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5.0 The one-way clutch: An introduction to AutoCATS 2-D Analysis

Chapter 4 of the AutoCATS Modeling Manual introduced the one-way clutch problem. The clutch problem illustrates how a closed loop is used to find the resultant variation of a critical assembly variable. As explained in the Modeling Manual, this assembly is designed to allow rotation in only one direction. The hub is attached to a drive shaft as shown in Figure 5.1. When the hub rotates clockwise relative to the ring, the roller slips on the inside of the ring. If the hub rotates counter-clockwise, then the spring allows the roller to wedge between the hub and the ring, causing the two to lock and rotate together. In this analysis, the rollers are considered to be vendor-supplied, while the tolerances on the hub and ring need to be determined. Tolerances are initially selected by the designer according to the manufacturing processes he believes may be used.

Figure 5.1. One-way clutch assembly.

Figure 5.2. Vector loop for one-way clutch.

 Independent Variables: HUB/3-6 = 27.645mm ± 0.05mm ROLLER/2-7 = 11.430mm ± 0.010mm ROLLER/2-5 = 11.430mm ± 0.010mm RING/1-5 = 50.800mm ± 0.0125mm Dependent Variables: HUB/6-7 = 4.81mm ± ?  1 at DATUM2 = 7.018[[ring]]± ?  2 at JOINT4 = 172.982[[ring]]± ?

The clutch must also be able to release when the hub is rotated clockwise again. This can be assured by specifying the DEPendent angle 1 at DATUM2 (shown in Figure 5.2) be between 8[[ring]] and 6[[ring]]. AutoCATS names angles according to the node at which they are located. Lengths are named according to the numbers of the nodes that they connect. A vector-loop assembly model of this clutch may be created graphically with the AutoCATS 2-D Modeler (see section 1.9).

The following fonts will be used throughout this example problem:

SCREEN OUTPUT

USER INPUT

Carriage Return <CR>

Throughout the program, choices will appear in parenthesis. The choice in capital letters is the default and only a carriage return is required for this choice.

5.1 Start Up

After creating a vector-loop model of the one-way clutch and a CATS neutral file with the AutoCATS 2-D Modeler, execute the 2-D Analyzer. The Analyzer can be run from any directory as long as its path is included in your path environment variable. The analysis program is started by typing ANALYZER at the DOS prompt:

An introductory screen will appear. After a few seconds, the AutoCATS 2-D Analyzer MAIN MENU will appear. To retrieve the neutral file created by the Modeler, choose the FILE option.

 AutoCATS 2-D Analyzer MAIN MENU OPTION NAME DESCRIPTION FILE Open/Save/Update a neutral file. ENTER Enter model data. 1D ANALY 1-D Model analysis options. 2D ANALY 2-D Model analysis options. GLOBAL List global command description. /EXIT Exit program. .... GLOBAL COMMANDS .... /HELP /BLOCK /REF < > /SYSTEM /EXIT CATS> Type F OPEN NEW UPDATE SAVE AS DIRECT .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF /TERM < > SYSTEM FILE>

Type O <CR> and then type the filename CLUTCH as shown below. The Analyzer can be run from any directory as long as its path is included in your path environment variable. Preferably you'll want to run the Analyzer from the directory that your neutral file is in. Depending on the directory from which you ran AutoCAD and/or where you've written the neutral file, you may have to provide the full path here as well.

 Enter filename to be accessed: CLUTCH FILE>> CLUTCH.NF Is this the correct database (Y/n)?

Press <CR>. The neutral file will be opened, and control will return to the MAIN MENU. To analyze the 2-D vector-loop model stored in the neutral file, select 2D ANALY. This will display the 2D ANALY submenu and will allow you to analyze your 2-D clutch model.

 AutoCATS 2-D Analyzer MAIN MENU OPTION NAME DESCRIPTION FILE Open/Save/Update a neutral file. ENTER Enter model data. 1D ANALY 1-D Model analysis options. 2D ANALY 2-D Model analysis options. GLOBAL List global command description. /EXIT Exit program. .... GLOBAL COMMANDS .... /HELP /BLOCK /REF < > /SYSTEM /EXIT CATS> Type 2D PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>

Notice that the main menu above is shown in Block form and the 2D ANALY submenu is shown in linear form (see section 4.0). Linear menus will featured for the remainder of this chapter. If you wish, you can toggle to linear form now by typing /BLOCK <CR>.

5.2 Equating Variables

Two vectors define the radius of the roller, ROLLER/2-5 and ROLLER/2-7. These two vectors must be considered equivalent because each vector represents an equivalent dimension and tolerance. Dimensions may be equated from the MODIFY submenu.

 Type M LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE  .... GLOBAL COMMANDS ....  /HELP /UP /TOP /BLOCK /REF < > /SYSTEM  MODIFY> Type E No dimensions have been defined as equivalent (A)dd a set (S)ave changes (Q)uit

We need to add a set of equivalent dimensions.

 Type A (no ) IDENTIFY EQUIVALENT DIMENSIONS  NO. DIM. NAME DIMENSION  1 RING/1-5 50.8000  2 ROLLER/2-5 11.4300  3 ROLLER/2-7 11.4300  4 HUB/3-6 27.6450  Identify a set of equivalent dimensions by entering the numbers  above that identify them (separated by spaces).   TO END SEQUENCE:

The roller radii (numbers 2 and 3) are the dimensions to be equivalenced.

 Type 2 3 ROLLER/2-5 ROLLER/2-7 Make the following dimensions equivalent? (Y/n)

Acknowledge the correct dimensions.

 Type Y or just to acknowledge the default. The following sets of dimensions have been identified as equivalent: NO. 1: ROLLER/2-5 ROLLER/2-7 (A)dd a set (D)elete a set (S)ave changes (Q)uit

Save the changes and exit.

5.3 Parameters

We now move to the PARAMeter table to select an analysis model, acceptance fraction, and whether to include feature tolerances in our analysis. All of these options can be selected by choosing PARAM from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type P < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

The selections in this table are used to define parameters for both analysis and allocation. The default analysis settings are: Root Sum Square analysis, acceptance fraction of 3 sigma (~2700 ppm rejects), and feature tolerances included. When you wish to choose other options, use the arrow keys to move around the screen, place an X next to an option you wish to select and delete the X next to the current option. The ALLOCATION OPTIONS and SPECIFICATION SELECTION LIST will be discussed later in section 5.6. There are no changes to be made at this time. (We will use the default settings.)

Type <ESC> Q (sequentially, not simultaneously)

5.4 Kinematic Assembly Variables

The KINEMAT option allows you to see the variations predicted for kinematic assembly variables (determined from closed loops). To view the analysis results, select KINEMAT from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type K The results of the closed loop analysis appear as follows: < CLOSED LOOP ANALYSIS RESULTS > Assembly Name: CLUTCH No. Closed Loops: 1 Feature Tolerances: Applied Target Acceptance Fraction (Zasm): 3.00 Loop Names: LOOP_1 Controlled Dimensions: Nominal Symmetric Standard Part Name/Dimen Dimension Tolerance Deviation (RSS) ---------------:-------------:-----------:----------- RING/1-5 : 50.80000 : .01250 : .00417 ROLLER/2-7 : 11.43000 : .01000 : .00333 HUB/3-6 : 27.64500 : .05000 : .01667 ---------------:-------------:-----------:----------- Kinematic Assembly Variables: Variations Variable Name DEG of FDM Worst Case RSS Case 6-SIG Case --------------:-------------:-----------:-----------:----------- JOINT4 : ROTATION : 1.28375 : .68017 : .89401 DATUM2 : ROTATION : 1.28375 : .68017 : .89401 HUB/6-7 : TRANSLATION : .88404 : .46472 : .61080 --------------:-------------:-----------:-----------:----------- Results to file CLUTCH.OUT (y/N)?

Notice the rotational variation at DATUM2 (1). At worst case, CATS predicts that this angle will vary by ±1.28375deg., but the RSS statistical analysis shows that 99.73% of the time (3 sigma), the variation will be only ±.68017deg.. This illustrates the incredible advantage to using statistical rather than worst case methods. The Six Sigma analysis results (see section 2.7) shown above are for a default dynamic k (mean "drift" factor) of .25 (Cpk=.75) for each manufactured dimension. Taking these factors into account, AutoCATS predicts a variation of ±.89401deg..

Save the results to the file CLUTCH.OUT for later viewing.

Type Y <CR>

5.5 Tolerance Analysis Without Feature Tolerances

At this point, it may be valuable to compare the closed loop analysis results obtained in the previous section with results obtained without including the effects of feature tolerances. To analyze the model without including the effects of the feature tolerances, return to the PARAMeter table and remove the X from the field labeled "Include Feature Tolerances."

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>  Type P Remove the X from the Include Feature Tolerances option as shown. < PARAMETER TABLE >  ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the __ Include Feature Tolerances selected item.  Press Q to exit, H for help, C to update Type Q

To repeat the closed loop tolerance analysis, this time without the effect of feature tolerances, select the KINEMAT option from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type K The results of the closed loop analysis appear as follows:  < CLOSED LOOP ANALYSIS RESULTS > Assembly Name: CLUTCH No. Closed Loops: 1 Feature Tolerances: Not applied Target Acceptance Fraction (Zasm): 3.00 Loop Names: LOOP_1 Controlled Dimensions: Nominal Symmetric Standard Part Name/Dimen Dimension Tolerance Deviation (RSS) ---------------:-------------:-----------:----------- RING/1-5 : 50.80000 : .01250 : .00417 ROLLER/2-7 : 11.43000 : .01000 : .00333 HUB/3-6 : 27.64500 : .05000 : .01667 ---------------:-------------:-----------:-----------   Kinematic Assembly Variables: Variations Variable Name DEG of FDM Worst Case RSS Case 6-SIG Case --------------:-------------:-----------:-----------:----------- JOINT4 : ROTATION : .98061 : .65787 : .87716 DATUM2 : ROTATION : .98061 : .65787 : .87716 HUB/6-7 : TRANSLATION : .67151 : .44945 : .59926 --------------:-------------:-----------:-----------:----------- Results to file CLUTCH.OUT (y/N)?

Notice as shown in the output header that feature tolerances were not applied. As before, notice the rotational variation at DATUM2 (1). The worst case model predicts that this angle will vary by ±.98061deg., the RSS statistical model predicts a 3-sigma variation of ±.65787deg., and the Six Sigma model predicts a 3-sigma variation of ±.87716deg.. By not including the feature tolerances, the RSS and Six Sigma variational predictions decreased by about 3 percent, and the Worst Case prediction decreased by more than 20 percent.

The difference in results shows the importance of including feature tolerances, if possible, in your AutoCATS model. Differences like these may be large enough to cause unexpected rejects. AutoCATS can help you discover these problems and fix them before your design goes into production.

Save the results to the file CLUTCH.OUT for later viewing.

Type Y <CR>

5.6 Analysis of Design Specifications

The DESNSPEC option allows you to see how many assemblies (in parts per million) are outside of the design limits you specified while building your AutoCATS model. Design specifications are tolerances that you, as the designer, specify on critical assembly dimensions. The only critical assembly dimension (defined as a design specification) in this instance is the DEPendent angle at DATUM2 (1), between reference vectors ROLLER/2-5 and ROLLER/2-7.

5.6.1 Worst Case Analysis

From the 2D ANALY submenu return to the PARAMeter table to include feature tolerances in your analysis, and to choose WC in order to use the Worst Case analysis model.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>   Type P < PARAMETER TABLE >  ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- X_ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 __ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

Select WC for the analysis model and re-select the Include Feature Tolerances option. Be sure to clear the selection for RSS analysis, as shown above. Notice that the DEPendent angle design specification has been selected by default.

Type <ESC> Q

We now want to see the worst case analysis results for the one DEPendent angle design specification that we have defined. Choose the DESNSPEC option from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>  Type D < DESIGN SPEC ANALYSIS RESULTS > Assembly Name: CLUTCH Analysis Model: WC Target Acceptance Fraction (Zasm): 3.00  -----< Spec # 1 >------------------------------------<< OUTPUTS >>--------- Spec Type : DEP. ANGLE : With Feature :Without Feature References: ROLLER/2-7 ROLLER/2-5 : Tolerances : Tolerances --------------------------------------------:--------------:---------------p> : Mean: 7.01840 Computed Variation: ± 1.28375: ± .98061 Nominal: 7.01840 : Upper Tol: +.98160 : SPEC VIOLATED:SPEC SATISFIED Lower Tol: -1.01840 : : Max Limit: 8.00000 : : Min Limit: 6.00000 : : --------------------------------------------:--------------:---------------p> Do you want this written to CLUTCH.OUT (y/N)?

Notice that the computed variation when feature tolerances are included exceeds both spec tolerances. This means that some assemblies will not meet specifications. How many? The RSS and 6-Sigma statistical analysis options will allow us to predict how many rejects there will be.

Type Y <CR>

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type P < PARAMETER TABLE >  ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update Type Q PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type D < DESIGN SPEC ANALYSIS RESULTS > Assembly Name: CLUTCH Analysis Model: RSS Target Acceptance Fraction (Zasm): 3.00 -----< Spec # 1 >------------------------------------<< OUTPUTS >>--------- Spec Type : DEP. ANGLE : With Feature :Without Feature References: ROLLER/2-7 ROLLER/2-5 : Tolerances : Tolerances --------------------------------------------:--------------:---------------p> : Mean: 7.01840 Computed Variation: ± .68017: ± .65787 Nominal: 7.01840 : Upper Tol: +.98160 Upper Tail Z (sigma): 4.33: 4.48 Lower Tol: -1.01840 Lower Tail Z (sigma): 4.49: 4.64 Max Limit: 8.00000 USL Rejects (ppm): 7.5: 3.9 Min Limit: 6.00000 LSL Rejects (ppm): 3.6: 1.7 --------------------------------------------:--------------:---------------p> TOTAL REJECTS (PPM): 11.1: 5.6 --------------------------------------------:--------------:---------------p> Do you want this written to CLUTCH.OUT (y/N)?

This analysis shows that with the tolerances as they currently are, there will be very few rejects. By including feature tolerances, we would expect 11 rejects for every million assemblies (7.5 assemblies with dependent angles too large and 3.6 assemblies with dependent angles too small).

However, the acceptance fraction specified in the PARAMeter table is 3-sigma (or 99.73%)--meaning that 2700 rejects would be acceptable. The next section shows how the current tolerances can be loosened to reduce costs while keeping the number of rejected assemblies below the target acceptance fraction.

Save the results to the file CLUTCH.OUT for later viewing.

Type Y <CR>

5.7 Tolerance Allocation

In Section 5.2, we discussed how the PARAMeter table is used to select analysis options. The PARAMeter table is used to select options for allocation as well. When we performed statistical DESNSPEC analysis, we saw that the number of predicted rejects was lower than what we had defined in the PARAMeter table as acceptable. The ALLOCATE option allows the user to let AutoCATS increase or decrease tolerances and/or nominals to meet the acceptance fraction we've specified!

5.7.1 Tolerance Allocation by Proportional Scaling

AutoCATS compares the sum of the assigned component tolerances to the assembly tolerance. If their sum exceeds or is less than the design specification limits, the component tolerances are then scaled by a constant proportionality factor, preserving the relative magnitudes of the individual tolerances.

From the 2D ANALY submenu, enter the PARAMeter table to select PROPOR. SCALING.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type P < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

The ANALYSIS MODEL, TARGET ACCEPTANCE FRACTION, and Include Feature Tolerances option apply to tolerance allocation as they do with analysis. The ALLOCATION OPTIONS allow the user to use a variety of methods to perform both nominal and tolerance allocations. The SPECIFICATION SELECTION LIST is a list of the design specifications defined for your model. Since tolerances can only be allocated to satisfy one design specification at a time, one of these must be selected before allocating. For the clutch, the rotational variation at DATUM2 (1), between the reference vectors ROLLER/2-5 and ROLLER/2-7, is the only design specification that has been defined.

For this example, select tolerance allocation by proportional scaling, which is the default allocation method. We will continue with the RSS analysis model.

Type <ESC> Q

Recall that the ALLOCATE option allocates tolerances so that the number of rejects predicted by AutoCATS matches the acceptance fraction specified in the PARAMeter table. Before allocating, however, we must remember that the roller is a vendor-supplied part. Because we have no control over its manufacture, its tolerances should not be allocated, but held fixed. To fix tolerances on dimensions such as this, return to the ALOCDATA option in the MODIFY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type M ALOCDATA allows you to modify default allocation parameters such as fixed flags and weight factors. LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM MODIFY>  Type A   < ALLOCATION AND PROCESS DATA > Assembly Name: CLUTCH Nominal Symmetric Process Stat Dyn Wgt_Fac Fix Part Name/Dimen Dimension Tolerance Std Dev Cp K K Tol Nom y/N ----------------------------------------------------------------------------- 1 RING/1-5 50.80000 .012500 .004166 1.00 .000 .250 1_ 1_ N 2 ROLLER/2-7 11.43000 .010000 .003333 1.00 .000 .250 1_ 1_ Y 3 HUB/3-6 27.64500 .050000 .016666 1.00 .000 .250 1_ 1_ N 4 _______ ____ ____ ____ __ __ _ 5 _______ ____ ____ ____ __ __ _ 6 _______ ____ ____ ____ __ __ _ 7 _______ ____ ____ ____ __ __ _ 8 _______ ____ ____ ____ __ __ _ 9 _______ ____ ____ ____ __ __ _ 10 _______ ____ ____ ____ __ __ _ 11 _______ ____ ____ ____ __ __ _ 12 _______ ____ ____ ____ __ __ _ 13 _______ ____ ____ ____ __ __ _ 14 _______ ____ ____ ____ __ __ _ 15 _______ ____ ____ ____ __ __ _ Press Q to exit, H for help, C to update

Place a Y as shown in the Fix column for the roller radius (ROLLER/2-7). This will fix the tolerances and nominals for ROLLER/2-7 for any type of allocation. Notice that this input screen is also where you can modify other allocation parameters such as weight factors for both tolerances and nominals (see sections 3.3 and 3.8). As explained in Section 3.8, you may also modify process data such as the process capability ratio (Cp), process standard deviation, and static and dynamic k's. Type <ESC> Q to save your changes and type <CR> to return to the 2D ANALY menu.

Now we can allocate to loosen tolerances just enough to meet the 3.00 sigma acceptance fraction that we have specified. Select ALLOCATE.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>   Type A < ALLOCATION RESULTS > Assembly: CLUTCH Analysis Model: RSS Target Acceptance Fraction (Zasm): 3.00 Tolerance Allocation Option: Proportional Scaling Nominal Allocation Option : None -----< Spec # 1 >--------------------------------------------------------- Spec Type : DEP. ANGLE Nominal: 7.01840 References: ROLLER/2-7 ROLLER/2-5 Max Limit: 8.00000 Min Limit: 6.00000 --------------------------------------------------------------------------<> : SPECIFIED VALUES : ALLOCATED VALUES : Optimized Perc Part Name/Dimen : Nominal ±Tol : Nominal ±Tol : Std Dev Cont --------------- : --------- ------- : --------- ------- : --------- ------ RING/1-5 : 50.8000 .01250 : 50.8000 .01944 : .00648 5.30 ROLLER/2-7 : 11.4300 .01000 : 11.4300 .01000 : .00333 5.65 * HUB/3-6 : 27.6450 .05000 : 27.6450 .07776 : .02592 86.06 --------------- : -----------Form Tolerances----------- : --------- ------ JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .00 * JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .36 * JOINT5 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * JOINT5 : 0.0 .00500 : 0.0 .00500 : .00167 .35 * JOINT7 : 0.0 .01250 : 0.0 .01250 : .00417 2.22 * JOINT7 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * --------------- : ----------------- : ----------------- : --------- ------ COMPUTED ASSEMBLY VARIATION -- DEP. ANGLE .33278 100.00 Mean ± Var : 7.0184 .68017 : 7.0184 .99834 : : ----------------- : ----------------- : Min. Max. : 6.3382 7.6986 : 6.0201 8.0167 : ----------------:-------------------:-------------------:----------------- REJECTS Z PPM : Z PPM : Upper: 4.33 7.5 : 2.95 1590.3 : Lower: 4.49 3.6 : 3.06 1105.5 : Total: 11.1 2695.8 * = Fixed Tolerance  Do you want this written to CLUTCH.OUT (y/N)?

Notice the roller radius dimension on the vendor-supplied part in the output table. It is flagged as a fixed tolerance and a change has not been suggested. In addition, the form tolerances specified at JOINT4, JOINT5, and JOINT7 are also all flagged as fixed tolerances. Only the tolerances on RING/1-5 and HUB/3-6 have been adjusted. Notice that each has been increased by the same factor and that the allocated values result in the number of rejects we specified (~ 2700 ppm). Save the results to the file CLUTCH.OUT for later viewing.

Type Y <CR>

5.7.2 Tolerance Allocation by Weight Factors

The advantage of proportional scaling is that it keeps tolerances in their original proportion. However, the designer may wish to base the proportion of tolerances on something other than his original choices. Weight Factor allocation allows the user to assign a weight factor to each dimension, which may be based on the relative cost of the manufacturing process of the component, the sensitivity of the critical assembly variable to it, etc. Larger weight factors indicate to the AutoCATS algorithm that changes in the tolerances of the specified component should be more when loosening tolerances and less when tightening them.

 Type P   < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER X_ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM __ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

Select the WEIGHT FACTORS option from the ALLOCATION OPTIONS for TOLERANCES as shown above.

Type <ESC> Q

Now weight factors must be assigned to each component. To do so, once again select the ALOCDATA option in the MODIFY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>  Type M   LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM MODIFY> Type A   < ALLOCATION AND PROCESS DATA > Assembly Name: CLUTCH Nominal Symmetric Process Stat Dyn Wgt_Fac Fix Part Name/Dimen Dimension Tolerance Std Dev Cp K K Tol Nom y/N ----------------------------------------------------------------------------- 1 RING/1-5 50.80000 .012500 .004166 1.00 .000 .250 5_ 1_ N 2 ROLLER/2-7 11.43000 .010000 .003333 1.00 .000 .250 0_ 0_ Y 3 HUB/3-6 27.64500 .050000 .016666 1.00 .000 .250 1_ 1_ N 4 _______ ____ ____ ____ __ __ _ 5 _______ ____ ____ ____ __ __ _ 6 _______ ____ ____ ____ __ __ _ 7 _______ ____ ____ ____ __ __ _ 8 _______ ____ ____ ____ __ __ _ 9 _______ ____ ____ ____ __ __ _ 10 _______ ____ ____ ____ __ __ _ 11 _______ ____ ____ ____ __ __ _ 12 _______ ____ ____ ____ __ __ _ 13 _______ ____ ____ ____ __ __ _ 14 _______ ____ ____ ____ __ __ _ 15 _______ ____ ____ ____ __ __ _ Press Q to exit, H for help, C to update

In this instance, let's assume that the ring dimension might be produced by a grinding operation and that the hub dimension will probably be milled. The designer might want to be able to loosen the ring's tolerances more than the hub's. Thus, let's assign (somewhat arbitrarily) a weight factor of 5 for RING/1-5 and a weight factor of 1 for HUB/3-6 as shown.

 Type Q and to return to the 2D ANALY submenu. Type A to view the results. < ALLOCATION RESULTS > Assembly: CLUTCH Analysis Model: RSS Target Acceptance Fraction (Zasm): 3.00 Tolerance Allocation Option: Weight Factors Nominal Allocation Option : None -----< Spec # 1 >--------------------------------------------------------- Spec Type : DEP. ANGLE Nominal: 7.01840 References: ROLLER/2-7 ROLLER/2-5 Max Limit: 8.00000 Min Limit: 6.00000 --------------------------------------------------------------------------<> : SPECIFIED VALUES : ALLOCATED VALUES : Optimized Perc Part Name/Dimen : Nominal ±Tol : Nominal ±Tol : Std Dev Cont --------------- : --------- ------- : --------- ------- : --------- ------ RING/1-5 : 50.8000 .01250 : 50.8000 .06285 : .02095 55.38 ROLLER/2-7 : 11.4300 .01000 : 11.4300 .01000 : .00333 5.65 * HUB/3-6 : 27.6450 .05000 : 27.6450 .05027 : .01676 35.98 --------------- : -----------Form Tolerances----------- : --------- ------ JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .00 * JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .36 * JOINT5 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * JOINT5 : 0.0 .00500 : 0.0 .00500 : .00167 .35 * JOINT7 : 0.0 .01250 : 0.0 .01250 : .00417 2.22 * JOINT7 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * --------------- : ----------------- : ----------------- : --------- ------ COMPUTED ASSEMBLY VARIATION -- DEP. ANGLE .33278 100.00 Mean ± Var : 7.0184 .68017 : 7.0184 .99834 : : ----------------- : ----------------- : Min. Max. : 6.3382 7.6986 : 6.0201 8.0167 : ----------------:-------------------:-------------------:----------------- REJECTS Z PPM : Z PPM : Upper: 4.33 7.5 : 2.95 1590.3 : Lower: 4.49 3.6 : 3.06 1105.5 : Total: 11.1 2695.8 * = Fixed Tolerance Do you want this written to CLUTCH.OUT (y/N)?

Notice that the header shows the allocation was done by weight factors. Notice that the allocated tolerance for HUB/3-6 represents a very small increase from its original tolerance, but RING/1-5's allocated tolerance is much larger than originally. If a different ratio is desired, other weight factors could be used to arrive at an acceptable design. For example, 0.06285 is probably too large a tolerance for a grinding operation. Either a different process can be used or different weight factors reassigned. The on-line Tolerance Reference Handbook can be used to verify reasonable tolerance ranges for a given process.

Type Y <CR>

5.7.3 Tolerance Allocation by Minimum Cost

Tightening and loosening of tolerances can have a relatively large effect on the cost of the total design, depending on the component manufacturing processes. When cost vs. tolerance data is known or can be estimated, AutoCATS can run an optimization algorithm to determine the minimum cost allocation of tolerances among component parts. Tolerances are loosened on dimensions produced by expensive processes and tightened for cheaper processes. The optimal tolerance allocation is subject to the constraint that the sum of the component tolerances cannot exceed the specified assembly tolerance.

 Type P < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 X_ RSS __ 2.58 SIGMA (.99) 2 __ __ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM __ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE X_ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item.  Press Q to exit, H for help, C to update Select the MINIMUM COST option from the ALLOCATION OPTIONS for TOLERANCES as shown above. Type Q

When using Minimum Cost allocation, the designer must supply an empirical cost-vs-tolerance curve for each part based on the manufacturing process used (see Section 1.6). Appendix E contains some suggested cost-vs-tolerance data for common processes.

To supply the values for A, B, and k in the cost-tolerance function, select the COSTDATA option in the MODIFY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type M LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM MODIFY> Type C TOLERANCE VS. COST INPUT TABLE ASSEMBLY NAME: CLUTCH COST FUNCTION: A + B*(TOL)^K FIX BASIC PART NAME/ DIM. Y/N DIMEN. PROCESS A B K ---------------------------------------------------------------------------- 1 RING/1-5 N 50.8000 GROUND .000000 .013336 -.78276 2 ROLLER/2-7 Y 11.4300 LAPPED .000000 .000000 -.00000 3 HUB/3-6 N 27.6450 MILLED .000000 .095444 -.44314 4 ------ ------- ------- ------- 5 ------ ------- ------- ------- 6 ------ ------- ------- ------- 7 ------ ------- ------- ------- 8 ------ ------- ------- ------- 9 ------ ------- ------- ------- 10 ------ ------- ------- ------- 11 ------ ------- ------- ------- 12 ------ ------- ------- ------- 13 ------ ------- ------- ------- 14 ------ ------- ------- ------- 15 ------ ------- ------- -------  Press Q to exit, H for help

Using the data supplied in Appendix E for the various manufacturing processes, we chose values of B and k as shown above. Since A represents the fixed cost for each part, it does not play a role in the optimization of the tolerance allocation; thus we have given it no value here. Also, since the roller is vendor-supplied, its dimension is fixed and it also does not have a part in the optimization routine.

 Type Q and to return to the 2D ANALY submenu. Type A to view the results of minimum cost allocation. < ALLOCATION RESULTS > Assembly: CLUTCH Analysis Model: RSS Target Acceptance Fraction (Zasm): 3.00 Tolerance Allocation Option: Minimum Cost Nominal Allocation Option : None -----< Spec # 1 >--------------------------------------------------------- Spec Type : DEP. ANGLE Nominal: 7.01840 References: ROLLER/2-7 ROLLER/2-5 Max Limit: 8.00000 Min Limit: 6.00000 --------------------------------------------------------------------------<> : SPECIFIED VALUES : ALLOCATED VALUES : Optimized Perc Part Name/Dimen : Nominal ±Tol : Nominal ±Tol : Std Dev Cont --------------- : --------- ------- : --------- ------- : --------- ------ RING/1-5 : 50.8000 .01250 : 50.8000 .05224 : .01741 38.27 ROLLER/2-7 : 11.4300 .01000 : 11.4300 .01000 : .00333 5.65 *  HUB/3-6 : 27.6450 .05000 : 27.6450 .06107 : .02036 53.09 --------------- : -----------Form Tolerances----------- : --------- ------ JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .00 * JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .36 * JOINT5 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * JOINT5 : 0.0 .00500 : 0.0 .00500 : .00167 .35 * JOINT7 : 0.0 .01250 : 0.0 .01250 : .00417 2.22 * JOINT7 : 0.0 .00150 : 0.0 .00150 : .00050 .03 * --------------- : ----------------- : ----------------- : --------- ------ COMPUTED ASSEMBLY VARIATION -- DEP. ANGLE .33278 100.00 Mean ± Var : 7.0184 .68017 : 7.0184 .99834 : : ----------------- : ----------------- :  Min. Max. : 6.3382 7.6986 : 6.0201 8.0167 : ----------------:-------------------:-------------------:----------------- REJECTS Z PPM : Z PPM : Upper: 4.33 7.5 : 2.95 1590.3 : Lower: 4.49 3.6 : 3.06 1105.5 : Total: 11.1 2695.8 * = Fixed Tolerance   Do you want this written to CLUTCH.OUT (y/N)?

Notice that the suggested tolerance for RING/1-5 is much greater than the value of 0.01944 arrived at by proportional scaling. This is because a small increase in its tolerance results in a relatively large decrease in cost.

Also notice that we achieved similar results with the weight factor allocation. This means that the weight factors we selected (5 and 1) might be fairly good estimations of the processes' relative costs. If exact cost-tolerance data is not known, weight factors can be used to estimate relative process costs. Again, 0.05224 is probably too large a tolerance for a grinding operation (see the on-line Tolerance Reference Handbook). A different process (perhaps turning) should be assigned to RING/1-5 and the optimization run again.

Type Y <CR>

5.8 Percent Contribution Chart

The percent contribution chart is an attractive feature which provides a graphical representation of how much variation each controlled dimension contributes to the overall variation of a particular design specification assembly variable (see Figure 5.3). We want to see how the different variables affect our critical DEPendent angle 1 at DATUM2.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type % Figure 5.3. Percent contribution to the DEPendent angle design specification.

Notice that the flatness feature tolerance at JOINT7 makes a noticeable cntribution. JOINT7 is the joint between the roller and the hub.

Type <CR>

5.9 Sensitivity Diagram

The sensitivity diagram provides a graphical representation of how sensitive a particular design specification variable is to dimensioned variables (see Figure 5.4). We want to see the sensitivity of the critical DEPendent angle 1 to the controlled dimensions. Choose SENSDIAG from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type S Figure 5.4. Sensitivities of the DEPendent angle design specification.

Notice that the DEPendent angle is most sensitive to the radius of the roller, ROLLER/2-7. Its sensitivity to everything else is almost identical.

Type <CR>

At this time we will explore the 6-SIG analysis option. As discussed in section 2.7, during any manufacturing process, the mean of the process may not be centered between its tolerance limits because of tool wear, setup error, fixture bias, and so forth. Component mean shifts can accumulate in the same way tolerances accumulate, resulting in an increased number of rejects. The Six Sigma model, developed by the Motorola Corporation, is a mathematical model for tolerance accumulation which accounts for mean shifts. Better information about each process is required to provide more realistic estimates about the effects of process variations.

 Type P < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 __ RSS __ 2.58 SIGMA (.99) 2 __ X_ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ __ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM X_ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ X_ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> __ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

Select the 6-SIG analysis model option and PROPOR. SCALING as shown above.

Type <ESC> Q

As explained in Section 1.4, this option allows more realistic estimates of the effects of process variations, but it requires better information about each process. Select MODIFY from the 2D ANALY submenu to see what kinds of information can be provided.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D> Type M LOOP FEATURE DESNSPEC ALOCDATA COSTDATA EQUATE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM MODIFY>

The ALOCDATA option allows the user to edit both allocation and process defaults. In this instance, we want to view the current process defaults.

 Type A < ALLOCATION AND PROCESS DATA > Assembly Name: CLUTCH Nominal Symmetric Process Stat Dyn Wgt_Fac Fix Part Name/Dimen Dimension Tolerance Std Dev Cp K K Tol Nom y/N ----------------------------------------------------------------------------- 1 RING/1-5 50.80000 .012500 .004166 1.00 .000 .250 5_ 1_ N 2 ROLLER/2-7 11.43000 .010000 .004000 1.00 -0.5 .000 0_ 0_ Y 3 HUB/3-6 27.64500 .050000 .016666 1.00 .000 .250 1_ 1_ N 4 _______ ____ ____ ____ __ __ _ 5 _______ ____ ____ ____ __ __ _ 6 _______ ____ ____ ____ __ __ _ 7 _______ ____ ____ ____ __ __ _ 8 _______ ____ ____ ____ __ __ _ 9 _______ ____ ____ ____ __ __ _ 10 _______ ____ ____ ____ __ __ _ 11 _______ ____ ____ ____ __ __ _ 12 _______ ____ ____ ____ __ __ _ 13 _______ ____ ____ ____ __ __ _ 14 _______ ____ ____ ____ __ __ _ 15 _______ ____ ____ ____ __ __ _  Press Q to exit, H for help, C to update

Motorola's Six-Sigma model allows the user to define static and dynamic k's, which account for process mean shifts and drifts respectively (see Section 2.7). Let's assume, for example, that after inspecting a batch of rollers (a vendor-supplied part) which have arrived at your manufacturing facility, their average radius is 11.425 mm instead of 11.430 mm, with a standard deviation of .0040 mm. This difference in nominals could be considered a process "mean shift" and can be accounted for by assigning a static-k of -0.5 to ROLLER/2-7 (since -0.005 mm, the difference between the two nominals, is 0.5 times its symmetric tolerance).

Enter this static k for ROLLER/2-7 as shown above. Also enter a standard deviation of 0.004, and change the dynamic k to 0.0. This will update the process information for your model and make it more accurate. You may or may not decide to change the dynamic k values of 0.250 shown for the other two components, depending on how much "drift" there will be in their respective processes. For this example, we will leave them at their default values.

To view the results of this Six-Sigma analysis, choose the DESNSPEC option from the 2D ANALY submenu.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>   Type D < DESIGN SPEC ANALYSIS RESULTS > Assembly Name: CLUTCH Analysis Model: 6-SIG Target Acceptance Fraction (Zasm): 3.00  -----< Spec # 1 >------------------------------------<< OUTPUTS >>--------- Spec Type : DEP. ANGLE : With Feature :Without Feature References: ROLLER/2-7 ROLLER/2-5 : Tolerances : Tolerances --------------------------------------------:--------------:---------------p> : Mean: 7.13706 Computed Variation: ± .88368: ± .86663 Nominal: 7.01840 : Upper Tol: +.98160 Upper Tail Z (sigma): 2.93: 2.99 Lower Tol: -1.01840 Lower Tail Z (sigma): 3.86: 3.94 Max Limit: 8.00000 USL Rejects (ppm): 1696.9: 1407.5 Min Limit: 6.00000 LSL Rejects (ppm): 56.8: 41.5 --------------------------------------------:--------------:---------------p> TOTAL REJECTS (PPM): 1753.7: 1449.0 --------------------------------------------:--------------:---------------p> Do you want this written to CLUTCH.OUT (y/N)?

Note how much of an effect the mean shift of the roller has on the critical DEPendent angle. It increases the mean angle by 0.119deg. and the rejects in the upper tail over 200 times! AutoCATS can help you predict these effects and help to provide allocation solutions.

Type Y <CR>

A powerful design tool built into AutoCATS is the ability to adjust nominal dimensions to move the mean of the assembly distribution to a desired location, such as the center of its tolerance zone. Nominal allocation is similar to tolerance allocation, but involves changes in the mean or nominal values of component dimensions instead of changes in component tolerances. The center of the distribution is changed rather than the spread of the distribution. Just as we can assign weight factors to component tolerances for tolerance allocation, we can assign weight factors for each individual nominal dimension. The relative weights determine how much change is assigned to each component.

Let's consider once again the example in Section 5.10. The nominal DEPendent angle in the original design was not centered between its spec limits, and with the mean shift of 0.005 mm in the roller dimension (ROLLER/2-7), the nominal DEPendent angle is now even more off-center.

We want to know how we can change the remaining nominal dimensions of the clutch (HUB/3-6 and RING/1-5) to have the nominal DEPendent angle be 7.00deg.--instead of its original 7.0184deg. or its predicted shifted value of 7.13706deg.. This will "center" the nominal between it spec limits (8deg. and 6deg.) and thus minimize the number of rejects.

 Type P < PARAMETER TABLE > ANALYSIS TARGET ACCEPTANCE SPECIFICATION SELECTION LIST MODEL FRACTION (Zasm) TYPE REFERENCE 1 REFERENCE 2 ------------------------------------------------------------------------------- __ WC X_ 3.00 SIGMA (.9973) 1 X_ DEP ROLLER/2-5 ROLLER/2-7 __ RSS __ 2.58 SIGMA (.99) 2 __ X_ 6-SIG __ 3.29 SIGMA (.999) 3 __ __ 3.89 SIGMA (.9999) 4 __ __ 4.50 SIGMA (.999993) 5 __ __ 6.00 SIGMA (.999999998) 6 __ _______ User Defined Sigma 7 __ 8 __ ALLOCATION OPTIONS 9 __ NOMINALS TOLERANCES 10 __ ------------------------------------- 11 __ X_ CENTER __ WEIGHT FACTORS 12 __ __ LOWER SPEC LIM __ PROPOR. SCALING 13 __ __ UPPER SPEC LIM __ PRECIS. FACTOR 14 __ __ NONE __ MINIMUM COST <<< INSTRUCTIONS >>> X_ NONE Select one option from each column. Type any character next to the X_ Include Feature Tolerances selected item. Press Q to exit, H for help, C to update

Select the CENTER option in the ALLOCATION OPTIONS for NOMINALS menu, as shown above. Also, select NONE under TOLERANCES.

 Type Q Type A to review the results of this nominal-centering allocation. < ALLOCATION RESULTS > Assembly: CLUTCH Analysis Model: 6-SIG Target Acceptance Fraction (Zasm): 3.00 Tolerance Allocation Option: None Nominal Allocation Option : Centering -----< Spec # 1 >--------------------------------------------------------- Spec Type : DEP. ANGLE Nominal: 7.01840 References: ROLLER/2-7 ROLLER/2-5 Max Limit: 8.00000 Min Limit: 6.00000 --------------------------------------------------------------------------<> : SPECIFIED VALUES : ALLOCATED VALUES : Optimized Perc Part Name/Dimen : Nominal ±Tol : Nominal ±Tol : Std Dev Cont --------------- : --------- ------- : --------- ------- : --------- ------ RING/1-5 : 50.8000 .01250 : 50.7942 .01250 : .00556 4.97 ROLLER/2-7 : 11.4300 .01000 : 11.4300 .01000 : .00402 10.47 * HUB/3-6 : 27.6450 .05000 : 27.6508 .05000 : .02222 80.74 --------------- : -----------Form Tolerances----------- : --------- ------ JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .00 * JOINT4 : 0.0 .00500 : 0.0 .00500 : .00167 .45 * JOINT5 : 0.0 .00150 : 0.0 .00150 : .00050 .04 * JOINT5 : 0.0 .00500 : 0.0 .00500 : .00167 .45 * JOINT7 : 0.0 .01250 : 0.0 .01250 : .00417 2.84 * JOINT7 : 0.0 .00150 : 0.0 .00150 : .00050 .04 * --------------- : ----------------- : ----------------- : --------- ------ COMPUTED ASSEMBLY VARIATION -- DEP. ANGLE .29456 100.00 Mean ± Var : 7.1371 .88368 : 7.0000 .88368 : : ----------------- : ----------------- : Min. Max. : 6.2534 8.0207 : 6.1163 7.8837 : ----------------:-------------------:-------------------:----------------- REJECTS Z PPM : Z PPM : Upper: 2.93 1696.9 : 3.39 343.3 : Lower: 3.86 56.8 : 3.39 343.3 : Total: 1753.7 686.6 * = Fixed Tolerance Do you want this written to CLUTCH.OUT (y/N)?

Notice that if the nominal ring radius RING/1-5 were decreased from 50.8 to 50.7942 and HUB/3-6 were increased from 27.645 to 27.6508, the nominal DEPendent angle would be 7deg. exactly and the distribution would be centered between the specification limits. Notice that these results are for default nominal weight factors of 1, as displayed in the ALOCDATA input screens. A different ratio of nominal weight factors would provide a different result. A mean centered between assembly spec limits provides the minimum number of rejects for the given tolerances. Notice the predicted rejects for the allocated values--686.6 PPM. If 2700 PPM rejects is acceptable, any of the four types of tolerance allocation could also be used in conjunction with the CENTER option to simultaneously loosen tolerances the appropriate amount.

Type Y <CR>

5.12 Save Analysis Matrices

If you are interested, the matrices that are used in the analysis (and which were discussed in Chapter 2) can be saved for viewing by choosing XMATSAVE.

 PARAM MODIFY KINEMAT DESNSPEC ALLOCATE %CONTRIB SENSDIAG XMATSAVE .... GLOBAL COMMANDS .... /HELP /UP /TOP /BLOCK /REF < > /SYSTEM 2D>   Type X Writing raw sensitivity matrices to file MATRIX.OUT. Hit to continue Type Using any DOS text editor, you can look at the matrices we just saved to the file MATRIX.OUT. The output will look like the following. AMAT RING/1-5 ROLLER/2-7 HUB/3-6 .122187920 -.122187971 .000000000 .992506981 -1.99250692 -1.00000000 .000000000 .000000000 .000000000 BMAT JOINT4 DATUM2 HUB/6-7 .000000000 39.0750008 -1.00000000 .000000000 -4.81053686 .000000000 1.00000000 1.00000000 .000000000 CLOSED LOOP SENSITIVITY MATRIX RING/1-5 ROLLER/2-7 HUB/3-6 -.206319342 .414196296 .207876967 .206319292 -.414196195 -.207876915 8.18411567 -16.3069071 -8.12279190 FMAT 1.00000000 .000000000 -.122188054 -.122188054 .000000000 .000000000 .000000000 1.00000000 -.992506921 -.992506921 1.00000000 1.00000000 .000000000 .000000000 .000000000 .000000000 .000000000 .000000000  CLOSED LOOP FEATURE MATRIX -.483165551E-08 -.207876967 .206319329 .206319329 -.207876967 -.207876967 .234901721E-07 .207876915 -.206319280 -.206319280 .207876915 .207876915 1.00000073 8.12279190 -8.18411532 -8.18411532 8.12279190 8.12279190

5.13 Ending the Session

The latest version of the model data is saved when the program is exited.

 FILE ENTER 1D ANALY 2D ANALY GLOBAL /EXIT .... GLOBAL COMMANDS .... /HELP /BLOCK /REF < > /SYSTEM /EXIT CATS>  Type /E The current data will be saved in the original neutral file. If you have made modificationos to the model and you wish to keep the original file from begin changed, you must use the SAVE AS command in the FILE submenu. DO YOU WANT TO EXIT THIS PROGRAM (Y/n)? Type Y or just to acknowledge the default. Creating database file: CLUTCH.NF Session Terminated 05-25-94 : 15:12:30 Stop - Program terminated C:\AUTOCAD\CATS>

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