Multi-objective optimization of concave radial forging process parameters based on response surface methodology and genetic algorithm

Sun X., He X., Cao K.

Abstract In order to alleviate the problem of excessive stress and easy wear on the rotary swaging die during the process of rotary swaging high-strength tungsten wire, the die structure was changed, the transition taper was designed, and the structural parameters were optimized to achieve the purpose of reducing the stress and extending the life of the rotary swaging die. The results show that the improvement of the die structure can largely reduce the effective stress of the die, and it is found that the transition fillet has the greatest influence on the effective stress of the die, followed by the cone angle of the transition taper, and the length of the transition taper has the least effect on the effective stress of the die. Finally, the optimal die structure parameters after improvement were obtained by orthogonal experiments: the cone angle of transition taper is 4°, the length of transition taper is 10 mm, and the radius of transition fillet is 3 mm.

Cao J., Zhang J., Zhao F., Chen Z.

• A two-stage evolution strategy is proposed for solving multi-objective problem. • The convergence and diversity should be balanced in multi-objective optimization. • A local searching method can improve the diversity of solutions in the space. • Experimental results have been presented by using statistical method. The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution’s diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems.

Darki S., Raskatov E.Y.

The radial forging process (RFP) is an advanced technology that many scientists have recently been trying to optimize and improve in order to enhance the quality of products and save energy in manufacturing. However, controlling the process when employed on large products is very difficult due to the appearance of cracks. During RFP, a tube is repeatedly and continuously exposed to stroking and feeding. Thus, when the die comes into contact with the product, the rotational feed stops. Afterwards, when the hummers break contact with the tube, the axial and rotational feeds are applied simultaneously in order to obtain a good surface finish at a specific rotation angle feed. Implementing RFP is a costly and lengthy process largely done through trial and error. It depends on variables such as material temperature, rotation speed, rate of feed, parameters of die geometry, die pressure, and amplitude. Thus, a symmetric 3D model simulation has been conducted with commercial FEM software. The results include the cantors of residual stress (RS), strain velocity, and temperature. Equally, the contact forces have been measured as experimental results, and there is a good correspondence between the two types of results.

Li H., Wang K., Luo R., Zhu Z., Deng S., Luo R., Zhang J., Fang F.

Due to the current trend towards lightweight design in automotive industry, hollow stepped gear shafts for automobile and its radial forging process are widely investigated. Utilizing coupled finite element thermo-mechanical model, radial forging process of a hollow stepped gear shaft for automobile was simulated. The optimal combination of three process parameters including initial temperature, rotation rate and radial reduction was also selected using orthogonal design method. To examine the strain inhomogeneity of the forging workpiece, the strain inhomogeneity factor was introduced. The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft, respectively. Optimal forging parameters are determined as a combination of initial temperature of 780 °C, rotation rate of 21°/stroke and radial reduction of 3 mm.

Burns E., Newkirk J., Castle J., Creamer J.

Micro-slotting, a microscale relaxation residual stress measurement technique, has been shown in recent years to be a reliable method for measuring local residual stresses in metallic materials. This study demonstrates the unique application of the micro-slotting residual stress measurement technique for measuring near-edge tangential residual stresses around cold-expanded holes in Ti-6Al-4V plates. Knowledge of the near-edge elastic strains induced by the hole processing, in combination with plastic strain information obtained using electron backscatter diffraction, allowed for interpretation of fatigue life differences and crack growth behavior between the as-drilled and cold-expanded conditions. The similar crack initiation lives of the as-drilled and cold-expanded open-hole coupons were attributed to the similar elastic and plastic strains present at the hole edges. The subsequent crack growth resistance observed for the cold-expanded holes was a result of the large compressive residual stress region induced by cold expansion.

Ishkina S., Charni D., Herrmann M., Liu Y., Epp J., Schenck C., Kuhfuss B., Zoch H.

Infeed rotary swaging is a cold forming production technique to reduce the diameter of axisymmetric components. The forming is achieved discontinuously by a series of radial strokes that are spread over the shell of the part. Due to tolerances within the rotary swaging machine, these strokes perform individually and the resulting stroke pattern is not homogeneous with regards to circumferential and longitudinal distribution. Nevertheless, in combination with the high number of performed strokes and the large contact area between the dies and the part, the external part properties, such as diameter, roundness and surface roughness, show even values along the finished part. In contrast, strength-defining internal part properties, like microstructure and residual stress components, are more sensitive to the actual pattern and temporal sequence of the individual strokes, which is investigated in this study. The impact of process fluctuations during the conventional process, which are induced by the tolerances of machine tool components, was verified by numerical simulations, physical tests and measurements of residual stress distributions at the surface and at depth. Furthermore, a method is introduced to maintain the stroke following angle ∆φ at zero by flat dies, and thus the actual pattern and temporal sequence of the strokes was homogenized. The results show that the residual stress fluctuations at the surface could be controlled and reduced. Furthermore, it is demonstrated that the depth profile of the residual stresses at a distance of 300 µm from the surface developed independently from the process fluctuations.

Bora T.C., Mariani V.C., Coelho L.D.

This paper presents an improved non-dominated sorting genetic algorithm II (NSGA-II) approach incorporating a parameter-free self-tuning by reinforcement learning technique called learner non-dominated sorting genetic algorithm (NSGA-RL) for the multi-objective optimization of the environmental/economic dispatch (EED) problem. To evaluate the performance features, the proposed NSGA-RL approach is investigated on ten multi-objective benchmark functions. Besides, to evaluate the effectiveness of the proposed approach, the standard IEEE (Institute of Electrical and Electronics Engineers) of 30-bus network with six generating units (with/without considering losses) is adopted, with operating cost (fuel cost) and pollutant emission as two conflicting objectives to be optimized at the same time. In comparison to literature, it was observed that the proposed approach provides a better satisfaction level in conflicting objectives with well distributed Pareto front, in comparison with the classical NSGA-II method, and to other existing methods reported in the literature. The NSGA-RL was found to be comparable to them considering the quality of the solutions obtained, with the advantage of non-time spent for parameters tuning.

Moumi E., Wilhelmi P., Schenck C., Herrmann M., Kuhfuss B.

In rotary swaging, the material flow is not fully controlled by closure of the forming dies. This is especially noticeable in plunge rotary swaging of rod, where the workpiece is positioned into the forming zone und processed locally. As result, an uncontrolled elongation of the workpiece in axial direction takes place and an axial position shift of the workpiece relative to the dies occurs. This is a special challenge in production of linked micro parts, where single parts are interconnected in order to enable the handling as a strip and thereby a roll-to-roll production. The axial shift influences not only the subsequent positioning of neighbouring parts, but also the final geometry of the currently processed part. The presented investigation analyses the material flow during plunge micro rotary swaging on basis of in-process measurements of the workpiece shift on both sides of the forming zone as well as with the help of contour measurements of the processed parts. It is shown that the measured shift is strongly influenced by the workpiece clamping and fixation and that it can be controlled by applying low axial forces to the workpiece on one or both sides of the forming zone. Further, the geometry of the workpiece can be affected by these measures.

Wu Y., Dong X.

A general method for constructing admissible velocity fields without velocity discontinuities is proposed and applied to derive continuous and non-uniform velocity field for radial forging process. Compared with the previous velocity fields which are classified as parallel velocity fields or contain velocity discontinuities, this newly derived velocity field can describe more realistic mechanics of radial forging process. Based on this velocity field, an analytical model is developed by the upper bound approach. This model is verified by comparing the predicted forging load, displacement distribution and plastic strain with both published experimental data and results of the finite element simulation. To investigate the influences of radial reduction rate and axial feed on the strain inhomogeneity along the axial direction, the plastic strain distribution at the center of the workpiece is predicted. It is concluded that the radial reduction rate and the axial feed contribute to the strain magnitude and the degree of strain inhomogeneity respectively.

Zhou G., Ma Z., Li G., Cheng A., Duan L., Zhao W.

Possessing the unique properties of lower mass and higher performances, the structure with Negative Poisson’s Ratio (NPR) can be widely used in aerospace and vehicle industry. By combing the NPR structure filled core and the traditional crash box, a novel NPR crash box is first proposed in this work to improve the performances of the crash box. The performances of the novel NPR crash box are fully studied by comparing to the traditional crash box and the aluminum foam filled crash box. A parameterized model of the NPR crash box, which integrates the design parameters of the basic NPR cell structure, is built to improve the analysis and optimization efficiency, the accuracy of the parameterized model is also verified by comparing to traditional FEM model. Multi-objective optimization model of the NPR crash box is established by combining the parameterized model, optimal Latin square design method and response surface model approach. Non-dominated sorting genetic algorithm-II (NSGA-II) is then applied to optimize the design parameters of the basic NPR cell structure to improve the performances of the NPR crash box. The results indicate that the novel NPR crash box can improve the performances of the crash box remarkably and the combination of parameterized model and multi-objective genetic algorithms optimize the NPR crash box efficiently. The presented new method also serves as a good example for other application and optimization of NPR structure.

Zhu F., Wang Z., Lv M.

To control the precision forging product forming quality, a multi-objective optimization method for process parameters design was proposed by applying Latin hypercube design method and response surface model approach. Meanwhile, the deformation homogeneity and material damage of forging product was first presented for evaluating the forming quality. Then, as a case of study, the radial precision forging for a hollow shaft with variable cross section and wall thickness was carried out. The 3D rigid-plastic finite element (FE) model of the radial precision forging was established. The parameters on the forming quality evaluation function study were discussed to investigate the multi-objective optimization model. Non-dominated sorting genetic algorithm-II (NSGA-II) was adopted to obtain the Pareto-optimal solutions. A compromise solution was selected from the Pareto solutions by using the mapping method. Experiments with the same parameter settings were compared with the simulations. After conducting radial forging and mechanical property experimental study on the forging product by multi-objective optimization process parameters, the feasibility of the multi-objective optimization method for the precision forging product forming quality was verified.

Azari A., Poursina M., Poursina D.

The application of finite element method and intelligent systems techniques to predict the applied force during the radial forging process is studied. Radial forging is a unique process used for the precision forging of round and tubular components, with or without an internal profile. More than 800 radial forging machines are currently operating worldwide. Since the maximum forging force per die is constant, determining the die force before the process can prevent die damage and material wastage. Then, the results of the FE simulation are applied for two intelligent forecasting systems in artificial neural network and adaptive neuro-fuzzy inference system. Initial billet temperature, die inlet angle, feed rate, and reduction in cross-section are applied as input parameters, and radial forging force is applied as the output parameter. Finally, the results of these two intelligent systems are compared with the multiple regressions method. A sensitivity analysis is carried out to determine how the radial forging force is influenced by the input parameters.

Kroiß T., Engel U., Merklein M.

In this paper a comprehensive approach is presented for the consideration of the interactions between process, tool and machine during the design of cold forging tools and processes by simulation. The interactions occur due to the high forming loads in cold forging and yield considerable deflections of press and tooling system. These, in turn, influence the workpiece dimensions. The entire approach comprises an efficient determination of the deflection characteristic of stroke-controlled press and tooling system and its condensed modeling in combination with the FE simulation of a cold forging process. Building on that, an analytic process model is developed that is based on a set of variant simulations. It permits an optimization of the values of influencing parameters to achieve high workpiece accuracy without subsequent adjusting effort. Initially, the analytic process model required a high number of variant simulations. By acquiring knowledge on the specific process behavior in an analysis of effects and interactions a considerable reduction of simulation runs by a factor of almost 12 was achieved in the case study on full forward extrusion. The approach is supplemented by an analytic model of the die load. In addition, scatter and uncertainties of target values depending on the ones of the influencing parameters can be estimated by applying the Monte Carlo method to the analytic process model.

Sanjari M., Saidi P., Karimi Taheri A., Hossein-Zadeh M.

Utilizing the Finite Element Method (FEM), the strain field in the radial forging process of tube is calculated at different process conditions and compared with the experimental results achieved using the microhardness test. The effect of various process parameters such as friction, axial feed, back push and front pull forces and die angles on the strain field are investigated. Using the results of the analysis, it is shown that the deformation inhomogeneity, introduced by an Inhomogeneity Factor (IF), is maximum in the inner zone of tube, while the minimum and the maximum effective strains are appeared at the inner zone of tube and about the core of the tube thickness, respectively. Also, it was found that inhomogeneity decreases by increasing the die angle, decreasing the back push force and decreasing the friction factor.

Chen J., Chandrashekhara K., Mahimkar C., Lekakh S.N., Richards V.L.

Hot radial forging is used to reduce porosity and increase strength for large-diameter billets. The goal of this research is to study void closure behavior in the hot radial forging process. A nonlinear coupled finite element model is developed to investigate the deformation mechanism of internal void defects during the hot radial forging process. The model is formulated in a three-dimensional frame and a viscoplastic material model has been used to describe the material behavior subjected to large deformation and high temperature. A global–local technique is employed to obtain accurate solutions around the void region. The effects of void location, mandrel, die shape, and the reduction of the tube thickness on the final void reduction are systematically investigated. The predicted reductions for central longitudinal voids in hot upsetting and hot rolling processes are in good agreement with experimental findings. The simulation results provide a valuable procedure for the design of porosity reduction during the hot radial forging process.

Deng W., Song Z., Lei J., Luo K., Zhang Y., Yu M.

Raoufi K., Sutherland J.W., Zhao F., Clarens A.F., Rickli J.L., Fan Z., Huang H., Wang Y., Lee W.J., Mathur N., Triebe M.J., Desabathina S.S., Haapala K.R.

Advanced manufacturing is challenging engineering perceptions of how to innovate and compete. The need for manufacturers to rapidly respond to changing requirements and demands; obtain, store, and interpret large volumes of data and information; and positively impact society and our environment requires engineers to investigate and develop new ways of making products for flexible and competitive production. In addition to the associated operational, technological, and strategic advantages for industry, advanced manufacturing creates educational, workforce, and market opportunities. Thus, this literature review is aimed at investigating the current state and emerging trends in advanced manufacturing. Specifically, this study addresses advances in manufacturing process technologies, focusing on shaping processes (mass reducing, mass conserving, and joining) as well as non-shaping processes (heat treatment and surface finishing), and metal-based additive manufacturing. This literature review finds myriad efforts have been undertaken by researchers in industry, academia, and government labs from around the world, which have supported the development and implementation of new process technologies to improve manufacturing systems extending from unit process and shop floor operations to facility and supply chain management activities. However, as evidenced by recent and emerging global challenges in energy, critical materials, and health care, the manufacturing industry must continue the innovative development of advanced materials, manufacturing processes, and systems that ensure cost-efficient, rapidly flexible, high-quality, and responsible production of goods and services.

Xu W., Wang Z., Zhu X., Zhang B., Zheng Z., Lv M., Wang H.

Cold radial forging (CRF) is recognized as one of the most effective manufacturing processes for the production of hollow components. Nonetheless, even minor alterations in the alloy composition during the cold deformation processing phase can significantly influence the material’s manufacturability. This study addresses the challenges associated with high optimization costs, complex data acquisition, and the prediction of forming quality when integrating multiple processes, such as heat treatment and material composition. We propose the development of an intelligent predictive model aimed at forecasting the forming quality of the 20CrMnTiH alloy during CRF, utilizing a back-propagation neural network optimized by genetic algorithm (GA-BP). The assessment of forming quality is based on parameters such as damage, residual stress, and equivalent strain. The study investigates the impact of alloy composition and spheroidal annealing (SA) process parameters on forming quality. The performance of the three GA-BP prediction models is superior in terms of the coefficient of determination (R2) and mean square error (MSE), when compared to a conventional BP neural network and four other machine learning techniques, including gradient-boosted decision trees, random forests, support vector regression, and logistic regression. A comprehensive comparative analysis of the evaluation metrics across all three prediction models, alongside multi-objective optimization, indicates that the Pareto solution set generated by NSGA-II exhibits optimal distribution uniformity. The optimized process parameters (0.17%C-0.24%Si-0.81%Mn-0.03%P-0.03%S-1.15%Cr-0.05%Ni-0.06%Ti, Te: 60℃, ATi: 4.57 h) resulted in a reduction of residual stresses by 12%, equivalent strain by 15%, and component damage by 30%. The results demonstrate that the methodology proposed in this paper not only enhances the quality of CRF molding but also significantly improves the accuracy of the predictive model for forming quality.

Yadav S., Gautam S.K., Upadhyaya R., Singh N.K., Singh K.K., Namdev A.

Abstract This paper presents a novel approach to optimizing the die design for forging used in connecting rods. The combination of Taguchi (orthogonal L9) and the finite element method (FEM) was employed to achieve this optimization. The main objective of this study was to analyze the impact of design parameters on die-filling and yield improvement. The orthogonal L9 design was generated with three input parameters and one response variable. These input parameters were derived from the design dimensions of the forging tool, specifically flash land, draft, and flash thickness. The response variable was the maximum yield percentage, which was obtained through finite element simulations of the forging processes. By conducting an orthogonal analysis, the relationships between the response variable and the input parameters were established. The simulation results were then used to compare the outcomes of two different designs. It was found that Preform one outperformed the other design, achieving an impressive yield of 88% at a forging load of 1.37 × 104 N, with complete die filling observed.

Hawryluk M., Polak S., Rychlik M., Barełkowski A., Jakuć J., Marzec J.

This article presents research results regarding the development of a new manufacturing technology for an element assigned to belt conveyor flights in the extractive industry through hot die forging (of a forging with a double-sided flange) instead of the currently realized process of producing such an element by welding two flanges onto a sleeve or one flange onto a flange forging. The studies were conducted to design an innovative and low-waste technology, mainly with the use of numerical modelling and simulations, partially based on the current technology of producing a flange forging. Additionally, during the development of the forging process, the aspect of robotization was considered, both in respect of the forging tools and the process of transportation and relocation of forging between the impressions and the forging aggregates. A thermo-mechanical model of the process of producing a belt conveyor flight forging with deformable tools was elaborated by means of the Forge 3NxT program. The results of the conducted numerical modelling made it possible, among other things, to develop models of forging tools ensuring the proper manner of material flow and filling of the impressions, as well as temperature and plastic deformation distributions in the forging and also the detection of possible forging defects. For the technology elaborated this way, the tools were built together with a special instrument for flanging in the metal, and technological tests were performed under industrial conditions. The produced forgings were verified through a measurement of the geometry, by way of 3D scanning, as well as the hardness, which definitively confirmed the properness of the developed technology. The obtained technological test results made it possible to confirm that the elaborated construction, as well as the tool impressions, ensure the possibility of implementing the designed technology with the use of robotization and automatization of the forging process.

Zhang Z., Wu F., Wu A.

To address the issue of local optima encountered during the multi-objective optimization process with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, this paper introduces an enhanced version of the NSGA-II. This improved NSGA-II incorporates polynomial and simulated binary crossover operators into the genetic algorithm’s crossover phase to refine its performance. For evaluation purposes, the classic ZDT benchmark functions are employed. The findings reveal that the enhanced NSGA-II algorithm achieves higher convergence accuracy and surpasses the performance of the original NSGA-II algorithm. When applied to the machining of the high-hardness material 20MnCrTi, four algorithms were utilized: the improved NSGA-II, the conventional NSGA-II, NSGA-III, and MOEA/D. The experimental outcomes show that the improved NSGA-II algorithm delivers a more optimal combination of process parameters, effectively enhancing the workpiece’s surface roughness and material removal rate. This leads to a significant improvement in the machining quality of the workpiece surface, demonstrating the superiority of the improved algorithm in optimizing machining processes.

Wang Y., Xiong L., Feng D., Zhao S., Guo Y.

With the wide application potential of wrought aluminium alloy in aerospace, automobile and electronic products, high-quality aluminium bars prepared by the radial forging (RF) process have received extensive attention. Penetration performance refers to the depth of radial plastic deformation of forgings, which is the key factor in determining the quality of forging. In this work, the penetration performance of the radial forging process for 6063 wrought aluminium bars is investigated by simulation using FORGE software. The minimum reduction amount of the hammer is calculated based on the forging penetration theory of forging. The influence of process parameters including forging ratio (FR) and billet temperature on the effective stress and hammer load in the RF process are investigated. The RF-deformed billet is then produced with the optimal process parameters obtained from the simulation results. The average grain size of aluminium alloy semi-solid spherical material is used to evaluate the forging penetration. Simulation results showed that the effective strain at the edge and the centre of the RF-deformed billet gradually increases, but the increasing speed of the effective strain at the edge becomes low. The hammer load first decreases quickly and then gradually maintains stability by increasing the FR. It is found that low billet temperature and high FR should be selected as appropriate process parameters under the allowable tonnage range of RF equipment. Under an isothermal temperature of 630 °C and a sustaining time of 10 min, the difference in the average grain dimension between the edge and the centre positions of the starting extruded blank is 186.43 μm, while the difference in the average grain dimension between the edge and the centre positions of the RF-deformed blank is 15.09 μm. The improvement ratio of penetration performance for the RF-deformed blank is obtained as 91.19%.