刘大伟, 谭万鑫, 金昕, 任廷志. 变速椭圆齿轮泵的非线性振动模型与拍击特性[J]. 农业工程学报, 2021, 37(7): 15-23. DOI: 10.11975/j.issn.1002-6819.2021.07.003
    引用本文: 刘大伟, 谭万鑫, 金昕, 任廷志. 变速椭圆齿轮泵的非线性振动模型与拍击特性[J]. 农业工程学报, 2021, 37(7): 15-23. DOI: 10.11975/j.issn.1002-6819.2021.07.003
    Liu Dawei, Tan Wanxin, Jin Xin, Ren Tingzhi. Nonlinear vibration model and rattling characteristics of elliptical gear pump with timing-varying input speed[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(7): 15-23. DOI: 10.11975/j.issn.1002-6819.2021.07.003
    Citation: Liu Dawei, Tan Wanxin, Jin Xin, Ren Tingzhi. Nonlinear vibration model and rattling characteristics of elliptical gear pump with timing-varying input speed[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(7): 15-23. DOI: 10.11975/j.issn.1002-6819.2021.07.003

    变速椭圆齿轮泵的非线性振动模型与拍击特性

    Nonlinear vibration model and rattling characteristics of elliptical gear pump with timing-varying input speed

    • 摘要: 变速椭圆齿轮泵是一种具有大排量、低脉动的新型容积泵,为提升其在高转速下的动力学性能,降低振动和噪声,对该齿轮泵在周期负载作用下的拍击振动行为进行研究。阐明了基于外部非圆齿轮变速驱动的椭圆齿轮泵流量脉动平抑原理,给出了变速椭圆齿轮泵中两级非圆齿轮机构的传动比函数;基于集中参数法,考虑轮齿间的弹性变形、静态传递误差、齿侧间隙及周期负载等因素,构建了变速椭圆齿轮泵的非线性拍击动力学模型,运用龙格-库塔法求解系统的动态响应,定量分析了变速椭圆齿轮泵的拍击特性以及关键参数对拍击门槛转速的影响。结果表明:随着变速椭圆齿轮泵输入转速的增加,系统先后经历无拍击、单边拍击和双边拍击状态,在设计参数下系统的拍击门槛转速为985 r/min,当拍击发生后齿间动态啮合力均方根会迅速增大;提高泵口压强或系统制造精度能够提升拍击门槛转速,泵口压强由0增至3.5 MPa,系统的拍击门槛转速由118 r/min增至1 637 r/min,从动椭圆转子静态传递误差幅值由7×10-2 mm降低至1×10-2 mm,拍击门槛转速由441 r/min提升至985 r/min,而增加转子偏心率,会导致拍击门槛转速先缓慢升高后迅速降低,为抑制变速椭圆齿轮泵的拍击振动和噪声及提升无拍击状态下最大瞬时流量提供理论依据。

       

      Abstract: A pair of outer noncircular gear has widely been used to prevent severe flow pulsation in a variable-speed elliptic gear pump. The displacement is normally several times that of the circular gear pump with the same pump cavity volume, while the instantaneous flow rate is uniform. The structure can be expected to broadly apply in agriculture, petroleum, chemical industry, food, medical treatment, and transportation. However, the beating vibration and noise that occurred easily can be detrimental to the performance of a pump, because of the special internal excitation of non-circular gear. Therefore, it is necessary to explore the nonlinear dynamics of the pump, and thereby reveal the mechanism of a rattle for better design of a high-quality elliptical gear pump with variable speed. In this study, a transmission ratio function of a two-stage non-circular gear mechanism was constructed in a variable-speed elliptical gear pump using the flow pulsation suppression of an elliptic gear pump driven by external non-circular gear. A nonlinear rattle vibration model was established in a variable-speed elliptical gear pump using the separation of elastic rotating angle considering the elastic deformation of the teeth, the static transmission error, the backlash between teeth, and the periodic load. A Runge-Kutta method was utilized to calculate the dynamic responses for the vibration curve, excitation composition, and amplitude at different rotate speeds. A systematic analysis was made on the evolution in the rattle state and system intensity, as well as the influences of pump port pressure, transmission error, and eccentricity on the rattle threshold rotation speed. The results showed that the vibration of the internal rotor was greater than that of external non-circular gear in a variable-speed elliptical gear pump. Moreover, the vibration of two-stage non-circular gears contained the time-varying instantaneous center excitation frequency, the tooth meshing excitation frequency, the multiplication, difference, and sum of these frequencies. The two-stage non-circular gears successively experienced the states of no impact, unilateral impact and bilateral impact with the increase of input rotation speed. Compared with the outer noncircular gears 1 and 2, the internal rotors 3 and 4 vibrated more violently, and entered the rattle state earlier. The dynamic meshing force rose linearly and slowly, when there was no rattle. Once the rattle occurred, the dynamic meshing force rose rapidly. Improving the pump port pressure or the manufacturing accuracy of gears can improve the rattle threshold rotation speed of a variable-speed elliptical gear pump. Among the two pairs of non-circular gears, the internal rotors 3 and 4 had a greater influence on the rattle threshold rotation speed. The rattle threshold rotation speed increased slowly and then decreased rapidly, as the rotor eccentricity advanced. Therefore, the flow rate of a pump cannot be improved, although the eccentricity can contribute to the pump displacement, due mainly to the reduction of rattle threshold rotation speed.

       

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