Tolerance Stack-Up Example: Clevis Pin Assembly
This worked example walks through a complete 1D tolerance stack-up analysis for a clevis pin assembly. You'll learn how to identify the critical dimension, build the stack, calculate WC and RSS results, and document your analysis.
The Assembly
A clevis pin connects a rod end to a yoke (clevis). The critical dimension is the lateral clearance between the rod end and the clevis walls. Too little clearance and the assembly binds; too much and there's excessive slop.
Assembly Components
- Clevis (yoke) — Inner width between walls
- Rod end — Width of the bearing housing
- Washers (2×) — One on each side for spacing
Step 1: Identify the Critical Dimension
The total clearance (gap) between the rod end and clevis walls. This is distributed across both sides of the rod end.
Target Specification
- Minimum clearance: 0.10mm (assembly must not bind)
- Maximum clearance: 0.50mm (limit slop for function)
Step 2: Build the Dimension Chain
List every dimension that contributes to the clearance, starting from one clevis wall and ending at the other:
| Dimension | Nominal | Tolerance | Direction |
|---|---|---|---|
| Clevis inner width | 25.00mm | ±0.10mm | + (adds to gap) |
| Washer 1 thickness | 1.00mm | ±0.05mm | − (subtracts) |
| Rod end width | 22.50mm | ±0.08mm | − (subtracts) |
| Washer 2 thickness | 1.00mm | ±0.05mm | − (subtracts) |
Why these directions? The clevis width creates space (positive), while the rod end and washers occupy space (negative). The clearance is what's left over.
Step 3: Calculate Nominal Gap
Nominal Gap = 25.00 − 1.00 − 22.50 − 1.00
Nominal Gap = 0.50mm
Step 4: Calculate Worst-Case (WC)
Sum all tolerance magnitudes:
WC Tolerance = 0.10 + 0.05 + 0.08 + 0.05 = ±0.28mm
WC Min = 0.50 − 0.28 = 0.22mm
WC Max = 0.50 + 0.28 = 0.78mm
⚠️ WC Result: FAIL
WC Max (0.78mm) exceeds the target maximum of 0.50mm. In the worst case, the assembly would have excessive slop.
Step 5: Calculate RSS
Square each tolerance, sum, take square root:
RSS = √(0.10² + 0.05² + 0.08² + 0.05²)
RSS = √(0.0100 + 0.0025 + 0.0064 + 0.0025)
RSS = √0.0214 = ±0.146mm
RSS Min = 0.50 − 0.146 = 0.354mm
RSS Max = 0.50 + 0.146 = 0.646mm
⚠️ RSS Result: MARGINAL
RSS Max (0.646mm) still exceeds 0.50mm, but RSS Min (0.354mm) is well within bounds. Statistical fallout rate would be low but non-zero.
Step 6: Sensitivity Analysis
Which dimension contributes most to the variation?
| Dimension | Tolerance² | % Contribution |
|---|---|---|
| Clevis inner width | 0.0100 | 46.7% |
| Rod end width | 0.0064 | 29.9% |
| Washer 1 | 0.0025 | 11.7% |
| Washer 2 | 0.0025 | 11.7% |
Insight: The clevis inner width (±0.10mm) contributes 47% of the variation. Tightening this tolerance from ±0.10 to ±0.05 would have the biggest impact.
Step 7: Design Decision
Based on this analysis, the engineer has options:
- Tighten clevis tolerance — Reduce from ±0.10 to ±0.05mm. Reduces WC to ±0.23mm.
- Accept RSS analysis — If production volume justifies statistical approach and some fallout is acceptable.
- Redesign nominal — Reduce rod end width to increase nominal gap.
- Add selection/matching — Sort parts and match assemblies (costly but works).
Documenting the Analysis
A complete tolerance stack-up report for design review should include:
- Assembly description and sketch reference
- Target min/max specification with rationale
- Complete dimension chain table
- WC and RSS calculations
- Sensitivity analysis identifying top contributors
- Assumptions (e.g., "No thermal expansion considered")
- Recommendation and decision
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Key Takeaways
- Define the critical dimension clearly — What are the min/max acceptable values and why?
- Get the directions right — Positive dimensions add to the gap, negative ones subtract.
- Run both WC and RSS — Understand the conservative and statistical outcomes.
- Use sensitivity to focus effort — Tighten the biggest contributors first.
- Document your assumptions — Future engineers need to know what you assumed.