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Example Problems 
PROE
Verification:
CHAPTER 6: PARALLEL STACKED BLOCKS 

Home : Example Problems : ProE 2D  Verification  Parallel Blocks 
Figure 6.1: Schematic of the parallel blocks with dimension variables.
6.0 Problem Description
A stacked blocks assembly is traditionally considered a onedimensional tolerance problem. In this case, though, we wish to explore the twodimensional effects of surface variation on this assembly. The variable of interest is the gap between the vertical surface on the right and the top right corner of the topmost block. If the surfaces of each block were perfectly parallel to each other, then the gap variation would simply be the error in positioning the stack relative to the vertical surface. Since the block surfaces are not perfectly parallel, the stack may lean from side to side.
A parallelism geometric tolerance will be applied to each block. This effectively defines the degree to which each block can rotate.
Table 6.1: Manufactured Variables (Independent).
Variable Name  Basic Size  Initial Tolerance (+/) 
A  3.200 in   * 
B  0.736 in  0.005 in 
C  1.000 in   * 
D  0.800 in  0.005 in 
E  0.800 in  0.005 in 
F  0.800 in  0.005 in 
G  0.800 in  0.005 in 
H  1.000 in   * 
* These vectors are for positioning modeling elements. They are not dimensioned lengths, so they do not have tolerances associated with them. They will not appear in the sensitivity matrices.
6.1 Design Requirements
Table 6.2: Assembly Variables and Specification Limits.
Variable Name  Basic Size  Upper Spec. Limit (USL)  Lower Spec. Limit (LSL) 
Gap Width  0.7360 in  0.7460 in  0.7260 in 
6.2 Modeling Considerations
6.3 Design Goal
The purpose of this chapter is to illustrate the effects of the surface variations on the variation of the Gap. The parallelism geometric tolerances are used to introduce rotational variation into the assembly.
6.4 Part DRFs And Feature Datums
Figure 6.2: Diagram showing the location of the part DRFs and feature datums.
6.5 Kinematic Joints
Four rigid joints are used to model this assembly.
Figure 6.3: Kinematic joint diagram.
Table 6.3: Kinematic Joints Of The Parallel Blocks.
Joint Number  Part One  Part Two  Joint Type 
1  Crank  Block 1  Rigid 
2  Block 1  Block 2  Rigid 
3  Block 2  Block 3  Rigid 
4  Block 3  Block 4  Rigid 
Remarks>> Rigid joints are used to avoid introducing any kinematic degrees of freedom into this assembly. This allows us to solve for the Gap variation using a single open loop. Planar joints could also be used to model the contact between the blocks. The sliding plane degree of freedom is automatically turned off by the modeler because there is no vector created in the sliding plane. If a planar joint is used between block 1 and the base, there is a vector in the sliding plane and the translational degree of freedom must be turned off manually.
6.6 Network Diagram, Vector Loops, and Design Specifications
Figure 6.4: Network diagram and loop diagram for the parallel blocks assembly.
Remarks>> The direction of open loops is important when gap and position specifications are used. TI TOL assumes the first part is fixed in space and the parts "downstream" all rotate relative to it. This arises due to the noncommutative property of matrix multiplication. To generate the correct open loop direction, create the fixed endpoint first and the moving endpoint second.
Enter .01 and .01 for the gap specification limits.
6.7 Geometric Tolerances
Figure 6.5: Geometric tolerance diagram.
The bottom of each block is parallel to the top of the block within a .004 in bandwidth.
6.8 Sensitivity Matrices
Table 6.4: CB^{1}A Matrix
B  D  E  F  G  
X  1.00000  0.00000  0.00000  0.00000  0.00000 
Y  0.00000  1.00000  1.00000  1.00000  1.00000 
0.00000  0.00000  0.00000  0.00000  0.00000 
Table 6.5: GB^{1}F Matrix
1  2  3  4  
X  3.20000  2.40000  1.60000  0.80000 
Y  1.00000  1.00000  1.00000  1.00000 
1.00000  1.00000  1.00000  1.00000 
6.9 Predicted Assembly Variation
Table 6.6: Independent Variable Tolerances and Control Factors
Dim Name  Nominal  +/ Tol  Process Std Dev  Process Description  K 
B  0.7360  0.00500  0.00150  None  0.25 
D  0.8000  0.00500  0.00150  None  0.25 
E  0.8000  0.00500  0.00150  None  0.25 
F  0.8000  0.00500  0.00150  None  0.25 
G  0.8000  0.00500  0.00150  None  0.25 
Table 6.7: Geometric Tolerances
Name  Part Name  Type  Joint  Tolerance Band  Char. Length 
1  Block 1  Parallelism  1  0.00400  2.0 in 
2  Block 2  Parallelism  2  0.00400  2.0 in 
3  Block 3  Parallelism  3  0.00400  2.0 in 
4  Block 4  Parallelism  4  2.0 in 
Table 6.8: RSS Percent Contributions To Gap (Geometric Tolerances Included)
Variable Name  Contribution  Statistical RSS 
1  4.5511e6  40.24 
B  2.7778e6  24.56 
2  2.5600e6  22.63 
3  1.1378e6  10.06 
4  2.8444e7  2.51 
Table 6.9: Absolute Sensitivities Of Gap (Geometric Tolerances Applied)
Variable Name  Sensitivity  Normalized 
1  3.20000  35.56 
2  2.40000  26.67 
3  1.60000  17.78 
B  1.00000  11.11 
4  0.80000  8.89 
Table 6.10: RSS Percent Rejects (Geometric Tolerances Applied)
Gap  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  0.7460  0.00336  2.97  1472.85  1.4729e3 
Lower  0.7260  2.97  1472.85  1.4729e3  
Nom Dim  0.7360  Total  2945.71  2.9457e3 
Table 6.11: SSC Percent Rejects (Geometric Tolerances Applied)
Gap  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  0.7460  0.003367  2.72  3219.76  3.2198e3 
Lower  0.7260  2.72  3219.76  3.2198e3  
Nom Dim  0.7360  Total  6439.52  6.4395e3 
Table 6.12: SSA Percent Rejects (Geometric Tolerances Applied)
Gap  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  0.7460  0.00336  1.47  70326.75  7.0327e2 
Lower  0.7260  1.47  70326.75  7.0327e2  
Nom Dim  0.7360  Total  140653.49  1.4065e1 
6.10 Tolerance Allocation
No tolerance or nominal allocation will be performed on the parallel blocks assembly. The variations that contribute the most to the Gap variation are geometric tolerances, which can't be adjusted by the TI TOL tolerance allocation routines.
PROE Modeler: Clutch
 Stack Blocks
 Remote Positioner 
AutoCAD Modeler: Clutch
 Stack
Blocks  Remote
Positioner 
CATIA Modeler: Crank Slider 
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