Balancing method without trial weights for rotor systems based on similitude scale model

doi:10.1007/s11465-018-0478-x

Front. Mech. Eng.

2018, Vol. 13

Issue (4) : 571-580 https://doi.org/10.1007/s11465-018-0478-x

RESEARCH ARTICLE

Balancing method without trial weights for rotor systems based on similitude scale model

Ruiduo YE^1,², Liping WANG^1,², Xiaojie HOU^1,², Zhong LUO^1,²(

), Qingkai HAN³

¹. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
². Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, China
³. School of Mechanical Engineering, Dalian University of Technology, Dalian 116000, China

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Abstract

A balancing method without trial weights based on the dynamic similitude scale model was proposed as a solution to the balancing problem of a large-scale rotor system. This method could be used to directly obtain the required coefficients for the balancing problem of the prototype system through a similarity model test without a prototype test. Thus, the weight test process of the prototype system was effectively eliminated in the proposed balancing method. First, with the rotor system as the research object, the analytical expression of the influence coefficient was derived on the basis of rotor dynamics theory. Then, through calculation and dimensional analysis methods, the similitude relationships of the rotor system and the influence coefficient were deduced on the basis of dynamic similitude theory. The correctness of the proposed similitude relationships was verified through numerical simulation and experiment. The balancing method without trial weights was proposed based on the similitude relationship of the influence coefficient. The effect of the balancing method without trial weights was compared with that of the traditional influence coefficient method through numerical simulation, and the results verified the correctness and effectiveness of the proposed balancing method. The results of this study provide theoretical supplements for the balancing method and the similitude design of the rotor system.

Keywords rotor system dynamic similitude balancing without trial weights influence coefficient

Corresponding Author(s): Zhong LUO

Just Accepted Date: 09 October 2017 Online First Date: 14 November 2017 Issue Date: 31 July 2018

Cite this article:

Ruiduo YE,Liping WANG,Xiaojie HOU, et al. Balancing method without trial weights for rotor systems based on similitude scale model[J]. Front. Mech. Eng., 2018, 13(4): 571-580.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-018-0478-x
https://academic.hep.com.cn/fme/EN/Y2018/V13/I4/571

Fig.1 Schematic of the rotor system

Tab.1 Basic dimensions of the rotor system

Fig.2 Simplified structure of the rotor system

Tab.2 Prototype shaft parameters

Tab.3 Prototype disk parameters

Tab.4 Model shaft parameters

Tab.5 Model disk parameters

System type	Bearing location	Stiffness/(N?m⁻¹)	Damping/( $N · s · m − 1$ )	Axial position/mm
Prototype	1	$1.50 × 106$	700	189.0
Prototype	2	$2.00 × 106$	700	1359.0
Model	1	$2.65 × 105$	124	133.6
Model	2	$3.54 × 105$	124	961.0

Tab.6 Supporting stiffness and damping

Tab.7 Critical speed of the prototype and model

Fig.3 Vibration mode of the prototype and model. (a) The first-order and (b) second-order modes of the prototype; (c) the first-order and (d) second-order modes of the model

Rotating speed/(r?min⁻¹)	Sensor location	Plane 1/(mm∠(° ))	Plane 2/(mm∠(° ))	Plane 3/(mm∠(° ))	Plane 4/(mm∠(° ))
1800	1	$3.8 × 10 − 5 ∠ − 8.8$	$3.4 × 10 − 5 ∠ − 9.5$	$2.6 × 10 − 5 ∠ − 9.1$	$1.6 × 10 − 5 ∠ − 9.1$
1800	2	$1.7 × 10 − 5 ∠ − 5.5$	$2.2 × 10 − 5 ∠ − 4.3$	$2.8 × 10 − 5 ∠ − 2.9$	$3.2 × 10 − 5 ∠ − 1.7$
3200	1	$3.3 × 10 − 5 ∠ − 10.2$	$3.0 × 10 − 6 ∠ − 178.9$	$5.1 × 10 − 5 ∠ 171.6$	$9.6 × 10 − 5 ∠ 171.3$
3200	2	$8.9 × 10 − 5 ∠ 174.8$	$6.5 × 10 − 5 ∠ − 179.6$	$2.9 × 10 − 5 ∠ − 156.0$	$3.1 × 10 − 5 ∠ − 46.6$

Tab.8 Influence coefficients of the prototype rotor system

Rotating speed/(r?min⁻¹)	Sensor location	Plane 1/(mm∠(° ))	Plane 2/(mm∠(° ))	Plane 3/(mm∠(° ))	Plane 4/(mm∠(° ))
1800	1	$2.2 × 10 − 4 ∠ − 9.5$	$1.9 × 10 − 4 ∠ − 9.4$	$1.5 × 10 − 4 ∠ − 9.5$	$9.2 × 10 − 5 ∠ − 9.5$
1800	2	$9.7 × 10 − 5 ∠ − 6.5$	$1.2 × 10 − 4 ∠ − 4.5$	$1.6 × 10 − 4 ∠ − 2.9$	$1.8 × 10 − 4 ∠ − 1.7$
3200	1	$2.0 × 10 − 4 ∠ − 10.2$	$1.7 × 10 − 5 ∠ − 174.7$	$2.8 × 10 − 4 ∠ 171.6$	$5.3 × 10 − 4 ∠ 171.2$
3200	2	$5.2 × 10 − 4 ∠ 174.9$	$3.7 × 10 − 4 ∠ − 179.8$	$1.7 × 10 − 4 ∠ − 157.6$	$1.7 × 10 − 4 ∠ − 46.8$

Tab.9 Influence coefficients of the model rotor system

Rotating speed/(r?min⁻¹)	Sensor location	Error/(%∠(° ))
Rotating speed/(r?min⁻¹)	Sensor location	Plane 1	Plane 2	Plane 3	Plane 4
1800	1	$0.95 ∠ 0.62$	$0.17 ∠ 0.05$	$1.31 ∠ 0.43$	$1.65 ∠ 0.44$
1800	2	$0.87 ∠ 0.99$	$0.36 ∠ 0.20$	$1.51 ∠ 0.05$	$0.54 ∠ 0.08$
3200	1	$4.99 ∠ 0.00$	$0.17 ∠ 4.20$	$4.33 ∠ 0.07$	$2.77 ∠ 0.10$
3200	2	$2.29 ∠ 0.10$	$0.63 ∠ 0.22$	$2.41 ∠ 1.52$	$2.49 ∠ 0.12$

Tab.10 Prediction error of the influence coefficient

Fig.4 Comparison of the influence coefficients of the prototype and prototype prediction. (a) Plane 1; (b) Plane 2; (c) Plane 3; (d) Plane 4

Fig.5 Prototype and model rotor test systems. (a) Prototype rotor system; (b) model rotor system

Tab.11 Structural parameters of the prototype and model rotor systems

Rotating speed/(r?min⁻¹)	Prototype/(μm∠(° ))	Model/(μm∠(° ))	Prototype prediction/(μm∠(° ))	Prediction error/(%∠(° ))
1000	$0.0114 ∠ − 76.48$	$0.0482 ∠ − 67.18$	$0.0085 ∠ − 67.18$	$25.26 ∠ 9 .30$
1200	$0.0251 ∠ − 82.89$	$0.1014 ∠ − 73.88$	$0.0179 ∠ − 73.88$	$28.59 ∠ 9 .01$
1400	$0.0456 ∠ − 86.23$	$0.1855 ∠ − 75.92$	$0.0328 ∠ − 75.92$	$28.09 ∠ 10 .31$

Tab.12 Prediction error of the influence coefficients

Fig.6 Frequency response of the prototype and model. (a) Prototype system; (b) model system

Fig.7 Dynamic balancing effect of the rotor system. (a) Plane 2; (b) Plane 3

1	Foiles W C, Allaire P E, Gunter E J. Review: Rotor balancing. Shock and Vibration, 1998, 5(5–6): 325–336 https://doi.org/10.1155/1998/648518
2	Zhang S, Zhang Z. Design of an active dynamic balancing head for rotor and its balancing error analysis. Journal of Advanced Mechanical Design Systems & Manufacturing, 2015, 9(1): JAMDSM0001 https://doi.org/10.1299/jamdsm.2015jamdsm0001
3	Han P, Huang S, He G, et al. Experiment based method to evaluate the quality of influential coefficient in rotor dynamic balancing. Journal of Vibration and Shock, 2003, 22(2): 81–85 (in Chinese)
4	Li X, Zheng L, Liu Z. Balancing of flexible rotors without trial weights based on finite element modal analysis. Journal of Vibration and Control, 2013, 19(3): 461–470 https://doi.org/10.1177/1077546311433916
5	Wang W, Gao J, Jiang Z, et al. Principle and application of no trial weight field balancing for a rotating machinery. Journal of Vibration and Shock, 2010, 29(2): 212–215 (in Chinese)
6	Bin G, Yao J, Jiang Z, et al. A method of influence coefficient for rotor dynamic balancing based on the finite element model. Journal of Vibration, Measurement & Diagnosis, 2013, 33(6): 998–1002 (in Chinese)
7	Luo Z, Zhao X, Zhu Y, et al. Determination method of the structure size interval of dynamic similar models for predicting vibration characteristics of the isotropic sandwich plates. Journal of Vibroengineering, 2014, 16(2): 608–622
8	Coutinho C P, Baptista A J, Dias Rodrigues J. Reduced scale models based on similitude theory: A review up to 2015. Engineering Structures, 2016, 119: 81–94 https://doi.org/10.1016/j.engstruct.2016.04.016
9	Zhu Y, Wang Y, Luo Z, et al. Similitude design for the vibration problems of plates and shells: A review. Frontiers of Mechanical Engineering, 2017, 12(2): 253–264
10	De Rosa S, Franco F, Polito T. Structural similitudes for the dynamic response of plates and assemblies of plates. Mechanical Systems and Signal Processing, 2011, 25(3): 969–980 https://doi.org/10.1016/j.ymssp.2010.10.004
11	Zhao J, Wang F, Yu B, et al. Experimental study on the ride comfort of a crawler power chassis scale model based on the similitude theory. Chinese Journal of Mechanical Engineering, 2015, 28(3): 496–503 https://doi.org/10.3901/CJME.2015.0306.024
12	Wu J. Prediction of lateral vibration characteristics of a full-size rotor-bearing system by using those of its scale models. Finite Elements in Analysis and Design, 2007, 43(10): 803–816 https://doi.org/10.1016/j.finel.2007.05.001
13	Baxi C B, Telengator A, Razvi J. Rotor scale model tests for power conversion unit of GT-MHR. Nuclear Engineering and Design, 2012, 251(699): 344–348 https://doi.org/10.1016/j.nucengdes.2011.09.060
14	Hu P. The model experiment analysis of bending vibration of the large rotor system. Mechanical Research Application, 1998, 11(3): 36–38 (in Chinese)
15	Luo Z, Yan Y, Han Q, et al. Analysis of dynamic similarity of the rotor-bearing system and its effects of bearing parameters. Journal of Vibration and Shock, 2012, 31(Suppl): 12–16 (in Chinese)
16	Zhong Y, He Y, Wang Z. Rotor Dynamics. Beijing: Tsinghua University Press, 1987, 3–7 (in Chinese)
17	Kang Y, Lin T W, Chang Y J, et al. Optimal balancing of flexible rotors by minimizing the condition number of influence coefficients. Mechanism and Machine Theory, 2008, 43(7): 891–908 https://doi.org/10.1016/j.mechmachtheory.2007.06.005
18	Li Z. Similarity and Modeling. Beijing: National Defense Industry Press, 1982, 27–52 (in Chinese)
19	Yao M H, Zhang W. Using the extended Melnikov method to study multi-pulse chaotic motions of a rectangular thin plate. International Journal of Dynamics and Control, 2014, 2(3): 365–385 https://doi.org/10.1007/s40435-013-0031-z
20	Qin Z Y, Han Q K, Chu F L. Analytical model of bolted disk-drum joints and its application to dynamic analysis of jointed rotor. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2014, 228(4): 646–663 https://doi.org/10.1177/0954406213489084
21	Zhang D, Fu J, Zhang Q, et al. An effective numerical method for calculating nonlinear dynamics of structures with dry friction: Application to predict the vibration response of blades with underplatform dampers. Nonlinear Dynamics, 2017, 88(1): 223–237 https://doi.org/10.1007/s11071-016-3239-6
22	Jalan A K, Mohanty A R. Model based fault diagnosis of a rotor-bearing system for misalignment and unbalance under steady-state condition. Journal of Sound and Vibration, 2009, 327(3–5): 604–622 https://doi.org/10.1016/j.jsv.2009.07.014
23	Yang X D, Zhang W. Nonlinear dynamics of axially moving beam with coupled longitudinal-transversal vibrations. Nonlinear Dynamics, 2014, 78(4): 2547–2556 https://doi.org/10.1007/s11071-014-1609-5

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