Abstract
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.
Highlights
In the past two decades, variation propagation modelling in multistage manufacturing processes has been actively researched
This work derived a model of variation propagation in multistage machining processes using dual quaternion (DQ)
The use of the DQs led to a new strategy in modelling the variation propagation, which branched off from the techniques used in classical stream of variation
Summary
In the past two decades, variation propagation modelling in multistage manufacturing processes has been actively researched. The same mathematical tools can be used to represent the features of a part Such advantages lead to a better computational efficiency of DQs relative HTM-based operations [18, 19]. Since the same mathematical tools are used to represent and transform a part, fixture, and toolpath, the mathematical cumbersomeness associated in the operations is reduced Given such advantages, dual quaternions have been used in wide range of applications such as in robotic controllers [20], face recognition [21], and object animation [22]. The use of DQs in transformation, representation, and projection operations, associated with parts and fixtures, leads to a completely different strategy to solve the same modelling problem addressed by variation propagation models such as SoV and SDT. The axis of rotation, n ∈ R3, is obtained from the vectors n1 ∈ R3 and n2 ∈ R3 eq 1⁄4
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