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7.0 The remote positioner: An introduction to open loop specs.

The remote positioner problem introduces assembly tolerances requiring open loop definitions. The remote positioning mechanism is used in wind tunnel testing and is to be designed as a set of linkages connected by pins. The assembly allows the orientation of the arm inside the tunnel to be linearly controlled by the input linkage located outside the tunnel. A tolerance analysis should be performed with the arm in several positions since it will be oriented to several different angles during wind tunnel testing. This example will only look at the case where the input linkage is rotated 180deg. from the positive X axis.

Figure 7.1 Remote positioner assembly.

Figure 7.2 shows the remote positioner and the open loop assembly specs which are critical to its operation. The figure shows each assembly spec and the datums to which each is referenced. Both the position and parallelism of Part 5 are critical. Part 5 must be parallel to the input linkage, Part 1, within a tolerance bandwidth of .1 in., and the tip of Part 5 must be at its nominal position within a circular tolerance zone of diameter .2 in.

Figure 7.2 Parallelism and true position design specifications.

Figure 7.3 Vector loops for the remote positioner.

 Independent Variables A - PART_1 = 22.0000 +/- .005 in B - PART_3 = 10.4000 +/- .005 in C - PART_2 = 22.0000 +/- .005 in D - GROUND = 5.2000 +/- .003 in E - GROUND = 9.0067 +/- .004 in F - PART_2 = 12.9000 +/- .005 in G - PART_4 = 49.3000 +/- .010 in H - PART_5 = 12.9000 +/- .005 in I - PART_3 = 49.3000 +/- .010 in J - PART_5 = 22.0000 +/- .005 in Dependent Variables [[Phi]]1 - PART_1/PART_3 = 120.00 +/- ? [[Phi]]2 - PART_2/PART_3 = 60.00 +/- ? [[Phi]]3 - GROUND/PART_3 = 0.00 +/- ? [[Phi]]4 - PART_2/PART_4 = 132.60 +/- ? [[Phi]]5 - PART_4/PART_5 = 47.40 +/- ? [[Phi]]6 - PART_3/PART_5 = 132.60 +/- ?

7.1 Start Up

After creating or calling up a vector-loop model of the remote positioner assembly from the TI/TOL 2D Modeler, enter the analyzer environment by selecting Analyze from the TOL-2D main menu. The Edit options of the Analyzer main window allow the user to verify or modify the initial tolerance data.

The following analyses of the remote positioner assembly introduce kinematic variations analysis and demonstrate how to use the process library.

7.2 Analysis Set I

The first analysis of the remote positioner assembly will include a kinematic variations analysis with a root sum squares method and with geometric tolerances applied. This is done by selecting the Root Sum Squares and the Apply Geometric Tolerances commands from the Options menu. To view the kinematic variations analysis results select the Kinematic Variations option of the Analyze menu. The results are shown below.

 TI/TOL 2D MECHANICAL ASSEMBLY TOLERANCE ANALYSIS V3.0 ANALYSIS RESULTS Tue Sep 06 1994 [15:48:52] ============================================================================== Assembly Model File: REMOTE_TUTORIAL Geometric Tolerances: Applied Analysis Model: Root Sum Squares (RSS) ============================================================================== <<< I N P U T S >>> ------------------- Controlled Dimensions: Process Process Dimension Name Nominal +/- Tol Std Dev Description K ----------------:----------:---------:---------:----------------------:------ A : 22.0000 : 0.00500 : 0.00167 : None : n/a B : 10.4000 : 0.00500 : 0.00167 : None : n/a I : 49.3000 : 0.01000 : 0.00333 : None : n/a H : 12.9000 : 0.00500 : 0.00167 : None : n/a J : 22.0000 : 0.00500 : 0.00167 : None : n/a C : 22.0000 : 0.00500 : 0.00167 : None : n/a F : 12.9000 : 0.00500 : 0.00167 : None : n/a G : 49.3000 : 0.01000 : 0.00333 : None : n/a D : 5.2000 : 0.00300 : 0.00100 : None : n/a E : 9.0067 : 0.00400 : 0.00133 : None : n/a ----------------:----------:---------:---------:----------------------:------ Geometric Tolerances: Name Type Joint Tolerance -------------:------------------:----------:----------- FC_37 : True Position : Joint1 : 0.00100 FC_38 : True Position : phi1 : 0.00100 FC_43 : True Position : phi6 : 0.00100 FC_39 : True Position : phi2 : 0.00100 FC_41 : True Position : phi4 : 0.00100 FC_42 : True Position : phi5 : 0.00100 FC_40 : True Position : phi3 : 0.00100 -------------:------------------:----------:----------- <<< O U T P U T S >>> --------------------- Kinematic Assembly Variables: Variable Name Nominal +/- RSS Variation ----------------:------------:-----------------

The output displays the RSS variation in the six assembly angles specified.

7.3 Analysis Set II

Manufacturing processes have inherent standard deviation values associated with them. If the process used to manufacture a particular component of an assembly is known, the standard deviation associated with the process can be assigned to the corresponding dimension.

Specific processes will be assigned to two of the dimensions in the remote positioner assembly. Processes are specified by selecting the Process Data option of the Edit menu. No processes are initially specified for any of the assembly dimensions as shown in the Process Data window below.

A list of available processes can be viewed by selecting the Show Process List command from the Help menu in the Process Data window. The Processes window is shown below.

Notice that each process has a numerical code associated with it. The process described by the numerical code 1:6 above will be assigned to both ends of the bottom cross bar in the remote positioner assembly (variables H and J). This is done by entering the code 1:6 in the Process column next to variables H and J in the Process Data window as shown below.

The updated process data should be saved by selecting the Save option of the File menu in the Process Data window as shown below.

The tolerances associated with the assigned processes should be fixed since such tolerances are not subject to change during a tolerance allocation procedure. This is done by selecting the Allocation Data command from the Edit menu. The Fixed status should be toggled to YES for the tolerances associated with dimension variables H and J. The updated allocation data should be stored by selecting the Save option of the File menu in the Allocation Data window as shown below.

A tolerance allocation will now be performed to achieve the target assembly sigma for the assembly. The target assembly sigma should still be set at 3.00 since it has not been modified. There are two specifications associated with the remote positioner assembly, so the Select Specification command in the Allocate menu should be used. The specification labeled SP_32 in the window below is the parallelism specification. Select it and click on the OK button.

The tolerance allocation results should be as shown below.

 TI/TOL 2D MECHANICAL ASSEMBLY TOLERANCE ANALYSIS V3.0 ANALYSIS RESULTS Tue Sep 06 1994 [16:07:44] ============================================================================== Assembly Model File: REMOTE_TUTORIAL Geometric Tolerances: Applied Analysis Model: Root Sum Squares (RSS) ============================================================================== <<< I N P U T S >>> ------------------- Controlled Dimensions: Process Process Dimension Name Nominal +/- Tol Std Dev Description K ----------------:----------:---------:---------:----------------------:------ A : 22.0000 : 0.00500 : 0.00167 : None : n/a B : 10.4000 : 0.00500 : 0.00167 : None : n/a I : 49.3000 : 0.01000 : 0.00333 : None : n/a H : 12.9000 : 0.00500 : 0.00150 : CNC Mach. Center, Mi : n/a J : 22.0000 : 0.00500 : 0.00150 : CNC Mach. Center, Mi : n/a C : 22.0000 : 0.00500 : 0.00167 : None : n/a F : 12.9000 : 0.00500 : 0.00167 : None : n/a G : 49.3000 : 0.01000 : 0.00333 : None : n/a D : 5.2000 : 0.00300 : 0.00100 : None : n/a E : 9.0067 : 0.00400 : 0.00133 : None : n/a ----------------:----------:---------:---------:----------------------:------ Geometric Tolerances: Name Type Joint Tolerance -------------:------------------:----------:----------- FC_37 : True Position : Joint1 : 0.00100 FC_38 : True Position : phi1 : 0.00100 FC_43 : True Position : phi6 : 0.00100 FC_39 : True Position : phi2 : 0.00100 FC_41 : True Position : phi4 : 0.00100 FC_42 : True Position : phi5 : 0.00100 FC_40 : True Position : phi3 : 0.00100 -------------:------------------:----------:----------- Specification Limits: Upper Limit: 0.05000 Lower Limit: -0.05000 <<< O U T P U T S >>> --------------------- Kinematic Assembly Variables: Variable Name Nominal +/- RSS Variation ----------------:------------:----------------- A : N : 1.00 : 0.00500 : 1.00 : 0.01437 : 1.00 : 0.00479 : B : N : 1.00 : 0.00500 : 1.00 : 0.01437 : 1.00 : 0.00479 : I : N : 1.00 : 0.01000 : 1.00 : 0.02874 : 1.00 : 0.00958 : H : Y : 1.00 : 0.00500 : 1.11 : 0.00500 : 1.11 : 0.00150 : J : Y : 1.00 : 0.00500 : 1.11 : 0.00500 : 1.11 : 0.00150 : C : N : 1.00 : 0.00500 : 1.00 : 0.01437 : 1.00 : 0.00479 : F : N : 1.00 : 0.00500 : 1.00 : 0.01437 : 1.00 : 0.00479 : G : N : 1.00 : 0.01000 : 1.00 : 0.02874 : 1.00 : 0.00958 : D : N : 1.00 : 0.00300 : 1.00 : 0.00862 : 1.00 : 0.00287 : E : N : 1.00 : 0.00400 : 1.00 : 0.01149 : 1.00 : 0.00383 : ----------------:---:--------:---------:------:---------:------:---------:<> Specification Results: Specification Name: SP_32 Specification Type: Parallelism Nominal Dimension: 0.0000 Geometric Tolerances: Applied Analysis Model: RSS Target Assy Sigma: 3.00 Spec Limit Assy Std Dev Assy Sigma Rejects (ppm) DPU -------:-----------:-------------:----------:---------------:-------------<> Upper : 0.05000 : 0.01667 : 3.00 : 1349.82 : 1.3498e-03 Lower : -0.05000 : : 3.00 : 1349.82 : 1.3498e-03 -------:-----------:-------------:----------:---------------:-------------<> Total : 2699.65 : 2.6996e-03

7.4 Analysis Set II

Next, tolerance allocation will be performed using the SSC model. Select the Six Sigma Component Drift command from the Options menu and the Weight Factors Allocate command from the Allocate menu. Leave all other settings the same. The tolerance allocation results are shown below.

 TI/TOL 2D MECHANICAL ASSEMBLY TOLERANCE ANALYSIS V3.0 ANALYSIS RESULTS Tue Sep 06 1994 [16:09:24] ============================================================================== Assembly Model File: REMOTE_TUTORIAL Geometric Tolerances: Applied Analysis Model: Six Sigma Component Drift (SSC) ============================================================================== <<< I N P U T S >>> ------------------- Controlled Dimensions: Process Process Dimension Name Nominal +/- Tol Std Dev Description K ----------------:----------:---------:---------:----------------------:------ A : 22.0000 : 0.00500 : 0.00167 : None : 0.25 B : 10.4000 : 0.00500 : 0.00167 : None : 0.25 I : 49.3000 : 0.01000 : 0.00333 : None : 0.25 H : 12.9000 : 0.00500 : 0.00150 : CNC Mach. Center, Mi : 0.25 J : 22.0000 : 0.00500 : 0.00150 : CNC Mach. Center, Mi : 0.25 C : 22.0000 : 0.00500 : 0.00167 : None : 0.25 F : 12.9000 : 0.00500 : 0.00167 : None : 0.25 G : 49.3000 : 0.01000 : 0.00333 : None : 0.25 D : 5.2000 : 0.00300 : 0.00100 : None : 0.25 E : 9.0067 : 0.00400 : 0.00133 : None : 0.25 ----------------:----------:---------:---------:----------------------:------ Geometric Tolerances: Name Type Joint Tolerance -------------:------------------:----------:----------- FC_37 : True Position : Joint1 : 0.00100 FC_38 : True Position : phi1 : 0.00100 FC_43 : True Position : phi6 : 0.00100 FC_39 : True Position : phi2 : 0.00100 FC_41 : True Position : phi4 : 0.00100 FC_42 : True Position : phi5 : 0.00100 FC_40 : True Position : phi3 : 0.00100 -------------:------------------:----------:----------- Specification Limits: Upper Limit: 0.05000 Lower Limit: -0.05000 <<< O U T P U T S >>> --------------------- Kinematic Assembly Variables: Variable Name Nominal +/- SSC Variation ----------------:------------:----------------- A : N : 1.00 : 0.00500 : 0.75 : 0.01075 : 0.75 : 0.00358 : B : N : 1.00 : 0.00500 : 0.75 : 0.01075 : 0.75 : 0.00358 : I : N : 1.00 : 0.01000 : 0.75 : 0.02151 : 0.75 : 0.00717 : H : Y : 1.00 : 0.00500 : 0.83 : 0.00500 : 0.83 : 0.00150 : J : Y : 1.00 : 0.00500 : 0.83 : 0.00500 : 0.83 : 0.00150 : C : N : 1.00 : 0.00500 : 0.75 : 0.01075 : 0.75 : 0.00358 : F : N : 1.00 : 0.00500 : 0.75 : 0.01075 : 0.75 : 0.00358 : G : N : 1.00 : 0.01000 : 0.75 : 0.02151 : 0.75 : 0.00717 : D : N : 1.00 : 0.00300 : 0.75 : 0.00645 : 0.75 : 0.00215 : E : N : 1.00 : 0.00400 : 0.75 : 0.00860 : 0.75 : 0.00287 : ----------------:---:--------:---------:------:---------:------:---------:<> Specification Results: Specification Name: SP_32 Specification Type: Parallelism Nominal Dimension: 0.0000 Geometric Tolerances: Applied Analysis Model: SSC Target Assy Sigma: 3.00 Spec Limit Assy Std Dev Assy Sigma Rejects (ppm) DPU -------:-----------:-------------:----------:---------------:-------------<> Upper : 0.05000 : 0.01667 : 3.00 : 1349.82 : 1.3498e-03 Lower : -0.05000 : : 3.00 : 1349.82 : 1.3498e-03 -------:-----------:-------------:----------:---------------:-------------<> Total : 2699.65 : 2.6996e-03

Notice that the SSC method requires tighter tolerances than the RSS method to achieve a target assembly sigma of 3.00. This is because the SSC model accounts for the component nominals varying with time. The SSC model accomodates these shifts by increasing each component standard deviation by 25%, and then running an RSS analysis.

7.5 Ending the Session

To exit the TI/TOL 2D Analyzer environment and return to the modeling environment, select the Exit command from the File menu in the Analyzer main window.

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