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Transfer Coefficient & Contribution

In product assembly, tolerance build‑up is not a simple sum—it is shaped by assembly relationships and part geometry. Dimensional tolerances do not transfer linearly.

This paper introduces the transfer coefficient to quantify how much each part’s tolerance contributes to the final closed‑loop dimension. We also define contribution to measure the influence of each part’s tolerance on the overall assembly variation.

Transfer Coefficient

Definition

The transfer coefficient measures how much a component loop's variation affects the closed loop. It equals the ratio of closed‑loop variation caused by a component loop to that component loop’s own variation.

Let  L0 be the closed loop and  the component loops, with L0=f(L1,L2,…,Ln).

For the -th component loop:

•If , the loop is increasing. 

•If , the loop is decreasing.

Physical Meaning

The transfer coefficient quantifies how strongly dimensional and tolerance variations from a component loop propagate to the closed loop:

•Higher  → stronger propagation. 

•Lower  → weaker propagation.

Transfer Coefficient: Physical Interpretation

Let:

•A₁ – Component loop dimension 

•α – Assembly angle 

•A₀ – Closed loop dimension

The relationship is:A0=A1 cos α

The dimensional tolerance transferred from A₁ to A₀ is:A1 cos α

This means both the nominal value and the tolerance of A₁ are scaled by .

Here, the transfer coefficient is , which directly controls how variations in the component loop propagate to the closed loop.