Module 7: Surface Modeling using Variable Section Sweeps

Lab ExercisesIf you are ready to start on the exercises for this module, please click the links below.

Exercise 1: Creating Surfaces on the Bottle Exercise 2: Designing a Compressor Blade (Challenge) Exercise 3: Designing a Camshaft (Challenge)

Lecture ReviewIf you would like to review a text-based version of the materials presented in this lecture, please click here.

IntroductionThe Variable Section Sweep is another powerful tool that enables you to create surface features by sweeping a section along one or more trajectories. Trajectories control the section’s orientation, rotation, and shape. The shape of the section can be constant or variable.You can control the shape of the surface features created using Variable Section Sweep, mathematical relations, and datum graph features.

ObjectivesAfter completing this module, you will be able to:

Describe the use of variable section sweeps. Create surface features using the Variable Section Sweep tool. Control the orientation of the section plane. Modify the cross-section using the Evalgraph and Trajpar options. Describe the rules for creating variable section sweeps.

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Describing Variable Section Sweeps Variable section sweeps are used to create geometry along one or more

selected trajectories. Trajectories control the section’s orientation, rotation, and shape. You use variable section sweeps when you need to change section geometry along the length of the sweep. You can sketch the trajectories or select existing datum curves and edges.

You can create a sweep using a constant section or a variable section. o Variable Section – Constrains the sketch entities to other trajectories

(pivot plane or existing geometry) or use section relations with the Trajpar parameter to make the sketch variable. The references to which the sketch is constrained changes the shape of the section. Also, defining the dimensioning scheme by a graph or relations (with trajpar) makes the sketch variable. Sketch regenerates at points along the trajectory and updates its shape accordingly.

o Constant Section – Sketch does not change its shape as it is being swept along the trajectories. Only the orientation of the frame on which the section is located changes.

The main components of the Variable Section Sweep tool are the trajectories. The types of trajectories include Origin (Spine), Normal, and X-Trajectory. You select the Origin trajectory first and then specify whether the additional trajectories are X or Normal trajectories. The sketched section is attached to the Origin trajectory and moves along its length to create geometry.

About the figure The figure in the slide has two trajectories defined, the original trajectory and

the X-Trajectory. A sketched section that sweeps across the trajectories. The section changes as the trajectories change profiles.

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Trajectories for Variable Section Sweep Origin Trajectory

The first trajectory that is selected is always referred to as the Origin or ‘Spine’ trajectory. A start point is specified at one end of this trajectory. This start point sets up where the sketching plane will intersect the trajectory.

Additional Trajectories Additional trajectories can be defined to control the section plane orientation

and the section shape. The use of additional trajectories to define the shape of the section is

discussed later.About the figures:The first figure has two curves that can be used as trajectories. The second figure has the two surface edges that are defined as trajectories.

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Section Plane OrientationSection Plane Control

This controls how the section plane is positioned along the trajectories. This is done by constraining the entity that the sketching plane is normal to (sets the Z-vector for the sketch orientation).

Normal to Trajectory – The section stays normal to a specified trajectory. If the Origin trajectory is selected, the variable section sweep will act like the generic sweep, that is, the section will remain normal to the Origin trajectory along its length.

When you are in the sketch orientation: The X-vector will always point to the right of the screen. The Y-vector will always point to the top of the screen. The Z-vector will always point out of the screen.

About the figures: Only one trajectory is used as the Origin trajectory. The section plane remains normal to the Origin trajectory.

Section Plane Orientation (cont.)Section Plane Control

This controls how the section plane is positioned along the trajectories. This is done by constraining the entity that the sketching plane is normal to (sets the Z-vector for the sketch orientation).

Normal to Projection – The section plane remains normal to the 2-D projection of the Origin trajectory along the specified direction. A planar

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reference is specified to which the section plane is normal. This direction can be specified by a plane normal, linear edge, or an axis.

When you are in the sketch orientation: The X-vector will always point to the right of the screen. The Y-vector will always point to the top of the screen. The Z-vector will always point out of the screen.

About the figures: The second trajectory is also added, but the section plane remains normal to

datum plane DTM5. The section plane remains normal to the datum plane TOP, but the X-vector

is oriented normal to the Origin trajectory. Notice the end of the created surface. 

Section Plane Orientation (cont.)Section Plane Control

This controls how the section plane is positioned along the trajectories. This is done by constraining the entity that the sketching plane is normal to (sets the Z-vector for the sketch orientation).

Constant Normal Direction – The section plane normal vector stays parallel to a specified direction reference. The direction of the Z-vector is held in a constant direction. This direction can be specified by a plane normal, linear edge, or an axis.

When you are in the sketch orientation: The X-vector will always point to the right of the screen. The Y-vector will always point to the top of the screen. The Z-vector will always point out of the screen.

About the figures:

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The section plane remains normal to datum plane DTM5. There is no change in the geometry from the Normal to Projection option.

The section plane remains normal to the datum plane TOP. But the X-vector is oriented parallel to the plane. Notice the end of the created surface.

Section Plane Orientation (cont.)Horizontal/Vertical ControlOnce the Z-vector has been specified, the only degree of freedom to the section plane that is left is a rotational degree of freedom about the Z-axis. This can be specified as:

Automatic – Pro/ENGINEER automatically defines it for you. X-Trajectory – The X-vector of the section plane will always point at the

intersection of the sketching plane and trajectory specified as the X-Trajectory.

Normal to Surface – Enables you to take the surface normals along the trajectory for orienting the sketch.

About the figures: The figure to the bottom left shows an example of the automatic control

wherein Pro/ENGINEER automatically defines the rotation about the Z-axis. The figure to the bottom right shows that the X-vector of the section points at

the intersection of the sketching plane and X-Trajectory resulting in a twisted shape for the final variable section swept surface.

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Using Additional Trajectories You can create variable section sweeps with as many additional trajectories

as required. Every trajectory added results in a trajectory reference that appears in

Sketcher mode. If a sketch is attached to these references, the referencing entity follows the trajectory as though it were riding on a rail.

If one of the trajectories is tagged as a tangent trajectory, a centerline appears in the sketch that represents the tangent direction of the surface(s) that intersect that trajectory. If these centerlines are referenced, the referencing entity rides along the tangent of the surface. This is useful when trying to get a variable section sweep to be tangent along its trajectories of formation to some other surface.

About the figures: The figures on top show the section defined with two trajectories. The

resulting feature is depicted alongside it. The figures below show another variable section sweep example (added to

the previously created geometry). In this case, the section is made tangent to the adjoining surfaces. The resulting geometry is depicted alongside it. 

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Using Datum Graph Tools and RelationsEvalgraphTo understand the use of the Evalgraph function in variable section sweep, you need to understand the Evalgraph function itself.

Evalgraph is a function that can be used in a relation. It references a datum graph feature that has already been created. In our example here, a relation is added to the model to control the depth of

a feature relative to its width. However, the relationship desired is not a simple mathematical relationship. Instead, the desired behavior has been captured in a datum graph named CONTROL which has been created.

Using the syntax shown, the relation is written as shown. Thus, when the value of the width is changed, the depth is set to the Y value

of the graph corresponding to an X equal to width.About the figures:

In figure 1, there is no relation added in the model dimensions. In figure 2, the relation is added in the model. WIDTH and DEPTH are

parameters added in the model, which are controlled with a relation. As the WIDTH dimension is changed, the DEPTH dimension changes on regeneration. The values are taken from the graph that defines the range of change in dimensions.

Figure 3 is similar to figure 2. A change in the WIDTH dimension changes the DEPTH dimension.

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Using Datum Graph Tools and Relations (cont.)Trajpar Trajpar, short for Trajectory parameter, is a parameter that is only available in variable sweep and helical sweep features.

Along the length of a sweep, Trajpar varies from 0 to 1, linearly plotting the distance. For example, at the start of the sweep, Trajpar = 0.

If the sweep’s total length along the Origin trajectory is 3, then at a distance of 1.5 down the trajectory, the value of Trajpar equals 0.5. Therefore at the end of the sweep, Trajpar equals 1.0.

About the figures: Section and Trajectories: In the example shown, we start with a variable

section sweep with two trajectories. A rectangular section spans the two trajectories and therefore only needs a height dimension, depicted here as sd4.

Variable Section Sweep: In the absence of any relations, the sweep results in the figure shown in the middle of the page.

Relation Added for Height: If the following section relation is used, - sd4=trajpar+1, the sweep appears as shown in the figure on the top right. You can see that at the start of the sweep, the height of sd4=0+1=1. Half way down you can see sd4=0.5 +1=1.5 and at the end, sd4=1+1=2.

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Using Datum Graph Tools and Relations (cont.)The remaining figure (bottom right) was developed with the following equation:sd4=sin(360*t)+1.5At the start of the sweep, sd4=sin(0*1)+1.5, which results in sd4=1.5At ¼ of the way through the sweep, sd4=sin(360*.25)+1.5, which results in sd4=2.5At ½ way through the sweep, sd4=sin(360*.5)+1.5, which results in sd4=1.5At ¾ of the way through the sweep, sd4=sin(360*.75)+1.5, which results in sd4=0.5At the end of the sweep, sd4=sin(360*1)+1.5, which results in sd4=1.5

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Using Datum Graph Tools and Relations (cont.)The Evalgraph and Trajpar options can be used simultaneously in defining a variable dimension in the sweep.

The example in the slide shows the use of Evalgraph and Trajpar simultaneously.

It starts with a variable section sweep that follows a straight Origin trajectory. The section that follows it is a symmetrically constrained square with 4 equal radius fillets on each of the corners.

A datum graph called WIDTH_CONTROL has been created in the model.  A section relation is added, as shown, to control the length (sd30) of the

section’s straight lines. Changing this one dimension changes the length of all 4 straight lines in the section.

The result of this relation is shown on the lower right. Note the impact of this relation on the shape of the sweep.

Rules for Creating Variable Section Sweep Origin trajectory entities must be tangent. X-Trajectories and Origin trajectories cannot intersect, but they can meet at

one end. For Normal to Projection, the projection of entities on the defined reference

must be tangent, as viewed in the projection direction. All trajectories must intersect the sketching plane. All additional trajectories of the feature must intersect the sweep’s sketching

plane.

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Rules for Creating Variable Section Sweep (cont.)There are more rules to be considered for any variable section sweep:

The length of the shortest trajectory sets the length of the sweep. The additional trajectories do not need to be as long as the Origin trajectory. The sweep feature is created as far as the endpoint of the shortest trajectory. Modifying the lengths of trajectories modifies the length of the sweep

All trajectories must be continuous.  A composite curve can be used for a trajectory. 

Exercise 1: Creating Surfaces on the BottleObjectivesAfter successfully completing this exercise, you will know how to:

Create surface features using the Variable Section Sweep tool. Modify the shape of variable section swept surfaces using mathematical

relations and datum graph features.

ScenarioYou are assigned the project of designing a bottle part using surface modeling. You create surface features on the bottle part using the Variable Section Sweep tool.

Task 1. Open and review the model.

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1. In the Folder Browser  , browse to the module_07 folder. o Right-click on the module_7 folder and select Set Working

Directory. o Open the BOTTLE_START.PRT.

2. Cursor over each of the features in the model tree and review them as they highlight on the screen.

 

Reviewing features

 3. In the model tree, right-click the datum graph CONIC and select Edit

Definition. o Click Done. o Press ENTER to accept the existing name. o Examine the sketch for the datum graph feature.

 

Datum Graph

 4. Click Complete Sketch  .

Task 2. Create front and back surfaces.  

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1. Turn off the display of datum planes. 2. Start the Variable Section Sweep Tool  from the feature toolbar.

o Select the Origin trajectory, as shown in the following figure. 

Selecting the Origin Trajectory

 3. Press CTRL and select the additional trajectories, as shown in the following

figure. 

Selecting Additional Trajectories

 4. Click Create Section  .

o Sketch an arc connecting two of the Sketcher points, as shown in the following figure.

o Make sure that the arc center is not on the vertical reference. 

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Sketching the arc

 5. Click Complete Sketch  .

o Click Complete Feature  . 

Completed Surface

 6. With the variable section swept surface still selected, start the Mirror

Tool  from the edit toolbar. o Select datum plane FRONT and click Complete Feature  .

 

Mirroring the Front Surface

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Task 3. Create boundaries for the left surface. 

1. Click Datum Curve  from the feature toolbar. o Click Thru Points > Done. o Select the start and end points for the curve, as shown in the following

figure. o Click Done.

 

Selecting the Start and End Points

 2. Double-click the Tangency element to define tangency.

o Select the edge reference for tangency at the start point, as shown in the following figure on the left.

o Click Okay. o Select the edge reference for tangency at the end point, as shown in

the following figure on the right. 

 Defining Tangency

 3. Click Flip and Okay.

o The curve should appear, as shown in the following figure. o Click Done/Return and Ok to complete creating the curve.

 

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Tangent Curve

 4. Repeat the previous steps to create another curve through the bottom

vertices. o Define tangency and select adjacent edges as tangent references.

 

Creating Curves Through Points

 5. In the model tree, right-click Group SKETCH_2 and select Hide.

Task 4. Create the left surface using boundaries.  

1. Start the Boundary Blend Tool  from the feature toolbar.o Press CTRL and select the top and bottom curves that you just created,

as shown in the following figure. 

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Selecting the First Direction Curves

 2. Right-click and select Second Direction Curves.

o Right-click to query and select the left intent chain edge, as shown in the following figure.

o Press CTRL, then right-click to query and select the right intent chain edge.

 

  Selecting the Second

Direction Curves

 3. Select the Constraints tab.

o Change the boundary condition for the Direction 2-First Chain from Free to Tangent.

o Change the boundary condition for the Direction 2-Last Chain from Free to Tangent.

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o Click Complete Feature  . 

Completed Surface

 Task 5. Create the right surface of the bottle.  

1. In the model tree, right-click Group SKETCH_3 and select Hide. 2. Press CTRL + D to orient the model to the standard orientation. 3. Start the Variable Section Sweep Tool  from the feature toolbar.

o Right-click to query and select the intent chain shown in the following figure as the Origin trajectory.

o Click the yellow arrow to change the start point to the bottom vertex, as shown in the following figure.

 

  Selecting the Origin Trajectory

 4. Press CTRL, right-click to query and then select the rear intent chain, as

shown in the following figure. 

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Selecting Additional Trajectory

 5. Select the References Tab.

o Select Constant Normal Direction for the Section Plane Control option.

o Select datum plane TOP.  

Section Plane Control

 6. Check the T check box for both the Origin and Chain 1 trajectories in the

References tab to make them tangent. o Click Create Section  . o Sketch and dimension a conic, as shown in the following figure.

 

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Sketching a Conic Section

 7. Click Complete Sketch  .

o Click Complete Feature  . 

Completed Surface

 Task 6. Change the shape of the sweep by varying the pitch of the conic along

the trajectory.  

1. With the previous variable section swept surface still selected, right-click and select Edit Definition.

o Click Create Section  . o Click Tools > Relations. o Type the following relation:

/* Vary the RHO value of the conic along the trajectorysd11 = evalgraph ("CONIC", trajpar*200) /200

The dimension symbols in your sketch may be different from what is shown in the figure. You should use the corresponding dimension symbol in the relation.

 

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Sketch Symbols for Relation

 Refer back to the image of the datum graph. Trajpar is multiplied by the X value of the graph (200). The Evalgraph result is divided by 200 to scale down the Y values from 70 and 20 to 0.35 and 0.10 respectively.

2. Click OK in the Relations dialog box.o Click Complete Sketch  .

3. Click Complete Feature  . o Notice the change in shape of the conic as it is swept.

 

Redefined Sweep

 Notice that the curvature of the sweep is reduced along its trajectory according to the sketch of the datum graph.

4. Select anywhere on the model background to de-select all items. 5. In the model tree, press CTRL and select SKETCH 1, Curve id 403, and Curve

id 406. o Right-click and select Hide.

6. Click File > Save a Copy. o Type BOTTLE_MAIN_SURFS as the new name and click OK.

7. Click File > Erase > Current and Yes.

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This Completes the exercise.

Exercise 2: Designing a Compressor Blade (Challenge)ObjectivesAfter successfully completing this exercise, you will know how to:

Create a variable section sweep feature that uses an X-Trajectory to orient itself.

Make a section follow multiple trajectories.

ScenarioYou are designing a jet engine compressor. Aerodynamicists have already provided you with the necessary trajectories and the desired cross-section to design a blade. To use the given inputs and to retain mathematical control over the resulting surfaces, you have chosen to use the Variable Section Sweep tool. 

The Assembly of the Blades

 Task 1. Retrieve the model.  

1. In the Folder Browser  , click on the module_07 folder to view its contents.

o Open the AXIAL_COMPRESSOR_BLADE.PRT.  

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Axial Compressor Blade Model

 2. In the model tree right-click Curve id 71, and select Edit Definition.

o Double-click Equation and review the equation used to create the curve.

o Close the editor containing the equation. o Click Cancel and Yes.

Task 2. Begin the creation of the blade with a variable section sweep.  

1. Select anywhere on the background to de-select all items. 2. Start the Variable Section Sweep Tool  from the feature toolbar.

o Select the curve on the left as the Origin trajectory, as shown in the following figure.

o Press and hold CTRL, and select the second curve, to define the second trajectory, as shown in the following figure.

 

Trajectories for Variable Section Sweep

 3. Select the References tab in the dashboard.

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o Set the second trajectory to be the X-Trajectory by enabling the X check box for the Chain 1 trajectory.

4. Click Create Section  . o Notice how the X-Trajectory locates itself in the positive X-direction

from the Origin trajectory. (To the right of the origin). 

Section Plane

 5. Click Sketch > Data from File > File System.

o Select BLADE_XSEC.SEC and click Open. o Click above the model to place the sketch. o Right-click on the X location handle and drag it to relocate it to the left

arc center of the sketch. o Drag the location handle to place the section on the trajectory cross-

hairs. Also, drag the rotation handle upward to bring the right arc center close to the X-Trajectory, as shown in the following figure.

 

Placing the Section

 6. Click Accept Changes  from Scale Rotate dialog box.

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o Delete the angled centerlines. o Constrain the right arc center to lie on the X-Trajectory reference, as

shown in the following figure. 

Section for Variable Section Sweep

 7. Click Complete Sketch  . 8. Click Complete Feature  .

o The model should appear, as shown in the following figure. 

Resultant Surface

Task 3. Reshape the blade by using a different X-Trajectory.  

1. In the model tree, right-click on Curve id 105 and select Resume. o A new curve should appear, as shown in the following figure. o Rotate the model to view the curve.

 

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Resumed Curve

 2. Select the variable section swept surface that was created previously.

o Select the References Tab. o Click Chain 1 and then select the curve you resumed, as shown in the

following figure. 

Selecting a new X-Trajectory

 3. Click Complete Feature .

o In the model tree, right-click on Curve id 71 and select Hide. 4. Click Save  from the main toolbar and click OK.

o Click File > Erase > Current and Yes.This completes the exercise.

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Exercise 3: Designing a Camshaft (Challenge)ObjectivesAfter successfully completing this exercise, you will know how to:

Create a surface feature using the Variable Section Sweep tool. Control the shape of a variable section sweep feature mathematically. Use the Trajpar and Evalgraph features simultaneously.

ScenarioYou are a part of the team that is designing a racing car. The senior engine designer has decided on a mechanism and lift profile for the intake and exhaust valves. He has provided you with a graph of the desired profiles and has asked you to develop the camshaft. The graph shows degrees of rotation versus offset distance. The mechanism has been designed such that a 1.00 diameter base circle on the camshaft represents the zero lift profile on the cam. You have chosen the Variable Section Sweep feature as a tool to design this part since it enables you to control the shape mathematically.

Task 1. Open the model.  

1. In the Folder Browser  , click on the module_07 folder to view its contents.

2. Open CAM.PRT. 

The Shaft

 3. Turn off the display of datum features.

Task 2. Review the datum graph features.

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1. In the model tree, right-click on the INTAKE_PROFILE datum graph and select Edit Definition.

o Click Done. Press ENTER to accept the default name for the graph. o Review the section that defines the Intake Cam profile, as shown in the

following figure.   o The graph uses a set of imported points to define the cam profile. o Click Complete Sketch .

 

Reviewing the Graph

 2. Review the imported points.

o In the Folder Browser , click Working Directory .  o Select INTAKE_PROFILE.PTS, right-click and select Open.

 

Reviewing the Point File

 3. Collapse the browser panel.  4. Select the Model Tree .

o Right-click EXHAUST_PROFILE and select Edit Definition. o Click Done. Press ENTER to accept the default name for the graph. o Review the section that defines the Exhaust Profile.

 

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Reviewing the Graph

 5. View the point data from the dashboard.

o Double-click on the spline. o Select the File tab in the dashboard. o Click Coordinate Info  . o Click Close in the information dialog box after you finish viewing.

6. Click Complete Sketch .

Task 3. Create the Intake Cam surface.  

1. Start the Variable Section Sweep Tool  from the feature toolbar.o Right-click to query and then select the intent chain edge as the Origin

trajectory, as shown in the following figure. 

Selecting the Edge

 2. Click Create Section  .

o Sketch an open section, as shown in the following figure. 

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The Cam Section

 3. Click Tools > Relations.

o Refer to the following figure and then Type the following relation lines: /* Control the height of the sketch based on the

INTAKE_PROFILE sd4 = 0.125 + evalgraph ("INTAKE_PROFILE" ,

trajpar*360) / 100

The dimension symbols in your sketch may be different from what is shown in the figure. You should use the corresponding dimension symbol in the relation.

 

  Dimensions in Symbolic

Form

 

The 0.125 is in the relation to define the offset of the base cylinder of the cam from the cylindrical shaft surface.  The base cylinder of the cam defines the zero lift position (the rest position of the follower.  The system parameter EVALGRAPH is included to take the value of the height of the cam from the graph INTAKE_PROFILE at every point on the trajectory.The trajectory length parameter (Trajpar) is included as variable a ratio from 0-1.

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You then multiply by 360 since you are defining the cam profile around the cylindrical shaft (360 degrees).Finally, you divide the resultant dimension by 100 since you are provided with the graph with an x-axis scale of 100.

4. Click OK in the Relations dialog box. o The sketch updates to reflect the relation.

 

The Section Driven by Relation

 5. Click Complete Sketch  .

o Click Complete Feature  . o The model should appear, as shown in the following figure.

 

The Intake Cam

 

Task 4. Create the Exhaust Cam surface.

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1. Start the Variable Section Sweep Tool  from the feature toolbar.o Select the intent chain edge as the Origin trajectory, as shown in the

following figure. 

Selecting the Origin Trajectory

 2. Click Create Section  .

o Sketch an open section, as shown in the following figure. 

Defining the Cam Section

 3. Click Tools > Relations.

o Refer to the following figure and then type the following relation lines. /* Control the height of the sketch based on the

EHAUST_PROFILE sd4 = 0.125 + evalgraph ("EXHAUST_PROFILE" ,

trajpar*360) / 100 

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  Symbolic Dimensions

 4. Click OK in the Relations dialog box. 5. Click Complete Sketch  .

o Click Complete Feature  . o The model should appear, as shown in the following figure.

 

Finished Cam Model

 Task 5. Change the profile of the Intake Cam lobe.  

1. In the model tree, right-click INTAKE_PROFILE and select Edit Definition. o Click Done. Press ENTER to accept the default name for the graph. o Click Modify Values  and select the spline.

 

Modifying the Spline Definition

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 2. Select the File tab and click Open Coordinates  .

o Select INTAKE_PROFILE_2.PTS and click Open. o The new points represent a more aggressive cam profile for the Intake

Cam. o The graph should appear, as shown in the following figure.

 

The Modified Spline with New Points

 3. Click Complete Sketch  .

o The original and updated models appear in the following figure. 

Revised Cam Model

 4. Click Save  from the main toolbar and click OK. 5. Click File > Erase > Current and Yes.

This completes the exercise.

SummaryAfter successfully completing this module, you should know how to:

Describe the use of variable section sweeps. Create surface features using the Variable Section Sweep tool. Control the orientation of the section plane. Modify the cross-section using the Evalgraph and Trajpar options. Describe the rules for creating variable section sweeps.

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