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    Surface Machining

    NATIONAL INSTITUTE FOR AVIATION RESEARCHWichita State University

    Revision 5.13

    Copyright 2004. All rights reserved.

    www.cadcamlab.org

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    None of this material may be reproduced, used or disclosed, in part or in whole, without the expressed written permission of:

    National Institute for Aviation ResearchWichita State University

    Wichita, KS

    Copyright 2004. All rights reserved.

    www.cadcamlab.org

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    Table of Contents, Page i Wichita State University

    TABLE OF CONTENTS

    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    Machining Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    Area Oriented Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    Operation Oriented Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    Operation Oriented Machining Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Roughing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Sweep Roughing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Surface Machining Workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    Advanced Machining Workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    Roughing Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    Sweep Roughing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    Geometry Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Machining Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

    Roughing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    Geometry Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    Machining Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

    Macros Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    Additional Roughing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

    Sweeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

    Geometry Tab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

    Machining Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    ZLevel Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

    Spiral Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    Pencil Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

    Contour-driven Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

    Isoparametric Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

    Machining Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

    Reworking Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

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    Multi-Axis Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

    Rotary Axis Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

    Five Axis Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

    Multi-Axis Sweeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

    Multi-Axis Contour Driven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

    Multi-Axis Isoparametric Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

    Multi-Axis Flank Contouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Multi-Axis Curve Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

    Multi-Axis Helix Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

    Practice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

    Angled Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

    Butterfly Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

    Cowling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

    Double Flange Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

    Mounting Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

    Pressure Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

    Shaft Rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Valve Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

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    Roughing Operations, Page 72 Wichita State University

    Additional Roughing

    In many cases you may want to utilize some of the Prismatic Machining tools as well as

    Surface Machining tools.

    Open the Rocker Mount Machining Process file from theRocker Mount folder This

    problem will use both prismatic and surface tools to complete the exercise. This problem

    will also be used with the Sweep Roughing operation, so be sure to save as you go along.

    The very top of this part is flat, therefore a facing operation would work well to remove all

    of the material above the part. Profile contouring would also remove the outside area very

    well, much better than the roughing operation.

    The Part Operation has already been defined for you. If you are not already in the Prismatic

    Machining workbench, you will need to go there.

    Start a Facing operation in Manufacturing Program.1. You should already be very

    familiar working with the Prismatic Machining tools. The next few steps are going to be

    very general, so if you have trouble, refer back to your Prismatic Machining book.

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    Define the bottom of the facing operation as the top of the final part. There are small

    triangular areas that you can use for the bottom definition.

    Define the boundary of the facing operation as the boundary of the stock material.

    Also define the top of the facing operation as the top of the stock material. This should

    have all of the geometry defined. Next you will define the machining parameters.

    Change theTool path styleto Back and forth. Under theRadialtab, set theEnd of pathtoOut, and change theTool side approach clearanceto -0.5in. By setting the clearance

    to a negative value, you will be keeping the tool in contact with the stock material. This is

    ideal so that the tool will remain under a load.

    Set a 0.25in maximum axial depth of cut. This will complete the machining parameters.

    Define the following facing tool. This is a large part, so a large tool is optimum.

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    Define macros to finish the facing operation. It is left to you to decide what type of

    macros that you want.

    Now to profile around the outside.

    Start a Profile Contouring operation after the facing operation. Define the profile, topand bottom for the geometry definition. Be sure to make the bottom a soft bottom, as

    well as define the bottom on the bottom of the stock, not the part.

    Define the profile as a closed tool path, with a one way tool path style. Also, set a

    0.050in breakthrough, with 3, 0.375" radial paths. Cut a maximum of 0.5" deep each

    pass. This will have the machining parameters set. The last job is to define the tool and

    macros.

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    Change to the following tool.

    Set macros that you feel will be appropriate. Again, the choice is yours on macros. You

    can make them as exotic or generic as you desire.

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    Now that you have a few prismatic machining operations, you are ready to integrate the

    surface machining tools.

    Switch to the Surface Machining workbench. Notice the workbench changes, but the

    part stays the same. Integrating workbenches is as simple as switching between them.

    Start a Roughing operation after the Profile Contouring operation. The roughing

    operation will be used to remove the excess material near the part contours.

    Define thePartdefinition. All you will need to do is select the part definition from the

    sensitive area, then select the final part partbody.

    Change theOffset on partto 0.5in. The next set of operations will take care of the excess

    thickness.

    Make sure aSpiraltool path style is used, with a 50% stepover ratio. A 0.25"

    maximum cut depth should be sufficient. Once done, define the following tool.

    Now all that needs defined is the Automatic Motions.

    Turn onOptimize retractwith a 0.25in axial safety distance. Switch theAutomatic

    Motionto a helical mode, with a 5deg ramping angle and a 60% helix diameter. An

    approach and radial safety distance of 0.125" should work well. This should be enough

    to define the macros.

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    Notice anything interesting?

    When the roughing operation is used after any other operation, it will only cut the material

    that is remaining. The roughing operation is smart enough to recognize where material

    remains and where it does not. This will be investigated further later on. For now, be sure

    to save and move on.

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    Sweeping

    The sweeping operation is a good, all-around general surface sweeping operation. The tool

    makes passes along a surface of any contour, making the finished cut. Although the

    sweeping operation could be used for roughing, it is highly un-advisable. The sweeping

    operation is for final cuts only.

    With your Rocker Mount Machining Process open, start a sweeping operation after

    Roughing.1. Sweeping operations are going to be defined in a similar manner to

    sweep roughing operations.

    Geometry Tab

    Sweeping is going to be very familiar to the sweep roughing operation. Take a quick look at

    the sweeping operation sensitive area.

    The two new additions to the sensitive window is the StartandEndplanes. These two

    planes define a limiting along the cut of the surface that will keep the tool from passing.

    This is different from the limiting contour in the sense that the limiting contour can be theentire surface, but the tool is only allowed to machine from the start to the end plane along

    the surface.

    Select thePartdefinition, and the select the finished part. Just like with the other

    operations, by selecting the part definition, you will be defining the entire part body.

    Change theOffset on partto be 0.0in. This will make sure you machine the final part.

    Take a quick look at the tool paths.

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    Granted, there are a lot of things wrong with these toolpaths, but as you can quickly see, the

    sweeping operation will cut across the entire part, regardless of the features.

    Select theEndplane from the sensitive area, then select the flat side as shown below.

    This will define the end plane to be on the side of the part. At this point, the end plane does

    no good, however, once you offset it, it will become more useful.

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    With the third mouse button, select on theEndplane. With the contextual menu,

    selectOffset. Set the offset to -2in. The -2" is required to make the plane move inward. If

    your plane goes outward with a negative, then use a positive value.

    Take another look at the tool paths.

    Notice they now stop at the end plane. The start and end planes work well for defining

    limits on how you want the part cut.

    With the contextual menu, remove theEndplane. This will go back to machining the

    entire surface.

    Now to move on to the machining parameters.

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    Machining Parameters

    Take a quick look at the various machining parameters.

    Machining Tab

    Tool Path Style Defines the type of cut that is to be made across the part.

    There are three options available.

    Machining Tolerance Defines the tolerance of the machine being used

    Reverse tool path Reverses the computed tool path

    Max Discretization Allows you to override the step size of the machiningoperation

    Step Defines the maximum step size allowed

    Plunge Mode Controls if the tool plunges, or dives into the material. This

    option is only available with the One-Way tool path styles.

    No check No plunge checking is made

    No plunge Tool is halted as soon as it is to plunge into the material

    Same height Tool remains at the same Z-height when it is supposed to

    plunge

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    Radial Tab

    Stepover Defines how the sidestep is calculated

    Constant Tool moves over a maximum distance, keeping the scallop

    height at the defined size

    Via Scallop Height Tool steps over varying distances, remaining within the

    MaximumandMinimum Distance, while keeping a constant

    scallop height thickness

    Maxi. distance between pass Defines the maximum distance stepped each radial pass

    Min. distance between pass Defines the minimum distance the tool can step each radial

    pass

    Scallop height Defines the maximum scallop height allowed

    Stepover side Defines which side the tool steps, left or right

    View Direction Defines the normal direction for the tool path computation

    Along Tool Axis The normal for the tool path is computed looking down along

    the tool axis

    Other Axis The tool paths are calculated looking along another tool axis

    to determine the stepover distance

    Collision Check Collisions between the part and the tool would be avoided

    Note: The only time the View Direction would need to be changed would be if you were

    machining a large sloped surface. Otherwise, by changing the view direction to something

    other than the tool axis, you run the risk of not machining all the surfaces.

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    Axial Tab

    Multi-pass Defines how the multiple axial steps are calculated

    Number of levels Defines the number of axial levels

    Maximum cut depth Defines the maximum depth that the tool cuts each pass

    Total depth Defines the overall depth of the part thickness

    Note: Multiple axial steps with the sweeping operation should be used sparingly. The axial

    offset is just a vertical offset. They do not move out radially. This means that the final pass,

    the pass against the part surface is computed, then a copy is made of those tool paths and

    they are moved up along the tool axis a particular amount. This generates problems in

    vertical, or near vertical areas where you will be cutting a lot of material the first pass, and

    then not a lot of material for all passes afterwards. Generally, you are going to want to use

    roughing and sweep roughing to get the part cut down to where only one finishing pass is

    necessary.

    Zone Tab

    Zone Controls what type of area is machined. There are a number of options.

    All All zones get machined

    Frontal Walls Only the front and back walls get machined. The front and

    back walls are determined by the forward motion of the tool.

    Lateral Walls Only machines the walls on the left and right hand side of the

    tool paths

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    Horizontal Zones Only machines areas that are within the horizontal slope angle

    Min lateral slope Minimum angle to be considered a lateral wall

    Min frontal slope Minimum angle to be considered a frontal wall, typically the same as

    lateral slope

    Max horizontal slope Maximum angle that will be considered a horizontal plane

    Island Tab

    Island skip Indicates that islands, or gaps in the surface should be jumped over,

    not gone around

    Direct This option, available only when Island skip is turned on, will cause

    the tool to move directly over the island, and not make a retract and

    approach motion

    Feedrate length Defines the size of a gap or island that will cause a direct island skip.

    Any hole or pocket larger than this length will generate a retract and

    approach motion.

    Now it is time to change a few machining parameters to determine the effects they make on

    the tool paths.

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    Take a quick note of the unchanged tool paths.

    Note that the tool starts in the back left corner of the part and ends in the front right corner.

    Turn onReverse tool path. Instead of the tool starting in the front right and ending in the

    back left like you might expect when you reverse the tool paths, it instead starts in the front

    left and ends in the back right.

    Since the tool is in a zig-zag motion, the cutter is continually switching between climb and

    conventional milling. If you were machining in a one way motion, the reverse tool path

    would make the difference between climb and conventional milling.

    Turn offReverse tool path. In theRadialtab, change theScallop heightto 0.005in.

    Notice when you change the scallop height, the Maxi. distance between passchanges to

    0.155". The two fields are linked together by some means. Fortunately, most times you will

    not have aConstantstepover.

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    Change theStepoverto Via scallop height. This will activate theMin. distance between

    passoption.

    Now you have all three distance fields available to you.

    There is one rule that you must follow for theVia scallop height to work properly. The

    scallop height distance should be between the minimum and maximum distance between

    passes. If you have a minimum step of 0.125" and a scallop height of 0.005", the tool will

    always make a step of 0.125" because that is set as a minimum. The opposite is also true. If

    you have a maximum distance set to 0.005", and a scallop height of 0.020", the tool will

    always make a 0.005" step, and your scallop height will be much smaller than what you are

    trying for. This results in various problems as you might suspect.

    Change the maximum distance to 0.125", the minimum distance to 0.005", with a

    scallop height of 0.010". This will cause the tool to allow for varying sized steps as it goes

    across the part. The tool will do its best to maintain a scallop height of 0.010", but will

    guarantee that the step size will never go under 0.005" or above 0.125".

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    Again, take a quick note of where the tool starts and stops. Currently it starts in the back

    left corner of the part, then makes its way to the right.

    Change theStepover sidetoRight. Notice now that the tool starts in the back right side

    and then steps left. Between this option and theReverse tool pathoption, you can change

    the overall starting and machining direction of the tool paths.

    Change theStepover sideback toLeft. Under theAxialtab, set theNumber of levelsto

    3, with aMaximum depth of cutat 0.125". Now the sweeping operation makes three

    levels of cut. If you look closely at the tool paths, you should notice that the tool paths are

    only a vertical offset from the bottom set of tool paths.

    Since this is a purely vertical offset, it does not work very well to remove excessive

    material. You are much better off to remove the excessive material with a sweep roughing

    operation prior to the sweeping operation.

    Set theNumber of levels back to 1, and then change the ZonetoFrontal walls. Set the

    Min. frontal slopeto 75deg. This will cause the sweeping operation to only cut the frontal

    walls, or walls that the tool will hit head-on.

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    Notice only a small frontal area gets machine. Basically, anything within 15deg (90-75) ofvertical, and on the frontal plane gets machined. Everything else is ignored.

    Change the Min. frontal slopeto 25deg. Now a lot more gets machined. By decreasing

    the minimum frontal slope angle, you are allowing more and more of the non-frontal,

    non-vertical walls to get machined.

    Change theZonetoLateral Walls, with a minimum angle of 45deg. This time the walls

    on the sides get machined. The 45deg allows the part to be partially machined on the frontal

    zones.

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    As you might suspect, theHorizontal zonesoption works in a very similar fashion where it

    will machine only horizontal areas, and none of the lateral or frontal walls. In most cases,

    you will find that you want to machine all zones.

    Change theZoneback toAll. Now take notice of what happens when the tool approaches

    the holes in the bottom of the part.

    Notice how the tool paths do not go over the hole, nor do they retract from one side and

    approach the other. Instead, the tool zig-zags its way around the hole and pocket area, then

    comes back later to clean up what was left behind. Even though, there will still be small

    peaks that will make drilling a straight and accurate hole quite difficult.

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    Turn onIsland skipunder theIslandtab. Although somewhat better, this will still yield

    the same problem as before.

    The tool now retracts once it gets to the hole, rapids over, then approaches back down on the

    other side. A small mound will still be present with this scenario.

    Turn onDirect, with aFeedrate lengthof 2in. Now the tool paths are a little more of

    what you would want.

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    Notice now, the tool passes over the hole as though it is not there. You should also note

    though that the tool does still retract and approach over the pocket area.

    Change theFeedrate lengthto 10in. This will now cause the tool to pass over the slot as

    though it is not there either. Increasing the feedrate length is one way to make sure you pass

    over all the open areas.

    You could have also change the machining direction to fix the problem of jumping over the

    slot. By machining in another direction, the tool would not see the slot as being long, butinstead, just a narrow jump.

    The only time that the direct island skip has troubles is when the Z-height changes between

    two levels of a pocket.

    The tool paths are now starting to look really good. However, this is still an incorrect

    operation. The tool used is not a good choice. Granted, the physical dimensions of the tool

    are just fine, but if you remember, this is the same tool that was used for roughing earlier.

    Very seldom are you going to want to rough and finish cut with the same tool.

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    Change to the tool tab. Currently, the previous tool is used as the default tool. You need

    to force a tool change so you can change the parameters of the tool.

    Change theNameof the tool to T4 Ball Mill, and press Enter. By changing the name of

    the tool, you are forcing a tool change.

    Change the tool to be a ball nose end mill, with all the same dimensions as before. You

    should just need to select the Ball-end tool checkbox to convert the tool into a ball nose

    tool.

    This nearly has the sweeping operation complete. The only thing left is to define good

    macros.

    Switch to the macros tab. Notice that you are now back to the standard surface machining

    macro style. If you want to review the different macro types and available macros, referback to the sweep roughing exercise.

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    Select theApproachmacro and change the Modeto Box. This will create the imaginary

    box around the tool path to create a nice, S-Curve shape into the part.

    Change the box macro to have the following parameters. This will make the box have a

    1" height, 0.375" width, and 0.5" depth.

    Change theRetractmacro to a circular macro, with the following parameters. As you

    might have noticed, using the pre-defined macros allow for a quick definition of the macros.

    Many times it is advantageous to use the pre-defined macros instead of trying to custom

    build macros all the time.

    This will finish your Sweeping operation.

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    Sweeping, although it works good for an all-purpose finishing operation should not be used

    to completely finish parts all the time.

    Save and close the document.

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    Other available courses

    CATIA V5 and ENOVIA

    CATIA Basic Concepts

    CATIA Part Design & Sketcher

    CATIA Assembly Design

    CATIA Drafting

    CATIA Wireframe & Surfaces

    CATIA Prismatic Machining

    CATIA Surface Machining

    CATIA Fitting Simulation & Kinematics

    CATIA Functional Tolerancing & Annotation CATIA Stress Analysis

    ENOVIA DMU Viewer

    ENOVIA LCA Basic Concepts

    ENOVIA LCA Advanced Concepts

    ENOVIA LCA Product Design

    To enroll in any of the above courses, contact us at: (316) 978-3283

    toll-free at: 1-800-NIARWSU or email: [email protected]

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    Wireframe & Surfaces

    NATIONAL INSTITUTE FOR AVIATION RESEARCHWichita State University

    Revision 5.14

    Copyright 2005. All rights reserved.

    www.cadcamlab.org

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    None of this material may be reproduced, used or disclosed, in part or in whole, without the expressed written permission of:

    National Institute for Aviation ResearchWichita State University

    Wichita, KS

    Copyright 2005. All rights reserved.

    www.cadcamlab.org

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    Table of Contents, Page i Wichita State University

    TABLE OF CONTENTS

    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Wireframe & Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Pull Down Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    Edit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    Generative Shape Design Workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Bottom Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Generative Shape Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Developed Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11BiW Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    Wireframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13On curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16On plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20On surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Circle / Sphere center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Tangent on curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Between . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Point Repetition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Projecting points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    Intersection points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Extremum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Polar Extremum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Point-Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Point-Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Angle/Normal to curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Tangent to curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Normal to surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Bisecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Intersection lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    Projecting lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Polyline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

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    Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Offset from plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Parallel through point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Angle/Normal to plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Through three points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Through two lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    Through point and line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Through planar curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Normal to curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Tangent to surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Mean through points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Plane Repetition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

    Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Center and radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Center and point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Two points and radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Three points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Bitangent and radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Bitangent and point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Tritangent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Center and tangent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

    Corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

    Connect Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Helixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Spirals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Project curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Combine curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Reflect Line curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Intersection curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Parallel Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1373D Curve Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Curve comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

    Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Work on Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

    Creation on the fly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Modifying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Datums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Object repetition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

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    Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Extruded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

    Variable Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Rough Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Offset with Multiple Sub-elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

    Explicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180With reference surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 180With two guide curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188With pulling direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

    Linear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Two limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Limit and middle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198With reference surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 199With reference curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201With tangency surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203With draft direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205With two tangency surfaces . . . . . . . . . . . . . . . . . . . . . . . 209

    Circular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Three guides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Two guides and radius . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Center and two angles . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Center and radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Two guides and tangency surface . . . . . . . . . . . . . . . . . . . 218One guide and tangency surface . . . . . . . . . . . . . . . . . . . 220

    Conical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222Two guide curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222Three guide curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224Four guide curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Five guide curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

    Adaptive Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230Fill surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235Multi-section surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Blend surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Spines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

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    Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Joining Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Healing Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278Curve smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281Splitting Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282Trimming Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

    Untrimming Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290Disassembling Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Extracting Boundaries and Faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294Sketch Extract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298Creating the Nearest Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300Fillets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

    Shape Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302Edge Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308Variable Radius Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310Face to Face Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312Tritangent Fillet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

    Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315Translate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315Rotate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Affinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320Axis to Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

    Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324Rectangular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324Circular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

    Extrapolating Curves and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328Multi-Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

    Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339Curve Connect Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339Surface Connect Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Draft Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347Surfacic Curvature Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351Porcupine Curvature Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Geometric Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362Dress-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

    Geometrical Set Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Inserting a Geometrical Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Changing Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368Operations on Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

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    Ordered Geometrical Set Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374Inserting an Ordered Geometrical Set . . . . . . . . . . . . . . . . . . . . . . . . . . 374Modifying Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376Operations on Ordered Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378Scanning Ordered Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380Inserting in an Ordered Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

    Switching to a Regular Geometrical Set . . . . . . . . . . . . . . . . . . . . . . . . . 382

    Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383Parents/Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383Historical Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384Quick Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386Inserting Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388Sets of planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389Keep and No Keep Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

    Keep Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393No Keep Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

    Current Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397Deleting Useless Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

    Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

    Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423Problem 1 - Perfume Bottle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423Problem 2 - Tubing Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424Problem 3 - Antenna Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426Problem 4 - Sheetmetal Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428Problem 5 - Hook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

    Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431Shape - Generative Shape Design - General . . . . . . . . . . . . . . . . . . . . . 431Shape - Generative Shape Design - Work On Support . . . . . . . . . . . . . 433

    Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435Part Design Using Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

    Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435Thick Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437Close . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438Sew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439Pad/Pocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

    Boolean Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

    Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445Generative Shape Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

    Bump Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446Wrap Curve Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449Wrap Surface Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451Shape Morphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

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    Appendix D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457Developed Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

    Unfold Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457Develop Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

    Appendix E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

    BiW Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463Junction Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463Diabolo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467Mating Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Bead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4743D Working Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

    Appendix F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

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    Circular

    A circular swept surface forces the cross section to be circular. As with the linear sweep,

    the profile is defined implicitly based on your options, rather then as a separate profile

    element.

    Open theSwept Surfaces irculardocument. You should see some wireframe

    geometry.

    Select the sweep icon. TheSwept Surface Definitionwindow appears.

    Three guides

    Change theProfiletype to circle and the SubtypetoThree guides. The options change.

    Subtype Specifies what type of circle swept surface you are going to create.

    This determines theMandatory elementsand theOptional elements.

    You can choose fromThree guides, Two guides and radius, Center

    and two angles, Center and radius, Two guides and tangency surfaceorOne guide and tangency surface.

    Mandatory elements

    Guide curve 1,2,3 Defines the three curves through which the circle will pass

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    Select the four curves as shown below and select Preview. The surface passes through

    the three guide curves and uses the other curve as its spine. The cross section remains

    circular with respect to the normal planes of the spine.

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    Key 1.5 for theRadiusand selectPreview. There are four possible solutions. The first

    one is highlighted.

    Select the >> button until you get the second solution, then selectOK.

    Hide this surface.

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    Center and two angles

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypeto Center and two angles. The options change.

    Mandatory elements

    Center curve Defines the curve that represents the center of the circle

    Reference curve Defines the curve used as the base for the angles as well as the

    radius of the circle

    Angle 1,2 Specifies a starting and ending angle for the circle

    Optional elements

    Use fixed radius Specifies the radius you want the circle to have, thus using the

    Reference curveonly for an angle reference

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    Select the two curves as shown below, key -45.0 for Angle 1and 45.0 forAngle 2.

    Select the reference curve again to define the spine and selectPreview. The surface

    appears centered around the first curve and passing through the second curve. If you were

    to turn on theUse fixed radiusoption and specify a value, the reference curve would only be

    used to determine the angles and the surface would not pass through the curve.

    SelectOK. The surface is created.

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    Center and radius

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypeto Center and radius. The options change.

    Mandatory elements

    Center curve Defines the curve that represents the center of the circle

    Radius Specifies the radius of the circle

    Select the curve as shown below, key 1.5 for theRadiusand selectPreview. The surface

    appears. By default the spine is theCenter curve. This option is excellent for making quick

    pipes or tubing.

    SelectOK. The surface is created.

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    Two guides and tangency surface

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypetoTwo guides and tangency surface. The options change.

    Mandatory elements

    Limit curve with tangency Defines the curve on theTangency surfacethat will

    define one end of the circle

    Tangency surface Defines the surface to which the circle will be tangent

    Limit curve Defines the other end of the circle

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    Select the curves and surface as shown below and select Preview. Two solutions appear.

    Both are tangent to the existing surface and contain the two curves. By default the first

    curve is the spine.

    Keep the first solution and select OK. The surface is created.

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    One guide and tangency surface

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypetoOne guide and tangency surface. The options change.

    Mandatory elements

    Guide curve 1 Defines one limit of the circle

    Tangency surface Defines the surface to which the circle will be tangent

    Radius Specifies the radius of the circle. It needs to be large

    enough for the circle to exist between the tangent of

    the surface and the curve.

    Optional elements

    Trim with tangency surface Trims theTangency surface

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    Select the curve and surface as shown below, key 1.5 for theRadiusand selectPreview.

    Two solutions appear. Both solutions go from the curve to the tangent of the surface using a

    radius of 1.5 inches. Again, by default, the first curve is the spine.

    Keep the first solution and select OK. The surface is created.

    Save and close your document.

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    Conical

    A conical swept surface forces the cross section to be a conic. You can choose to have two,

    three, four or five guides to define the surface. However, the number of guides you use will

    limit the number of tangencies you can define. Regardless of which options you choose, the

    cross section will always remain conical.

    Open theSwept Surfaces onical

    document. You should see some wireframegeometry and some surfaces.

    Select the sweep icon. TheSwept Surface Definitionwindow appears.

    Two guide curves

    Change theProfiletype to conic and theSubtypetoTwo guide curves. The options

    change.

    Subtype Specifies what type of conical swept surface you are going to create.

    This determines theMandatory elementsand theOptional elements.

    You can choose fromTwo guide curves, Three guide curves, Four

    guide curvesorFive guide curves.

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    Mandatory elements

    Guide curve 1,Last Defines the two curves that will be used as the beginning and

    the end of the conic

    Tangency Defines the tangency at that guide curve

    Angle Modifies the tangency by a specified angle

    Parameter Specifies the conic parameter to use. The parameter

    determines the type of conic that will be created.

    Select the two curves and the respective surfaces and the line as shown below, key 0.5

    for theParameter,and selectPreview. The surface appears; it is tangent to the two

    existing surfaces and due to the parameter, is parabolic in shape. The parameter determines

    the type of conical curve that is created, as explained in the conic section. The parameter

    can vary as it follows the spine, if you use a law.

    Note: You were able to define two tangencies but you had to define a parameter.

    SelectCancel. The window closes.

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    Three guide curves

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypetoThree guide curves. The options change.

    Mandatory elements

    Guide curve 1,2, Last Defines the three curves that will be used to define the

    conic. The first and last define the beginning and the

    end of the conic. The second one defines a curve that

    the conic will pass through, instead of using a

    parameter value.

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    Select the three curves, the two surfaces and the line as shown below and select

    Preview. The surface appears, passing through the second guide curve instead of using a

    parameter.

    SelectCancel. The window closes.

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    Four guide curves

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypetoFour guide curves. The options change.

    Mandatory elements

    Guide curve 1,2,3, Last Defines the four curves that will be used to define the

    conic. The first and the last one define the beginning

    and end of the conic. The other two define curves that

    the conic will pass through. With this option, only one

    tangency can be defined.

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    Select the four curves, the surface and the line as shown below and select Preview. The

    surface appears, passing through all four curves and tangent to the surface.

    SelectCancel. The window closes.

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    Five guide curves

    Select the sweep icon again. TheSwept Surface Definitionwindow appears.

    Change theSubtypetoFive guide curves. The options change.

    Mandatory elements

    Guide curve 1,2,3,4, Last Defines the five curves that will be used to define the

    conic. The first and the last one define the beginning

    and end of the conic. The other three define curves

    that the conic will pass through. With this option, no

    tangencies can be defined.

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    Select the five curves and the line as shown below and select Preview. The surface

    appears, passing through all five curves.

    SelectOK. The surface is created.

    Save and close your document.

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