Accurate rotor installation is essential in order to ensure the performance, reliability, and safety of aero-engines. However, manufacturing errors introduced during the assembly process have the potential to propagate and drive the entire assembly out of their desired specifications. According to the reviewed studies, advanced mathematical models show notable improvements in rotor assembly precision. Reported outcomes include reduction of maximum coaxiality errors from 48.8m to 17.9m, reduced fitting-axis offsets from 21.3m to 8.5m, docking error reductions of 50%–65%, and prediction deviations maintained below 14%. Additional findings show 22.5% reduction in vibration amplitude, 44.1% reduction in unbalance, and error reduction rates reaching 86% using intelligent optimization approaches. This review provides a systematic and comprehensive analysis of the state-of-the-art mathematical models employed for the error propagation analysis in aero-engine rotor assembly. These models are effectively used for evaluating and mitigating errors from the conceptual design to the final assembly. The primary objective of this review study is to identify the most widely adopted mathematical model used for error propagation analysis in aero-engine rotor assembly. Forty-five scholarly research papers, including journal articles, patents, and a conference paper have been thoroughly reviewed to provide key insights pertaining to error propagation rotor assembly. The findings of this study underscore the growing importance of mathematical models in improving aero-engine rotor assembly precision, particularly HMT based models thus paving the way for more efficient and robust aero-engine manufacturing processes. This review serves as a valuable source of knowledge for researchers and engineers, guiding them in selecting the most appropriate model to improve assembly accuracy and ensure the safe functioning of aero-engines.
MantripragadaRWhitneyDE. Modeling and controlling variation propagation in mechanical assemblies using state transition models. IEEE Trans Robot Autom1999; 15: 124–140. https://doi.org/10.1109/70.744608
EwinsDJ. Control of vibration and resonance in aero engines and rotating machinery - an overview. Int J Press Vessel Piping2010; 87: 504–510. https://doi.org/10.1016/j.ijpvp.2010.07.001
5.
WhitneyDEGilbertOLJastrzebskiM. Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies. Res Eng Des1994; 6: 191–210. https://doi.org/10.1007/BF01608399
HussainTYangZPopovAA, et al. Straight-build assembly optimization: a method to minimize stage-by-stage eccentricity error in the assembly of axisymmetric rigid components (two-dimensional case study). J Manuf Sci Eng2011; 133(3): 031014. https://doi.org/10.1115/1.4004202
9.
YangZMcWilliamSPopovAA, et al. A probabilistic approach to variation propagation control for straight build in mechanical assembly. Int J Adv Manuf Technol2013; 64: 1029–1047. https://doi.org/10.1007/s00170-012-4071-x
10.
HussainTMcWilliamSPopovAA, et al. Geometric error reduction in the assembly of axi-symmetric rigid components: a two-dimensional case study. Proc Inst Mech Eng Part B: J Eng Manuf2012; 226: 1259–1274. https://doi.org/10.1177/0954405412443471
11.
YangZHussianTPopovAA, et al. A comparison of different optimization techniques for variation propagation control in mechanical assembly. IOP Conf Ser Mater Sci Eng2011; 26: 012017. https://doi.org/10.1088/1757-899X/26/1/012017
12.
YangZMcWilliamSPopovAA, et al. Dimensional variation propagation analysis in straight-build mechanical assemblies using a probabilistic approach. J Manuf Syst2013; 32: 348–356. https://doi.org/10.1016/j.jmsy.2012.11.008
13.
JinSDingSLiZ, et al. Point-based solution using Jacobian-Torsor theory into partial parallel chains for revolving components assembly. J Manuf Syst2018; 46: 46–58. https://doi.org/10.1016/j.jmsy.2017.11.003
14.
WangLSunCTanJ, et al. Improvement of location and orientation tolerances propagation control in cylindrical components assembly using stack-build assembly technique. Assem Autom2015; 35: 358–366. https://doi.org/10.1108/AA-03-2015-023
15.
SunCZWangLTanJB, et al. Improvement of variation propagation control in mechanical assembly using adjustment assembly technique. Appl Mech Mater2017; 870: 459–464. https://doi.org/10.4028/www.scientific.net/amm.870.459
16.
SunCLiuZLiuY, et al. An adjustment method of geometry and mass centers for precision rotors assembly. IEEE Access2019; 7: 169992–70002. https://doi.org/10.1109/ACCESS.2019.2955124
17.
SunCLiCLiuY, et al. Prediction method of concentricity and perpendicularity of aero engine multistage rotors based on PSO-BP neural network. IEEE Access2019; 7: 132271–132278. https://doi.org/10.1109/ACCESS.2019.2941118
18.
CaoYLiXZhangZ, et al. Dynamic prediction and compensation of aerocraft assembly variation based on state space model. Assem Autom2015; 35: 183–189.
19.
DingSJinSLiZ, et al. Statistical variation analysis using Pearson distribution family based on Jacobian-Torsor model. MATEC Web Conf2017; 139: 00011. https://doi.org/10.1051/matecconf/201713900011
20.
LiRLiuYSunC, et al. Measurement and adjustment of the centroid deviation of aero-engine rotors based on unbalance decoupling. Measurement2023; 212: 112660.
21.
ShiSLiuJGongH, et al. Assembly accuracy analysis and phase optimization of aero-engine multistage rotors considering surface morphology and non-uniform contact deformation. Precis Eng2024; 88: 595–610. https://doi.org/10.1016/j.precisioneng.2024.04.003
22.
YangRHuangJChenZ, et al. Measurement and optimization method for aero-engine rotors based on binocular multi-line laser sensing and virtual assembly. Measurement2025; 242: 115808.
23.
ZhangLLiRShaoC, et al. Measurement and optimization of coaxiality in the assembly of aero-engine rotor by decoupling evaluation datum and component datum. Measurement2025; 259: 119718.
24.
ZhangYSunHZhangX, et al. A fidelity evaluation method for digital twin model of aero-engine assembly characteristics. J Manuf Syst2025; 78: 444–456.
25.
DingSWangSTongH, et al. Concentricity control for multistage rotor assembly based on contour vectorization. Int J Adv Manuf Technol2024; 132: 147–166. https://doi.org/10.1007/s00170-024-13310-7
26.
ZhangXFuXFuB, et al. Multi-objective optimization of aeroengine rotor assembly based on tensor coordinate transformation and NSGA-II. CIRP J Manuf Sci Technol2024; 51: 190–200. https://doi.org/10.1016/j.cirpj.2024.04.004
27.
WuHSunCLuQ, et al. Unbalance prediction method of aero-engine saddle rotor based on deep belief networks and GA-BP intelligent learning. J Intell Manuf2024; 36: 2829–2840. https://doi.org/10.1007/s10845-024-02392-5
28.
HuibinSUNMengLIUChenleWEI. Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data. Chin J Aeronaut2024; 37: 404–416.
29.
ChenJXieLZhaoB, et al. Statistical characteristics analysis of damage parameters of aero-engine rotor system based on artificial neural network. In: Proceedings - 2023 9th International Symposium on System Security, Safety, and Reliability, ISSSR, 2023. IEEE, pp. 95–105.
30.
ZhaoYMuXLiuJ, et al. A decoupling algorithm-based technology for predicting and regulating the unbalance of aircraft rotor assembly considering manufacturing errors. Machines2023; 11(10): 970. https://doi.org/10.3390/machines11100970
31.
HanSYangTZhuQ, et al. Unbalance position of aeroengine flexible rotor analysis and identification based on dynamic model and deep learning. Proc Inst Mech Eng Part C: J Mech Eng Sci2023; 237: 4410–4429. https://doi.org/10.1177/09544062221149316
32.
LiRSunCLiuY, et al. Prediction of the parallelism error and unbalance of aero-engine rotors based on intelligent algorithm. IEEE Trans Instrum Meas2023; 72: 1–10. https://doi.org/10.1109/TIM.2023.3289542
33.
LiTWenZZhaoB, et al. A novel collaborative optimization assembly process method for multi-performance of aeroengine rotors. Int J Adv Manuf Technol2023; 125: 1827–1843. https://doi.org/10.1007/s00170-023-10808-4
34.
ZhouTHuLJinX, et al. Measuring point planning and fitting optimization of the flange and spigot structures of aeroengine rotors. Machines2023; 11(18): 786. https://doi.org/10.3390/machines11080786
35.
KangJHeJPengZ, et al. A novel method for stacking optimization of aeroengine multi-stage rotors based on 3D deviation prediction model. Mech Mach Sci2023: 735–746. https://doi.org/10.1007/978-3-030-99075-6_59
36.
ShenXChenG. Study on the nonconcentricity of the high-pressure rotor of the aero-engine. J Mech Sci Technol2023; 37: 4989–5002. https://doi.org/10.1007/s12206-023-0906-7
37.
ZhangBLuHLiuS, et al. Aero-engine rotor assembly process optimization based on improved Harris Hawk Algorithm. Aerospace2023; 10(1): 28. https://doi.org/10.3390/aerospace10010028
38.
LiJZhaoGZhangP, et al. A digital twin-based on-site quality assessment method for aero-engine assembly. J Manuf Syst2023; 71: 565–580.
39.
SunCWangYCLuQ, et al. Coaxiality and perpendicularity prediction of saddle surface rotor based on deep belief networks. Assem Autom2022; 42: 761–72. https://doi.org/10.1108/AA-06-2022-0163
40.
WangZWuDWangH, et al. Geometric modeling analysis method for stacking assembly deviation of aero engine rotor. Assem Autom2022; 42: 809–816. https://doi.org/10.1108/AA-05-2022-0130
41.
ZhangMLiuYWangD, et al. A coaxiality measurement method for the aero-engine rotor based on common datum axis. Measurement (Lond)2022; 191: 110696. https://doi.org/10.1016/j.measurement.2022.110696
42.
MeiYSunCLiC, et al. Research on intelligent assembly method of aero-engine multi-stage rotors based on SVM and variable-step AFSA-BP neural network. Adv Eng Inform2022; 54: 101798. https://doi.org/10.1016/j.aei.2022.101798
43.
DingSZhengX. Variation analysis considering the partial parallel connection in aero-engine rotor assembly. Energies (Basel)2022; 15(12): 4451. https://doi.org/10.3390/en15124451
44.
LiMWangYSunQ, et al. Assembly accuracy prediction and optimization of aero-engine rotor under the separation condition of assembly and measurement. Int J Adv Manuf Technol2022; 120: 3103–3112. https://doi.org/10.1007/s00170-022-08912-y
45.
LiRLiuYTanJ. Determination of COG based on propagation of positioning and orientation errors in aero-engine rotors. IEEE Trans Instrum Meas2022; 71: 1–11. https://doi.org/10.1109/TIM.2022.3184364
46.
ZhangMLiuYLiR, et al. Perpendicularity detection of multistage rotor considering compensation of datum error. IEEE Trans Instrum Meas2022; 71: 1–9. https://doi.org/10.1109/TIM.2022.3189733
47.
ZhouTGaoHWangX, et al. Error modeling and compensating of a novel 6-DOF aeroengine rotor docking equipment. Chin J Aeronaut2022; 35: 312–324. https://doi.org/10.1016/j.cja.2021.04.009
48.
XuYLiuJWanZ, et al. Rotor fault diagnosis using domain-adversarial neural network with time-frequency analysis. Machines2022; 10(8): 610. https://doi.org/10.3390/machines10080610
49.
SunQLiuXYichaoGAO, et al. Method for calculating eccentricity of rotor assembly axis based on radial runout measurement. Google Patents, 2022.
50.
ZhouTGaoHWangX, et al. Prediction method of aeroengine rotor assembly errors based on a novel multi-axis measuring and connecting mechanism. Machines2022; 10: 387.
51.
DingSZhengXBaoJ, et al. An improved Jacobian-Torsor model for statistical variation solution in aero-engine rotors assembly. Proc Inst Mech Eng Part B: J Eng Manuf2021; 235: 466–483. https://doi.org/10.1177/0954405420958769
52.
ChenYCuiJSunX. A vibration suppression method for the multistage rotor of an aero-engine based on assembly optimization. Machines2021; 9(9): 189. https://doi.org/10.3390/machines9090189
53.
MuXWangYYuanB, et al. A New assembly precision prediction method of aeroengine high-pressure rotor system considering manufacturing error and deformation of parts. J Manuf Syst2021; 61: 112–124. https://doi.org/10.1016/j.jmsy.2021.08.010
54.
DingSHeYZhengX. A probabilistic approach for three-dimensional variation analysis in aero-engine rotors assembly. Int J Aeronaut Space Sci2021; 22: 1092–1105. https://doi.org/10.1007/s42405-021-00384-w
55.
SunHWangJChenK, et al. A tip clearance prediction model for multistage rotors and stators in aero-engines. Chin J Aeronaut2021; 34: 343–357. https://doi.org/10.1016/j.cja.2020.09.015
56.
ZhouTGaoH. Modeling and simulation of the assembly accuracy of aero-engine rotors in the docking processes using a specially designed novel multi-DOF NC motion platform. Aerosp Sci Technol2021; 113: 106648. https://doi.org/10.1016/j.ast.2021.106648
57.
WangXCaoZSunC, et al. Positioning and orientation error measurement and assembly coaxiality optimization in rotors with curvic couplings. Measurement (Lond)2021; 186: 110167. https://doi.org/10.1016/j.measurement.2021.110167
58.
ChenYCuiJSunX. An assembly method for the multistage rotor of an aero-engine based on the dual objective synchronous optimization for the coaxality and unbalance. Aerospace2021; 8(4): 94. https://doi.org/10.3390/aerospace8040094
59.
ChenYCuiJSunX. An unbalance optimization method for a multi-stage rotor based on an assembly error propagation model. Appl Sci (Switzerland)2021; 11: 1–17. https://doi.org/10.3390/app11020887
60.
LiuYLiRSunC, et al. Research on rotary parts vibration suppression based on coaxiality measurement and unbalance constraint. Appl Sci (Switzerland)2021; 11(12): 5747. https://doi.org/10.3390/app11125747
61.
ChenYCuiJSunX, et al. Research on multistage rotor assembly optimization methods for aeroengine based on the genetic algorithm. Complexity2021; 2021: 1–14. https://doi.org/10.1155/2021/8847690
62.
SunWLiTYangD, et al. Dynamic investigation of aeroengine high pressure rotor system considering assembly characteristics of bolted joints. Eng Fail Anal2020; 112: 104510. https://doi.org/10.1016/j.engfailanal.2020.104510
63.
ZhangMZhangMLiuY, et al. Precision measurement and evaluation of flatness error for the aero-engine rotor connection surface based on convex hull theory and an improved PSO algorithm. Meas Sci Technol2020; 31: 085006. https://doi.org/10.1088/1361-6501/ab8170
64.
SunCChenDLiC, et al. A novel constrained optimization-build method for precision assembly of aircraft engine. Assem Autom2020; 40: 869–879. https://doi.org/10.1108/AA-06-2018-085
65.
ChenJXLinSWZhouXL. A comprehensive error analysis method for the geometric error of multi-axis machine tool. Int J Mach Tools Manuf2016; 106: 56–66. https://doi.org/10.1016/j.ijmachtools.2016.04.001
66.
YangFJinSLiZ. A comprehensive study of linear variation propagation modeling methods for multistage machining processes. Int J Adv Manuf Technol2017; 90: 2139–2151. https://doi.org/10.1007/s00170-016-9490-7
67.
LiCLiL. An analytical framework for error propagation effects in multiprocess manufacturing. Math Probl Eng2023; 2023: 1–18. https://doi.org/10.1155/2023/2769757
68.
WangYJiangPLengJ. An extended machining error propagation network model for small-batch machining process control of aircraft landing gear parts. Proc Inst Mech Eng Part G: J Aerosp Eng2017; 231: 1347–1365. https://doi.org/10.1177/0954410016652153
69.
CuiZNiJHeL, et al. Analysis of error propagation in multi-stage machining of PTFE thin-walled parts: A weighted-directed complex network approach. Measurement (Lond)2026; 258: 119527. https://doi.org/10.1016/j.measurement.2025.119527
70.
ZuoXLiBYangJ, et al. Application of the Jacobian-Torsor theory into error propagation analysis for machining processes. Int J Adv Manuf Technol2013; 69: 1557–1568. https://doi.org/10.1007/s00170-013-5088-5
71.
GuoFZouFLiuJH, et al. Assembly error propagation modeling and coordination error chain construction for aircraft. Assem Autom2019; 39: 308–322. https://doi.org/10.1108/AA-07-2018-100
72.
XiYGaoZChenK, et al. Error propagation model using Jacobian-Torsor model weighting for assembly quality analysis on complex product. Mathematics2022; 10(19): 3534. https://doi.org/10.3390/math10193534
73.
GuoSMeiXJiangG. Geometric accuracy enhancement of five-axis machine tool based on error analysis. Int J Adv Manuf Technol2019; 105: 137–153. https://doi.org/10.1007/s00170-019-04030-4
74.
XiaH-JPengW-COuyangX-B, et al. Identification of geometric errors of rotary axis on multi-axis machine tool based on kinematic analysis method using double ball bar. Int J Mach Tools Manuf2017; 122: 161–175. https://doi.org/10.1016/j.ijmachtools.2017.07.006
75.
GuoSJiangGMeiX. Investigation of sensitivity analysis and compensation parameter optimization of geometric error for five-axis machine tool. Int J Adv Manuf Technol2017; 93: 3229–3243. https://doi.org/10.1007/s00170-017-0755-6
76.
LooseJPZhouSCeglarekD. Kinematic analysis of dimensional variation propagation for multistage machining processes with general fixture layouts. IEEE Trans Autom Sci Eng2007; 4: 141–151. https://doi.org/10.1109/TASE.2006.877393
77.
ZuoFJinXZhangZ, et al. Modeling method for assembly variation propagation taking account of form error. Chin J Mech Eng2013; 26: 641–650. https://doi.org/10.3901/CJME.2013.04.641
78.
HuangQShiJYuanJ. Part dimensional error and its propagation modeling in multi-operational machining processes. J Manuf Sci Eng2003; 125: 255–262. https://doi.org/10.1115/1.1532007
ShiHLJiangPY. Quality control in multistage machining processes based on a machining error propagation event-knowledge graph. Adv Manuf2024; 12: 679–697. https://doi.org/10.1007/s40436-024-00481-5
81.
JiangPJiaFWangY, et al. Real-time quality monitoring and predicting model based on error propagation networks for multistage machining processes. J Intell Manuf2014; 25: 521–538. https://doi.org/10.1007/s10845-012-0703-0
82.
LiuDJiangP. The complexity analysis of a machining error propagation network and its application. Proc Inst Mech Eng Part B: J Eng Manuf2009; 223: 623–640. https://doi.org/10.1243/09544054JEM1330
83.
GuoFFangZ. The statistical analysis of the dynamic performance of a gear system considering random manufacturing errors under different levels of machining precision. Proc Inst Mech Eng Part K: J Multi Dyn2020; 234: 3–18. https://doi.org/10.1177/1464419319862165
84.
WangKDuSXiL. Three-dimensional tolerance analysis modelling of variation propagation in multi-stage machining processes for general shape workpieces. Int J Precis Eng Manuf2020; 21: 31–44. https://doi.org/10.1007/s12541-019-00202-0
85.
XieKWellsLCamelioJA, et al. Variation propagation analysis on compliant assemblies considering contact interaction. J Manuf Sci Eng2007; 129: 934–942. https://doi.org/10.1115/1.2752829
86.
WangHCeglarekD. Variation propagation modeling and analysis at preliminary design phase of multi-station assembly systems. Assem Autom2009; 29: 154–166. https://doi.org/10.1108/01445150910945606
87.
SongJWangBHaoX. Optimization algorithms and their applications and prospects in manufacturing engineering. Materials2024; 17(16): 4093. https://doi.org/10.3390/ma17164093
