Variation propagation modeling of multistage machining processes enables variation reduction by making an accurate prediction on the quality of a part. Part quality prediction through variation propagation models, such as stream of variation and Jacobian-Torsor models, often focus on a 3-2-1 fixture layout and do not consider form errors. This paper derives a mathematical model based on dual quaternion for part quality prediction given parts with form errors and fixtures with N-2-1 (N>3) layout. The method uses techniques of Skin Model Shapes and dual quaternions for a virtual assembling of a part on a fixture, as well as conducting machining and measurement. To validate the method, a part with form errors produced in a two-stationed machining process with a 12-2-1 fixture layout was considered. The prediction made following the proposed method was within 0.4% of the prediction made using a CAD/CAM simulation when form errors were not considered. These results validate the method when form errors are neglected and partially validated when considered.

多阶段加工过程的变异传播建模通过对零件质量进行准确预测来减少变异。通过变异传播模型（例如变异流和 Jacobian-Torsor 模型）进行零件质量预测，通常侧重于 3-2-1 夹具布局，不考虑形状错误。本文推导出一个基于对偶四元数的数学模型，用于给定具有形状误差的零件和N -2-1 ( N>3) 布局。该方法使用皮肤模型形状和双四元数技术在夹具上进行零件的虚拟组装，以及进行加工和测量。为了验证该方法，考虑了在具有 12-2-1 夹具布局的两工位加工过程中产生的具有形状误差的零件。在不考虑形状误差的情况下，按照所提出的方法进行的预测与使用 CAD/CAM 模拟所做的预测的预测值相差在 0.4% 以内。这些结果在忽略形式错误时验证了该方法，并在考虑时部分验证了该方法。