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Example Problems	AutoCAD Verification: Pawl and Ratchet
Home : Example Problems : AutoCad - Verification - Pawl and Ratchet

Figure 6.1: Schematic of the pawl and ratchet and corresponding dimension variables.

This model consists of a ratchet, pawl and a housing to which both are attached. The pawl arm has a cylindrical end that stops the clockwise rotation of the ratchet at increments equal to the spacing of the teeth. The assembly is used to rotationally position an object attached to the ratchet.

Table 6.1: Manufactured Variables (Independent).

The assembly variable of interest is the angular orientation of the ratchet, called Phitooth. The variation of this angle should be no more than ±0.4º

Table 6.2: Assembly Variables and Specification Limits.

Remarks>> It will require two closed loops to solve for these six dependent variables.

• Cylinder radii Rtip1 and Rtip2 can be considered independent dimensions because the cylinder is ground or stamped instead of turned. This will allow the radius to vary independently at all points. Therefore, for this assembly, Rtip1 and Rtip2 should not be equivalenced.
  
  
• Phitip1 and Phitip2 both occur at the same cylinder center. CATS has built-in features to handle such cases, but for the most robust model, the user may want to create separate cylindrical datums for each of the clylindrical slider joints.

The goal for this problem is to compare the use of geometric tolerancing vs. traditional tolerancing methods, and to see how each affects the final assembly variations. In order to explore this issue, the assembly will first be modeled using standard dimension tolerances. It will then be modeled with the appropriate dimension tolerances replaced by ANSI Y14.5 geometric tolerances, and the analysis repeated. The PPM rejects for each case will be used to compare the results.

Figure 6.2: Diagram showing the location of the part DRFs.

Remarks>> The cylindrical feature datum on the end of the pawl has two rotational degrees of freedom associated with it. Though CATS has built-in methods of identifying them, it may be best to create two separate cylindrical datums in that location, one for each cylindrical slider joint.

In the AutoCATS version, the user may also want to replace the cylindrical DRF of the ratchet with a rectangular DRF in order to keep from duplicating the rotational degree of freedom introduced by the revolute joint at the same point. In the UNIX versions of CATS, the user can explicitly turn off the redundant degree of freedom in the analyzer.

Four joints are required to model the ratchet and pawl.

Figure 6.3: Kinematic joint diagram.

Remarks>> The two cylindrical slider joints are each associated with a single cylindrical feature datum, so that there are two dependent angles that occur at the cylindrical datum. It is important to place the pawl’s DRF at a location other than this shared cylindrical datum in order for the analyzer to calculate the correct sensitivities for the two dependent angles. The DRF defines a reference vector used by both angles. If the DRF for the pawl is located at the cylindrical datum, then no reference vector is defined.

Table 6.3: Kinematic Joints of the Ratchet and Pawl.

The network diagram in figure 5.4 shows that two loops are necessary to describe the pawl and ratchet assembly. A design specification has been applied to the dependent angle Phitooth.

Figure 6.4: Network diagram and loop diagram for the pawl and ratchet

Remarks>> Loop 2 contains two pairs of redundant vectors. Redundant vectors occur because each loop that passes though a part must pass through that part’s DRF. They are important in this case because they create reference vectors that define the dependent angles. If CATS does not automatically make the two redundant vectors equivalent to each other, it must be done manually or the analysis results will be invalid.

In order to generate loops like those shown, first manually create Loop_2. The autoloop generator option can then create Loop_1.

Four geometric tolerances have been applied to the pawl and ratchet assembly.

Figure 6.5: Geometric tolerance diagram.

Remarks>> For this comparison of geometric tolerances versus dimension tolerances, when using true position, angularity, and profile geometric tolerances , the manufactured part tolerances to which they correspond must be turned off (i.e. set to zero). In other words, it would be redundant to use these three types of geometric tolerances and their manufactured tolerance counterparts at the same time, and would effectively double the variation associated with each dimension.

In order to compare traditional and geometric tolerancing, the geometric tolerance bandwidths must be equivalent to the original dimesion tolerances. For example,

a2 = a4 = 2 * (±TolRtip1,Rtip2)

a3 = CharLen * tan(±Tolthetaroot)

For this case, the characteristic length is equal to Rside2 (remember that CATS assumes that geometric tolerances are given as a bandwidth, while dimension tolerances are assumed to be symetric). The analysis that follows will be split into two parts. For part 1, the standard length and angle tolerances will be used and the geometric tolerances will be set to zero. For part 2, the tolerances of Xpawl, Ypawl, Rtip1, Rtip2, and thetaroot will be set to zero, and the geometric tolerances will be turned on. Part 2 will be split into two cases. For case 1, the position tolerance will be equal to the tolerances of Xpawl and Ypawl. For case 2, the position tolerance will be set equal to the root sum square of the tolerances of Xpawl and Ypawl (see figure 6.6).

Figure 6.6: Two cases of position tolerance.

F Matrix

-B^-1F Matrix

Table 6.4: Independent Variable Tolerances and Control Factors

Table 6.5: Kinematic Assembly Variables (No Geometric Tolerances)

Table 6.6: RSS Percent Contributions To phitooth (No Geometric Tolerances)

Table 6.7: RSS Percent Rejects (Geometric Tolerances Set To Zero)

Table 6.8: Geometric Tolerances--Case 1

Remarks>> For Case 1, the position tolerance zone is set equal to the tolerances of Xpawl and Ypawl. Remember that dimension tolerances are symetric, while geometric tolerances are given as bandwidths.

Table 6.9: Kinematic Assembly Variables (Geometric Tolerancing, Case 1)

Table 6.10: RSS Percent Contributions To phitooth (Geometric Tolerancing, Case 1)

Table 6.11: RSS Percent Rejects (Geometric Tolerancing, Case 1)

Remarks>> For Case 1, the PPM rejects is nearly identical to those that occur with traditional dimension tolerances. This is as it should be, since the two analyses are mathematically equivalent. The purpose of this analysis has been to illustrate this point.

Table 6.12: Geometric Tolerances--Case 2

Remarks>> For Case 2, the position tolerance zone is set equal to the root sum square of the tolerances of Xpawl and Ypawl.

Table 6.13: Kinematic Assembly Variables (Geometric Tolerancing, Case 2)

Table 6.14: RSS Percent Contributions To phitooth (Geometric Tolerancing, Case 2)

Table 6.15: RSS Percent Rejects (Geometric Tolerancing, Case 2)

Remarks>> Increasing the size of the position tolerance zone has a large effect on the number of rejects. Geometric tolerancing has some nice features, but in this assembly, enlarging the tolerance zone greatly increases the rejects.