# Digital Simulation and Analysis of Assembly-Deviation Prediction Based on Measurement Data
## 1 Introduction  
Aircraft engines, gas turbines and other power equipment components are characterized by a large number of components, complex shape and structure, demanding requirements on processing accuracy, a complex assembly process and so on, as commonly encountered in the manufacturing process. At the design stage, the lack of scientific evaluation system for component tolerance allocation or unreasonable tolerance allocation affects the accuracy of the assembly and the assemblability of the components. At the processing stage, the commonly used traditional one-dimensional and two-dimensional methods of measurement tend to ignore the impact of three-dimensional error. However, the assembly requires a perfect match between three-dimensional parts, which means that even the correct one-dimensional or two-dimensional size does not ensure that the parts can be successfully assembled. At the assembly stage, aircraft engines, gas turbines and other sophisticated equipment have demanding requirements on the accuracy of assembly for working in high-temperature and high-pressure environments [1]. When the processed component exceeds the allowable range of tolerance, it can result in rework that incurs unnecessary time and financial costs. Usually, assembly time accounts for about 20% to 50% of the total production time [2]. Forced assembly occurs even more frequently, which has a significant impact on the quality, performance and lifespan of gas turbines and other important equipment. In some cases, it even causes damage to all the equipment [3]. Assembly is realized in a three-dimensional space, where there are many 3D chains present in non-parallel planes, as well as the geometric deflation effects of angular tolerances and transfer coefficients. A 3D chain represents a kind of complex nonlinear dimensional chain. By establishing a mathematical model for the deviation of the 3D dimensional chain with space vectors, [PERSON] [4] analyzed the impact caused by the deviation of each constituent ring on the deviation of the closed ring according to the sensitivity matrix in it. [PERSON] et al. [5] established the vector ring model of the 3D chain through the concept of vector and then applied it to build the \"dichotomous\" 3D model of deviation simulation. Analytical verification of assemblability and simulation verification of assembly accuracy and performance are the two primary components of digital assembly. Developed countries place profound value on digital assembly. For instance, Boeing has employed model-based design (MBD) in the development of the 787 airliner to achieve rapid development under three-dimensional digital design and simulation technology, leading to a significant reduction in assembly process-planning time [6]. Companies such as GE, Pratt & Whitney and Rollo have optimized the original aero-engine rotor assembly simulation technology with augmented reality technology, resulting in a 50% reduction in the error rate of workers assembling the harness and a 25% reduction in completion time [7]. The digital assembly of aircraft engines and gas turbines has garnered immense attention from numerous scholars. [PERSON] [8] has made strides in this area, by successfully establishing a diagnostic mathematical model of core machine performance, and subsequently analyzing the errors of significant measurement parameters associated with the core machine. [PERSON] et al. 's [9] contributions to this field include the proposal of a dual-objective optimization principle, utilizing the Monte Carlo method to optimize rotor noncentricity and unevenness. [PERSON] [10] has made remarkable headway by introducing the method of Pearson distribution family, which has been instrumental in the modeling and analysis of assembly deviation within typical rotor parts found in aero-engines. Similarly, [PERSON] et al. [11] have made notable contributions, obtaining integrated runout results based on component-measurement outcomes, and determining optimal assembly angles via optimization calculations.