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Every mechanical assembly faces a hidden challenge that can make or break product quality: tolerance stacking. When multiple part tolerances combine in an assembly, their cumulative effect can lead to parts that won't fit, assemblies that bind, or products that fail quality inspection. Understanding this phenomenon is crucial for any engineer working in manufacturing.
Tolerances protect function. They also add cost. The job of tolerance allocation is to assign the allowed variation for every dimension so the assembly works, manufacturing can build it, and the product isn't unreasonably expensive.
This article (7–9 min read) shows practical allocation strategies, how to use process capability (Cp/Cpk), and a worked example that balances cost and risk.
A poorly allocated tolerance budget causes:
Allocation is where design meets manufacturing: the optimal solution minimizes cost while meeting requirements and preserving manufacturability.
Practical tip: Always start allocation with the function — identify the minimum tolerances that preserve product performance, then relax where possible.
Manufacturing cost vs. tolerance typically follows a nonlinear curve: cost is fairly flat for loose tolerances, then rises slowly, and climbs sharply as tolerances tighten toward the process limits.
Key points:
Simple conceptual formula (illustrative, not universal):
where T is tolerance (width), n > 0 controls steepness, and a,b tune baseline cost and sensitivity.
Use cost curves from vendor quotes or your shop’s historical data whenever possible.
Two naïve approaches:
Equal allocation:
Weighted (sensitivity-based) allocation:
How to compute a simple weighted allocation:
This balances where money buys the most functional improvement.
Rule of thumb: if a feature has low sensitivity (small s_i) and high cost to tighten, leave it loose and tighten high-s_i features instead.
Cp and Cpk summarize a process's ability to make parts within a tolerance.
Definitions:
How to use them:
Practical steps:
Don't assume default machine capability — ask your supplier for σ or Cpk data on the specific feature/process/material.
Different manufacturing processes have typical tolerance ranges (guideline — always verify):
When allocating:
Below is a simple inline SVG placeholder for a tolerance-cost curve — replace with vendor-based chart for real projects.
Caption: cost increases slowly for loose tolerances, then sharply as you approach process limits.
Scenario:
Goal: allocate tolerance widths T_A, T_B, T_C such that:
For cost_i = k_i / T_i, the marginal cost is:
Set magnitudes equal (drop negative sign):
Solve ratios:
Using k_A=100, k_B=50, k_C=200:
Normalize to sum 0.5:
Interpretation:
Worked-example takeaway: equal splits are rarely optimal — use sensitivity and cost to guide allocation.
Use spreadsheets or simple scripts for step 5 — Monte Carlo simulation helps when distributions matter.
Tip: GD&T lets you control form/profile instead of stacking multiple linear tolerances — often cheaper and more robust.
Thermal expansion can erode tight tolerance allocations if operating temperatures vary.
Linear expansion:
Example: aluminum α ≈ 23 × 10^-6 /°C, steel ≈ 12 × 10^-6 /°C.
If a 100 mm aluminum spacer is used over a −20°C → 80°C range (ΔT=100°C):
This 0.23 mm is a significant fraction of a 0.5 mm tolerance budget and must be included in the allocation (either as an environmental tolerance or by specifying material/assembly conditions).
Design actions:
If a vendor cannot provide capability data, assume conservative capability and validate with prototypes — underestimating process variability is costly.
Tolerance allocation is a trade-off: cost vs. risk. Use sensitivity, cost curves, and process capability to make data-driven decisions. Weighted allocation guided by marginal-cost balance typically outperforms equal splits. Always validate allocations with vendors and prototypes.