BREP & CSG

The geometric modelling technique has revolutionized the design and manufacture of products to a great extent. Although there have been various ways of representing an object, the most commonly used modelling technique is Solid Modelling. The two main ways to express solid models are Boundary Representation modelling and Constructive Solid Geometry modelling.

CONSTRUCTIVE SOLID GEOMETRY

Constructive solid geometry or C-REP/CREP, previously known as computational binary solid geometry, is a reliable modelling technique that allows creating of a complex object from simple primitives using Boolean operations. It is based on the fundamental that a physical object can be divided into a set of primitives or basic elements combined in a particular order by following a set of rules (Boolean operations) to create an object. Typically, they are objects of simple shapes such as cuboids, cylinders, prisms, pyramids, spheres, and cones. CSG cannot represent fillets, chamfers, and other context-based features.

The primitives themselves are regarded as valid CSG models, where each primitive is bounded by orientable surfaces (Half-spaces).

These simple primitives are in generic form and must be confirmed by the user to be used in the design. The primitive may require transformations like scaling, translation, and rotation to be assigned a coveted position.

There are two kinds of CSG schemes:

Primitive based CSG: It is a popular CSG scheme based on bounded solid primitives, R-sets.

Half-space based CSG: This CSG scheme uses unbounded Half-spaces. Bounded solid primitives and their boundaries are considered composite half-spaces and the surfaces of the component half-spaces, respectively.

Some attributes of CSG are as follows:

  • CSG is fundamentally different from the BREP model, where it does not store faces, edges and vertices. Instead, it evaluates them as needed by algorithms.
  • CSG database stores topology and geometry.
  • The validity checking in the CSG scheme occurs indirectly. Each primitive combined using a Boolean operation (r-sets) to build the CSG model fits its validity.
  • The standard data structures used in CSG are graphs and trees.
  • CSG representation is of considerable importance to manufacturing.
BOUNDARY REPRESENTATION

In solid modelling and computer-aided design, boundary representation or B-rep / BREP—is the process of representing shapes using the limits. Here a solid is described as a collection of connected surface elements. BREP was one of the first computer-generated representations to represent three-dimensional objects.

BREP defines an object by their spatial boundaries. It details the points, edges, surfaces of a volume.

BREP can also be explained in terms of cell domain combination.

A cell is a connected limitation of the underlying geometry. There are four kinds of cells as per the spatial dimension they inhabit:

  • Vertex
  • Edge
  • Face
  • Volume

A domain is a set of connected cells grouped to define boundaries. Fields define various components inside a non-manifold object.

Boundary representation of models consists of two kinds of information:

Topology: The main topological entities are faces, edges, and vertices.

Geometry: The main geometrical entities are surfaces, curves, and points.

The topological and geometrical entities are intertwined in a way where:

  • the face is a bounded portion of a character.
  • An edge is an enclosed piece of a curve.
  • A vertex lies at a point. Topological items allow making links between geometrical entities.

BREP comes with its share of advantages and disadvantages, which are:

  • It is appropriate for constructing solid models of unusual shapes.
  • A BREP model is relatively simple to convert to the wireframe model.
  • BREP uses only primitive objects and Boolean operations to combine them, unlike CSG (Constructive Solid Geometry).
  • In addition to the Boolean operations, B-rep has extrusion (or sweeping), chamfer, blending, drafting, shelling, tweaking and other actions that use these.
  • BREP is not suitable for applications like tool path generation.
DIFFERENCE BETWEEN BREP AND CSG

 

Boundary Representation (BREP) Constructive Solid Geometry (CSG)
BREP describes only the oriented surface of a solid as a data structure composed of vertices, edges, and faces. A solid is represented as a Boolean expression of primitive solid objects of a simpler structure.
A BREP object is easily rendered on a graphic display system. A CSG object is always valid because its surface is closed and orientable and encloses a volume, provided the primitives are authentic in this
We review the possible surface types, the winged-edge representation schema, and the Euler operators for B-rep. For CSG, the basic operations include classifying points, curves, surfaces concerning a solid, detecting redundancies in the representation, and approximating CSG objects systematically.

 

Reference: https://catiatutor.com/reading-a-part-body-through/

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Design principles of Jigs and Fixtures

The art of metalworking has a primary concern, locating the part to be machined relative to the platform. A CNC machine starts machining at a specific point corresponding to the fixture and proceeds from there. Therefore, the preciseness with which a job is machined is dependent on the accuracy that holds in the fixture. The accurate location of every part loaded into the fixture is essential. Any deviation in part location adds to the dimensional tolerance that must be assigned to the finished pieces. Furthermore, improper supporting and securing the part in the fixture affects surface finishes by temporarily or permanently deforming it. Hence, techniques for supporting, clamping, and locating must be considered together to assure repeatability from part to part.

Basic principles of Jigs and Fixtures design

LOCATING POINTS: Locating the work is a prime necessity and requires suitable facilities. The correct setup ensures smooth insertion of a workpiece in the proper position and removing a workpiece from a jig without operational hassles or time consumption. The workpiece position needs to be precise with the guiding tool in the jig or setup pieces in the fixture.

FOOLPROOF: A foolproof design of jigs and fixtures does not permit a tool or workpiece to be placed in any other way other than the intended one.

REDUCTION OF IDLE TIME: Jigs and Fixtures must be designed in such a way that ensures smooth loading, clamping, machining, and unloading of a

WEIGHT OF JIGS AND FIXTURES: A jig and fixture must be compact, easy to handle, and low cost regarding the number of materials used without giving up stiffness and rigidity.

JIGS PROVIDED WITH FEET: Some jigs require feet so that they can be placed on the table firmly.

MATERIALS FOR JIGS AND FIXTURES: Jigs and Fixtures are usually created with hardened materials to resist wear & tear and avoid frequent damage—for example, Mild steel, Cast iron, Die steel, High-speed steel, Caesium.

CLAMPING DEVICE: A suitable clamp is rated for its strength. It should be able to hold a workpiece firmly in its position while bearing the strain of the cutting tool simultaneously, without springing.

Broad rules of Jigs & Fixtures Design
  • Compare the production cost of work between the existing tools and the tool to be made and see if the manufacturing price is not more than the expected gain.
  • Determine location points and outline clamping arrangement.
  • Make sure the clamping and binding pieces are as quick to act & efficient as possible.
  • Make the jig and fixture foolproof.
  • Make sure the locating points are adjustable.
  • Do avoid intricate clamping arrangements.
  • Round all corners.
  • Make sure the operator has handles to make handling tasks easier.
  • Provide ample amount of clearance.
  • Provide holes for chips to escape.
  • Systematically locate clamps to resist the pressure of the cutting tool while machining.
  • To avoid springing action, place all clamps in proximity opposite to the bearing point of the workpiece.
  • Test the jigs before putting them in a shop.
The 3-2-1 principle

Locating a part to be machined involves mainly three steps: Supporting, Positioning, and Clamping.

Two main intentions when placing a job on a jig/fixture are:

  • Precisely positioning the part at the desired coordinates.
  • Curbing all six degrees of movement so that the part cannot budge.

An extensively used method for obtaining these objectives is the 3-2-1 principle or six degrees of freedom for part location.

 

Image Source: Quora

The 3-2-1 method is a work-holding principle where three pins are located on the 1st principle plane, i.e., either XY, YZ, ZX. And two pins are located on the 2nd plane perpendicular to the 1st plane, and at last, one pin on the plane is mutually perpendicular to the 1st and 2nd planes. The aim is to constrain the movement of the workpiece along all three axes.

Design objectives of Jigs and Fixtures

Before sitting down to design jigs/fixtures, the designer must consider the following points:

  • The tool must be foolproof to prevent any mishandling or accidental usage by the operator.
  • Easy to operate for increasing efficiency.
  • Easy to manufacture using the lowest costs.
  • Its ability to weather the tool life instead of appropriate materials.
  • Must be consistent at producing high-quality parts.
  • Must be safe and secure to use.

The designer must know the basics of the process and the tools associated with it for which the jig/fixture is designed. Overall objectives to look out for a while developing such tools are:

  • Cycle time.
  • Type of Jig/Fixture.
  • Part Assembly sequence or Machining locations.
  • Joining or machining process.
  • Clamping method and clamping sequence.
  • Required output accuracy.
  • Type of equipment to be used with the jig.
  • Method of ejecting finished output and transferring it to the next. Platform, whether the manual or automatic mode.
  • The type of material, recommended weight, number of spots involving welding.

Reference: National Institute of Technology, Calicut

 

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Designing Jigs and Fixtures

The design of jigs and fixtures is dependent on numerous factors which are analysed to achieve optimum output. Jigs should be made of rigid light materials to facilitate secure handling, as it has to be rotated severally to enable holes to be drilled from different angles. It is recommended that four feet should be provided for jigs that are not bolted on the machine tool, to enable the jig to wobble if not well positioned on the table and thereby alert the operator. Drill jigs provide procedures for proper location of the work-piece concerning the cutting tool, tightly clamp and rigidly support the work-piece during machining, and also guide the tool position and fasten the jig on the machine tool.

To achieve their expected objectives, jigs and fixtures consist of many elements:

  • Frame or body and base which has features for clamping
  • The accuracy and availability of indexing systems or plates
  • The extent of automation, capacity, and type of machine tool where jigs and fixtures will be employed
  • Bushes and tool guiding frames for jigs
  • The availability of locating devices in the machine for blank orientation and suitable positioning
  • Auxiliary elements
  • The strength of the machine tool under consideration
  • The precision level of the expected product
  • Fastening parts
  • The available safety mechanisms in the machine tool
  • The study of the fluctuation level of the machine tool

 

 

The factors below are to be reflected upon during design, production, and assembly of jigs and fixtures due to the targeted increase in throughput, quality of products, interchangeability, and more accuracy.

  • Guiding of tools for slim cutting tools like drills
  • Type of operations
  • Inspection requirements
  • Provision of reliable, rigid, and robust reinforcement to the blank
  • Production of jigs and fixtures with a minimum number of parts
  • Fast and accurate location of the jig or fixture blank
  • Rapid mounting and un-mounting of the work-piece from the jig or fixture
  • Set up time reduction
  • Standard and quality parts must be used
  • Reduction of lead time
  • Easy disposal of chips
  • Enhanced flexibility
Elements of Jigs and Fixtures

The significant features of Jigs and Fixtures are:

The body: The body is the most outstanding element of jigs and fixtures. It is constructed by welding of different slabs and metals. After the fabrication, it is often heat-treated for stress reduction as its main objective is to accommodate and support the job.

Clamping devices: The clamping devices must be straightforward and easy to operate, without sacrificing efficiency and effectiveness. Apart from holding the work-piece firmly in place, the clamping devices are capable of withholding the strain of the cutting tool during operations. The need for clamping the work-piece on the jig or fixture is to apply pressure and press it against the locating components, thereby fastening it in the right position for the cutting tools.

Locating devices: Thepin is the most popular device applied for the location of work-piece in jigs and fixtures.The pin’s shank is press-fitted or driven into a jig or fixture. The locating width of the pin is made bigger than the shank to stop it from being pressed into the jig or fixture body because of the weight of the cutting tools or work-piece. It is made with hardened steel.

Jig bushing or tool guide:Guiding parts like jig bushings and templates are used to locate the cutting tool relative to the component being machined. Jig bushes are applied in drilling and boring, which must be wear resistant, interchangeable, and precise. Bushes are mainly made of a reliable grade of tool steel to ensure hardening at a low temperature and also reduce the risk of fire crackling.

 

 

Selection of Materials

There is a wide range of materials from where jigs and fixtures could be made, to resist tear and wear, the materials are often tempered and hardened. Also, phosphor bronze and other non-ferrous metals, as well as composites, and nylons for wear reduction of the mating parts, and damage prevention to the manufacturing part is used. Some of the materials are discussed below:

  • Phosphor Bronze: phosphor bronze is used in the production of jigs and fixtures for processes that involve making of interchangeable nuts in clamping systems like vices, and also incorporated feedings that require screws. As the manufacturing of screws is costly and also wastes a lot of time, the reduction of their tear and wear is often achieved by using replaceable bronze mating nuts made with phosphor bronze.
  • Die Steels: the three variants of die steel - high chromium (12 %), high carbon (1.5 to 2.3%), and cold working steels are applied in the production of jigs and fixtures for the making of thread forming rolls, as well as cutting of press tools. When alloyed with vanadium and molybdenum for it to retain toughness at very high temperature, die steels are applied in the fabrication of jigs and fixtures that are used in high-temperature work processes which include extrusion, forging, and casting processes.
  • High-Speed Steels: High-speed steels which contain more quantity of tungsten and less quantity of chromium and vanadium have high toughness, hardness retention at high temperature, and excellent wear, tear and impact resistance. When tempered, they are applied in the production of jigs and fixtures for reaming, drilling, boring, and cutting operations.
  • Carbon Steels: when tempered with oil, carbon steels are applied in the making of some jig and fixture parts which are exposed to tear and wear like the locators and jig bushes.
  • Mild steels: Mild steel, which contains about 0.29% of Carbon, is very cheap and because of their easy availability is often the choicest material for the making of jigs of fixtures.

Other materials for the making of jigs and fixtures include Nylon and Fibre, steel castings, stainless steel, cast iron, high tensile steels, case hardening steels, and spring steels.

Reference

Charles ChikwenduOkpala, EzeanyimOkechukwu C “The Design and Need for Jigs and Fixtures in Manufacturing” Science Research.Vol. 3, No. 4, 2015, pp. 213-219. DOI: 10.11648/j.sr.20150304.19

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DFMA and DFMEA

During the last few decades, with the developments in technology, manufacturers have been enabled to source parts globally. More and more manufacturers have entered the competition as it grows fierce. Companies in developing nation market offer products at lower prices. To sustain business and achieve growth, many manufacturers are coming up with new products to cater to the consumers and widen it as well. They must be very marketable and of high quality. The Design for Manufacturing and Assembly (DFMA) method enables firms to develop quality products in lesser time and at lower production costs.

Design for Manufacturing and Assembly (DFMA)

Design for Manufacturing and Assembly or DFMA is a design process that targets on ease of manufacturing and efficiency of assembly.

Simplifying the design of a product makes it possible to manufacture and assemble it in the minimum time and lower cost. DFMA approach has been used in the automotive and industrial sectors mostly. However, the process has been adopted in the construction domain as well.

DFMA is a combination of two methodologies which are:

  • Design for Manufacturing (DFM): DFM focuses on the design of constituent parts to ease up their manufacturing process. The primary goal is to select the most cost-efficient materials and procedures to be used in production and minimize the complexity of the manufacturing operations.
  • Design for Assembly (DFA): DFA focuses on design for the ease of assembly in the product. The aim is to reduce product assembly cost and minimize the number of assembly operations.

Both DFM and DFA seek to reduce material, labour costs associated with designing and manufacture of a product. For a successful application of DFMA, the two activities should operate in unison to earn the most significant benefit. Through the DFMA approach, a company can prevent, detect, quantify, and eliminate waste and manufacturing inefficiency within a product design.

Design Failure Mode and Effect Analysis (DFMEA)

Design Failure Mode and Effect Analysis (DFMEA) is a methodical string of activities to identify and analyze potential systems, products, or process failures.

Design Failure Mode and Effects Analysis or DFMEA focuses on finding potential design flaws and failures of components before they can make a significant impact on the end users of a product and the business distributing the product.

DFMEA identifies –

The potential risks introduced in a  new or modified design,

 The effects and outcomes of failures,

The actions that could eliminate the failures, and

provides a historical written record of the work performed. 

DFMEA is an ideal process for any sector where risk reduction and failure prevention are crucial, which includes:

  • Manufacturing
  • Industrial
  • Aerospace
  • Software
  • Service industries

 

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Faceted Modeling and NURBS

Modern CAD systems and CAD packages enable designers to model objects and retrieve them in their formats. Some formats are interchangeable while some enforce restrictions, upon which, it becomes difficult to transfer an object model from one form to another.

This article describes some of the most used CAD formats in the industry. But before we look into various CAD formats, it is essential to understand the concept of Faceted geometry and Analytic geometry (NURBS).

FACETED GEOMETRY

Faceted geometry, also known as discrete geometry, are models which consist of groups of polygons which is often triangles.

Most Computer-Aided Design (CAD) systems typically use continuous surface and edge definitions based on NURBS. CAE simulations break down this NURBS representation into facets by a process known as meshing. The faceted models are quite appealing to engineering marketing, as such simulations are less bothered with exact physical reality and tend to emphasize on creating eye-catching visuals, such as airflow over a car, which can be incorporated into a marketing brochure. File formats typically used for faceted models are: .3ds, .dxf, .obj, .stl (Stereolithography).

Almost all the faceted formats, except for STL, reflect material properties such as glass and metal by providing groupings of facets. However, such groupings are inadequate for a CAE simulation.

ANALYTIC GEOMETRY (NURBS)

NURBS or Non-uniform rational basis spline describes curves and surfaces with mathematical functions, and form the most common analytic geometry representations. The NURBS geometry has unlimited resolution. The NURBS definition defines the location of the boundary points and uses control points with slope definition to determine the internal shape of curves and surfaces, thereby enabling a great deal of flexibility. NURBS geometry is typically produced in CAD systems such as CATIA, Pro/Engineer, Solidworks, NX, etc. A significant drawback of NURBS geometry is that they are generally specific to the CAD packages that created them, and interchanging formats can be error-prone and inaccurate.

DIFFERENCE BETWEEN FACETED GEOMETRY AND ANALYTIC GEOMETRY (NURBS)

 

Faceted geometry

NURBS geometry

Facets are always guaranteed to comply with the original definition

In NURBS geometry, different levels of model detail are created without losing fidelity

Faceted geometry describes a shape as a mesh, points usually connected by triangles

Analytic geometry defines curves and surfaces with mathematical functions

Faceted geometry has limited resolution

NURBS geometry has unlimited resolution

Evaluating  a faceted surface, one can get a shape defined by linear interpolation between known discrete points

One can assess a NURBS surface anywhere and get coordinates lying on the surface

Simple definition

Includes topology

 

Cons of Faceted geometry

Cons of NURBS geometry

Fixed resolution

More computing intense

No topology

High data exchange

 

Although faceted geometry has its use, NURBS geometry is superior for design and manufacturing processes. Due to the high demands on geometric precision, NURBS geometry finds its place in CAE applications. But if the modeling requirements ask for stunning visuals, faceted models are worth giving a try.

 

 

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FEA, CFD and Mold Flow Analysis

Over the years, the term “Design Analysis” has found a significant place for itself in the manufacturing sector. Instead of making a prototype and creating elaborate testing regimens to analyze the physical behavior of a product, engineers can evoke this information quickly and accurately on the computer.

Design analysis is a specialized computer software technology designed to simulate the physical behavior of an object.

If an object will break or deform or how it may react to heat are the sort of queries design analysis can answer. Design analysis helps in minimizing or even eliminate the need to build a physical prototype for testing. As a result, the technology has gone mainstream as a prized product development tool and found its presence in almost all sectors of engineering.

This article discusses three major design analysis software, namely:

  • Finite Element Analysis (FEA)
  • Computational Fluid Dynamics (CFD)
  • Mold Flow Analysis
Finite Element Analysis (FEA)

The Finite Element Analysis (FEA) is a specialized simulation of a physical entity using the numerical algorithm known as Finite Element Method (FEM). It is used to reduce the number of physical prototypes and experiments and analyze objects in their design stage to develop better products faster. The term ‘finite’ is used to denote the limited, or finite, number of degrees of freedom used to model the behavior of each element.

FEA will analyze an object in question by breaking down its entire geometry into small ‘elements,’ which are put under simulated conditions see how the elements react. It displays the results as color-coded 3D images where red denotes an area of failure, and blue indicates fields that maintain their integrity under the load applied. However, note it down that FEA gives an approximate solution to the problem.

Mathematics is used to understand and quantify a physical phenomena such as structural or fluid behavior, wave propagation, thermal transport, the growth of biological cells, etc. Most of these processes are described using Partial Differential Equations. Finite Element Analysis has proven to be on of the most prominent numerical technique for a computer to solve these PEDs.

FEA is used in:

Problems where analytical solution is not easily obtained,

And mathematical expressions required because of complex geometries, loadings and material properties.

Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a specilaized simulation used for the analysis of fluid flows through an object using numerical solution methods. CFD incorporates applied mathematics, physics and computing software to evaluate how a gas or liquid flows and how it affects an object as it flows past. CFD is based on Navier-Stokes equations which describe the way velocity, temperature, pressure, and density of a moving fluid are related.

Aerodynamics and hydrodynamics are two engineering streams where CFD analyses are often used. Physical quantities such as lift and drag or field properties as pressures and velocities are computed using CFD. Fluid dynamics is connected with physical laws in the form of partial differential equations. Engineers transform these laws into algebraical equations and can efficiently solve these equations numerically.The CFD analysis reliability depends on the whole structure of the process. The determination of proper numerical methods to develop a pathway through the solution is highly important. The software, which conducts the analysis is one of the key elements in generating a sustainable product development process, as the amount of physical prototypes can be reduced drastically.

CFD is used in almost all industrial domains, such as:

  • Food processing
  • Water treatment
  • Marine engineering
  • Automotive
  • Aerodynamics
  • Aerospace

With the help of CFD, fluid flow can be analyzed faster in more detail at an earlier stage, than by tesing, at a lower cost and lower risk. CFD solves the fundamental equations governing fluid flow processes, and provides information on important flow characteristics such as pressure loss, flow distribution, and mixing rates.

CFD has become an integral part of engineering and design domains of prominent companies due to its ability to predict performance of new designs and it intends to remain so.

Mold Flow Analysis

Moldflow, formerly known as C-mould, is one of the leading software used in processwide plastics solutions. Mold flow computes the injection molding process where plastic flows into a mold and analyzes the given mold design to check how the parts react to injection and ensure that the mold will be able to produce the strongest and uniform pieces. Two of the most popular mold flow analysis software are Moldflow and Moldex3D used exclusively by many mold makers.

There are three types of Mold flow analysis which are as follows:

  • Moldflow Filling Analysis (MFA): It facilitates visualization of shear rate and shear stress plus determination of fiber orientation and venting. MFA can predict fill pattern and injection pressure while optimizing gating and runner system.
  • Moldflow Cooling Analysis (MCA): MCA specializes in finding hot spots and calculating time to freeze. It helps in determining uneven cooling between core and cavity while specifying required cooling flow rates.
  • Moldflow Warpage Analysis (MWA): Moldflow warpage is all about predicting, finding and determining warpage due to orientation.

We can see benefits of using different analysis procedures that correctly understand the power of the different simulation tools. During the product design, many these methods affect the cost and quality of the product, thereby ensuring the optimum productivity as aimed by the manufacturer.

 

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Future of Reverse Engineering

Reverse engineering found its use in various industries gradually, as more and more industry leaders adopted this approach and implemented the same, thereby easing out their own work-process. Here is a list of industries that use reverse engineering as a part of their methods:

  • Manufacturing/Heavy machine
  • Automotive
  • Software development
  • Military projects
  • Space expeditions
  • Aerospace
  • Architecture
  • Oil & gas
The future

It is the 21st century. These are great times for design engineers. Over the past two decades, their job has been dramatically changed, with the transformation of finite element analysis (FEA) software from mainframe to desktop computer. With the easy availability of computer-aided design software packages, reverse engineering technology has become a practical means to create a 3D virtual model of an existing physical part. That, in turn, has made the use of 3D CAD, CAM, or other CAE applications easier.

The convenience in the usage, affordability and the ability of its software to tightly integrate with a CAD program has made this process a much favored among engineers. At the same time, the costs of scanners and other hardware used to input measurements have been dropping, and the hardware is becoming smaller and easier to use, according to the hardware makers.

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Geometric Dimensioning and Tolerancing (GD&T)

The design model is a depiction of a part design. However, the design model can never be an accurate representation of the product itself. Due to shortcomings in manufacturing and inspection processes, physical parts never match the design model exactly. An essential aspect of a design is to specify the lengths the part features may deviate from their theoretically accurate geometry. It is vital that the design intent and functionality of the part be communicated between the design engineers and the manufacturing unit. It is where the approach of GD&T comes into play.

Geometric dimensioning and tolerancing or GD&T is a language of symbols and standards used on engineering drawings and models to determine the allowable deviation of feature geometry. 

GD&T consists of dimensions, tolerances, definitions, symbols, and rules that enable the design engineers to convey the design models appropriately. The manufacturing unit uses the language to understand the design intent.

To master GD&T, one needs to understand the crucial concepts, which includes:

  • Machining tolerances: Tolerances mean the allowable amount of deviation from the proposed drawing. Machined parts look flat and straight through the naked eye, but if viewed with calipers, one can find imperfections all over. These imperfections or variations are allowed within the tolerance constraints placed on the parts. Tolerances should be kept as large while preserving the functions of the part.
  • The Datum Reference Frame: DRF is the most important aspect of GD&T. It is a three-dimensional cartesian coordinate system. It’s a skeletal reference to which all referenced geometric specifications are related.
  • GD&T Symbols: It is essential to be familiar with numerous symbols and types of applied tolerance in GD&T. The language of symbols makes it easier to interpret designs and improve communications from the designer to the shop. By using GD&T standard, the design intent is fully understood by suppliers all over the world.

  • Feature Control Frame: The feature control frame describes the requirements or instructions for the feature to which it is attached. A feature control frame contains only one message. If a feature needs two messages, the feature would need the corresponding amount of feature control frames for every message required.
  • Basic Dimensions: Basic dimensions are exact numerical values in theory, which defines the size, orientation, form, or location of a part or feature. 
  • Material Condition Modifiers: It is often necessary to state that a tolerance applies to a feature at a particular feature size. The Maximum Material Condition (MMC) allows an engineer to communicate that intent.

GD&T is an efficient way to describe the dimensions and tolerances compared to traditional approximation tolerancing. The engineer might design a part with perfect geometry in CAD, but the produced part, more often than not, turns out to be not accurate. Proper use of GD&T improves quality and reduce time and cost of delivery by providing a common language for expressing design intent.

 

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Geometric Modeling

The culture of design & manufacturing incorporates various crucial aspects for the production of a market efficient product. Computer-aided Engineering or CAE comes up as a central part of the entire manufacturing process. Over the years, the function of CAE has evolved so much that it has developed its applications depending upon the type of usage and execution.  Geometric Modeling happens to be one of the most popular CAE applications.  

The computer/software generated mathematical representation of an object’s geometry is called Geometric Modeling. As curves are easy to manipulate and bend as per application, geometric modeling uses curves extensively to construct surfaces. The formation of curves can be achieved by,

A set of points,

Analytic functions, or

Other curves/functions

The mathematical representation of an object can be displayed on a computer and used for generation of drawings; which go on for analysis and eventual manufacturing of the object. In general, there are three conventional steps to create a geometric model:

  • Creating key geometric elements by using commands like points, lines, and circles.
  • Applying Transformations on the geometric elements using commands like rotation, achieve scaling, and other related transformations functions.
  • Constructing the geometric model using various commands that integrates the elements of the geometric model to form the desired shape.
 REPRESENTAION OF GEOMETRIC MODELS
  • Two Dimensional or 2D: It projects a two-dimensional view and is used for flat objects.
  • 1 2D: It projects the views beyond the 2D and enables viewing of 3D objects that have no sidewall details.
  • Three Dimensional or 3D: This representation permits complete three-dimensional viewing of the model with intricate geometry. The most leading process of geometric modeling in 3D is Solid modeling.
TYPES OF GEOMETRIC MODELINGS

Depending upon the representations of objects, geometric modeling system can be classified into three categories, which are:

  • Solid modeling

Also known as volume modeling, this is the most widely used method as it provides a complete description of solid modeling.

  • Wireframe modeling

It is a simple modeling system, which is used to represent the object by the help of lines only. Hence, it is also known as Line model representation. However, wireframe modeling is not enough to express complex solids; therefore, it is used to describe only wiring systems.  

  • Surface modeling

This type of modeling represents the object by its surface, and it is used to describe the object with a clear view of manufacturing. By this clear point of view, surface modeling cannot be used to develop an internal surface of any model. Surface modeling uses Bezier and B-spines.

Requirements of Geometric Modeling

The various requirements of geometric modeling are as follows:

  • The cross-section, hidden lines, dimensions are needed for Graphical Visualization.
  • Interchangeable manufacturing tolerance analysis is required while inspection of parts.
  • There should also be properties evaluation and geometrical evaluations in Area, Volume, and property evaluation in Weight, Density, etc..
  • Need for Finite element analysis and Kinematic analysis.
  • Parts classification, planning, etc. in manufacturing.

Geometric modeling is a vast and elaborate field of CAE and requires in-depth study. The next articles dive deep into the various types and facets of geometric modeling.

 

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Mesh

For those acquainted with mechanical design and reverse engineering, they can testify to the fact that the road to a new product design involves several steps. In reverse engineering, the summary of the entire process involves scanning, point cloud generation, meshing, computer-aided designing, prototyping and final production. This section covers a very crucial part of the process — Meshing or simply put, Mesh.

To put a simple definition, a mesh is a network that constitutes of cells and points.

Mesh generation is the practice of converting the given set of points into a consistent polygonal model that generates vertices, edges and faces that only meet at shared edges. It can have almost any shape in any size. Each cell of the mesh represents an individual solution, which when combined, results in a solution for the entire mesh.

 

mesh

Mesh is formed of facets which are connected to each other topologically. The topology is created using following entities:

  • Facet - A triangle connecting three data points
  • Edge - A line connecting two data points
  • Vertex - A data point
Mesh Property

Before we proceed to know the types of meshes, it is necessary to understand the various aspects that constitute a mesh. It is important to know the concept of a polygonal mesh.

A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple polygons as that simplifies rendering. It may also be composed of more general concave polygons or polygons with holes.

Objects created with polygon meshes must store different types of elements. These include:

  • Vertex: A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates
  • Edge: A connection between two vertices
  • Face: A closed set of edges, in which a triangle face has three edges, and a quad face has four edges
  • Surfaces: They are often called smoothing groups. Generally, surfaces are not required to group smooth regions

A polygon mesh may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:

  • Face-vertex meshes
  • Winged edge meshes
  • Corner tables
  • Vertex-vertex meshes
Types of meshes

Meshes are commonly classified into two divisions, Surface mesh and Solid mesh. Let us go through each section one by one.

Surface Mesh: A surface mesh is a representation of each individual surface constituting a volume mesh. It consists of faces (triangles) and vertices. Depending on the pre-processing software package, feature curves may be included as well.

Generally, a surface mesh should not have free edges and the edges should not be shared by two triangles.

The surface should ideally contain the following qualities of triangle faces:

  • Equilateral sized triangles
  • No sharp angles/surface folds etc. within the triangle proximity sphere
  • Gradual variation in triangle size from one to the next

The surface mesh generation process should be considered carefully. It has a direct influence on the quality of the resulting volume mesh and the effort it takes to get to this step.

surface mesh

Solid Mesh: Solid mesh, also known as volume mesh, is a polygonal representation of the interior volume of an object. There are three different types of meshing models that can be used to generate a volume mesh from a well prepared surface mesh.

The three types of meshing models are as follows:

  • Tetrahedral - tetrahedral cell shape based core mesh
  • Polyhedral - polyhedral cell shape based core mesh
  • Trimmed - trimmed hexahedral cell shape based core mesh

Once the volume mesh has been built, it can be checked for errors and exported to other packages if desired.

solid mesh

Mesh type as per Grid structure

A grid is a cuboid that covers entire mesh under consideration. Grid mainly helps in fast neighbor manipulation for a seed point.

mesh grid

Meshes can be classified into two divisions from the grid perspective, namely Structured and Unstructured mesh. Let us have a look at each of these types.

Structured Mesh: Structured meshes are meshes which exhibits a well-known pattern in which the cells are arranged. As the cells are in a particular order, the topology of such mesh is regular. Such meshes enable easy identification of neighboring cells and points, because of their formation and structure. Structured meshes are applied over rectangular, elliptical, spherical coordinate systems, thus forming a regular grid. Structured meshes are often used in CFD.

structured mesh

Unstructured Mesh: Unstructured meshes, as the name suggests, are more general and can randomly form any geometry shape. Unlike structured meshes, the connectivity pattern is not fixed hence unstructured meshes do not follow a uniform pattern. However, unstructured meshes are more flexible. Unstructured meshes are generally used in complex mechanical engineering projects.

Unstructured Mesh

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