GlossaryKind of term: Manufacturing termTolerance stack-up
What is a tolerance stack-up?
A tolerance stack-up is the accumulation of tolerances along a chain of dimensions into one resulting dimension, and the analysis of how far it can vary.
The resulting dimension is sometimes called the closing dimension, because it closes the chain. The result is often a distance between features that is not dimensioned directly, or a gap or clearance between parts in an assembly. Each dimension in the chain is a link, and the deviation of every link carries through to the result. A one-dimensional stack adds links along one direction, including geometric tolerances that act in that direction; once angles or variation in several directions matter, a two- or three-dimensional analysis is needed.
What does a tolerance stack-up depend on?
Two methods are in common use. Worst case adds the tolerances of all links in full: as long as every link is within tolerance, the result stays within the calculated limits. A statistical method, such as root sum of squares (RSS), assumes the deviations are independent, centred and roughly normal, with similar spread. The calculated variation is then smaller, which allows wider link tolerances at the price of a calculated chance that the result falls outside its limits. That only holds when the processes behind the links are stable and in control; a process deliberately steered to one side of its tolerance does not fit the assumption. The more links in the chain, the further apart the two results lie. Form, orientation and location tolerances can enter as links; with a maximum material requirement (Ⓜ) their contribution depends on the actual size of the feature.
How does a tolerance stack-up work in practice?
With chain dimensioning, a distance between two features that is not dimensioned directly is the sum of several links. If a function depends on that distance, every link has to be tightly toleranced. Dimensioning the functional dimension directly, between the features that carry the function or from the datum the function rests on, often allows wider tolerances on the other dimensions. The chain does not disappear: it moves to dimensions the function depends on less. Proposing this to the customer can make sense, but the decision rests with the designer, because the change can affect mating parts. A stack-up can also arise on the shop floor. If you work from a different datum in the setup than the drawing uses, the drawing dimension becomes the result of your own machining dimensions, and those need tighter working tolerances. Whether tighter links cost more depends on the process, the machine, the inspection effort and the quantity.
What is a tolerance stack-up often confused with?
A tolerance stack-up is not chain dimensioning: chain dimensioning is a way of dimensioning a drawing, the stack-up is the accumulation of deviations into one resulting dimension. It also occurs with datum-based dimensioning, wherever a dimension is not given directly or parts meet in an assembly. Nor is it a dimensional tolerance: a dimensional tolerance applies to one dimension, the stack-up concerns what several dimensions do together.
Frequently asked questions
Why are some dimensions so tight on the drawing?
Often because they are links in a chain that ends in a functional dimension, such as a clearance or a hole spacing. The more links, the smaller each link's tolerance has to be for the result to hold in the worst case.
Can you propose different dimensioning to the customer?
Yes. Show the chain you have found and how dimensioning the functional dimension directly achieves the same function with wider tolerances on the other dimensions. The designer decides, because the change can affect other parts.
What is the difference between a worst-case and a statistical stack-up?
Worst case adds every tolerance in full; the result stays within its limits as long as every link is good. A statistical method assumes the deviations will not all sit at their limits at once. That allows wider links, with a calculated chance of rejects.