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Because of the complexity of real problems, many assembly models will require more than one vector loop. Multi-loop modeling will be introduced using the three part Stack Blocks assembly.

CREATING THE ASSEMBLY DRAWING

The drawing with its dimensions and tolerances is given below in Figure 5-1. The assembly dimension of interest is the contact length A, between the Ground DRF and the Cylinder/Ground contact point.

Assembly datum points must exist wherever a DRF, feature datum, joint, or specification endpoint is to be created. The assembly datum points must not be created as a group. Each must be done individually. Assembly datum planes or feature surfaces must exist to define the sliding planes for all joints other than revolute. There must also be an assembly datum plane created to use as the 2-D reference plane. All assembly datum points must be created in this 2-D reference plane.

It is important to properly orient the parts within the assembly to prevent geometric error. All intersections should be true intersections or contact points can not be created correctly. Also, the drawing must be to scale or else errors will occur in reading the data. These errors will propagate throughout the analysis.

Figure 5-1. Dimensioned Stack Blocks.

For the remainder of this chapter, the following code will be used:

Select -- Select a menu option.

Pick -- Pick a point, plane, part, or modeling element on the drawing.

Enter -- Enter a value or name on the command line.

ENTERING THE TI/TOL 2D ENVIRONMENT

After an accurate assembly model of the Stack Blocks (complete with assembly datum planes and points) has either been created or called up in Pro/Engineer, the TI/TOL 2D application can be run.

• Select Info from the ASSEMBLY menu.
• Select TOLERANCE from the INFO menu.
• Select TOL-2D from the TOLERANCE menu. You are now in the TOL 2D environment and can proceed with the tolerance modeling.

SETTING THE DISPLAY

The first step in running the TI/TOL 2D application is to set the display. The Display option allows the user to define the plane in which the tolerance commands will be applied.

• Select Display from the TOL-2D main menu.
• Select 2D Ref Plane from the DISPLAY menu. The message window will prompt you for a 2D reference plane. The GET SELECT menu will also pop up.
• Pick An assembly reference plane (ADTM) that is parallel to the face of the Stack Blocks by clicking on it with the mouse. The message window will prompt you for a plane that is perpendicular to the 2D reference plane.
• Pick Any plane in the assembly that is perpendicular to the first plane.
• Select Done/Return from the DISPLAY menu.

Note: If an appropriate assembly datum plane has not been created, Done/Return out of TI/TOL 2D and create one. Re-enter as outlined above.

A reference plane for the TOL-2D commands has now been defined. The size of the tolerance symbols can also be modified with the Display option. The default size is 2.00.

• Select Symbol Size from the DISPLAY menu. The message window will prompt you for the new symbol size.
• Enter 1.85 as the new symbol size.
• Select Done/Return from the DISPLAY menu.

DEFINING DATUM REFERENCE FRAMES

The steps for the multi-loop problem will parallel those for creating the single loop problem. The only difference is that more loops are created (three in this example) and so the process is slightly longer.

Datum reference frames (DRF's) and feature datums must be created as shown in figure 5-2.

Figure 5-2. The Stack Blocks with Part DRF's and feature datums defined.

Creating the Ground DRF

• Select Datums from the TOL-2D main menu.
• Select Create from the DATUMS menu.
• Select Datum Ref Fr. from the CREATE menu.
• Select Rectangular from the DRF TYPE menu. The message window will prompt for the DRF location.
• Pick The point at the intersection of the vertical plane and the horizontal plane, as shown in Figure 5-2. The message window will prompt you for a feature surface to establish the DRF direction.
• Pick The horizontal surface of the bottom step of the Ground. The message window will prompt for the part to which the DRF belongs.
• Pick The Ground.
• Select Done Sel from the GET SELECT menu.

Note: If an assembly datum point has not been created in the correct location, Done/Return out of TI/TOL 2D and create it. Assembly datum points and planes cannot be created inside of TI/TOL 2D, but if the user exits TI/TOL 2D by means of Done/Return, the work on the model up to that point will be saved in the database. The user can create the required point or plane, re-enter TI/TOL 2D, and resume modeling where they left off.

Creating the Block DRF

• Select Rectangular from the DRF TYPE menu.
• Pick The point at the lower left corner of the Block, as shown in Figure 5-2. The message window will prompt you for a feature surface to establish the DRF direction.
• Pick The bottom surface of the Block.
• Pick The Block.
• Select Done Sel from the GET SELECT menu.

Note that the DRF's require an axis identification or a direction specification. Cylindrical DRF's automatically identify the longitudinal axis which is perpendicular to the cylinder's face. Rectangular DRF's, however, require the identification of a surface on the part which will establish the orientation of the DRF.

Creating the Cylinder DRF

• Select Cylindrical from the DRF TYPE menu. The message window will prompt you for the DRF location and the GET SELECT menu will pop up.
• Pick The center point of the Cylinder by clicking on the appropriate APNT symbol. The message window will prompt you for the part associated with the DRF.
• Pick The Cylinder.
• Select Done Sel from the GET SELECT menu.

The cylindrical datum reference frame will be created and the cylindrical DRF symbol will appear at the center point of the Cylinder.

DRF's have now been created for all three parts of the Stack Blocks assembly. If any DRF was created incorrectly, it must be deleted with the Delete command in the TOL-2D main menu.

Deleting a DRF

• Select Delete from the TOL-2D main menu. The message window will prompt you to select the entity you wish to delete. Use Query Sel to ensure that the correct modeling entity is selected. The Sel By Menu option can also be used by remembering that the DRF's are listed in the order in which they were created.
• Pick The incorrect DRF
• Select Done Sel from the GET SELECT menu.

The incorrect DRF will be deleted and a new one can be created.

Modifying a DRF

A DRF may have its name and active degrees of freedom modified by the user. The name modification will be invisible in the modeler menus (for example when using Sel By Menu), but will be the node name seen when in the analyzer. Cylindrical DRF's may have their rotational degree of freedom turned off (or back on) in the modeler. We will change the Cylinder DRF name to Phi1.

• Select Datums from the TOL-2D menu.
• Select Modify from the DATUMS menu.
• Select Name from the DATUM MOD menu. The message window will prompt you for the DRF to modify.
• Pick The Cylinder DRF. Use Query Sel or Sel By Menu to pick the correct modeling element. The message window will prompt you for the new DRF name.
• Enter Phi1 as the new name.

DEFINING FEATURE DATUMS

Before joints can be created feature datums that define the paths from the joint location back to the DRF's of both parts associated with the joint must first be created. In the Stack Blocks problem three rectangular feature datums are required. Assembly points should already have been created in the Pro/Engineer modeler at the required locations (see Figure 5-2).

• Select Datums from the TOL-2D main menu.
• Select Create from the DATUMS menu.
• Select Feature Datum from the CREATE menu.
• Select Rectangular from the FD TYPE menu. The message window will prompt you for the location of the feature datum.
• Pick The point on the Ground defined by the intersection of the vertical plane of the first "step" and the horizontal Ground DRF plane.
• Pick The horizontal Ground DRF plane.
• Pick The Ground. The first feature datum will now appear on the model.
• Pick The point on the Ground defined by the intersection of the vertical plane of the far right "step" and the horizontal Ground DRF plane.
• Pick The horizontal Ground DRF plane.
• Pick The Ground. The second feature datum will now appear on the model.
• Pick The point on the upper left-hand corner of the Block. The message window will prompt you for a feature surface that will establish the direction of the feature datum.
• Pick The top surface of the Block. The message window will prompt you for the part associated with the feature datum.
• Pick The Block. The third feature datum will now appear on the model.
• Select Done Sel from the GET SELECT pop up menu.

All of the feature datums for the Stack Blocks assembly have now been created. If a feature datum was created incorrectly, it can be deleted by following the same procedure outlined for deleting a DRF. Feature datums can also have their names and active degrees of freedom modified in the same manner as outlined for DRF's.

DEFINING JOINTS

The next step in the TI/TOL 2D analysis is to locate the contact joints between each part. These joints represent the kinematic constraints between mating parts. The DRF's and feature datums created previously will be used to locate the joints by tracing a path back to the respective part DRF through controlled and kinematic dimensions. The paths back to the DRF's will vary depending on how the parts are dimensioned. For example, the path from the edge slider joint (joint 5) to the Ground DRF may appear either of the two ways below in Figure 5-3. For our model, the right-hand path will be used.

Figure 5-3 Two possible paths back to the Ground DRF.

The following steps will outline how to create the five kinematic joints required for the Stack Blocks assembly.

Creating the Cylindrical Slider Joint Between Ground and Cylinder (Joint 1)

• Select Joints from the TOL-2D main menu.
• Select Create from the JOINTS menu.
• Select Cyl Slider from the JOINT TYPE menu. The message window will prompt you for the joint location.
• Pick The point of contact between the Ground and the Cylinder. The message window will prompt you for the sliding plane orientation.
• Pick The vertical surface on the Ground that contacts the Cylinder. The message window will ask for the first part.
• Pick The Ground. The message window will prompt for the path to the Ground DRF. It is a direct path.
• Pick The Ground DRF. The message window will now prompt for the second part.
• Pick The Cylinder. The message window will prompt for the path to the Cylinder DRF. It is a direct path.
• Pick The Cylinder DRF.

Note: If Sel By Menu is used to select the part DRF's, the Done Sel option on that same menu must be used after each DRF selection to complete the sequence.

Creating the Cylindrical Slider Joint Between the Cylinder and Block (Joint 2)

• Select Cyl Slider from the JOINT TYPE menu.
• Pick The point of contact between the Block and the Cylinder.
• Pick The surface on the Block that the Cylinder slides on.
• Pick The Block. The datum path back to the Block DRF passes through a feature datum.
• Pick The feature datum on the upper left-hand corner of the Block.
• Pick The Block DRF.
• Pick The Cylinder.
• Pick The Cylinder DRF.

Creating the First Edge Slider Joint Between the Ground and Block (Joint 3)

• Select Edge Slider from the JOINT TYPE menu.
• Pick The point of contact between the vertical surface of the Ground and the Block.
• Pick The vertical surface on the Ground that the Block slides on.
• Pick The Ground. The datum path back to the Ground DRF is a direct path.
• Pick The Ground DRF.
• Pick The Block.
• Pick The Block DRF.

Creating the Second Edge Slider Joint Between the Ground and Block (Joint 4)

• Select Edge Slider from the JOINT TYPE menu.
• Pick The point of contact between the bottom surface of the Block and the first step on the Ground.
• Pick The bottom surface of the Block.
• Pick The Block. The datum path back to the Block DRF is a direct path.
• Pick The Block DRF.
• Pick The Ground. The path back to the Ground DRF passes through a feature datum.
• Pick The feature datum on the Ground located below the first "step."
• Pick The Ground DRF.

Creating the Third Edge Slider Joint Between the Ground and Block (Joint 5)

• Select Edge Slider from the JOINT TYPE menu.
• Pick The point of contact between the bottom surface of the Block and the second step on the Ground.
• Pick The Bottom surface of the Block.
• Pick The Block. The datum path back to the Block DRF is a direct path.
• Pick The Block DRF using Query Sel.
• Pick The Ground. The path back to the Ground DRF passes through a feature datum.
• Pick The feature datum on the Ground located below the second "step."
• Pick The Ground DRF.

All of the contact joints necessary to create loops have been added to the drawing (see Figure 5-4 below). If a joint was created incorrectly, the Delete command in the TOL-2D main menu can be used to delete the incorrect joint. The procedure is identical to deleting a DRF. The joint can then be created correctly before continuing with the tolerance modeling.

Figure 5-4 Kinematic joints of the Stack Blocks.

Modifying Joints

A joint may have its name and active degrees of freedom modified by the user. The name modification will be invisible in the modeler menus (for example when using Sel By Menu), but will be the node name seen when in the analyzer. For this example, no joint degrees of freedom will be modified, but the names of the edge slider joints will be changed to Phi2, Phi3 and Phi4.

• Select Joints from the TOL-2D menu.
• Select Modify from the JOINTS menu.
• Select Name from the JOINT MOD menu. The message window will prompt you for the joint to modify.
• Pick The first edge slider joint (joint 3) using Query Sel. The message window will prompt you for the new name.
• Enter Phi2 as the new name for the joint.
• Select Name from the JOINT MOD menu.
• Pick The second edge slider joint (joint 4).
• Enter Phi3 as the new name for the joint.
• Select Name from the JOINT MOD menu.
• Pick The third edge slider joint (joint 5).
• Enter Phi4 as the new name for the joint.

DEFINING LOOPS

The next step in the modeling process is to create the kinematic loops which relate all assembly parts and contact joints to the resultant assembly dimensions. Although the Specification command in the TOL-2D main menu precedes the Loops command, closed loops must be created before closed loop specifications (dependent lengths and angles) can be applied. However, open loop specifications should be created before loops are generated. The Stack Blocks assembly requires three closed loops. The first will be generated manually to demonstrate that process. The remaining two will be generated using Autoloop. All three can be created using AutoLoop, but the loops will be slightly different than those shown. The assembly variations calculated will be the same for both sets of loops, though.

Creating Loops

The first loop will be created manually.

• Select Loops from the TOL-2D main menu.
• Select Create from the LOOP menu.
• Select Closed from the LOOP TYPE menu. Message window will prompt for the first joint of the closed loop.
• Pick The edge slider joint on the first "step" (joint 4). Message window will prompt for the remaining joints to define the closed loop, ending with the first joint selected.
• Pick The edge slider joint on the second "step" (joint 5).
• Pick The edge slider joint on the first "step" (joint 4).

Loop 1 will now be created and appear as shown in Figure 5-5. The remaining two loops will be created using the Autoloop option.

Figure 5-5. Stack Blocks Loop 1.

• Select Autoloop from the LOOP TYPE menu.

Loop 2 and Loop 3 will appear as in Figure 5-6 below.

Figure 5-6. Stack Blocks Loop 2 and Loop 3.

Deleting Loops

Loops can be deleted by following the same procedure as for deleting part DRF's. If there are one or more closed loop specifications applied to a closed, those specifications must be deleted before the modeler will allow that closed loop to be deleted. Open loops have no such restrictions.

MODIFYING LOOPS

Loop vectors can be modified in three ways. The user can change the vector names and vector tolerances. They can also equivalence vectors for cases when the variations of two vectors are not independent of each other. For example, if the radius of a cylinder is over-sized at one point, it is likely to be over-sized at all other points.

Modifying Vector Names

The user can apply new names to the loop vectors. These new names will remain invisible until the user enters the Analyzer.

• Select Modify from the LOOP menu.
• Select Vector Names from the LOOP DESC menu. The message window will prompt you for the vector loop to modify.
• Pick Any vector on Loop 3 (see Figure 5-6). A vector will be highlighted.
• Enter E for the closure vector between the edge slider joint (Joint 3) and the
• Ground DRF. The second vector to name will be highlighted.
• Enter A for the vector from the Ground DRF to cylindrical slider joint between the Ground and the Cylinder (Joint 1). The next vector will be highlighted.
• Enter B for the first Cylinder radius. The next vector will be highlighted.
• Enter C for the second Cylinder radius. The next vector will be highlighted.
• Enter D for the closure vector between the cylindrical slider joint (Joint 2) and the feature datum on the Block. The next vector will be highlighted.
• Enter I for the vector between the feature datum on the Block and the Block
• DRF. The final vector in the loop will be highlighted.
• Enter I (again) for the vector between the Block DRF and the edge slider joint (Joint 3).
• Pick Any vector in Loop 1 (see Figure 5-5).
• Enter H for the vector from joint 4 to the Block DRF.
• Enter L for the vector from the Block DRF to joint 5.
• Enter K for the vector from Joint 5 to the feature datum below it.
• Enter J for the vector from the far right feature datum to the Ground DRF.
• Enter F for the vector from the Ground DRF to the feature datum to its right.
• Enter G for the vector from the feature datum to joint 4.

Note: The order of the vector naming scheme outlined above will only be valid if the DRF's, feature datums, and joints were created in the order outlined in the first part of this chapter. If they were created in a different order, the order that the vector are highlighted will probably be different.

Modifying Vector Tolerances

Each vector that corresponds to a manufactured dimension must have a tolerance associated with it. Vectors that represent kinematic assembly dimension (closure lengths) should not be assigned a tolerance.

• Select Vector Tol from the VECT DESC menu. The message window will prompt you for the dimension vector.
• Pick Cylinder radius B. The message window will prompt you for the new symmetric tolerance.
• Enter .2 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick Cylinder radius C.
• Enter .2 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick The vector between the Block DRF and the feature datum on the upper left corner of the Block (vector I). Use Query Sel or Sel By Menu options if necessary.
• Enter .075 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick The vector between the Block DRF and the edge slider joint on the upper left corner of the Block (also vector I). Use Query Sel or Sel By Menu options if necessary.
• Enter .075 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick Vector F on the Ground.
• Enter .125 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick Vector G on the Ground.
• Enter .15 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick Vector J on the Ground.
• Enter .35 for the dimensional tolerance.
• Select Vector Tol from the VECT DESC menu.
• Pick Vector K on the Ground.
• Enter .125 for the dimensional tolerance.

Equivalencing Two Vectors

The Stack Blocks model requires two sets of vectors be equivalenced. The variations of the radii of the Cylinder are not independent of each other. They will be equivalenced in order to link their variances in the tolerance model. There are also two vectors on the Block that lie on top of each other (the two that were labeled I). They are actually the same dimension, so they also must be equivalenced.

• Select Equiv Vect from the VECT DESC menu. The message window will prompt for the first dimension vector.
• Pick Vector B on the Cylinder. The message window will prompt for the equivalent dimension vector.
• Pick Vector C on the Cylinder.
• Select Equiv Vect from the VECT DESC menu.
• Pick Vector I between the Block DRF and the feature datum on the upper left corner of the Block.
• Pick Vector I between the Block DRF and the edge slider joint (Joint 3) on the upper left corner of the Block.

DEFINING DESIGN SPECIFICATIONS

A Dependent length specification will be applied between the Cylinder and Ground. This specification relates the point of contact between two parts.

Creating a Dependent Length Specification

• Select Specification from the TOL-2D main menu.
• Select Create from the SPEC menu.
• Select Depend Len from the SPEC TYPE menu. The message window will prompt you for the dependent vector location.
• Pick Vector A from the Ground DRF to the cylindrical slider joint between the Ground and the Cylinder. The message window will now prompt you for the maximum and minimum tolerance.
• Enter .3 as the maximum tolerance on the dependent length specification.
• Enter -.3 as the minimum tolerance on the dependent length specification.

The dependent length specification will be applied and the specification symbol shown in Figure 5.7 will appear along the specified vector. An incorrect design specification can be deleted by using the Delete command in the TOL-2D main menu.

Figure 5-7. Dependent Length Specification for the Stack Blocks Problem.

DEFINING GEOMETRIC TOLERANCES

TI/TOL 2D includes geometric tolerancing options. Geometric tolerances allow an engineer to account for machined surface variations such as flatness, circularity and perpendicularity. These surface variations can accumulate and propagate kinematically through the model the same as dimensional variations.

Applying a Flatness Tolerance to the Ground

• Select Geometric Tol from the TOL-2D main menu.
• Select Create from the GEOM TOL menu.
• Select Flatness from the GEOM TYPE menu. The message window will prompt you for the part associated with the geometric tolerance.
• The GET SELECT menu will also pop up.
• Pick The Ground. The message window will prompt you for the joint associated with the tolerance.
• Select The cylindrical slider joint (joint 1). The message window will prompt you for the tolerance.
• Enter .08 to be the flatness tolerance band for the feature.
• Select Flatness from the GEOM TYPE menu.
• Pick The Ground.
• Select The edge slider joint (joint 3).
• Enter .08 to be the flatness tolerance band for the feature.

Applying a Circularity Tolerance to the Cylinder

• Select Circularity from the GEOM TYPE menu.
• Pick The Cylinder.
• Pick Joint 1.
• Enter .02 to be the circular tolerance at that joint.
• Select Circularity from the GEOM TYPE menu.
• Pick The Cylinder.
• Pick Joint 2.
• Enter .02 to be the circular tolerance at the joint.

The specified circular tolerances will be created and the circular tolerance symbols will appear at the joints. The new geometric tolerance symbols will be placed on top of the symbols that already exist at the specified joints (see Joint 1 and Joint 2).

Applying a Flatness Tolerance to the Block

• Select Flatness from the GEOM TYPE menu.
• Pick The Block.
• Select The cylindrical slider joint (joint 2).
• Enter .05 to be the flatness tolerance band for the feature.
• Select Flatness from the GEOM TYPE menu.
• Pick The Block.
• Select The edge slider joint (joint 4).
• Enter .05 to be the flatness tolerance band for the feature.
• Select Flatness from the GEOM TYPE menu.
• Pick The Block.
• Select The edge slider joint (joint 5).
• Enter .05 to be the flatness tolerance band for the feature.

The model should now appear similar to Figure 5-8 below.

Figure 5-8. Geometric Tolerances for the Stack Blocks.

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