Machining Simulation Research Articles

Optimizing construction project management via genetic algorithms – A state-of-the-art review

Construction projects involve complex trade-offs between conflicting objectives such as minimizing duration and costs while ensuring feasibility, safety, and quality. This paper reviews research on leveraging genetic algorithms (GAs)–adaptive bioinspired search techniques–to enhance decision-making in construction management spanning planning, scheduling, and control. The versatility of GAs in tackling combinatorial optimization problems is established through various applications optimizing workflows, resource allocation, and crew coordination for enhanced project performance. Empirical analyses validate GAs generating superior trade-off solutions regarding project timeline, budgetary compliance, profitability, and safety over conventional methods such as mathematical programming or regression. Challenges remain regarding further enhancing the solution quality and fine-tuning the GA parameters. Nonetheless, by efficiently exploring vast solution spaces, GAs enable the scientific translation of construction data into actionable insights for augmenting complex project decisions. Exciting innovation opportunities exist in synergistically hybridizing GAs with promising contemporaries, such as machine learning, simulation, and robotics. Collectively, the existing literature underscores GAs' immense and relatively untapped potential of GAs to develop next-generation AI-powered tools for optimizing construction productivity, cost efficiency, sustainability, and lean automation.

Terrain-Based Coverage Manifold Estimation: Machine Learning, Stochastic Geometry, or Simulation?

Terrain-Based Coverage Manifold Estimation: Machine Learning, Stochastic Geometry, or Simulation?

Unveiling Advanced Computational Applications in Quantum Computing: A Comprehensive Review

The field of advanced computing applications could experience a significant impact from quantum computing, which is a rapidly developing field with the potential to revolutionize numerous areas of science and technology. In this review, we explore into the various ways in which complex computational problems could be tackled by utilizing quantum computers, including machine learning, optimization, and simulation. One potential application of quantum computers is in machine learning, where they could be used to improve the accuracy and efficiency of algorithms. Complex optimization problems, such as those encountered in logistics and finance, can be addressed using quantum computers as well. Furthermore, the utilization of quantum computers could enable the simulation of intricate systems, such as molecules and materials, leading to significant applications in fields like Physics and Material Technology. Although quantum computers are currently in the early stages of development, they possess the potential to propel numerous areas of science and technology forward in a significant manner. Further research and development are needed to fully realize the potential of quantum computing in the field of advanced computing applications.

Dynamic price competition market for retailers in the context of consumer learning behavior and supplier competition: Machine learning-enhanced agent-based modeling and simulation

This study analyzes the impact of consumer learning behavior and supplier price competition on retailer price competition in a complex adaptive system. Using machine Learning-enhanced agent-based modeling and simulation, the study applies fuzzy logic and genetic algorithms to model price decisions, and reinforcement learning and swarm intelligence to model consumer behavior. Simulations reveal that different learning behaviors result in different retailer competition patterns, and that supplier price competition affects the strength of retailer price competition. Simulation results demonstrate that consumer learning behavior influences retailer competition, with self-learning consumers leading to higher-priced partnerships, and collective-learning consumers leading to a shift in price competition among retailers. In contrast, perfect rationality consumers result in low-price competition and the lowest average margin and profit. Additionally, the competitive price behavior of suppliers impacts retailers' price competition patterns, with supplier price competition reducing retailer price competition in the perfect rationality consumer market and enhancing it in the self-learning and collective-learning consumer markets, leading to lower average prices and profits for retailers. This study presents a simulated market for price competition among suppliers, retailers, and consumers that can be expanded by subsequent scholars to test related hypotheses.

Determinant of Dynamics and Interfacial Forces in Ultraprecision Machining of Optical Freeform Surface through Simulation-Based Analysis.

This study delves into the intricacies of ultraprecision machining, particularly in the context of machining optical freeform surfaces using Diamond Turning Machines (DTMs). It underscores the dynamic relationship between toolpath generation, hydrostatic bearing in DTMs, and the machining process. Central to this research is the innovative introduction of Metal Matrix Composites (MMCs) to replace the traditional materials used in designing linear bearings. This strategic substitution aims to dynamically enhance both the accuracy and the quality of the machined optical freeform surfaces. The study employs simulation-based analysis using ADAMS to investigate the interfacial cutting forces at the tooltip and workpiece surface and their impacts on the machining process. Through simulations of STS mode ultraprecision machining, the interfacial cutting forces and their relationship with changes in surface curvatures are examined. The results demonstrate that the use of MMC material leads to a significant reduction in toolpath pressure, highlighting the potential benefits of employing lightweight materials in improving the dynamic performance of the system. Additionally, the analysis of slideway joints reveals the direct influence of interfacial cutting forces on the linear slideways, emphasising the importance of understanding and controlling these forces for achieving higher-precision positioning and motion control. The comparative analysis between steel and MMC materials provides valuable insights into the effects of material properties on the system's dynamic performance. These findings contribute to the existing body of knowledge and suggest a potential shift towards more advanced precision forms, possibly extending to pico-engineering in future systems. Ultimately, this research establishes a new standard in the field, emphasising the importance of system dynamics and interfacial forces in the evolution of precision manufacturing technologies.

Hot deformation behavior of Ni50.4Ti34.6Hf15 high-temperature shape memory alloy

Due to their extreme requirements, conventional Ni–Ti shape memory alloys (SMAs) are no longer suitable for aerospace applications. Adding Hf to Ni–Ti SMAs can significantly enhance their suitability for aerospace applications, particularly in high-temperature environments. In this regard, the hot/thermal deformation behavior of Ni50.4Ti34.6Hf15 high-temperature shape memory alloys (HTSMAs) was systematically investigated by using a Gleeble-3800 thermocompression simulation machine. The results prove that the Ni50.4Ti34.6Hf15 alloys have more strain sensitivity than the temperature during the hot/thermal deformation process. In detail, the flow stress increases with the increase in strain rate and decreases with the increase in deformation temperature. From the microstructure evolution point of view, the recovery effect will increase with the increase in deformation temperature, and the recrystallization effect will increase with the increase in strain rate. Following the obtained stress-strain curves, the flow behavior of Ni50.4Ti34.6Hf15 alloys during hot/thermal deformation was established. A modified constitutive equations model was proposed using careful consideration of deformation temperature and strain rate. It was found that the calculated strain activation energy was 363.945 kJ/mol in the range of 700∼800 °C and 512.489 kJ/mol in the range of 900∼1000 °C. Based on the constitutive equation, the calculated values were consistent with the experimental values, which indicated reliable analysis with high prediction accuracy. Furthermore, the thermal processing maps under different conditions were constructed, and it was determined that the optimum hot/thermal deformation processing parameters of Ni50.4Ti34.6Hf15 alloys were 940∼1000 °C and 0.01–0.04 s−1.

A New Design of Automatic Rabbit Feeding System

In Malaysia, rabbit farming is growing quickly, but there are many difficulties with it. One of these difficulties is the time-consuming procedure of feeding the rabbits. Thus, this paper presents an automatic rabbit feeding system machine that is able to reduce the time required to feed the rabbit. t can operate automatically, which will cut down significantly on labor requirements. force. The device used the eight-step George E. Dieter design, which outlines the best way to create an autonomous rabbit feeding system. SolidWorks software was used to translate the concept into the simulated machine system with the overall dimensions of 1820 mm x 1184 mm x 1630 mm. Analysis engineering and Life Cycle Assessment (LCA) on the simulated machine was conducted and it was found that the machine was able to discharge and distribute pellets up to 4 cages. As a result, this product is able to solve the issue that rabbit farmers encounter when it comes to feeding their animals.

Reconstruction Algorithm for Complex Dexel Models Based on Composite Block Partition

Abstract In machining simulations, dexel models are often used to represent objects to achieve high accuracy and real-time performance. However, this approach leads to the loss of original surface information and topological relationships, thereby affecting the visualization effect of simulations. Furthermore, existing reconstruction methods have the drawbacks of generalization or redundancy. To reconstruct the surface of dexel models efficiently and accurately, this paper proposes an algorithm based on “composite block” partition, which converts the dexel model into a polyhedral model. The algorithm begins by partitioning the entire dexel model within the grids into several composite blocks based on the “Connectivity Principle” and generating their end faces. Subsequently, the transitional zone’s surface is reconstructed based on the connectivity relationships of the boundaries of composite blocks. Finally, an optimization process refines the boundaries to generate smoother side faces at a low computational cost. The paper first validates the algorithm’s reconstruction capability and the effectiveness of edge refinement through the reconstruction of various dexel models with different precision levels. It is observed that edge refinement does not introduce excessive additional computation, doubling the overall efficiency compared to existing algorithms. Furthermore, by changing model volumes and performing separate reconstructions, it’s noted that as the volume increases, the incremental growth in conversion time gradually decreases. This makes the algorithm particularly suitable for reconstructing large-scale complex dexel models. Finally, the application of this algorithm in virtual-real simulation systems and industrial digital twin systems is briefly introduced.

Machine learning-based assessment and simulation of land use modification effects on seasonal and annual land surface temperature variations

Rapid urban sprawl adversely impacts the local climate and the ecosystem components. Islamabad, one of South Asia's green and environment-friendly capitals, has experienced major Land Use Land Cover (LULC) changes over the past three decades consequently, elevating the seasonal and annual Land Surface Temperature (LST) in planned and unplanned urban areas. The focus of this study was to quantify the fluctuations in LULC and LST in planned and unplanned urban areas using Landsat data and Machine Learning algorithms involving the Support Vector Machine (SVM) over the 1990–2020 data period. Moreover, hybrid Cellular Automata-Markov (CA-Markov) and Artificial Neural Network (ANN) models were employed to project the future changes in LULC and annual LST, respectively, for the years 2035 and 2050. The findings of the study reveal a distinct difference in seasonal and annual LST in planned and unplanned areas. Results showed an increase of ∼22 % in the built-up area but vegetation and bare soil decreased by ∼10 % and ∼12 %, respectively. Built-up land showed a maximum annual mean LST followed by bare-soil and vegetative surfaces. Seasonal analysis showed that summer months experience the highest LST, followed by spring, autumn and winter. Future projections revealed that the built-up areas (∼27 % in 2020) are likely to increase to ∼37 % and ∼50 %, and the areas under the highest annual mean LST class i.e., ≥28 °C are likely to increase to ∼19 % and ∼21 % in planned, and ∼38 % and ∼42 % in unplanned urban areas for the years 2035 and 2050, respectively. Planned areas have better temperature control with urban green spaces, and controlled infrastructure. The Capital Development Authority of Islamabad may be advised to control the expansion of built-up areas, grow urban forests, and thus mitigate the possible Urban Heat Island (UHI) effect.

Incorporating Simulators into a Training Curriculum for Forestry Equipment Operators

Forestry equipment simulators offer opportunities for new operators to become familiar with operating logging machines as well as a promising solution to the high costs of training forestry equipment operators. Current literature lacks a synthesis on how best to train forestry equipment operators using simulators. The goal of this review was to identify effective ways to incorporate forestry equipment simulators into an equipment operator training curriculum. We analyzed a total of 14 independent studies in which construction and forestry equipment operators were trained on simulators and engaged in discussions with nine professionals in the field of heavy equipment operator training. In this review, traditional machine training and simulator training practices are introduced. Then, four key aspects of skill acquisition for forestry equipment operators are identified. Information collected from peer-reviewed literature and discussions with industry experts are used to consider how each aspect of skill acquisition is addressed in both traditional training using real machines and simulator-based training. Drawing on these sources, benefits and drawbacks of traditional machine training and simulator-based training for forestry equipment operators are synthesized and discussed. Finally, a model for an integrated and adaptive training curriculum that incorporates principles and technologies from both traditional machine training and simulator training is presented.

Implementation of Finite State Automata to Simulation of Automatic Clothes-Folding

Inconsistencies and differences clothes-folding methods are often a major problem in the military. Everyone has thier method to fold and their method is still traditional. Besides, the neatness of the clothes in the military is emphasized. This method certainly took up their time and energy then the folding was different to each other. To solve this problem, a simulation machine is made to fold the clothes automatically. This system works using Finite State Automa type Non-Deterministic Finite Automata. Finite State Automata are used because they are simple and do not require storage space. The result of this research is a design of an automatic clothes-folding that can be implemented properly and correctly for UNHAN RI’s students. This automatic clothes-folding has succeeded to create consistent folds even though user tried with different clothes.

A Method for Estimating Alfalfa (Medicago sativa L.) Forage Yield Based on Remote Sensing Data

Alfalfa (Medicago sativa L.) is a widely planted perennial legume forage plant with excellent quality and high yield. In production, it is very important to determine alfalfa growth dynamics and forage yield in a timely and accurate manner. This study focused on inverse algorithms for predicting alfalfa forage yield in large-scale alfalfa production. We carried out forage yield and aboveground biomass (AGB) field surveys at different times in 2022. The correlations among the reflectance of different satellite remote sensing bands, vegetation indices, and alfalfa forage yield/AGB were analyzed, additionally the suitable bands and vegetation indices for alfalfa forage yield inversion algorithms were screened, and the performance of the statistical models and machine learning (ML) algorithms for alfalfa forage yield inversion were comparatively analyzed. The results showed that (1) regarding different harvest times, the alfalfa forage yield inversion model for first-harvest alfalfa had relatively large differences in growth, and the simulation accuracy of the alfalfa forage yield inversion model was higher than that for the other harvest times, with the growth of the second- and third-harvest alfalfa being more homogeneous and the simulation accuracy of the forage yield inversion model being relatively low. (2) In the alfalfa forage yield inversion model based on a single parameter, the moisture-related vegetation indices, such as the global vegetation moisture index (GVMI), normalized difference water index (NDWI) and normalized difference infrared index (NDII), had higher coefficients of correlation with alfalfa forage yield/AGB, and the coefficients of correlation R2 values for the first-harvest alfalfa were greater than 0.50, with the NDWI correlation being the best with an R2 value of 0.60. (3) For the alfalfa forage yield inversion model constructed with vegetation indices and band reflectance as multiparameter variables, the random forest (RF) and support vector machine (SVM) simulation accuracy was higher than that of the alfalfa forage yield inversion model based on a single parameter; the first-harvest alfalfa R2 values based on the multiparameter RF and SVM models were both 0.65, the root mean square errors (RMSEs) were 329.74 g/m2 and 332.32 g/m2, and the biases were −0.47 g/m2 and −2.24 g/m2, respectively. The vegetation indices related to plant water content can be considered using a single parameter inversion model for alfalfa forage yield, the vegetation indices and band reflectance can be considered using a multiparameter inversion model for alfalfa forage yield, and ML algorithms are also an optimal choice. The findings in this study can provide technical support for the effective and strategic production management of large-scale alfalfa.

Exploring player’s feelings on clarinet mouthpiece geometry using artificial blowing machines and airflow simulations

The mouthpiece geometry of single-reed instruments has been known to have a great impact on sound quality and playability. Although many researchers have investigated the effects of the geometry using artificial blowing machines or user case studies, few attention has been paid to the essential cause of physical changes in the instrument. In this study, we propose a method combining the artificial blowing machine and numerical flow simulations to explore the player’s feelings about the airflow and sound generation in the clarinet mouthpiece. With the artificial blowing machine, the mouth pressure, as well as lip force, were systematically changed using a pressure regulator and strain gauge. At particular conditions, the numerical flow simulation was conducted by solving fluid–structure interactions with the Navier–Stokes equations and the one-dimensional beam equation. The playability of the mouthpiece was shown by the changes in oscillation threshold pressures and sound spectral characteristics, whereas the cause of the changes could be described by the airflow pressures inside the mouthpieces. The results suggest that the combination of the artificial blower and the flow simulations can be effectively used for clarifying the cause of changes in players’ feelings.

Patient-Free Simulation: Analysis of Hospitalized Patients Treated without CT Simulation

Palliative radiation therapy (RT) can be a necessary element of treatment for hospitalized cancer patients who may be critically ill. We have implemented patient-free simulation machine starts using existing diagnostic imaging for treatment planning, eliminating the need for simulation. We hypothesize machine starts reduce time in the department without detriment to clinical outcomes. An IRB-approved database of patients receiving RT was queried for hospitalized patients treated with a machine start. Variables including time on machine and in department, and clinical outcomes were collected. A binary clinical endpoint variable indicated whether the goal of RT was achieved (extubation, hemostasis, etc.). A similar cohort of inpatients receiving CT simulation and mediastinal RT was compared with the machine start group. Mann-Whitney U test was used for comparison between groups. Hypothesis testing for proportions was used to compare patients meeting clinical endpoints. A total of 23 patients were treated with 25 machine starts. The median age was 65 (range 43-82) and median KPS was 50. A total of 15 patients were in the intensive care unit of which 12 were mechanically ventilated (MV). The most common histology was NSCLC (14). RT was most commonly 8-10 Gy in 1 fraction (88%, range 7-30 Gy in 1-10 fractions). Field arrangement was equally weighted AP/PA fields in 84%. Treated sites were mediastinum (17), bone (3), abdomen/pelvis (2), neck (2), and brain (1). Diagnostic CT of the treatment area was obtained a median of 6 days prior to RT (0-57 days). Machine starts within 4 days of admission were significantly more likely to meet the intended clinical endpoint (87% vs 47%, p = 0.02). On day of machine start, patients' median time in the department was 32 minutes (10-141 min). Of machine starts with treatment times available (22), median time in the LINAC vault was 15 minutes (5-31 min). The median shifts from the initial CBCT were 0.9 cm in the superior-inferior direction (0-2.7 cm), left-right 0.9 cm (0-5.9 cm) and anterior-posterior 0.5 cm (0-3 cm). One patient required repeat CBCT after initial shifts. In a similar cohort of patients who underwent CT simulation followed by RT to the mediastinum, the average time in the department was 122 minutes, compared with 45 minutes for machine start patients treated to the mediastinum (p = 0.02). Primary clinical endpoint was achieved in 65% of machine starts. 61% of patients clinically improved and were stable for discharge. Of the MV patients, 42% were successfully extubated and 58% were discharged. Of patients who died (74%), average time to death was 53 days after RT (4-126 days). Among the MV subgroup, 83% died an average of 49 days from RT (4-126 days). Machine starts are a timely and accurate alternative to traditional planning with CT simulation that results in approximately 60% less time in the department. This is an acceptable RT planning technique for a population that demands greater medical attention and resources.

Imitation Model of a Dual-Mass Machine with Universal Joint Shaft Transmission

The research is devoted to developing a mathematical model describing the dynamics of a dual-mass machine unit with a cardan gear, taking into account the catalogue data of an induction motor. A reference simulation model of a machine unit of sequential structure driven by a given induction motor is obtained. The simulated machine unit consists of a reducer and two rotating masses with a cardan gear with a given torsional stiffness between them. The differential equations of motion of the machine unit were calculated. A mathematical description of mechanical characteristics on the basis of Klos formulae has been developed and the influence of machine unit parameters on its performance in start-up, steady-state and emergency modes of operation has been studied. The analysis of arising oscillations and dynamic loads is carried out and the results of numerical implementation of the obtained results are presented.

Façade design of side-lit spaces for different climates and surroundings by machine learning and NSGAIII

This work aims to propose a simplified decision tool for the design of side-lit spaces that accounts for the impacts of climate and surroundings. The framework was developed using a smart optimization algorithm NSGA-III in combination with CatBoost ensemble machine learning technique and simulation. WWRs and overhang depths were optimized to maximize daylight penetration, minimize glare risk and reduce energy demand in different climates, orientations, space proportions, and surrounding obstruction angles. Besides, optimal solutions were used to determine the range of attainable targets for daylight, glare, and energy metrics in each climate, which can be used as requirements of national codes and standards. For example, for WDR = 3:2 and an OA of 20, energy demand varied between 260 and 266 kWh/m2, ASE remained at 40–50%, and sDA was reported 100% for south-oriented cases in Tehran. A sensitivity analysis was also performed to provide insights into how various design parameters affected daylight and energy performance in architectural spaces. The results revealed that daylight availability metrics were highly sensitive to the Window-to-Wall Ratio (WWR), while glare metrics were primarily affected by obstruction angle. Energy consumption was mainly influenced by room depth, WWR, window orientation, and obstruction angle. Notably, these parameters ranked similarly across all considered climates, albeit with varying degrees of significance. Results were presented in the form of guide charts that offer a practical tool for designing buildings in highly obstructed contexts and enable non-programmer architects and designers to make informed decisions.

All-dielectric metasurface refractive index sensor with high figure of merit based on quasi-bound states in the continuum

All-Dielectric metasurfaces are widely used in the field of sense due to their small size, freedom of design, and low radiation loss. However, the optical sensor still has the problem of wide full width at half maximum (FWHM), which leads to a low figure of merit (FOM). In order to solve this problem, an all-dielectric metasurface based on quasi-bound states in the continuum (q-BIC) was proposed for refractive index sensing. The sensor structure consisted of a prism/metasurface/analyte, where the metasurface was composed of periodically arranged subwavelength asymmetric silicon gratings. The asymmetry of the structure led to the coupling of the tangential and radiative field components in the superficial layer at the resonance position, which formed a q-BIC resonance peak with a narrow FWHM in the reflection spectrum. We explained the causes of the q-BIC resonance peak generation by finite element analysis, and analyzed the factors affecting the FWHM, and also simulated the machining errors. The results showed that by reducing the asymmetry of the sensor, it could have a high FOM, with a FOM of 1.35 × 107 RIU−1. In addition, simulated machining errors within ±5 nm showed that small machining errors did not lead to the disappearance of q-BIC, which proved that the sensor had good robustness. These findings had provided ideas for the accurate detection of trace substances.

Principles and approaches for the machining simulation of ceramic matrix composites at microscale: A review and outlook

Ceramic Matrix Composites (CMC) are advanced materials composed of ceramic fibers embedded in a ceramic matrix, resulting in a highly durable and lightweight composite structure offering exceptional high-temperature performance, excellent mechanical properties, and superior resistance to wear and corrosion. CMC find applications in industries such as aerospace, automotive, energy, and defense, where high strength and thermal stability are crucial. Despite their numerous advantages, machining CMC presents unique challenges. The hardness and brittleness of ceramics make them difficult to machine using conventional methods. The abrasive nature of ceramic particles can rapidly wear down cutting tools, leading to decreased tool life and increased costs. Numeric simulations for the machining of CMC are therefore particularly interesting due to their ability to provide insights into tool-material interactions and optimize machining parameters without the need for expensive and time-consuming physical trials. This paper discusses existing methods and approaches from different materials like Carbon Fiber Reinforced Plastics (CFRP) and monolithic ceramics and puts forward an outlook for the numerical simulation of the machining process of CMC.© 2017 Elsevier Inc. All rights reserved.

Potent multi-target natural inhibitors against SARS-CoV-2 from medicinal plants of the Himalaya: a discovery from hybrid machine learning, chemoinformatics, and simulation assisted screening

The emergence and immune evasion ability of SARS-CoV-2 Omicron strains, mainly BA.5.2 and BF.7 and other variants of concern have raised global apprehensions. With this context, the discovery of multitarget inhibitors may be proven more comprehensive paradigm than its one-drug-to-one target counterpart. In the current study, a library of 271 phytochemicals from 25 medicinal plants from the Indian Himalayan Region has been virtually screened against SARS-CoV-2 by targeting nine virus proteins, viz., papain-like protease, main protease, nsp12, helicase, nsp14, nsp15, nsp16, envelope, and nucleocapsid for screening of a multi-target inhibitor against the viral replication. Initially, 94 phytochemicals were screened by a hybrid machine learning model constructed by combining 6 confirmatory bioassays against SARS-CoV-2 replication using an instance-based learner lazy k-nearest neighbour classifier. Further, 25 screened compounds with excellent drug-like properties were subjected to molecular docking. The phytochemical Cepharadione A from the plant Piper longum showed binding potential against four proteins with the highest binding energy of −10.90 kcal/mol. The compound has acceptable absorption, distribution, metabolism, excretion, and toxicity properties and exhibits stable binding behaviour in terms of root mean square deviation (0.068 ± 0.05 nm), root-mean-square fluctuation, hydrogen bonds, solvent accessible surface area (83.88–161.89 nm2), and molecular mechanics Poisson-Boltzmann surface area during molecular dynamics simulation of 200 ns with selected target proteins. Concerning the utility of natural compounds in the therapeutics formulation, Cepharadione A could be further investigated as a remarkable lead candidate for the development of therapeutic drugs against SARS-CoV-2. Communicated by Ramaswamy H. Sarma

An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling

5-axis CNC (Computer Numerical Control) milling is widely used to create complex part geometries in the industrial area. The cutting tool creates the swept volume as it moves along the defined path. The swept volume is subtracted from the initial stock for the machining simulation. Although a swept volume consists of three parts such as ingress, egress, and swept envelope, the number of faces of the swept volume is higher than three. In this work, parametric equations of the faces of the swept volume were obtained for a flat-end mill in four steps. The model is based on the decomposition of the tool into circles along the tool orientation vector since a flat-end mill can be modeled as a cylinder. The fundamental principle is that each circle is tangent to the swept envelope of the cylinder. Locations of the grazing points with respect to a local coordinate system were determined by applying the Envelope Theory to the parameterized circle of the cylinder. Then, each face of the swept volume was represented based on the equation of the parameterized circle. The model was verified by using an alternative analytical model. As a result, boundaries of the swept volume were represented fully analytically for a flat-end mill in 5-axis CNC milling in an efficient way.