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Example Problems
AutoCAD Modeler:
The one-way clutch, an introduction to CATS model creation
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The one-way clutch (see figure 4.1) problem illustrates how a closed loop is used to find the resultant tolerance of an important assembly variable. Due to symmetry, only one vector loop is necessary to model this assembly. This assembly is designed to allow rotation in only one direction. The hub is attached to a shaft, which in turn is attached to a driving mechanism. When the hub rotates counter-clockwise relative to the ring, the roller slips on the inside of the ring. If the hub rotates clockwise, then the spring allows the roller to wedge between the hub and the ring, causing the two to lock and rotate together. For proper operation the contact angle between the roller and the ring must be between 8 and 6 degrees.

Figure 4-1. One-Way Clutch assembly.


CREATING THE ASSEMBLY DRAWING

First, an accurate assembly drawing must be created containing all parts in their assembled positions. The drawing with dimensions and tolerances is given below in Figure 4-2. The drawing may be either loaded by calling up clutch.dwg or it may be created in AutoCAD.The file is located in c:\autocad\cats\drawings (if Autocad is in c:\autocad). The assembly model must be created with the dimensions shown. Dimensions may be keyed in or selected using AutoCAD construction tools. If the dimensions are estimated using coordinates, or not using construction tools such as INTersection and CENter then the dimensions may not be exact.

It is IMPORTANT to realize that care must be taken to assure proper part orientation within the assembly to prevent geometric error. All intersections should be true intersections or contact points will not be formulated between parts. Also, the drawing must be to scale or else errors will occur in reading the data. These errors will ripple throughout the analysis. For example, a point may actually register as 5,5 but may be 5.0001, 5.0001. This seemingly insignificant error will propagate through the assembly creating more errors.

Figure 4-2. Dimensioned One-Way Clutch.

DEFINING PARAMETERS

SetUp

Before the CATS application may be run, certain parameters such as text and symbol size must be set. These parameters are stored with-in the model file so they do not have to be reset for each CATS session. If SETUP is not selected CATS will automatically select set-up when any of the other functions are selected.

Enter CATS on AutoCAD's command line.

This activates the CATS menu.

Select SETUP from the CATS menu.

You will now be prompted for the text and symbol size, parallel factor, and menu selections.

Enter 3.0 for the text and symbol size.

All text and symbols in the CATS analysis will automatically be this size.

A pop-up menu will appear if the mouse is not located on the main menu, just as in AutoCAD. If the mouse is on the main menu simply select the Parameters menu from the upper right corner of the menu screen. The text height may be either

  1. keyed in,
  2. selected from the menu, or
  3. entered by showing CATS the height of the text by designating two vertical points with the mouse.

    Enter 0.0001 as the parallel factor.

This specifies how close two lines may be before they are considered parallel.

Enter Yes to implement the icon menus.

As you become more familiar with the program the icon menus may be replaced by menu driven prompts for quicker selections.


DEFINING PARTS

Creating the Ring

Once the parameters have been set, each part must be given a unique name and a data reference frame (DRF) must be established for each part. The following steps will define the outer ring of the assembly and establish its DRF.

Select PARTS from the CATS menu.

Parts will be named and datum reference frames will be selected for each part. A datum reference frame is a point on the part where all dimensions are referenced.

Select NEW_P from the PARTS menu to begin creating DRF's.
Select CENter of outer circle.

All dimensions for the ring will be measured from this point. Remember to use AutoCAD's construction tools.

Enter Ring to be the first part.

The outer part is now called RING and its DRF is at the center of the part. All letters will be converted to uppercase. If more than eight characters are entered the part name will be truncated. If just a return were entered the part name would become the default value, PART_1, shown <PART_1>. Remember when entering a part name to use a unique name for each part. CATS will not accept a duplicate name.

Select CYLINDRICAL from the datum icon menu.

The DRF for the ring is now cylindrical. Notice the different symbols for a cylindrical and a rectangular DRF.

DRFs require an axis identification. Cylindrical DRFs automatically identifies the longitudinal axis which is perpendicular to the cylinder's face. Rectangular DRFs require identification of one axis running either along the height or width of the object.

Enter Yes to create the next part.


Creating the Roller

We will now step through the same procedure for each of the two remaining parts.

Select CENter of the upper small circle.
Enter Roller to name the part.
Select CYLINDRICAL from the datum icon menu.
Enter Yes to create another part.

A return may also be inputted to default a yes reply.


Creating the Hub

Select DATUM from the Tools + DATUM pop-down menu.

The Hub center and Ring center are at same point but are not the same DRF. Once a datum has been created you may select it as the location for another element by using the construction tool DATUM.

Select the RING DRF symbol.
Enter Hub to name the part.
Select RECTANGULAR from the icon menu to create a DRF.

To select a point on the positive x-axis of the DRF, select a point along the x-axis shown through the center of the Hub in Figure 4-3. For example, use CTRL-O to toggle orthogonal snap and then select anywhere to the right of the DRF center. In addition, a coordinate relative to joint location can be specified by entering @1,0.

Enter No to stop creating new parts.

 

Figure 4-3. The One-Way Clutch problem with Parts defined.

All parts have now been defined. The drawing should look like Figure 4-3 above except without the X-Y axis definitions.


Error Recovery

If your drawing does not resemble Figure 4-3, then individual datum reference frames may be deleted using the DELETE P command, refer to page 3-6. Save the drawing now under a different name (eg clutchp.dwg). Remember that all AutoCAD functions are available within CATS. By saving the file under a different name the original drawing is unaltered. To restore the standard AutoCAD menu type CAD at the command line. After saving the file, type CATS at the command line to enter back into the CATS Modeler.


DEFINING JOINTS

The second step in CATS analysis is to locate the contact joints between each part. These joints represent the kinematic constraints between mating parts. DRF paths are also specified. They relate the joint location to the DRF origin by tracing a path from the joint to the DRF through controlled and dependent dimensions.


Revolute joint between Hub and Ring

Select JOINTS from the CATS menu.

This brings up the JOINTS menu allowing the creation of joints.

Select NEW_J to begin creating new joints
Select DATUM from the Tools + DATUM pop-down menu.
Select the RING's DRF as the datum for the contact joint location.
Select REVOLUTE from the joint icon menu.

A revolute joint is a pin joint which allows the ring to rotate relative to each frame of the clutch.

First DRF path back to part, RING

Select Zoom In

This option may be implemented at anytime and it will not interrupt the command. This function zooms into the windows specified by you picking to corners. To return to the previous zoom simply enter zoom out.

Select the DRF on the first part, the RING.

The Ring's DRF is a circle with a cross through it. The DRF symbol or the text below it "DRF RING" may be selected.

Enter Return for the default path from the joint directly to the DRF.

A path does not appear because the path has a zero length.

Enter Yes to verify the correct path back to the DRF.

The DRF path for the first part is now completed. Next, the DRF path from the contact joint to the second part will be created.

DRF path for second part, the HUB

Select the DRF on the second part, the HUB.

The rectangular DRF is a square with the words "DRF HUB."

Enter Return to default directly to the DRF from the contact joint.
Enter Yes to verify the correct path back to the DRF.
Enter Zoom Out to zoom to the previous window.

It was necessary to use Zoom In to differentiate between the DRF of the hub and the DRF of the Ring. Another way to solve this problem is to use the MV Label menu option in the DISPLAY menu to move the labels to different locations.

Enter Yes to continue creating new joints.

The first contact joint which connects the Hub to the Ring has now been created. We will now step through each of the remaining joints.


Cylindrical joint between Roller and Ring

Select the INTersection of the ROLLER and the RING.
Select CYLINDRICAL from the joint icon menu.

A cylindrical joint is a contact joint where two parallel cylinders are in contact. Note that this is not a cylindrical slider joint.

First DRF path to first part, the RING.

Select Zoom In

Zoom in on the RING and the HUB's DRF to make sure that the selections are correct.

Select the RING's DRF to be the DRF on the first part.
Select Zoom Out.
Enter Return to default to the DRF on the RING.
Enter Yes to verify the correct path back to the DRF.

Now enter the second DRF path back to the second part, the ROLLER.

Select the DRF on ROLLER to be the second part's DRF.
Enter Return to default directly to the DRF from the contact joint.
Enter Yes to verify the correct path back to the DRF.
Enter Return to continue making joints.


Cylindrical Slider joint between Roller and Hub

Select the INTersection between the ROLLER and the HUB.
Select Cylindrical Slider from the joint icon menu.

A cylindrical slider joint is a contact point where a cylinder may translate or rotate on a plane surface.

Select a point NEA rest the HUB where the ROLLER and the HUB intersect and is parallel to the x-axis. This is the cylindrical sliding plane.

First DRF path back to first part, the ROLLER.

Select the DRF on the first part, ROLLER.
Enter Return to default directly to the DRF from the contact joint.

The path will go directly back to the DRF from the interface point.

Enter Yes to verify the correct path back to the DRF.

Now create the DRF path back to the second part, the HUB

Select Zoom In to zoom into the HUB DRF.
Select the DRF on the second part, the HUB.
Select Zoom Out to zoom out to the previous window.
Select the next datum origin by using the key sequence:

  1. Enter .X
    This is an AutoCAD function called an X/Y/Z point filter. When .x is entered then only the x coordinate is specified, it then prompts for the remaining coordinates .yz.
  2. Select the CENter of the RING for the .x coordinate.
  3. Select a point on the sliding plane of the joint for the .yz coordinate (Remember to use construction tools, ie NEArest).

Select RECTANGULAR from the datum icon menu.

This creates a feature datum along the DRF path.

Enter Return to default directly to the DRF from the feature datum.
Enter Yes to verify the correct path back to the DRF.
Enter No to stop creating new joints.

All of the contact points necessary to complete the analysis for one loop have been added to the drawing (see Figure 4-4 below). Now the LOOPS feature is applied to relate the entire system.

Figure 4-4. Joints for One-Way Clutch problem.


Error Recovery

The DRF paths may be edited during creation. If the user answers No to the question asked "Is this path correct?" the DRF path will be prompted for again. The feature datums associated with the particular joint selected may also be erased.

When you select EDIT J, the program will trace through each DRF path for the selected joint. This is helpful in showing the user which DRFs are associated with each joint and the DRF paths.

To delete a created joint select DELETE J from the menu bar, refer to page 3-10. To delete feature datums simply erase them using AutoCAD's erase function. BE CAREFUL not to delete a feature datum which has been used in other DRF paths.

At this point, save the drawing once again under a different name (eg clutchj.dwg).


DEFINING LOOPS

The next step in the CATS process is to create the kinematic loops which relate all assembly parts and contact joints to the resultant assembly dimensions. Refer to figure 4-2 for the nominal dimensions and tolerances for the assembly.

Loop Creation

The loop we will create will relate the joints 4, 5 and 7.

Select LOOPS from the CATS main menu to create loops.
Select AUTOLOOP from the LOOPS menu.

The kinematic loops will be created by CATS automatically.

Enter Yes to verify that the loop is correct.

Check that the loop is identical to figure 4-5 before answering Yes.

We will now be prompted for the tolerances on all independent lengths on the loop.

Enter 0.0125 for the tolerance on the RING's radius nominal length, 50.8000.

Most tolerances may be selected from the pop-up menus or typed in from the keyboard. The nominal length will be highlighted in red.

Select 0.01 for the tolerance on the ROLLER's radius nominal length, 11.4300.
Enter Return for the tolerance on the ROLLER's radius nominal length.

Once a tolerance has been implemented into the program it becomes the default for the next tolerance.

Enter Return to default a 0.00 tolerance on the nominal angle, 90deg..

Most engineers do not specify a tolerance on angles; therefore, angles always have a default tolerance of 0deg.. Otherwise, a value should be entered.

Select 0.05 for the tolerance of the HUB's radius nominal length, 27.6450.
Enter Return to default a 0.00 tolerance on the nominal angle, 90deg.
Enter 61.0,70.0 as a location to place the name of the loop.

Or, you may select a location for the starting of the text LOOP_1. Once the user is familiar with the program then a point may be selected. The location of the loop name should be so that the loop name is easily readable and not overlapping any other information such as joints or part names.

The loop related with joints 4, 5, and 7 will now be completed using the additional information just obtained. The loop should appear as Figure 4-5 on the following page.

Figure 4-5. One-Way Clutch problem with defined loop.


Error Recovery

During the creation of the loops one may check the loops to make sure they are correct. If they are not correct answer No to the prompt "Is this loop correct?" If you realize that the loops are incorrect after the loop is made you may delete loops by simply selected DELETE L. Save your latest version (eg clutchl.dwg) again!


DEFINING FEATURE CONTROLS

ANSI Y14.5 feature controls are included in the CATS modeler. These feature controls allow an engineer to account for machining surface variations such as flatness, circularity and perpendicularity.

Flatness feature control on Hub

The first feature control will be flatness on the Hub.

Select FEATURES from the CATS menu.
Select NEW_F to begin adding feature controls to the drawing.
Select FLATNESS feature control from the feature control icon menu.

Flatness may vary on a part because of machining or rolling. The part may still be considered flat within a certain tolerance zone. This tolerance is specified by using feature controls.

Select Zoom In to zoom in on the HUB's DRF.
Select the HUB's DRF.

This will select the part on which the flatness feature control will apply.

Select Zoom Out and zoom to the previous window.
Select Joint 7

This is the contact point where the feature control applies. Joints may also be selected by their symbol or number.

Enter 26,69 or select a point for the feature control symbol location.
Enter 0.025 to be the flatness tolerance band for that feature.
Enter Yes to continue creating feature controls.

Roundness feature control for the Ring

The first feature control has now been implemented. We will continue by creating a feature tolerance for the Ring.

Select the ROUNDNESS feature control from the icon menu.

Roundness measures the amount a circle varies from being a circle. For example, it may actually be an ellipse.

Select Zoom In to zoom in on the RING's DRF.
Select the RING's DRF.

This will select the part on which the roundness feature control will apply.

Select Zoom Out to zoom to the previous window.
Select Joint 5
Enter 63,101 for the feature control symbol location.
Enter 0.01 to be the roundness tolerance band at that point.
Enter Yes or Return to continue creating feature controls.

Roundness feature controls for the Roller

Roundness feature controls should be implemented on the Roller.

Select the ROUNDNESS feature control from the icon menu.
Select the ROLLER's DRF.

This is the part to which the roundness feature control applies.

Select Joint 7 for the first joint which roundness applies.
Enter 63,81 for the feature control symbol location.
Enter 0.003 for the roundness tolerance band at those points.
Enter Yes to create another feature control
Select the ROUNDNESS feature control from the icon menu.
Select the ROLLER's DRF.
Select Joint 5 for the second joint which roundness applies.
Enter 63,94 for the for the feature control symbol location.
Enter 0.003 for the roundness tolerance band at those points.
Enter Yes to continue creating feature controls.

Concentricity feature control for the Ring

The final feature control which should be implemented is on the Ring.

Select the CONCENTRICITY feature control from the icon menu.
Select the RING's DRF.

This is the part to which the concentricity feature control applies.

Select Joint 4 for the joint where concentricity applies.
Enter 25,52 for the feature control symbol location.
Enter 0.01 for the roundness tolerance band at those points.
Enter No to discontinue creating feature controls.

The assembly drawing should now look like Figure 4-6.

Figure 4-6. Feature Controls for the One-Way Clutch problem.


Error Recovery

To delete a feature control select DELETE F from the side menu and select the desired feature control. Once the model is correct to this point save the file (eg clutchf.dwg).

DEFINING DESIGN SPECIFICATIONS

Design specifications should be implemented into the CATS model to specify acceptable variations for critical assembly dimensions.

Dependent Angle Specification

The specification in this problem will be concerned with the dependent angle between the two ROLLER radii (see figure 4-7). As stated in the problem description, this angle must be between 8 and 6 degrees to ensure proper operation of the clutch.

Select SPECS from the CATS menu.
Select NEW_S to add the design specification to the drawing.
Select DEPENDENT ANGLE from the specification icon menu.
Select ROLLER/2-5 blue vector as the angle's first vector.

A dependent angle places limits on a dependent angle which is located between two vectors in the same loop which have a common vertex. ROLLER/2-5 is the name for the vector which passes through the ROLLER from node 2 (the ROLLER's DRF) to node 5 (or joint 5). The node numbers are shown in figure 4-7.

Select ROLLER/2-7 blue vector as the angle's second vector.
Select LIMits from the SymTols pop-up menu.

Notice that the nominal angle between the two vectors is 7.0184deg..

Enter 8.0 degrees as the maximum dimension of the dependent angle.
Enter 6.0 degrees as the minimum dimension of the dependent angle specification.
Enter 28,90 as a location to place the name of the specification.

Figure 4-7. Relative Angle Specification with datum numbers shown.

The model is now complete. The drawing should now appear as in Figure 4-8 on the following page.

Figure 4-8. Completed modeler for the One-Way Clutch problem.


Error Recovery

Specifications may be deleted by selecting DELETE S from the side menu. Refer to page 3-17 for the DELETE S command. Save the completed file under a new name (eg clutchs.dwg)

CREATING THE NEUTRAL FILE

Once all the information has been obtained from the modeler, the information must be stored in a file which the CATS Analyzer may analyze.

Select CATSFILE from the CATS menu.
Select WRITE_NF to create neutral file.
Enter Return to default the file's name to clutch.nf

A neutral file will now be created containing information from the modeler. A neutral file may be given any name and any extension.

The model for the clutch problem is now complete. In the current directory a neutral file called clutch.nf will contain the model data which may now be used by the CATS Analyzer. To look at the file, view it with a text editor. The model file should appear as in Appendix A. NOTE: If the file is viewed in a word processor such as WordPerfect, keep the file in ASCII format.


PRO-E

Modeler: Clutch | Stack Blocks | Remote Positioner
Analyzer: Clutch | Stack Blocks | Remote Positioner
Verification: Clutch | Stack Blocks | Remote Positioner | Bike Crank | Parallel Blocks | NFOV

AutoCAD

Modeler: Clutch | Stack Blocks | Remote Positioner
Analyzer: Clutch | Stack Blocks | Remote Positioner
Verification: Clutch | Stack Blocks | Remote Positioner | Bike Crank | Ratchet | Parallel Blocks | NFOV

CATIA

Modeler: Crank Slider


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