齿轮泵最大困油压力解析式的建立与验证

Establishment and verification of analytic formula for maximum trapped-oil pressure in external gear pump

为探求建立出能够计算齿轮泵最大困油压力的解析式以克服试验和仿真上的局限性,针对困油过程的压缩阶段,分有、无侧隙的2种情况,该文采用细长孔的流量公式计算出侧隙内的压差泄漏量,并在困油轴向泄漏路径适当简化的基础上,计算出困油的轴向泄漏量。然后由困油区内"困油容积对时间的变化率等于泄漏量"所处的瞬态位置计算出最大困油压力,其正确性采用现有文献的试验结果来验证。结果表明,在案例参数下,当侧隙由30μm变化到200μm,最大困油压力位置与卸荷槽关闭点所在位置的偏离率由18.2%下降到3.5%,说明侧隙越大,最大困油压力所处位置越接近于卸荷槽关闭点所在位置;侧隙内的卷吸流数量级为6,压差流数量级为4,卷吸流可以忽略不计;最大困油压力发生在理论卸荷槽所在位置和实际卸荷槽所在位置之间,大小受出口压力和转速共同的线性影响,采用细长孔的流量公式计算侧隙流量比薄壁孔流量公式更为精确。所建解析式可快速地精确求出最大困油压力及所处位置,可为最大困油压力的预估和卸荷槽布局提供参考。

For overcoming the limitations of trapped-oil pressure test on a higher rotate speed or greater outlet pressure and the defects of trapped-oil pressure simulation operation with accumulated error and so on, the analytic formula for seeking the maximum trapped-oil pressure value was established in an external gear pump. In the compression stage of a complete trapped-oil process with one state of smaller backlash value and another state of biggish backlash value; Firstly, the backlash flow made by pressure difference was calculated by the slender-hole flow formula substituted for a conventional short-hole flow formula; secondly, from the simplified paths of axial trapped-oil leakage, axial trapped-oil leak flow was derived; according to the above calculated trapped-oil leak flows; thirdly, the special transient position was found that the rate of trapped-oil volume on time was equal to total trapped-oil leak flow, then the maximum trapped-oil pressure value was calculated and was verified by test results of the current literature. All results calculated by analytic formula showed that, under the parameters of that modulus was 4.75 mm, the number of teeth was 10, the center distance was 58 mm, the gear width was 20 mm and pressure angle was 20°50＇, when the relief groove was just closed and backlash value was varied from 30 to 200 μm, the deviation rate of the maximum trapped-oil pressure position and the closed position of the relief groove was down from 18.2% to 3.5%. The bigger the backlash value was, the closer the maximum trapped-oil pressure position was to the closed relief groove position; the magnitude order of shear flow made by speed was 6 and the flow made by pressure difference was 4, in comparison to differential pressure flow, shear flow could be neglected; the maximum trapped-oil pressure was occurred in between the theoretical position and the actual position of the relief groove, and the maximum trapped-oil pressure value was linearly influenced by the outlet pressure and rotate speed; The slender-hole flow formula that flow rate had linear relationship with the pressure difference was more suitable for calculating backlash flow than conventional short-hole flow formula that flow rate had linear relationship with the square root of pressure difference, etc. Finally, the it is concluded that the built analytic formula can quickly calculate the maximum trapped-oil pressure and its position, because of omitting a lot of process operation and reducing its accumulated error, the result is more accurate, and a new reference is provided to estimate the maximum trapped-oil pressure and the layout of relief groove.