Optimal Loading Path Research Articles

Topology optimisation of multiple robot links considering screw connections

AbstractThis paper presents a method for the lightweight design of robotic links subject to dynamic loads and requirements on the overall system stiffness. It includes (1) a decomposition scheme to enable separate component optimization and (2) an approach based on topology optimization for optimal load path design of screw connections. The approach reduces computing cost and mass of designs with screw connections.

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. This framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration.Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

Multi-objective optimization of loading path for sheet hydroforming of tank bottom

As a critical component of the propellant tank, the tank bottom is subjected to complex loads such as internal pressure and vibration and has high requirements for structural load-bearing capacity. Hydroforming deep drawing is one of the techniques for the integral forming of the tank bottom. As the tank bottom is a large-size thin-walled structure, defects such as cracks and wrinkles are prone to occur during the hydroforming deep drawing process. Aiming at reducing these defects, the hydraulic pressure loading path and blank holder force loading path of the hydroforming deep drawing process are studied, and a multi-objective optimization method is proposed to improve the surface accuracy and thickness distribution uniformity of the tank bottom. The complex loading path curve optimization problem is transformed into a functional relationship between hydraulic pressure and blank holder force with time. The hydraulic pressure and blank holder force at each time node are used as design variables, and the maximum wall thickness reduction rate, rupture trend factor, wrinkle height, and wrinkle trend factor are used as optimization targets. The radial basis function (RBF) neural network is used to establish the approximate model between the loading path and the optimization target, and the multi-objective particle swarm optimization (MOPSO) algorithm is used to optimize the solution. Taking the hemispherical tank bottom as an example, the optimal hydraulic pressure loading path and blank holder force loading path are obtained, and the quality of the formed part is improved.

Joining of Metal–Plastic Composite Layered Tubes by Hydroformed Threaded Coupling

Abstract Metal–plastic composite tubular structures that combine the high strength and stiffness of metallic tubes with the lightweight and flexible properties of plastic tubes, exhibit considerable potential to provide lightweight structures with improved performance compared to conventional monolithic tubular parts. However, the lack of well-confirmed technologies for connecting metal–plastic composite tubes that can ensure good structural stability and strength has proven problematic in actual applications. In this study, an innovative mechanical joining process via a hydroformed threaded coupling is proposed to achieve the successful joining of a metal–plastic composite layered tube (CLT). For the threaded connection, the CLT with an internal thread to act as a sleeve and the coupling tube with an external thread to act as a screw were joined together. A three-layer CLT composed of AISI 304 stainless steel/polyvinyl chloride (PVC)/AISI 304 stainless steel was investigated by free bulging and thread hydroforming. For successful forming into a threaded CLT, the optimal loading path was designed using analytical forming pressure and numerical contracting stroke. The mechanical tests based on compression and lateral three-point bending tests provided several key indicators for the quantitative performance of the thread-coupled parts. The reliability and applicability of the threaded coupling confirmed that the proposed joining process has strong potential for successful utilization in connecting metal–plastic composite tubes for structural applications.

An Innovative Approach of Parameter Loading Path Design for Grain Refinement and Its Application in Ni80A Superalloy.

In order to obtain the desired mechanical properties of products, an innovative method of loading parameter designs for acquiring the desired grain refinement is proposed, and it has been applied in the compression process of Ni80A superalloy. The deformation mechanism maps derived from processing maps based on the Dynamic Materials Model (DMM) theory were constructed, since the critical indicator values corresponding to dynamic recrystallization (DRX) and dynamic recovery (DRV) mechanisms were determined. The processing-parameter domains with DRX mechanisms were separated from the deformation mechanism map, while such domains were chaotic and difficult to apply in innovative parameter loading path design. The speed-loading path derived from strain rate-loading path in a compression process was pursued. The grain refinement domains are discretized into a finite series of sub-domains with clear processing parameters, and the optimal strain rate of each sub-domain is determined by step-by-step finite element simulation. A 3D response surface of the innovative optimal loading path of strain rate was fitted by interpolating methods. Finally, the isothermal compression experiments for Ni80A superalloy were conducted, and the microstructure observations indicated that the desired grain refinement was achieved. This innovative method of parameter loading path design contributes to the microstructure adjustment of the alloys with DRX mechanism.

Optimization of the rod forces in the reticular support structure of JUNO central detector

The structure of Jiangmen Underground Neutrino Observatory (JUNO) central detector is a complex structure subjected to a complex environment. The inner continuous acrylic spherical shell is connected to the outer reticulated stainless-steel (SS) shell through SS rods, and all these structural components are supported by an SS supporting frame. The inner shell is subjected to considerable buoyancy since the detection liquid inside the inner shell has less density than the outside water. Optimization of load path of such an underground structure subjected to buoyancy and pressure loads is difficult due to these complex situations, and in this paper, we tackle the problem of finding the optimal load path to minimize the rod forces. We adopt three types of design variables relevant to the load path, i.e., rod locations, chimney liquid level, and disc spring stiffness. Specifically, B-spline function is adopted to map the rod locations so as to significantly reduce the number of variables, and the chimney liquid level that influences the pressure distribution is taken as a new type of design variable. Subsequently, a numerical method combining the finite element analysis and a derivative-free optimization algorithm is proposed. Based on the optimization results, influences of the design variables, including their types, number, and initial values, on the optimal solutions are discussed in depth. The results suggest that the chimney liquid level and disc spring stiffness have a global effect of shifting rod force distribution, while distribution of rod forces strongly depends on the rod locations. The proposed method is shown to be effective to find an optimal load path of a complex spherical shell structure under various nonlinear constraints.

Separation of dynamic recrystallization parameter domains from a chaotic system for Ti–6Al–4V alloy and its application in parameter loading path design

In order to acquire uniform and refined microstructures for Ti–6Al–4V alloy, the parameter loading path design plays a crucial role. Here, it is pursued to separate dynamic recrystallization parameter domains from a chaotic parameter system. A succession of isothermal compression tests in a temperature range of 1023–1323 K and strain rate range of 0.01–10 s−1 were performed to obtain the basic computation data. The processing maps were constructed, and the mapping relationships between microstructural mechanisms and power dissipation efficiency indicator (η) in such maps were identified by verification of microstructural observations. Then the inner relationships between processing parameters and microstructural mechanisms were mapped as a three-dimensional (3D) space, from which the grain refinement parameter domains with dynamic recrystallization mechanism were separated. But these domains were still chaotic, so finite element (FE) simulations were used to scatter and clear this system. The optimal parameter loading paths were determined. Five verification experiments with different varying strain rates were performed, and the grain refinement was more obvious than any constant strain rates. One of the optimization results shows that the original grains with average size of 200 μm are refined as 9.7 μm, while at a constant strain rate the original grains are refined as 22.3 μm.

Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

Myocardium possesses a hierarchical structure that results in complex three-dimensional (3D) mechanical behavior, forming a critical component of ventricular function in health and disease. A wide range of constitutive model forms have been proposed for myocardium since the first planar biaxial studies were performed by Demer and Yin (J. Physiol. 339 (1), 1983). While there have been extensive studies since, none have been based on full 3D kinematic data, nor have they utilized optimal experimental design to estimate constitutive parameters, which may limit their predictive capability. Herein we have applied our novel 3D numerical-experimental methodology (Avazmohammadi et al., Biomechanics Model. Mechanobiol. 2018) to explore the applicability of an orthotropic constitutive model for passive ventricular myocardium (Holzapfel and Ogden, Philos. Trans. R. Soc. Lond.: Math. Phys. Eng. Sci. 367, 2009) by integrating 3D optimal loading paths, spatially varying material structure, and inverse modeling techniques. Our findings indicated that the initial model form was not successful in reproducing all optimal loading paths, due to previously unreported coupling behaviors via shearing of myofibers and extracellular collagen fibers in the myocardium. This observation necessitated extension of the constitutive model by adding two additional terms based on the I8(C) pseudo-invariant in the fiber-normal and sheet-normal directions. The modified model accurately reproduced all optimal loading paths and exhibited improved predictive capabilities. These unique results suggest that more complete constitutive models are required to fully capture the full 3D biomechanical response of left ventricular myocardium. The present approach is thus crucial for improved understanding and performance in cardiac modeling in healthy, diseased, and treatment scenarios.

Deformation characteristics in hydro-mechanical forming process of thin-walled hollow component with large deformation: experimentation and finite element modeling

The automobile exhaust manifold regularly has a multi-valved shape that used to be formed by the combination of stamping and welding. The current study intended to investigate and develop a tube hydro-mechanical forming (THMF) process to form an integral automobile exhaust manifold that has the characters of large deformation and small corner. It included three stages such as pre-forming stage, die-forming stage, and calibration stage. In addition, the non-feasibility of one-step hydroforming process was proved by FE modeling and experimental for the target component. An optimal loading path was obtained through the principle of dichotomy for pre-forming stage and die-forming stage, corresponding to the maximum thinning ratio of 19.7% and 13.27% respectively. The variation of stress and strain states were analyzed for the whole process. As a consequent, the thickness distribution exhibited a V-shaped along axial direction at each stage, while a fluctuated distribution after die-forming was presented along radial direction in the multi-valved area. For the final component, a maximum thinning ratio of 28.53% and the large deformation above 60% obtained from FE modeling kept a reasonable agreement with that achieved from experiments. It showed that THMF has advantages of not only decreasing the internal pressure but also improving the formability of tube.

Tailor layered tube hydroforming for fabricating tubular parts with dissimilar thickness

To produce highly functional tubular parts with locally different properties, tailor welded tubes (TWTs), which are made by tube-to-tube welding of tubes having different thicknesses or mechanical properties, are hydroformed. Notwithstanding the numerous applications of TWT hydroforming processes, TWT presents some disadvantages and considerable risk owing to the presence of a weld seam. This study proposes and characterizes the tailor layered tube (TLT) hydroforming process, which can fabricate hollow tubular parts with dissimilar thicknesses by using TLTs without welding. The proposed TLT hydroforming process was implemented and characterized both numerically and experimentally to validate its feasibility. The optimal loading path to prevent defects including insufficient bulging and wrinkle were analytically determined and verified by experiments. The deformation behaviors of TLT were also characterized at various processing parameters. The results demonstrate that the proposed TLT hydroforming process can be a feasible alternative for achieving tailored properties even with dissimilar thicknesses, with high reliability.

Loading path optimization of T tube in hydroforming process using response surface method

In this paper, the 3D drawing software UG is used to establish the geometric modeling of T tube for hydroforming process, and the software DYNAFORM is used to simulate the forming performance of T-shaped tube under different loading paths to obtain the simulation value of forming performance parameters. Next, the response surface method is used to analyze the influence of the main factors on hydroforming formability. The loading path, including axial feeding, internal pressure, and backward displacement, and friction coefficient are included in the main factors; the minimum thickness value, the height of branch tube, and the radius of limiting circle angle are considered as important characteristics that govern the forming performance. According to the optimization evaluation criteria, the perturbation plots and the interaction effect of different test factors, the main factors are optimized, and the best value of loading path was selected. Finally, the comparison of simulation and experiment under the optimal loading path shows that the error between experiment and simulation is within 5%, indicating that the loading path optimization method has high accuracy and good feasibility.

Thickness improvement in hydroforming of a variable diameter tubular component by using wrinkles and preforms

A combination method of beneficial wrinkle and preform shape is proposed to solve the problem of non-uniform thickness distribution during hydroforming of a variable diameter tubular component. The effect of loading path for the hydroform part and the preform shape are simulated by LS-DYNA. At the same time, the wall thickness deviation of the maximum and minimum of the hydroformed part is considered as the optimal target and the loading path for the preform shape is optimized to obtain the beneficial wrinkles by response surface methodology. Simultaneously, hydroforming experiments were conducted to verify the simulation results. Study shows that the loading path plays an important role in the forming of the beneficial wrinkles, which influence the cracking and the wrinkling defects. Only the loading path is appropriate can the beneficial wrinkles be formed and the wrinkles are flattened in the subsequent calibrating process. Response surface methodology is an effective way to obtain the optimal loading path, and the desired loading path can be achieved by controlling the relationship of the axial feeding and the internal pressure.

Optimization of pressure paths in hydrodynamic deep drawing assisted by radial pressure with inward flowing liquid using a hybrid method

Hydroforming is a convenient method for applying fluid to produce parts with high strength-to-weight ratio. Hydrodynamic deep drawing assisted by radial pressure with inward flowing liquid process is considered as a type of hydroforming. In this method, radial and chamber pressures are two most important parameters. The values of these parameters at any moment play important roles on the quality of final part. In this study, based on a hybrid method, the chamber and radial pressure paths in hydrodynamic deep drawing assisted by radial pressure with inward flowing liquid process are optimized. In this method, an adaptive simulation that is integrated with the fuzzy control system with the artificial bee colony (ABC) algorithm is used to determine the optimized radial and chamber pressure paths. The achievement of a conical part with minimum thinning and without wrinkling has been defined as the optimization goal. The validity of radial and chamber pressure paths obtained from optimization algorithm is verified through an experiment. Results showed that utilization of the optimized loading path yields a part with lower maximum thinning and without wrinkling.

Optimization of loading path in hydroforming of parallel double branched tube through response surface methodology

In this work, the response surface methodology along with the finite element method was employed to optimize the loading path for hydroforming parallel double branched tube parts. A combination of experimental design, numerical simulations and regression analysis was utilized, to determine the mathematical models between objectives and design variables. Consequently, the effectiveness of the models was evaluated through variance analysis and was utilized to predict the behavior of the tube hydroforming process. The effects and corresponding interactions of the design variables on the parallel double branched tube hydroforming were illustrated and discussed. Moreover, the response surface methodology and desirability method were applied, in order to obtain the optimal loading path within the given optimization criteria. The optimized result was in good agreement with the experimental results.

Research on the optimization mechanism of loading path in hydroforming process

In this paper, the optimization mechanism of loading path in hydroforming process is researched. Firstly, the geometric model of an X-shaped tube is established by using 3D drawing software UG; the DYNAFORM software is used to simulate the forming performance of the X tube under different loading paths. The backward displacement is taken as the main factor of the loading path, and the loading path is presented in the form of three factor graphs; it can show the relationship of the main factors of the loading path visually, accurately, and precisely, which are axial feed, internal pressure, and back displacement. Secondly, the orthogonal test method is used to select the optimal loading path, and the back propagation (BP) neural network based on genetic algorithm is used to optimize the loading path of X tubes. Through synthetic consideration of the interrelation of the minimum wall thickness, the maximum wall thickness, the height of branch, and the contact area between branch tube and back punch, the average performance index function is established in the BP neural network control algorithm to optimize the learning efficiency and shorten the calculation time. Finally, verified by experiment, the optimization method of loading path for X tube hydroforming process could control the precision error of results between the simulation and the experiment within 5%, and has high accuracy and good feasibility.

Optimization Methodology for an Automotive Cross-Member in Composite Material

Optimization methods are useful and effective techniques for the design and development of components from the weight reduction point of view. This paper presents an optimization methodology applied to the front cross-member of a Maserati chassis for metal replacement application with the objective of the minimization of the mass of the structure using composite materials. Firstly, a topological optimization of the front side of the vehicle is performed, and the available design space is considered to determine the optimal load path of the design volume and, consequently, to assess a preliminary geometry of the component under scrutiny. Secondly, free-size optimization of the preliminary cross-member design is developed, initially neglecting and subsequently considering the manufacturing constraints. In addition, a linear analysis of the cross-member, modeled as a rigid component, is carried out to evaluate the maximum contribution of this component on the structural performance of the front side of the vehicle. Finally, size and shuffle optimizations are carried out on the new design concept to determine the number and the thickness of the composite plies, and the optimal stacking sequence, respectively, in order to fulfill the structural requirements. A comparison between the new composite structure and the aluminium Maserati cross-member is presented.

Controlling of material flow in the quasi-bulk forming of thin-walled corrugated rings through optimization of contact pressure

Corrugated rings made of difficult-to-deform superalloy sheet with extremely thin wall are hardly manufactured since the forming processes are rather sensitive to parameters, such as axial feeding, cavity pressure, contact pressure, and so forth. The quasi-bulk forming method proposed in the author’s previous work, which gets rid of axial compression, was demonstrated to be an effective solution. In this work, forming strategy based on the controlling of material flow in this process is further developed. Since the pressure-carrying medium (i.e., viscous medium) is of high viscosity, the sealing pressure of this process is lowered down in comparison with that of forming processes utilizing nonviscous fluid as forming medium. The contact pressure at blank ends becomes adjustable as a result. Effects of contact pressure at sealing/blank interface (Pm) on the blank draw-in were investigated numerically. An optimal load path of Pm was obtained. Regulatory mechanism of contact pressure was presented, and contact pressure was considered to be the resultant pressure caused by the static pressure (Ps) and cavity pressure (Pv). Thereafter, process optimization was conducted through adjusting the path of Pv to approximate to the optimal path of Pm. On the basis of that, geometrical parameters of die cavity were improved and forming experiments were conducted accordingly to form two sorts of nickel-based superalloy corrugated rings. Sufficient blank draw-in was observed and thickness thinning is acceptable. The forming strategy, which is based on the adjustment of contact pressure, was verified to be feasible to improve the manufacturability of thin-walled corrugated rings.

A probabilistic approach for optimising hydroformed structures using local surrogate models to control failures

A probabilistic approach is proposed to optimise hydroformed structures by taking into account the potential variabilities. An efficient implementation requires an appropriate strategy for uncertainty representation and propagation. Moreover, the probability of failure associated to each failure mode must be accurately estimated. To this end, the failure modes are controlled locally only at the highly strained regions which reduces the problem complexity and increases the precision of the generated surrogate models. In this study, finite element simulations with material formability diagrams are used to predict the critical zones in which failure modes may initiate. The predicted zones agree well with the experimental and numerical simulations. By this simplification, the optimisation problem is formulated differently while retaining the relevant physical features of the process. To illustrate this strategy, tee-shaped tube hydroforming process is proposed due to its complexity to demonstrate the benefits of the probabilistic approach. The optimisation problem is formulated within deterministic and probabilistic frameworks to determine the optimal loading paths. It will be shown that probabilistic optimum allows better process mechanics and improved thickness distribution in the hydroformed tube. This approach can be extended to other metal forming processes and easily implemented for industrial products within reasonable computational time.

Optimizing loading path and die linetype of large length-to-diameter ratio metal stator screw lining hydroforming

In order to meet the high temperature environment requirement of deep and superdeep well exploitation, a technology of large length-to-diameter ratio metal stator screw lining meshing with rotor is presented. Based on the elastic-plasticity theory, and under the consideration of the effect of tube size, material mechanical parameters, friction coefficient and loading paths, the external pressure plastic forming mechanical model of metal stator screw lining is established, to study the optimal loading path of metal stator lining tube hydroforming process. The results show that wall thickness reduction of the external pressure tube hydroforming (THF) is about 4%, and three evaluation criteria of metal stator screw lining forming quality are presented: fillet stick mold coefficient, thickness relative error and forming quality coefficient. The smaller the three criteria are, the better the forming quality is. Each indicator has a trend of increase with the loading rate reducing, and the adjustment laws of die arc transition zone equidistance profile curve are acquired for improving tube forming quality. Hence, the research results prove the feasibility of external pressure THF used for processing high-accuracy large length-to-diameter ratio metal stator screw lining, and provide theoretical basis for designing new kind of stator structure which has better performance and longer service life.

Feasibility study on optimized process conditions in warm tube hydroforming

Feasibility study has been performed to estimate the optimized process conditions in warm tube hydroforming based on the simulated annealing optimization method. Precise prediction and control of process parameters play an important role in forming at warm conditions. Optimal pressure and feed loading paths are obtained for aluminium AA6061 tubes through the simulated annealing algorithm in conjunction with finite element simulations. Numerous axisymmetric geometries are investigated and the effects of expansion ratio, corner fillet to thickness ratio, and initial diameter to thickness ratio are studied. For the feasibility estimation, warm hydroforming experiments have been conducted on aluminum AA6061 under optimal designed conditions. The results show that the optimization procedure used in this research is a reliable and feasible tool in determination of optimal process conditions for the sound warm hydroforming process.