Designing tolerances for machined parts; pin connection on an axle and a bushing
I ran into a fun design exercise during documenting an assembly that required semi-accurate (sloppy, really) dowel pin interfaces. Each of the hole diameters were modeled to the exact same size.
Now you can already see a problem: if the holes are the same size and the connecting piece is also the same size, they each have to be positioned absolutely perfectly to have them mate properly, or at all. And since real-world manufacturing doesn’t work like that, we have to talk tolerances.
The exercise begins by defining how much wiggle-room, or ‘slop’ is allowed in the assembly. Let’s say that in this design, the dowel pin was there only to approximately locate some other feature, so I figured that 0.5 mm of slop was an acceptable amount. See the figures below to get a feel for the problem.
Fig. 1. Illustration of the problem. An axle slides into a bushing, being clocked in with a dowel pin. Use your imagination as to why.
Fig. 2. Technical drawing for the part. I left the feature control frames and the size tolerance for part 2 still empty, since we’re still continuing the conversation. Also, datums A and B for parts 1 and 2 are not referenced to the same entity, I just used the same letters for familiarity’s sake. Consider this figure to be two separate drawings.
We want our parts to fit in any configuration, that is, regardless of feature size (RFS). Even if the holes are manufactured to their smallest allowable sizes and are slightly misaligned, the pin should still slide in. At their nominal sizes, the holes should be perfectly aligned—which is impossible. We must then make least one of the holes bigger.
Vid. 1. If the holes are both at exactly 6 mm, no variation in position can be allowed since they will interfere.
Vid. 2. If one or both holes are larger, some positional deviation is allowed.
The pin manufacturer allows a max of +0.1 mm deviation for hole size. So we’ll give that to hole 1. That leaves us with 0.4 mm of slop to assign to hole 2. If both holes are made to their largest allowable sizes and are perfectly aligned, we hit our 0.5 mm maximum slop target.
Since the assembly also needs to work when the holes are their smallest (maximum material condition, MMC), the second hole must always be larger than nominal. To get a realistic positional tolerance of 0.1 mm for both holes, hole 2 must always be more than 6.2 mm in size. So we define hole 2 to be 6 +0.2/+0.4 mm. This now ensures that the parts will assemble at MMC; by additionally using the MMC modifier in the feature control frames, we get bonus tolerance when the holes are made larger. That gives us a max positional tolerance of 0.2 mm for hole 1 and 0.3 mm for hole 2.
Fig. 3. Applied tolerance to part 2.
When I first sorted out these tolerances, it wasn’t immediately obvious how they’d play together. The core lesson I learned is that positional tolerance is only realized through some of the features giving it—either by a hole being larger or a pin being smaller. To make a sanity check whether the tolerances I’ve applied make sense, I found that booting up any graphics design software, drawing and moving some circles around is really helpful.
Fig. 4. Circles.