Written by Charles Gillis, RE.
Every dimension on every feature on every mechanical component has variation. The allowable variation is specified by the designer through tolerances associated with each dimension. Understanding the effects of these variations on the assembly and assigning appropriate tolerances to dimensions requires performing tolerance stack-ups. Sometimes referred to as tolerance analysis or tolerance assignment, performing stack-ups bring together understanding of manufacturing processes and dimensioning standards (e.g. ASME Y14.5) to meet the assembly’s functional requirements; they are a critical element of good design practice.
The choice of tolerance is as important as any other design choice. Tolerances must not be chosen arbitrarily, but rather with good understanding of assembly requirements, manufacturing process capabilities, and cost. Good designs allow the largest tolerances possible to achieve the functional requirements. Manufacturing methods evolve and improve over time, and larger tolerances give manufacturers greater flexibility to choose methods: part routing, machine tool choice, setups, etc. Overly restrictive tolerances tie the hands of manufacturers and drive costs up. Excessive precision may meet the functional requirements, but is a very poor design choice.
Tolerance stack-up calculations are performed during the design phase to understand sources of variation within a physical assembly, for sensitivity analysis, and to verify that the design intent has been captured on dimensional specifications (detail drawings). Performing stack-up calculations allows designers to assign tolerances based on manufacturing capability, to determine assembly process capability, and to implement process control. This section presents the reasons and methods for conducting tolerance stack-up calculations, including several different mathematical approaches and the appropriateness of each approach. The purpose is to enable the reader to understand the effects of tolerance stack-ups on design choices, ultimately enabling better design choices.
•D. Madsen and D. Madsen, Geometric Dimensioning and Tolerancing, 8th Edition, Goodheart-Willcox, Tinley Park, Il, 2009
•A. Newmann and S. Newmann, GeoTol Pro - A Practical Guide to Geometric Tolerancing per ASME Y14.5-2009, Society of Manufacturing Engineers, Dearborn, MI, 2009
•ASME Y14.5 - 2009: Dimensioning and Tolerancing
DESIGN PRACTICE
Good design practice involves an iterative process:
1.Determine which component dimensions contribute to critical assembly dimensions (the tolerance stack-up chain).
2.Assign preliminary tolerances.
3.Analyze the assembly tolerances.
4.Determine fitness of design, iterate as necessary.
Component dimensions are “in-specification” (in spec) if they are manufactured within their specified tolerances. The combined effect of the individual variations in an assembly may not be in spec, even if the components are. It is sometimes discovered through tolerance analysis that a concept will not achieve the assembly tolerance needed.
When a tolerance stack-up shows the assembly to be “out-of-spec,” the designer reduces and/or re-distributes component dimension tolerances using some of the following methods:
1.Redesign the assembly to reduce the number of components in the stack-up chain, or utilize features that can be produced through inherently more precise processes.
2.Change the component dimensioning scheme to better represent assembly method, apply different geometric controls, or reduce the number of dimensions in the stack-up chain.
3.Eliminate fits from the stack-up chain.
4.Utilize precision locating methods (see Chapter 4) to reduce variation introduced by fits.
5.Reassign / reduce component dimension tolerances.
THE TOLERANCE STACK-UP CHAIN
The first step in a tolerance stack-up is to determine the chain of dimensions contributing to the stack-up. Consider the assembly of components in Figure 3-17. In order for the components to be assembled, it is necessary for the tab of the left component to fit within the slot of the right component. The detail drawings illustrating relevant dimensions are shown in Figure 3-18. The designer is interested in the allowable variation on the size of the lower gap of the tab / slot features, as well as the upper gap of the tab / slot features. Two stack-up calculations are required to determine that positive, non-zero gap distances exist on both the top and bottom clearances.
For chains involving only a few dimensions, it may be tempting to take shortcuts. However, an organized approach is the best approach in determining the tolerance stack-up chain. The procedure is as follows:
1.Understand the assembly. Analyzing unfamiliar designs may require some time to get oriented.
2.Gather the detail component drawings, which may be in process.
3.Make an assembly sketch. Hand-drawn is best, as it is often helpful to illustrate gaps and clearances, show components at extreme positions and orientations, and show other dimensions out of scale.
4.Choose a sign convention (e.g., positive up, positive to the right).
Figure 3-17: Sample Assembly for Analysis
Figure 3-18: Detail Drawings of Component Parts
5.Determine which dimension needs to be solved. This requires a good understanding of the problem in order to convert a design concern into a specific dimension that must be discovered. The concern being addressed by the analysis may require that several stack-ups be evaluated. A stack-up to determine if a retaining ring will fit within its groove would seek to calculate the clearance gap dimension (groove width – ring thickness) and ensure it is positive. More complicated problems can be properly defined and understood with the aid of the sketch.
6.Draw the assembly dimension and label it ‘A’ for assembly. The assembly dimension is the unknown dimension you’re solving for. It should be the only dimension that is not obtained from the component detail drawings.
7.Identify contributing dimensions. Determine which dimensions on the component detail drawings contribute to the size, position, and / or orientation of the assembly dimension sought. These dimensions may be given with bilateral equal or unequal tolerances, unilateral tolerances, limit tolerances, title block tolerances, or geometric controls. Draw the other dimensions on the assembly sketch per the detail drawings. Label them.
8.Make each dimension into a vector by assigning an origin and destination. The choice of origin and destination is arbitrary, but it is