Variation Propagation in Multistage Machining Processes Using Dual Quaternions

F Yacob,D Semere

doi:10.1088/1757-899x/689/1/012019

Abstract

The application of rigid transformations matrices in variation propagation has a long tradition in manufacturing community. However, the matrix-based modeling of variation propagation in multistage machining processes is complicated. Moreover, there is a need to improve the computational efficiency of manipulation of geometrical models for variation analysis purposes. This paper introduces the representation of rigid transformation by dual quaternions, which have a computational advantage and mathematical elegance compared to matrices. In comparison to a commercial tool, the implementation of the purposed method predicted parallelism with an average error of 4.3 % in a hypothetical two stage machining process. The proposed approach has a potential to be an alternative to matrix based rigid transformation practices in variation and tolerance analysis.

Highlights

Variation in manufactured parts is an expected characteristic due to variation in machining processes
This paper introduces the representation of rigid transformation by dual quaternions, which have a computational advantage and mathematical elegance compared to matrices
Variation propagation modelling and analysis in multistage machining based on matrices is non-trivial task

Summary

Introduction

Variation in manufactured parts is an expected characteristic due to variation in machining processes. One of the common methods, Stream of Variation, utilizes matrix representation of the rotational and translational transformation of geometrical models [1]. Such approaches become mathematically more complex when some of the assumptions relaxed. Dual quaternions perform better in terms of computational efficiency, speed and robustness compared to matrices [8], [9]. The angle and the axis of rotation of the deviated assembly feature from corresponding locators’ plane is first computed for registration purpose. Once the registration is completed, the machining variation is induced by varying the depth cut These steps are repeated at each station to predict the product geometry in subsequent stages

Dual quaternions

Assembling part to a fixture

Setup in multistage processes

Findings

Conclusion