为满足外啮合齿轮泵根切齿轮副的设计需要，基于滚齿加工原理，由创建根切半径的计算公式起，推导出一套完整的根切重合度计算公式，据此分析了基本参数对该根切重合度的影响，所得结果由根切齿轮副的三维虚拟模型加以验证。结果表明，根切会使主动齿轮的齿顶点可能进入不了啮合，目前常用齿顶重合度代替根切重合度的计算方法不可靠；除模数外的其它齿形基本参数对根切重合度均有影响，其中变位系数的影响最大；采用齿条刀具的最佳齿顶圆角半径，可以保证根切重合度等于齿顶重合度；当实际的根切重合度过大时，通过降低齿条刀具齿顶圆角半径，可以改善齿轮副的传动质量等。所得根切重合度公式也能为其他常规的根切齿轮副设计，提供一种新的方法。%In order to meet the design needs of gear pairs with undercut in external gear pumps , based on the machining principleof gear hobbing, from creating a calculation radius formula of gear undercut circle , a complete set of calculation formula of spurgear contact ratio factor suitable for gear pairs with undercutis derived .Based on this formula, the influence of gear basic parameters tothe spur gear contact ratio factor with undercut was analyzed ; finally, all theobtainedresults wereverified by three -dimension (3D) virtualmodel of spur gear pairs with undercut .The results show that, because of the gear undercut, the apex of driving gear tooth maybeexcluded from being meshed, the common calculation method of spur gear apex contact ratio factor instead of spur gear undercut contactratio factoris not reliable at present.The spur gear undercut contact ratio factor alwaysis affected bygear basic parametersexcept gearmodule, among them, the influence of gear modification coefficient is the largest .Spur gear undercut contact ratio factor canbeensuredtoequal to spur gear apex contact ratio factor by employing the best rack tool tipradius .When the actual spur gear undercut contact ratiofactoris too large, the transmission quality of gear pairs was improved by reducing the rack tool tipradius , and etc.It is concluded thata new method for the other conventional undercutgear pairs designis providedby the complete calculation formula of spur gear undercutcontact ratio factor.
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