Dynamic modeling and simulation of blade-casing system with rubbing considering time-varying stiffness and mass of casing

doi:10.1007/s10483-025-3244-7

Abstract

Abstract:

As a common fault of the aero-engine, the blade-casing rubbing (BCR) has the potential to cause catastrophic accidents. In this paper, to investigate the dynamic responses and wear characteristics of the system, the laminated shell element is used to establish the finite element model (FEM) of a flexibly coated casing system. Using the shell element, the blade is modeled, and the surface stress of the blade is calculated. The stress-solving method of the blade is validated through comparisons with the measured time-domain waveform of the stress. Then, a dynamic model of a blade-flexibly coated casing system with rubbing is proposed, accounting for the time-varying mass and stiffness of the casing caused by coating wear. The effects of the proposed flexible casing model are compared with those of a rigid casing model, and the stress changes induced by rubbing are investigated. The results show that the natural characteristics of the coated casing decrease due to the coating wear. The flexibly coated casing model is found to be more suitable for studying casing vibration. Additionally, the stress changes caused by rubbing are slight, and the change in the stress maximum is approximately 5% under the influence of the abrasive coating.

Key words: dynamic modeling, flexibly coated casing, rubbing, coating wear, nonlinear vibration

2010 MSC Number:

O322

Hui MA, Hong GUAN, Lin QU, Xumin GUO, Qinqin MU, Yao ZENG, Yanyan CHEN. Dynamic modeling and simulation of blade-casing system with rubbing considering time-varying stiffness and mass of casing. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 849-868.

TrendMD

Figures/Tables 20

Fig. 1

Fig. 2

Table 1

Parameters of blade"

Parameter	Radius of disk $R d$ /mm	Blade length $l$ /mm	Density $ρ$ /(kg $⋅$ m $− 3$ )	Modulus of elasticity $E$ /GPa	Poisson's ratio $ν$
Value	216.52	88.6	4 370	125	0.3

Table 1

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 2

Comparison of stress results"

Acceleration load	Experiment $σ z$ /MPa	Simulation $σ z$ /MPa	Error/%
0.8 $g$	3.12	3.100	0.6
1 $g$	3.64	3.875	6.4
1.2 $g$	4.10	4.650	13.4

Table 2

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Table 3

Natural frequencies of casings with wear and without wear"

Case	$f n1$ /Hz	$f n2$ /Hz	$f n3$ /Hz	$f n4$ /Hz
Casing without wear	973.16	975.61	1 001.90	1 004.30
Casing with wear	959.58	959.64	965.87	965.96

Table 3

Fig. 15

Table A1

The first four natural frequencies of the coated casing with fixed support in Ref. [47]"

Model	$f n1c$ /Hz	$f n2c$ /Hz	$f n3c$ /Hz	$f n4c$ /Hz
Proposed model	1 929.1	1 930.3	1 950.7	1 954.9
ANSYS model	1 929.8	1 930.8	1 951.4	1 955.4
Error/%	$− 0.036$	$− 0.026$	$− 0.036$	$− 0.026$

Table A1

Fig. A1

References 51

[1]	PADOVA, C., DUNN, M. G., BARTON, J., TURNER, K., TURNER, A., and DITOMMASO, D.Casing treatment and blade-tip configuration effects on controlled gas turbine blade tip/shroud rubs at engine conditions. Journal of Turbomachinery, 133, 011016 (2011)
[2]	FAN, S. C., TANG, X. H., and ZHANG, Y. D.Failure analysis of third-stage rotor blade of high-pressure compressor in aero-engine (in Chinese). Failure Analysis and Prevention, 9, 110–114 (2014)
[3]	WU, Z. Y., ZHAO, L. C., YAN, H., YAN, G., CHEN, A., and ZHANG, W. M.Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation. Applied Mathematics and Mechanics (English Edition), 45(1), 111–136 (2024) https://doi.org/10.1007/s10483-024-3071-5
[4]	YANG, Y., OUYANG, H. J., ZENG, J., MA, H., YANG, Y. R., and CAO, D. Q.Investigation on dynamic characteristics of a rod fastening rotor-bearing coupling system with fixed-point rubbing. Applied Mathematics and Mechanics (English Edition), 43(7), 1063–1080 (2022) https://doi.org/10.1007/s10483-022-2819-7
[5]	ZHU, Z. M., WEN, C. M., LONG, T. L., JIN, L., and LI, Y. Q.Bifurcation analysis of a rotor-casing coupling system with bolted flange connection under the effect of rotor-casing rubbing fault. Processes, 11(5), 1301 (2023)
[6]	LI, Y. Q., ZHU, Z. M., WEN, C. M., LIU, K., LUO, Z., and LONG, T. L.Rub-impact dynamic analysis of a dual-rotor system with bolted joint structure: theoretical and experimental investigations. Mechanical Systems and Signal Processing, 209, 111144 (2024)
[7]	SUN, Q., MA, H., ZHU, Y. P., HAN, Q. K., and WEN, B. C.Comparison of rubbing induced vibration responses using varying-thickness-twisted shell and solid-element blade models. Mechanical Systems and Signal Processing, 108, 1–20 (2018)
[8]	MA, X. X., YU, R. H., LI, H. W., JING, J. P., and ZHANG, Z. G.Vibration mitigation in a spline-shafting system via an auxiliary support: simulation and experiment. Mechanical Systems and Signal Processing, 224, 112120 (2025)
[9]	MA, H., GUAN, H., QU, L., YANG, T. R., ZENG, Y., CHEN, Y. Y., ZHU, Z. M., and WANG, H. J.Blade-coating-casing rubbing induced vibration responses and wear characteristics. Tribology International, 194, 109571 (2024)
[10]	JIN, Y. L., LIU, Z. W., YANG, Y., LI, F. S., and CHEN, Y. S.Nonlinear vibrations of a dual-rotor-bearing-coupling misalignment system with blade-casing rubbing. Journal of Sound and Vibration, 497, 115948 (2021)
[11]	HOU, Y. H., CAO, S. Q., and KANG, Y. H.Study on the frequency modulation phenomenon in the rotor system with blade-casing rub-impact fault. International Journal of Nonlinear Mechanics, 159, 104626 (2024)
[12]	WEN, C. M., ZHU, Z. M., FU, X. Z., LONG, T. L., and LI, B.Dynamic analysis of a bolted joint rotor-bearing system with a blade-casing rubbing fault. Processes, 11, 2379 (2023)
[13]	KANG, Y. H., CAO, S. Q., HOU, Y. H., CHEN, N., and LI, B.Dynamics research on the rubbing process and rubbing forms of rotor-blade-casing systems. International Journal of Nonlinear Mechanics, 147, 104242 (2022)
[14]	YANG, Y., CAO, D. Q., and WANG, D. Y.Investigation of dynamic characteristics of a rotor system with surface coatings. Mechanical Systems and Signal Processing, 84, 469–484 (2017)
[15]	WANG, N. F., LIU, C., JIANG, D. X., and BEHDINAN, K.Casing vibration response prediction of dual-rotor-blade-casing system with blade-casing rubbing. Mechanical Systems and Signal Processing, 118, 61–77 (2019)
[16]	WANG, N. F., LIU, C., and JIANG, D. X.Experimental analysis of dual-rotor-support-casing system with blade-casing rubbing. Engineering Failure Analysis, 123, 105306 (2021)
[17]	CHEN, G.Simulation of casing vibration resulting from blade-casing rubbing and its verifications. Journal of Sound and Vibration, 361, 190–209 (2016)
[18]	CHEN, G.Characteristics analysis of blade-casing rubbing based on casing vibration acceleration. Journal of Mechanical Science and Technology, 15(4), 1513–1526 (2015)
[19]	WANG, H. F., CHEN, G., and SONG, P. P.Simulation analysis of casing vibration response and its verification under blade-casing rubbing fault. Journal of Vibration and Acoustics, 138, 031004 (2016)
[20]	ZENG, J., MA, H., YU, K., GUO, X. M., and WEN, B. C.Rubbing response comparisons between single blade and flexible ring using different rubbing force models. International Journal of Mechanical Sciences, 164, 105164 (2019)
[21]	HONG, J., LI, T. R., LIANG, Z. C., and ZHANG, D. Y.Research on blade-casing rub-impact mechanism by experiment and simulation in aeroengines. Shock and Vibration, 2019, 3237960 (2019)
[22]	LI, B. Q., MA, H., ZENG, J., GUO, X. M., and WEN, B. C.Rotating blade-casing rubbing simulation considering casing flexibility. International Journal of Mechanical Sciences, 148, 118–134 (2018)
[23]	GUO, X. M., ZENG, J., MA, H., ZHAO, C. G., YU, X., and WEN, B. C.A dynamic model for simulating rubbing between blade and flexible casing. Journal of Sound and Vibration, 466, 115036 (2020)
[24]	ZHOU, T., JIA, Y. F., ZOU, L. M., JIANG, Z. N., WANG, W. M., and HU, M. H.Vibration characteristics of blade-casing rubbing fault considering rotor-stator coupling. Mechanical Systems and Signal Processing, 218, 111589 (2024)
[25]	JIN, M.The nonlinear dynamic characteristics of the aero-turboshaft engine rotor blade casing rubbing system with the curvic couplings considering the elastoplastic stage. Engineering Analysis with Boundary Elements, 161, 78–102 (2024)
[26]	KANG, Y. H., CAO, S. Q., GAO, T., and YOU, Z. Z.Development and validation of a rotating blade-casing rubbing model by considering the blade deformation and abradable coating. Journal of Sound and Vibration, 2023, 117853 (2023)
[27]	KOJTYCH, S. and BATAILLY, A.Open NASA blade models for nonlinear dynamics simulations. Journal of Engineering for Gas Turbines and Power, 146, 011009 (2024)
[28]	WATSON, M., FOIS, N., and MARSHALL, M. B.Effects of blade surface treatments in tip-shroud abradable contacts. Wear, 338-339, 268–281 (2015)
[29]	TANG, N., ZHANG, B., LORD, C., and MARSHALL, M.Identification of blade operational mode shapes during wear of abradable coating. Journal of Sound and Vibration, 472, 115204 (2020)
[30]	BERTHOUL, B., BATAILLY, A., STAINIER, L., LEGRAND, M., and CARTRAUD, P.Phenomenological modeling of abradable wear in turbomachines. Mechanical Systems and Signal Processing, 98, 770–785 (2018)
[31]	YANG, Y., CAO, D. Q., and WANG, D.Investigation of dynamic characteristics of a rotor system with surface coatings. Mechanical Systems and Signal Processing, 84, 469–484 (2017)
[32]	CAO, D. Q., YANG, Y., CHEN, H. T., WANG, D. Y., JIANG, G. Y., and LI, C. G.A novel contact force model for the impact analysis of structures with coating and its experimental verification. Mechanical Systems and Signal Processing, 70, 1056–1072 (2016)
[33]	BATAILLY, A., LEGRAND, M., MILLECAMPS, A., and GARCIN, F.Numerical-experimental comparison in the simulation of rotor/stator interaction through blade-tip/abradable coating contact. Journal of Engineering for Gas Turbines and Power, 134(8), 082504 (2012)
[34]	BATAILLY, A., CUNY, M., LEGRAND, M., and PHILIPPON, S.Numerical-experimental confrontation in the simulation of tool/abradable material interaction. Journal of Engineering for Gas Turbines and Power, 135(6), 062102 (2013)
[35]	BATAILLY, A., AGRAPART, Q., MILLECAMPS, A., and BRUNEL, J.Experimental and numerical simulation of a rotor/stator interaction event localized on a single blade within an industrial high-pressure compressor. Journal of Sound and Vibration, 375, 308–331 (2016)
[36]	LEGRAND, M., BATAILLY, A., and PIERRE, C.Numerical investigation of abradable coating removal in aircraft engines through plastic constitutive law. Journal of Computational and Nonlinear Dynamics, 7(1), 011010 (2012)
[37]	XIAO, J. G. Y., CHEN, Y., TIAN, J., YANG, H. O., and WANG, A.Numerical investigation of rub-induced composite fan blade vibrations and abradable coating removals. Composite Structures, 226, 111274 (2019)
[38]	XIAO, J. G. Y., CHEN, Y., TIAN, J., YANG, H. O., and WANG, A. E.Interactions between blades and abradable coatings: a numerical approach considering geometrical nonlinearity. International Journal of Mechanical Sciences, 191, 106052 (2021)
[39]	SALVAT, N., BATAILLY, A., and LEGRAND, M.Modeling of abradable coating removal in aircraft engines through delay differential equations. Journal of Engineering for Gas Turbines and Power, 135(10), 102102 (2013)
[40]	WOLLMANN, T., LYE, R., EBERT, C., BECKER, B., BENETT, C., ROUSE, J., ZUMPANO, G., and GUDE, M.Investigation into the effects of abradable evolution and ovalisation during blade-casing interactions. Tribology International, 189, 108900 (2023)
[41]	AGRAPART, Q., NYSSEN, F., LAVAZEC, D., DUFRÉNOY, P., and BATAILLY, A.Multi-physics numerical simulation of an experimentally predicted rubbing event in aircraft engines. Journal of Sound and Vibration, 460, 114869 (2019)
[42]	SUN, W., ZHANG, S. T., LIU, J. M., OUYANG, P. X., LIU, T., WU, C., and YANG, J. H.Numerical prediction of the influence of rub-induced thermal stress on the abradability of CuAl-polyester sealing coating. Journal of Thermal Spray Technology, 32, 1093–1107 (2023)
[43]	LIN, J. W., WU, B., ZHANG, J. H., WEI, Z. L., ZHANG, X. L., and DAI, H. W.Blade-coating rub-impact force analysis using a dissipative contact force model with plastic deformation. Journal of Mechanical Science and Technology, 38(12), 6731–6745 (2024)
[44]	ZHAO, T. Y., LI, K., and MA, H.Study on dynamic characteristics of a rotating cylindrical shell with uncertain parameters. Analysis and Mathematical Physics, 12, 97 (2022)
[45]	GUAN, H., MA, H., QU, X. C., WU, Z. Y., ZENG, J., XIONG, Q., and WANG, H. J.Dynamic stress analysis of cracked rectangular blade: simulation and experiment. International Journal of Mechanical Sciences, 267, 109015 (2024)
[46]	XIONG, Q., GUAN, H., MA, H., WU, Z. Y., GUO, X. M., and WANG, W. W.Dynamic characteristic analysis of rotating blade with breathing crack. Mechanical Systems and Signal Processing, 196, 110325 (2023)
[47]	ZHANG, Y., YANG, S. H., TAI, X. Y., MA, H., GUAN, H., MU, Q. Q., QU, L., and DING, X. F.Study on rubbing-induced vibration characteristics considering the flexibility of coated casings and blades. Machines, 12, 481 (2024)
[48]	GUAN, H., XIONG, Q., MA, H., YANG, Y., ZENG, J., WANG, P. F., and BAO, Y. L.Study on dynamic characteristics of the gear-dual-rotor system with multi-position rubbing. Mechanism and Machine Theory, 191, 105501 (2024)
[49]	WANG, P. F., ZHAO, X., YANG, Y., MA, H., HAN, Q. K., LUO, Z., LI, X. P., and WEN, B. C.Dynamic modeling and analysis of two-span rotor-pedestal system with bearing tilt and extended defect: simulation and experiment. Applied Mathematical Modelling, 125, 1–28 (2024)
[50]	GUAN, H., MA, H., CHEN, X., MU, Q. Q., ZENG, Y., CHEN, Y. Y., WEN, B. C., and GUO, X. M.Nonlinear vibration of rotor-bearing system considering base-motion and bearing-misalignment. Mechanism and Machine Theory, 206, 105933 (2025)
[51]	JI, W. H., YU, Z. Y., MA, H. W., SUN, W., and YANG, T. Z.Hyper-reduction modeling and energy transfer analysis of fluid-transporting series-parallel pipes. International Journal of Mechanical Sciences, 287, 109974 (2025)