the components such as the sprockets. In Fig.3.1 a three sprocket arrangement is presented. If all three diameters are fixed and the only variable is the height of ...
Tridimensional Computerized Modeling
ISBN 978-973-0-15929-5
9 789730 159295
Valeriu Dragan
90000
Tridimensional Computerized Modeling
Valeriu Drăgan
Bucharest 2013
1906 Tridimensional Computerized Modeling © Valeriu Drăgan 2013
ISBN 978-973-0-15929-5
Contents Introduction Modeling a cog wheel I Modeling a jack screw II Designing a chain transmission III Modeling a centrifugal fan volute IV Volute core for fluid dynamics simulations V Centrifugal compressor rotor VI VII Simple turbofan mixing VIII Scalloped air mixer for turbofan engine Automatic digitization of scanned 3D models IX Transposing a sketch into points Cartesian X coordinates References
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Foreword Technical drawing has always been a fundamental branch of design – both in engineering and architecture or urban planning. Today, technical drawing – at a professional level is almost exclusively done with computerized aid, the only niches which still use, for the preliminary stages, hand drawing being the ones which aim for aesthetic qualities ( since even ergonomic design is now computer aided). This state of affairs is brought on, in most part, by the weight of the numerical simulations (CFD, FEA etc.) required by the design process, as well as the development of 3D printing technologies or, in general, of computerized numerical command machines. The current paper is thought out as a series of three dimensional drawing examples of parts common to aerospace and mechanical engineering. The examples aim to present as many options and techniques available in the SolidWorks CAD software. Although not all the functions and tools available were used or exemplified, it is a personal belief that the ones which were insisted upon provide a good starting point for users who wish to reach a more advanced level. Certain models were chosen in order to include many stages, so that the approach, or workflow, will not fade behind technical details such as tools, features, options and so on. At the beginning of each chapter a “strategy” is presented in broad lines especially in order to accentuate on its usefulness. In technical drawing we often encounter models which, although at first glance look easy to render, prove 1
themselves to be impossible to depict with accuracy without using certain techniques (as it is the case with chain transmissions). This is the reason why it is important to study the subject or part (which may imply the study of all geometrical and functional relations) as well as the available drawing techniques (with their respective capabilities and limitations). Although imagination and exercise (experience) are complementary, they have a fundamentally different nature, therefore both must be “trained”. The idea that the experience gained in designing certain types of parts can be transferred to every other design problem is absurd. Often, the only transferable knowledge refers to the way a designer interprets the geometric problem and, in some cases, the specifics of the software used. This is the reason why diversity is very important in the choice of the parts used for training as well as in the approach of the modeling process itself – this is, off course, if it does not interfere with the accuracy or usefulness of the drawing (from the perspective of its later use in other engineering software). In conclusion, the paper wishes to present, in the shortest space possible, a diverse spectrum of geometrical models specific to aerospace design. This is done with the hope that, in doing so, the imagination of the reader will be stimulated and, at the same time, the most basic modeling techniques will be presented to the most of their potential.
Eng. Valeriu Drăgan, Ph.D 2
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Introduction Computer aided design (CAD) software programs have many common features, mostly due to the engineering requirements and rigors of part and assembly design and also to the norms used for representation and dimensioning of technical drawings and drafts. Amongst the common features of CAD programs are the basic settings – such as the tolerances, rendering accuracy, viewports or the ability to import and export files in universal formats for other engineering programs (CAx). Also, a common way to organize a CAD suite is to partition it into three modules: Part Design (for designing the basic components of an assembly), Assembly Design (for putting together two or more parts or other sub-assemblies) and Generative Drafting (for quickly and rigorously drafting the technical drawings of the part or assembly). The purpose of this work is to present through examples, the main instruments for part modeling and therefore all discussions and tutorials will refer only to the Part Design module. The CAD program used for modeling the parts is SolidWorks, hence the terminology, feature names and menus are specific to this particular software. However, the principles and main ideas presented herein are, to a high degree, transferable to other CAD programs as long as the user is aware of the capabilities and particulars of the CAD package at their disposal. A good starting point in designing a model is to make sure that the units (S.I, Imperial, etc.) and the tolerances are convenient to the final goal of the designer (i.e. for fluid dynamics applications the tolerances are typically very low, 5
sometimes of the order of microns). Also, the working space environment should facilitate the model visualization for each stage in the modeling process. SolidWorks allows the user to modify the default settings both in the unit, tolerance or rendering settings and other implicit values (e.g. extrusion length). Also, the viewports have adjustable perspectives as well as a wide range of background textures – which may come in handy, especially in the Assembly Design mode. Currently, the per-se design of any mechanical component requires, in almost all the cases, the simulation of the operating conditions – not only in order to make sure that the part/assembly works properly but also for optimization purposes. Therefore it is necessary to transfer the CAD geometry from the native program format to a meshing or numerical simulation program. This transfer is generally done through the use of universal, standardized formats such as: -
Stereolithographic (*.STL). Developed initially for 3D printing, the process involves the layer by layer lithography of the 3D model. The process and method is described in the US Patent 4,575,330 by Charles Hull. In this format the surfaces are reconstructed though a triangle paving method named “tessellation”( although the etymology of the word refers to quadrilaterals - – lat. tessera ~ square; gr. τεσσερα ~ four). Vertices from the original surfaces are automatically selected and used to create a paved surface mesh with triangles. All the coordinates of the exported vertices are positive, the reference system must therefore be changed so that it is placed in the corner of the object’s bounding box. Another aspect of the *.STL format
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is that it holds no measuring unit information, hence the units must be specified (or implied) at import. -
ACIS (*.SAT) Perhaps one of the most versatile formats, an acronym for „Alan, Charles, Ian's System”, the ACIS file format was introduced in the late 80’s. In SolidWorks, in order to export the 3D curves, the user must tick the checkbox accordingly, since this is not a default setting.
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ParaSolid (*.x_t; *.x_b) From a theoretical standpoint, this file format is supposed to be the best in terms of surface quality due to its sophisticated data encoding. A disadvantage of this format is the impossibility to save 3D curves.
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IGES (*.IGS; *.IGES) Initial Graphics Exchange Specification, developed in the late 70’s by the U.S. National Bureau of Standards under the code NBSIR 80-1978, it is one of the most commonplace universal format. With the advent of the STEP format in the 90’s, the further development of the IGES is discontinued however it remains to this day virtually ubiquitous in CAD software.
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STEP (*.STP; *.STEP) Described fully by the ISO 10303-21, it is one of the most modern file formats, being constantly improved even in the early 2000s.
SolidWorks also allows the files to be saved as 3D portable document files (*pdf) which can be read by any reader of this format without the need to install any SolidWorks
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modules. In the *.pdf, the user is allowed to view the 3D model by rotating, translating or orbiting around the object but also to modify the rendering style or illumination. Each of the universal file formats has its advantages and disadvantages and it is up to the user to develop the know-how and decide which one to use in a particular situation. Most of the import operations are typically automated however surface healing will sometimes be required. For CFD meshing, it is often necessary to reconstruct the geometry by hand in order to insure that the gaps between adjacent surfaces are smaller than the smallest mesh cell (sometimes as small as 10-5 [mm]). At this time it is useful to mention the special compatibility between the simulation suite associated with SolidWorks, Cosmos and Flow Simulation (FloWorks) which use the native geometry of the model. Another meshing software which – at least in theory – can import native SolidWorks files is Ansys ICEM-CFD. For part modeling, SolidWorks is able to perform basic operations - Extrude, Loft, Rotate, Sweep – for boss and cut as well as more complex operations such as Wrap, Free Form, Radiate, Surface – Offset, Face – Replace, Heal or Spline on Surface. Also, the program has a well developed set of tools for additional references (lines, points, planes or coordinate systems) which aid the user in both modeling and visualization. Since most of the basic features and tools are common for all CAD programs – in one shape or another, it is my hope that the next tutorials will serve outside the framework of the program used to make them.
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Chapter I – Modeling a cog wheel
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I – Modeling a cog wheel The main problem to be solved within this chapter is the tracing of the cog outline for a cogged wheel. The current example uses a method which is relatively intuitive and easy to apply and leads to a geometrical calculation for several vertices on the outline contour. In this example the cog is symmetrical and is an evolvent (involute) curve. Because of this shape, the slope of the force vector by which torque is transmitted from one wheel to another remains constant in time – leading to smoother operation. The design process is quite lengthy but this is a good opportunity for the user to learn the basic functions of the sketching module of the CAD software. 1.Establishing the design parameters
2.Intersecting the base circle
3. Constructing a point on the 4. Reiterating evolventic profile
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5.Determining the symmetry axis
6.Obtaining profile
7.Finalizing the wheel sketch
8. Creating the body of the part
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the
first
cog
1. Drawing the plane sketch of the wheel The outline of the cog is defined by an evolvent curve which in turn is defined by a series of constructive parameters which the user puts in. A good way to start drawing the sketch is from a circle of a given radius R (in this case R=100 mm) and a pressure angle α (for this exercise α = 20°). Figure 1.1 depicts the circle with the radius R, a horizontal construction line, the oblique construction line at α as well as a circle tangent to the oblique construction line and concentric with the base circle. In order to mark the fact that a line or curve is used only for construction the option for construction must be ticked. It is recommendable that the oblique line is of infinite length therefore this option could be ticked as well. A good advantage in using the option for construction is that the respective curve will not conflict with a regular curve in the case of an Extrude, Loft or other operations, also it helps visualize the sketch better, giving it a more orderly appearance.
Fig.1.1 – The initial construction lines for the cogged wheel sketch 15
Adding relations to the various sketch elements (points, segments, curves etc.) can be done manualy by rightclicking on the point or curve and selecting the desired relation from the menu Add Relation. Conversly, if the user feels that a relation should be eliminated this can be done directly from the Feature Manager.Design Tree. The construction for the base circle diameter of the wheel is somewhat intuitive (since there is only one interior concentric circle tangent to the oblique contact line), whereas for the addendum (outside) circle diameter of the wheel it is necessary to know the number of cogs on our wheel, which can be calculated with the following equation:
N
D pitch m
(1.1)
Where m is the module selected for the wheel. In this particular case m=2 which leads to an addendum diameter of Dadd =104 mm and a number of N=50 cogs.
2. Adding points on the cog flank We start by introducing a dimension on the segment tangent to the base circle and secant to the pitch circle. This entity will be renamed using its Properties menu. It is necessary to tick the option driven so that it is refreshed should the sketch be modiffied at a later date. The point of intersection between the cog flank and the base circle can be obtained by "wrapping" the length L around the base circle circumference.
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Fig.1.2 – Determining the cog flank - base circle intersection point Figure 1.2 presents the geometrical construction of the evolvent flank of the cog with the base circle. The construction is relatively simple, the only condition being that the length of the arc is equal with the reference length L. A way to carry out the construction is to draw a circular arc with the curvature radius equal to the base circle and one end fixed in the tangence point of the base circle and the contact line. This arc should then be dimensioned and renamed "C". In order to dimension the length of the circular arc and not the chord click successively on the ends of the arc and then on the arc itself. The symbol indicating the dimensioning an arc is the one shown in Fig.1.3.
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Fig.1.3 a. - Construction of a point on the cog flank
Fig.1.3 b. – The other points used to define the flank of the cog
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As seen above, an additional construction line D is necessary. This line is tangent to the newlly created arc in its other end (not the fixed end). Because by deffinition the relation between L, C and D is D=C+L, (1.2) we can obtain the coordinate of the point on the flank. In order to do that, a user may use the mathematical relation tool in the CAD program (Tools – Equations). Therefore, after dimensioning and renaming we introduce the relation. "D@Sketch1" = "L@Sketch1"+"C@Sketch1" (For the points situated below the circle diameter, the equation becomes "D@Sketch1" = "L@Sketch1"-"C@Sketch1" ) Thus we obtain each point on the flank of the cog, each having the property of being equally spaced (on a polyline) from the starting point.
3. Determining the symmetry axis of the cog In order to optimize the placement of the points on the flank it is useful to know where the symmetry axis of the cog is located (to reduce the risk of constructing points which are, although mathematically valid, outside the actual flank). The angular deviation of the symmetry line from vertical can be determined with the following equation (which can also be imposed using Tools – Equations)
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360 / N 4
(1.3)
where N is the number of cogs, N=50 in this particular exercise.
Fig.1.5 – Construction of the symmetry axis of the cog
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4. Sketching the actual cog If all the curves and segments used thus far have been declared as construction lines (for construction), we can start to sketch the actual cog using spline curves directly into the primary sketch (Sketch1). This however is not the best way to carry out the current task because it overloads the sketch which can lead to confusion and errors when manipulating it at a later date.
Fig.1.6 – The points on the flank determined in Sketch1
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A cleaner way to draw the cog flank profile is to initiate a new sketch, coplanar with the one containing the geometrical construction. Using a spline curve we then unite the points to create a sufficiently accurate description of the evolvent profile of the cog.
Fig.1.7 – The construction of the cog profile
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Using trim and mirror we easily obtain the sketch in Fig.1.8 which we can now use to finish our model.
Fig.1. 8 – The cog profile after trimming (left) and after mirroring (right)
By applying a circular pattern (Tools – Sketch Tools – Circular Pattern) with the calculated number of cogs we obtain the rest of the cogs as seen in Fig.1.9. An alternative which some may prefer is to extrude a single cog and then use a circular pattern feature to obtain the rest of the wheel. The sketch is now close to being complete. All we need to do is connect the cogs with circular arcs. A quick way to do this is to draw a circle with the corresponding radius and then trim it in order to remove the arcs which are not useful.
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Fig.1.9 – The useful contour of the cog wheel Once the sketch is finished, we can use the Extrude feature to generate a 3D model of the wheel. It is obvious that a lot more details would need to be added to a real wheel but those details are not the purposes of this introductory tutorial.
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Fig.1.10 – The extruded outline of the cog wheel There are cases in which the cog wheel, although cylindrical must have inclined cogs. Based on the extruded wheel we can use the feature Twist (Insert – Features – Flex – Twist) in order to give the cogs the desired helical shape. Furthermore, if necessary, a symmetrical part of the initial wheel can be added using Mirror (Insert – Features – Mirror – bodies to mirror).
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Fig.1.11 – Possible variations of the current cog wheel
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Chapter II - Modeling a jack screw
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II - Modeling a jack screw This mechanical part does not present a high level of difficulty as far as tridimensional modeling is concerned, although all its features must be conformal to the designer specifications - which implies the use of correlations and references in order to match the helical path with the cutting sketch. 1.Sketching the profile 2.Obtaining the revolved body
3.Adding details
4.Helix determination
5. Placing the cutting sketch
6.Finishing the body
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1. Shaping the revolved body The first operation relies on the observation that from a volumetric stand point the body of the model is axisymmetrical. Therefore, using the Revolve feature applied over the profile outlined in Fig.2.1 we obtain the crude shape of the model, as seen in Fig.2.2.
Fig.2. 1 – Fragment of the sketch used for the Revolved feature
Fig.2. 2 – The axi-symmetrical crude shape of the screw The chosen axis of rotation is also a part of the sketch. In order to expedite the modeling process the fillets and chamfers can be directly drawn into the sketch. This is however not recommended since, at a later date, the features might need adjusting which can be done more easily if using the Chamfer or Fillet features from the Features menu.
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2. Adding features to the model A channel can be milled into the part using the feature Extruded Cut (blind on the length envisioned by the designer), having as a cutting sketch a rectangle. The plane in which the sketch will be created is given by the planar face (marked red) in the extremity of the revolved body. For the hole in Fig.2.3b, the sketch can be made directly onto one of the horizontal plane and for the Extruded Cut feature, with the added option of direction 2, through all.
a.
b. Fig.2.3 – a. simple Cut Extrude and b. Both way Cut Extrude feature
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3. Chamfering and filleting If the designer wishes to vary the values of the chamfer or fillet parameters, it is recommended that these operations be made as separate features. A simplification can however be made if the parameters are the same for more than one fillets or chamfers by selecting the edges to be chamfered/filleted under the same feature operation.
Fig.2.4 – A Fillet feature between a cylindrical and a planar surface
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4. Making the thread of the screw As it became apparent from the modeling done thus far, the thread of the screw will be generated by cutting a spiral channel of a precise cross-section. For this operation, the following are necessary: 1. Generating a spiral 2. Drawing the planar sketch of the thread cross-section The spiral can be made using a sketch containing exactly one circle – in this case the sketch plane will be on the right-hand side of the screw extremity. Using the center of the lpane and the peripheral circle of the planar surface (using the snap function), we generate the base circle (marked red). Then, from the Insert – Curve menu we select Helix/Spiral and define the spiral Height and Pitch which are imposed by the designer. At this stage it is important to be aware whether the spiral is clockwise or counter clockwise (trigonometric).
Fig.2.5– The guide spiral and the circle which generated it
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The thread profile is a somewhat simpler operation. A remarkable thing is that the plane which contains it is not necessarily imposed as long as the top edge of the cutting sketch is at least as high (from the symmetry axis) as the cylindrical region to be threaded. Another restriction is that the pitch of the spiral must be equal to the sum of the bases of the trapezoidal sketch used for the threading. Therefore point V must be aligned with the extremities of the cylindrical region as seen in the figure below. A+B A
B
Fig.2.6 – The two curves used to thread the screw
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Fig.2.7 – The screw 3D model in its final form
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5. The dimensions for recreating the jack screw
Fig.2.8 – The screw dimensions
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Modeling the nut The nut corresponding to a screw can be easily obtained using the screw part file. We create a new *.sldpart file in which we draw the generic shape of the nut.
Fig.2.9 – The cylindrical shape of the nut model
Fig.2.10 – The emboss sketch
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Fig.2.11 – Boss Extrude operation using the sketch If the user wishes to add fillets to the edges of the bossed sketch, this feature may be added or modified at a later date using Features – Fillet, an alternative would be to revisit the sketch itself and use sketch fillet.
Fig.2.12 – Filleting of the bossed feature Finishing touches such adding a spotface and chamfering the circular edges can be done using Extruded 39
Cut and Chamfer features respectively. The figure below presents the two operations.
Fig.2.13 – a. Spotface; b. chamfering the outer contour
Fig.2.14 – chamfering the outer edges of the nut
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Using the Mirror feature we obtain the other half of the nut body. For this case we will use the option to mirror the entire body (bodies to mirror) so that everything will be subjected to the operation. Had the body been cylindrical to begin with, we might have opted for a partial mirroring using features to mirror.
Fig.2.15 – The complete raw shape of the nut In order to obtain an exact match between the thread of the screw and that of the nut, we will be using Indent (Insert – Features – Indent) to essentially perform a Boolean subtraction operation using the part we have created earlier. In order to do this, the screw part must be inserted into the nut part (Insert – Part). After the insertion the user must use the Mate instruments in order to align the two models. So it does
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help to make sure that the two parts have a similar, if not identical, reference system.
Fig.2.16 – Aligning the two parts We then proceed to cutting the thread of the screw into the nut body using the Indent feature.
Fig.2.17 – Sectioned view with the indenting operation
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The “target” body is represented by the nut while the screw is considered the “tool” body; tick on the cut checkbox and set the tolerance to the desired value (0.00 is the implicit default value). After deleting the screw body – which we no longer need – using the Delete body feature (Insert – Features – Delete body), we are left with the final part. The figure below presents it in sectioned axonometric view.
Fig.2.18 – The finished nut part
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Chapter III – Designing a chain transmission
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III – Designing a chain transmission In the field of mechanical engineering there is, in some application, the need for flexible transmissions either by belts or chains. SolidWorks allows the user to design such transmissions with the Belt/Chain function, available both in the part design and in the assembly design module. This function factors in the geometrical relations between each of the components such as the sprockets. In Fig.3.1 a three sprocket arrangement is presented. If all three diameters are fixed and the only variable is the height of the middle sprocket, there is no geometric construction to determine the position. In fact, as it will become apparent, the problem has no algebraic solution either. Of course there are unorthodox methods to solve the problem (involving the use of design tables and iterative calculations), however it is much easier to use the functions already integrated in the program. Therefore, the design theme is to draw an assembly with the configuration similar to the one below in which all dimensions, with the exception of the middle sprocket, are fixed.
Fig.3.1 – The generic start geometry for the drive chain
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Because the total length of certain flexible transmissions (such as cog belts or chains) must be well determined and determined by the size of the cog or inner/outer plate. The standard procedure involves entering each element (wheel/sprocket) as a block (Tools – Block – Make) after which the chain is entered (Tools – Sketch Entities – Chain/Belt). From the chain/belt definition menu the user may set the contact order and the total length of the chain or belt by ticking the option driving.
Fig.3.2 – Setting up the order in which the three components are liked by the chain/belt
Obviously one of the dimensions of the initial drawing must be left undetermined. For this exercise, the undetermined dimension is the vertical position of the central sprocket. Figure 3.3 depicts two versions of the assembly for
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a chain, one with a length of 500 mm and the other with a length of 515 mm.
a
b Fig.3.3 – The sketch modified by imposing various total chain lengths One of the immediate uses for this drawing is the precise determination of the central sprocket. In the beginning of this chapter there was a mention about a different method to obtain this geometrical dimension, 49
with the use of design tables. This variation, much more complicated than the previous must, however, be considered as a last resort for the cases where the sprocket geometry does not allow us to make use of the integrated functions of the CAD software. Considering the planar geometry problem, it can be reduced to the determination of the angle α which describes the tangency point between the chain and the sprocket. Figure 3.4 presents the similar triangles which form between the sprockets and the chain.
Fig.3.4 – Detail with the similar triangles formed in the lefthand side of the three sprocket assembly In order to simplify the demonstration, we will concentrate only on the first pair of similar triangles. Because from the problem hypothesis, the two radii are known to be R1 and R2, and also the distance between the two centers is d, by imposing a relation between the length L and the curvilinear arc lengths C1 and C2, we reach a fully defined
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geometrical construction. Intuitively the problem has a unique solution - that is, if one of the restrictions is to have the contact point, C2, of the central sprocket in the first quadrant. Figure 3.5 presents the geometric signification of the notations used. R2 C2
L R1
h α
d
C1 Fig.3.5 – The signification of the geometrical notations (the color scheme indicates that the sketch is has more dimensions than necessary) The mathematical solution begins by writing the relation between the known geometrical parameters C1, C2, L, d, h and the imposed chain length X. X=C1+C2+L
X
180
( R1 R2) L
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(3.1.) (3.2.)
from which we deduce the expression for L:
L X
180
( R1 R 2)
(3.3.)
We also know that
L
d cos( )
(3.4.)
Equalizing the two expressions and rearranging the terms we obtain
180
( R1 R2)
d X 0 cos( )
(3.5.)
A quick remark is that the above equation is transcendental and therefore has no algebraic solution, in spite of the fact that it has only one solution. Typically one can easily use an iterative numerical method to obtain the solution to the problem. Using a Design Table and iterative calculations (which can be done in a spreadsheet) we can, however draw with a controllable degree of accuracy - the desired dimensions. It is useful to edit the table in a separate window – which can be opened with Microsoft Excel – because the solver module must be activated by hand. After the solver has found a suitable solution, the data for all the geometrical parameters can be transferred to the sketch.
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Chapter IV - Modeling a centrifugal fan volute
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IV - Modeling a centrifugal fan volute From a theoretical standpoint, the pressure ratio obtained by a compressor determines whether or not it can be classified as a fan (for pressure ratios lower than 2, a reason being that the compressibility effects are negligible). The following example refers to the volute of an electrical powered centrifugal fan. Because the volute is made up of two pieces, a body and a lid, the chapter is divided into two dedicated sections.
1.Sketching the volute spiral
2.Finishing the contour
3.Creating the body of the volute
4.Adding the shaft bearing
5.Adding the bosses and spotfaces
6.Adding threaded holes
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1.Copying the outline sketch
2.Modelling the indent tool
3.The indentation
4.Corelating the holes
5.Sketching the inlet
6.Finishing the lid
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1. Modeling the inner surfaces of the volute The sketch begins by drawing a plane spiral (Insert – Curve – Helix/Spiral - spiral) which will cover only 180°, the rest being modeled as a straight segment.
Fig.4.1 – Base circle and the resulting spiral After the main body of the volute has been sketched, it needs to be extruded in order to obtain the rough body of the volute.
Fig.4.2 – The volute body outline 57
The Fillet feature should be used instead of the sketch fillet because the control over a circular arc and spline curve trim is difficult to control and may lead to faulty geometries.
2 Forming the base of the volute Begin by selecting one of the planar faces of the model, like in Fig.4.3, and then use the Convert command to trace its outline in a new sketch. This new sketch can then be edited so that it essentially covers the entire volute body. In order to do that just delete the curves of the inner wall and close the discharge port with a straight segment like in Fig.4.4.
Fig.4.3 – The sketch resulted from the Convert command
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Now, extruding the sketch on the normal direction we get the rough shape of the volute – Fig.4.5.
Fig.4.4 – The sketch of the back wall of the volute
Fig.4.5 – Use a reference plane to sketch the shaft bearing (the center of the rotor is known since the initial spiral started off as a circle) 59
3. The rotor bearing The bearing through which the shaft of the brushless electric motor will pass is drawn onto the reference plane from Fig.4.5. Because it is a body of revolution, it will be modeled using the feature Revolved Boss/Base. Other properties such as chamfers or the central hole can be added later.
Fig.4.6 – Chamfering (left) and the bearing (right) The designer may also insert a Fillet feature between the lateral and back walls of the body of the volute – for both structural and aerodynamic purposes.
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4. Adding the bosses and spotfaces The volute is mounted into a larger assembly using two diagonally placed screws. In order to add the bosses and spotfaces it is necessary that we insert a new reference plane, parallel to the horizontal plane and placed central to the volute full height. The reference plane will later be used to mirror the spotface which is just an extruded cut of a planar sketch made on the upper surface of the volute. Both the spotface and the boss sketch can be made in the same plane but as distinct sketch entities. Figure 4.7 presents the two entities while being created. It is necessary to leave the default option merge results especially in the boss case.
Fig.4.7 – The boss(left) and the top spotface (right)
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Using the Mirror feature command, the bottom spotface can also be created, making use of the symmetry plane created before.
Fig.4.8 The bottom spotface created by mirroring the cut extrude feature
5. The threaded holes For a rigorous representation of such holes some CAD programs – including SolidWorks – have a Hole Wizard which gives the user the possibility to create access a variety of standardized holes as well as creating costume ones. In this particular case we will use Tap for the hole type and the metric standard. The holes should be centered using the snap selection of the center of the circular arc corresponding to the boss and spotface feature.
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Fig.4.9 – The finished body of the volute in isometric axonometric view
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The volute lid Since the volute is comprised of two parts, the body and the lid, the latter will have to be modeled separately. Additionally we will be using the sheet metal design for the lid part.
6. Tracing the outline of the lid Using the Convert command, the bottom wall of the volute body can be transposed into a new sketch. Using copypaste (use the shortcuts ctrl+c & ctrl+v) we transfer the sketch into a plane previously created in the lid part.
Fig.4.10 – The copied sketch
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Using the command Base Flange applied to the sketch we obtain the sheet metal body (with the properties set in the Base Flange menu). On one of the lid sides we insert the sketch of the top section of the volute part and then align it using Edit Sketch – Move.
7. Indenting the interior profile In the current design we wish to create a slight indentation on the lid. Therefore a new part will be created to serve as a tool for the Indent feature.
Fig.4.11 – The top outline of the volute body (imported into the tool part (left) and the finished tool part (right) We now use the Indent feature to deform the lid sheet. In order to do this we insert the tool part (Insert – Part), into the lid part and then – using Mate commands we align the tool with the outline of the top of the volute body. Note that the outline in Fig.4.11 has been previously imported
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and aligned in the lid part and then copied again into the tool part to create the indenting tool. One possible problem that may arise is that, depending on the way the mating was carried out, the Indent feature is not available. In this case the user may deactivate the constraints, without compromising the alignment of the parts, from the Feature Manager of the tool part -– BodyMove/Copy and Suppress on the existing components. As a good practice, after the indenting feature has been added, the user should check a Section view, Fig.4.3, of the resulting shape to insure the results are as envisioned.
Fig.4.12 – The sectioned view of the volute lid and the tool body which has not yet been removed from the lid part
66
The tool body used for the indenting process should be removed after the feature has been added. This should be done using Insert – Features – Delete body; do not delete it directly since the indentation will be affected. An alternative solution, which some may regard as more elegant from an engineering stand point, is the use of Design Library tools. SolidWorks allows the user to add or edit a desired shaping tool through Design Library – Forming Tools – Embosses – Circular Emboss (in our case). Care must be taken with the orientation of the tool. The example below shows how a circular emboss tool can be altered to suite the particular needs of this exercise. To edit the tool, right-click on it and choose open. This will open the part at which point it becomes fully editable.
Fig.4.13 – The initial tool (left) and the edited tool (right)
Fig.4.14– Inserting the feature yields shape similar to Fig.4.12
67
The major advantage of this method is that it gives the user the possibility to flatten the sheet metal. This feature creates the actual shape of the sheet metal and also marks the lines of deformation for the fabrication of the part. Another variation is to use a Forming tool (Insert – Sheet metal – Forming tool). In this instance we will not alter an existing tool but create a new one from a *.sldpart file. The first step is to open the part with the tool created for the first method described and insert the Forming tool property. After establishing which of the faces will contact the sheet metal, we reach something similar to the forming tool in Fig.4.13.
Fig.4.15 – The face that will contact the sheet metal (top) and the face setting the depth of the tool (bottom) An additional feature is the possibility to eliminate faces from the sheet metal part along with the forming tool process. 68
Once finished, in order to be able to recall this tool, the part must be saved in the folder ”[...]Solidworks\data \design library\ forming tools” in an already existing folder or a new one created by the user. To reuse the object we just open the Design Library and select it under the name it has been saved.
Fig.4.16 - A section view after the forming operation
8. Volute inlet As in any centrifugal compressor, the air inlet is central. This particular case is modeled after the US Patent US6884033B2 which describes a spiral inlet (that follows the contour of the discharge volute). For the finishing touches it is necessary to align the holes on the volute body with the ones in the lid. Using Insert - Part we import the body of the volute and then align it using mates.
69
An observation is that the sheet metal of the lid is thin enough not to require a thread. Therefore the holes do not need to be made using the Hole Wizard and can be directly made using the Extruded Cut feature. It is important to make sure that the thread of the screw fits through the holes in the lid therefore we will use the snap selection mode as in Fig.4.17.
Fig.4.17 – Snapping the circular hole sketch The inlet will be modeled from a planar spiral (Insert – Curve – Helix/Spiral) resulted from a circle concentric to the axis of the rotor. In order to edit the spiral, we will have to use the Convert command and project it into a sketch.
70
Fig.4.18 – The initial spiral (left) and the outline of the inlet (right) Since for the current example the inlet shape is not correctly positioned, relative to the inner contour of the volute, the sketch will have to be repositioned. In order to keep the sketch centered, it is useful to draw a guideline before moving/rotating/mirroring the sketch so that there is always a correlation with the center of the rotor. The guideline may be removed after the repositioning process. In this example we only need to use Sketch Rotate around the centerline. An alternative is to vary the spiral start angle.
71
Fig.4.19 – Use the green sketch as a guide
Fig.4.20 – The final alignment of the inlet section
72
Fig.4.21 – Axonometric view of the lid (and volute body) after the Extruded Cut. The final step is to eliminate from the lid part the body of the volute which we have used as a reference tool. The safest way to carry this out is to use Insert – Feature –
73
Delete Body. Otherwise the references may be lost which will lead to errors.
Fig.4.22 – The final shape of the lid body If the user considers it necessary, more features - such as fillets or chamfers - may be added later on.
74
Chapter V - Volute core for fluid dynamics simulations
75
76
V - Volute core for fluid dynamics simulations In this chapter we will look into the modelling of the inner core of an industrial turbine engine volute. This is a common practice for CFD (Computational Fluid Dynamics) simulations. The first part of the chapter presents a general method to model a volute core - applicable in most volute geometries. The second part presents a quicker approach based on a few observations regarding the geometrical properties of this particular volute. 1.Sketching
2.Section lofting
3.Establishing guidelines
4.Section modeling
5.Outlet lofting
6.Cover lofting
77
7.Interiour filling
8.Forming the inner wall
9.Forming the vaneless diffuser
78
1. Sketching the spiral using basic references Figure 5.1 presents the overlapping of the centerline sketch and the circular arc radii sketch. Because the volute is defined as a series of circular arcs, rather than an analytical curve, the dimensions in the two sketches are necessary.
Fig.5.1 - The reference points and radii for the volute core Figure 5.1 also presents the details regarding the volute tongue (in this case its center, curvature radius and angle)
79
2. Shaping the volute tongue It is important - in this particular case - not to fully define tongue of the volute in one singular sketch. This is because the imposed cross-sections have different shapes. Because the modeling strategy employs the use of Loft features between the sections, the two sketches may later be used as guide curves.
Fig.5.2 - Detail regarding the sketches which define the volute tongue
80
3. Modeling the core volume Since the cross-section (A) is defined by a topologically different sketch than the cross-sections (B) and (C), the intermediary sections (e.g. between A and B, highlighted in Fig.5.3) will be different.
C
B
A
Fig.5.3 – Detail with the shape of the volute tongue It is important that, although from an aerodynamic perspective, altering section A so that it matches section C is would not be significant, any differences between the original design and the 3D model must be motivated and accounted for.
81
A
C
Fig.5.4 – Lofting from section C to section A In order to create the volume we will use the Loft feature from sketches A and C using the guide curve the sketch marked in red. This way, we will correctly control the passage from one section to the other. Note that the passing from A to B the necessity for a guide sketch is even more imperative. The surplus volume will be removed towards the end of the process and therefore can be neglected for now.
82
Fig.5.5 – Defining the reference planes for the section sketches The reference planes for the two sketches which bind the final volume are defined by the sketch of the volute tongue. Therefore the planes are generated as normal to the sketch in its two extreme points.
Fig.5.6 – Sample of lofted section
83
Fig.5.7 – The finished shape of the volute tongue section It is true that the true volume (the one which will remain in the final model) is relatively small compared with the surplus. However, this was necessary in order to insure the correctness of the volute tongue rendition.
4. Modeling the rest of the volute From the center of curvature of each section we build the guide circular arc. This will serve to aid the lofting feature between the two cross-sections.
84
All guide arcs should be kept in the symmetry plane of the volute so that their use as guide curves will not distort or deform the tridimensional shape of the volute
Fig.5.8 – Modeling the loft between the volute sector and the volute lip
85
V1
Fig.5.9 – The crossing from one sector to the other Similarly, the other circular arcs should be constructed using the corresponding center and radius of curvature. As a mode of operation, V1 is defined by the distance to the origin of the coordinate system and the angular position.
86
Fig.5.10 – Horizontal view of the volute body created thus far Plane 8 is constructed normal to the circular arc defined for the previous cross-section, and is the plane in which the cross-section sketch will be made; the green line is not used for the construction of the reference plane 8 and only serves to illustrate the direction of the plane normal.
87
Fig.5.11 – Each of the sections will be modeled similarly In the absence of a proper guide curve, there is a risk that the interior of the volute may get deformed or distorted. Although small, these distortions or abatements from the aerodynamic design must be avoided. Hence, the guide curves must be carefully managed and controlled.
88
I
G Fig.5.12 – The guide curves on the lower plane (each of which should have a corresponding line in the upper plane) In addition to the peripheral guidelines, represented by the circular arcs with progressive curvature radii, more guide curves can be added on the lower and upper planes of the volute; these guide curves will help maintain the correct 3D shape of the lofted section. Reference planes in which the supplementary guides will be sketched should be inserted as parallel to the horizontal plane at the point of the initial cross-section. The supplementary guide arcs have all the same radius, equal to the outer radius of the vaneless diffuser of the centrifugal compressor for which the volute has been designed.
89
5. Closing the volute core As observed in Fig.5.13, the volute discharge section D (marked in red) and the sketch of the previous section, are fundamentally different. The main difference is the fillet of the inner edge in section D whereas section F has a sharp edge. Lofting the two sketches is virtually impossible to control, therefore closing the volume will have to be done in steps. First we finish the volute exhaust section - which is circular.
F
D
Fig.5.13 – Differences between the sections make lofting difficult to control
90
D
Outlet section Fig.5.14 – Finishing the outlet section of the volute Traditionally the volute exhaust section is circular. A simple lofting feature can be used to shape the final portion of the volute. The loft does not necessarily require guide curves but the user must make sure that the volute is still symmetrical. Although the following step is not obvious, it does serve a practical purpose that is to create a solid wall onto which a planar sketch can be inserted.
91
F
D
Fig.5.15 – Closing the volute We begin by observing that, because the profile of the volute tongue is variable, it is impossible to extrude the entire face F towards face D (because this would make the edges come out of the surface of the volute core). Hence, only a partial extrusion is made, as seen in Fig.5.15. Since sketches D and F have different filleting radii, they will be closed using the Loft feature.
92
D
F
Fig.5.16 – Lofting the exterior parts of sections D and F A final loft operation is required to close the exterior surface of the volute core, we will use the free faces, D and F, as the ends for the loft. Another option would be to use the Convert tool to transpose the faces into planar sketches, but this is a complication that we will not need here.
93
a
b Fig.5.18 – a. The inner gap of the volute core; b. Filler sketch; As stated in the beginning of this chapter, the inner region of the volute core will be filled with a sketch before making the interior shape. The filler sketch is presented in Fig.5.18 along with the result from the Extrude feature.
94
6. Shaping the inner wall This exercise refers to modeling a volute core for CFD use, therefore the shape of the walls (including the inner wall) must have as little abatements as possible. Therefore it is preferable to shape the cylindrical inner wall in a single operation. Two equally good options are available Extruded Cut and Revolved Cut.
a
b Fig.5.19 – The cutting sketch (top); The volute shape after the Extruded Cut (bottom) The sketch used for the Extruded Cut can be drawn in any plane parallel to the symmetry plane. 95
7. Modeling the vaneless diffuser For the vaneless diffuser - the final component of the volute core for the CFD simulation - several approaches are available. In this particular case we will sketch a circular ring with the interior radius equal to that of the vaneless diffuser and the outer radius equal to that of the cylindrical wall of the volute. Once the sketch has been drawn in the symmetry plane, it can be extruded in both directions (perpendicular to the sketch plane), with half the diffuser total height.
Fig.5.20 – Final 3D model of the volute
96
Alternative construction method Certainly there are more ways than one to obtain the tridimensional model of a particular design. In our case, because the model allows it, we will present a quicker version. For this part of the exercise we will be using the plane sketch of the volute. Obtaining it can be done in several ways, in this case we will first use a cutting operation (ExtrudedCut), eliminating one of the sides on the symmetry plane. Them, by inserting a 2D sketch in the symmetry plane we use Convert to obtain the outline of the volute.
Fig.5. 21 – Cutting the volute on its symmetry plane
97
It bears mentioning that, for exercise sake, the user could restart the sketching process of the volute sketch, based on the indications in the annex. Next, copy the sketch into a new part file and complete it with the interior circle of radius R=300 mm, then transform in construction lines the segments which are not of immediate use - see Fig.5.22. After this, use the Extrude feature to obtain the body in Fig.5.23.
Fig.5.22 – The volute plane sketch
Fig.5.23 – The half body of the volute after extrusion
98
Variable fillets will be used to create the curvature on the outer edge of the volute core Fillet (Insert – Fillet – Variable radius fillet). After selecting (in order) the edges of the outer contour of the core we start setting the values for the filleting radii - use the annex for reference.
Fig.5.24 – The body obtained after the variable fillet addition Further, we need to insert a new reference plane, defined by the construction lines from the volute sketch. The reference plane will contain a half circle with the known radius R=125 mm.
Fig.5.25 – The sketch of the volute outlet 99
Using the Loft feature we finish the outlet geometry. For better control, the user should be using guidelines (note that the construction lines are not available as guidelines).
Fig.5. 26 – Detail with the outlet section loft
Fig.5. 27 – The vaneless diffuser is added using the Extrude feature (h=10 mm)
100
a.
b. Fig.5. 28 – a. Volute modeled through the simplified method b. Volute modeled through the generalized method
101
102
Annex – Dimensions for the volute core
2
3
4
1
5
12 6
11
7
10
9
8
Fig.A.1 – The dimensions for the construction lines and section numbering
103
Tabel A.1 – Geometries and dimensions of the sections Section 2
Dimension
3
4
5
6
104
7
8
9
10
105
11
12
13
106
14
1
15
Fig.A.2 – Filleting radii of the exterior of the volute edge
107
14
1
13
15
Fig.A.3 – Detail with the dimensions and section numbering of the volute lip region
108
Chapter VI – Centrifugal compressor rotor
109
110
VI – Centrifugal compressor rotor Centrifugal compressors are frequently used in turbo machineries either industrial or aeronautical, having a wide array of operating regimes. The main advantage over axial flow compressors is their high pressure ratio per stage, which can reach 9:1 as opposed to 1.7:1 for axial fans or compressor stages. Designing centrifugal compressors as well off design point calculations can be made using basic thermodynamics, combined with streamline and boundary layer codes. Most of the times the blade has ruled surfaces - although more modern designs have more complex geometries. In this particular application we will look at a centrifugal rotor having 9 main and 9 splitter ruled surface blades. The hub and shroud will be copied from a different part and modified to form the final rotor.
1.Curve import
2.Surface filling
111
3.Surface lofting
4. Extending the surfaces
5. Surface filling and knitting
6. Adding details for the hub sketch
7. Create the revolution body 8. Finishing with a circular and fillet the blades pattern
112
1. Curve import Since the airfoil curves defining the compressor blades are tridimensional - and since typically the design software exports arrays of Cartesian or cylindrical coordinates - the best way to import the geometry is with Insert - Curve – Curve Through XYZ points. The native file extension used by SolidWorks is *.sldcrv, but the program ca very well read *.txt files in which the coordinates of the points are written in columns. After the curve import, they should be displayed similar to Fig.6.1.
Fig.6.1 – Axonometric view with the pressure and suction sides of the hub airfoil of the main blade
113
In older versions of the program (e.g. SolidWorks 2007) the curves needed to be converted into 3D sketches and then hidden from view. This step is no longer necessary in the later versions.
2. Shaping the blade Our blade geometry is completely determined by the four 3D curves which generate the ruled surface. However, in some cases the Loft feature for 3D sketches may not be available (due to various rebuilding errors). A safer way to construct the blade surfaces is to use Loft Surfaces. The 3D curves can be used to construct "lids" for the shroud and hub airfoils using Insert – Surface – Fill.
Fig.6.2 - Fill Surface for all airfoils (Main and splitter) In some cases, if the command returns errors it may be necessary to simplify the curve. 114
Once the airfoil surfaces have been created we can use the Insert – Surface – Loft command. If the curves have been defined from the leading to the trailing edge, the loft should not require guide curves and will be done automatically.
Fig. 6.3 - The pressure and suction surfaces of the blades created using Loft Surfaces In order to avoid rebuilding errors due to the airfoil curves not being exactly on the hub or shroud, it is best to use the Extend Surface command. Since we will be required to fill the newly created top and bottom airfoils, it is best to tick the option linear. This will insure that the new curves do not overlap or have gaps between them - which would thwart the filling process.
115
Fig. 6.4 - Surface extension insures that the blade surfaces intersect the hub and shroud - this is particularly useful for CFD applications.
Fig.6.5 - Offsetting the cap surface may serve the same purpose but it may only be used to cover much smaller gaps 116
After extending the surfaces, make sure the tip and bottom are filled.
Fig.6.5 - The new tip surface fill
a
b Fig. 6.6 - Use Knit (create solid and merge entities) to obtain the blade body
117
3. Inserting the hub and shroud sketches For this exercise we will consider that the hub and shroud sketches are reused from a different part. Select each sketch and use ctrl+c to copy it and ctrl+v to paste it into the current part. Make sure that the sketch plane is correct.
Fig. 6.7 - The hub and shroud raw sketches The hub sketch may be edited in order to add features to it. The above figure would, however be fine for CFD (Computational Fluid Dynamics) meshing.
118
Fig.6.8 – The edited details added to the hub sketch For the hub of the rotor it is enough to select the line that coincides with the rotation axis and apply the Revolved Boss/Base feature. The axis of reference will come in handy later when we will use it for the Circular Pattern. If the Fillet feature returns rebuilding errors switch to FeatureXpert, typically this should solve the problem. If not, you might manage to fix it by cleaning up the geometry. The filleted blades should look similar to Fig.6.9.
119
Fig. 6.9 - The fillet between the blades and the hub
4. Adding the circular pattern Using the feature Circular Pattern (Insert – Pattern/Mirror – Circular Pattern), the rest of the blades can be easily obtained. The axis of reference will be used for this operation. It is best to use the option bodies to pattern, even if that means that the hub will also be copied.
Fig. 6.10 - The finished rotor
120
Table 6.1 - Blade coordinates for a new centrifugal rotor X 16.9158 16.724 16.5865 16.4504 16.3135 16.1746 16.0345 15.8944 15.7544
Y 7.6484 7.53285 7.34977 7.1655 6.98183 6.7997 6.61847 6.43725 6.25594
Z 0.00652 0.01723 0.02687 0.03643 0.04599 0.05555 0.06511 0.07467 0.08421
X 16.9898 16.8881 16.8198 16.7546 16.6877 16.6209 16.5538 16.484 16.4132
Y 7.76056 7.70261 7.60372 7.50246 7.40237 7.30229 7.20238 7.10443 7.00737
Z 2.08681 2.10227 2.11633 2.13048 2.14513 2.16009 2.17509 2.19087 2.20708
15.6146
6.07454
0.09367
16.3415
6.91098
2.2237
14.5319
4.89375
0.16207
15.5563
5.92834
2.42142
13.3781
3.78052
0.23101
14.7538
4.96806
2.65614
12.1483
2.75289
0.30061
13.942
4.02462
2.92537
10.8478
1.82603
0.44428
12.3145
2.19839
3.6203
9.51368
1.02209
0.82292
11.5707
1.36783
4.23162
8.19254
0.361
1.442
10.9611
0.56562
5.00807
6.92985
-0.1282
2.30002
10.5098
-0.2451
5.87837
5.82225
-0.6788
3.32082
10.2042
-1.1034
6.76704
5.72447
-0.7342
3.42439
10.1925
-1.1449
6.80976
5.62777
-0.7906
3.52845
10.1808
-1.1863
6.85248
5.53211
-0.8473
3.63331
10.1696
-1.2278
6.89518
5.43798
-0.9057
3.73858
10.1588
-1.2695
6.93793
5.34474
-0.9652
3.84408
10.148
-1.3111
6.98068
5.25277
-1.0262
3.94983
10.1374
-1.3545
7.02156
5.16169
-1.0884
4.05559
10.127
-1.4012
7.05882
5.0715
-1.1524
4.16114
10.1167
-1.4497
7.09369
4.98196
-1.2173
4.26661
10.1064
-1.4999
7.12614
4.89309
-1.283
4.37215
10.096
-1.5511
7.15692
4.81203
-1.3829
4.45224
10.0857
-1.6072
7.17609
4.7702
-1.5152
4.45496
10.0769
-1.6656
7.1674
121
4.84954
-1.533
4.33032
10.0744
-1.703
7.12265
4.94184
-1.4905
4.2176
10.0809
-1.6986
7.06328
5.03479
-1.4253
4.11531
10.0913
-1.6716
7.01055
5.1286
-1.3629
4.01206
10.1031
-1.6326
6.96567
5.2229
-1.3016
3.90855
10.1152
-1.5932
6.92125
5.31805
-1.2417
3.80501
10.1277
-1.5531
6.87752
5.41459
-1.1847
3.70116
10.1405
-1.5124
6.83436
5.51163
-1.1277
3.59773
10.1533
-1.4718
6.79122
5.60964
-1.0714
3.49488
10.1665
-1.4312
6.74813
6.71269
-0.528
2.46506
10.4994
-0.5689
5.87293
7.95657
-0.0323
1.58328
10.9646
0.2526
5.02001
9.28607
0.56893
0.92207
11.5843
1.05262
4.24924
10.6273
1.33869
0.50052
12.3303
1.88281
3.63963
13.2003
3.23064
0.24603
13.1473
2.77211
3.24132
14.3742
4.32217
0.17764
13.971
3.69808
2.94188
15.4765
5.48582
0.10976
14.7785
4.64558
2.67424
15.6249
5.6603
0.10021
15.5826
5.60436
2.43881
15.7694
5.83807
0.09073
16.3728
6.58282
2.23979
15.9139
6.01583
0.08121
16.4472
6.67702
2.22267
16.0575
6.19422
0.07169
16.5215
6.77141
2.20568
16.1991
6.37429
0.06219
16.5945
6.86683
2.18942
16.3407
6.55435
0.05265
16.6671
6.96268
2.17356
16.4818
6.73481
0.04311
16.7389
7.05916
2.15809
16.6186
6.91854
0.03364
16.81
7.15629
2.143
16.7539
7.10339
0.02419
16.8803
7.25399
2.12831
16.8885
7.28873
0.01472
16.9498
7.35234
2.11398
17.0043
7.48447
0.00585
17.0184
7.4514
2.10007
17.0648
7.56212
2.08852
17.0681
7.68129
2.08178
122
Table 6.2. Hub coordinates for the new centrifugal rotor X 4.45845 4.45845 4.45845 4.45845 4.45845 4.45845 4.45845 4.85779 5.33746 5.89508 6.52574 7.22205 7.97439 8.77136 9.6003 10.448 11.3014 12.148 12.7436 13.3393 13.9349 14.5305 15.1262
Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Z 10 9.24083 8.48167 7.7225 6.96333 6.20417 5.445 4.69418 3.96946 3.28329 2.64783 2.07432 1.57244 1.14982 0.81161 0.56031 0.39579 0.31547 0.28679 0.25811 0.22943 0.20075 0.17207
15.7218 16.3175 16.9131 17.5087 18.1044 18.7 19.75 20.8 21.85 22.9 23.95 25
0 0 0 0 0 0 0 0 0 0 0 0
0.14339 0.11471 0.08604 0.05736 0.02868 0 0 0 0 0 0 0
123
124
Annex – Importing 3D curves and surface lofting – Turbofan stator In this section a quick Lofting example is presented. The purpose is to reconstruct the geometry of a turbofan stator blade. In the European Patent EP 1921263 A2 such a geometry is described through Cartesian coordinates of the curves describing the vane sections. Because the geometry may not, in some cases, include information regarding the trailing or leading edge of the vane, a safe way to import it as a single curve is to have a starting point on the smallest possible curvature.
Fig. 1 – The imported curve (top) and the 3D sketch generated from it using Convert (bottom)
125
Directly inserting the curves does not allow the user to import closed contours. This is because no point can be introduced twice and the end point would have to coincide with the start point. Ideally for a blade or vane, the airfoil would be separated into two curves starting and ending on the leading and trailing edge (LE/TE) respectively. In this case, however, we consider that there is no information regarding the LE or TE. As is the case in Fig.1, the curve is interrupted at the point where the curvature is lowest. This is so that the spline interpolation can be approximated by a straight line (although in real cases the respective portion would have to be redone using at least 2 points upstream and downstream, since most splines are cubic). The coordinates must be arranged so that the start and stop points of each individual airfoil section coincide as closely as possible. Using Convert in a 3D sketch we can transform the imported curves into a sketch which we can later edit and close the perimeter of the airfoil In order to avoid any rebuild errors we can use Surface Loft (Insert – Surface – Loft) instead of the feature (Insert – Features – Loft) which creates solid bodies. The surface loft is typically more permitting and can deal with complicated geometries. At this point, the surfaces generated do not yet form a solid body, therefore the geometry is not quite finished – and can cause errors if we would try to use CFD/FEA analysis on it using the integrated software packages. To create a solid body we use Fill (Insert – Surface Fill) for the airfoils with the tick on try to create solid. This will generally succeed in creating a solid body. 126
Figure 2 depicts the solid body of the vane in full and in section view.
Fig. 2 – The active surface of the turbofan stator vane
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Chapter VII - Simple turbofan mixing chamber - Using Design Tables and Equations -
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VII – Simple turbofan mixing chamber Modern turbine engines used in both civil and military aviation use turbofan technologies due to its increased efficiency. Turbofan engines have two axial compressors coupled in parallel (the core compressor and the by-pass fan). For high by-pass ratio turbofans the bulk of the thrust is given by the secondary flow, the core providing ~20% of the net thrust. Depending on the mission it is designed for, the propulsion system may have a high or low by-pass ratio. A mixing chamber is typically associated with by-pass ratios below 4:1. What the mixer does is essentially to blend the hot core with the cool by-pass flow, which leads to a theoretical increase in thrust of ~3% (if the by-pass factor does not exceed 4:1). The present chapter presents the tridimensional modeling process for a typical lobed air mixer. Since the geometry must be applicable to a large array of applications, the geometric parameters must be varied. Design tables, implemented in SolidWorks, are used to make these variations which are correlated using Equations.
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1.Sketching and naming contour of the lobes
the 2. Sketching and constraint applications to the inlet
3. Shaping the 3D semi-lobe
4. Shaping the lobe
5. converting the lobe into a shell
6. Finishing the full mixer
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1. Sketching the lobe contour Initiate a sketch in the front plane and draw the lobed outlet shape using the generic sketch described in Fig.7.1
Fig.7.1 – The parameters and constraints that define the outlet lobe
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The sketching begins by placing two circles of arbitrary radii in the 2D sketch, Fig.7.2 a. Then, after imposing a tangential constraint, we draw a line segment between the two circles, Fig.7. 2b (the constraint will be automatically marked). Trim the parts which are of no interest, Fig.7.2c. In order to keep the lobe angle editable, and at the same time maintain the symmetry, the oblique line must be re-drawn in two separate segments, Fig.7.2 d.
a.
b.
c.
d. Fig.7.2 – The steps needed to sketch the outlet lobe
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After completing the second segment we can move to dimensioning the sketch. For the current example we will be using the dimensioning in Fig.7.1, but this is not the only way to carry out this operation.
The first segment imposes the normal-to-curve constraint The second segment is collinear with the first and regulates the core angle of the lobe
Fig.7.3 – A functional description of the two segments that make up the interior lobe shape
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Insert a reference plane parallel with the sketch of the lobe and begin sketching the circular inlet of the mixer. This sketch is defined by the angular restrictions (which have to match the core angle of the lobe) and by a radius of arbitrary magnitude. Because the lobe sketch permits this, the slant of the oblique segment will be defined by constraining one of the ends on the inferior lobe and the second in the origin of the axis system of the reference plane.
The second segment is collinear with the first and has an arbitrary length, defining the inlet mixer radius The first segment is constrained by the total length and slant of the inner lobe Fig.7.4 – Sketching the circular sector corresponding to the mixer inlet It is useful to edit the name of the constraints (click right on the dimension – Properties - Name) so that it will be easier to work with the design table. The names will be editable in the design table itself, should the need arise.
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2. Modeling the first lobe Next we impose the guide curves for the Loft feature which will link the two sections. Since this is only a simple mixing chamber, the two guidelines will be line segments. They can be drawn all in a single 3D sketch, as seen below.
Fig.7.5 – The 3D sketch of the guide curves for the loft After the loft we obtain the 3D model of a semi-lobe.
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Fig.7. 6 – The 3D lofted semi-lobe (left) and the lobe after the mirror feature is applied (right) Because the strategy involves a circular pattern, it is necessary to have a full lobe which we will instance. Since the semi-lobe is symmetrical it can be mirrored (Features – Mirror) on one of its sides. Figure 7.6 depicts the full lobe.
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3. Obtaining the finished lobe Up until now we have only modeled the full body of the lobe, however the real model is just the thin shell that follows the outer contour of the lobe. Using the Shell feature (Insert – Features – Shell) and selecting the faces we need eliminated - See Fig.7.7 - the final lobe shape is reached.
Fig.7.7 – The faces that need to be eliminated by the Shell feature (left) and the finished result (right)
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4. Finishing the mixing chamber and editing the model In the horizontal plane, from the top view we trace a line segment along the Oz axis and then we insert an axis coincident with it (Features – Reference Geometry – Axis).
Fig.7.8 – The rotation axis for the circular pattern using the Oz axis as a reference We can now finish the geometry by inserting a Circular Pattern (Insert – Pattern – Circular Pattern) using the option bodies to pattern, around the axis newly created.
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Once the pattern is finished, we can create the Design Table (Insert – Design Table), which will manage the parameters of the model, including the sketch dimensions and the feature parameters. The table below presents the editable parameters of the model.
Base lobe height@Sketch1
Core half angle@Sketch1
D1@Circular nozzle plane distance
Circular nozzle radius@Sketch2
c
10
107
71
18
50
92
1
D1@CirPattern4
Superior obe height@Sketch1
15
D3@CirPattern4
Lobe base radius@Sketch1
Values
Lobe tip rasius@Sketch1
Tabel 7.1 – The list of the editable parameters of the mixer
360
10
The signification of the parameters in the table above is as follows: D1@ Circular nozzle plane distance c D3@CirPattern4 D1@CirPattern4
- the distance between the two sketch planes - thickness (measured towards the inner side of the mixer) of the Shell feature - total angle covered by the pattern (constant 360°) - number of lobes of the mixer, n; which is correlated with the half-angle of the lobe:
360 2n
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(7.1)
This mathematical relation will be introduced using the Equation tool. Open the sketch of the lobe and edit it to add the Equation (Tools – Equation – Add). By directly clicking on the dimensions, we can insert them into the formula. The syntax, in this particular case (where all dimensions have been renamed) is : "half angle@Sketch1" = 360/(2*"D1@CirPattern4")
Fig.7.9 – Notice the marking of the mathematical relation between the two parameters with the symbol Σ.
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Once saved the design table, it can be re-edited in order to vary the geometric parameters according to the user requirements.
Fig.7.10 – Various geometries generated by the design table
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5. Using pre-set shapes An alternative for re-naming the dimensions is introducing them as variables (double click on the dimension Link Values).
Fig.7.11 – The sketch of the semi-lobe with the defined variables, the symbol marking is ∞
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It must be pointed out that the variable introduction is not necessarily linked to a geometrical dimension. In fact, one can insert abstract variables which do not represent a geometrical dimension, this can be made from the equation insertion menu with the syntax: X = 147 ‘ abstract variable where X is the abstract variable and 147 is its nondimensional numerical value whereas the text after the apostrophe represents the user comment or caption. It is possible to save the configuration in the SolidWorks database by clicking on Configuration Manager – Add to Library under the name "Air Mixing Chamber" in order to make it more easily identifiable. Obtaining various configurations only requires changing the entries from the Design Table. Moreover, in the newer SolidWorks versions, there is the possibility of inserting the parameters in a design menu which will control the geometrical parameters without the need to open the design table. This can be made easily by clicking on the part - Create Property Manager and, from the menu that becomes available, select the parameters we wish to vary - by marking them Enabled; the same applies to the Reference values which must be marked as such. The menu also permits the rearranging the order in which the parameters are displayed and their names (Label).
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Chapter VIII - Scalloped air mixer for turbofan engine
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VIII – Scalloped air mixer for turbofan engine This chapter presents the geometrical modeling of a more complex version of the air mixer from the previous chapter. The scalloped air mixers are the most mature mixing devices in the aeronautical industry. At this point, the chevron technology is still being refined and has not reached full maturity. The main scope of this chapter is to present a method to obtain the 3D model of the air mixer, but since a similar exercise has just been presented we will also have a secondary goal. Therefore, we will try to obtain the geometry without having a technical drawing or clear dimensions. Instead we will rely solely on the drawings presented in the US Patent US 20110126512 to obtain a scalable model of the mixer. 1. Outlining the outer contour 2. The guideline arc
3. Outlining the inner contour
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4. Tracing the guidelines
5. Lofting a semi-lobe
6. Completing a lobe
7.Circular pattern
8. Filling the lobe gaps
9. Scalloping the mixer
10. Finishing the mixer
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1. Outlining the outer curve A first stage is to crop Fig.7 from the Honeywell patent US 20110126512 which depicts the profile of the lobes. Notice the level differences between the outer and inner curve (in the left hand side of the figure); this is due to the fact that they belong to different angular positions of the circumference.
Fig.8.1. Side view of the scalloped air mixer (US 20110126512) In Fig.8.1 we can also observe the contour used for the scalloping of the lobes - the hatched region will have to be removed once the main body of the mixer will be modeled. We initiate a planar sketch then select the option Tools – Sketch tools – Sketch picture. This will allow us to insert the picture of the original patent drawing which will serve as a visual reference for the modeling.
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Although this is not the most rigorous of all methods, its precision can be good if the user operates with care. This method could also be used for revere engineering however the errors might be quite significant. In the case of scalloped mixers, the aerodynamics is quite forgiving compared with other turbomachinery parts so this method might just be enough for some cases. Using a spline curve we can trace the outer and inner contours of the mixer. The contours must be in two separate sketches and also in different reference planes (since they will guide the loft in two different angular positions).
Fig.8.2 – Sketching the first guide curve, before the trim As a recommendation, in situations like this - where the user does not have exact dimensions for the model - a series of references must be established with construction lines or space coordinates.
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Also it is better to draw the tracing in a different sketch than the one in which the picture was inserted since we will have to hide (Feature Manager Design Tree – Hide) it once it has served its purpose.
2. Tracing the inner curve The second curve will be obtained after introducing a circular arc - which is part of the generator curve of the circular nozzle section. We start by inserting a new reference plane, parallel with the frontal plane and tangent to the first guide curve on the end corresponding to the circular section (mixer inlet). Since we know the number of lobes, n=16, we can calculate the angle of the circular arc using the relation:
360 2n
(8.1)
which, in this case, leads to θ = 11.25°. Although a graphical solution can be made (and will be presented later), in this instance we will calculate the arc radius by hand and introduce dimension in the sketch.
R
h 1 cos( )
(8.2)
Therefore, the radius (which will be scaled once the 3D model will be finished) is R ≈ 505.8622 [mm].
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The first guide curve
A B Fig.8.3 – Axonometric view with the first guide curve and the generator arc For the actual sketching of the second guide curve, we will have to un-hide the sketch containing the picture (click right – show). Then we insert a new reference plane, normal to the arc in B (Features – Reference Geometry – Reference Plane – normal to curve). An observation is imposed, the sketching plane in this case is not the visualization plane (since from the patent we only have a side view). In other words, the second guide curve is not viewed in its sketching plane but rather in a projected view at an angle θ = 11.25°, relative to the left plane (in which the first guide curve is sketched). That being said, we initiate a planar sketch in Plane 3 (see Fig.8.4), and choosing point B for starting, we draw the outline of the second guide curve. Make sure that the view is the Left plane, not Plane 3.
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A
B
Fig.8.4 – The reference Plane 3, which contains the second guide curve (top) and the actual curve (bottom)
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It is preferable that the lengths of the projections of the two guide curves is the same. This helps since the lobe section should best be drawn as a planar sketch (as opposed to a 3D sketch). In order to accomplish this, use the trim command to clean up the sketches.
3. Shaping the lobe contour The patent describes a proprietary method of sketching the lobes (optimized from a gas-dynamic stand point), with the lobes described by a set of three equations. However, for the purposes of this tutorial we will use circular lobes, for simplicity. We start by generating another reference plane, parallel with the frontal plane and tangent to one of the guide curve in point C or D, as in Fig.8.5. C A
B
D Fig.8.5 – The plane in which the lobe section will be sketched 156
Because the length of the two guide curves is the same, points C and D are coplanar and contained in Plane 4. After initiating the 2D sketch in Plane 4 we insert two circles with the centers in C and D. These circles will only be used for construction, as references for the actual lobe design. C
B A
D Fig.8.6 – Construction circles (left) and the semi-lobe of the mixing chamber in frontal view (right)
4. Modeling the first semi-lobe In order to loft the two sections (the one in Plane 2 and the one in Plane 4) the sketches must be closed contours. The mixing chamber core is essentially the same, see Fig.8.7.
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Also in Fig.8.7 we see a third guide curve which serves a dual role, to insure the correct 3D lobe geometry and to be a reference for the axis (Features – Reference Geometry – Axis) of the circular pattern which will be done later on. C A B
D
Fig.8.7 – The final contours defining the first semi-lobe before the lofting operation
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Fig.8.8 – The 3D lofting process of the semi-lobe using the two closed sketches and the three guide curves.
5. Completing the lobe Because the geometry of the lobe we have thus far created is symmetrical, in order to finish one lobe it is enough to use a Mirror operation (Features – Mirror). It is unimportant if the symmetry plane is the on the left hand side
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or the right hand side, as both will yield results ready for the circular patterning operation.
Fig.8.9 – Modeling the first lobe using the Mirror feature having the left plane for symmetry (left) or Plane 3 for symmetry (right)
6. Modeling the body of the mixing chamber Once the first lobe is created, it is easy to build the rest of the lobes using Features – Circular Pattern, having
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the axis we have created in sub-section 4 and ticking equal spacing for 16 lobes on a pattern angle of 360°.
Fig.8.10 – The crude shape of the mixing chamber Preferably, the Circular Pattern should have the bodies to pattern ticked instead of surfaces to pattern or features to pattern.
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In some cases it is possible to have gaps between the mixing chamber lobes. This can be a side effect of the analytical calculation we used to determine the curvature radius in sub-section 2. If the accuracy would have been higher, the gap might have been eliminated, although in order to be sure this problem does not arise it is better to use a graphical solution. Since the error in this particular case is small, it will be accepted for now (see the more rigorous construction at the end of this chapter). A quick fix for filling the gaps is to use the Loft feature and use the faces as the two ends of the loft.
Fig.8. 11 – Detail with the loft between the lobes
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Fig.8.12 – The full body of the mixer
7. Shelling the 3D model Thus far we have only created the "full" geometry of the mixing chamber. Using the Shell feature this full body can be transformed into a proper mixing chamber geometry i.e. transform the part into a thin wall body. Before this, however, there is still one operation that needs taking care of, the correction of the curvature of the inlet section. In order to do this, we use a new lofting operation between the existing inlet of the geometry created and a proper circular sketch located in a parallel reference plane, as in Fig.8.13.
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Fig.8.13 – Correcting the circular inlet When using the Shell command, in order to eliminate the surfaces where the flow will pass, it is sufficient to select them with a click right.
Fig.8.14 – The shell of the mixing chamber
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8. Scalloping the mixing chamber The mixing chamber described in the patent is scalloped, which implies the cutting of the downstream section using a predetermined curve. For this we will use the Revolve cut feature with a curve traced from Fig.8.1. For visualization reasons, it is simpler to hide the geometry created thus far by using suppress from the Feature Manager of the first loft and then reactivate the sketch with the picture from the patent (click right - Show). Select the left plane and initiate a new 2D sketch in which trace the cutting contour, like in Fig.8.14.
Fig.8.15 – The cutting sketch for the scalloping
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Do not neglect to draw an axis for the revolved cut, which should coincide with the axis of the circular pattern. Also, in order to complete the scalloping it is necessary to unsuppress all the modeling features by clicking right and selecting unsuppressed the shell from the Feature Manager. The cut is made by selecting the segment which serves as a revolution axis and then Features – Revolve Cut. For the case in which the extremities are not fully covered by the cutting sketch, SolidWorks allows the user to select the bodies to keep, in this case, body 1.
Fig.8.16 – The cutting volume (left) and the resulting bodies (right) After scaling the body to the desired specifications Insert – Features – Scale (the scale factor depends on the true dimensions of the turbine engine nozzle), the mixer is
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finished. This body can later be integrated and tested thermodynamically into a turbo machinery assembly.
Fig.8.17 – Finished mixer An alternative to the revolved cut is the use of the feature Indent (Insert – Features). This cuts a solid body (or surface) by intersecting it with a given surface (in our case a revolution surface). We will be using the same cutting sketch - note the differences between the curve in Fig.8.15 and the one in Fig.8.18. After adjusting the sketch, we will create a revolution surface Insert – Surface –Revolve, selecting as a symmetry axis the Axis 1 of the model. Figure 8.19 presents depicts the surface.
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Fig.8.18 – The sketch used for the cutting surface (note the absence of the axis line and the open contour)
Fig.8.19 – The body of the mixer and the cutting surface During the indent operation it is necessary to specify the Target body and the surface (or surfaces) used to cut it (Tool body region). Also, the tolerances must be set. 168
Fig.8.20 – Selecting the key surfaces for this operation
Fig.8.21 –The cutting surface must be removed after the Indent
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After finalizing the operation, the model can be cleaned by eliminating the cutting surface using Insert – Features – Delete Body, Fig.8.22.
Fig.8.22 – The finished mixer
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Alternative for rigorously determining the inlet radius for the As seen in sub-section 6, the less rigorous geometrical construction leads to gaps between the lobes of the mixer which forces the user to do an additional correction step. Furthermore, this correction is not perfect and the error will propagate. The following section presents a more accurate way to model the mixer. Activate the front plane and initiate a planar sketch and draw a pair of construction lines around the fixed reference point in order to mark the apparent height difference between the two guide curves. Then, from an arbitrary point (it is important to avoid any constraints), located on the vertical axis, draw a circular arc sector with θ=11.25° Fig.8.23. From point B we draw a line up to point C Fig.8. 24.
Fig.8.23 – The reference line and the construction of the circular arc of known angular 171
A B C
D a.
b. Fig.8.24 – a. The height from B to C . b. Setting up the congruence condition for the radial segments Trace now the segment [AC] with an imposed length equal to that of segment [AD] using Equations (Tools – Equations). As visible in Fig.8.24.b, the segments [AC] and [AD] are now congruent. Therefore, the circular arc is now fully described and conforms to the angular dimension required. A consequence of this is that the curvature radius is now precisely the radius of the circular nozzle. As an exercise, it might be interesting to remodel the mixer geometry using this method and then compare the results.
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Fig.8.25 – Differences between the rigorous construction method (top) and the approximate method (bottom)
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Chapter IX - Automatic digitization of scanned 3D models
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IX - Automatic digitization of scanned 3D models Tridimensional scanning is one of the most popular methods in rapid prototyping or even reverse engineering and, in some cases, the control of mechanical parts. The flexibility and portability of 3D scanning systems compensate the accuracy differences between them and CMM (Coordinate Measurement Machine) methods. SolidWorks offers the possibility to manage the 3D scanning process with NextEngine Scan compatible equipment and to process the data quasi-automatically. The ScanTo3D module contains the processing menus for scanned surfaces or the scanned Mesh. The two menus are available for any imported geometry (scanned or otherwise) from one of the compatible file formats (*.stl, *.3ds, *.wrl, *.obj etc.). Care must be taken when accessing these menus because the Files of Type must be Mesh Files; Otherwise, by directly selecting the file format from the import menu (e.g.*.stl), the program will interpret the file differently and will not allow the use of the automatic processing That being said, we will now try to make our own automated system for digitizing 3D scanned objects. This system will be dedicated to axial flow turbo machineries and can therefore be simplified. The automation consist in recording a Macro (Tools – Macro – Record) which will record - then repeat for other cases - the operations and commands that the user puts in. As a good practice keep the commands and references as generic as possible so that the macro can be used on a wide variety of particular cases.
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1. Scanned object import
2. Inserting a reference plane at the model mid height
3. Determining the sketch of the intersection between the plane and the model surface
4. Transforming the polygonal sketch into a spline curve (Tools – Spline Tools – Fill Spline)
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1. Geometry import and establishing the reference points As mentioned before, the way the import is made matters in activating or not of some features of the program. In this example we will import the *.stl file of a scanned object. Once the geometry has been imported, we can start recording the macro (Tools – Macro – Record). The location where the macro is being saved should be chosen carefully since the final file may be substantial. The first reference we establish is the height of the scanned section. We place a dimension (Sketch – Smart Dimension) and rename it so that we can call it out when inserting the reference plane.
Fig.9.1 – The dimensioning of the scanned section height Next, we insert a reference plane (Reference Geometry – Plane) in the middle of the scanned section. Since the constraint imposed to the reference plane is dependent on the dimension made earlier, we will define the reference plane as parallel to the one in which the airfoils are aligned and at an arbitrary distance. The distance itself is of little importance but the orientation is crucial, a bad choice can
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result in the plane not intersecting the model. The parameter which determines the correct distance of the reference plane will now be defined with an Equation (Tools – Equations – Add). In principle, the name of the parameter will be - by default - “D1@Plane1”, but for more control it may be identified either by renaming it or by inserting a Design Table (Insert – Design Table). The equation linking the position of the reference plane with the dimensioned height of the model is "D1@Plane1"="RD1@Annotations"/2.
Fig.9.2 – The reference plane located at mid height of the imported 3D model
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2. Obtaining the intersection sketch This macro aims to obtain a spline curve that defines correctly and as smoothly as possible the airfoil section of the scanned turbo machinery blade. By using the intersecting tool (Tools – Sketch Tools – Intersection Curve) and by selecting the reference plane and the imported model surface we obtain the “Intersection Curve”, note that the result is actually a planar sketch (not a curve such as the ones in the Insert – Curve menu, as the name would suggest).
Fig.9.3 – The resulting intersection sketch Although some scanned models may be "clean" from a geometric stand point, the next step can prove useful in removing the small imperfections of the sketch (Tools – Sketch Tools – Repair Sketch).
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3. Smoothing the airfoil The last stage of the recording is to smooth the sketch we have just created. Using the Fit Spline (Tools –Spline tools – Fit spline - closed) we obtain, from the poly-line sketch (which should be removed by ticking delete geometry), a spline curve. The smoothness level is however linked to the tolerance we wish the curve to be created, the user must be aware of the information losses associated with this process.
Fig.9.4 – The finished spline curve After the mid span section sketch has been finished, it can be copied into a new part in which it can later be used for reconstructing the blade geometry. The same process can be repeated for multiple scanned sections, thus transforming the *.stl scanned geometry into a vector graphics 3D file. Because of the high degree of automation, a “clean” CAD version can quickly be obtained.
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Of course, the macro may be set to extract more than one blade cross sections, hence reducing the need for multiple runs. However, 3D scan files tend to be bulky on account of holding coordinate information of millions of points. The following figures show the end result of successive runs of a similar macro which extracts the top and bottom of the imported geometry.
0 – 5 mm Fig.9.6 – Processed slices of a similar, two-slice macro
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10 – 15 mm
20 – 25 mm 184
30 -35 mm
40 – 45 mm Fig.9.6 – Continued
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Fig.9.7 – Reconstructing the scanned blade can easily be made by copying the airfoils into a single part and lofting them one by one
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Chapter X - Transposing a sketch into points Cartesian coordinates - Using Macros -
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X - Transposing a sketch into points Cartesian coordinates using Macros A frequent problem in the design industry is the transfer of sketches from a standardized format in another. Although this can be achieved with relative ease by using universal formats, in some cases it is better to have the exact coordinates of the points defining the sketch. This is not a problem for polilines but becomes a complex problem for splines or composite 3D curves. There are many variations on the spline curve which can lead to slight differences in the rebuilding final result. A solution to this is the fine discretization of the curve so that the differences are minimized. Once the curve has been discretized and the points correspond to the user requirements, they can be converted into a sketch and their coordinates written in a text file via a Macro. An example of how to program such a Macro is presented at the end of this chapter. The original sketch
Transforming it into a single curve using Fit Spline
Inserting reference points (Reference geometry – Point)
Converting the points into a single 3D or 2D sketch
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1. Transforming a sketch into a single spline In order to simplify the automated process, we will chose to discretize the sketch in this example only after converting it into a single spline curve Fit Spline (Tools – Spline Tools). It is best that the user does this operation manually since the information losses can vary from one sketch to another and it is best to keep them to a minimum.
Fig.10.1 – The original sketch (polyline + spline) We edit the sketch using Fit Spline (constrained) setting in the desired tolerance - without deleting the original sketch; this will prevent the sharp corners of the sketch from being deleted.
Fig.10.2 – The sketch converted into a single closed spline This step requires the selection - after creating the spline - of the initial sketch and un-tick for construction which was automatically activated by the Fit Spline operation. Doing this allows us to project the reference vertices onto the original sketch.
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2. The spline discretization Starting from this point, we can begin recording the Macro in order to automate the rest of the process. We close the sketch and, by selecting the newly obtained spline we use Reference geometry - Point to insert an arbitrary number of points onto curve. A good idea is to make the points uniformly distributed along the curve - especially if the curve is a spline (for straight lines it is better to have only the endpoints and for the circular arcs three points).
Fig.10.3 – Inserting 100 reference points along the single spline
3. Inserting all the points into one sketch Initiate a new sketch, in this case planar (but the same applies to 3D sketches), and use the Convert command to insert all the points into it. Because the reference points will be shown individually it is best to select all the elements of the part by holding shift and clicking on the first and last element of the part in the Design Tree.
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Fig.10.4 – The sketch which incorporates all teh elemets, created after using Convert. At last, we obtain the sketch which includes all the initial points in addition to the newly created reference points. This step is useful since the Macro that writes the coordinates into the text file, only reads the coordinates of the points in one sketch at a time. Therefore, the workload is diminished by having all the points we need in a single sketch. The Macros described at the end of the chapter can be used by creating a new Macro (Tools – Macro – New Macro), copying the text directly and saving it under a custom name.
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‘Macro for transferring the Cartesian coordinates of the points in a sketch into a text or MS Excel file ’
Option Explicit Dim SW As SldWorks.SldWorks Dim SWmodel As SldWorks.ModelDoc Dim SWselect As SldWorks.SelectionMgr Dim SWfeat As SldWorks.Feature Dim SWfeat_sketch As SldWorks.Feature Dim SW_point As Variant Dim Ox() As Double Dim Oy() As Double Dim Oz() As Double Dim n As Long 'current number' Dim k As Integer 'sketch number of points' Sub main() Set SW = Application.SldWorks Set SWmodel = SW.ActiveDoc Set SWselect = SWmodel.SelectionManager Set SWfeat = SWselect.GetSelectedObject(1) Set SWfeat_sketch = SWfeat.GetSpecificFeature SW_point = SWfeat_sketch.GetSketchPoints k = UBound(SW_point)
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ReDim Ox(UBound(SW_point)) ReDim Oy(UBound(SW_point)) ReDim Oz(UBound(SW_point)) For n = 0 To k Ox(n) = SW_point(n).X Oy(n) = SW_point(n).Y Oz(n) = SW_point(n).Z Next n Open "D:\SW output1.xls" For Output As #1 'prints a Microsoft Excel space delimited data array' Print #1, " #pnt Ox Oy Oz" For n = 0 To k Print #1, (n + 1); " "; (Ox(n) * 1000); " "; (Oy(n) * 1000); " "; (Oz(n) * 1000) Next n Close #1 Open "D:\SW output1.txt" For Output As #2 'prints a text file formated for SolidWorks "Curve Trough XYZ tool" ' For n = 0 To k Print #2, (Ox(n) * 1000); " "; (Oy(n) * 1000); " "; (Oz(n) * 1000) Next n Close #2 End Sub
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‘Macro for inserting evenly distributed reference points in a given sketch' ‘The Macro inserts ten evenly distributed points along the contour of a given sketch which can contain poly-lines and splines.‘ Dim swApp As Object Dim Part As Object Dim SelMgr As Object Dim boolstatus As Boolean Dim longstatus As Long, longwarnings As Long Dim Feature As Object Sub main() Set swApp = Application.SldWorks Set Part = swApp.ActiveDoc Set SelMgr = Part.SelectionManager swApp.ActiveDoc.ActiveView.FrameState = 1 boolstatus = Part.Extension.SelectByID2("Spline1@Sketch1", "EXTSKETCHSEGMENT", -0.05101302188563, 0.03708803994623, 0, False, 0, Nothing, 0) Dim vRefPointFeatures As Variant vRefPointFeatures = Part.FeatureManager.InsertReferencePoint(2, 2, 0, 10) Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) Part.EditSketch Part.ClearSelection2 True
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boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Spline1", "SKETCHSEGMENT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line1", "SKETCHSEGMENT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line2", "SKETCHSEGMENT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line3", "SKETCHSEGMENT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line4", "SKETCHSEGMENT", 0, 0, 0, True, 0, Nothing, 0) Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Spline1", "SKETCHSEGMENT", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line1", "SKETCHSEGMENT", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line2", "SKETCHSEGMENT", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line3", "SKETCHSEGMENT", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Line4", "SKETCHSEGMENT", 0, 0, 0, False, 0, Nothing, 0) Part.ClearSelection2 True Part.SketchManager.InsertSketch True Part.Insert3DSketch boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) boolstatus = Part.SketchUseEdge2(False) Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Point1", "DATUMPOINT", 0, 0, 0, False, 0, Nothing, 0)
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boolstatus = Part.Extension.SelectByID2("Point2", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point3", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point4", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point5", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point6", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point7", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point8", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point9", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point10", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) Part.ClearSelection2 True Part.SketchManager.InsertSketch True Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Point100", "DATUMPOINT", 0, 0, 0, False, 0, Nothing, 0) Part.ClearSelection2 True boolstatus = Part.Extension.SelectByID2("Point1", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point2", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point3", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point4", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0)
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boolstatus = Part.Extension.SelectByID2("Point5", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point6", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point7", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point8", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point9", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) boolstatus = Part.Extension.SelectByID2("Point10", "DATUMPOINT", 0, 0, 0, True, 0, Nothing, 0) Part.BlankRefGeom boolstatus = Part.Extension.SelectByID2("Sketch1", "SKETCH", 0, 0, 0, False, 0, Nothing, 0) Part.BlankSketch End Sub
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References [1] Matt Lombard, Solidworks 2013 Bible, ISBN: 978-1-11850840-4 [2] Matt Lombard, SolidWorks 2011 Parts and Assemblies Bible, ISBN: 978-1-118-37606-5 [3] Matt Lombard, SolidWorks 2011 Parts Bible, ISBN: 978-1-11800275-9 [4] Charles W. Hull, Apparatus for production of three-dimensional objects by stereolithography, US 4575330 A, Mar 11, 1986 [5] Representation for Communication of Product Definition Data: IGES 5.2 (Initial Graphics Exchange Specification Version 5.2), US Product Data Association, November 1993, ISBN 978-1-885389008 [6] ISO 10303-21:2002 Industrial automation systems and integration -- Product data representation and exchange -- Part 21: Implementation methods: Clear text encoding of the exchange structure [7] Amit Kumar, Peter King, Airfoil for a compressor, EP 1921263 A2, General Electric Company, May 14, 2008 [8] Denni Liao, Volute inlet of fan, US 6884033 B2, Cheng Home Electronics Co., Ltd. Apr 26, 2005
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[9] Morris Anderson, Turbofan gas turbine engine aerodynamic mixer, US 20110126512 A1, Honeywell International Inc. Jun 2, 2011 [10] Philip P. Walsh, Paul Fletcher, Gas Turbine Performance, Second Edition, Blackwell Science Ltd 2008, ISBN: 9780632064342 [11] Neil Sclater, Mechanisms and Mechanical Devices Sourcebook, 5th Edition, McGraw-Hill's AccessEngineering, 2011, ISBN: 9780071704427 [12] David Japiske, Centrifugal Compressor Design Performance, December 1, 1996, ISBN-13: 978-0933283039
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[13] S Larry Dixon, Cesare Hall, Fluid Mechanics and Thermodynamics of Turbomachinery, Seventh Edition, 2013, ISBN13: 978-0124159549 [14] http://www.3ds.com/products-services/solidworks/solidworkstutorials/ [15] http://www.solidworkstutorials.com/ [16] http://learnsolidworks.com/ebooks/ebook
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