The Big Picture With A Tolerance Stack-Up:

Product design engineers have multiple considerations to make when they begin the design process. One of the often underappreciated details in mechanical design is a tolerance "stack-up" analysis. For those that are unfamiliar with mechanical design, it's essential to understand a few basics:

1. Professionally manufactured and/or prototyped parts are fabricated to pre-determined tolerances. When you ask for a part to be 1 inch long, the reality is that it’s not ever exactly 1 inch long. It’s close, and it can get closer (more exact) the more you’re willing to pay, but it’s never exactly 1 inch long. And every part you order is going to be slightly different than the previous one. The deviation from “exact” or “nominal” values depends on how “tight” your tolerance is (i.e. how precise do you need/want the part to be?).
2. Tighter tolerances are generally more expensive to produce as they require better machinery and more attention from the machine operator.  

Every business looking to get parts manufactured needs to have a set tolerance for the parts in mind. While it is impossible to precisely get the specifications to where you want them, understanding how much leeway you have for the tolerances helps determine how much variance your design can withstand. 

Specifying Tolerances:

Tolerances are typically specified on the part's or prototype's engineering drawing. Typically this is done via the significant digits on the drawing. Components that are shown with dimensions that have two zeros after the decimal point (e.g., 3.47 inches) are typically cut to a tolerance of 0.01 inches. This means that the finished part will have dimensions that fall somewhere between 3.46 and 3.48 inches. If the same part were shown on the drawing with dimensions of 3.470 inches, then a tolerance of 0.005 (five-thousandths of an inch) would typically apply (unless otherwise specified). The finished part, in this case, would have dimensions between 3.465 and 3.475.

When it comes to mating parts (fitting pieces together), tolerances are critical. Consider a machine that is made by joining together several different components, each with their own tolerances. If every part is produced at the low (or small) end of the tolerance window, will the machine still fit together? Conversely, if all of the parts are made at the high (or large) end of the tolerance window, will the machine still fit together? This is particularly important when it comes to pairing holes and fasteners that mate multiple parts together. The smallest inconsistency has the chance to completely throw off the final product. Keeping the final product in mind when you are setting tolerances can help ensure that a quality product remains the endgame. 

Let's take a look at an example. Here are two cylindrical parts joined by a set screw:

The set screw, when screwed into the external cylinder, fits into a channel found cut into the internal cylinder. This allows the external cylinder to rotate about the internal cylinder while simultaneously preventing lateral motion (separation of the two cylindrical pieces). The set screw is designed to fasten the two parts together and allow the rotational movement of one cylinder about the other. To ensure all of the parts fit together correctly, the following tolerances must be considered:

1. The diameter of the set screw itself (assumed for this example to be 0.1000)
2. The width of the channel on the internal cylinder (shown as nominal value 0.12)
3. The diameter (or radius) of the set screw’s hole on the external cylinder (assumed for this example to be 0.1000)
4. The distance between the center of the hole on the external cylinder and the edge of the external cylinder (shown below as nominal value 0.50)
5. The distance between the center of the internal cylinder channel and the edge of internal cylinder (shown as nominal value 1.50)
   

When designing in 3D CAD software, one typically inputs the nominal dimensions. That is, you specify precisely what dimensions you want and the parts all line up perfectly in the Computer Aided Design (CAD) software. Take a look at the measurements we specified for our example:

In real life, however, the parts are never precisely perfect. Additionally, the closer to perfect you need them, the more expensive they will be to produce. Figuring out how close to perfect measurements you need or how much variance your design can tolerate becomes critical. 

So let's specify a few different tolerances for a few of the critical dimensions we outlined above and see how this might affect our design. For simplicity, we're going to assume that the set screw and the external cylinder hole are cut to near-exact (highly precise, 0.1000) dimensions such that variability in their size is not a factor. We're also going to assume that the internal cylinder is of fixed length. Reference the following table for a summary of potential outcomes based on the specified tolerances:

Now let’s start combining worst-case tolerances to see if we can find any fit issues with our different mating parts. What’s the worst case?

Worst case fit would involve offsetting the channel on the internal cylinder in one direction (e.g., the high tolerance side for the part, 0.13 inches from part edge to channel center) while the same time offsetting the hole location on the external cylinder in the other direction (e.g., the low tolerance side for the part, 0.24 inches from part edge to hole center). If the manufactured part is made to a 0.01" specification, will the set screw still fit in the channel without contacting the wall? The answer is "no." In this case, the hole's alignment and channel are now 0.02 inches offset from its nominal location. This is because the set screw is 0.10 inches wide, and the channel is 0.12 inches, and we assume the usual location of the screw is in the middle of the channel (0.01 inches on each side of it). 

Moving the hole an extra 0.02 inches in one direction means the set screw will no longer fit in the channel, which means our device's functionality is compromised. Add to that worst-case manufacturing for the width of the channel itself. If the 0.12-inch wide channel is machined to 0.11 inches (the low tolerance side for the part), this further compounds the issue. Taking all three of these worst-case values under consideration, it is clear that the set screw will be 0.015 inches too far in one direction and will therefore not fit in the channel.

So how do you account for tolerance stack up in design and engineering?

The answer is that you need to tighten up the tolerances you request from the machine shop or change the nominal values in your design to allow more flexibility for expected variability in the machined parts. Don't be afraid to invest more money into getting the tolerances closer to the optimal design and being mindful of how the mated pairings work together to determine their tolerances. We ran the same analysis at tolerances of 0.005 and 0.001, respectively (without changing the design).

1. In the first case the part misses by 0.0025 inches (just barely).
2. In the second case the part fits even in the worst case. The worst case has the alignment shifting 0.0025 which is less than the 0.01 buffer that is built into the design.

It's important to note that 0.001 (1/1000th of an inch) is a too-tight tolerance for most applications - particularly for prototypes. If you're building a mechanism that needs to be highly precise, this might make more sense. For most other applications, it will probably be overkill. With that in mind, we might want to change our design a little bit to allow for an 0.005" tolerance to work even in the worst-case scenario. We generally find that 0.005" is a reasonable tolerance for most critical dimensions in many prototypes. At the same time, 0.01" is an appropriate tolerance for non-critical measurements (those that don't mate closely with other parts). 

Be forewarned, however, that every project is different. Finding the right tolerance entirely depends on the needs of the particular project. If you're looking for a reliable firm for your product design and prototyping needs, we can be of assistance. Contact Creative Mechanisms today to see how we can help take your product to the next level.