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The Tolerance Stack-Up Analysis skill provides capabilities for dimensional tolerance analysis and stack-up calculations, enabling verification of assembly fits and functional requirements through systematic tolerance chain analysis.
Capabilities
Worst-case tolerance analysis
Statistical (RSS) tolerance analysis
Monte Carlo tolerance simulation
GD&T-based stack-up analysis
Assembly feasibility verification
Tolerance allocation optimization
CETOL/3DCS integration
Stack-up report generation
Usage Guidelines
Tolerance Analysis Methods
Method Comparison
Method
Approach
Application
Result
Worst-case
All tolerances at limit
Safety critical
Maximum variation
RSS
Statistical combination
High volume production
Probable variation
Monte Carlo
Random sampling
Complex assemblies
Distribution
6-Sigma
Process capability
Quality control
Defect rate
Worst-Case Analysis
Linear Stack-Up
Gap = Nominal gap +/- sum of all tolerances
For a simple assembly:
Gap_min = Nominal - sum(all positive contributors)
Gap_max = Nominal + sum(all negative contributors)
Or using sensitivity:
Gap = sum(ai * xi)
Tolerance = sum(|ai| * ti)
Where:
ai = sensitivity coefficient (+1 or -1)
xi = nominal dimension
ti = tolerance on dimension i
Direction Convention
Define positive direction:
- Dimensions adding to gap: positive (+1)
- Dimensions subtracting from gap: negative (-1)
Example (shaft in hole):
Gap = Hole_dia - Shaft_dia
Hole: +1 (increases gap)
Shaft: -1 (decreases gap)
Statistical Analysis
Root Sum Square (RSS)
Statistical tolerance (RSS):
T_rss = sqrt(sum(ti^2))
For unequal distributions (weighted):
T_rss = sqrt(sum((ai * ti)^2))
Assumes:
- Normal distribution
- Independent variables
- Process centered at nominal
Process Capability
Cp = (USL - LSL) / (6 * sigma)
Cpk = min((USL - mean)/(3*sigma), (mean - LSL)/(3*sigma))
For 6-sigma quality:
Cpk >= 2.0
PPM defective < 3.4
For tolerance analysis:
sigma = T / (3 * k)
Where k depends on desired Cpk:
k = 3 for Cpk = 1.0
k = 4 for Cpk = 1.33
k = 6 for Cpk = 2.0
Monte Carlo Simulation
Simulation Process
1. Define distribution for each dimension
- Normal: mean, sigma
- Uniform: min, max
- Skewed: appropriate parameters
2. Generate random samples (N = 10,000+)
3. Calculate assembly result for each sample
4. Analyze output distribution
5. Determine percent out-of-spec
Distribution Selection
Scenario
Distribution
Parameters
Machined feature
Normal
Nominal, T/6 (Cpk=2)
Purchased part
Normal/Uniform
Per vendor data
Press fit
Truncated normal
Limits at tolerance
Unknown process
Uniform
Min, max
GD&T in Stack-Ups
Including GD&T
Position tolerance contribution:
Dia_positional / 2 = linear contribution (per direction)
For MMC position:
Contribution = (Position_tol + Bonus_tol) / 2
Bonus tolerance:
Bonus = |Actual_size - MMC_size|
Datum Reference Frame
Stack-up must follow datum precedence:
1. Establish primary datum (constrains normal)
2. Establish secondary datum (constrains one rotation)
3. Establish tertiary datum (constrains remaining DOF)
Feature control frame specifies:
|Position|0.5 MMC|A|B|C|
Analysis Process
Stack-Up Procedure
Define the Problem
What gap/clearance is being analyzed?
What is the acceptance criterion?
What components are involved?
Create the Loop Diagram
Start at one surface
Follow chain to other surface
Identify all contributors
Assign directions
Gather Data
Nominal dimensions
Tolerances (bilateral, unilateral)
Process capabilities
Distribution data
Perform Calculation
Calculate nominal gap
Calculate worst-case variation
Calculate statistical variation
Compare to requirement
Document Results
Stack-up spreadsheet
Loop diagram
Conclusions and recommendations
Tolerance Allocation
Optimization Strategies
If tolerance too tight:
1. Increase gap nominal (if possible)
2. Tighten critical dimension tolerances
3. Add adjustment or shim
4. Change assembly method
5. Accept higher defect rate
If tolerance too loose:
1. Relax non-critical tolerances
2. Reduce manufacturing cost
Cost-Tolerance Relationship
Approximate relationship:
Cost ~ 1 / Tolerance^n
Where n ~ 1.5 to 2 for machining
Tighten tolerances on:
- Lower cost features
- Higher sensitivity contributors
