Variation propagation models play an important role in part quality prediction, variation source identification, and variation compensation in multistage manufacturing processes. These models often use homogenous transformation matrix, differential motion vector, and/or Jacobian matrix to represent and transform the part, tool and fixture coordinate systems and associated variations. However, the models end up with large matrices as the number features and functional element pairs increase. This work proposes a novel strategy for modelling of variation propagation in multistage machining processes using dual quaternions. The strategy includes representation of the fixture, part, and toolpath by dual quaternions, followed by projection locator points onto the features, which leads to a simplified model of a part-fixture assembly and machining. The proposed approach was validated against stream of variation models and experimental results reported in the literature. This paper aims to provide a new direction of research on variation propagation modelling of multistage manufacturing processes.

变化传播模型在多阶段制造过程中的零件质量预测，变化源识别和变化补偿中起着重要作用。这些模型通常使用均匀的变换矩阵，差分运动矢量和/或Jacobian矩阵来表示和变换零件，工具和夹具坐标系以及相关的变化。但是，随着数量特征和功能元素对的增加，模型最终会获得较大的矩阵。这项工作提出了一种新颖的策略，用于使用双四元数对多阶段加工过程中的变量传播进行建模。该策略包括通过双四元数表示夹具，零件和刀具路径，然后在特征上投影定位器点，从而简化了零件夹具装配和加工的模型。针对变化模型和文献中报道的实验结果验证了该方法的有效性。本文旨在为多阶段制造过程的变异传播建模提供新的研究方向。