Tolerance stack-up for small manufacturers: a practical walkthrough

A shaft that will not go into its housing, a cover that does not close, a gap that is sometimes 0.2 mm and sometimes negative. These are stack-up problems, and they are usually found on the shop floor. A stack-up on paper, before release, finds them earlier. This walkthrough uses one simple example from start to finish.

The example

A shaft carries a spacer, a bearing and a retaining ring inside a housing. We need the axial gap between the bearing and the ring’s groove wall to stay positive (the ring must fit) and below 0.5 mm (limited end float).

#	Dimension	Nominal (mm)	Tolerance (mm)	Direction
A	Shaft shoulder to groove	30.00	±0.05	+
B	Spacer width	10.00	±0.05	−
C	Bearing width	15.00	±0.12	−
D	Ring thickness	1.50	±0.05	−

The numbers are illustrative.

Step 1: Build the loop

Start at one side of the gap, walk through every dimension to the other side, and give each a sign: positive if it opens the gap, negative if it closes it.

Step 2: Nominal gap

Gap = A − B − C − D = 30.00 − 10.00 − 15.00 − 1.50 = 3.50 mm?

That is clearly not what we wanted: our target was 0 to 0.5 mm. The nominal check alone just caught a design error. Suppose the real design has A = 26.75 mm. Then:

Gap = 26.75 − 10.00 − 15.00 − 1.50 = 0.25 mm.

This is why the nominal line is worth writing down even when it seems obvious.

Step 3: Worst case

Worst-case tolerance of the gap is the sum of all tolerances:

0.05 + 0.05 + 0.12 + 0.05 = ±0.27 mm

So the gap ranges from 0.25 − 0.27 = −0.02 mm to 0.25 + 0.27 = 0.52 mm. Both limits fail: at the minimum the ring does not fit, at the maximum end float exceeds 0.5 mm.

Step 4: RSS (statistical)

RSS assumes the dimensions vary independently and are centered:

√(0.05² + 0.05² + 0.12² + 0.05²) = √(0.0025 + 0.0025 + 0.0144 + 0.0025) = √0.0219 ≈ ±0.148 mm

The statistical range is about 0.10 to 0.40 mm, inside the requirement. Whether you can rely on it depends on volume and process capability, not on the arithmetic.

Step 5: Fix the dominant tolerance

The bearing width (±0.12) contributes most. It is a purchased part, so its tolerance is fixed by the bearing standard and the manufacturer; choose the bearing tolerance class accordingly, or change the design so the bearing width leaves the loop (for example, locate the bearing from a shoulder on the other side).

If the bearing stays in the loop, options in order of cost:

1. Use a selective shim or a wave spring to absorb variation.
2. Tighten A (a machined dimension on your part) from ±0.05 to ±0.02.
3. Use a ring available in several thicknesses and select at assembly.

With A at ±0.02, the worst case becomes 0.02 + 0.05 + 0.12 + 0.05 = ±0.24 mm, so the gap ranges from 0.01 to 0.49 mm. It now passes, but with almost no margin at either end, and it cost a tighter machined tolerance. The bearing still contributes half of the stack, which tells you the most robust fix is in the design (a shim, a spring or a different locating scheme), not in the machining.

Choosing the method

Situation	Method
Prototypes, small batches, unknown suppliers	Worst case
Safety-critical fits	Worst case
High volume, capable processes, independent dimensions	RSS, or RSS with a correction factor
Many dimensions and 3D variation	Variation analysis software

Setting up a stack-up spreadsheet

You do not need special software for one-dimensional stacks. A spreadsheet with these columns covers most cases:

Column	Content
Item	Dimension reference on the drawing
Description	What the dimension is
Nominal	Nominal value
± Tolerance	Half the total tolerance band, after converting unequal limits
Direction	+1 or −1 along the loop
Contribution	Nominal × direction
Squared tolerance	For the RSS column

Sum the contributions for the nominal gap, sum the tolerances for worst case, and take the square root of the summed squares for RSS. Keep the sheet with the drawing revision it was made for.

Unequal tolerances

Real drawings often have unequal limits such as 10 +0.10 / −0.00. Convert them to a mean and an equal tolerance before stacking: 10.05 ±0.05. Using the nominal 10 with “±0.10” overstates the variation and shifts the result.

Including geometric tolerances

Geometric tolerances enter the loop when they move the feature along the direction of the stack. A position tolerance of Ø0.2 on a hole contributes ±0.1 to a stack in any direction across the hole axis. A perpendicularity tolerance on a shoulder contributes to an axial stack only over the length where the mating part bears against it. Bonus tolerance from maximum material condition can enlarge the zone; for worst-case analysis of clearance fits, include the bonus at the extreme that hurts.

When the stack fails

Before tightening tolerances, look at the design options. They are often cheaper:

• Remove a dimension from the loop by locating parts from the same datum.
• Add an adjustment: shims, slots, eccentric pins, set screws.
• Absorb variation with compliant parts: wave springs, O-rings, flexible couplings.
• Select at assembly: sort parts or choose ring thicknesses.

Tightening a machined tolerance is the last resort, because it raises the price of every part forever.

A habit worth building

Write the stack-up for every gap that must stay positive or bounded, before the drawing is released. Keep it with the drawing. When someone proposes “just tightening everything”, the stack-up shows which tolerance actually matters.