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    FROM 2D/3D CAD TO FEM ANALYSIS: THE DEVELOPMENT OF AN APPLICATION ATRKB

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    From 2D/3D CAD to FEM Analysis:the Development of an Application at RKBCiprian Radu, Catalin Danaila

    RKB Bearing Industries - Advanced Software Engineering Unit

    Abstract: RKB Bearing Industries produces a wide range of bearings of different size, but mostof all it is specialized in manufacturing custom-made bearings for special applications. In thispaper, the development of an oil platform will be followed to make clear how the transitionfrom handmade 2D paper sketch to CAD design has led to an overall enhancement of thequality, performance, reliability and delivery time of our bearings. We will show how 2D/3DCAD tools and FEM analysis software are used to study the behavior of the bearings requiredby specific applications, providing customers with the best possible technical solutions.

    Key words: Bearing, Design, 2D, 3D, CAD, FEM, Oil platform

    1. History

    Since the earliest times, the need to draw a plan or a sketch of the things to bebuilt or manufactured appeared. It is very possible that technical drawingspredated even the written language. The drawing board inscripted with a templeplan from the city of Lagash in Babylon is the oldest known technical drawing (3 rd millennium B.C.). The ancient Greeks (Euclid, Pythagoras, Thales, Plato, andAristotle) had a big contribution on how drawings are made today, with their studyof geometry. One of the oldest examples from the medieval period is the Plan ofSaint Gall (figure 1), which was created somewhere between 819 and 826 A.D. anddepicts an entire Benedictine monastic compound, including churches, houses,stables, kitchens, workshops, brewery, infirmary, and even a special house forbloodletting [10].

    The contemporary technical drawing has its roots in 15 th century, in theRenaissance Era, with artists like the Italian architect Filippo Brunelleschi, who is thefirst to use mathematical perspective to redefine Gothic and Romanesque spaceand to establish new rules of proportion and symmetry (figure 2). In the 18 th century,the mathematician Gaspard Monge was the first to use descriptive geometry,

    when he drew up a fortification plan that would prevent enemies from seeing orfiring at a military position (figure 3). The isometric drawing was later introduced, in early 19 th century, by EnglishmanWilliam Farish [11] (figure 4).

    Before the 18 th century, there was no need for interchangeable parts, the components were selected randomly, sothat they fit together, and there was no accurate drawing for them. All products were made one at a time, whichmade each one of them unique. Through the 19 th century, many of the designs started with a handmade sketch,which was then changed into a wooden model before being constructed [10].

    One of the first efforts to create a program, standardize drawings and establish a mechanical drawing school,came from Philadelphia Franklin Institute, in 1824. Architecture was among the first design disciplines that made useof conventions of plan, elevation and section, in design and production. The higher complexity of the architecturalprojects generated a separation between design and construction. The Industrial Revolution pushed engineers touse architectural conventions [13; 14].

    Together with the Industrial Revolution came the mass production of the same part, and designs started to bemade with the interchangeable concept in mind. For this to be accomplished, parts needed to be identical, withindesigned tolerances. Naturally, this is possible only with detailed technical drawings of every part of the assembly tobe built. Sometimes the drafting was handmade by the project engineer, but, due to the massive amount of workthat was necessary, this job was usually left in the hands of specialized drafters. The drafters used a smooth surface

    Fig. 1 - The Plan of Saint Gall

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    with right angle corners and straight sides, onto which they placed a piece of paper. For drawing, they used a T-square that was attached on one of the sides of the table and that could slide across the paper [16; 17].

    Fig. 2 - Filippo Brunelleschis drawing Fig. 3 - Example of descriptive geometry Fig. 4 - Example of geometricperspective drawing views

    There, parallel lines could be drawn by only using the T-square and a technical pen, but usually the T-square wasused to hold other devices like rulers, squares and triangles, that helped the drafter draw lines in different positionsand angles. For the arcs and the circles the drafter basically used the compasses, while for the complex curves heused particular pieces of plastic. In order to draw recurring objects, like letters, numbers and other standard symbols,drafting templates were used [13]. With the development of the products, the drawings also became more andmore complex. Even for two lines at a certain angle, several moves were needed; with the T-square, the draftingprocess became a very time consuming process [14].

    So, a new device appeared, namely the pantograph, which is a "drafting machine" that helped the drafter havean accurate right angle anywhere on the page, quite quickly. Even with the help of such tools like the pantograph,the drafter had a very difficult job. Not only he had to master the methodology of drawing lines, arcs, circles,standard texts and symbols, with regard to the physical object, but he also had to have a good understanding ofgeometry, trigonometry and an excellent spatial comprehension [12; 15] (figure 5).

    Fig. 5 - Drafting equipment

    Since drafters' drawings were based on very complex techniques and were used directly in the manufacturingprocess, they required precision, accuracy and attention to detail. In big factories, with complex products with amultitude of interchangeable parts, there were entire departments of drafters, but that fact was destined to changewith the birth of Computer-Aided Design (CAD) [12].

    2. Computer-Aided Design (CAD)

    CAD is basically a graphical representation of data. A prime example of computer graphics is the SAGE (Semi-Automatic Ground Environment), used by the Air Defense Command and Control System in the 1950s. SAGEconverted radar information into computer-generated images, which were displayed by means of a Cathode RayTube (CRT). As an input device, it also used a light pen, so as to select information directly from the CRT screen [19].

    In 1963, an important advancement in graphics technology was made by Ivan Sutherland, with his Sketchpadsystem, described in detail in his doctoral thesis at MIT. Running on a room-sized Lincoln TX-2 computer, the

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    Fig. 6 - The Sketchpad system

    Sketchpad system was able to create images that could berotated, moved, scaled, stored and modified with the help of a lightpen, which is considered to be the predecessor of the mouse (figure6). This revolutionized the way people could interact withcomputers. The graphical capabilities of the Sketchpad showed thepotential for computerized drawing in design. While he was aprofessor of electrical engineering at the University of Utah,Sutherland continued his research on head-mounted displays(HMDs) [19]. Later on, in 1968, together with the founder of theUniversity's Computer Science Department, he cofounded "Evansand Sutherland", that pioneered computer modeling and software[19].

    At first, CAD was accessible only to big corporations that couldpay big amounts of money for the complicated equipment andallocate big human resources to the maintenance, operation and

    software development, specific for each factory. This meant that only large corporations, like car manufacturers andother industry giants, had access to the new CAD systems, while the small companies continued using the old

    methods. Beginning with the late 1980s, the appearance of CAD software that could run on personal computersmeant that CAD was now accessible to mid-size and small companies as well. One CAD operator could now do the

    job of three to five drafters, using the traditional methods, and furthermore, many engineers started to make theirown drafting work. This immediately led to the start of a massive downsizing of the drafting departments; the time ofthe drawing board was coming to an end [19; 20].

    3. 2D Computer-Aided Design (2D CAD)

    The development of the personal computer started to have an effect on the entire design process, not only indrafting techniques, from the request of a customer to the delivery of the finished product. These days, CAD hasbecome not only a platform to replace the old drafting tools, but also, due to the increase in computational power,the means to do detailed analyses of the products before being launched in production [18].

    Before explaining the possible advantages of CAD, the steps of a design project will be presented. Any developingproject has several distinct stages [20]:

    1. customer demand,2. problem definition,3. synthesis of the possible solutions,4. analysis and optimization,5. evaluation of the optimum solution,6. final design and specification,7. product release to market.

    In today's competitive market, customer demand is extremely diverse and changes rapidly. In order to survive,companies need to answer a lot quicker to satisfy customer needs. Being specialized in the development of custom-made bearings for special applications, RKB uses CAD systems to get improved product performance, reliability and

    manufacturing timetables.As an example of how the Group makes use of these systems, the steps that RKB has taken to provide two bearingsfor an oil platform will be followed.

    In the old days, the development of a design started with time consuming manual drafting, resulting in detaileddrawings that afterward were manually analyzed using complex mathematical formulas. When this process wasdone, the improvements that resulted had to be implemented in the drawings, which meant going back to thedrawing board for the drafters [21].

    Today, there are many programs for CAD drafting: AutoCAD, Solid Edge, AutoSketch, eDrawings, and more. CADdrafting has several advantages [21; 22]:

    - the time to make a drawing with CAD tools is a lot shorter;- during the modeling process, CAD systems use mathematical operations that can be easily stored and

    retrieved for review, analysis and modification;- a 2D database of all the drawings can be built, which means that they can be easily accessed and

    modified for new projects or improved for ongoing projects;- the friendly interface lets the operator quickly use the drafting tools, templates and standardized symbolsand letters;

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    Fig. 7 - Application sketch with the position of the bearings

    - elimination of human drawing errors;- shift from paper-based work to electronic

    paperless one.

    RKB Bearing Industries has the full benefit of the 2Ddrafting and uses AutoCAD for the representation ofits 2D bearing drawings, assemblies and components.For the RKB application, the 23248CAW33XS1A and23048CAW33XS1A spherical roller bearings havebeen used (figure 7).

    The assembly drawings are made in a standardtemplate, used for all RKB bearing drawings, which isinserted very easily. In this template, the followinginformation is introduced: release date, type ofbearing, identification number, weight, manufacturer(RKB plant), total mass and a component table (with

    the order number, description, quantity, material, unit of measurement of each part) (figures 8, 9). The drawings also

    contain detailed information regarding the assembly: relative position of the components, dimensions, tolerances,reference plans, load ratings, radial clearance, and optimum operating temperature.

    Fig. 8 - RKB spherical roller bearing 23248CAW33XS1A Fig. 9 - RKB spherical roller bearing 23048CAW33XS1A

    4. 3D Computer-Aided Design (3D CAD)

    The drafting capabilities of CAD systems are useful to make production drawings and have good representations

    of the technical information required for manufacturing, but do little to help designers [1].

    Bearing A

    Bearing B

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    There can be represented a wide range of curves and, due to point to point representation, it is perfect forCAM applications;

    - the solid model represents the surface of the model with the added attributes of volume and mass (figure13). This type of representation allows the calculation of the product's physical proprieties. The model can beobtained through constructive solid geometry (that uses Boolean operations) or boundary representation(that uses surface boundaries: faces, edges and vertices);

    - the hybrid solid model is a mixture of wireframe, surface modeling and solid geometry.

    Even though bearings generally consist of only four main components (inner ring, outer ring, cage and rollers), RKBBearing Industries gets important benefits from using 3D CAD, as this paper will emphasize following the oil platformproject development. Through 3D CAD, RKB can use FEM analysis to test and improve the bearings design.

    First of all, it is crucial to see how an RKB bearing goes from 2D to 3D in the CATIA V5 environment. The informationfrom the 2D drawings (figures 14, 17, 20, 23) is sufficient to create the 3D model, provided that it is used in a properway. The starting point is a sketch, that mimics the 2D model; then, using a circular generator, as all the componentsin a bearing are circular, we get the 3D model.

    Fig. 10 - Wireframe view Fig. 11 - Surface view,polygon mesh

    Fig. 12 - Surface view, truecurve surfaces

    Fig. 13 - Solid model,constructive solid geometry

    In 3D CAD the designer is enabled to make sections of the model along different patterns. This operation is

    particularly useful in assemblies, to study the geometrical interaction between different components. We show asection of each 3D model to see the resemblance to the starting 2D model (figures 16, 19, 22).One of the first advantages of a 3D model is the easiness with which one can get a better understanding of how

    the real object looks like (figures 15, 18, 21, 24).

    Fig. 14 - Outer ring 2D model Fig. 15 - Outer ring 3D model Fig. 16 - Outer ring 3D model section

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    Fig. 17 - Inner ring 2D model Fig. 18 - Inner ring 3D model Fig. 19 - Inner ring 3D model section

    Fig. 20 - Cage 2D model Fig. 21 - Cage 3D model Fig. 22 - Cage 3D model section

    Fig. 23 - Roller 2D model Fig. 24 - Roller 3D model

    With the information from the 2D assembly (figure 25) and the 2D components, we can take all the 3D models ofthe parts and create a 3D assembly model (figure 26).

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    Fig. 34 - Loaded rollers withmisalignment

    By using the "Clearance function", it becomes possible to determine the clearance values between bearingcomponents. This fact is very important, especially when the radial or axial clearance of the bearing has to beverified and then compared with the true value given by the bearing technical sheet.

    Fig. 31 - Clearance between the cage and the inner ring Fig. 32 - Clearance between the rollers and the cage

    Fig. 33 - Clearance between the rollers and the cageafter modifications to the rollers diameter

    Designers can also see the effect that external factors can have on thebearing. For example, in case of misalignment, one can establish how many andat what degree the rollers would be affected (figure 34). This can be helpful forthe designer to see the effect of different parameters that can be modified overthe contact area.

    For the oil platform application, from the assembly sketch where the two RKBbearings would be mounted, we have created a 3D model, containing (figure35):

    1. 23248CAW33XS1A spherical roller bearing,2. 23048CAW33XS1A spherical roller bearing,3. housing,4. shaft,5. spacer,6. pinion.

    This model is not only used to see how the bearings fit inside the application of our customer, but also and most ofall to see how the bearings will behave under the different loads to which the entire mechanism is subjected. For thecalculation of the reaction forces inside the bearing, another major step in CAD has been taken: FEM - Finite ElementMethod, which shows the level of commitment that RKB has in providing its own customers with the best possibleproduct.

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    Fig. 35 - 3D model of the oil platform application

    5. Finite Element Method (FEM)

    Before a product is launched in the market, it is necessary to test its functionality and reliability and check if itbehaves as intended in the design. An engineering analysis needs to be performed, and this can be done in twoways: analytical and experimental.

    The experimental analysis requires a prototype of the product to be tested (in real life conditions) and data to be

    collected for interpretation. This type of analysis gives designers a very good feedback regarding the performance ofthe product, but it is costly and very time consuming, and sometimes the bad results from tests push the designersback to the "drawing board" [6].

    In the analytical analysis , the CAD model is subjected, in a software environment, to simulated conditions, using anumber of mathematical formulas. The analytical analyses represent numerical solutions of the test, being able tosolve even the very complicated stress problems. The great advantage of analytical analysis is that, if properly used,it gives designers a quick feedback over the product performance [8].

    On the market, there are several well known FEM programs, like ANSYS, Abaqus, LS-DYNA, Nastran.The FEM uses codes less complicated than most of the word processing and spreadsheet packages. Basically, FEM

    doesn't use very complex formulas for an entire process of the examined system; it divides the examined subject intomany segments, and calculates each one of them. The result of the entire problem is the sum of each finite element,each one of them being interconnected with its neighbors [2].

    The connection is made through the nodes, and the interaction, for example, is given by the stress that appears ineach point, due to the force that they are subjected to [2].

    Fig. 36 - Stress at a point Fig. 37 - Finite element

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    Before showing the steps necessary for a FEM analysis, the types of problems that can be encountered with thismathematical method are presented below:

    - linear statics : it is the basic type of analysis. In this case, the stress is proportional, linear , to the force that isgenerating it. Static comes from the fact that the forces do not vary in time, or if they do, the change is soinsignificant that it can be safely ignored. In a linear static case, a beam under constant load can beanalyzed as a linear static problem. Another example is the steady state temperature distribution within amaterial with a constant property structure. In the case of temperature differences, thermal expansionsappear, generating thermal stress [8];

    - buckling : it is a linear static analysis. A structure is considered to have a stable equilibrium, which means thatwhen the load is removed, the structure is assumed to return to its original state. However, under certaincombinations of load, the structure continues to deform without any modification of the input data. In thiscase, the structure has become unstable, has buckled. For elastic or linear, in buckling analysis it isconsidered that the structure does not yield and that the direction of input data (applied forces) does notchange. Elastic buckling includes the effects of differential stiffness, which implies a higher order strain-displacement relation, which is a function of the geometry, of the element type and of loads. In physicalterms, the differential stiffness represents the softening or stiffening of the material. In the buckling analysis,

    the eigenvalues, which represent the scaling factor, are first calculated. Then they are used to multiply theloads and obtain the new values, namely the buckling loads. The only buckling load that is of interest is thelowest one, since the structure will fail before reaching any of the higher buckling loads [2; 8];

    - normal modes : in this type of analysis, the natural frequencies and mode shapes of a structure arecomputed. By natural frequencies, it is understood the frequency at which a structure will tend to vibrate.The deformed shape of the structure at a specific natural frequency is called the mode shape. Because itincludes the natural vibrating frequency, the normal mode analysis is also known as the real-eigenvalueanalysis. Normal mode analysis gives a thorough understanding of the dynamic characteristics of structures.In static analysis the displacements are equivalent to those in reality and, because there is no loadconsidered, each shape component can be scaled by an arbitrary factor [6];

    - nonlinear statics : nonlinear structural analysis must be used if large displacements occur with linear materials,if nonlinear materials are studied under load, or if it is necessary to understand the behavior of a compositematerial (linear material combined with nonlinear material). An example of nonlinear statics is when astructure is loaded beyond its wield point, when permanent deformation occurs and linear statics no longerapplies. In nonlinear material, the material stiffness matrix will change during computation. Another examplewhere nonlinear statics can be applied is the contact problem, where a gap or a sliding effect occursbetween components during the load application or removal. Taking in consideration that this type ofphenomenon appears between the roller and raceways, nonlinear statics analysis is recommended to studythe bearing behavior [2; 8];

    - dynamic response : it consists of frequency and transient response. The frequency response analysiscomputes the structural response to a steady-state oscillatory excitation (rotating machinery, unbalancedtires, helicopters blades etc.). In frequency response, the loads are applied within a frequency domain. Theforces can be in the form of enforced forces or motions. The most common engineering problem is to applysteady-state sinusoidal varying loads to several points of a structure and calculate its response within afrequency range. Transient response analysis computes the behavior of a structure under well determinedtime-varying excitations. The result of a transient response analysis consists of displacements, velocities,accelerations and stresses, which appear in the structure analyzed [2].

    A finite element analysis consists of three main steps:

    1. Preprocessing : in this stage the user constructs the model of the parts to be analyzed, then the geometry isdivided into a number of discrete elements which are interconnected through the nodes. Some of thenodes will have fixed displacements, while others will have prescribed loads. These models can be very timeconsuming to prepare, and the FEM software on the market try to give the best user friendly interface towork with. Some of these software packages can overlay a mesh over a preexisting CAD model, and so thefinite element analysis becomes a part of the CAD technology [6]. This is the case of the model from the oilplatform project, which is presented in this review. First of all, the 3D model is imported from CATIA to ANSYS.During importing process, the assembly components are differently colored by default for a bettervisualization and selection of the assembly components (figure 38). The gear has been eliminated from themodel because it is not the subject of our study.

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    Fig. 38 - 3D model imported from CATIA to ANSYS

    The next step is the meshing of the model. The mesh consists of over 237525 nodes (hexaeders andtetrahedrons) and 65117 elements (figure 39).

    Fig. 39 - 3D model with mesh

    When meshing the parts, it is of paramount importance to give special attention both to the geometry andto the points of interest in the analysis. Usually, the parts are divided into much smaller components at thepoints of contact, or where the parts might break: these areas represent stress concentrators. This process is

    crucial, because in this way the results will be more accurate and much closer to reality [4] (figure 40).

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    Not all the information from a FEM model is of interest. In the case of the RKB model, several key data thatneeded to be extracted has been identified:

    - the number of rollers in contact with the rings : under load, only 4-5 rollers are in contact with the rings(figure 42). This is of vital importance for the operating life of the bearing; the contact area betweenthe rollers and the rings is also displayed;

    Fig. 42 - Number of rollers in contact

    - the stress distribution : it is of great importance to the designer, in order to locate the weak spots inwhich the system might brake under load. With this information, he can change the design and seethe effect that the modification might have over the results [4];

    Fig. 43 - Equivalent (von-Mises) stress distribution in the assembly

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    - reaction forces : these forces give the actual load on the bearings:

    Fig. 44 - Reaction forces in the bearings

    - the cases in which the parts have suffered irreversible deformation ;- displacement : it shows the effect of the loads on the bearings, so that it can be easily determined ifthe deformations are elastic or plastic [4];

    - stress in the bearings : it gives the contact stress values that appear inside the bearing, the mostimportant being the contact stress values between the roller and the raceways of the inner andouter rings (figure 45).

    Fig. 45 - Equivalent (von-Mises) stress distribution in the bearings

    F: system input force,FA: 23048CAW33XS1A bearing reaction force,FB: 23248CAW33XS1A bearing reaction force.

    F = 2243 kN

    FB = 912,73 kN

    FA = 1330,27 kN

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    The comparison between the linear and nonlinear analysis shows that the nonlinear method is more consistent andcloser to reality (figure 46).

    The result of this investigation on the oil platform application is that RKB bearings can withstand even the mostdemanding forces they might be subjected to in real life conditions.

    Fig. 45 - Comparison between linear and nonlinear analysis

    6. Conclusions

    FEM analysis does not eliminate real tests. In order to have precise FEM analysis results, they should be comparedwith the results from real tests. The FEM model should go through a continuous improvement process, based on realtests, experience of the designer and new mathematical evolutions in CAD technology. CAD technology is amultibillion dollar industry; it is used from car crash simulations to factory floors testing, from aerodynamic testing tocomplete simulation of an airplane, from electrical circuits testing to fluid simulations.

    For RKB it is of paramount importance to provide its customers with products of the highest possible reliability. Beingcommitted to this principle, RKB makes use of the best available technology.

    References

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    Review, No. 73, 2005.[5] Kuric I., Computer Aided Systems , University of Zilina, Faculty of Mechanical Engineering, Department of

    Machining and Automation, Slovak Republic, 2005.[6] Koyama T., Applying FEM to the Design of Automotive Bearings , Automotive Bearing Technology Department,

    Motion and Control Magazine, No. 2, 1997.[7] McMahon C., Browne J., CADCAM: Principles, Practice and Manufacturing Management , Practice Hall, 1998.[8] Roylance D., Finite Element Analysis , Department of Materials Science and Engineering, Massachusetts Institute

    of Technology, Cambridge, 2001.[9] Yamashita T., Introduction of 3D CAD in Bearing Development , Engineering Administration Department, Bearing

    Engineering Center, Koyo Engineering Journal, English Edition, No. 159E, 2001.[10] http://en.wikipedia.org/wiki/User:Mdd/Architectural_drawing[11] http://www.search.com/reference/Perspective_(graphical)[12] http://www.elinedesign.com/drafting_methods.htm[13] http://www.artdesignweb.com/learn_art/drawing/drawing_technical.htm[14] http://www.wikid.eu/index.php/Technical_drawing[15] http://www.absoluteastronomy.com/topics/Technical_drawing[16] http://www.statemaster.com/encyclopedia/Technical-drawing[17] http://www.drftsmn.com/2010/03/technical-drawing/[18] http://punetech.com/an-overview-of-computer-aided-design-cad/[19] http://senthilnet.com/cad-cam-history.html

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