THE THREE STEPS OF TOLERANCE ANALYSIS

Transforming your mechanical CAD designs into real and tangible parts is one of the most rewarding feelings as an engineer.  However, a lot of things can go wrong during this transition.  One of the most common and most overlooked problems are tolerances.  Have you ever tried mounting your TV on your wall, but the holes don’t line up perfectly?  Or do you have to jiggle your keys every time you open the front door?  These issues occur because of poorly controlled tolerances.

Please note that the process described in this post is a smaller outline of a more detailed process described on my whitepaper.  For a more rigorous study of making a tolerance analysis and the tolerance stack, check out my whitepaper.

A Tolerance “Stack”

Even if the production methods allow you to design tight tolerances on a single part, you need to consider the tolerances of all the parts around it to make sure that the overall system functions correctly.

Let’s look at an example design: a microscope fixture.  The bottom surface of our microscope needs to be held at a specific height above a slide (6 ± 0.25 mm), so we plan to design a microscope stand, a slide holder, and a mounting plate for the parts to be mounted on.  We plan to machine all the parts using a CNC milling machine which has an accuracy of ± 0.2 mm.  The machining tolerance zone is smaller than the required tolerance zone, so no problem, right?

Well, actually no.  Each of the machined parts may be 0.2 mm away from what we want.  So, if the microscope stand is 0.2 mm taller after machining, and if the slide holder comes out 0.2 mm thinner, then the slide would actually be 0.4 mm away from the nominal 6.0 mm, causing the image to be out of focus.

In a case like this, you would need to do a tolerance analysis of the tolerance stack-up to make sure the design will work.  A tolerance analysis looks at all the relevant tolerances in a system and adds them so that we can improve the design to meet a certain design requirement.  A tolerance stack-up analysis is usually done on a spreadsheet.  Feel free to use this template to get started.  We will be using this template later in this article to walk through the analysis.

Each time a tolerance analysis is conducted it can generally be split into three steps: Prepare, Stack, and Adjust (or PSA).  The whole tolerance analysis should be conducted twice.  First, you want to take an early look in the Architecture Phase to determine if the general design planned is feasible from a tolerance perspective.  Secondly, you will want to revisit your design in the Detail Design Phase before release to make sure you can confidently purchase parts without worrying about tolerance stack issues.

3 Steps of Tolerance Analysis

Step 1A: Prepare – Rough Block Diagram

Because tolerance analyses are often done before detailed design is complete, I highly recommend making a rough block diagram of your system.  Basic diagrams clarify important interfaces and dimensions before the design is detailed, and they serve as an important tool for communicating your findings at design reviews.

This blog will continue examining the example mentioned earlier: A microscope fixture.  A rough sketch of the parts envisioned for this design are shown below.

Step 1B: Prepare – Find the Manufacturing Tolerances

Now that you have a better sense of the parts used in the stack, you can start finding each part’s manufacturing tolerances.  In the Architecture Phase the goal is to get a rough-order-of-magnitude or “ROM” estimation of each part’s tolerances to catch if your design is way off and needs larger architectural or manufacturing changes.

In the Detail Design Phase, you will want some more confidence in the tolerances you are researching which may entail contacting specific suppliers and comparing different supplier tolerances. For injection molded parts and cast metal parts, a vendor may provide you with a Design for Manufacturability (DFM) document that highlights issues with your design.  Even if the manufacturer had previously quoted certain tolerances, the tolerances may be adjusted (for better or worse) after a rigorous DFM that looks at thin features or possible warping during manufacturing.

I would recommend looking for tolerances on rapid prototyping manufacturer websites. Most prototyping manufacturers automate their process, so they are more likely to post tolerance information online.  For instance, we commonly use Protolabs for machining prototype parts, and they have good design guides with tolerances for CNC milled parts, CNC turned parts, and sheet metal parts.

We will plan to mount the microscope on the microscope stand using some alignment features.  Assume our microscope has a datasheet that claims the tolerance between the bottom of the microscope and a mounting pin is 0.05 mm.

Let’s plan to fit the mounting pin on the microscope into a clearance hole on the microscope stand.  Looking again at the microscope datasheet, we see that the mounting pin has a diameter of 3.95 ± 0.03 mm.  A common ISO 286 tolerance zone for a hole is H7 which has an asymmetric 0.012 mm tolerance zone (4.000 +0.012, -0.000 mm).  For other hole/shaft fits, you can use the tool on Engineer’s Edge.  This tolerance zone is asymmetric, but we will revisit this fit in the stack phase to see how it can be used.

Next, we can assume that the microscope stand and slide holder are made using a CNC milling machine, so we would like to find some tolerances for these parts.  Looking at our manufacturer website, they claim that their usual machining tolerance is 0.005” (0.13 mm).

Finally, the slide thickness will have its own tolerance. If we are early in the design process, we can do a Google search for glass slide manufacturers and take a rough guess at the slide thickness tolerance assuming we will revisit it later.  In this case let’s assume we contacted our slide manufacturer, and the manufacturer quotes their thickness tolerance zone to be within 0.13 mm.

Although the microscope fixture uses generally simple part geometries, it’s worth noting that you should try to visualize how each part will be made, as some production methods can have vastly different tolerances depending on the part orientation.  For instance, sheet metal tolerances between two edges on the same plane can have much tighter tolerances than the dimension between an edge and a bend as shown below.  3D printed parts may also be sensitive to the build orientation.  In general, machined parts have tighter tolerances when the part is only held in one orientation, but tolerances increase between features when the part is flipped or moved within the machine.  For all these manufacturing methods, smaller dimensions may also have tighter tolerances than larger dimensions.

Step 2: Stack – Fill out the Tolerance Stack

Now that we have an idea of the relevant part tolerances, it’s time to create our Tolerance Stack using the template provided.  Let’s enter each tolerance found earlier into the spreadsheet.  It helps if there is a logical order to the tolerances entered in the spreadsheet, so we will look at each dimension along the way from the bottom of the microscope to the top of the slide.

We first enter the tolerance from the microscope bottom to the microscope mounting pin.  Enter the description of the relevant features in the From and To columns and the numerical tolerance on the top line.  Ignore the nominal dimension column for this study, and don’t change the formulas in the gray columns because these will update automatically.  The second section in your tolerance stack should now look like this:

It’s a good idea to be verbose with what dimension you are referring to in the From and To columns so that your thinking can be more clearly communicated to a reviewer and to give yourself a reminder during design.

Next, some care needs to be taken when considering the fitment between the microscope mounting pin and the hole in the microscope holder.  Because this is a clearance hole, there can be some misalignment, and we need to consider the worst-case condition for our tolerance stack.  In this case, we get a maximum misalignment of the microscope to the microscope holder in the Least Material Condition where the hole is at 4.012 mm and the pin is at 3.92 mm.  This means that there is a possible misalignment of 0.046 mm as shown below.

To capture this possible misalignment in our tolerance stack, we need to add another line showing this position tolerance possibly including some notes on how this tolerance was achieved.

The rest of the tolerances are machining tolerances between features on the microscope holder, slide holder, and slide.  We can enter that information into the spreadsheet as shown.  Notice how each dimension is fully described in order from the microscope to the slide.

Finally, you can see the total tolerance of the stack in the third section of the spreadsheet.

For now, the focus of this exercise is the top line of this section: Arithmetic Stack (Worst Case).  The value in the tolerance column represents the sum of all the tolerances in the stack.  It looks like we will currently not be able to meet the requirements because our total possible misalignment is ± 0.486 mm but our requirements state that we need to be within ± 0.25 mm.  We now need to make some fixes to the architecture which we will do in the next step, Adjust.

Step 3: Adjust – Modify Tolerances to Meet Requirements

For tight tolerance applications, you will commonly find yourself adjusting the tolerance stack or the mechanical architecture to meet the requirements.  If the designed tolerances are too loose, you can try some of the following techniques.

1. Reduce the number of parts in the stack
2. Use tighter tolerances on the parts (Alternative vendors or manufacturing methods)
3. Consider using or modifying off-the-shelf precision parts
4. Introduce compliance and float into the system, and perform critical alignment during operation
5. Relax the tolerance requirements (if possible)
6. Use the Statistical Stack, and Adjusted Statistical Stack

First, we will focus on technique 4: introducing compliance into the system.  This concept introduces more complexity to your design, but it is likely to significantly reduce the total tolerance stack of your system.  Instead of fixing each part at a single position and making the machining tolerances tight for all the parts, consider allowing most of the parts to have loose tolerances or move in space. Then introduce an engagement step or clamping step where the critical parts are aligned with a single part.

In our microscope holder example, this could be a custom designed Microscope Head that is spring loaded against the top surface of the slide.  In this case we don’t care as much about the tolerances of the other parts, and only need to control the dimension between the Microscope mount features and the slide surface.  Our system and tolerance stack would then look like:

We are now within our target tolerance zone!  This architecture should work for our design, but it’s worth noting that the complexity has increased: you now have to design the spring mechanism and investigate if the additional forces on the slide cause it to break or warp.

So far, we have been using the Arithmetic Stack (Worst Case) row to determine if the design is feasible.  In the list of possible design adjustment techniques above, we may also consider technique 6 for our example which analyzes the stack using the Statistical Stack (RSS) or Adjusted Stack (RSS * 1.5).  These calculations use the Statistical perspective of the tolerance stack: it is unlikely that all the parts will be at their absolute worst case condition at the same time, so statistical methods (RSS) can be used to better quantify a more realistic and smaller tolerance zone.  The RSS stack multiplied by a factor of 1.5 is sometimes preferred as a more conservative estimate.

Sometimes the tolerances are just too tight to design around, and you need to start looking at more expensive operations.  Some additional options are listed below.

1. Introduce additional design controls (GD&T, inspections)
2. Alignment/calibration in production
3. Use Precision Manufacturing methods

If you need to make architecture or manufacturing changes, repeat the process: Prepare and research what the updates entail, add or remove parts in the Stack, and Adjust the design until the tolerances are reasonable and you can proceed with more detailed design.

Finally, make sure the tolerances mentioned on the tolerance stack match the tolerances used on the mechanical drawings.  Once your drawings and tolerance analysis spreadsheet are aligned, your tolerance analysis is completed, and you are ready for release!

Conclusion

Our Tolerance Analysis walkthrough can help serve as a guide when you look at the tolerances of your own designs.

Tolerance analyses don’t just apply to mechanical parts; in the engineering world, most measurements are approximate and knowing the tolerances of the components you buy can help you better gauge the performance of the overall system.  For example, most electronic components have tolerances associated with their values, or operate within a range of acceptable supply voltages or currents.

Although every project is different, if you remember to Plan, Stack, and Adjust during each of your tolerance analyses, you can quantify the total tolerance of your system, and more confidently release your mechanical designs for production.

About the Author

Neil Foxman is a Senior Systems Engineer at Simplexity’s San Diego office.  In 2014, he graduated with a Bachelor of Science in Mechanical Engineering from Tufts University and has since taken Electrical Engineering master’s degree courses at University of California, San Diego.  Since joining Simplexity in 2015, Neil has worked on a variety of mechanical, electrical, and software designs.