采煤机截割部传动系统非线性特性研究
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摘要
以采煤机截割部齿轮传动系统为研究对象,建立了非线性动力学模型,将非线性动力学理论应用到采煤机截割部齿轮传动系统中,综合考虑阻尼比和激振频率对系统非线性动力学的影响,运用变步长四阶Runge-Kutta方法对非线性系统微分方程进行了求解,得到不同参数下系统响应的相平面图和庞加莱截面图。结果表明:阻尼比越小,太阳轮位移响应的非线性影响越大;激振频率在一定区间由小变大时,太阳轮位移响应由周期性变为混沌性,再变为周期性。此研究方法为采煤机截割部齿轮传动系统的相关非线性问题提供了理论支撑。
The nonlinear dynamics model of gear transmissionsystem of shearer cutting unit is established. The nonlinear dynamics theory of gear is applied to the transmission system of shearer cutting unit, and the effect of damping ratio and vibration frequency on the nonlinear dynamics of the system is considered. Fourth order Runge-Kutta method with variable step is employed to solve the nonlinear systems differential equations. The phase plan and Poincare section of the system response are obtained with different parameters. The results show that the nonlinear influence of the displacement response of the solar wheel is stronger when the damping ratio is lower. And when the excitation frequency from small to large in a certain interval, the displacement response of the solar wheel becomes chaos, and then changes back to periodic phenomenon. This research method provides theoretical support for the related nonlinear problem of the gear transmission system of the shearer cutting unit.
The nonlinear dynamics model of gear transmissionsystem of shearer cutting unit is established. The nonlinear dynamics theory of gear is applied to the transmission system of shearer cutting unit, and the effect of damping ratio and vibration frequency on the nonlinear dynamics of the system is considered. Fourth order Runge-Kutta method with variable step is employed to solve the nonlinear systems differential equations. The phase plan and Poincare section of the system response are obtained with different parameters. The results show that the nonlinear influence of the displacement response of the solar wheel is stronger when the damping ratio is lower. And when the excitation frequency from small to large in a certain interval, the displacement response of the solar wheel becomes chaos, and then changes back to periodic phenomenon. This research method provides theoretical support for the related nonlinear problem of the gear transmission system of the shearer cutting unit.
引文
[1]煤炭技工教材编审委员会.采煤机[M].北京:煤炭工业出版社,2000.The national coal mechanic teaching materials committee.Shearer[M]Beijing:China coal industry publishing house,2000.
[2]孙涛,沈允文.行星齿轮传动非线性动力学模型与方程[J].机械工程学报,2002,38(3):6-10.SUN Tao,SHEN Yunwen.Study on Nonlinear Dynamic Behavior of Planetary Gear Train Dynamic Model and Govening Equations[J].Journal of Mechanical Engineering,2002,38(3):6-10.
[3]鲍和云,朱如鹏.基于增量谐波平衡法的星型齿轮传动非线性动力学分析[J].机械科学与技术,2008,27(8):1038-1042.BAO Heyun,ZHU Rupeng.Nonlinear Dynamic Ansysis of 2-Stage Star Gear Train Based on Incremental Harmonic Balance Method[J].Mechanical Science and Technology for Aerospace Engineering,2008,27(8):1038-1042.
[4]王立华,李润方,林腾蛟,等.齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.WANG Lihua,LI Runfang,LIN Tengjiao,et al.Research on Nonlinear Vibration Characteristics due to Timevarying Mesh Stiffness and Gear Backlash in Gear System[J].China Mechanical Engineering,2003,14(13):1143-1146.
[5]林腾蛟,王丹华,冉雄涛,等.多级齿轮传动系统耦合非线性振动特性分析[J].振动与冲击,2013,32(17):1-7.LIN Tengjiao,WANG Danhua,RAN Xiongtao,et al.Coupled Nonlinear Vibration Analysis of a Multi-stage Gear Transmission System[J].Journal of Vivration and Shock,2013,32(17):1-7.
[6]巫世晶,刘振皓,王晓笋,等.基于谐波平衡法的复合行星齿轮传动系统非线性动态特性[J].机械工程学报,2011,47(1):55-61.WU Shijing,LIU Zhenhao,WANG Xiaosun,et al.Nonlinear Dynamic Characteristics of Compound Planetary Gear Train Sets Based on Harmonic Balance Method[J].Journal of Mechanical Engineering,2011,47(1):55-61.
[7]刘振皓,巫世晶,王晓笋,等.基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学[J].振动与冲击,2012,31(3):117-122.LIU Zhenhao,WU Shijing,WANG Xiaosun,et al.Nonlinear Dynamics of Compound Planetary Gear sets Based on Incremental Harmonic Balance Method[J].Journal of Vivration and Shock,2012,31(3):117-122.
[8]李同杰,朱如鹏,鲍和云,等.行星齿轮传动系的周期运动及其稳定性[J].振动工程学报,2013,26(6):815-822.LI Tongjie,ZHU Rupeng,BAO Heyun,et al.Coexisting Periodic Soltiongs and Their Stability of Nonlinear Planetary Gear Train[J].Journal of Vibration Engineering,2013,26(6):815-822.
[9]赵丽娟,王乘云.采煤机截割部建模与动力学仿真研究[J].工程设计学报,2010,17(2):119-123.ZHAO Lijuan,WANG Chengyun.Department of modeling and dynamics simulation of shearer cutting[J].Chinese Journal of Engineering Design,2010,17(2):119-123.
[10]徐建博.采煤机截割部传动系统动态特性研究[D].阜新:辽宁工程技术大学,2015.XU Jianbo.Study of Cutting Part Transmission System for Dynamic Characteristics[D].Fuxin:Liaoning technical university,2015.
[2]孙涛,沈允文.行星齿轮传动非线性动力学模型与方程[J].机械工程学报,2002,38(3):6-10.SUN Tao,SHEN Yunwen.Study on Nonlinear Dynamic Behavior of Planetary Gear Train Dynamic Model and Govening Equations[J].Journal of Mechanical Engineering,2002,38(3):6-10.
[3]鲍和云,朱如鹏.基于增量谐波平衡法的星型齿轮传动非线性动力学分析[J].机械科学与技术,2008,27(8):1038-1042.BAO Heyun,ZHU Rupeng.Nonlinear Dynamic Ansysis of 2-Stage Star Gear Train Based on Incremental Harmonic Balance Method[J].Mechanical Science and Technology for Aerospace Engineering,2008,27(8):1038-1042.
[4]王立华,李润方,林腾蛟,等.齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.WANG Lihua,LI Runfang,LIN Tengjiao,et al.Research on Nonlinear Vibration Characteristics due to Timevarying Mesh Stiffness and Gear Backlash in Gear System[J].China Mechanical Engineering,2003,14(13):1143-1146.
[5]林腾蛟,王丹华,冉雄涛,等.多级齿轮传动系统耦合非线性振动特性分析[J].振动与冲击,2013,32(17):1-7.LIN Tengjiao,WANG Danhua,RAN Xiongtao,et al.Coupled Nonlinear Vibration Analysis of a Multi-stage Gear Transmission System[J].Journal of Vivration and Shock,2013,32(17):1-7.
[6]巫世晶,刘振皓,王晓笋,等.基于谐波平衡法的复合行星齿轮传动系统非线性动态特性[J].机械工程学报,2011,47(1):55-61.WU Shijing,LIU Zhenhao,WANG Xiaosun,et al.Nonlinear Dynamic Characteristics of Compound Planetary Gear Train Sets Based on Harmonic Balance Method[J].Journal of Mechanical Engineering,2011,47(1):55-61.
[7]刘振皓,巫世晶,王晓笋,等.基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学[J].振动与冲击,2012,31(3):117-122.LIU Zhenhao,WU Shijing,WANG Xiaosun,et al.Nonlinear Dynamics of Compound Planetary Gear sets Based on Incremental Harmonic Balance Method[J].Journal of Vivration and Shock,2012,31(3):117-122.
[8]李同杰,朱如鹏,鲍和云,等.行星齿轮传动系的周期运动及其稳定性[J].振动工程学报,2013,26(6):815-822.LI Tongjie,ZHU Rupeng,BAO Heyun,et al.Coexisting Periodic Soltiongs and Their Stability of Nonlinear Planetary Gear Train[J].Journal of Vibration Engineering,2013,26(6):815-822.
[9]赵丽娟,王乘云.采煤机截割部建模与动力学仿真研究[J].工程设计学报,2010,17(2):119-123.ZHAO Lijuan,WANG Chengyun.Department of modeling and dynamics simulation of shearer cutting[J].Chinese Journal of Engineering Design,2010,17(2):119-123.
[10]徐建博.采煤机截割部传动系统动态特性研究[D].阜新:辽宁工程技术大学,2015.XU Jianbo.Study of Cutting Part Transmission System for Dynamic Characteristics[D].Fuxin:Liaoning technical university,2015.