Systematic GPS tolerancing
(continued from Hybrid tolerancing)
Systematic GPS tolerancing requires a structured process for tolerancing. The first step is to identify the features in the component that interface with other components in the product. Amongst these features the designer then has to identify the ones that define how the component is positioned (oriented and located) in the product. These are the datum features that define the global datum system for the component.
Once these features are defined, the designer has to decide which one wins, if they are not in perfect alignment with each other. This decides the sequence of the datum features in the global datum system.
The shaft in figure 1 is intended to fit into a housing, where the two bearing surfaces run against corresponding bearing surfaces in the housing. The axial end stop for the shaft is the back side of the hub. A retainer disk will be mounted against the end surface on the right, centered on the smaller diameter and held by a nut threaded onto the thread at far right end of the shaft.
So for the shaft in the example, the two bearing surfaces are the features that control the orientation of the component (the two angles locked by the axis) and the location of the component in the two directions perpendicular to the axis. Therefore they shall be the primary datum for the shaft.
Figure 1: Shaft with bearing surfaces identified as datum features F and R and coaxiality tolerance for the datum features
Figure 1 shows the shaft with the bearing surfaces identified as datum features F and R. It also shows a coaxiality tolerance for the datum features to a common datum made up of the two bearing surfaces themselves. The meaning of the tolerance is shown in figure 2. The tolerance creates a pair of coaxial cylinders that the median lines of the bearing surfaces have to fit within.
Figure 2: The meaning of the tolerance shown in figure 1
This tolerance prevents the problems shown in figure 3 and 4 that we could not prevent with dimensional tolerancing. It is typically necessary to have geometrical tolerances that control the deviations of the datum features, so the coordinate system for the component becomes well defined and robust.
Figure 3: Shaft with off-set bearing surfaces
Figure 4: Shaft with misaligned bearing surfaces
The axial position of the shaft is controlled by the backside of the hub. Therefore this has to be the secondary datum in the global datum system. To ensure that the coordinate system for the component becomes well defined and robust, we add a perpendicularity tolerance to this feature back to the primary datum, see figure 5.
Figure 5: Shaft with backside of the hub identified as datum feature B and perpendicularity tolerance for the datum feature back to the primary datum F-R
Figure 5 shows the shaft with the backside of the hub identified as datum feature B. It also shows a perpendicularity tolerance for this datum feature back to the common datum made up of the two bearing surfaces. The meaning of the tolerance is shown in figure 6. The tolerance creates a space between two planes, perpendicular to datum F-R that the backside of the hub has to fit within.
Figure 6: The meaning of the tolerance shown in figure 5
These two tolerances ensure that the coordinate system for the shaft, which is aligned with the axis created by the bearing surfaces and has its axial zeropoint at the backside of the hub is well defined and robust. It prevents the type of misaligment of the backside of the hub seen in figure 4 in the dimensional tolerancing example.
Once the global datum system has been established, geometrical tolerances referencing this datum system can be used to lock the remaining features of the component in place.
For example, we need to lock the location of the end face that the retainer will fit up against when the shaft is mounted in the housing. It has to be in the right location, so there is a gap that will allow the shaft to turn when it is mounted in the housing. This can be accomplished with the tolerance shown in figure 7.
Figure 7: Shaft with position tolerance to the end face referencing the primary datum F-R and the secondary datum B
Figure 7 shows the shaft with a position tolerance for the end face. The tolerance references the bearing surfaces as primary datum F-R and the backside of the hub as datum feature B. A theoretically exact dimension (TED) of 80,25 mm defines the distance of the middle of the tolerance zone from datum B. The meaning of the tolerance is shown in figure 8. The tolerance creates a space between two planes, perpendicular to datum F-R in a fixed distance from datum B that the end face has to fit within.
Figure 8: The meaning of the tolerance shown in figure 7
When combined with dimensional tolerances for the diameters of the bearing surfaces, as shown in figure 9, these three geometrical tolerances avoid all the shortcomings of the tolerancing in the dimensional tolerancing example.
Figure 9: Shaft with systematically applied geometrical tolerances supplemented with size tolerances expressing the functional requirements to the features unabiguously
The secret to systematic GPS tolerancing is that all the tolerance zones are locked together in one coordinate system. Because the tolerance zones are linked together in a way we could not accomplish with hybrid tolerancing, the tolerance values can be increased while still ensuring the function of the component.
Henrik S. Nielsen