| 白壮华1， 林何1,2*.星型人字齿轮传动系统非线性分岔特性[J].轻工机械,2023,41(1):79-84 |
| 星型人字齿轮传动系统非线性分岔特性 |
| Non Linear Bifurcation Characteristics of Star Herringbone Gear Transmission System |
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| DOI：10.3969/j.issn.1005 2895.2023.01.013 |
| 中文关键词: 星型人字齿轮 非线性分岔 Poincaré截面 Runge Kutta法 混沌 |
| 英文关键词:star herringbone gear non linear bifurcation Poincaré cross section Runge Kutta method chaos |
| 基金项目:国家自然科学基金资助项目（51805402）；陕西省自然科学基础研究计划项目（2019JQ 851）；中国纺织工业联合会科技指导性计划项目（2020068） |
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| 中文摘要: |
| 为探究星型人字齿轮传动系统分岔动力学特性，课题组采用集中质量法建立了星型人字齿轮系统的纯扭转非线性动力学模型，通过Runge Kutta法求解了系统非线性振动微分方程，利用相图、Poincaré截面法和分岔特性等分析手段研究了不同转速条件下啮合阻尼比对系统振动响应及分岔特性的影响。结果表明：系统在不同转速下会表现出丰富的非线性动力学行为；随着啮合阻尼比的增大，系统通过倒分岔从混沌状态进入倍周期状态，再由倍周期状态进入单周期状态。因此，在保证系统传动效率的前提下适当提高系统的啮合阻尼比，能够明显弱化系统的混沌运动，减小其振动响应，提高系统稳定性，对系统噪声的降低和寿命的延长具有一定的帮助。 |
| 英文摘要: |
| To investigate the bifurcation dynamic characteristics of the star herringbone gear transmission system, a pure torsional nonlinear dynamic model of the star herringbone gear system was established by lumped mass method, and the nonlinear vibration equation of the system was solved by Runge Kutta method. The effects of meshing damping ratio on the vibration response and bifurcation characteristics of the system at different rotational speeds were analyzed by phase diagram, Poincaré section method and bifurcation characteristics. The results show that the system exhibits abundant nonlinear dynamic behavior at different rotational speeds. With the increase of meshing damping ratio, the system goes from chaotic state to period doubling state and then from period doubling state to single cycle state through inverted bifurcation. Therefore, on the premise of ensuring the transmission efficiency of the system, properly increasing the meshing damping ratio of the system can obviously weaken the chaotic motion of the system, reduce its vibration response, improve the stability of the system, and help to reduce the noise of the system and prolong its service life. |
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