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Example Problems
AutoCAD
Analyzer:
CHAPTER 6: Stacked Blocks
CHAPTER 6: Stacked Blocks
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Example Problems |
AutoCAD
Analyzer:
CHAPTER 6: Stacked Blocks |
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6.0 Stacked blocks: An introduction to the multi-loop problem.
This example demonstrates how multiple vector loops are used to solve for assembly variations. Three blocks of various shapes and sizes are stacked together to form the following assembly (Figure 6.1).
Figure 6.1. Assembly of stacked blocks.
Because of the number of parts and contact points (joints) in the assembly, network graph theory dictates that we use three vector loops to solve for all of the unknown assembly variations of this problem. As explained in the Modeler Manual, we will use the three loops shown in Figure 6.2. The initial tolerances were determined by the type of manufacturing processes to be used to produce the parts. This chapter will present procedures for only basic analysis of this assembly. To review other and more advanced analysis procedures, see Chapter 5. Various results are shown in the verification manual.
Figure 6.2. Vector loops used to solve for assembly variations of stacked
blocks.
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Independent Variables A - CYLINDER/ 1-4 and 1-7 = 6.620 ± 0.2mm |
Dependent Variables (lengths only) D1 - GROUND/3-4 = 18.718 ± ? mm |
6.1 Start Up
After creating a vector-loop model of the stacked blocks assembly and a CATS neutral file with the AutoCATS 2-D Modeler, execute the 2-D Analyzer and open the neutral file by typing F O STKBLKS Y <CR> from the Main Menu. Select the 2D ANALY option to start your analysis. For more specific instructions on getting started, review section 5.1.
6.2 Equating Variables
The two vectors representing the radii of the cylinder (CYLINDER/1-4 and CYLINDER/1-7) must be equivalenced, since they represent the same dimension. The same process produces them and they are of the same batch. They may be equivalenced from the MODIFY submenu.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE |
Notice that BLOCK/2-5 and BLOCK/2-6 have already been identified as equivalent. Although these are two different names, they represent the same dimension because JOINT5 and DATUM6 are at the same location.
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The following sets of dimensions have been identified as equivalent: NO. 1: BLOCK/2-5 BLOCK/2-6 (A)dd a set (D)elete a set (S)ave changes (Q)uit A IDENTIFY EQUIVALENT DIMENSIONS CYLINDER/1-7 The following sets of dimensions have been identified as equivalent: |
6.3 Kinematic Assembly Variations
Choose the 2D ANALY option from the Main Menu and then select KINEMAT to see the kinematic assembly variations determined by the three closed loops. The results can be saved to the file STKBLKS.OUT for later viewing.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE < CLOSED LOOP ANALYSIS RESULTS > Controlled Dimensions: Kinematic Assembly Variables: Results to file STKBLKS.OUT (y/N)? Y<CR> |
Three tolerance accumulation models are compared side-by-side: Worst Case, Statistical (RSS), and Six Sigma. The Six Sigma model includes a default "mean drift" factor of 0.25 for each component tolerance. Notice that the variation of the critical dependent LENgth that we're interested in (GROUND/3-4) will be ±.60911mm at the most, but that it will be ±.30110mm 99.73% of the time (Zasm=3.00). Also notice that the angular variation at all four dependent angles is equal (~1.005deg. for Worst Case).
6.4 Analysis of Design Specifications
Since our design spec (dependent LENgth) is a closed loop spec, we can see from selecting the KINEMAT option that its RSS 3[[sigma]] variation will be ±.30110mm. Our design limits (as defined in the Modeler) were ±.300mm. The two numbers are very close. How many more rejects than 2700 ppm will this small difference result in? The DESNSPEC option allows you to see how many parts per million are outside of the specified design limits. The results can be saved to the file STKBLKS.OUT for later viewing.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE < DESIGN SPEC ANALYSIS RESULTS > -----< Spec # 1 >------------------------------------<<
OUTPUTS >>--------- |
The analysis predicts that there will be nearly 2800 ppm rejects--100 ppm more than that specified by our target acceptance fraction. This is probably acceptable; however, section 6.7 will illustrate how much the tolerances will need to be tightened to bring the acceptance fraction to exactly 3.00 sigma.
6.5 Percent Contribution Chart
What contributes to the ±.30110mm variation in GROUND/3-4? A graphical representation of how component dimensions and their tolerances affect the default dependent LENgth design spec can be obtained by choosing %CONTRIB.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
Figure 6.3 Percent Contribution to dependent LENgth design spec (GROUND/3-4) |
Notice that the major contributor to the variation of the critical dependent LENgth GROUND/3-4 is CYLINDER/1-4. It is the source of over 75% of GROUND/3-4's variance.6.6 Sensitivity Diagram
In section 6.5, we saw that CYLINDER/1-4 was the largest contributor to the ±.30110mm variation in GROUND/3-4. Was this due to its relatively large tolerance (.20 mm), GROUND/3-4's sensitivity to it, or both? A graphical representation of how sensitive design specifications are to component dimensions can be obtained by choosing SENSDIAG.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE
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Notice that GROUND/3-4 is most sensitive to CYLINDER/1-4. It is almost equally sensitive to BLOCK/2-5 and the two form tolerances (flatness and roundness) at JOINT7. If tolerances need to be tightened, those on CYLINDER/1-4 and BLOCK/2-5 will have the most effect. The designer might wish to base his choice of allocation weight factors for these dimensions on this sensitivity information.
6.7 Tolerance Allocation
Let's perform a simple proportional scaling tolerance allocation with the default PARAMeter settings. Select ALLOCATE from the 2D ANALY submenu.
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PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE < ALLOCATION RESULTS > Do you want this written to STKBLKS.OUT (y/N)? |
Notice how little the tolerances need to be tightened to meet the default 3-sigma acceptance fraction specified in the PARAMeter table. For example, CYLINDER/1-4's tolerances changed by only 73 ten-thousandths of a millimeter and BLOCK/
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PRO-E Modeler: Clutch
| Stack Blocks
| Remote Positioner |
AutoCAD Modeler: Clutch
| Stack
Blocks | Remote
Positioner |
CATIA Modeler: Crank Slider |
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