Surface blending for machining purposes: A brief survey and application for machining compound surfaces

Hatna, A.; Grieve, R. J.; Broomhead, P.

doi:10.1243/0954405011519178

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…Various time-independent methods have been proposed to blend parametric surfaces. Among them, rolling ball methods, which can be divided into constant radius [11] and variable radius [12] ones, are most widely used for rounding edges and corners of mechanical parts [13]. In addition, the potential method [14][15][16] was also proposed.…”

Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

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Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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“…The technique proposed in [19] has been used for surfaces not having constant radius. The method proposed by [19] has been combined with a curve smoothing process (along the intersection curves) expressed as in [23] …”

Section: The Shape Modeling Processmentioning

confidence: 99%

“…The method proposed by [19] has been combined with a curve smoothing process (along the intersection curves) expressed as in [23] …”

Section: The Shape Modeling Processmentioning

confidence: 99%

An object-oriented approach for mechanical components design and visualization

Dupac

2011

Engineering with Computers

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In this paper, development of shape modeling tools for engineering design, analysis, simulation, and visualization is presented. The approach based on the idea of function-based shape modeling is combined with the power and versatility of the object-oriented programming (OOP). An OOP code, initially developed as a teaching and learning tool for educational use in an undergraduate Modeling and Simulation course, to generate mechanism components is presented. Different parametric, explicit, and implicit functions or their combination are used to generate mechanical components shapes. Using a blending process, sophisticated shapes have been generated on the graphical interface. However, the ideas and concept of the OOP mechanical components design presented in this paper can be applied to other application areas.

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Analytical C2 Continuous Surface Blending

You,

Tian,

Tang

et al. 2024

Mathematics

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Surface blending is an important topic in geometric modelling and is widely applied in computer-aided design and creative industries to create smooth transition surfaces. Among various surface blending methods, partial differential equation (PDE)-based surface blending has the advantages of effective shape control and exact satisfaction of blending boundary constraints. However, it is not easy to solve partial differential equations subjected to blending boundary constraints. In this paper, we investigate how to solve PDEs analytically and develop an analytical PDE-based method to achieve surface blending with C2 continuity. Taking advantage of elementary functions identified from blending boundary constraints, our proposed method first changes blending boundary constraints into a linear combination of the identified elementary functions. Accordingly, the functions for blending surfaces are constructed from these elementary functions, which transform sixth-order partial differential equations for C2 surface blending into sixth-order ordinary differential equations (ODEs). We investigate the analytical solutions of the transformed sixth-order ordinary differential equations subjected to corresponding blending boundary constraints. With the developed analytical PDE-based method, we solve C2 continuous surface blending problems. The surface blending example presented in this paper indicates that the developed method is simple and easy to use. It can be used to effectively control the shape of blending surfaces and at the same time exactly satisfy C2 continuous blending boundary constraints.

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Surface blending for machining purposes: A brief survey and application for machining compound surfaces

Cited by 3 publications

References 35 publications

C2 Continuous Blending of Time-Dependent Parametric Surfaces

C2 Continuous Blending of Time-Dependent Parametric Surfaces

An object-oriented approach for mechanical components design and visualization

Analytical C2 Continuous Surface Blending

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