Abstract:To overcome the limitations of the available methods used for accurate calculation of backlash flow rate in external gear pumps, firstly by accurate analysis of tooth-profile near the minimum backlash position, together with meshing position variable and offset variable from theoretic meshing line, the formula to calculate length and height related to gap near the minimum backlash position was derived. And then, the corresponding backlash flow rates in a trapped-oil cycle were calculated by a variety of methods based on equivalent tooth-profile and actual tooth-profile. Under the same pressure difference, all results indicate that backlash flow rate is minimum in the beginning of trapped-oil section and is maximum in the end of trapped-oil section. The equivalent tooth-profile method can be used to calculate the backlash flow rate in the compression section of trapped-oil while cannot be used in the expansion section. The orifice flow theory is not suitable for calculation of backlash flow rate, especially at the termination of trapped-oil section, the bigger backlash value, or the higher pressure difference. The longest length of gap in backlash is readily unchanged at all meshing positions. Different meshing positions have little effects on gap value under a given offset. Finally, the important conclusion is that the popular equivalent tooth-profile method and the theory of thin-walled orifice are unsuitable for the backlash flow rate calculation.
李玉龙. 外啮合齿轮泵侧隙流量的精确计算[J]. 排灌机械工程学报, 2013, 31(8): 656-661.
Li Yulong. Accurate calculation of backlash flow in external gear pump. Journal of Drainage and Irrigation Machinery Engin, 2013, 31(8): 656-661.
[1]李玉龙.外啮合齿轮泵困油机理、模型及试验研究[D].合肥:合肥工业大学机械与汽车工程学院,2009.[2]Yanada,Ichikawa,Itsuji.Study of the trapping of fluid in a gear pumps [J].Power and Process Engineering,1987,201(A1):39-45.[3]Eaton M,Keogh,Edge K A.The modeling, prediction and experimental evaluation of gear pump meshing pressures with particular reference to aero-engine fuel pumps [J].Journal of Systems and Control Engineering,2008,220(5):365-379.[4]Eaton M, Keogh P S,Edge K A. Modeling and simulation of pressures within the meshing teeth of gear pumps[C]//Proceedings of International Conference on Recent Advances in Aerospace Actuation Systems and Components. Toulouse, France:[s.n.], 2001:13-15.[5]李玉龙,刘焜.外啮合齿轮泵动态困油模型及其参数影响分析[J].农业机械学报,2009,40(9):214-219. Li Yulong,Liu Kun.Dynamic model of trapped oil and effect of related variables on trapped oil pressure in external spur-gear pump[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(9):214-219.(in Chinese)[6]李玉龙,孙付春.齿轮泵困油的分析模型及侧隙计算[J].排灌机械工程学报,2011,29(2):118-122. Li Yulong, Sun Fuchun.Analysis model on trapped oil and backlash calculation in external gear pump [J].Journal of Drainage and Irrigation Machinery Enginee-ring,2011,29(2):118-122.(in Chinese)[7]李玉龙.基于低速困油模型的外啮合齿轮泵高速困油特性分析[J].农业工程学报,2012,28(9):35-39. Li Yulong.Characteristics analysis of high-speed trapped-oil in external gear pump based on low-speed trapped-oil model [J].Transactions of the CSAE,2012,28(9):35-39.(in Chinese)[8]李玉龙,孙付春.齿轮泵齿侧间隙与卸荷槽间距关系的定量分析[J].农业工程学报,2012,28(22):63-68. Li Yulong,Sun Fuchun. Quantitative analysis of relationship between backlash value and distance of two relief grooves in external gear pump [J]. Transactions of the CSAE,2012,28(22):63-68.(in Chinese)[9]Yanada H,Ichikawa T,Itsuji Y.齿轮泵困油现象的研究[J].液压与气动,1988(3):47-52. Yanada H,Ichikawa T,Itsuji Y.The phenomenon of trapped-oil in gear pump [J].Chinese Hydraulics & Pneumatics,1988(3):47-52.(in Chinese)[10]Brancati R,Rocca E,Russ R.计算啮合齿轮轮齿间油膜挤压的齿轮敲击振动模型 [J].传动技术,2006,20(3):15-20. Brancati R,Rocca E,Russ R.A Gear rattle model accounting for oil squeeze between the meshing gear teeth [J].Drive System Technique,2006,20(3):15-20.(in Chinese)[11]温诗铸,杨沛然.弹性流体动力润滑[M].北京:清华大学出版社,1992.[12]王积伟.液压与气压传动[M].北京:机械工业出版社,2010.