents a branch of the structural engineering of interest for the community, especially for advanced design applications in large spans elements.A straight beam of length l with variable inertia J(z) is provided in figure, subject to a generic live load condition q(z). The vertical displacement y(z) can be obtained from the solution of the differential equation of the elastic line, i.e., taking into consideration the inertia variability and neglecting, as first approximation, any shear contribution. Even if this solution is an approximate one, it is able to deal with the problem in its basic formulation.In this paper a solution for the problem stated is formulated using a series expansion of solutions, in a general load and cross section variability condition. Solution is thus obtained for a generic rectangular cross section beam with a variable height. Analytical solution is presented and evaluated using numerical evaluation of some cases of practical interest.

Design and Experimental Assessment of Variable-Geometry Dies for Polymer Extrusion

This paper presents a design methodology and experimental assessment of variable-geometry dies that enable the extrusion of plastic parts with a nonconstant cross section. These shape-changing dies can produce complex plastic components at higher manufacturing speeds and with lower tooling costs than injection molding. Planar, rigid-body, shape-changing mechanism synthesis techniques are used to create the links that comprise the variable-geometry die exit orifice. Mechanical design guidelines for production-worthy dies are proposed. Several dies were designed and constructed to provide significant changes in the cross-sectional shape and area of extruded parts. Experiments were conducted in a production environment. An analysis of the repeatability of the cross-sectional profiles along the length of the part is presented.

Enhanced performance thermoelectric module having asymmetrical legs

Key concepts like waste heat recycling or waste heat recovery are the basic ideas in thermoelectricity so as to the design the newest solid state sources of energy for a stable supply of electricity and environmental protection. According to several theoretical predictions; at device level, the geometry and configuration of the thermoelectric legs are crucial in the thermoelectric performance of the thermoelectric modules. Unlike to conventional geometry thermoelectric legs, asymmetrical (pyramidal) legs could help by lowering the overall thermal conductance of the device so as to increase the temperature gradient in the legs, as well as by harnessing the Thomson effect, which is generally neglected in conventional symmetrical (rectangular) thermoelectric legs. Curiously, experimental studies confirming the previous predictions have not been carried out so far, perhaps because of the existing constraints to fabricate thermoelectric legs with complex geometrical shapes. In this work, based on the promising enhancement of the thermoelectric performance in thermoelectric modules via legs with non-constant cross sections, it has been developed a novel design of a thermoelectric module having asymmetrical legs with truncated square pyramid shape, and by first time it has been validated experimentally its thermoelectric performance by realizing a proof-of concept device which shows to have almost twofold the thermoelectric figure of merit as compared to conventional one with a constant square cross section. Besides, the variables required to engineer enhanced performance thermoelectric devices are properly identified for use as power sources especially in low consumption portable devices. Therefore, the present results prove that geometrical configuration of the device legs can improve significantly the thermoelectric performance of the device.

The onset of recirculation flow in periodic capillaries: Geometric effects

In this paper we examine the onset of flow circulation in expansion regions of infinite tubes of periodic, non-constant cross-section. Three types of axisymmetric capillary shapes were considered; sinusoidal, parabolic and triangular. A full boundary element method (BEM) solution of Stokes’ equations was formulated for the specific case of an infinite periodic tube. Geometric parameters were varied to establish conditions for the onset of recirculation. Recirculation flow is first predicted to appear beyond a critical amplitude, for all types of tubes studied, with zones in tubes of triangular sections appearing at a lower amplitude. Second order recirculation zones were predicted for still higher amplitudes, in all the capillaries. A numerical study was undertaken to characterise the onset of first and second order recirculation flows in terms of geometric factors.

Numerical Simulation of Composite Hemp Fibers Behavior for Aircraft Application

Hemp fibres are using as reinforcement for compounds based on polymer in different industrial manufacturing (aerospace and automotive) for their interesting mechanical and ecological properties. The hemp fibres present a non-constant cross section and complex geometry that can have a high effect on their mechanical properties. In this study, a micro-traction test coupled with a numerical imaging treatment and a finite elements method are used. The mechanical tensile test allows to determinate the evolution of the traction load in function of the displacement until the fibre crack. The used fiber are incorporate in plastic material is order to obtained PP/hemp reinforcement composite part. Static and dynamic tests are proposed in order to study trhe behaviour of green material subjected to tensile load.

Nominal power density analysis of thermoelectric pins with non-constant cross sections

The investigation of the geometric structure of TEG (thermoelectric generator) pins is essential, as their geometry determines the performance of devices. In this study, nominal power density (NPD) is used to find a better geometric structure of thermoelectric pins of TEGs, since a comparison of maximum dimensionless efficiencies for different geometric pins cannot be used to identify the optimum geometry. The influence of shape parameter on NPD for TEG pins in linear, quadratic and exponential cross-sectional functions is studied. The NPD decreases when the shape parameter increases for different geometric pins, while the maximum values of NPD are the same. Then, the effects of dimensionless efficiency and the temperature ratio on the NPD are analyzed. The NPD decreases with the increase in dimensionless efficiency and temperature ratio. Pins with linear variation in cross section have the highest NPD among the three geometries of pins evaluated.

Characteristic Analysis of Carburized Quenching Processes for Bevel Gear of Automobile Driving Part

The mechanical properties of automobile bevel gears manufactured by carburized guenching process are evaluated by using a finite elements method. The gear teeth of super, helical, and warm gears typically have constant cross sections and the same module, which results in the same frictional wear and stress. Bevel gears, however, are of a cone shape and thus the cross section of gear tooth change in the axial direction. As a result, the hardness after heat treatment depends on the axial location of the gear tooth. Hardness distribution due to the non-constant cross section causes gear abrasion or damage. It is difficult, however, to measure the hardness in threedimensional way through experiments. Hence, this study attempts to simulate the carburized quenching process through a numerical analysis in order to interpret the three-dimensional heat-treatment effects. The analytical results include variations of each structure, hardness, temperature over various sections depending on the cooling rate. To verify this approach, the gear used in the experiment was designed based on the same condition of the analytical model. The Carburized Quenching was carried out and the characteristics of carbon penetration, micro-structure and surface hardness were investigated by means of SEM and EPS. The theoretical results were compared with experimental results to verify the analytical method for Carburized Quenching. Keywords: Automobile, carburized quenching, finite element analysis, gear, heat treatment.

Geometry optimization in buckling of a shape memory alloy column due to constrained recovery

Constrained recovery of a compressively prestrained shape memory alloy (SMA) is experimentally and theoretically investigated. Thermomechanical properties of the SMA during the process of constrained recovery are experimentally obtained. Optimization of geometry in buckling of an ideally straight, simply supported column with a nonconstant cross section due to constrained recovery is theoretically investigated. Using the experimentally obtained thermomechanical properties, the critical buckling force and temperature of the optimized column are calculated. Various experiments were conducted in order to verify the calculated results. The calculated critical load and predicted buckling temperatures show good agreement with buckling experiments reported in this article.

A Model for Rapid Tin Whisker Growth on the Surface of ErSn3 Phase

Spontaneous growth of tin whiskers on the finish of leadframes is an extremely slow process under moderate temperature conditions. It therefore becomes difficult to track the continuous growth of tin whiskers and to vary the experimental conditions to determine their root causes. Accordingly, the fundamental growth behaviors of tin whiskers are still not fully understood. In this study, rapid tin whisker growth was achieved by adding 1 wt.% Er to Sn-3.8Ag-0.7Cu solder alloy. The results showed unique tin whisker morphology with nonconstant cross-section. An explanation is proposed by adding kinetic energy to the conventional energy balance equation. In addition, a double compressive stress zone is proposed to demonstrate the driving force for tin whisker growth in rare-earth-bearing phases.