考虑接触效应的拉杆转子非线性动力学特性分析
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摘要
本文建立了两盘拉杆式转子轴承系统动力学模型,模型受不平衡力和非线性油膜力激励,拉杆转子轮盘之间接触刚度由接触理论计算得到,采用4阶龙格库塔法进行求解,并使用分岔图和Poincare映射对比分析了不同的转速下,拉杆转子与单盘整体转子的非线性动特性的差异。通过研究得到以下结论:随着转速变化,相比于单盘整体式转子,考虑盘间接触效应的影响会使系统非线性动力学行为更加复杂,在中高转速范围内拉杆转子系统响应状态在周期运动与准周期运动或混沌运动状态之间出现多次反复,拉杆转子系统初次发生分岔的转速值变大,响应的幅值减小,在低转速范围内,盘间接触状态对系统状态影响较小,系统不受转速变化影响。
Nonlinear dynamic model of rod-fastened rotor bearing system was established and the model is considering the influence of unbalanced force and nonlinear oil film force. The contact stiffness between the disks of rod-fastened rotor is calculated by the reasonable contact theory. The nonlinear dynamic characteristics are investigated using fourth-order RungeKutta method. Bifurcation diagram and Poincare map are applied to discuss the difference of integral rotor and rod-fastened rotor bearing system dynamic characteristics at different rotating speed. The conclusions are as following: Compared to the integral rotor system, after considering the contact characteristic of disks, the system nonlinear dynamic will be more complex with the rotating speed increasing. In the higher speed region, rotor system state repeatedly appears between periodic motion,quasi periodic motion and chaotic motion. The first bifurcation speed value of rod-fastened rotor system increases, and the magnitude of the response decreases. In the lower speed range, contact characteristic of disks has little effect on the state of the system, and the system is not affected by the speed change.
Nonlinear dynamic model of rod-fastened rotor bearing system was established and the model is considering the influence of unbalanced force and nonlinear oil film force. The contact stiffness between the disks of rod-fastened rotor is calculated by the reasonable contact theory. The nonlinear dynamic characteristics are investigated using fourth-order RungeKutta method. Bifurcation diagram and Poincare map are applied to discuss the difference of integral rotor and rod-fastened rotor bearing system dynamic characteristics at different rotating speed. The conclusions are as following: Compared to the integral rotor system, after considering the contact characteristic of disks, the system nonlinear dynamic will be more complex with the rotating speed increasing. In the higher speed region, rotor system state repeatedly appears between periodic motion,quasi periodic motion and chaotic motion. The first bifurcation speed value of rod-fastened rotor system increases, and the magnitude of the response decreases. In the lower speed range, contact characteristic of disks has little effect on the state of the system, and the system is not affected by the speed change.
引文
[1]沈存五,葛庆.燃气轮机中心拉杆式转子临界转速计算方法——子结构传递矩阵法[J].热力透平,2010(4):258-263.
[2]卢明剑,孙岩桦,周健,等.拉杆组合转子的刚度修正及动力学建模[J].航空动力学报,2016(9):2203-2209.
[3] Lu M, Geng H, Xu G, et al. Analytical and Experimental Study of Dynamic Characteristics of Rod Fastened Rotor-Bearing System Under Preload Saturation[J]. Proceedings of the Asme Turbo Expo,2013:V07AT29A019.
[4]程礼,钱征文,陈卫,等.结构参数对拉杆转子双稳态振动特性的影响[J].振动.测试与诊断,2012(5):767-772,862-863.
[5] Hei, D.,Lu,Y.J.,Zhang,Y.F.,et al.,Nonlinear dynamic behaviors of rod fastening rotor-hydrodynamic journal bearing system[J]. Arch.Appl. Mech. 2015, 85, 855-875.
[6] Qi Yuan, Jin Gao, Pu Li. Nonlinear Dynamics of the rod-fastened Jeffcott rotor[J]. Vib. Acoust, 2014,136:1-10.
[7]胡亮,柳亦兵,徐晓星,等.带横向裂纹的拉杆转子非线性动力学特性研究[J].噪声与振动控制, 2016, 36(50):11-14,20.
[8]胡亮,柳亦兵,赵立,等.碰摩拉杆转子非线性动力学响应特性[J].动力工程学报,2017,37(7):533-539.
[9] Liang Hu, Yibing Liu, Li Zhao, et al., Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic[J]. Archive of Applied Mechanics, 2016, 86(11):1869-1886.
[10] Liang Hu, Yibing Liu, Li Zhao, et al., Nonlinear dynamic behaviors of circumferential rod fastening rotor under unbalanced pretightening force[J]. Archive of Applied Mechanics, 2016, 86(9):1621-1631.
[11] Liang Hu, Yibing Liu, Wei Teng, et al.,Nonlinear coupled dynamics of a rod fastening rotor under rub-impact and initial permanent deflection[J]. Energies, 2016, 9(11):883.
[12]何鹏.分布式拉杆转子动力学特性分析[D].哈尔滨工业大学,2009.
[13]饶柱石,夏松波,汪光明.粗糙平面接触刚度的研究[J].机械强度, 1994, 16(2):72-75,71.
[14] Peng H, Liu Z, Wang G, et al.,Rotor Dynamic Analysis of Tie-Bolt Fastened Rotor Based on Elastic-Plastic Contact[C].ASME,2011Turbo Expo:Turbine Technical Conference and Exposition. 2011.
[15] Xin Lin, Qi Yuan, Yang Liu,et al.,ANALYSIS OF THE STIFFNESS OF HIRTH COUPLINGS IN ROD-FASTENED ROTORS BASED ON EXPERIMENTAL MODAL PARAMETER IDENTIFICATION[J]. ASME Turbo Expo 2014:Turbine Technical Conference and Exposition,2014.
[16]周莹,程义悦.考虑接触效应的燃气轮机拉杆转子动力学模型研究[J].装备机械,2014(3):53-57.
[17]张锁怀,吕超颖,李俊南.用分形接触理论研究拉杆转子轴承系统动力学模型[J/OL].机械科学与技术,2017(11):1-8.
[18] Capone G. Analytical Description of Fluid-dynamic Force Field in Cylindrical Journal Bearing[J]. L'Energia Elettrica 3, 1991, 3(3):105-110.
[19]邓转志.典型滑动轴承油膜力解析模型的对比分析及试验研究[D].华北电力大学(北京), 2009.
[2]卢明剑,孙岩桦,周健,等.拉杆组合转子的刚度修正及动力学建模[J].航空动力学报,2016(9):2203-2209.
[3] Lu M, Geng H, Xu G, et al. Analytical and Experimental Study of Dynamic Characteristics of Rod Fastened Rotor-Bearing System Under Preload Saturation[J]. Proceedings of the Asme Turbo Expo,2013:V07AT29A019.
[4]程礼,钱征文,陈卫,等.结构参数对拉杆转子双稳态振动特性的影响[J].振动.测试与诊断,2012(5):767-772,862-863.
[5] Hei, D.,Lu,Y.J.,Zhang,Y.F.,et al.,Nonlinear dynamic behaviors of rod fastening rotor-hydrodynamic journal bearing system[J]. Arch.Appl. Mech. 2015, 85, 855-875.
[6] Qi Yuan, Jin Gao, Pu Li. Nonlinear Dynamics of the rod-fastened Jeffcott rotor[J]. Vib. Acoust, 2014,136:1-10.
[7]胡亮,柳亦兵,徐晓星,等.带横向裂纹的拉杆转子非线性动力学特性研究[J].噪声与振动控制, 2016, 36(50):11-14,20.
[8]胡亮,柳亦兵,赵立,等.碰摩拉杆转子非线性动力学响应特性[J].动力工程学报,2017,37(7):533-539.
[9] Liang Hu, Yibing Liu, Li Zhao, et al., Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic[J]. Archive of Applied Mechanics, 2016, 86(11):1869-1886.
[10] Liang Hu, Yibing Liu, Li Zhao, et al., Nonlinear dynamic behaviors of circumferential rod fastening rotor under unbalanced pretightening force[J]. Archive of Applied Mechanics, 2016, 86(9):1621-1631.
[11] Liang Hu, Yibing Liu, Wei Teng, et al.,Nonlinear coupled dynamics of a rod fastening rotor under rub-impact and initial permanent deflection[J]. Energies, 2016, 9(11):883.
[12]何鹏.分布式拉杆转子动力学特性分析[D].哈尔滨工业大学,2009.
[13]饶柱石,夏松波,汪光明.粗糙平面接触刚度的研究[J].机械强度, 1994, 16(2):72-75,71.
[14] Peng H, Liu Z, Wang G, et al.,Rotor Dynamic Analysis of Tie-Bolt Fastened Rotor Based on Elastic-Plastic Contact[C].ASME,2011Turbo Expo:Turbine Technical Conference and Exposition. 2011.
[15] Xin Lin, Qi Yuan, Yang Liu,et al.,ANALYSIS OF THE STIFFNESS OF HIRTH COUPLINGS IN ROD-FASTENED ROTORS BASED ON EXPERIMENTAL MODAL PARAMETER IDENTIFICATION[J]. ASME Turbo Expo 2014:Turbine Technical Conference and Exposition,2014.
[16]周莹,程义悦.考虑接触效应的燃气轮机拉杆转子动力学模型研究[J].装备机械,2014(3):53-57.
[17]张锁怀,吕超颖,李俊南.用分形接触理论研究拉杆转子轴承系统动力学模型[J/OL].机械科学与技术,2017(11):1-8.
[18] Capone G. Analytical Description of Fluid-dynamic Force Field in Cylindrical Journal Bearing[J]. L'Energia Elettrica 3, 1991, 3(3):105-110.
[19]邓转志.典型滑动轴承油膜力解析模型的对比分析及试验研究[D].华北电力大学(北京), 2009.