Bending Model Research Articles

48‐3: Invited Paper: Research on Pad Bending Technology for the Extremely Narrow Bezel of Flexible OLED Screens

The bending radius of the flexible OLED down border was reduced to 0.15mm from 0.25mm by an improved bending model for the extremely narrow bezel mobile. The stability of the optimized bending model was demonstrated by simulation, and the preliminary production and environmental reliability were assessed too.

A data-driven bit projection system with motor yield prediction and advisory for directional drilling and well trajectory control

In the evolving of the oil and gas industry, where innovation and technological advancement are paramount, directional drilling stands as a pioneering technique that has revolutionized the extraction of hydrocarbon resources from beneath the Earth's surface. For drilling with mud motor, accurate projection of bit position from the latest survey and comprehensive evaluation of the current motor yield (MY) are essential to avoiding early well trajectory deviation and optimizing future directional plans. Currently, these responsibilities primarily rest on the shoulders of directional drillers (DDs), consuming valuable drilling operation time and being subject to biased human judgments. In this study, a data-driven bit projection system for directional drilling optimization and well trajectory control is developed. A kinematic model is first constructed for the projection of bit inclination (INC), azimuth (AZI), and north-east-vertical (NEV) in drilling with mud motors. Moreover, in scenarios involving curve section slide drilling, a machine learning model is developed to predict instant MYs observed between surveys, which is trained and tested on a dataset comprising drilling over 350 Delaware Basin curve section stands. Ultimately, a low MY reasoning algorithm is proposed to identify the dominant factor that causes the suboptimal MY output and provides recommendations for upcoming drilling plans. The proposed system is validated using 1189 vertical stands, 240 curve stands, and 1837 lateral stands from 17 different wells. The validation results illustrate that the bit NEV projection error averages below 0.82 ft for 90-foot surveys in vertical/lateral sections. In curve sections, the average MY prediction error is 0.96° one hundred feet or 7.6% in the relative sense and the average 30-foot bit NEV projection error is 0.228 ft, with the predicted MY as input. Compared with the physics-based bottomhole assembly (BHA) bending model and other data-driven approaches in the literature, the proposed system sees a large improvement in MY prediction and the bit NEV projection accuracies. With the minimal input data requirements, fast computation speed, and accurate projection/prediction results, the proposed bit projection system holds the opportunity of application in the autonomous directional drilling system, real-time drilling job evaluations, and well trajectory optimization.

Influence of process parameters on forming quality of largesize nickel-based alloy tubes

In order to improve the forming quality of largesize nickel-based alloy chemical tubes, the influence of different tube specifications and mandrel/tube clearances on the bending forming quality of largesize Hastelloy C-276 alloy tubes was studied. A finite element (FE) analysis model for NC rotary drawing bending (RDB) was established and verified. The results show that with the increasement of the clearance, the wall-thinning ratio [Formula: see text] of different tube specifications gradually decreases, and the wall-thickening ratio [Formula: see text] and ovality [Formula: see text] gradually increase. As the measuring angle increases, the [Formula: see text] of different specifications initially increases and then decreases. The [Formula: see text] exhibits a trend of initially increasing and then decreasing. It is reasonable to take about 1/8 of the wall thickness t for the mandrel/tube clearance. It is of great significance for guiding the bending forming of largesize nickel-based alloy chemical tubes and development of intelligent forming equipment.

Bending forming of lightweight large diameter thin-walled aluminum alloy aviation tube

To improve the forming quality of lightweight aviation tubes, the influence of different tube specifications, forming requirements and process parameters on bending forming of large diameter thin-walled (LDTW) LF2M aluminum alloy tubes (AATs) was studied. A finite element analysis model for LDTW AAT bending was established and verified. The results show that with the increase of mandrel extension length [Formula: see text], the wall-thinning ratio tends to increase. With the increase of [Formula: see text], the overall wall-thickening ratio decreases. With the increase of [Formula: see text], the ovality decreases first and then increases. The bending radius has a great influence on wall thickness variation. It has great significance to guide the bending forming of lightweight LDTW aluminum alloy aviation tube.

Experimental and numerical investigations of the water surface profile and wave extrema of supercritical flows in a narrow channel bend

Supercritical flows in channel bends, e.g., in steep streams, chute spillways, and flood and sediment bypass tunnels (SBTs), experience cross-waves, which undulate the free surface. The designs of these hydraulic structures and flood protection retaining structures in streams necessitate computing the locations and water depths of the wave extrema. This study numerically and experimentally investigates the water surface profiles along the sidewalls, the wave extrema flow depths, and their angular locations in a narrow channel bend model of the Solis SBT in Switzerland. The 0.2 m wide and 16.75 m long channel has a bend of 6.59 m radius and 46.5° angle of deviation. The tested flow conditions produced Froude numbers ≈ 2 and aspect ratios ranging from 1.14 to 1.83. Two-phase flow simulations were performed in OpenFOAM using the RNG k–ε turbulence closure model and the volume-of-fluid method. The simulated angular locations of the first wave extrema and the corresponding flow depths deviate marginally, within ± 6.3% and ± 2.1%, respectively, from the experimental observations, which signifies good predictions using the numerical model. Larger deviations, especially for the angular locations of the wave extrema, are observed for the existing analytical and empirical approaches. Therefore, the presented numerical approach is a suitable tool in designing the height of the hydraulic structures with bends and conveying supercritical flows. In the future, the model’s application shall be extended to the design of the height and location of retaining walls, embankments, and levees in steep natural streams with bends.

Three-dimensional hygro-thermo-mechanical bending analysis of anisotropic skewed parallelogram plates on a tri-parameter foundation using a wavelet method

In the paper, a brand-new three-dimensional hygro-thermo-mechanical bending model of anisotropic skewed parallelogram plates with extreme skew angle in large deformation supported by a tri-parameter nonlinear elastic foundation is proposed. By investigating the mutual coupled interaction of hygrothermal effects between in-plane distribution and thickness variation, nine kinds of spatially analytical hygrothermal fields in parallelogram domain are established by analyzing the Dirichlet, Neumann and Robin thermal boundary conditions of sinusoidally induced heat conduction at top and bottom surfaces. With coordinate transformation in oblique system considering the Von Kármán membrane strains, the highly coupled and strongly nonlinear governing partial differential equations have been derived. A wavelet solving procedure has been developed with the convergence process validated and precision of obtained solutions verified in good accordance with published results. Parametric studies have been carried out to investigate the large-deflection behavior of simply supported or clamped skew plates on Winkler–Pasternak foundation under combined mechanical and hygrothermal loads. The influence of skew angle, material orthotropy and foundation contact nonlinearity is examined, which reveals the geometrically nonlinear responses of plates are highly affected by large oblique angle, principle orientation of material orthotropy and foundation parameters.

Machine learning for the prediction of problems in steel tube bending process

Tube bending is a widely used process in marine, automotive, construction and other industries. Different methods are available for this process during which various problems and defects are encountered. This paper aims to develop the most relevant model for bending the tubes using a computer numerical controlled (CNC) bending machine on the first attempt without any defects. To achieve this goal, the parameters affecting the tube bending process on the bending machine are defined. Based on these parameters, 150 bending experiments are conducted in an industrial plant to collect data and their results are used as dataset for machine learning (ML) algorithms. Seven different state-of-the-art ML algorithms –logistic regression, decision tree, k-nearest neighbor, random forest, Naïve Bayes, support vector machine and eXtreme gradient boosting (XGBoost)– are implemented using Python's Scikit-Learn library. Their performance is compared using confusion matrix and classification metrics such as accuracy, precision, recall, F1-score, receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) value. Considering all the performance metrics, logistic regression performed best in terms of prediction on our dataset. XGBoost and support vector machine were quiet successful based on F1 score and AUC, respectively. Overall, logistic regression, Naïve Bayes, Support Vector Machine, and XGBoost showed performances above 90% across all metrics. Decision tree, k-nearest neighbor and random forest performed poorly compared to other algorithms for our data. The proposed ML method is expected to save costs by reducing material waste and labor time and to increase the process efficiency and the product quality.

Research on the Hot Straightening Process of Medium-Thick Plates Based on Elastic-Viscoplastic Material Modeling.

With the continuous improvement in the strength of medium-thick plate materials, the hot straightening of plates at high temperatures is increasingly influencing the final defect characteristics of products. In the high-temperature hot straightening process, the temperature and straightening speed of the plate significantly influence its intrinsic material properties, which, in turn, affect the straightening characteristics of the plate. However, most current material models used in the straightening process do not consider the relationship between temperature and strain rate, which leads to an inaccurate characterization of the actual material structure. Additionally, the continuous reverse bending mechanics model for straightening does not account for the impact of different bending strain rates on the bending characteristics of the plate in the thickness direction. In this study, a numerical calculation method was employed to investigate the evolution process of stress and curvature in the roll-type hot straightening process of medium-thick plates. Experimental data and mathematical methods were utilized to develop a viscous plastic material model that accounted for temperature and strain rate. Furthermore, a cross-sectional continuous reverse bending model was established, taking into account the temperature and straightening speed, enabling a reasonable interpretation of the mechanical parameter behaviors of medium-thick plates during high-temperature straightening.

Modelling the Charpy Impact Ductile-Brittle Transition of a Ship Plate Steel with CAFE Modelling

In the present work, a cellular automata finite element model (CAFE) was developed to model the ductile-brittle transition of a Grade A ship plate steel. Therefore, ductile and brittle cellular automata (CA) arrays of cells were created in the model to integrate material data at microstructural level, along with the ductile and brittle fracture processes. Microstructural data was analysed with Weibull distributions and incorporated in CAFE model using random number generators, along with ductile and brittle fracture parameters. Ductile fracture was modelled with Rousselier damage model; hence damage model parameters were calibrated with experimental data. Brittle fracture was modelled with Beremin model, and four different cleavage particles, found in a Grade A ship plate steel, were incorporated in CAFE model in order to model a competition of particles nucleating microcracks of critical size in the damage regions of Impact Charpy tests and four-point double-notch bend tests performed at low temperature. The mechanical properties the plate steel was measured in the transition region and incorporated in CAFE model, along with ductile-brittle transition rules. The present CAFE model was able to simulate distributions of microcracks in the notch region of four-point double-notch bend models (in the transition region), which correlated with experimental data. CAFE model was also able to simulate microvoids in the notch region of Charpy specimens along with the load-displacement Charpy curve for room test temperature, with very good agreement with experimental data. Once CAFE model was validated at micro and structural level, it was applied to model the typical scatter of impact Charpy energy values in the transition region of Grade A ship plate steel with good agreement with the measured ductile-brittle transition curved of the plate steel. Keywords: cellular automata, finite element modelling, ductile-brittle transition, damage modelling.

Nonlinear analysis on electro-elastic coupling properties in bended piezoelectric semiconductor beams with variable cross section

In this paper, the effects of nonlinear constitutive relation on the electro-elastic coupling behaviors in non-uniform piezoelectric semiconductor beams are investigated. On the basis of three-dimensional theory for piezoelectric semiconductor and double power series, one-dimensional bending model is developed. In order to deal with the nonlinear problem, a differential quadrature method based iteration procedure is proposed. Comparing with the results from finite element method, the proposed method has good convergence and high accuracy. In numerical analysis, the effects of nonlinearity and non-uniformity in piezoelectric semiconductor are discussed thoroughly. It is found the introduction of nonlinearity induces the loss of symmetric for all electrical field quantities but little changes the mechanical quantities. While the reduction of width along the length direction produces larger mechanical and electrical responses. Importantly, the effects of nonlinearity on the electrical field quantities are more evident in a piezoelectric semiconductor beam with rapidly varied cross section. Besides, we designed the piezoelectric semiconductor beams subject to double shear forces and a beam with locally varied cross section. In the designed structures, the potential barriers and wells are realized, which provide new approaches adjusting the electro-elastic behaviors in piezoelectric semiconductors. The study in this paper could be the guidance designing high performance electronic devices.

Numerical simulations on the structural heterogeneity and fracture bias effect of three-point bending specimen

Granite is a common surrounding rock in tunnels, nuclear waste repositories, and other underground engineering. It is essential to investigate granite’s mechanical behavior and fracture mechanism at the mesoscale. In this paper, the three-point bending model considering granite meso-heterogeneity was constructed, and the three-point bending test and acoustic emission (AE) simulation were carried out under different crack sizes and porosities, different prefabricated fracture offset distances, and bedding conditions. The results show that large-size mineral particles and intrinsic fractures mainly determine the sample’s crack propagation pattern. As the prefabricated crack’s deviation distance increases, the sample’s peak load, fracture energy, number of AE events, and internal damage range all gradually rise. The sample’s crack propagation path has a distinct step shape due to bedding, and tensile fractures primarily occur in the through-layer crack, whereas shear fractures mainly occur at the bedding plane. The specimen’s surface crack’s fractal dimension is positively associated with the cumulative acoustic emission energy during the fracture process. The conclusion of the research can offer a theoretical foundation for analyzing the stability of the surrounding rock.

Bent-half space model problem for Lame equation with surface tension

The study of fluid flow is a very fascinating area of fluid dynamics. Fluid motion has received more and more attention in recent years and numerous researchers have looked into this topic. However, they rarely used a mathematical analysis approach to analyse fluid motion; instead, they used numerical analysis. This serves as a significant justification for the researcher's decision to study fluid flow from the perspective of mathematical analysis. In this paper, we consider the ${\mathcal R}$-boundedness of the solution operator families of the Lam\'e equation with surface tension in bent half-space model problem by taking into account the surface tension in a bounded domain of {\it N}-dimensional Euclidean space ($N \geq 2$). The motion of the model problem can be described by linearizing an equation system of a model problem. This research is a continuation of [13]. They investigated the ${\mathcal R}$-boundedness of the solution operator families in the half-space case for the model problem of the Lam\'e equation with surface tension. First of all, by using Laplace transformation we consider the resolvent of the model problem, then treat the problem in bent half-space case. By using Weis's operator-valued Fourier multiplier theorem, we know that ${\mathcal R}$-boundedness implies the maximal $L_p$-$L_q$ regularity for the initial boundary value. This regularity is an essential tool for the partial differential equation problem.

ANALYSIS OF ASYMMETRIC PLASTIC BENDING DEFORMATION OF WELDED TUBE SHEETS AND DERIVATION OF A DAMAGE LAW FOR J SHAPE-C SHAPE -O SHAPE FORMING

The J shape-C shape -O shape (JCO) forming method of sheets for large-diameter longitudinally welded pipes has been widely used to manufacture oil and gas pipelines. The quality of welded pipes formed through the JCO process is directly affected by the accurate control of asymmetric bending springback and damage during the procedure. A finite element model (FEM) for JCO asymmetric bending was constructed to investigate the characteristics of asymmetric plastic bending deformation and the distribution laws of damage in JCO forming. This model was based on a nonlinear mixed hardening Lemaitre damage model coupled with the Quasi-Plastic-Elastic (QPE) model. Then, residual stress, forming shape, and damage degree of crimping, first bending, second bending, and third bending were analyzed. Moreover, the accuracy of the model was experimentally verified. Results demonstrate that, the asymmetric bending deformation process can be divided into five stages, including rigid body rotation phase, full elastic deformation phase, elastic–plastic uncladded deformation phase, elastic–plastic cladded phase, and springback phase. In the first bending, the stress centerline significantly misaligns with the mold centerline. Asymmetry is not evident in the second and third bending stages. Furthermore, the peak residual stress and peak damage can be effectively reduced by a larger punch radius, while the peak damage can be reduced by a larger die span. This study lays a foundation for optimizing the technical parameters of JCO forming. Keywords: JCO forming, asymmetric bending, finite element, QPE model, deformation characteristics

Optimal design of elastic plates

This paper is concerned with optimal design problems in the setting of the Kirchhoff–Love model for pure bending of a thin solid symmetric plate under a transverse load. For two isotropic elastic materials with a prescribed amount, the goal is to find their rearrangement within the domain that forms a least compliant structure. The homogenization method is used as a relaxation tool to overcome the lack of a classical solution of optimal design problem. Neccessary conditions of optimality were derived and an optimality criteria method for the single state compliance minimization problems is developed and tested on several examples.

Modeling and analysis of bending and torsional coupling vibration response of multi-piece wet friction clutch

Modeling and analysis of bending and torsional coupling vibration response of multi-piece wet friction clutch

Numerical investigation of mode I fracture toughness anisotropy of deeply textured shale

The fracturing behavior of shale is controlled by the complex interaction between texture plane and rock matrix. This study develops a numerical model of semicircular bending of textured shale, integrating considerations of texture inclination and strength using the finite discrete element method, to examine the impact of shale anisotropy on damage patterns and fracture toughness. The results disclose the following insights: (1) Mode I fracture toughness anisotropy is significant, with fracture toughness showing a negative correlation with texture inclination and a positive correlation with texture strength. (2) Typical failure modes of SCB specimens encompass tensile failure across textured planes, tensile-shear mixed failure, tensile failure along texture planes, and tensile failure along the matrix. (3) For inclination angles ranging from 0° to 90°, cracks tend to deflect along the texture, leading to a fracture surface with high roughness. The fracture surface roughness was higher along the direction of maximum principal stress for the 0° and 90° specimens compared to the Divider specimens, while it was lower along the thickness direction compared to the Divider specimens. (4) The toughening mechanism of textured shales is categorized into three classes: separation along the texture, fracture path deflection, and texture cracking. Texture strength mainly influences texture cracking, while texture inclination primarily affects the deflection of crack paths and separation along the texture. (5) The criterion for predicting modified fracture toughness accurately predicts the anisotropic fracture toughness of shale compared to the conventional criterion for predicting fracture toughness.

Application of Installations with Uniform-Strength Beams as Working Deformation Standards

A method for obtaining homogeneous deformation along the length of the measuring section of a uniform-strength beam and the possibility of its application as part of a working deformation standard are considered. The results of the analysis of the bending model and the design of a uniform-strength beam are presented. In the focus of attention are the parameters included in the measurement equation and related to methodological factors, as well as influencing the result of relative deformation measurements. The subjects of research are the presence of contact friction forces, heterogeneity of material properties, the special nature of the load application (bending, torsion, the presence of residual stresses in the body, geometrical parameters of the calibration beam, orientation of primary transducers on the beam, application of bending load, measurement of deflection and displacement of the neutral layer). The advantages and disadvantages of using a uniform-strength beam for determining the characteristics of primary strain transducers during testing, calibration, and verification were established. The deviation of signals of primary transducers located outside the axial cross-section when oriented along the beam axis and along the force lines converging at the point of load application was experimentally revealed. The error due to the orientation of the primary transducers on the beam depending on the angle between the lateral faces can range from 0.15 to 0.23 %. The study adds to the theoretical knowledge base on the possibility of using a cantilever uniform-strength beam as a load-bearing element in calibration installations. The conclusions may be useful for testing, calibrating, and verifying primary strain transducers.

Experimental and numerical investigations on non-synchronous vibration and frequency lock-in of transonic compressor rotor blades

Non-synchronous vibration (NSV) problems in axial compressors are challenging and frequently result in high vibration stress or structural failure within the frequency lock-in region. A deeper understanding of the lock-in phenomenon in NSV is necessary to improve blade reliability and safety. In this study, an experiment was conducted on a multistage transonic axial compressor to obtain frequency lock-in characteristics. The enforced motion of the flexible blade simulation method was used to study the frequency lock-in mechanism between blade vibration and tip unstable flow. The results showed that the aerodynamic frequency characteristic changed from a broadband spectrum to a distinct frequency peak as the NSV onset. The nonlinear vibration pattern could maintain the limited cycle oscillation for 26 s. The vibration stress of the frequency locked-in case was approximately 19 times that of the frequency unlocked one. The pressure fluctuations generated by the large-scale radial separation vortex structures were stronger than those of the tip leakage flow, and the third-order harmonic frequency of the circumferential instability flow was close to the first-order bending model natural frequency. The periodic shedding and reattachment process of flow separation provided the initial non-synchronous aerodynamic excitation source. The frequency lock-in phenomenon occurred at a maximum vibration amplitude of 2 % and 3 % tip chord length. The tip unstable flow characteristics were consistent and entirely dominated by blade vibration.

Load-bearing capacity of composite honeycomb sandwich high-speed train floor

ABSTRACT The honeycomb sandwich structure of composite materials has broad prospects for application in the lightweight design of vehicle bodies. This study investigated the influence of relative density and height on an aluminium honeycomb’s out-of-plane quasi-static compression performance through experiments and simulations. The accuracy of the carbon fibre/aluminium honeycomb sandwich panel’s three-point bending model is verified based on the Hashin failure criterion and experimental validation. Furthermore, the load-bearing capacity of the carbon fibre/aluminium honeycomb sandwich floor is analysed, and the factors influencing the load-bearing capacity of the floor are further explored. The results show that the relative density significantly impacts the out-of-plane quasi-static compression performance of aluminium honeycomb, while the height has a minor influence. Compared with the original CRH5-type floor structure, the carbon fibre/aluminium honeycomb sandwich floor has a weight reduction of 45.23%, and it meets the strength requirements under uniformly distributed and concentrated load conditions. Changing the honeycomb wall thickness and panel thickness distribution can improve the load-bearing capacity of the floor.

Comparison of approximation methods for bending of finite and infinite elastic plates: The traction boundary value problem

A generalized Fourier series method is designed to approximate the solution of the Neumann problem in a finite domain and in an infinite domain with a hole, for the mathematical model of bending of elastic plates with transverse shear deformation. The results in the two cases are compared and contrasted, and the analysis is illustrated by examples with specific boundary conditions.