Finite Element Mesh Research Articles

Model and mesh selection from a mCRE functional in the context of parameter identification with full-field measurements

Abstract In this paper, we propose a general deterministic framework to question the relevance, assess the quality, and ultimately choose the features (in terms of model class and discretization mesh) of the employed computational mechanics model when performing parameter identification. The goal is to exploit both modeling and data at best, with optimized model accuracy and computational cost governed by the richness of available experimental information. Using the modified Constitutive Relation Error concept based on reliability of information and the construction of optimal admissible fields, we define rigorous quantitative error indicators that point out individual sources of error contained in the identified computational model with regards to (noisy) observations. An associated adaptive strategy is then proposed to automatically select, among a hierarchical list with increasing complexity, some parameterized mathematical model and finite element mesh which are consistent with the content of experimental data. In addition, the approach is computationally enhanced by the complementary use of model reduction techniques and specific nonlinear solvers. We focus here on experimental information given by full-field kinematic measurements, e.g. obtained by means of digital image correlation techniques, even though the proposed strategy would also apply to sparser data. The performance of the approach is analyzed and validated on several numerical experiments dealing with anisotropic linear elasticity or nonlinear elastoplastic models, and using synthetic or real observations.

A high-order accurate moving mesh finite element method for the radial Kohn–Sham equation

In this paper, we introduce a highly accurate and efficient numerical solver for the radial Kohn–Sham equation. The equation is discretised using an up to 10th order finite element method, with its performance further improved by incorporating a parameter-free moving mesh technique. This approach greatly reduces the number of elements required to achieve the desired precision. In practice, the mesh redistribution involves no more than three steps, ensuring the algorithm remains computationally efficient. Remarkably, with a maximum of 13 elements, we successfully reproduce the NIST database results for elements with atomic numbers ranging from 1 to 92.

Personalized Heart Digital Twins Detect Substrate Abnormalities in Scar-Dependent Ventricular Tachycardia.

Current outcomes from catheter ablation for scar-dependent ventricular tachycardia (VT) are limited by high recurrence rates and long procedure durations. Personalized heart digital twin technology presents a noninvasive method of predicting critical substrate in VT, and its integration into clinical VT ablation offers a promising solution. The accuracy of the predictions of digital twins to detect invasive substrate abnormalities is unknown. We present the first prospective analysis of digital twin technology in predicting critical substrate abnormalities in VT. Heart digital twin models were created from 18 patients with scar-dependent VT undergoing catheter ablation. Contrast-enhanced cardiac magnetic resonance images were used to reconstruct finite-element meshes, onto which regional electrophysiological properties were applied. Rapid-pacing protocols were used to induce VTs and to define the VT circuits. Predicted optimum ablation sites to terminate all VTs in the models were identified. Invasive substrate mapping was performed, and the digital twins were merged with the electroanatomical map. Electrogram abnormalities and regions of conduction slowing were compared between digital twin-predicted sites and nonpredicted areas. Electrogram abnormalities were significantly more frequent in digital twin-predicted sites compared with nonpredicted sites (468/1029 [45.5%] versus 519/1611 [32.2%]; P<0.001). Electrogram duration was longer at predicted sites compared with nonpredicted sites (82.0±25.9 milliseconds versus 69.7±22.3 milliseconds; P<0.001). Digital twins correctly identified 21 of 26 (80.8%) deceleration zones seen on isochronal late activation mapping. Digital twin-predicted sites display a higher prevalence of abnormal and prolonged electrograms compared with nonpredicted sites and accurately identify regions of conduction slowing. Digital twin technology may help improve substrate-based VT ablation. URL: https://www.clinicaltrials.gov; Unique identifier: NCT04632394.

Optimization of the finite element meshing for the fabrication of a M3x12x0.5 screw, in 3D printing

Meshing optimization in the finite element method (FEM) is key to designing mechanical components such as screws. This study focuses on the M3x12x0.5 screw, improving its performance and durability through the appropriate selection of meshing parameters. FEM software was used to analyze its behavior under different loads, comparing it with a 3D printed model. The results showed improvements in the accuracy of predictions about resistance, deformation and stress distribution, allowing the design to be optimized. This highlights the relevance of simulation tools in the development of mechanical components.

Design and analysis of one-pad gas foil bearing with three-part gas film produced by adjusting the length of sliding beams

The one-pad sliding-beam gas foil bearing is studied in this paper. The size of the multiple sliding beams in the bearing is adjusted, which results in dividing the gas film pressure into three parts. The finite element mesh of the bottom foil is established based on rectangle and triangle elements, and the finite element model of sliding beams is established based on the plate element with five degrees of freedom. The separation and friction of the foils are considered, and the model of the foils is established based on minimum potential energy theorem and Newton–Raphson method. The mechanical model of the bearing is finally established by fluid-solid interaction. The calculation scheme is programmed by MATLAB, and the reliability of the model is verified by experiments. The numerical results show that with the increase of preload or the decrease of nominal clearance, the gas film pressure is divided into three parts gradually. Compared with the three-pad structure, the bearing in this paper has better bearing capacity. With nominal clearance being 30 µm, the maximum bearing capacity is obtained with a preload of 10 µm, and the maximum direct damping is obtained with a preload of 20 µm. A proper layout of sliding beams can improve the bearing capacity, but it could also weaken the dynamic performance. The variation of the initial bending stiffness distribution of sliding beams has little impact on the dynamic performance, but it can significantly affect the bearing capacity. When the stiffness of sliding beams of axial middle face is larger than that of the end face, the bearing capacity is obviously improved.

Application of the Phase Field Approach for Crack Propagation in Viscoelastic Solid Materials under Thermal Stress: A Case Study of Solder Fracturing

To date, solder has been a crucial component for interconnecting circuit boards (PCBs) and electronic components in the electronics industry. However, solder faces certain challenges, such as cracking due to thermal changes. This paper investigates solder cracking under thermal expansion. We employ a phase field model to study crack propagation under thermal stress in a square domain and in solder with a fillet shape. The model is based on those proposed by Takaishi-Kimura and Alfat, where the stress and strain tensors are modified to account for variations in the temperature field. In this study, we consider the solder material to be viscoelastic, while the other materials are treated as homogeneous and isotropic. A numerical example is computed using the adaptive mesh finite element method, with the code implemented in FreeFEM software. The results of this study are in good agreement with previous numerical and experimental findings.

Coupling of Discontinuous Galerkin and Pseudo-Spectral Methods for Time-Dependent Acoustic Problems

Many realistic problems in computational acoustics involve complex geometries and sound propagation over large domains, which requires accurate and efficient numerical schemes. It is difficult to meet these requirements with a single numerical method. Pseudo-spectral (PS) methods are very efficient, but are limited to rectangular shaped domains. In contrast, the nodal discontinuous Galerkin (DG) method can be easily applied to complex geometries, but can become expensive for large problems. In this paper, we study a coupling strategy between the PS and DG methods to efficiently solve time-domain acoustic wave problems. The idea is to combine the strengths of these two methods: the PS method is used on the part of the domain without geometric constraints, while the DG method is used around the PS region to accurately represent the geometry. This combination allows for the rapid and accurate simulations of large-scale acoustic problems with complex geometries, but the coupling and the parameter selection require great care. The coupling is achieved by introducing an overlap between the PS and DG regions. The solutions are interpolated on the overlaps, which allows the use of unstructured finite element meshes. A standard explicit Runge–Kutta time-stepping scheme is used with the DG scheme, while implicit schemes can be used with the PS scheme due to the peculiar structure of this scheme. We present one- and two-dimensional results to validate the coupling technique. To guide future implementations of this method, we extensively study the influence of different numerical parameters on the accuracy of the schemes and the coupling strategy.

PREDICTION OF WELD-ABILITY CHARACTERISTICS OF DUAL-PHASE STEEL HCT600X BY NUMERICAL SIMULATION

Dual-phase (DP) steel plates are characterized by very good absorption capacity, so they are used in the automotive industry for body deformation zone parts. They are attached to the frame of the car-body by welding. Laser welding of dual-phase steels is gaining increasing importance in the automotive industry. In the present paper, the possibility of predicting the strength and deformation characteristics of laser-welded HCT600X steel sheets was analyzed based on experiments and numerical simulations. Butt joints were formed by YLS-5000 laser in two variants, which differ by laser power input and welding speed. The HCT600X- HCT600X with welded joint was analyzed based on microstructure and mechanical tests. The tensile strength and hardness of the welded joints were greater than those of the base material (BM). The microstructure of the weld metal (fusion zone) consisted of martensite, austenite and bainite, in the heat-affected zone it consisted of a mixture of martensite, bainite, ferrite and residual austenite. In numerical simulation, the finite-element mesh was created by linear volume elements refined in the weld region, and the Gauss model of the surface heat source was applied when modelling laser welding. The results of numerical simulation of the microstructure and selected mechanical properties were correlated with the experimental results.

Determination of Strength Parameters of Composite Reinforcement Consisting of Steel Member, Adhesive, and Carbon Fiber Textile.

The main aim of the study was the determination of the strength parameters of composite bonded joints consisting of galvanised steel elements, an adhesive layer, and Carbon-Fiber-Reinforced Plastic (CFRP) fabric. For this purpose, shear laboratory tests were carried out on 60 lapped specimens composed of 2 mm thick hot-dip galvanised steel plates of S350 GD. The specimens were overlapped on one side with SikaWrap 230 C carbon fibre textile (CFT) using SikaDur 330 adhesive. The tests were carried out in three series that differed in overlap length (15 mm, 25 mm, and 35 mm). A discussion on the failure mechanism in the context of the bonding capacity of the composite joint was carried out. We observed three forms of joint damage, namely, at the steel-adhesive interface, fibre rupture, and mixed damage behaviour. Moreover, an advanced numerical model using the commercial finite element (FE) program ABAQUS/Standard and the coupled cohesive zone model was developed. The material behaviour of the textile was defined as elastic-lamina and the mixed-mode Hashin damage model was implemented with bi-linear behaviour. Special attention was focused on the formulation of reliable methodologies to determine the load-bearing capacity, failure mechanisms, stress distribution, and the strength characteristics of a composite adhesive joint. In order to develop a reliable model, validation and verification were carried out and self-correlation parameters, which brought the model closer to the laboratory test, were proposed by the authors. Based on the conducted analysis, the strength characteristics including the load-bearing capacity, failure mechanisms, and stress distribution were established. The three forms of joint damage were observed as steel-adhesive interface failure, fibre rupture, and mixed-damage behaviour. Complex interactions between the materials were observed. The most dangerous adhesive failure was detected at the steel and adhesive interface. It was also found that an increase in adhesive thickness caused a decrease in joint strength. In the numerical analysis, two mechanical models were employed, namely, a sophisticated model of adhesive and fabric components. It was found that the fabric model was very sensitive to the density of the finite element mesh. It was also noticed that the numerical model referring to the adhesive layer was nonsensitive to the mesh size; thus, it was regarded as appropriate. Nevertheless, in order to increase the reliability of the numerical model, the authors proposed their own correlation coefficients α and β, which allowed for the correct mapping of adhesive damage.

Co‐Simulation Interface Model Reduction for Large‐Scale Coupled Simulations

ABSTRACTThe paper presents a novel approach for reducing the co‐simulation interface representation between multiple large‐scale models. The methodology leverages model order reduction through component mode synthesis in some specific small deformation flexible multibody formulations that yield a constant transformation matrix between Cartesian coordinates and general multibody coordinates, such as the flexible natural coordinates formulation or the generalized component mode synthesis. The constant transformation matrix stemming from these techniques is further modified using modified Gram–Schmidt orthonormalization and the effective independence methodology to create a constant interface model reduction matrix. This matrix effectively connects a minimal set of interface nodes to the entire nodal domain, while simultaneously projecting the forces acting on the entire nodal domain onto the interface nodes. Notably, the proposed methodology scales the size of the required co‐simulation interface representation with the considered set of mode shapes rather than the size of the numerical finite element mesh. This co‐simulation interface model reduction strategy not only renders large distributed load models compatible with the Functional Mock‐Up Interface but also extends its applicability to any structural model beyond the flexible multibody scope, provided that deformations remain relatively small. Numerical validation with a simply supported beam, connected to springs at each node, demonstrates that the interface model reduction error is significantly smaller than the co‐simulation error. This suggests that substantial interface model reduction can be achieved without compromising accuracy. Moreover, additional numerical validation performed with a rotor‐drum model showcases the versatility and scalability of the proposed approach, particularly in addressing dynamic structural systems.

A novel framework for fatigue hotspot localization and damage assessment of multi-defect marine structures under random vibration

In ocean engineering, assessing vibration-induced fatigue under random loads is critical, particularly for ocean structures with multiple defects, as fatigue is highly sensitive to local structural flaws. Recently, incorporating structural dynamic characteristics into vibration fatigue assessments has emerged as a significant trend and formidable challenge, involving three key obstacles: precise localization of fatigue hotspots, extraction of key modes, and determination and integration of modal damage contributions. This paper introduces a novel framework for fatigue hotspot localization and damage assessment in the context of random vibration fatigue in ocean structures. By initially identifying fatigue hotspots and hot regions using stress mode shapes, refining the finite element mesh in hot regions, and conducting reanalysis, the exact locations of fatigue hotspots can be determined, enabling structural dimensionality reduction. The introduction of a modal damage contribution factor allows for the evaluation of each mode's damage contribution and the identification of key modes, further facilitating modal reduction. For the precisely localized fatigue hotspots, the proposed method combines the damage contributions of key modes, enabling rapid and accurate assessment of fatigue damage under random vibration loads. Finite element case studies and vibration fatigue test results demonstrate that the proposed framework effectively addresses the challenges of random vibration fatigue evaluation, achieving structural and modal reduction while significantly enhancing the efficiency of damage assessment without compromising accuracy.

Analysis of two-phase flows using position-based PFEM formulation

The numerical simulation of flows with topological changes is quite challenging, being approached in the literature by different techniques, highlighting fixed mesh methods, generally based on immersed boundary techniques, and particle-based methods, generally based on a Lagrangian description of the flow. One approach that has proven to be efficient is the particle and finite element method (PFEM), which combines the concepts of particle methods with the finite element method. In this context, this work deals with the development and implementation of techniques for simulating two-phase flows with free surface and topological changes in an alternative formulation of PFEM, where instead of velocities as nodal parameters, particle positions are used. Initially, the domains of the two fluids are represented by a cloud of particles to which the physical characteristics of the fluid they represent are attributed, as well as the initial conditions. A mesh of finite elements is built on this particle cloud to solve the equation of motion in Lagrangian description, with the physical characteristics, as well as the velocity and pressure fields, being interpolated by the shape functions of the finite elements. To avoid large distortions, and also mesh entanglement, at each step this mesh is destroyed and a new mesh is built. Delaunay triangulation is used to construct the mesh, together with the alpha-shape method to define the contours, together with a particle relocation technique that must guarantee the quality of the mesh (avoid extremely small elements or elements with a very small volume ), as well as ensuring the conservation of the number of particles of each fluid. This formulation is tested for cases of free surface flows, such as sloshing in reservoirs, taking into account the water-air interaction, and the results are compared with results from the literature.

A position-based PFEM formulation for free-surface non-Newtonian flows with application to fresh concrete

This work presents a methodology for free surface non-Newtonian incompressible flows using a particle position-based formulation of the Particle Finite Element Method (PFEM) [1], motivated by the simulation of fresh concrete flow. This method is based on the Lagrangian description of the flow and represents the fluid domain by cloud of particles, with a finite element mesh being built, taking the particles as nodes, to solve the motion equations and update the particle positions. To deal with large distortions of fluid flows, such mesh is constantly rebuilt, leading to a method very robust to deal with topological changes within the fluid domain. This approach requires updating the reference configuration, enabling the use of partially or fully updated Lagrangian descriptions. The weak solution is based on the stationary energy principle considering current nodal positions and pressures as variational parameters, deviating from the common practice of employing velocity and pressure as unknowns. Furthermore, smoothed versions of the Bingham and Herschel-Bulkley viscoplastic models are chosen to represent the fresh concrete behavior, keeping stresses independent of strain history and making updating the reference for the fluid simple, without the need for considering the stress distribution in the past reference. The implicit &amp;#945;-generalized strategy is chosen for time integration, enabling second order convergence and ensuring good stability due to the control over numerical dissipation at high frequencies. Finally, selected 2D and 3D examples are simulated to test and verify the proposed methodology.[1] IDELSOHN, S. R.; ONATE, E.; Del Pin, F. The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. International Journal for Numerical Methods in Engineering, John Wiley and Sons, Ltd, v. 61, n. 7, p. 964–989, oct 2004. ISSN 1097-0207.

Deep Learning-Based Reservoir Simulation Proxy Models

The behavior of oil reservoirs, characterized by geophysical, geochemical, and geological properties, can be understood through the simulation of computational models, involving the construction of meshes of finite volume elements with equations derived from fundamental principles. However, the execution of multiple simulations for activities such as optimization and uncertainty assessment results in substantial computational costs.To overcome this challenge, proxy models are proposed, aiming to replace reservoir simulators with adequate precision. This work proposes the implementation of data-based proxies for reservoir simulators using Artificial Neural Networks (ANNs). This approach utilizes time series of well controls as inputs, generating responses for Bottom Hole Pressures (BHPs) and/or flow rates.In recent years, proxy models based on neural networks have been applied to obtain predictions of flows and/or pressures in reservoirs. For example, Recurrent Neural Networks (RNNs), specialized in handling sequential data, were used by [1] to predict water flows in the Xiluodu hydroelectric reservoir in China. Convolutional Neural Networks (CNNs), specialized in pattern recognition in images and videos, were also employed by [2] to predict pressures and flow rates of injector and producer wells, respectively.In the scope of this study, distinct neural network architectures were evaluated to predict outputs of a synthetic two-phase model with partial faults. Given the adoption of mixed controls, where producer wells are controlled by BHP and injector wells by flow rate, the use of Multihead Neural Networks [3] was also investigated. This approach allows differentiated processing of input data, contributing to more robust and efficient learning.For each considered architecture, the impact of the number of timesteps in the samples and their size on the accuracy of predictions was analyzed. The results indicate that parallel hybrid architectures exhibit the best performance, forming a complementary mutual network where each architecture contributes with different learning approaches. Additionally, a higher number of samples contributes to reducing result dispersion, while an increase in the number of timesteps does not show a significant contribution to reducing mean error.We gratefully acknowledge the support provided by PETROBRAS, ANP, FINEP, PRH, EMBRAPII, FACEPE, CNPq, and CAPES, which has been instrumental in the successful execution of this work.

Numerical analysis of circular hollow section bar with stiffened flattened ends

Circular hollow sections are usually used in long-span roof truss systems due to the advantages they offer. One of the typology for connecting elements in such structures involves the flattening of bar ends, in order to provide a simpler and more economical connection. A new flattening typology called stiffened flattening is proposed, characterized by a non-flat geometry, with the creation of stiffeners in the lateral edges of the bar flattened ends. A theoretical, numerical and experimental study was carried out on the behavior of a plane truss composed of circular hollow sections, in which diagonal bars have stiffened flattening ends. The diagonal connecting system with the chord members uses connecting plates. The plates are welded to the chords and the diagonals are connected to latter through a single bolt. This work presents the numerical analysis of a circular hollow section bar with stiffened flattening ends subjected to compression. This is a study of the behavior of an isolated bar compressed from the truss, which corresponds to the most requested diagonal composed by circular hollow sections with stiffened flattening ends. The numerical analysis using finite elements method was developed through ANSYS software with the Parametric Design Language (APDL), in which parameters such as geometry, material, element type, definition of the finite element mesh, boundary conditions and application of compression loads are specified. A non-linear analysis was performed using shell element on the bar with stiffened flattened ends. The numerical analysis result satisfactorily represented the structural behavior of the isolated circular hollow section bar with stiffened flattening ends. It was possible to observe the buckling effect of the compressed circular hollow section bar and the effect of the axial load eccentricity due to the stiffened flattening of bar ends.

Numerical formulation for advanced analysis of semi-rigid steel-concrete composite frames

The present work aims at the implementation and validation of a displacement-based two-dimensional numerical formulation including several sources of non-linearities in steel-concrete composite frames, such as second-order effects, plasticity and beam-to-column semi-rigid connections. The co-rotational-based approach is used to describe the finite element formulation, allowing large displacements and rotations in the numerical model. Two rotational pseudo-springs in series are positioned in the finite elements ends. One of them are used to include the gradual loss of stiffness determined by the cross-sectional plastification. The limiting of the uncracked, elastic and plastic regimes is defined in the Normal Force-Bending Moment diagram. In the cross-sectional analysis, the Strain Compatibility Method (SCM) is used to capture the axial strains in the section components. In this way, the constitutive models of the materials are described by continuous functions. The cracked effect is considered by the effective moment of inertia of the concrete cross-section. The other spring include the effects of the semi-rigid beam-to-column connections through the moment-rotation relationship. A multi-linear model for beam-to-column connections is used. To validate the proposed numerical formulation, the results obtained are compared with numerical and experimental data available in the literature. Since the model proposed here starts with the concentrated simulation of nonlinear effects, an examination of the finite element mesh refinement is also carried out. These comparisons indicated for the validation of the numerical procedure proposed and implemented here, highlighting the precision of the formulation in both the pre- and post-critical structures behavior.

A numerical procedure to identify vugs and fractures in rock samples based on CT scan data

This article introduces novel algorithms for fractures and vugs recognition in computed tomography (CT) rock images. The proposed algorithms can be used in both two-dimensional (2D) and three-dimensional (3D) approaches to accurately identify fractures and vugs within rock samples. A detailed explanation of the implemented method is provided, elucidating the underlying principles of the algorithms. Furthermore, the method's applicability is investigated through testing with various models of pre-trained neural networks.The study contributes to rock image analysis by introducing effective techniques for identifying fractures and vugs in CT scans that can be applied for geological and engineering purposes. In a demonstrative application, this methodology was implemented to generate a two-dimensional finite element mesh, thereby facilitating the simulation of the Darcy equation using the Finite Elements Method.

Calculation of closed combustion performance based on evolution of gun propellant burning surface

Abstract In order to enhance the combustion performance evaluation ability of irregularly shaped gun propellants and accelerate the development of propellant energy-release control technology, the present work provides the calculation method of closed combustion performance based on the evolution of gun propellant burning surface. The 3-D structure of the gun propellant should be built, and then a steady-state heat conduction equation with a source term is set, which can be considered as the Poisson equation with a diffusion term. The variable in the equation is the burned web thickness of the propellant grain. Afterwards, finite element meshing was performed on the 3-D structure to obtain a dynamic database of equivalent surfaces with burned web size. The pressure during the closed combustion process can be obtained from the mass conservation equation as a function of the burned web thickness. Furthermore, the combustion time field can be derived based on the functional relationship between burning-rate and pressure. Ultimately, the variation of gas pressure versus time in the closed bomb could be obtained. The results showed that the burnout time of the tubular propellant was 1.6 ms shorter than that of the inner pore offset 0.5 mm under the design conditions. This research can provide researchers with a new method for calculating the closed combustion performance of irregular gun propellants, which can be applied to the design of propellant shapes and the study of launch safety of propellant charges.

FEM Parameters for Earthquake Analysis of Retaining Walls

Abstract The paper presents the main characteristics and features of numerical finite element (FE) models for the study of the seismic response of soil-retaining wall. Since walls are linear structures, 2D plane strain models are suitable for conducting of the analysis. The models need to include a finitely sized soil domain, whose boundary conditions are defined according to the way earthquake loading is defined, respectively as pseudo-static impact or dynamic impact as a function of time. The FE mesh must meet the criteria of sufficient density in order to ensure the necessary accuracy of the solution. With the use of multi-nodal finite elements the displacements function in the model is improved. Retaining walls as well as other structural elements and devices are modelled with 2D plate and 1D linear elements defined in terms of a full or limited set of stresses. To simulate the behaviour in the contact of the structural elements and soil, interface elements are introduced modelling the gapping and slipping in the contact. The material parameters are determined depending on the selected constitutive models. In dynamic earthquake analyses, parameters shall be introduced to take into account the reduction of the soil stiffness. Dynamic loading is usually introduced with an accelerogram whose selection is made on the basis of an analysis of the parameters of strong motion records.

Manufacturing design and static analysis of a gear shaft

This paper presents a gear shaft design that was constructed with the use of Solidworks, the manufacturing process of the design done by the use of the Edgecam software and also a Finite Element Analysis (FEA) which includes examining the part's displacement behavior with corresponding stress and deformation. The 3-dimensional finite element simulation and meshing of the model was done with the ANSYS Workbench. Boundary requirements including external loads were also utilized. The manufacturing design was done in two parts due to the high level of complexity associated with the gear shaft. The first part included the parametric configurations used for machining one end of the gear shaft and the second part included the parametric configurations used for machining the other end of the gear shaft. This means that when the machining process has to be done on the CNC machine, there will be two separate CNC codes to be utilized which can run successively. During the manufacturing design phase, important information was obtained, such as the overall time for machining of one or both ends of the gear shaft as well as the safety conditions that were utilized during the process.