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Example Problems	PRO-E Verification: CHAPTER 5: BICYCLE CRANK ASSEMBLY
Home : Example Problems : Pro-E 2D - Verification - Bike Crank

Figure 5.1 Exploded view of the bicycle crank assembly.

Figure 5.2: Schematic of the bicycle crank with dimension variables.

5.0 Problem Description

The bicycle crank is an assembly consisting of a pedal crank bar, a shaft that turns a sprocket, and a pin that holds them together. The specified assembly variable is U2, which is the gap between the base of the threaded portion of the pin and the edge of the crank against which the nut tightens.

Table 5.1: Manufactured Variables (Independent).

5.1 Design Requirements

Table 5.2: Assembly Variables (Dependent).

Remarks>> If the pin extends too far out of the hole, the nut cannot be tightened properly and the pin will not wedge snugly between the crank and the shaft.

5.2 Modeling Considerations

• Vector C must end at the crank hole center, not the shaft center. Use a cylindrical feature datum on the crank to link the parallel cylinders joint to the crank DRF.
  
  
• A, D, and E are given as diameters with diametral tolerances but used in the model as radii. Therefore their respective tolerances must be divided in half
  
  
• The shaft radius (E/2) is used twice. Those dimensions must be equivalenced.
  
  
• The shaft DRF is cylindrical. TI TOL assumes all cylindrical datums introduce a rotational degree of freedom into the tolerance model. In this case we don't want a degree of freedom at the shaft center, so it must be turned off manually.

5.3 Design Goal

The goal is to use the RSS model to adjust the non-fixed component tolerances until the assembly tolerance on U2 corresponds to the +/-3[[sigma]] specification limits.

5.4 Part DRFs And Feature Datums

Figure 5.3: Diagram showing the location of the part DRFs and feature datums.

Remarks>> Remember to remove the rotational degree of freedom associated with the shaft DRF.

5.5 Kinematic Joints

Figure 5.4: Kinematic joint diagram.

Table 5.3: Kinematic Joints of the Bicycle Crank.

5.6 Network Diagram, Vector Loops, and Design Specifications

One loop is necessary to describe the bicycle crank assembly. A design specification has been applied to the dependent length U2.

Figure 5.5: Network and loop diagrams for the bicycle crank.

Remarks>> Note that vector C ends and vector D/2 begins at the center of the crank hole and not at the center of the shaft. Vectors E/2 pass through the center of the shaft.

A, D and E are the original dimensions, but it is A/2, D/2 and E/2 that are used in the loops. Therefore, the tolerances assigned to those two vectors are half the original dimension tolerances.

To apply the proper specification limits, enter 2.0148 and -1.9852 at the prompts.

5.7 Geometric Tolerances

Three geometric tolerances have been applied to the bicycle crank assembly.

Figure 5.6: Geometric tolerance diagram.

Remarks>> Only those geometric tolerances that affect U2 should be included. The flatness of the shaft notch will cause a rotation of the crank relative to the crank on the opposite side of the bicycle, but will not contribute to the variation of U2. [[alpha]]3 is applied to the flat surface of the pin because the rotation it causes at the shaft/pin joint will affect U1 and U2. The surface straightness of the crank/pin joint will also cause a small rotation of the assembly, but the effect on U2 is insignificant. Therefore it is not included in the model.

5.8 Sensitivity Matrices

Table 5.4: -B^-1A Matrix

Table 5.5: -B^-1F Matrix

	1	2	3
U1	14.30067	14.30067	-3.31000
U2	-14.33559	-14.33559	-2.842 E-14
[[phi]]	0.00000	0.00000	-1.00000

5.9 Predicted Assembly Variation

Table 5.6: Independent Variable Tolerances and Control Factors

Table 5.7: Kinematic Assembly Variables (Geometric Tolerances Not Applied)

Table 5.8: RSS Percent Rejects (Geometric Tolerances Not Applied)

Table 5.9: Geometric Tolerances

Name	Part Name	Type	Joint	Tolerance Band	Char. Length
1	Crank	Circularity	1	0.01000	N/A
2	Shaft	Cylindricity	1	0.01500	N/A
3	Pin	Straightness	2	0.01000	14.1732 mm

Table 5.10: Kinematic Assembly Variables (Geometric Tolerances Applied)

Remarks>> For this model geometric tolerances do not contribute significantly to the critical assembly variation.

Table 5.11: Normalized Sensitivities To U2 (Geometric Tolerances Applied)

Variable Name	Sensitivity	Normalized
D/2	14.3356	12.40
E/2	14.3356	12.40
F	14.3356	12.40
1	14.3356	12.40
2	14.3356	12.40
A/2	14.3007	12.37
B	14.3007	12.37
G	14.3007	12.37
C	1.0000	0.87
3	0.0000	0.00

Table 5.12: RSS Percent Contributions To U2 (Geometric Tolerances Applied)

Table 5.13: RSS Percent Rejects (Geometric Tolerances Applied)

5.10 Tolerance Allocation

Weight Factor Tolerance Allocation

Table 5.14: RSS Weight Factor Tolerance Allocation (Geometric Tolerances Applied).

Table 5.15: SSC Weight Factor Tolerance Allocation (Geometric Tolerances Applied).

Table 5.16: SSA Weight Factor Tolerance Allocation (Geometric Tolerances Applied).

Table 5.17: WC Weight Factor Tolerance Allocation (Geometric Tolerances Applied).