A rotor system with double time delays supported by the high-speed self-acting gas-lubricated bearings with three-axial grooves is modeled to implement active delay control of the system. The differential transformation method is employed to solve the time-dependent compressible gas Reynolds equation due to its rapid convergence rate and minimal calculation error. Based on the precise integration method, a calculation method is proposed to analyze the dynamic responses of a gas bearing-rotor nonlinear system with time delays. The motion analysis of the self-acting gas-lubricated bearing-rotor system with double time delays is implemented by the orbit diagrams, the time series, and the phase diagrams. The influence of time delays and feedback control gains on the dynamic responses of the bearing-rotor nonlinear system is analyzed. The numerical results show that the amplitude of the responses of the system with time delays control is reduced, the motion is more stable and good control effect is achieved when the chosen feedback control gains match the time delays of the bearing-rotor system.
RimpelAKimD. Rotor dynamic performance of flexure pivot tilting pad gas bearings with vibration damper. Trans ASME J Tribol2009; 131: 021101–1–12.
2.
SchiffmannJFavratD. The effect of real gas on the properties of herringbone grooved journal bearings. Tribol Int2010; 43: 1602–1614.
3.
ErtasBHCamattiMMariottiG. Synchronous response to rotor imbalance using a damped gas bearing. Trans ASME J Eng Gas Turbines Power2010; 132: 032501–1–9.
4.
ZhangWMZhouJBMengG. Performance and stability analysis of gas-lubricated journal bearings in MEMS. Tribol Int2011; 44: 887–897.
5.
WangCC. Bifurcation and nonlinear dynamic analysis of united gas-lubricated bearing system. Comput Math Appl2012; 64: 729–738.
6.
LiuLXTeoCJEpsteinAH. Hydrostatic gas journal bearings for micro-turbomachinery. Trans ASME J Vib Acoust2005; 127: 157–164.
7.
ZhuXHAndresLS. Rotor dynamic performance of flexure pivot hydrostatic gas bearings for oil-free turbomachinery. Trans ASME J Eng Gas Turbines Power2007; 129: 1020–1027.
8.
YangLHQiSMYuL. Analysis on dynamic performance of hydrodynamic tilting-pad gas bearings using partial derivative method. Trans ASME J Tribol2009; 131: 011703–1–8.
9.
YangLHQiSMGengHP. Stability analysis on rotor systems supported by self-acting tilting-pad gas bearings with frequency effects. Chin J Mech Eng (English edition)2011; 24: 380–385.
10.
Bou-SaïdBGrauGIordanoffI. On the nonlinear rotor dynamic effects of aerodynamic bearings with simple flexible rotors. Trans ASME J Eng Gas Turbines Power2008; 130: 012503–1–9.
11.
WangCCJangMJYehYL. Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings. Chaos Solitons Fractals2007; 32: 566–582.
12.
WangCC. Theoretical and nonlinear behavior analysis of a flexible rotor supported by a relative short herringbone-grooved gas journal bearing system. Physica D Nonlinear Phenom2008; 237: 2282–2295.
13.
WangCCYauHT. Application of a hybrid numerical method to the bifurcation analysis of a rigid rotor supported by a spherical gas journal bearing system. Nonlinear Dyn2008; 51: 515–528.
14.
WangCC. Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated Bearing system. Nonlinear Anal Theory Methods Appl2009; 70: 2035–2053.
15.
YangPZhuKQWangXL. On the non-linear stability of self-acting gas journal bearings. Tribol Int2009; 42: 71–76.
16.
ZhangJZKangWLiuY. Numerical method and bifurcation analysis of Jeffcott rotor system supported in gas journal bearings. Trans ASME J Comput Nonlinear Dyn2009; 4: 011007–1–9.
17.
WangWMLüYJCaoZJ. Nonlinear behaviors and bifurcation of flexible rotor system with axial-grooved self-acting gas bearing support. Adv Sci Lett2011; 4: 1796–1802.
18.
Rashidi MaibodiRKarami MohammadiABakhtiari-NejadF. Bifurcation and nonlinear dynamic analysis of a rigid rotor supported by two-lobe noncircular gas-lubricated journal bearing system. Nonlinear Dyn2010; 61: 783–802.
19.
Rashidi MaibodiRKarami MohammadiABakhtiari-NejadF. Preload effect on nonlinear dynamic behavior of a rigid rotor supported by noncircular gas-lubricated journal bearing systems. Nonlinear Dyn2010; 60: 231–253.
20.
Rashidi MaibodiRKarami MohammadiABakhtiari-NejadF. Numerical analysis of a rigid rotor supported by aerodynamic four-lobe journal bearing system with mass unbalance. Commun Nonlinear Sci Numer Simulat2012; 17: 454–471.
21.
LuYJZhangYFShiXL. Nonlinear dynamic analysis of a rotor system with fixed-tilting-pad self-acting gas-lubricated bearings support. Nonlinear Dyn2012; 69: 877–890.
22.
AlimsMSHouZKNooriMN. Stability and performance of feedback control systems with time delays. Comput Struct1998; 66: 241–248.
23.
JiJC. Stability and Hopf bifurcation of a magnetic bearing system with time delays. J Sound Vib2003; 259: 845–856.
24.
JiJCHansenCH. Stability and dynamics of a controlled van der Pol-Duffing oscillator. Chaos Solitons Fractals2006; 28: 555–570.
25.
SunQZhangBWuXH. Numerical analysis for stability of trivial equilibrium solution of active control systems with double time delays (in Chinese). J Xian Jiaotong Univ2010; 44: 102–106.
26.
ZhaoJK. Differential transformation and its applications for electrical circuits (in Chinese), Wuhan: Huazhong University Press, 1986, pp. 168–172.
27.
JangMJChenCLLiuYC. Two-dimensional differential transform for partial differential equations. Appl Math Comput2001; 121: 261–270.
28.
AbdelHHassanIH. Differential transformation technique for solving higher-order initial value problems. Appl Math Comput2004; 154: 299–311.
29.
AbdelHHassanIH. Comparison differential transformation technique with adomian decomposition method for linear and nonlinear initial value problems. Chaos Solitons Fractals2008; 36: 53–65.
30.
ZhongWX. On precise time-integration method for structural dynamics (in Chinese). J Dalian Univ Technol1994; 34: 131–135.
