Variation propagation modelling in multistage machining processes using dual quaternions
- PDF / 1,583,916 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 12 Downloads / 158 Views
ORIGINAL ARTICLE
Variation propagation modelling in multistage machining processes using dual quaternions Filmon Yacob 1
&
Daniel Semere 1
Received: 6 May 2020 / Accepted: 15 October 2020 / Published online: 5 November 2020 # The Author(s) 2020
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. Keywords Point projection . Screw displacement . Stream of variation . Plücker coordinates
1 Introduction In the past two decades, variation propagation modelling in multistage manufacturing processes has been actively researched. A significant contribution has been made in the directions of part quality prediction [1–4], variation source identification [5, 6], variation compensation [7, 8], and process-oriented tolerancing [9] in multistage manufacturing processes. These contributions are often studied under the concept of stream of variation (SoV) and model of a manufactured part [10]. The concept of SoV may apply techniques such as differential motion vector [11], equivalent fixture error [6], and kinematic analysis [12]. The concept of the model of the manufactured part applies small displacement torsor (SDT) [10, 13]. Despite the wide range of applications and extensions of these models, the fundamental mathematical modelling tools
* Filmon Yacob [email protected] Daniel Semere [email protected] 1
Department of Production Engineering, KTH Royal Institute of Technology, Brinellvägen 68, 114 28 Stockholm, Sweden
remained the same. All of the aforementioned models use homogenous transformation matrix (HTM), differential motion vector, and/or Jacobian matrix to represent and transform the part, tool and fixture coordinate systems and associated variations [10]. The variation propagation model’s complexity, matrix dimensions, and number of coordinate system significantly increase as the number of features and machining stations increase, especially when considering generic fixtures, locating surfaces, and machining error [1, 4, 14, 15]. In the case of SoVrelated methods, for in
Data Loading...
