1D Tolerance Stack-Up Cheat Sheet.
Tolerance analysis is like quality control math for assemblies. It checks how all those tiny part variations add up - so even when components aren't perfect, the final product still works like a charm.
Good tolerance analysis ensures that:
• Things keep working - even when parts aren't perfect
• Rework is cut down by catching fit issues early
• Cost and precision is balanced - no need to over-engineer
Key Terms - Made Simple
→ This is the path you're analyzing.
Lower number = tighter tolerance.
Worst case = ultra-safe,
RSS = stat-savvy,
Monte Carlo = simulation-heavy
Tolerance Stack-up Analysis
1. Define functional requirement, focus area and scope for analysis
• What's the goal? Hole alignment? Assembly clearance control?
• Be super specific - stack-ups focus on one critical outcome
2. Map and illustrate the Stack Path
• Trace the path from start to end - feature by feature
• Sketch it with parameters, direction and point of interest for clarity
3. Identify input parameters with nominal value, tolerance and direction
• Use functional dimensions related to interfaces and 2D drawing
• Add all parameters to a table for clarity
• Optional: add parameter info, class and impact
4. Select calculation method
• Select either Worst Case, Root Sum Square or Monte Carlo depending on safety and requirements
5. Calculate result
• Sum up values or write functional expression with parameters
6. Evaluate result and compare to functional limits
• Does your total variation fit the acceptable range?
• If not → tweak tolerances, redesign or loop back
Distributions
Set distribution type for each parameter
• Normal - Variation around mean, most common
• Bernoulli - Binary outcome e.g. assembly position due to clearance
• Uniform - Every value within limits is equally likely
• Trapezoidal - Used when extremes are limited
Methods and Capabilities
Define method based on requirements
• Worst Case - For safety-critical, 2-parameter fits. Sum of max/min limits - very conservative
• Root Sum Square - For medium-long linear stacks. Assumes normal variation - good balance
• Monte Carlo - For complex/non-linear, mixed distributions. Random sampling - most realistic
Check process capability
Are your parts being made within control?
• Cpk = min[(USL-μ)/(3σ) , (μ-LSL)/(3σ)]
- Cpk > 1.33 : Use RSS
- Cpk > 1.00 : Use WC
• Cp = (USL - LSL)/(6σ)
- Cp ≈ 1.33 : Use RSS
- Cp ≈ 1.00 : Use WC
Tolerance Capabilities by process
• Shows which tolerance grades different manufacturing processes can realistically achieve
• CNC machining provides the tightest tolerances
• Injection molding, sheet-metal processing, laser cutting, and especially 3D printing offer progressively looser accuracy
• The color-coding indicates what is easy, normal or difficult for each process
• Emphasizes the importance of choosing tolerances that match the process capability
IT grade tolerances for a 30 mm Dimension
• Shows how ISO 286 IT grades correspond to actual numerical tolerances
• For a nominal size of 30 mm, IT8 gives tolerance of 16.5μm
• This converts to approximately 0.0165 mm, rounded to 0.20 mm for ease of use
• Table highlights how tolerances increase with both IT grade and part size
Injection Molding Tolerance Group (TG) for a 32 mm Dimension
• Shows how DIN EN ISO 20457 tolerance groups define achievable accuracy in injection-molded parts
• For a nominal size of 32 mm, TG5 corresponds to a tolerance of about 0.23 mm
• Table illustrates how tolerances vary with both part size and chosen TG level
• Highlights the impact of material behavior, shrinkage, and process variation on achievable precision
Other Stack-Up Types
Tips and tricks
Alignment - holes across parts, optics, or sensors
Gaps - enclosures, seals, or flush surfaces
Function - load, force, thermal, stiffness, volume
Always check assemblies, not just parts.
Don't over-specify (tighter ≠ better)
Variation stacks up- design for it
= tighter tolerances than you probably need. Use RSS or MC when it makes sense.
Ignoring how parts actually work together
Misjudging functional relationships? That's how you get bad stack-up math
Over-tolerancing
You're not helping - you're just adding complexity and raising costs for no real gain
Forgetting what manufacturing can (actually) do
If it can't be built reliably, it's just expensive scrap waiting to happen.
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