Central Bending Research Articles

АНАЛІЗ ВПЛИВУ КУТА СТРІЛОПОДІБНОСТІ НА ХАРАКТЕРИСТИКИ СТАТИЧНОЇ АЕРОПРУЖНОСТІ КРИЛА НАВЧАЛЬНО-ТРЕНУВАЛЬНОГО ЛІТАКА

The article is dedicated to the analysis of static aeroelastic phenomena in the wing of a trainer aircraft and the general influence of wing sweep on critical speeds. Aeroelasticity studies the interaction between aerodynamic and elastic forces and the impact of this interaction on the aircraft's structure. There are two types of aeroelasticity: static and dynamic. The article reviews and analyzes publications related to this issue. The analysis of the research shows that when designing an aircraft, it is necessary to determine the aeroelastic characteristics of its aerodynamic surfaces. In addition to structural rigidity, the sweep angle also influences these phenomena. The scientific novelty of the study lies in the fact that, unlike the analyzed research, the designed wing structure of a trainer aircraft is considered.For the designed trainer aircraft, the critical speeds of static aeroelastic phenomena were determined. The calculation of the influence of the wing sweep angle on the divergence speeds of the trainer aircraft confirms previously obtained results regarding this influence. When the sweep is increased or decreased for wings with the same span, the torsional rigidity of the wing decreases due to the increase in the length of the line of centers of rigidity. However, the most significant impact on the aeroelastic characteristics is made by the shift of the bending center when the sweep angle changes.With forward sweep, the arm of the aerodynamic forces relative to the bending center increases, thereby reducing the critical divergence speeds. For straight sweep, as the sweep increases, the bending center moves forward, and at a certain point, the bending center is located in front of the aerodynamic center. This means that the wing twist angle decreases as the aerodynamic force increases, which, in the considered planar case, eliminates the occurrence of divergence.The preliminarily determined maximum flight speed does not exceed the critical speeds of divergence and aileron reversal. This result represents the practical value of the study. To achieve higher flight speeds, wings with straight sweep should be used. More precise computational or experimental methods for determining aeroelastic characteristics should be used in the subsequent design stages to prevent aeroelastic phenomena across the entire operational range of speeds and altitudes of the trainer aircraft.

Discretization of Thin-Walled Sections with Variable Wall Thickness

At the stage of designing thin-walled aircraft structures, to simplify calculations, their cross sections are idealized. To do this, the section with the skin and the longitudinal elements reinforcing it is replaced (when determining normal stresses) by a discrete one, consisting of concentrated areas at characteristic points. In this case, the equality of the moments of inertia of the initial and discrete sections is preserved. Such idealization is used in the calculation of thin-walled rods for normal and shear stresses (Wagner model). For sections consisting of a system of rectangular strips of constant thickness, discretization allows to set approximate values of normal and shear stresses and accurately find the locations of the singular points of the bending center (in an open contour) and the center of rigidity (in a closed one). The discrete model of a strip consists of three lumped areas: two at the edges and one in the center. The paper proposes to extend the discrete model to sections in which the skin thickness changes according to a linear law. In addition to the rectangular strip, it is possible to use elongated triangles and trapezoids, replaced by three and four concentrated areas, respectively. The possibility of using a discrete model for calculating some thin-walled sections of open and closed contours is considered. The section of an open contour is studied - the problem of transverse bending without torsion of a channel having flanges with a linearly variable thickness. Differences in the flows of tangential forces calculated from the exact and discrete models are shown. The coincidence of the results in determining the position of the bending center according to two models was established. When studying the application of a discrete model to a closed contour, its simplified option is proposed. The problem of transverse bending without torsion and finding the center of rigidity in a section with a contour line in the form of a trapezoid with front and rear walls of constant thickness and upper and lower skins and a similar section with a contour in the form of a rectangle was considered. Differences in the flows of tangential forces calculated by exact and discrete models are established. For a closed section in the form of a rectangle, the decrease in the moment of inertia for torsion due to the redistribution of material in the cross section was studied separately. It has been established that when finding the position of the center of rigidity, the discrepancy between the results of the exact and discrete models in sections with geometric parameters close to real ones was less than 1% for a rectangular contour, and 4% for a trapezoidal contour. The results indicate the possibility of extending the application of the discrete model of thin-walled cross section to the design calculations of thin-walled rods with variable skin thickness, representing practical structures.

Warm Air Bending of AZ31B Sheets Based on an Online Local Contact Heating Method

Abstract Warm forming holds significant potential in shaping challenging materials due to its comprehensive advantages compared to cold and hot forming. Effective heating is crucial for precise warm forming processes. This study explored an innovative warm air bending technique employing an online local contact heating method. Heat transfer during the preheating stage and the air bending of AZ31B sheets were investigated through experiments and finite element analysis at temperatures ranging from room temperature (24 °C) to 250 °C, considering the thermomechanical coupling effect. The results indicate a significant increase in the bending center angle, advancing from 69.8 deg to more than 119 deg as the heating temperature rises from room temperature to 250 °C. Fractures were effectively eliminated when the sheet heating temperatures exceeded 150 °C. Simultaneously, as the localized heating temperature increases, a corresponding decrease in the rebound angle is observed, reducing from 10.6 deg to 2.3 deg. The findings validate the feasibility of warm air bending using online local contact heating in industrial applications, with regard to forming quality and production efficiency.

Study on the optimization of high-speed turnout crossing structures based on actual elastic deformation of point and splice rails

In this paper, to address the shortcomings of the crossing structure design based on the elastic bending center method and the lack of related research, an optimization method for high-speed turnout crossing structures was proposed based on the actual elastic deformations of point and splice rails. Based on the finite element theory, the actual loading characteristics and spatial variable section characteristics of point and splice rails were fully considered, and a refined simulation analysis model of the switching system of point and splice rails in crossing areas was established. Moreover, the elastic deformation lines of point and splice rails in the nonworking state were obtained for the first time, which were consistent with actual situations. On this basis, system optimization was performed for the connecting parts of the crossing with a movable point in a high-speed turnout. In the crossing structure simulation model, the length adjustment values of the first–sixth spacer blocks between the branch line–wing and point rails and between the mail line–wing splice rails were ≤1 mm. Moreover, the lengths of the seventh–ninth spacer blocks decreased by gradually increasing amounts, and the length of the ninth spacer block decreased the most (∼6 mm). The length of the second spacer block between the point and splice rails slightly increased, but the length of the third spacer block significantly decreased by 6 mm. The length adjustment value of the distance block between the point and splice rails was smallest (0.7 mm). The calculated optimal lengths of the connecting parts of the crossing were found to be close to the empirical values used in actual manufacturing processes, and the dimension optimization patterns were completely consistent with actual situation, which validates the proposed optimization method. Thus, the proposed method can effectively improve the coordination between rails and connecting parts in crossing areas, substantially reduce internal stresses in crossing systems, and improve their assembly performance and service life. Moreover, the proposed optimization parameters can provide valuable references for the research on next-generation high-speed turnouts (400 km/h) and for improving the designs of existing high-speed turnouts.

Experimental study of buoyancy and centrifugal effects on supercritical heat transfer in U-bend and contiguous straight tubes

The buoyancy-induced thermal non-uniformity in heat transfer of supercritical fluids is a major issue that must be addressed in transcritical systems like organic Rankine cycle. In cases where U-bends are involved in heat exchangers, the introduction of centrifugal effect and its decaying nature makes the heat transfer process even more complex. In this work the buoyancy and centrifugal effects on local heat transfer to supercritical R410A were experimentally studied in a U-bend and its contiguous horizontal straight tubes (tube diameter d = 4.35 mm, bend diameter D = 43.5 mm). Measurements were performed at four circumferential positions along the heated length. Results show that bend-induced enhancement reached the maximum at the bend center, where heat transfer coefficients at the outside, top, bottom, and inside increase by 88%, 49%, 28% and 19% respectively. U-bend also caused a significant enhancement on contiguous horizontal straight tubes. In the upstream straight section, the affected distance can reach 11.5d, and the downstream affected range is more than 23d. The enhancement and the affected distance generally increased with heat flux, mass flux, and inlet temperature, but barely affected by pressure. Further analysis indicates that the centrifugal force dominated heat transfer in the bend section. Moving away from the bend, it gradually decayed, buoyancy force recovered and eventually played the major role. Existing dimensionless numbers failed to represent this transition, and a new parameter ψ* was proposed to evaluate the competition between the buoyancy effect and the decaying centrifugal effect. With a threshold value of 1, ψ* can quantitatively characterize the local heat transfer.

Общая устойчивость балок двутаврового постоянного сечения. Развитие расчетных положений

The paper presents the derivation of formulas for the method of calculating bent elements for general stability, given in SP 16.13330, which is based on the theory of thin-walled elastic rods and the system of differential equations of V. Z. Vlasov. Formulas are given for a single-span beam with a hinged mounting of supports. A general equation has been compiled for calculating the bending stability coefficient φ_1, which allows adapting the requirements of SP16.13330 standards to various types of load action in the beam span. The results are presented for twenty-five different types of external load action. The formulas take into account the arbitrary location of the load along the height of the beam section, from the lower edge of the lower belt to the upper edge of the upper belt. The values of the critical moment M_cr, at which a new form of equilibrium state arises in the beam, are determined, according to the conclusions of the work [6]. The critical moment M_cr is calculated in the form of a stability problem of the first kind – the loss of a stable position of an element of a rectilinear shape (the load acts along the line of the bending center, the neutral axis of the beam is rectilinear, the material is elastic). The formulas of the presented table can be used to perform verification calculations.

Curved hologram generation method for speckle noise suppression based on the stochastic gradient descent algorithm

In this paper, a curved hologram generation method with suppressed speckle noise is proposed. In the process of generating the curved hologram, the angle spectrum method is used to calculate the 3D object in layers. By analyzing the loss function relationship between the diffraction image of the curved hologram and the target light field, the loss function is calculated. The phase of the hologram is updated based on the stochastic gradient descent algorithm, thereby obtaining the optimal phase distribution of the curved hologram. When the curved hologram is reproduced at different bending center angles, the reconstructed image of the corresponding angle can be seen. The proposed method has obvious advantages compared with the error diffusion method and Fresnel diffraction algorithm. The feasibility of the proposed method is verified by the experiments.

DEVELOPMENT OF THE COMBINED TECHNOLOGICAL PROCESS OF BLANK STACKS FLANGES FORMATION BY THE METHOD OF STAMPING BY ROLLING AND ROTARY DRAWING

The article presents the results of the development and research of the combined technological process of forming the outer and inner flanges of the lids of fractional and distillation columns on sheet blanks by the method of stamping by rolling and rotary drawing. For this purpose, equipment has been developed that allows to form both outer and inner flanges of the blank in one run of the conical roll. Studies have shown that technological capabilities of the process are limited by the risk of destruction of the top layers of the outer flange bending center and its corrugation, as well as by the neck formation or destruction of the peripheral areas of the inner flange. To assess the deformability of the outer flange, the stress-strain state of its bending center was investigated. According to the set stress values, the stress state of the material is determined, the maximum value of which on the surface of the bending zone is Formula for determining the minimum radius of the mandrel, which when using the values of the critical ductility of the material allows to prevent destruction. As well, an expression for determining the maximum width of the flange, provided that the destruction of peripheral areas is prevented, is obtained. As corrugations formation is the main danger in forming the external flanges by the stamping by rolling method (SR), the expression for determining the maximum width of the flange under the condition of a stable process is obtained. If it is necessary to get more developed flanges, it is proposed to provide thinning of their walls by rotary extraction at the second stage. When forming the inner flanges of the blank stacks radial compressive stresses and tangential tensile stresses in the material are brought about. The action of tangential stresses causes loss of stability of the flange by way of neck formation. The value of the critical strains increases with the approach to the state of plain-strain deformation. Therefore, it is recommended to develop process parameters based on construction of the critical strains diagrams.

Analyses of the plastic deformation of coated conductors deconstructed from ultra-high field test coils

REBCO coated conductors are now being used for building very high-field magnets with large electromagnetic stresses, both expected ones due to transport current × stresses and additional stresses resulting from the large screening currents inherent in wide tapes. Post mortem analyses of several recent test coils operated above 40 T show that significant conductor plastic deformation occurs, even for JBR stresses well below the ∼1 GPa yield of the Hastelloy substrate of the conductor. To investigate these deformation mechanisms, conductors were unwound after coil test and carefully examined with respect to their length-wise Ic which revealed many areas of local damage. Regions of interest were examined by metallographic cross-section, Hall microscopy, magneto-optic imaging and scanning electronic microscopy. Important damage frequently occurred to the outer edges of pancakes in the coil ends, which were often plastically deformed over the whole turn circumference, especially when this outer edge was a slit edge. Internal conductor damage was also seen, especially delamination between the buffer and REBCO layers at slit edges. Careful sectioning of the tape at ∼10 mm intervals showed that the plastic deformation of the turns was complex and variable around the turn circumference, with tape cross-sections that exhibited continuous shape change in the outer turns. The bending center line of tapes often shifted from the tape center line toward the edge closest to the coil center, indicating asymmetric effects of transport and screening current stresses across the conductor width. A surprising and vital result is that damage was prevalent when the slit edge was also the edge at which transport current flowed. This damage was absent when the transport current flowed at the not-slit edge, implying great sensitivity of the effect of screening current stresses to localized conductor damage.

Investigation of tube fracture in the rotary draw bending process using experimental and numerical methods

The quality of tubes obtained by rotary draw bending (RDB) depends on many process parameters whose selection is essential to prevent defects such as fracture, wrinkling, springback and lack of tube’s ovality. Whereas the finite element method (FEM) is a useful method for defects detection in the metal forming processes, the Gurson-Tvergaard Needleman (GTN) damage model is used in the numerical simulation of RDB for fracture prediction of BS 3059 steel tube. The numerical results were verified with the experimental ones for thickness distribution in the tube outer wall and also fracture prediction. The effect of some RDB parameters such as pressure of pressure die, boosting velocity of pressure die, friction between the tube and pressure die, mandrel position and number of mandrel balls were studied on the fracture, wrinkling and tube’s ovality. The results showed that using a low value for the boosting velocity of pressure die caused the tube fracture and using the high value for that increased the wrinkling possibility of the tube inner wall. The results indicated that the fracture possibility increased by increasing the number of mandrel balls and decreaseing the distance between the mandrel position and the bending center. The tube’s ovality will be increased by decreasing the number of mandrel balls and increasing distance between the mandrel position and the bending center.

Experimental investigation of effective parameters in the tube rotary draw bending process

The rotary draw bending (RDB) process is one of the complex forming processes which is widely used for tube bending. There are different parameters in this process that incorrect selection of them cause the happening of some defects such as thinning and tube ovality. In the present study, the effects of main parameters of the RDB process is investigated on the thinning and ovality of BS 3059 steel tube using the experimental tests. Therefore, a design of experiment (DOE) base on the Taguchi method is used to investigate the effect of mandrel diameter, pressure of pressure die and mandrel position on the thinning of tube outer wall and the tube ovality. Four different values of 7 MPa, 10 MPa, 12 MPa, and 15 MPa are considered for the pressure of pressure die and four values of 7 mm, 15 mm, 20 mm and 34 mm for the mandrel position. The mandrel position is the distance between the mandrel and bending center. Two different chain link mandrels are used with balls diameter of 33.5 mm and 34.5 mm. The results showed that the mandrel position had the most significant effect on the thinning and tube ovality. Although the increase of mandrel position improved the thinning defect in the tube outer wall, the tube ovality increased by the increase of mandrel position from 20 mm to 34 mm. The results showed that the pressure of 7 MPa, mandrel position of 15 mm and the mandrel diameter of 33.5 mm were the best parameters for RDB of BS 3059 steel tube.

Using Boundary Element Method to Calculate the Bending Center of General Section

Using Siant — Venant bending theory, transverse bending of a general section cylinder, it comes down to solving two boundary integral equations of the same type, the bending function and additional torsion function of the cylinder are obtained. On this basis, using boundary element method to determine the bending center of general section. Finally, to illustrate the application of the method, a numerical example is given.

Body Freedom Flutter Study and Passive Flutter Suppression for a High Aspect Ratio Flying Wing Model

Normal mode and flutter analysis are conducted for a high aspect ratio aft swept flying wing model, and body freedom flutter is found to be the most critical aeroelastic instability for this air vehicle model. To determine the influence of various kinds of design parameters on BFF characteristics, eight factors are considered in the parametric study, i.e. wing vertical bending stiffness, weight and center of gravity of the wing root payload and the wing tip mass balance, wing half span, aft swept angle and the station of wing body blended line. After the parametric analysis, the mass and center of gravity of the wing root payload are selected as design variables, and the baseline model is utilized in the design optimization study subject to critical flutter speed constraint. Finally, the optimal mass balance design is suggested to suppress the body freedom flutter phenomenon passively and maximize the payload.

A novel infrared detector using highly nonlinear twisting vibration

A new resonant infrared (IR) detector is proposed. The twisting motion of the thin film torsion bar is first used. The resonant frequency gives the information of the temperature change of the moving element caused by IR absorption. The dynamic sensing using the electrostatic force can remove the drift without the heat generation. The large nonlinearity of the thin film torsion bar combined with the frequency measurement increases the advantage of the high sensitivity. The IR detector is fabricated by the surface micromachining using sub-μm thick poly-Si film. Its structure consists of two parts. One is the thin film torsion bars and another is the bending center part. They can be basically designed separately. The center part has bi-layer structure to induce bending against the temperature increase caused by the IR absorption. One fabricated IR detector has the resonant frequency of about 35kHz and shows the sensitivity of 30Hz/K and the shifting ratio of 830ppm/K. This sensitivity is larger than the previously reported Si detectors. The shifting ratio is larger than devices including the high-frequency quartz and ZnO detectors.

Rotationally-Resolved Spectroscopy of the Donor Bending Mode of (D2O)2

High-resolution spectra of the intramolecular bending modes of deuterated water dimer, (D2O)2, have been measured using a quantum cascade laser based cavity ringdown spectrometer. Two perpendicular bands have been observed and are assigned as the K(a) = 1 ← 0 and K(a) = 2 ← 1 bands of the bending mode of the hydrogen bond donor. The tunneling splittings in the complex are well-resolved, and it is found that excitation of the donor bend has little effect on tunneling of the hydrogen bond acceptor, but causes significant perturbations on the tunneling motion which exchanges the roles of hydrogen bond donor and acceptor. The presence of this perturbation has prevented a detailed assignment of the tunneling levels in the excited state at this time. An accurate value for the band center of the donor bend is calculated to be 1182.2 cm(-1), which is in good agreement with previous theoretical calculations performed on an ab initio potential energy surface.

On numerical realization of the problem of torsion and bending of prismatic bars of arbitrary cross section

We have developed software for computation of geometric characteristics and analysis of tangential stresses of prismatic bars with an arbitrary cross section in the stages of preprocessing, processing, and postprocessing of data in a finite-element analysis. Based on the principle of virtual works, we obtain variational functionals for the Saint-Venant problem of torsion of a prismatic bar and bending by a transverse force that does not cause torsion. These functionals are directly used to obtain resolving relations of the finite-element method. On the basis of the Betti reciprocal theorem, the coordinates of the center of bending are determined. We formulate all relations for the warping function, which enables us to avoid problems associated with ambiguity in the case of using the Prandtl function of stresses for a multiply connected domain.

Plane strain solution and cross-section flattening analysis in tube bending with linear hardening law

Formulae based on plane strain assumption are deduced to calculate principal stresses, von Mises stress and cross-section flattening ratio of tubes subjected to combined bending and additional tension. The analysis shows that additional tensile force causes movement of neutral layer toward bending center and makes deformation behavior under rotary draw bending different with that under pure bending. The principal stresses and the von Mises stress are proportional to yield stress, linear hardening factor and the neutral layer movement and inversely proportional to centerline radius/diameter ratio. With radial displacement at tube’s extrados taken into consideration, the von Mises stress increases with greater neutral layer movement but reduces with larger centerline radius/diameter ratio. Analytical and numerical von Mises stresses distribute nonuniformly in the cross section, and large von Mises stresses localize at the tube’s extrados. Both the maximum values of the two results localize on the outermost surface of the tube. In addition, the variation tendencies of analytical, numerical and experimental change rates of minor axis of the distorted cross section are in good agreement, increasing with smaller centerline radius/diameter ratio. The analytical results are greater than the numerical results but smaller than the experimental results.

Particle orbit in a radial-sector scaling FFAG

The particle orbit in the bending magnet of a radial-sector FFAG accelerator is derived analytically in the approximation valid for a small bending angle. The orbit is described in terms of the distance from the machine center, r, and its variation is derived as a function of the bending angle. Also, the variation of the distance from the bending center, ρ, is derived as a function of the bending angle. The result shows how the ratio, r/ρ, can be made independent of the particle momentum, which is one of the conditions of the scaling property.

MODE ANALYSIS AND SYSTEMATICAL DESIGN OF WIDE-BANDWIDTH PHOTONIC CRYSTAL 60° WAVEGUIDE BENDS WITH HIGH TRANSMISSION

We present a procedure to enhance the transmission efficiency of a photonic crystal slab waveguide bend by introducing an air hole with the same radius at the center of bend and optimizing the positions of three neighboring holes in the corner. The improvement relies only on the method of displacing holes which is technologically preferred to controlling variations in hole size or shape. We employ the effective refractive index approach and two-dimensional plane wave expansion method to analyze the guide modes of the straight waveguide and waveguide bend. The transmission character of bent waveguides is investigated using two-dimensional finite-difference time-domain method. Numerical studies demonstrate that the approximate method of mode analysis is unsuitable to our model. Alternatively, we systematically study the effect of different positions of the holes on the transmission. The optimized bends for the high transmission with broad bandwidth are proposed.

Influence of Additional Tensile Force on Springback of Tube Under Rotary Draw Bending

According to the characteristics of tube under rotary draw bending, the formulae were derived to calculate the springback angles of tubes subjected to combined bending and additional tension. Especially, as the neutral layer (NL) moves to the inner concave surface of the bend, the analytical values agree very well with the experimental results. The analysis shows that the additional tensile force causes the movement of the NL toward the bending center and makes the deformation behavior under rotary draw bending or numerically controlled (NC) bending different with that under pure bending, and also it could enlarge the springback angle if taking the movement of the NL into consideration. In some range, the springback angle would increase slightly with larger wall thickness/diameter ratio and decrease with wall thinning. The investigation could provide reference for the analysis of rotary draw bending, the design of NC tube bender and the related techniques.