基于多轴联动的内啮合强力珩齿拓扑修形方法研究

Research on topological modification method of internal gearing power honing based on multi-axis linkage

  • 摘要: 作为常用的齿轮精加工的工艺之一,内啮合强力珩齿加工工艺在对齿轮修形时,需要定制与工件相对应的专用金刚石修整轮,使得工艺通用性不高,加工成本较大。文章提出了一种内啮合强力珩齿拓扑修形方法,实现了用标准珩磨轮对工件齿轮齿面任意拓扑修形。建立内啮合强力珩齿拓扑修形齿面数学模型,得到标准珩磨轮和工件齿轮的映射关系,将拓扑修形时机床运动的A轴、X轴的附加运动与电子齿轮箱一起用高阶多项式表示,将多项式中的运动参数变化对加工齿面的影响用敏感度矩阵表示,以修形齿面为目标,以敏感度矩阵中的敏感系数为梯度,利用动态规划算法求解出运动参数,并得到修形后的工件齿面。仿真结果表明该方法可以通过多轴联动实现对齿面拓扑修形,修形误差较小,成本大大降低,方法具有普适性。

     

    Abstract: As one of the commonly used gear finishing processes, the internal gearing power honing process requires a special diamond dressing wheel corresponding to the workpiece to be customized when the workpiece gear is reshaped, which makes the process less versatile and the processing cost is high. This paper proposes a topological modification method for internal gearing power honing, which realizes arbitrary topological modification of the tooth surface of workpiece gears with standard honing wheels. The mathematical model of topological modification tooth surface of internal gearing power honing is established, and the mapping relationship between the standard honing wheel and the workpiece gear is obtained, and the additional motion of the A-axis and X-axis of the machine tool motion during topology modification is expressed by a high-order polynomial together with the electronic gearbox, the effect of the variation of the motion parameters in the polynomial on the machining tooth surface is expressed by the sensitivity matrix, with the modified tooth surface as the goal, the sensitivity coefficient in the sensitivity matrix as the gradient, the dynamic programming algorithm is used to solve the motion parameters, and the modified workpiece tooth surface is obtained. The simulation results show that the method can realize the topological modification of the tooth surface through multi-axis linkage, the modification error is small, the cost is greatly reduced, and the method is universal.

     

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