两叶与三叶摆线型转子泵尺寸极值的推导

DERIVATION OF THE MAXIMUM DI-MENSION FOR ROTOR PUMP WITH TWO-LOBE OR THREE-LOBE CYCLOID ROTOR

转子泵的转子叶数可能是两叶或三叶。对于摆线型转子来说,转子转动中心到叶峰圆弧中心的距离d2与节圆半径R的比值k(k=d2/R)是一个很重要的参数。该比值越大,则转子越瘦高,泵腔容积利用系数越大,流量就越大。但若这个比值大于某一极值,则转子型线将自我交叉。加工后,转子间就存在很大的侧隙,流量和压力将迅速下降。推导出该转子摆线齿谷曲率半径的简易计算公式以及比值k的极值的明显表达式和精确的数值,为此种转子泵的转子设计提供了理论依据。

Number of lobe of rotor in rotating pump may be two or three. For cycloid rotor, the ratio k(k=d2/R)of the distance d2 (from rotating center of the rotor to the center of the circular addendum) to the radius R of pitch circle is a very important parameter. The larger the ratio is, the thinner the rotor will be, the larger the volume coefficient of the cavum will be, and the larger the flux will be. However, if this ratio exceeds an extre-mum, then the profile of the rotor will intersect itself. There will be large backlash between rotors after cutting. Thus the flux and pressure will decline sharply. A simple formula to calculate radius of curvature of the cycloid valley of the rotor and an explicit expression to calculate extremum of the ratio k(k =d2/R) are derived. Exact values of the extremum of the ratio are calculated. This work sets a theoretical base for the design of the rotor in this kind of rotating pump.