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Example Problems 
PROE
Verification:
CHAPTER 7: NFOV LENS ASSEMBLY 

Home : Example Problems : ProE 2D  Verification  NFOV 
Figure 7.1: Schematic of the NFOV lens assembly with dimension variables.
7.0 Problem Description
The Narrow Field of Vision Lens (NFOV) assembly consists of four partstwo lenses, a housing, and a retaining ring. The assembly is symmetric about its center line. There are two assembly variables of interest. The first is the gap between the inside surfaces of Lens 2 and Lens 1. The second is the tilt of Lens 2 relative to Lens 1.
Table 7.1: Manufactured Variables (Independent).
Variable Name  Basic Size  Initial Tolerance (+/) 
Lens Thickness A  0.303 in  0.001 in 
Radius of Curvature B_C  10.7185 in  0.0107 in 
Retainer Lip Angle  84.8[[ring]]   
Retainer Flange Depth E  0.503 in  0.001 in 
Retainer Radius F  1.0275 in  0.0005 in 
Housing Length H  7.071 in  0.002 in 
Lens Depth I  0.459 in  0.001 in 
7.1 Design Requirements
Table 7.2: Assembly Variables and Specification Limits.
Variable Name  Basic Size  Upper Spec Limit (USL) 
Lower Spec Limit (LSL) 
Contact Length D  0.0563 in     
Lens/Retainer Gap G  0.2492 in     
Contact Angle [[phi]]  5.2000 [[ring]]     
X1 (GAP)  7.7792  7.7863  7.7737 
Y1  0.0000     
1  0.0000     
X2  7.7792     
Y2  0.0000     
2  0.0000  .00075 (.0286[[ring]])  .00075 (.0286[[ring]]) 
7.2 Modeling Considerations
7.3 Design Goal
The objective of this analysis is to find the assembly variations of the GAP and the TILT. In addition, the component tolerances will be optimized to meet +/6[[sigma]] assembly tolerances on the GAP.
7.4 Part DRFs And Feature Datums
Figure 7.2: Diagram showing the location of the part DRFs and feature datums.
Remarks>> Lens 1 has a cylindrical DRF and a cylindrical feature datum located on top of each other. The feature datum is necessary in order to introduce the correct rotational degree of freedom into the closed loop. The closed loop requires a rotation at the lens center of curvature, but that rotation should not be included in the open loops. Therefore when defining the path from the cylindrical slider joint back to the Lens 1 DRF, first take it to the cylindrical feature datum, and then to the DRF. When defining the path from the planar joint back to the Lens 1 DRF, do not include the cylindrical feature datum. Don't include the cylindrical feature datum when defining paths from the specification endpoints back to the Lens 1 DRF either. Finally, turn off the rotational degree of freedom of the Lens 1 DRF, but not that of the cylindrical feature datum. This will remove the rotational degree of freedom from the open loops but not the closed loop.
The DRFs for the Housing and Lens 2 are located at the same coordinates. The modeler will place the DRF labels on top of each other. This makes it necessary to use the 'query select' or 'menu select' functions to ensure the correct DRF is selected for each joint.
When manufacturing Lens 2, the flat contact surface is ground, and then the curvature of each lens surface is ground relative to it. Thus the DRF of Lens 2 is located on the plane formed by its contact surface.
7.5 Kinematic Joints
Four joints are required to model half of the NFOV lens assembly.
Figure 7.3: Kinematic joint diagram.
Table 7.3: Kinematic Joints of the NFOV Lens.
Joint Number  Part One  Part Two  Joint Type 
1  Lens 1  Retainer  Cylindrical Slider 
2  Retainer  Lens 1  Planar 
3  Retainer  Housing  Rigid 
4  Housing  Lens 2  Rigid 
Remarks>> The planar joint between the Retainer and Lens 1 may seem counterintuitive. However, because we have split the lens assembly in half, one of the dependent length variables of interest is the variation in the distance between the contact surface of the retainer and housing and the leftmost point of Lens 1. A planar joint introduces a degree of freedom in that direction into the model, and allows us to solve for the length variation G.
7.6 Network Diagram, Vector Loops, and Design Specifications
One loop is sufficient to describe the NFOV assembly. The vector loop follows dimensioned lengths and passes though each part DRF and each joint. A design specification has been applied to the gap between the inside surfaces of the two lenses, and another has been applied to the angular tilt between the two lenses.
Figure 7.4: Network diagram and loop diagram for the NFOV lens assembly.
Remarks> Only one open loop is shown in the diagram above because the open loops used to calculate the air gap variation and the tilt of the lenses are identical. However, TI TOL requires a separate open loop for each open loop design specification, so two identical loops must be created inside the modeler.
Within the open loops themselves, there are two sets of redundant vectors (A and B). These occur because TI TOL requires the loops to pass through the Lens 1 DRF before passing through the joint to the retainer. The analyzer does not automatically equivalence them, so the user must do it by hand in order to get valid results.
The characteristic length for the orientation specification is the diameter of Lens 2 (3.0 inches). Lens 2 is chosen because the specification is that Lens 2 be oriented relative to Lens 1 within a .0015 inch bandwidth.
For the gap specification, enter .001 and .001 at the prompts. For the tilt (relative orientation) specification, enter .00075 and .00075 at the prompts.
7.7 Geometric Tolerances
ANSI Y14.5 geometric tolerances are added to account for machined surface variations. They are applied to mating surfaces. Usually, one or two surface variations may be specified at each joint.
Figure 7.5: Geometric tolerance diagram.
Remarks>> The angular variations contributing to the tilt between the two lenses are caused entirely by geometric surface variations acting at the joints. The runout and perpendicularity at the rigid joints all cause rotations. In addition to those, the variation of the contact surface between the Retainer and Lens 1 may be lobed and cause an additional rotation. To model that rotation, an angularity, profile, or flatness geometric tolerance may be applied to the planar joint between the Retainer and Lens 1, and the diameter of the contact ring used as the characteristic length. This introduces an equivalent rotation into the assembly (it has not been done in this model).
7.8 Sensitivity Matrices
Table 7.4: B^{1}A Matrix
A  B_C  E  F  H  I  
D  0.00000  0.09101  0.00000  1.00000  0.00000  0.00000 
G  1.00000  0.00413  1.00000  0.09101  0.00000  0.00000 
[[phi]]  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000 
Table 7.5: B^{1}F Matrix
1  2  3  3  4  
D  0.09101  0.09101  0.00000  0.00000  0.00000 
G  1.00413  1.00413  0.00000  0.00000  0.00000 
[[phi]]  0.00000  0.00000  0.00000  0.00000  0.00000 
B^{1}F Matrix (continued)
4  5  5  6  
D  0.00000  0.00000  0.00000  0.00000 
G  0.00000  0.00000  0.00000  0.00000 
[[phi]]  0.00000  0.00000  0.00000  0.00000 
Table 7.6: CDB^{1}A Matrix
A  B_C  E  F  H  I  
X1  1.00000  0.00413  1.00000  0.09101  1.00000  1.00000 
Y1  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000 
1  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000 
X2  1.00000  0.00413  1.00000  0.09101  1.00000  1.00000 
Y2  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000 
2  0.00000  0.00000  0.00000  0.00000  0.00000  0.00000 
Table 7.7: GDB^{1}F Matrix
1  2  3  3  4  
X1  1.00413  1.00413  1.00000  0.00000  1.00000 
Y1  0.00000  0.00000  0.00000  7.53000  0.00000 
1  0.00000  0.00000  0.00000  1.00000  0.00000 
X2  1.00413  1.00413  1.00000  0.00000  1.00000 
Y2  0.00000  0.00000  0.00000  7.53000  0.00000 
2  0.00000  0.00000  0.00000  1.00000  0.00000 
GDB^{1}F Matrix (continued)
4  5  5  6  
X1  0.00000  1.00000  0.00000  0.00000 
Y1  7.53000  0.00000  0.45900  0.45900 
1  1.00000  0.00000  1.00000  1.00000 
X2  0.00000  1.00000  0.00000  0.00000 
Y2  7.53000  0.00000  0.45900  0.45900 
2  1.00000  0.00000  1.00000  1.00000 
7.9 Predicted Assembly Variation
Table 7.8: Independent Variable Tolerances and Control Factors
Dim Name  Nominal  +/ Tol  Process Std Dev  Process Description  K 
A  0.3030  0.00100  0.00033  None  0.25 
B_C  10.7185  0.01070  0.00357  None  0.25 
E  0.5030  0.00100  0.00033  None  0.25 
F  1.0275  0.00050  0.00017  None  0.25 
H  7.0710  0.00200  0.00067  None  0.25 
I  0.4590  0.00100  0.00033  None  0.25 
Table 7.9: Kinematic Assembly Variables (Geometric Tolerances Not Applied)
Variable Name  Nominal  WC  +/ Assembly Variation (ZASM = 6.00)  
RSS  SSA  SSC  
D  0.0563  0.00148  0.00219  0.00219  0.00292 
G  0.2492  0.00209  0.00283  0.00283  0.00378 
5.2000  0.00000  0.00000  0.00000  0.00000 
Table 7.10: RSS Percent Rejects (Geometric Tolerances Not Applied)
Dep Len. U2  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  7.7863  0.00088  8.03  4.44e10  0.0000 
Lower  7.7737  6.25  2.05e4  2.0478e10  
Nom Dim  7.7792  Total  2.05e4  2.0478e10 
Table 7.11: Geometric Tolerances
Name  Part Name  Type  Joint  Tolerance Band  Char. Length 
1  Lens 1  Circularity  1  0.00200  N/A 
2  Retainer  Runout  1  0.00040  N/A 
3  Retainer  Runout  3  0.00040  2.1 
4  Housing  Runout  3  0.00040  2.1 
5  Housing  Runout  4  0.00040  3.0 
6  Lens 2  Perpendicularity  4  0.00040  3.0 
Remarks>> The characteristic lengths are used to convert the geometric tolerance bandwidths to an equivalent rotational variation. The formula used to convert them is
+/d[[beta]] = tan^{1}(bandwidth/characteristic length)
where +/d[[beta]] is the equivalent angular variation in radians. The longer the characteristic length given by the user, the smaller the angular variation introduced into the model.
Table 7.12: Kinematic Assembly Variables (Geometric Tolerances Applied)
Variable Name  Nominal  WC  +/ Assembly Variation (ZASM = 6.00)  
RSS  SSA  SSC  
D  0.0563  0.00153  0.00219  0.00219  0.00292 
G  0.2492  0.00269  0.00301  0.00301  0.00391 
5.2000  0.00000  0.00000  0.00000  0.00000 
Table 7.13: Normalized Sensitivities To GAP (Geometric Tolerances Applied)
Variable Name  Sensitivity  Normalized 
1  1.00413  11.03 
2  1.00413  11.03 
A  1.00000  10.98 
E  1.00000  10.98 
H  1.00000  10.98 
I  1.00000  10.98 
3  1.00000  10.98 
4  1.00000  10.98 
5  1.00000  10.98 
other    1.04 
Table 7.14: RSS Percent Rejects (Geometric Tolerances Applied)
Dep Len. U2  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  7.7863  0.00090  7.87  1.78e9  0.0000 
Lower  7.7737  6.12  4.56e4  4.5641e10  
Nom Dim  7.7792  Total  4.56e4  4.5641e10 
Table 7.15: Normalized Sensitivities To TILT (Geometric Tolerances Applied)
Variable Name  Sensitivity  Normalized 
3  1.00000  25.00 
4  1.00000  25.00 
5  1.00000  25.00 
6  1.00000  25.00 
Table 7.16: RSS Percent Rejects (Geometric Tolerances Applied)
Orientation TILT  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  .00075  8.2203e5  9.12  0.00  0.0000 
Lower  .00075  9.12  0.00  0.0000  
Nom Dim  0.0000  Total  0.00  0.0000 
Remarks>> The TILT variation of the assembly will cause essentially no rejects. The only variations that contribute to the TILT are geometric tolerances. For this reason, no allocation can be performed on the assembly based on the TILT specification.
7.10 Tolerance Allocation
Weight Factor Tolerance Allocation
Table 7.17: RSS Weight Factor Tolerance Allocation (Geometric Tolerances Applied).
Dim Name  Fix  WF  Original  Allocated  
+/ Tol  Cp  +/ Tol  Cp  Std Dev  
A  N  1.00  0.00100  1.00  0.00098  1.00  0.00033 
B_C  N  1.00  0.01070  1.00  0.01049  1.00  0.00350 
E  N  1.00  0.00100  1.00  0.00098  1.00  0.00033 
F  N  1.00  0.00050  1.00  0.00049  1.00  0.00016 
H  N  1.00  0.00200  1.00  0.00020  1.00  0.00065 
I  N  1.00  0.00100  1.00  0.00098  1.00  0.00033 
Gap GAP  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  7.7863  0.00094  7.56  1.98e8  1.9762e14 
Lower  7.7737  Target Sig  5.89  1.98e3  1.9802e9 
Nom Dim  7.7792  6.00  Total  1.98e3  1.9802e9 
Table 7.18: WC Weight Factor Tolerance Allocation (Geometric Tolerances Applied).
Dim Name  Fix  WF  Original  Allocated  
+/ Tol  Cp  +/ Tol  Cp  Std Dev  
A  N  1.00  0.00100  0.00073  
B_C  N  1.00  0.01070  0.00780  
E  N  1.00  0.00100  0.00073  
F  N  1.00  0.00050  0.00036  
H  N  1.00  0.00200  0.00146  
I  N  1.00  0.00100  0.00073 
Gap GAP  Spec Limit  WC Variation  
Lower  7.7863  0.00551  Satisfied 
Lower  7.7737  Satisfied  
Nom Dim  7.7792 
Remarks>> The Worst Case tolerance allocation option scales the component tolerances up or down until the (assembly mean) +/ (assembly variation) is equal to the specification limits if the mean is centered. If the mean is not centered, it scales the tolerances until either (assembly mean) + (assembly variation) equals the USL and the new minimum is larger than the LSL, or (assembly mean)  (assembly variation) equals the LSL and the new maximum is smaller than the USL.
Table 7.19: SSC Weight Factor Tolerance Allocation (Geometric Tolerances Applied).
Dim Name  Fix  WF  Original  Allocated  
+/ Tol  Cp  +/ Tol  Cp  Std Dev  
A  N  1.00  0.00100  0.75  0.00074  0.75  0.00025 
B_C  N  1.00  0.01070  0.75  0.01049  0.75  0.00262 
E  N  1.00  0.00100  0.75  0.00074  0.75  0.00025 
F  N  1.00  0.00050  0.75  0.00037  0.75  0.00012 
H  N  1.00  0.00200  0.75  0.00147  0.75  0.00049 
I  N  1.00  0.00100  0.75  0.00074  0.75  0.00025 
Gap GAP  Spec Limit  Assy Std Dev  Assy Sigma  Rejects PPM  Rejects DPU 
Upper  7.7863  0.00094  7.56  1.98e8  1.9762e14 
Lower  7.7737  Target Sig  5.89  1.98e3  1.9802e9 
Nom Dim  7.7792  6.00  Total  1.98e3  1.9802e9 
PROE Modeler: Clutch
 Stack
Blocks  Remote
Positioner 
AutoCAD Modeler: Clutch
 Stack
Blocks  Remote
Positioner 
CATIA Modeler: Crank Slider 
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