内啮合齿轮泵压力腔包络角图形化求解研究
|
摘要
齿轮泵的压力腔包络角与齿轮副所承受的液压径向力直接相关。传统计算方法都将压力腔包络角视为定值,忽略其数值随齿轮转动的变化。该研究针对渐开线内啮合齿轮泵,提出了一种基于图形模型的压力腔包络角确定方法。首先,运用双展成法推导内啮合齿轮副的数学方程,进而利用三维建模软件建立某时刻下的齿轮副图形模型;然后,基于所获得的图形模型定义压力腔边界点分布,提出确定某时刻下压力腔边界点位置的算法;最后,根据压力腔边界点算法,通过循环运算得到压力腔包络角随齿轮旋转的数值变化。本研究能够得到内啮合齿轮泵压力腔包络角随齿轮旋转的数值变化,为准确分析内啮合齿轮泵的径向力变化特性和合理设计径向力抵消结构提供了理论依据。
The pressure-chamber angle is directly associated with the axial force acted on gear pairs of the gear pump. The traditional method usually neglects the influence of gear rotation on pressure-chamber and assumes the angle as a constant. Taking the involute internal gear pump as the subject,we propose an approach for calculating the pressure-chamber angle based on the geometrical models. Firstly,the mathematical models of the internal gear pairs are derived by a double envelope method. And then,with the help of 3D modeling software,geometrical models of internal gear pairs at some instants are built. Secondly,based on the derived geometrical models,boundary points of pressure chambers of internal gear pumps are defined and algorithms are designed to locate positions of these points. Finally,with these boundary points,the instantaneous values of pressure-chamber angles can be calculated during the rotation of the pinion. The result will provide a theoretical basis for the precise analysis of hydraulic axial forces and also a correct design for neutralizing these axial forces.
The pressure-chamber angle is directly associated with the axial force acted on gear pairs of the gear pump. The traditional method usually neglects the influence of gear rotation on pressure-chamber and assumes the angle as a constant. Taking the involute internal gear pump as the subject,we propose an approach for calculating the pressure-chamber angle based on the geometrical models. Firstly,the mathematical models of the internal gear pairs are derived by a double envelope method. And then,with the help of 3D modeling software,geometrical models of internal gear pairs at some instants are built. Secondly,based on the derived geometrical models,boundary points of pressure chambers of internal gear pumps are defined and algorithms are designed to locate positions of these points. Finally,with these boundary points,the instantaneous values of pressure-chamber angles can be calculated during the rotation of the pinion. The result will provide a theoretical basis for the precise analysis of hydraulic axial forces and also a correct design for neutralizing these axial forces.
引文
[1]Ivantysyn J,Ivantysynova M.Hydrostatic Pumps and Motors[M].New Delhi:Academia Books International,2001.
[2]Johnston D N,Drew J E.Measurement of Positive Displacement Pump Flow Ripple and Impedance[J].Proc.I Mech E,Part I:J Systems and Control Engineering,1996,(210):65-74.
[3]Manring N D,Kasaragadda S B.The Theoretical Flow Ripple of an External Gear Pump[J].ASME J Dynamic Systems,Measurement and Control,2003,125(3):396-404.
[4]何存兴.液压元件[M].北京:机械工业出版社,1982.
[5]赵连春,许贤良,孙长敬.三惰轮复合齿轮泵密封块瞬态径向力分析[J].重庆大学学报:自然科学版,2001,24(6):45-47.
[6]李宏伟,高绍站.内啮合齿轮泵齿轮轴的受力分析[J].液压与气动,2007,(5):70-72.
[7]Litvin F L,Krylov N N,Erikhov M L.Generation of Tooth Surfaces by Two-parameter Enveloping[J].Mechanism and Machine Theory,1975,(10):365-373.
[8]Litvin F L,Seol I H.Computerized Determination of Gear Tooth Surface as Envelope to two Parameter Family of Surfaces[J].Computer Methods in Applied Mechanics and Engineering,1996,(138):213-225.
[9]Yang S C.Study on an Internal Gear with Asymmetric Involute Teeth[J].Mechanism and Machine Theory,2007,42(8):977-994.
[10]Litvin F L.Gear Geometry and Applied Theory[M].Englewood Cliffs:Prentice-Hall,1994.
[2]Johnston D N,Drew J E.Measurement of Positive Displacement Pump Flow Ripple and Impedance[J].Proc.I Mech E,Part I:J Systems and Control Engineering,1996,(210):65-74.
[3]Manring N D,Kasaragadda S B.The Theoretical Flow Ripple of an External Gear Pump[J].ASME J Dynamic Systems,Measurement and Control,2003,125(3):396-404.
[4]何存兴.液压元件[M].北京:机械工业出版社,1982.
[5]赵连春,许贤良,孙长敬.三惰轮复合齿轮泵密封块瞬态径向力分析[J].重庆大学学报:自然科学版,2001,24(6):45-47.
[6]李宏伟,高绍站.内啮合齿轮泵齿轮轴的受力分析[J].液压与气动,2007,(5):70-72.
[7]Litvin F L,Krylov N N,Erikhov M L.Generation of Tooth Surfaces by Two-parameter Enveloping[J].Mechanism and Machine Theory,1975,(10):365-373.
[8]Litvin F L,Seol I H.Computerized Determination of Gear Tooth Surface as Envelope to two Parameter Family of Surfaces[J].Computer Methods in Applied Mechanics and Engineering,1996,(138):213-225.
[9]Yang S C.Study on an Internal Gear with Asymmetric Involute Teeth[J].Mechanism and Machine Theory,2007,42(8):977-994.
[10]Litvin F L.Gear Geometry and Applied Theory[M].Englewood Cliffs:Prentice-Hall,1994.