考虑齿轮腹板柔性的齿轮-转子横向振动特征研究
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摘要
航空用齿轮具有结构轻量化和低刚性的特点,在齿轮副内部激励作用下容易发生横向振动,研究航空齿轮横向振动固有特性对航空齿轮设计十分必要。考虑齿轮腹板柔性、轴承刚度、齿轮轮齿啮合柔性,利用转子动力学有限元软件Samcef建立齿轮-转子有限元模型,计算出高速齿轮转子系统的固有频率、振型以及临界转速。基于Timoshenko节点动力学模型,计算出高速齿轮转子系统的固有频率、振型以及临界转速。两种模型计算出的齿轮-转子系统固有特性进行对比表明:考虑齿轮腹板柔性的Samcef有限元方法,可以得到齿轮-转子系统齿轮横向振动的频率值及振型,没有考虑齿轮柔性的Timoshenko梁单元方法,不能得到齿轮横向振动的频率值及振型。
The aeronautical gear has the characteristics of light weight and low rigidity. It is easy to take lateral vibration under the internal excitation of the gear pair. It is necessary to study the inherent characteristics of the lateral vibration of the aeronautical gear for the design of the aeronautical gear. The flexibility of the gear web,the stiffness of the bearing and the gear meshing stiffness are considered,the finite element model of the gear rotor is established by the finite element software for rotor dynamics named Samcef,and the natural frequency,vibration mode and the critical speed of the high-speed gear rotor system are calculated. Compared with the inherent characteristics of the gear rotor system without consideration of flexibility,it is shown that the frequency values and modes of the lateral vibration of the gear rotor system can be obtained by considering the flexibility of the gear web. Without considering the flexibility of gears,the frequency and mode shapes of lateral vibration of gears can't be obtained.
The aeronautical gear has the characteristics of light weight and low rigidity. It is easy to take lateral vibration under the internal excitation of the gear pair. It is necessary to study the inherent characteristics of the lateral vibration of the aeronautical gear for the design of the aeronautical gear. The flexibility of the gear web,the stiffness of the bearing and the gear meshing stiffness are considered,the finite element model of the gear rotor is established by the finite element software for rotor dynamics named Samcef,and the natural frequency,vibration mode and the critical speed of the high-speed gear rotor system are calculated. Compared with the inherent characteristics of the gear rotor system without consideration of flexibility,it is shown that the frequency values and modes of the lateral vibration of the gear rotor system can be obtained by considering the flexibility of the gear web. Without considering the flexibility of gears,the frequency and mode shapes of lateral vibration of gears can't be obtained.
引文
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[2]宋旭圆.旋转圆盘行波振动分析及静止态谐响应计算[D].沈阳:东北大学,2012:7-9.
[3]任光明.盘形齿轮的横向振动和稳定性研究[D].北京:北京航空航天大学,1997:10-12.
[4]李其汉,晏砺堂,赵福安.盘形锥齿轮振动特性和故障分析[J].航空学报,1987,8(10):482-487.
[5]晏砺堂,李其汉.盘形锥齿轮的横向振动特性分析[J].航空动力学报,1988,(3):199-202.
[6]李向鹏,张春辉,王时英.基于Mindlin理论的齿轮横向振动模型[J].振动与冲击,2011,30(12):230-234.
[7]佘银柱,吕明,王时英.阶梯变厚度齿轮的横向弯曲振动[J].机械科学与技术,2013,32(1):116-119.
[8]NELSON H D.A finite rotating shaft element using timoshenko beam theory[J].Journal of Mechanical Design,1980,102(4):793-803.
[9]KAHRAMAN A,?ZGüVEN H N,HOUSER D R,et al.Dynamic Analysis of Geared Rotors by Finite Elements[J].Journal of Mechanical Design,1990,114(3):507-527.
[10]ZHANG Yimin,WANG Qibin,MA Hui,et al.Dynamic analysis of three-dimensional helical geared rotor system with geometric eccentricity[J].Journal of Mechanical Science&Technology,2013,27(11):3231-3242.
[11]CHEN Siyu,TANG Jinyuan,ZHOU Changjiang,et al.Modal and whirling analysis of coupled lateral and torsional vibration of herringbone gear[J].International Journal of Dynamics&Control,2014,2(3):404-414.
[12]CHEN Siyu,TANG Jinyuan,LI Yuanping,et al.Rotordynamics analysis of a double-helical gear transmission system[J].Meccanica,2016,51(1):251-268.
[13]HU Zehua,TANG Jinyuan,ZHONG Jue,et al.Frequency spectrum and vibration analysis of high speed gear-rotor system with tooth root crack considering transmission error excitation[J].Engineering Failure Analysis,2015,60:405-441.
[14]钱露露,唐进元,陈思雨,等.单级齿轮传动系统有限元节点动力学模型及高速动态性能分析[J].机械工程学报,2016,52(17):155-161.
[15]SAXENA A,CHOUKSEY M,PAREY A.Effect of mesh stiffness of healthy and cracked gear tooth on modal and frequency response characteristics of geared rotor system[J].Mechanism&Machine Theory,2017,107:261-273.
[16]李明,孙涛,胡海岩.齿轮传动转子-轴承系统动力学的研究进展[J].振动工程学报,2002,15(3):249-256.
[17]费钟秀.复杂转子耦合系统有限元建模及其动力特性研究[D].杭州:浙江大学,2013:3-7.
[18]雷顿财,唐进元.一种面齿轮传动时变啮合刚度数值计算方法[J].中国机械工程,2014,25(17):2300-2304.
[19]罗祝三,孙心德.滚动轴承在任意方向的支承刚度[J].南京航空航天大学学报,1992(3):248-256.