Dimensional error calculations in details seldom target to turbine assemblies with many parts in series and parallels up to the transfer of specific dimensional errors in fluid domain. This paper proposes the algebraic theorems for three dimensional error accumulation from every contact pair up to the key surface in the fluid domain of turbines. Liaison feature of contact pairs firstly yields a new variable array that contains both the three dimensional changes and the timing of occurrence for every contact pair. Variable array gives born to operators and related algebraic theorems. Algebraic theorems convert part liaisons into compact formulations. If the propagation in solid or fluid domain takes finite element method, formulation will generate the process that calculates the specific deformations and deviations through these solid and/or fluid domains for the assembly. Case studies find the algebra and methodology have advantages in a compact expression of contact pairs formed in series-parallel assembly processes, and an effect organization of dimensional error accumulations with solid and/or fluid propagations inside.

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