Documentation/Modules/Tolerance Stackup

Tolerance Stackup

Dimensional variation analysis

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

  • Linear elastic material behavior unless noted otherwise.
  • User is responsible for load combinations and load factors per the selected design code.
  • Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

  • Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
  • Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

CheckINDUSEUISO
Worst-case stackimplemented———
RSS stackimplemented———

Tolerance Stackup (tolerance)

Purpose

Analyze dimensional variation accumulation in assemblies using worst-case and statistical (RSS) methods, with optional Monte Carlo simulation. Supports GD&T stack analysis for manufacturing tolerance planning.

Physics & theory

Each dimension in a chain contributes uncertainty . Worst-case stack assumes all tolerances at extreme simultaneous values: . Root-sum-square (RSS) assumes independent normal distributions: , typically yielding tighter assembly tolerance than worst-case for the same part tolerances.

Monte Carlo draws random deviations per dimension and sums to build distribution of assembly dimension — mean and standard deviation quantify expected variation. ASME Y14.5 GD&T defines tolerance zones; this module operates on numeric tolerance values extracted from drawings.

Manufacturing modules support design-for-manufacture decisions early in product development. Tolerance analysis should identify critical dimensions in the stack — tightening non-critical tolerances increases cost without improving function.

Fit selection balances assembly ease, alignment precision, and load transmission. Interference fits provide torque capacity without keys but require controlled press force and material compatibility.

Governing equations

Numerical method

Closed-form WC and RSS (engine in manufacturing module). Optional Monte Carlo with uniform or normal sampling over monteCarloSamples iterations. Separate X/Y stacks when 2D variation provided.

Inputs

ParameterDescription
tolerancesArray of ± tolerances per dimension
tolerancesY (optional)Secondary stack direction
monteCarloSamplesSimulation count (0 = skip)
Nominal stack directionAdditive chain definition

Outputs

  • Worst-case total
  • RSS total
  • Monte Carlo mean and standard deviation (if run), per-direction stacks.

Design codes & checks

  • Indicative: Worst-case and RSS stack
  • US: ASME Y14.5 dimensioning and tolerancing
  • ISO: ISO 286 tolerance principles (related)

Assumptions & limitations

  • Linear stack chains; no geometric tolerance zone conversion from GD&T without manual equivalent.
  • RSS assumes normal, independent variations — not valid for skewed processes.
  • Monte Carlo quality depends on sample count and input distribution assumptions.
  • No assembly shift or thermal expansion unless added as dimensions.

References

  1. ASME Y14.5-2018. Dimensioning and Tolerancing.
  2. Wick, C. H., et al. Tolerance Stack Up Analysis, 2nd ed. ASME Press.
  3. ISO 286-1:2010. Limits and fits.
  4. Srinivasan, V. Statistical Tolerance Analysis. ASME Handbook.
  5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
  6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Stack-up arithmetic; low migration complexity.