外啮合齿轮泵困油机理、模型及试验研究
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摘要
困油现象是外啮合齿轮泵固有的特性之一,困油压力值的准确评估是控制和减轻困油的前提,本文以困油模型的建立和困油压力的精确仿真为目标展开研究,主要工作包括以下几个方面:
采用扫过面积的方法,以主动齿轮的啮合长度为变量,建立了异齿数齿轮泵的平均流量、流量不均匀系数、困油容积和困油流量的计算公式,为后续困油压力的仿真做好前期的准备工作。结果表明主大从小的异齿数组合对流量特性有利,对困油现象不利;而主小从大异齿数组合的影响则相反。
采用计算创建法与虚拟量测法相结合,给出了最小困油面积和卸荷面积计算与验证的问题。实例表明卸荷面积的变化为抛物线型,具体应用时,不同参数下的卸荷面积可采用不同指数和系数的抛物线来简化。
建立了困油压力仿真的模型。依据模型中是否考虑齿轮副的动力学分析,将困油模型分为静态模型和动态模型。采用数值模拟方法研究了含气比,侧板倾斜,有效体积模量,离心力和齿轮副的振动等因素对困油压力的影响。结果表明含气是造成处于膨胀阶段后期的困油压力基于零压附近的主要原因,入口含气比对困油压力的影响不大,而离心含气比以及出油口含气比在进入困油区后的放大效应的影响较大;过小的侧隙和过大的困油压力会加剧齿轮副的振动;动态模型仿真的压力峰值一般要比静态模型低,采用动态模型更可靠;从动轮侧的困油压力峰值一般也要大于主动轮侧的困油压力峰值。
针对仿真模型中的四大泄漏量进行了研究。轴向泄漏考虑了侧板倾斜和困油区的封闭轮廓在一个困油周期内的变化;静态时,齿面啮合泄漏依赖于其间的最小油膜厚度,侧隙泄漏依赖于侧隙的原始设计值;动态时,两者均依赖于啮合位置和振动位置的变化。实例表明卸荷泄漏、侧隙泄漏和啮合泄漏与困油流量基本处于同一数量级,是缓解困油压力的主要途径。
基于台架试验测量了从动轮侧的困油压力,并与理论分析结果进行了对比,从而对困油分析模型进行了验证。静、动态模型的仿真结果之间的差距较大,动态模型比较接近于试验结果。引流口的体积对困油压力造成的影响很小,可以忽略不计。
最后,对相关参数如何影响困油压力进行了动态模型的仿真分析,结果表明较小的模数、齿数、压力角、齿宽、齿顶高系数和较大的正变位系数,有利于困油压力的缓解,同时较大的正变位系数对流量脉动现象的改善也有一定效果。此外,对于高压、低速以及低压、高速工况下的困油特性进行了分析。
本文的研究工作为困油压力的精确预测提供了一种有效的方法,在齿轮泵设计尤其在泵的振动与噪声控制等方面,具有一定的理论意义和应用前景。
Phenomenon of trapped oil is an inherent characteristic of external gear pump; the accurate evaluating of value of trapped oil pressure is a precondition for controlling and relieving trapped oil pressure. With the targets of modeling and accurate simulation of trapped oil pressure, this paper performs a further research that contains the following main aspects:
For a external gear pump with different teeth of drive gear and driven gear, by using a method of swept volume and taking engagement length of drive gear as a variable, the paper establishes formulas of average flow, uneven flow coefficient and trapped oil volume, the flow of trapped oil, all of them are a preparatory work for subsequent simulation of trapped oil pressure. The results show that the combination of more teeth of drive gear with fewer teeth of driven gear is favorable for improving the flow characteristic and unfavorable for reducing the phenomenon of trapped oil, while the effect of the combination of fewer teeth of drive gear with more teeth of driven gear is just on the contrary.
The minimum area of trapped oil region and relief area are calculated by combining computation method with virtual measurement method. The results show that the curve of relief area is parabolic, different indices and coefficients of parabola can be adopted for simplificating calculation of actual relief area under different parameters in actual application.
The simulation model of the trapped oil pressure is established in the paper, and the model is divided into static model and dynamic model according to with or without dynamic factor of gear pair. The influence of percentage of gas in oil, slope of side plate, effective bulk modulus, and centrifugal force and gear pair vibration on trapped oil pressure is studied by numerical simulation. The results show that gas in oil is the major cause of zero-approaching trapped oil pressure in the later stage of expansion, and that inlet gas in oil has little effect on the trapped oil pressure, while the effect of percentage of centrifugal gas and percentage of outlet gas in oil is amplified in the trapped oil areas; and smaller backlash and higher oil pressure will aggravate vibration of gear pair. Normally the peak of simulated pressure in dynamic model is lower than that in static model, making dynamic model more reliable. At peak of trapped oil pressure in driven gear side is greater than that in drive gear side under normal circumstances.
Four kinds of leakages in the simulation model are investigated, among which, axial leakage takes slope of side plate and variation of trapped oil profile in a trapping period into account, in static state, meshing leakage from meshing tooth surface depends on the minimum film thickness therein, and leakage from backlash depends on original design values of backlash; in dynamic state, both of them depend on change of meshing position and vibration location. The results show that the relief leakage and backlash leakage and meshing leakage are basically the same as trapped oil flow in magnitude; these three kinds of leakages are main method for relieving the trapped oil pressure.
Trapped oil pressure in driven gear side is measured on test device and compared with the results of theoretical analysis, thus the simulation model has been verified. There is a larger gap in simulation results of static model and dynamic model, and the results in dynamic model are closer to the test results, the volume of drainage has little influence on trapped oil pressure, therefore it is negligible.
Finally, the influence of relevant parameters on trapped oil pressure is analyzed based on dynamic model. The results show that small modulus, number of teeth, pressure angle, gear width, addendum coefficient and big positive profile shift coefficient contribute to the relieving of trapped oil pressure. In particular, greater positive profile shift coefficient is very effective for relieving of the flow pulse and trapped oil. In addition, trapped oil pressure is forecasted in special working conditions such as high-pressure and low-speed or low-pressure and high-speed.
In conclusion, the research offers an effective method for the accurate prediction of trapped oil pressure, and is useful in the design of gear pump, especially, in vibration and noise controlling, etc. this study is of significance both in theoretical and applications.
采用扫过面积的方法,以主动齿轮的啮合长度为变量,建立了异齿数齿轮泵的平均流量、流量不均匀系数、困油容积和困油流量的计算公式,为后续困油压力的仿真做好前期的准备工作。结果表明主大从小的异齿数组合对流量特性有利,对困油现象不利;而主小从大异齿数组合的影响则相反。
采用计算创建法与虚拟量测法相结合,给出了最小困油面积和卸荷面积计算与验证的问题。实例表明卸荷面积的变化为抛物线型,具体应用时,不同参数下的卸荷面积可采用不同指数和系数的抛物线来简化。
建立了困油压力仿真的模型。依据模型中是否考虑齿轮副的动力学分析,将困油模型分为静态模型和动态模型。采用数值模拟方法研究了含气比,侧板倾斜,有效体积模量,离心力和齿轮副的振动等因素对困油压力的影响。结果表明含气是造成处于膨胀阶段后期的困油压力基于零压附近的主要原因,入口含气比对困油压力的影响不大,而离心含气比以及出油口含气比在进入困油区后的放大效应的影响较大;过小的侧隙和过大的困油压力会加剧齿轮副的振动;动态模型仿真的压力峰值一般要比静态模型低,采用动态模型更可靠;从动轮侧的困油压力峰值一般也要大于主动轮侧的困油压力峰值。
针对仿真模型中的四大泄漏量进行了研究。轴向泄漏考虑了侧板倾斜和困油区的封闭轮廓在一个困油周期内的变化;静态时,齿面啮合泄漏依赖于其间的最小油膜厚度,侧隙泄漏依赖于侧隙的原始设计值;动态时,两者均依赖于啮合位置和振动位置的变化。实例表明卸荷泄漏、侧隙泄漏和啮合泄漏与困油流量基本处于同一数量级,是缓解困油压力的主要途径。
基于台架试验测量了从动轮侧的困油压力,并与理论分析结果进行了对比,从而对困油分析模型进行了验证。静、动态模型的仿真结果之间的差距较大,动态模型比较接近于试验结果。引流口的体积对困油压力造成的影响很小,可以忽略不计。
最后,对相关参数如何影响困油压力进行了动态模型的仿真分析,结果表明较小的模数、齿数、压力角、齿宽、齿顶高系数和较大的正变位系数,有利于困油压力的缓解,同时较大的正变位系数对流量脉动现象的改善也有一定效果。此外,对于高压、低速以及低压、高速工况下的困油特性进行了分析。
本文的研究工作为困油压力的精确预测提供了一种有效的方法,在齿轮泵设计尤其在泵的振动与噪声控制等方面,具有一定的理论意义和应用前景。
Phenomenon of trapped oil is an inherent characteristic of external gear pump; the accurate evaluating of value of trapped oil pressure is a precondition for controlling and relieving trapped oil pressure. With the targets of modeling and accurate simulation of trapped oil pressure, this paper performs a further research that contains the following main aspects:
For a external gear pump with different teeth of drive gear and driven gear, by using a method of swept volume and taking engagement length of drive gear as a variable, the paper establishes formulas of average flow, uneven flow coefficient and trapped oil volume, the flow of trapped oil, all of them are a preparatory work for subsequent simulation of trapped oil pressure. The results show that the combination of more teeth of drive gear with fewer teeth of driven gear is favorable for improving the flow characteristic and unfavorable for reducing the phenomenon of trapped oil, while the effect of the combination of fewer teeth of drive gear with more teeth of driven gear is just on the contrary.
The minimum area of trapped oil region and relief area are calculated by combining computation method with virtual measurement method. The results show that the curve of relief area is parabolic, different indices and coefficients of parabola can be adopted for simplificating calculation of actual relief area under different parameters in actual application.
The simulation model of the trapped oil pressure is established in the paper, and the model is divided into static model and dynamic model according to with or without dynamic factor of gear pair. The influence of percentage of gas in oil, slope of side plate, effective bulk modulus, and centrifugal force and gear pair vibration on trapped oil pressure is studied by numerical simulation. The results show that gas in oil is the major cause of zero-approaching trapped oil pressure in the later stage of expansion, and that inlet gas in oil has little effect on the trapped oil pressure, while the effect of percentage of centrifugal gas and percentage of outlet gas in oil is amplified in the trapped oil areas; and smaller backlash and higher oil pressure will aggravate vibration of gear pair. Normally the peak of simulated pressure in dynamic model is lower than that in static model, making dynamic model more reliable. At peak of trapped oil pressure in driven gear side is greater than that in drive gear side under normal circumstances.
Four kinds of leakages in the simulation model are investigated, among which, axial leakage takes slope of side plate and variation of trapped oil profile in a trapping period into account, in static state, meshing leakage from meshing tooth surface depends on the minimum film thickness therein, and leakage from backlash depends on original design values of backlash; in dynamic state, both of them depend on change of meshing position and vibration location. The results show that the relief leakage and backlash leakage and meshing leakage are basically the same as trapped oil flow in magnitude; these three kinds of leakages are main method for relieving the trapped oil pressure.
Trapped oil pressure in driven gear side is measured on test device and compared with the results of theoretical analysis, thus the simulation model has been verified. There is a larger gap in simulation results of static model and dynamic model, and the results in dynamic model are closer to the test results, the volume of drainage has little influence on trapped oil pressure, therefore it is negligible.
Finally, the influence of relevant parameters on trapped oil pressure is analyzed based on dynamic model. The results show that small modulus, number of teeth, pressure angle, gear width, addendum coefficient and big positive profile shift coefficient contribute to the relieving of trapped oil pressure. In particular, greater positive profile shift coefficient is very effective for relieving of the flow pulse and trapped oil. In addition, trapped oil pressure is forecasted in special working conditions such as high-pressure and low-speed or low-pressure and high-speed.
In conclusion, the research offers an effective method for the accurate prediction of trapped oil pressure, and is useful in the design of gear pump, especially, in vibration and noise controlling, etc. this study is of significance both in theoretical and applications.
引文
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