Parametric Modeling of Surfaces using CATIA v5 Environment

GHIONEA Ionuţ Gabriel 1,a* , DEVEDŽIĆ Goran 2,b, ĆUKOVIĆ Saša 3,c 1Spl. Independenţei 313, University Politehnica of Bucharest, IMST, TCM Dept., Romania

2,3 Sestre Janjić 6, 34000 Kragujevac, University of Kragujevac, Faculty of Engineering, Serbia a* ionut76@hotmail.com, b devedzic@kg.ac.rs, c cukovic@kg.ac.rs

Keywords: CATIA v5, surface parametric modeling, design process, virtual model. Abstract. The goal of the CAD parametric modeling is to create a 3D representation, flexible and complex enough to encourage the engineer to easily consider a variety of designs with the cost of applying changes as low as possible. Geometric modeling systems provide a virtual environment similar to the real one in which the physical model is constructed/designed and manipulated. Using such a system, the engineer models, adds, deforms and edits parts in the process of detailing a shape. The virtual model may look the same as the real physical model, but it’s intangible. However, the 3D virtual model is accompanied by its mathematical description, parameters, restraints and these eliminates the need of measurements for prototyping or mass production, can be modified at any modeling phase, can be tested in various ways etc., which is a major disadvantage of using a physical part. This paper presents some theoretical aspects regarding the design process of products including surfaces and a few case studies showing the many possibilities in creating complex surfaces using the CATIA v5 software.

Introduction

In surface modeling systems, the mathematical description corresponding to a virtual model includes surface information in addition to the information about the sketches (2D and 3D) used in the surface creation. In the CAD environment, surface equations, curves equations, various points’ coordinates are updated as the virtual model is created, visualized, manipulated and modified on screen by the engineer. The mathematical model may include information about surface connectivity, on how the surfaces from a more complex shape are joined, which surfaces are adjacent to each other by which curves, on how each surface was obtained etc. [1]. All these informations are useful in many applications (as an example, a NC program to generate and to validate the tool paths on a milling machine will certainly use all the data available to check the gaps where the surface machining is impossible).

The mathematical description of the surface model created by a surface modeling system typically includes a list of surface equations, different attributes and parameters defining and working in these equations (B-splines, NURBS [2,3]) . Without correct surface connectivity information, the application program, like one that determines the tool paths in a NC approach, has to derive the boundaries of the surfaces and their connectivity information [4].

Modeling functions in the parametric environment

Typically, three methods are used to create a surface: by interpolating the input points, by interpolating a set of curves and by applying a state (translation, revolving, offset etc.) to a specified curve. The input method for each of these surface creation methods may differ, depending on the particular surface modeling system. Surface modeling systems are used to create models with complex surfaces mainly for two purposes: first, the virtual model evaluates the real product (by visualization, aesthetically, by simulation) that includes the surface and, second, the mathematical description is used to generate the NC tools paths to machine its surfaces [5,6].

The modeling functions supported by many surface modeling CAD programs may be classified in five groups. The first includes the modeling functions used to create a primitive shape and

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adjusting its size. These kinds of surfaces are rarely used as is, but with the capabilities of adding, intersecting or subtracting from each other let the engineer to quickly and easily create surface models closed to the final shape. The tools/functions in the first group will make an approximated and low detailed surface model.

The second group is composed of the modeling functions that can move a surface. Thus, the sweeping and multi-sections functions belong to this group. The sweeping function creates surfaces by translating or revolving profiles. When defining these profiles, the engineer imposes geometric constraints and enters dimension data instead of specifying the shape directly. The geometric constraints are the relations between shape elements (perpendicularity, tangency, parallelism, midpoint etc.). In this case, the system will generate the exact shape suitable to the dimension data. Thus, changing the geometric constraints or the dimensions, the profile is changed and so the surface is changed. This approach is called parametric modeling because various surfaces are generated by changing the parameters [5].

The third group includes the modeling functions used mainly for modifying existing shapes that can be blended, lofted, filled etc.

The fourth group contains the functions by which primary entities of a surface, such as vertices, edges, facets are directly manipulated. This approach is called boundary modeling.

The last group includes the functions by which the engineer can initiate a surface from predefined shapes. The use of these functions is called feature-based modeling.

David Weisberg, editor of the Engineering Automation Report, pointed out the fundamental problem with parametric modeling [7]: “The problem with a pure parametric design technique that is based upon regenerating the model from its history tree is that, as geometry is added, it is dependent upon geometry created earlier. This methodology has been described as a parent/child relationship, except that it can be many levels deep. If a parent level element is deleted or changed in certain ways it can have unexpected effects on child-level elements. In some cases the user was forced to totally recreate the model. Some people described parametric designing to be more similar to programming than to conventional engineering design.”

Parametric design concepts

Considering a scenario, of creating a parametric surface part, where the engineers start from scratch, modeling features sequentially, one by one, and spending time working on the most recent feature without needing to go back to edit previous features. In most cases, they don’t build models from scratch without periodically going back to adjust earlier features from time to time. In that process, they’ll identify and process most of the dependencies.

The parametric modeling paradigm enables engineers to create new concepts based on previous designs. Users can start with a 2D conceptual model and easily use it as the basis of a 3D model. Parametric modeling tools also enable concept designers to use all types of available data, including ideas, 2D drawings, sketches, surfaces, single parts, or entire assemblies and products. Because these modeling tools offer interoperability in a parametric manner, almost no model re-creation is necessary, giving designers more time to explore a wider range of design alternatives [8].

Special and common products, such as automotive/aerospace parts, jewelry, toys, sporting goods, electronics, various devices etc. include parametric surface and solid modeling. Within these product categories there are many items that incorporate complex/free-form shapes presenting some serious modeling challenges.

Case studies in creating parametric surfaces

An important argument to CATIA v5’s success is its parametric feature-based surface and solid modeling approach in initiating 3D models. The software builds a virtual CAD model of a complex product, and, by changing various parameters, it is able to alter/improve its size, dimensions, functionality, aspect etc. In this way, the engineer gain a great leap forward to rapidly create and

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explore design alternatives for parts and assemblies, especially in the context of complex products with many variants [5,8]. In these case studies there are presented some simple CATIA v5 applications to highlight the relative simplicity of creating sweep surfaces only from points and curves in a very intuitive manner. Sweep is a surface generated by sweeping a profile along a guide curve with respect to a spine. The profile can be a user-defined or a pre-defined profile.

In the first case study there are used nine points Point.1 … Point.9 inserted in the 3D space at certain coordinates. Between the three pairs of three points there are traced the curves Spline.1, Spline.2 and Spline.3. Using the Swept Surface tool with the Three guides option selected (Fig.1), the engineer creates a surface Sweep.1 connecting the three curves, interpolating the edges (having a circular form). Each point’s parameters used to create the curves affect the general shape of the resulted surface. As seen in Fig. 1, its width is imposed by the shortest curve (Spline.2).

Fig. 1. Sweep surface through three splines

Inserting three more points (Point.10, Point.11 and Point.12), through them is also created a new

curve, Spline.4. Using the option Two guides and radius (Fig. 2), a new surface Sweep.2 is obtained through the guiding curves Spline.3 and Spline.4 with a radius of 32 mm. Previously, a value of 29 mm was proved to be too small and the surface could not be formed.

Fig. 2. Sweep surface through four splines

In this example, the CATIA v5 program offers six variants to obtain the circular surface, two of

them being closed surfaces. Four examples are illustrated in Fig. 3.

Fig. 3. Different parametric versions of the same sweep surface through four splines

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Further, using the option Center and two angles the engineer creates a new surface Sweep.3 having a central curve Spline.3 and a shape imposed by a reference curve, Spline.4 (Fig. 4).

Fig. 4. Sweep surface created using a reference curve and angular parameters

The dialog box contains two field values for angular dimensions (positive and negative).

Depending of the reference curve and of the angles values, the Sweep.3 surface results in many variants, three of them are illustrated in Fig. 5.

Fig. 5. Different parametric versions of the sweep surface by variating the angle values

In the second case study, using some elements previously created and a new option, Two guides

and tangency surface, the engineer has the possibility to create a stitched and tangent surface to another already existing, based on a curve positioned on it and another considered as a limit. This option of tangent surface is useful to generate surfaces with a common edge and both being tangent along the edge. A new curve is traced in the XY plane in Sketch.1. In the Limit curve with tangency field is selected an edge from surface Sweep.3, which is also present in the Tangency surface field and, as the Limit curve, the profile from Sketch.1. As a recommendation, the curve specified in the Limit curve with tangency field is considered to belong to the surface where the tangency condition will be applied, a convenient and often used solution being the choice of an edge of the surface.

Fig. 6 presents two possible solutions for the surface Sweep.5, in both cases this surface will be tangent to Sweep.3. The shape of each possible surface is automatically computed and represented by CATIA based on certain parameters linked to the limit curves, surface Sweep.3 etc.

Fig. 6. Sweep surface created using a reference curve and angular parameters

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In the third case study, the One guide and tangency surface option is selected, the engineer choose a support curve (Spline.4), a tangency surface (Sweep.5) and enters the surface curvature radius. As seen in Fig. 7, two possible Sweep.6 solutions are available, one positioned along the Sweep.3 surface and the second being tangent to that surface.

Fig. 7. Sweep surface created using a guiding curve and another tangency surface

This option, especially due to the tangency condition and to the possibility of specifying the

curvature radius, is used most often to create connection surfaces. This radius parameter is very important, depending on whether or not it is possible to create the surface.

In the fourth case study, a multi-sections surface is created by sweeping at least two different curves along a control (spine) curve, the resulted surface must take in account one or more guiding curves. This study uses three planes ZX, Plane.1 and Plane.2, the first two are parallel and the third plane is inclined at an angle of 420 to Plane.1. Each plan contains an open curve using Sketch.1, Sketch.2 and Sketch.3 as supports.

These sketches are inserted in the Section column, they become sections of the Multi-sections Surface.1, but there are some constraints to be accomplished: the curves must be planar or three-dimensional, continuous in point, the user is able to select certain areas of tangency for the start and end curve, and these tangent surfaces are not parallel to the considered sections.

Fig. 8. Multi-sections surface

In the case of open profiles, the closing point is one of the extremities and may be modified by

reversing the direction of the red arrows at curve’s ends. Fig. 9 shows the same surface, but its

creation is impossible, it is knotting and an error message is shown. The user has the solution to reorient the red arrows for all the sections profiles, to edit the curves parameters that caused the error, or to use a guiding curve.

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Fig. 9. Twisted multi-sections surface

Conclusions

PLM system CATIA v5 (Dassault Systemes) offers a number of interesting shape modules and modeling tools. Its powerful module, Generative Shape Design includes many tools for creating surfaces from scratch, building complex shapes, editing and validating them. The software can be used to create 3D conceptual sketches or to create curves for surface lofting and model creation. Surfaces created in CATIA v5 environment can be used afterwards in the detailed 3D solid design to create complex products [8]. In industry, a project for a product is always a team effort long before the product is produced and put on the market. Each team member may impose his own parameters and constraints in every phase of the project, the result being a modern parametric design. When a parameter is modified, many others are disposed to be changed according to the relations established by the design engineer, keeping the part or the assembly (the product) in shape. These relations must be mathematically correct and then must respect the product’s design specifications.

Acknowledgement

The work has been funded by the Sectoral Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/.138963

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