KEVOS® MAKEOS · Engineering
Signed Three-Term Tolerance Stack
What are the worst-case limits of this signed assembly dimension?
Calculate exact interval bounds for a three-term linear dimension chain with asymmetric tolerances and signed coefficients.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Term 1: nominal dimension | mm | Nominal dimension in the signed assembly equation, measured from a consistent datum. |
| Term 1: lower deviation magnitude | mm | Positive distance from nominal down to the permitted minimum; 0 means no lower deviation. |
| Term 1: upper deviation magnitude | mm | Positive distance from nominal up to the permitted maximum; 0 means no upper deviation. |
| Term 1: signed coefficient | × | Coefficient in the linear equation: +1 adds, −1 subtracts and 0 excludes this term. |
| Term 2: nominal dimension | mm | Nominal dimension in the signed assembly equation, measured from a consistent datum. |
| Term 2: lower deviation magnitude | mm | Positive distance from nominal down to the permitted minimum; 0 means no lower deviation. |
| Term 2: upper deviation magnitude | mm | Positive distance from nominal up to the permitted maximum; 0 means no upper deviation. |
| Term 2: signed coefficient | × | Coefficient in the linear equation: +1 adds, −1 subtracts and 0 excludes this term. |
| Term 3: nominal dimension | mm | Nominal dimension in the signed assembly equation, measured from a consistent datum. |
| Term 3: lower deviation magnitude | mm | Positive distance from nominal down to the permitted minimum; 0 means no lower deviation. |
| Term 3: upper deviation magnitude | mm | Positive distance from nominal up to the permitted maximum; 0 means no upper deviation. |
| Term 3: signed coefficient | × | Coefficient in the linear equation: +1 adds, −1 subtracts and 0 excludes this term. |
Method and formulas
- Define y = c₁n₁ + c₂n₂ + c₃n₃. Each dimension lies between n − lower deviation and n + upper deviation.
- Multiply both limits by the signed coefficient, take the smaller and larger products, then sum the three lower products and three upper products.
- Example: 100 (−0.1/+0.2) − 60 (−0.05/+0.1) − 30 (−0.02/+0.03) mm gives 10 mm nominal, with limits 9.77 to 10.27 mm.
Limitations
- Linear size-only worst-case calculation; geometry, deformation and temperature require separate treatment.
- Coefficients may combine repeated terms for worst-case arithmetic. Correlated constraints can make the interval conservative. There is no RSS or probability claim.
- Three terms are supported. Carry validated limits when combining a longer sub-chain into one term.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- assembly clearance
- worst-case stack
- asymmetric tolerance
Who it is for
- Design engineers
- Drawing checkers
- Toolmakers
What you get
- Nominal result
- Minimum and maximum result
- Contribution of each term
Interpreting the result
- Write the physical equation first and check subtraction directions against the drawing.
- Compare both limits with the functional requirement; a positive nominal gap alone does not establish clearance.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 608–636. Topic reference; implementation and examples are original, and no source tables are reproduced.
- Method: direct interval arithmetic for a linear dimension equation; no statistical tolerancing standard is assumed.
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