Abstract
To reveal the mechanism of the friction torque on the system stability, the system nonlinear coupled dynamic model is established based on the Lagrange–Maxwell equation, in which the influence of electromechanical parameters and terminal load is considered. The end friction torque is selected as the bifurcation parameter, and its influence on the system stability is studied. At the same time, in order to reduce the impact of the end friction torque on the stability of the system, from the electrical point of view, the motor q-axis voltage is selected as the control variable to construct a nonlinear state feedback controller to improve the stability of the system. In the process of building the controller, the sufficient and necessary conditions for the dynamic Hopf bifurcation and the type of system bifurcation are determined, and the system controller parameters are determined. Through numerical simulation verification, it is found that the designed controller has a better control effect, which provides a reference for practical applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bellamy M, Mickens RE (2007) Hopf bifurcation analysis of the Lev Ginzburg equation. J Sound Vib 308:337–342. https://doi.org/10.1016/j.jsv.2007.06.073
Benner P, Gugercin S, Willcox K (2015) A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev 57:483–531
Chen X, Hu J, Peng Z, Yuan C (2017) Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect. Nonlinear Dyn 88:277–292. https://doi.org/10.1007/s11071-017-3419-z
Chen X, Wei H, Deng T, He Z, Zhao S (2018) Investigation of electromechanical coupling torsional vibration and stability in a high-speed permanent magnet synchronous motor driven system. Appl Math Model 64:235–248. https://doi.org/10.1016/j.apm.2018.07.030
Gao W, Hao Z (2010) Active control and simulation test study on torsional vibration of large turbo-generator rotor shaft. Mech Mach Theory 45:1326–1336. https://doi.org/10.1016/j.mechmachtheory.2010.04.005
Idehara SJ, Flach FL, Lemes D (2018) Modeling of nonlinear torsional vibration of the automotive powertrain. J Vib Control 24:1774–1786. https://doi.org/10.1177/1077546316668687
Jiang S, Li W, Xin G, Sheng L, Yang X (2020) Analysis of torsional vibration characteristics and time delay feedback control of semi-direct drive cutting transmission system in shearer. Chaos Solitons Fractals 132:109607. https://doi.org/10.1016/j.chaos.2020.109607
Ju J, Li W, Wang Y, Fan M, Yang X (2018) Dynamics and nonlinear feedback control for torsional vibration bifurcation in main transmission system of scraper conveyor direct-driven by high-power PMSM. Nonlinear Dyn 93:307–321. https://doi.org/10.1007/s11071-018-4193-2
Lee K-H, Park J-E, Kim Y-K (2019) Design of a stiffness variable flexible coupling using magnetorheological elastomer for torsional vibration reduction. J Intell Mater Syst Struct 30:2212–2221. https://doi.org/10.1177/1045389X19862378
Liu S, Zhao S-S, Wang Z-L, Li H-B (2015) Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback. Chin Phys B. https://doi.org/10.1088/1674-1056/24/1/014501
Liu S, Zhao S, Niu B, Li J, Li H (2016) Stability analysis of a nonlinear electromechanical coupling transmission system with time delay feedback. Nonlinear Dyn 86:1863–1874
Lu C, Wu M, Chen X, Cao W, Gan C, She J (2018) Torsional vibration control of drill-string systems with time-varying measurement delays. Inf Sci 467:528–548. https://doi.org/10.1016/j.ins.2018.07.073
Lu K et al (2019) Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. Mech Syst Signal Process 123:264–297
Ma C, Wang X (2012) Hopf bifurcation and topological horseshoe of a novel finance chaotic system. Commun Nonlinear Sci Numer Simul 17:721–730. https://doi.org/10.1016/j.cnsns.2011.05.029
Mall P, Fidlin A, Krueger A, Groiss H (2017) Simulation based optimization of torsional vibration dampers in automotive powertrains. Mech Mach Theory 115:244–266. https://doi.org/10.1016/j.mechmachtheory.2017.05.010
Nerg J, Rilla M, Ruuskanen V, Pyrhoenen J, Ruotsalainen S (2014) Direct-driven interior magnet permanent-magnet synchronous motors for a full electric sports car. IEEE Trans Ind Electron 61:4286–4294. https://doi.org/10.1109/TIE.2013.2248340
Ren J-J, Liu Y-C, Wang N, Liu S-Y (2015) Sensorless control of ship propulsion interior permanent magnet synchronous motor based on a new sliding mode observer. ISA Trans 54:15–26. https://doi.org/10.1016/j.isatra.2014.08.008
Sheng L, Li W, Wang Y, Fan M, Yang X (2017) Sensorless control of a shearer short-range cutting interior permanent magnet synchronous motor based on a new sliding mode observer. IEEE Access 5:18439–18450. https://doi.org/10.1109/ACCESS.2017.2734699
Sun Y, Thomas M (2011) Control of torsional rotor vibrations using an electrorheological fluid dynamic absorber. J Vib Control 17:1253–1264. https://doi.org/10.1177/1077546309359759
Sun YY, Chuang HC, Xiao HF, Xu JW (2020) Prediction of the normal contact stiffness between elastic rough surfaces in lubricated contact via an equivalent thin layer. J Vib Control. 26(21–22). https://doi.org/10.1177/1077546320910540
Sun YY, Xiao HF, Xu JW (2019) Investigation into the interfacial stiffness ratio of stationary contacts between rough surfaces using an equivalent thin layer. Int J Mech Sci. https://doi.org/10.1016/j.ijmecsci.2019.105147
Szolc T, Konowrocki R, Michajlow M, Pregowska A (2014) An investigation of the dynamic electromechanical coupling effects in machine drive systems driven by asynchronous motors. Mech Syst Signal Process 49:118–134. https://doi.org/10.1016/j.ymssp.2014.04.004
Usop Z, Sarhan AAD, Mardi NA, Wahab MNA (2015) Measuring of positioning, circularity and static errors of a CNC Vertical Machining Centre for validating the machining accuracy. Measurement 61:39–50. https://doi.org/10.1016/j.measurement.2014.10.025
Wang X, Wang M (2008) A hyperchaos generated from Lorenz system. Phys A 387:3751–3758
Wei W, Liang H, Wuest T, Liu A (2018) A new module partition method based on the criterion and noise functions of robust design. Int J Adv Manuf Technol 94:3275–3285. https://doi.org/10.1007/s00170-016-9797-4
Xie B, Wang S, Wang Y, Zhao Z, Xiu J (2015) Magnetically induced rotor vibration in dual-stator permanent magnet motors. J Sound Vib 347:184–199. https://doi.org/10.1016/j.jsv.2015.02.033
Xu J, Wang Z, Tan C, Si L, Liu X (2018) Cutting pattern identification for coal mining shearer through a swarm intelligence-based variable. Transl Wavelet Neural Netw Sens. https://doi.org/10.3390/s18020382
Xu L, Gao Y (2015) Bifurcation and chaotic vibration in electromechanical integrated toroidal drive. J Vib Control 21:1556–1565. https://doi.org/10.1177/1077546313499388
Yu DL, Liu YZ, Wang G, Cai L, Qiu J (2006) Low frequency torsional vibration gaps in the shaft with locally resonant structures. Phys Lett A 348:410–415. https://doi.org/10.1016/j.physleta.2005.08.067
Zhang X, Yu SD (2009) Torsional vibration of crankshaft in an engine-propeller nonlinear dynamical system. J Sound Vib 319:491–514. https://doi.org/10.1016/j.jsv.2008.06.004
Zhou Y, Li H, Zhang H (2018) Model-free deadbeat predictive current control of a surface-mounted permanent magnet synchronous motor drive system. J Power Electron 18:103–115. https://doi.org/10.6113/JPE.2018.18.1.103
Zi B, Sun H, Zhang D (2017) Design, analysis and control of a winding hybrid-driven cable parallel manipulator. Robot Comput Integr Manuf 48:196–208. https://doi.org/10.1016/j.rcim.2017.04.002
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 52005232, 51775543), National Natural Science Foundation of Jiangsu Province, China (Grant No. BK20201024), the Natural Science Foundation of Jiangsu Normal University, China (Grant No. 19XSRX016)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Rights and permissions
About this article
Cite this article
Sheng, L., Li, W., Ye, G. et al. Bifurcation Characteristics Analysis and Control of Electromechanical Transmission System in Shearer. Iran J Sci Technol Trans Mech Eng 45, 813–825 (2021). https://doi.org/10.1007/s40997-021-00439-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40997-021-00439-z