A preferred sequence

From the simulated welding sequences, it was observed that sequences that alternate between opposing sides achieved a smaller deviation and variation in the measured twist than sequences that proceeded around the frame, clockwise or anticlockwise. The twist variation mode caused by a joining sequence was also found to depend on the starting location of the sequence. The joining sequences that started at the clamps and moved towards less supported areas achieved the smallest mean shift, with less variation of the dominant variation mode. This finding is similar to prior research on sequence synthesis that stipulates that the sequence should be performed from fixed-to-free ends (Hoffman and Santosa, 2003; Shiu et al., 2000). Conversely, the sequence of greatest similarity to that proposed by Liu and Hu (1995b), which stipulates the sequence should progress from weak-to-strong, induced a greater level of twist than the preferred sequences in this work. Importantly, twist was the most dominant variation in this work, and was used as the performance measure. This is different to prior work on joining process sequencing, in which no specific pattern of variation was considered. It is possible that for a different pattern or measure of variation, the desirable sequence synthesis approach may vary.

5.5

Chapter summary

A key finding of this work is an extended generalisation of the current idea of welding or clamping from the fixed to free end. The simulations in this chapter have shown that in a more complex situation where the structure loops back onto itself, the sequencing guidelines should more accurately be stated as follows:

The joining and clamping sequence should be specified with respect to the stiffness of the structure and should be performed from the most rigid area of the assembly towards the least rigid.

§5.5 Chapter summary 103

That is, when considering which join to place next, all prior joins, if any, along with the fixture clamping system, must also be considered. However, it is noted that this depends on the measure used to evaluate dimensional variability.

This chapter also highlighted the ability of the sequence to induce different types of variability in the output variation, in the presence of particular input variability. Consequently, in determining if the weld sequence will have an influence on the production, there needs to be a specific form of deformation or variation pattern present for the sequence to be used for dimensional control purposes.

This chapter has addressed Objective 2 (see Section 1.3.2) of this thesis by developing an understanding of the relationship between incoming and outgoing variations as a function of the assembly process, with consideration for both the clamp and joining process sequence. In doing so, it has also provided valuable information that begins to address Objective 3. Objective 3 will be addressed further in Chapter 6, where observed joining sequence trends will be analysed in greater detail, and under a variety of conditions. The findings of these chapters will then be developed for application in a sequence synthesis approach (Chapter 7).

Beam based sequence analysis

considering internal stresses

To address Objective 3 of this thesis, and more rigourously determine the requirements for optimal sequence selection, this chapter presents an investigation into the analysis of sequences using a two dimensional finite element model. Two areas of analysis are considered here: modelling assumptions and input variables. An increased number of factors are considered in the sequence analysis process compared to prior works, which reduces the modelling assumptions to improve the accuracy of the analysis. The importance of stress build-up is illustrated through a comparison of two models in a cantilever situation (Section 6.1.1): in the first, there is no transfer of residual stresses between joining operations; in the second, stress build-up is considered between the joining operations. The influence on the geometric deviation and variation is compared for these two models.

Two input geometry cases are then considered during the analysis process: a cantilevered beam situation as presented by prior researchers (Liu and Hu, 1995b; Shiu et al., 2000; Hoffman and Santosa, 2003), and a polygon geometry case that is based on the loop geometry used throughout this thesis (see Section 3.2.1). The polygon geometry case contrasts the standard case used by researchers, by highlighting the importance of structural design, and further emphasising the importance of considerations for internal stress build-up on the sequencing problem. To identify sequences that have the greatest robustness to input variations,

§6.1 Background 105

a number of different variation patterns are investigated. A robustness evaluation index is presented and applied to the sequencing results to determine the preferred robust sequence (Section 6.2.1). A clamping operation is then combined with the polygon sequencing problem to determine the influence of the built-up stresses on the spring-back geometry (Section 6.4.2). A discussion is then provided regarding the end goal of determining the requirements of a sequence synthesis methodology considering robust sequence selection, and the relationship between this and prior analysis results (Section 6.5).

6.1

Background

In Chapter 2, the limitations of sequence synthesis works and their respective sequence analysis foundations were identified. Chapter 5 demonstrated preferred sequence trends qualitatively; however, since this model is too complex to execute all possible sequences and determine the properties of a robust sequence, two dimensional beam based simulations will be used.

Three simulation variables are considered in this work: joining sequence, variation pattern inputs, and the design of the structure. Figure 6.1 illustrates these three variables, and their interactions, to be considered during sequence analysis for developing a synthesis methodology. Additionally, the modelling considerations are identified, and their relationship to the joining sequence highlighted.

Figure 6.1: Analysis assumptions and relationships between joining sequence, variability and structural design.

To illustrate the contrast between this work and prior research, the aspects relating to the modelling for sequence analysis are presented in Table 6.1.

Table 6.1: Summary of sequence analysis works for developing sequence synthesis methodologies.

Author

Joining sequence modelling Variation patterns

Design cases Spring-back Step history Deformation

Liu and Hu

(1995b) Stiffness ratio Geometric 2D linear One One Hoffman

and Santosa (2003)

Energy

recovery Geometric 2D linear One One

Shiu et al.

(2000)

Stress

minimisation Internal stress 1D linear One One Wärmefjord

et al.(2010b) Stiffness ratio Geometric

3D Contact

Non-linear Unknown

Multiple Industrial

This work Energy recovery Geometric & internal stress 2D Geometric Non-linear Three per design case Two

§6.1 Background 107