Parametric Geometric Model Research Articles

A compact quasi-zero stiffness metamaterial for energy absorption and impact protection

A compact mechanical metamaterial for impact protection is proposed in this study. During compression, the unit cell of the metamaterial exhibits quasi-zero stiffness (QZS) and quasi-zero Poisson’s ratio (QZPR) characteristics, along with large densification strain, making it suitable for protection against low-speed impacts. Firstly, the parametric geometric model of the metamaterial is established, with sinusoidal thin-walled structures serving as the primary load-bearing units. The grid structures are employed to connect the thin-walled structures into a unified system. Secondly, to shorten the design cycle, numerical methods for the mechanical properties of the buffer structure are developed. The motion equation of the thin-walled structure are expressed in terms of arc length coordinates and solved using the Runge–Kutta method and the shooting method. The grid structure deformation and the effect of material plastic reinforcement on the structural mechanical response are analyzed, and the energy absorption (EA) of the buffer structure is calculated. Both simulation and experimental results demonstrate the high accuracy of the proposed calculation method. Lastly, drop hammer experiments are conducted to evaluate the impact mitigation performance of the designed buffer structure. The results indicate that the structure exhibits excellent impact mitigation capabilities, highlighting its potential for practical applications.

Virtual-Trim: A parametric geometric modeling method for heterogeneous strut-based lattice structures

Abstract Geometric modeling has been integral to the design process with the introduction of Computer-Aided Design. With additive manufacturing (AM), design freedom has reached new heights, allowing for the production of complex lattice structures not feasible with traditional manufacturing methods. However, there remains a significant challenge in the geometric modeling of these lattice structures, especially for heterogeneous strut-based lattice structures. Current methods show limitations in accuracy or geometric control. This paper presents the Virtual-Trim, a novel method for the geometric modeling of heterogeneous strut-based lattice structures that is both efficient and robust. Virtual-Trim begins with user-defined wireframe models and geometric information to create STL (STereoLithography) models ready for AM, eliminating the need for labor-intensive Boolean operations. The fundamental principles and steps involved in Virtual-Trim are extensively described within. Additionally, various models using Virtual-Trim method are designed, and the performance of Virtual-Trim in terms of generation time and model size is analyzed. The successful printing of these models attests to the method’s excellent manufacturability.

A Finite Element Model for a 6 × K31WS + FC Wire Rope and a Study on Its Mechanical Responses with or without Wire Breakage

The special spatial structure and the long-term harsh working environment make the transient response of wire rope complicated, so accurate assessment and prediction of its mechanical characteristics are of great significance to ensure the safe and stable operation of related equipment. In this paper, a method is proposed for the analysis of the mechanical characteristics of a 6 × K31WS + FC wire rope with or without wire breakage. Firstly, an accurate parametric geometric model of the wire rope is established based on the Frenet frame method, the material properties of the wire rope are acquired by experiments, and the finite element model of the wire rope is built. Then, a mechanical model of the wire rope is proposed to verify the validity of the finite element model. Finally, the influences of the number, distribution, and location of the broken wires on the mechanical characteristics of the wire rope are thoroughly analyzed. This work proposes a comprehensive framework that can quantitatively analyze the mechanical characteristics of the complex wire rope with or without wire breakage, which provides a practical method for its reliability and maintenance evaluation and has guiding significance for the shape design and structural optimization of the wire rope.

Mitral valve geometrical echocardiographic analysis and 3D computational modeling of a normal mitral valve.

Aim: This research aims to develop a consistent computational model of a normal mitral valve (MV) and describe mitral regurgitation (MR) geometry based on Carpentier's classification. Materials & methods: MV geometry was assessed by 2D transthoracic echocardiogram in 100 individuals. A 3D parametric geometric model of the MV was developed. A computational model of a normal MV was performed. Results: The simulation of the valve function was successfully accomplished and its kinematics was analyzed. Differences in geometry were revealed between normal and type III MR. Conclusion: 3D computational models of the normal MV can be constructed relying on standard measurements performed by 2D echocardiography. Certain geometrical differences exist among the normal and the most severe type of MR.

Half-plane point retrieval queries with independent and dependent geometric uncertainties

This paper addresses a family of geometric half-plane retrieval queries of points in the plane in the presence of geometric uncertainty. The problems include exact and uncertain point sets and half-plane queries defined by an exact or uncertain line whose location uncertainties are independent or dependent and are defined by k real-valued parameters. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), an expressive and computationally efficient worst-case, first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We present an efficient O(k2) time and space algorithm for computing the envelope of the LPGUM line that defines the half-plane query. For an exact line and an LPGUM n points set, we present an O(log⁡nk+mk) time query and O(nk) space algorithm, where m is the number of LPGUM points on or above the half-plane line. For a LPGUM line and an exact points set, we present a O(k2+(klog⁡nlog⁡log⁡n)ε+m) time and O(n2log⁡n+kε) space approximation algorithm, where 0<ε≤1 is the desired approximation error. For a LPGUM line and an LPGUM points set, we present two O(k2+(klog⁡nklog⁡log⁡nk)ε+mk) and O(mk2+(klog⁡nklog⁡log⁡nk)ε) time query and O((nk)2log⁡nk+kε) space approximation algorithms for the independent and dependent case, respectively.

Research on Double-Arc Cutting Tool Design and Cutting Performance

With the increasing complexity of the workpiece surfaces in aerospace and automotive molding and other areas, an increasing number of cutting tools with different shapes and performance have become necessary. A new kind of cutting tool is developed with a double-arc revolving surface at the tool’s end to improve the processing quality in numerical control milling, referred to as a double-arc cutting tool (DACT) in this paper. The parametric geometric model of the DACT is established. Three types of cutting-edge curves are proposed (a cutting edge with a constant helix angle, a cutting edge with a constant pitch, and an orthogonal spiral cutting edge). Corresponding numerical simulation results are also provided as graphical representations. A DACT is manufactured and tested to verify its feasibility. Finally, two contrast experiments are conducted to prove that DACT has a higher processing quality than a ball-end mill (BEM). The advantage of the DACT is verified, which provides a theoretical basis for higher quality machining. The parametric design and application research provides a new method and theoretical basis for other new types of cutting tools.

STRESS-STRAIN STATE AND CRITICAL ROTATIONAL VELOCITIES OF AIR BLOWER ROTOR PART OF A HIGH BOOST ENGINE

The stress-strain state and critical rotation speeds of the air blower rotor part of highly forced engine are investigated. For this purpose, their parametric geometric and finite-element models are built. Due to the high speeds of rotation, the impeller disk acquires an umbrella-shaped deformed shape. This deformation can cause a gap to be selected between the impellers and the stator of the supercharger. In areas of abrupt change of shape on the impeller there is a concentration of stresses. In addition, the supercharger impeller is located cantilevered. This causes low critical speeds. These frequencies may fall within the operating range of angular velocities of the supercharger rotor. All these factors in the complex within a single calculation model were not previously taken into account. Instead, taking into account the dependences of stress, strain and critical velocity levels on the design parameters is of interest in the development of supercharger designs. In particular, the stiffness characteristics of the elastic rotor bearings were varied. The influence of these parameters on the critical rotation speeds of the rotor part of the air supercharger is determined. Recommendations have been developed for debugging from hazardous supercharger modes. In particular, it is proposed to reduce the radial stiffness of the shaft bearings by using elastic flexible rings. This can reduce critical rotor velocities beyond the operating range. In addition, a lighter material can be used to increase the strength of the impeller. It is also possible to limit the operating range of the angular rotational velocities of the rotor part of the investigated air blower. Analysis of the stress-strain state and the critical rotational velocities of the rotor were carried out on the basis of a unified generalized mathematical and numerical model. Keywords: rotor system, air blower, impeller, stress-strain state, critical rotation speed

Optimization of an ejector to mitigate cavitation phenomena with coupled CFD/BP neural network and particle swarm optimization algorithm

Ejector serves as a component to suck the coolant for taking the adverse heat away from the reactor core during the accident. Owing to the simple construction and high reliability, it is widely applied in the pipeline of the Pressurized Water Reactor (PWR). The potential harm is the hydraulic cavitation induced by the local negative pressure, which might lead to vibration beyond limit and even damage of pipeline. This paper aims to provide the improved designs of the ejector. To achieve this purpose, a parametric geometric model of ejector was established, the shape of the ejector was optimized by particle swarm optimization (PSO) algorithm, and the fluid physical quantities, including flow fluxes and vapor phase volumes, were extracted by computational fluid dynamics (CFD) simulation. The accuracy of CFD simulation was verified by laboratory experiments. Moreover, in order to expedite the optimization process, several back propagation (BP) neural networks were trained to predict the fluid quantities. The results show that the jet diameter has a significant influence on the flow state and the cavitation degree. The optimized structure of ejector leads to lower vapor phase area within the constraint of flow fluxes. This work is expected to provide a framework to reduce the vibration of pipeline motivated by cavitation in ejector.

Design of low-frequency and broadband acoustic metamaterials with I-shaped antichiral units

Controlling the propagation of low-frequency sound waves on the sub-wavelength scale is still a challenging problem. For the design of low frequency sound reduction materials, this paper introduces the I-shaped antichiral unit to the acoustic metamaterials with Mie resonance, which can manipulate the sub-wavelength acoustic waves and achieve effective low-frequency and broadband sound isolation. By adjusting the width of the ligament, the proportion of the omnidirectional bandgap is 65.6 % in the subwavelength range. Firstly, the designed acoustic metamaterials are constructed by rotating the I-shaped units with mutually orthogonal periodic distribution. The parametric geometric model of metamaterials is established, and the low-frequency and wide bandgap can be effectively realized by adjusting the ligament width. Then, the investigation of sound pressure and phase reveals that the bandgaps attribute to the Mie resonant mode. Furthermore, based on the transfer matrix method, the effective bulk modulus and effective mass density of acoustic metamaterials are derived. The results show that the frequency range of the negative effective parameters obtained is consistent with that of the band gap. Finally, experimental tests are carried out, the region where attenuation occurs is in good agreement with the bandgap range (1158–2500 Hz) predicted by eigenfrequency analysis. The experimental tests verify the effectiveness of the designed antichiral acoustic metamaterials for low frequency sound reduction. The introduction of the antichiral unit provides a broad space for the application of acoustic metamaterials in low-frequency sound reduction.The low-frequency and broadband can be effectively realized by adjusting the ligament width.The low-frequency can be effectively realized by adjusting the ligament width.The experimental tests verify the effectiveness of the designed antichiral unit.

Helicopter Main Rotor Blade Parametric Design for a Preliminary Aerodynamic Analysis Supported by CFD or Panel Method.

This work is the preliminary part of a research program which is aimed at finding some new methods and design solutions for helicopter main rotor multidisciplinary optimization. The task was to develop a parametric geometric model of a single-blade main rotor applicable for varied methods of numerical aerodynamic modeling. The general analytical assumptions for the parametric main rotor design were described. The description of the main rotor blade parametric design method based on Open GRIP graphical programming was presented. Then, the parametric model of a blade was used for aerodynamic models independently developed for panel method and advanced CFD solver. The results obtained from the CFD simulations and panel analysis for main rotor aerodynamics were compared and assessed using analytical calculations. The calculations and simulations for a single-blade and completed rotor were performed for different helicopter weights and rotor pitch angles. The results of different computer aerodynamic analysis environments were compared for the possibility of their application in an optimization loop. This is preliminary work that describes only a partial problem that could be used in the future as part of a comprehensive methodology for aerodynamic and structural optimization of a helicopter rotor. As an output of the research, new options for main rotor optimization are developed. The combined parametric modeling with aerodynamic analysis, as described in this paper, provide the preliminary design for a main rotor spiral, as an element of the optimization loop.

NURBS-Based Parametric Design for Ship Hull Form

Recently, the NURBS technique has been widely used in the 3D design software for ships. However, in most research, the NURBS technique is only applied to the mathematical representation of hull curves and surfaces, and the parametric deformation of hull surfaces based on geometric feature parameters is less understood. The aims of this paper are to establish the parametric design process of hull surfaces through the classification of geometric feature parameters and the design of feature curves, apply the NURBS technique to the parametric geometric modeling of hull curves and surfaces, and finally achieve the parametric deformation of hull surfaces driven by geometric feature parameters and develop the parametric deformation software. Taking the Series 60 ship as an example, we first analyze the hull geometric features and parameters, then design the longitudinal feature curves and cross-section curves based on the NURBS technique and establish the correlation between them, and finally generate the smooth hull surface by the skinning technique to achieve the parametric geometric deformation of the Series 60 ship. The research in this paper shows that the smoothness of the surfaces generated by the NURBS-based parametric design method is good. Additionally, the extracted feature parameters have a clear geometric meaning and can automatically generate hull forms to meet the design requirements quickly and effectively, which has some practical engineering value.

TO THE QUESTION OF COMPUTER PARAMETRIC DESIGN IN THE KOMPAS-3D SYSTEM

Computer-aided design is a highly productive means of improving the quality of technical products, reducing the cost of its development and operation. Geometric models are the basis for processing throughout the entire life cycle for complex object. Proper results significantly depend on their perfection.&#x0D; This special function is due to their leading role in the process of harmonizing the often controversial requirements of many technical and other disciplines to the designed industrial products. Its specific optimal variant is necessarily implemented by certain geometry. For effective search the latter, computer graphics models must provide not only the desired clarity and accuracy, but also the flexibility of modifications to the executed constructions. In this way, the created object is adapted to the existing various requirements for it.&#x0D; The modern implementation of the described strategy of automated design is a parametric approach to the development of industrial products. For its successful use in practice, it is necessary to pay appropriate attention to this topic when applicants for higher education study engineering graphics. Therefore, this direction is quite relevant.&#x0D; On the other hand, there are now theoretical developments that generalize the parametric geometric modeling. This applies, for example, the methodology of structural-parametric shaping, which was developed by the scientific school of applied geometry of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute". The above facts determine the appropriateness of acquainting students with new theoretical achievements in the field of computer-aided design, which will help improve their future professional activity.&#x0D; Thus, the main purpose of this publication is to present the proposed method to teaching computer design of industrial products in higher education institutions on the example of the Kompas-3D system. The described techniques are quite universal, they can also be used in other relevant software packages, in particular, AutoCAD, SolidWorks, CATIA, NX, ProEngineer etc.

Design and analysis of a six-wheeled companion robot with mechanical obstacle-overcoming adaptivity

Abstract. A six-wheeled companion exploration robot with an adaptive climbing mechanism is proposed and released for the complicated terrain environment of planetary exploration. Benefiting from its three-rocker-arm structure, the robot can adapt to complex terrain with its six wheels in contact with the ground during locomotion, which improves the stability of the robot. When the robot moves on the flat ground, it moves forward through the rotation of the wheels. When it encounters obstacles in the process of moving forward, the front obstacle-crossing wheels hold the obstacle, and the rocker arms on both sides rotate themselves with mechanical adaptivity to drive the robot to climb and cross the obstacle like crab legs. Furthermore, a parameterized geometric model is established to analyze the motion stability and the obstacle-crossing performance of the robot. To investigate the feasibility and correctness of design theory and robot scheme, a group of design parameters of the robot are determined. A prototype of the robot is developed, and the experiment results show that the robot can maintain stability in rugged terrain environments and has a certain ability to surmount obstacles.

Voronoi Diagram and Delaunay Triangulation with Independent and Dependent Geometric Uncertainties

We address the problems of constructing the Voronoi diagram (VD) and Delaunay triangulation (DT) of points in the plane with mutually dependent location uncertainties, testing their stability, and computing their components. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), a deterministic, expressive and computationally efficient first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We define an uncertain three-point circle and its properties and present in-circle-test algorithms for the dependent and the independent cases whose respective time complexity is [Formula: see text] and [Formula: see text], where [Formula: see text] is the number of parameters that describe the points location uncertainty and [Formula: see text] is the complexity of quartic [Formula: see text]-variable optimization. We define the uncertain VD and DT of [Formula: see text] LPGUM points and show that an unstable VD may have an exponential number of topologically different instances. We describe algorithms for testing VD and DT stability whose time complexity is [Formula: see text] and [Formula: see text] for the dependent and independent cases when the nominal (exact) VD is given. We present algorithms to compute the vertices, edges, and faces of uncertain VD and DT for the independent case whose complexity is [Formula: see text] time and [Formula: see text] space. Finally, we describe algorithms for answering exact and uncertain point location queries in a stable uncertain VD and for dynamically updating it in [Formula: see text] and [Formula: see text] average case time complexity for the independent and dependent cases.

Parametric optimization of magnetoelectric generator with double stator

A methodology for the optimization-parametric calculation of geometric parameters of the design of an axial-flux permanent magnet generator has been developed. The developed methodology can be used to calculate and optimize geometric parameters in an automated mode for almost any type of electromechanical energy converter. The operation of the developed system is based on the interconnections between the computer-aided design system, software package, and numerical calculation of the electromagnetic field with the possibility of feedback and parameterization and a computing environment such as Matlab. The parameterized geometric model is constructed on the example of an axial-flux permanent magnet generator with a double stator. Subsequently, parametric optimization of geometric parameters was performed using the developed algorithm. The use of the developed solution reduces the time spent by the researcher on the calculation of geometry and optimization. Parameterization is performed at all stages of construction of a single part, the geometry of which is planned to change, and in each part of the assemblies if any in a particular case. That is, with the help of the developed model, it is possible to program the optimization of both a separate structural element of the studied system and the object as a whole. In the process of optimization, the main geometrical parameters of the investigated end generator with double side changed: stator yoke, air gap, gear-groove zone of the stator, housing elements. As a result of parametric optimization of the geometry of the prototype, it was possible to reduce the geometric dimensions by optimizing the magnitude of the magnetic induction in some areas of the magnetic core of the studied generator. Due to the application of the developed algorithm, it was possible to reduce the cost of the generator, as well as the volume of the magnetic circuit by 18.1% and 24.3%, respectively. This indicates the effectiveness of the developed algorithm and the possibility of using this algorithm in further research

Design and Simulation of Ti6Al4V Cartilage Scaffold Based on Additive Manufacturing Technology

The combination of additive manufacturing technology and cartilage tissue scaffold construction provides a new way for clinical treatment of cartilage injury. The high priority of the cartilage scaffold is closely related to the excellent biomechanical properties, fatigue life and medical performance. In this paper, three kinds of cartilage scaffolds are designed, and three-dimensional parametric geometric and numerical simulation models are established. Based on the simulation analysis and comparison of the three kinds of scaffolds, a scaffold model is finally determined. The porosity reaches 87.38%, the equivalent elastic modulus is 9.64Gpa, and it has permanent fatigue life in service environment. It concluded that the designed Ti6Al4V titanium alloy scaffold is suitable for cartilage transplantation.

Research on ultimate bearing capacity state and structure optimization of main cable saddle

In order to make the main cable saddle structure lighter and reduce the cost, it is necessary to conduct in-depth research on the force transmission path, failure mode and ultimate bearing capacity of the main cable saddle. A parametric geometric model was established based on Autodesk Inventor software and imported into the large-scale general-purpose finite element software ABAQUS for numerical simulation research under ideal elastoplastic state, and the mechanical properties and ultimate bearing capacity of the main saddle were systematically studied. A structural optimization method with safety factor as the goal was proposed, and the original design was optimized for structural size. Then, the ultimate bearing capacity state of the cable saddle considering the influence of the steel's post-buckling strength is analyzed, and the structural bearing capacity evaluation index is proposed. The analysis results show that the ultimate bearing capacity of the preliminary design cable saddle is 3.00 times the design load, and it has sufficient safety reserves; the ultimate failure state of the cable saddle is the formation of a plastic hinge at the junction of the transverse rib, saddle channel cast steel and the web; By quantitatively analyzing the development of the plastic zone of each component of the cable saddle, the force transmission path and failure process of the structure can be analyzed more clearly, which provides a basis for the structural optimization of the cable saddle; and obtain the steel consumption under different safety factor target values (2.5, 2.0, 1.85, 1.5, 1.25), for example, when the safety factor target is 1.85, 38.8% of steel can be saved; when considering deformation index control, it is recommended that the target safety factor of the ideal elastoplastic analysis control is not less than 1.82.

Euclidean minimum spanning trees with independent and dependent geometric uncertainties

We address the problems of constructing the Euclidean Minimum Spanning Tree (EMST) of points in the plane with mutually dependent location uncertainties, testing its stability, and computing its total weight. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), an expressive and computationally efficient worst-case, first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We define uncertain EMST stability of n LPGUM points modeled with k real valued uncertainty parameters. We prove that when the uncertain EMST is unstable, it may have an exponential number of topologically different instances, thus precluding its polynomial-time computation. We present algorithms for comparing two edge weights defined by the distance between the edge endpoints for the independent and dependent cases with time complexity of O(klog⁡k) and O(T(k)) respectively, where T(k) is the time required to solve a quadratic optimization problem with k parameters. We describe an uncertain EMST stability test algorithm whose time complexity is O(n3klog⁡k) and O(nk+T(k)) for the independent and dependent case, respectively. We then present a more efficient O(nklog⁡nklog⁡n) time algorithm for the independent case and a method for computing the minimum and maximum total weight whose complexity is O(N3) time, where N=max⁡{k,n}.

Effects of longitudinal and transverse curvatures on optimal design of shell footbridge

Shell bridges have attracted extensive interest in engineering research and practice. This paper aims to evaluate the effects of longitudinal and transverse curvatures on the optimal design of the shell bridge. For this purpose, a slant-legged steel shell footbridge with the same initial and target volumes of steel was chosen to build parametric geometric models with different curvature radii, and then topology optimization was carried out using the bi-directional evolutionary structural optimization (BESO) technique to obtain optimized designs with high structural stiffness. Furthermore, linear static analysis and eigenvalue analysis demonstrate that the displacement, von Mises effective stress, and the first-order vertical vibration frequency satisfied all the requirements of design regulations. Numerical results indicate that not only the longitudinal curvature but also the transverse curvature have a significant effect on the optimized designs of steel shell footbridge. While the mean compliance increased with the transverse curvature radius, it first decreased and then increased with the longitudinal curvature radius.

TO THE QUESTION OF ARCHITECTURAL AND CONSTRUCTION ADAPTATION OF STRUCTURAL-PARAMETRIC SHAPING

Nowadays, computer means that have received the general name BIM (Building Information Modeling) are quite common for the automated design of architectural objects, i.e. building information modeling. The advantage of this approach is the comprehensive consideration of many factors that take place throughout the entire life cycle of various buildings. This helps to improve quality, reduce costs during construction and their further operation.The performed analysis of literary sources on the outlined topics showed that one of the basic components of BIM-technologies is computer geometric modeling. Computer geometric modeling not only visualizes the created objects, but also serves as a reliable basis for the coordination of conflicting requirements for them from a large number of professional disciplines that are involved in construction processes. Therefore, the proper improvement of the means of automated shaping is an urgent task for the further development of architectural design.Computer parametric geometric modeling is quite effective now. Its main advantage lies in providing flexible and productive modifications of the developed building or structure in accordance with the changing requirements of customers, the need to optimize the various technical or economic characteristics, etc. This approach is very progressive in comparison with the previous nonparametric methods. But it also has certain disadvantages. These features define the foundations for improving modern shaping.One of such directions is structural-parametric geometric modeling, which is used in mechanical engineering, in particular in the domestic aviation industry. From a theoretical point of view, it is a generalization of the parametric approach, since it is the simultaneous use of several different parametric models of analyzed object or process. At the same time, the studied variants differ in the composition and interaction of their elements, i.e. the structure, and the values of their parameters. As scientific research has shown, for the rational architectural and construction application the machine-building means of shaping require proper adaptation, i.e. the development of appropriate new methods and techniques of computer modeling. This publication is devoted to these aspects on the example of the designing of orthodox churches.