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As noted in the introduction to this thesis the exemplar domain at which the work described in this thesis is directed is sheet metal forming, more specifically Asymmetric Incremental Sheet Forming (AISF). AISF as a process was patented in 1967 by Lezak [132], however academic work related to AISF was not undertaken until much later. The first publication, to the best knowledge of the author, was in 2005 [115]. AISF is defined “as a sheet metal process that: (i) has a solid, small sized forming tool; (ii) does not have large, dedicated dies; (iii) has a forming tool which is in continuous contact with sheet metal; (iv) has a tool that moves under control, in three dimensional space (CNC)1 and (v) can produce asymmetric sheet metal shapes” [115]. Of note is that the sheet thickness of the part being manufactured reduces (in an irregular manner) as the shape is pushed out; taken to extreme AISF will result in undesired fractures being introduced into the part. The basic component of an AISF machine are the sheet metal blank, the blank holder where the sheet metal is fastened and the forming tool used to form the desired shape according to a prescribed path. The process is illustrated in Figure 2.2. The tool spins at w angular speed and moves horizontally and vertically atv speed to form the shape as shown in the figure. Single Point Incremental Forming (SPIF) or Two Point Incremental Forming (TPIF) are two alternatives to AISF. The distinction is that in TPIF a “die” is used to support the sheet metal over which the tool head is passing. SPIF is sometimes referred to as dieless AISF. With respect to the work described in this thesis; experiments were conducted using only SPIF; hence wherever the term AISF is used this refers to SPIF or dieless AISF.

AISF is mainly used for small production runs and prototyping. AISF supports a wide range of applications in industrial fields such as the aerospace industry, where the trend is to manufacture small numbers of parts. Interestingly the AISF concept has also been used in the medical contexts to produce artificial limbs and dental crowns. For further discussion on the applications of AISF the interested reader is referred to [114, 115].

The most significant issues associated with the AISF sheet metal forming processes are: (i) production time (it is a lengthy process, several hours to produce a single part); (ii) it is time consuming and requires trial and error experiments to determine the best parameters values for the process and (iii) deformation (geometric inaccuracies) resulting from the “springback” that is introduced as part of the process [86]. It is the latter that is of concern with respect to the work presented in this thesis. Springback is the geometric “elastic deformation” that manifests itself on completion of the AISF process (when the part is unclamped); as a result the produced shapes is not identical to the intended shape. An additional issue is that springback is unequally distributed and non-linear [36, 40, 209]. Springback tends to be induced by several factors: (i) the shape and dimensions

Figure 2.2: The AISF process. The basic elements of AISF are the metal forming

forceF, the tool speedv and the spin angular speedw. [114].

of the manufacturing tool (the tool head), (ii) the properties of the material from which the part is being manufactured and (iii) the geometry of the shape to be manufactured [13, 18, 65, 86, 114, 115, 140, 154]. It is generally acknowledged within the industry that the geometric shape of the part to be manufactured is the most significant factor. Hence the springback phenomena encountered in AISF is good exemplar application domain for the work presented in this thesis. Some further discussion regarding springback is thus presented in the following section.

2.2.1 Overview of Springback

There has been a substantial amount of reported work on springback analysis, prediction and compensation. This previously conducted work can be categorised into four main approaches:

1. Experimental Approaches: Work to identify the optimal parameters for a cer- tain (simplified) forming processes and to explain the relationship between these parameters through a series of “try-out” experiments.

2. Analytical approaches: Typically concerned with describing the changes in the “before” and “after” geometrical shape of a given part using, mathematically based, theoretical analysis techniques. Generally adopted in the context of simple shapes.

3. Modelling Approaches: Used for investigations with respect to more compli- cated 3D shapes. The idea is to develop models of the manufacturing process with

respect to different parameters. Normally, the Finite Element Method (FEM) or Artificial Neural Network (ANN) methods are employed to generate a fully oper- ational simulation environment whereby springback predictions can be made (and in some cases compensated for).

4. Regression Approaches: Work that has adopted a regression based approach to attempt to characterise springback. This approach incorporates the most recent work on springback analysis.

Note that other categorisations have also been proposed (see for example [154]). Some further detail concerning the above four approaches is given below. In each case appro- priate examples are given.

Using experimental approaches springback is typically analysed and characterised with respect to particular forming process parameters or material properties [34, 134, 169, 218]. Experimental approaches are typically used to identify the relationship of springback with respect to other parameters such: as sheet thickness, tool radius, tool head size and the different properties of the material used. Two processes, called “V- bending” and “U-bending”, are the most popular techniques used with respect to the experimental approach since as a result of the “bending” the induced springback is large and can thus be easily detected and analysed. Examples of this approach can be found in [47] where V-bending was used and Zhang et al. [230] where U-bending was adopted. Despite the simplicity of the approach it does not sufficiently take into consideration actual manufacturing process conditions [34]; it is also time-consuming and expensive [134].

In the case of the analytical approaches springback prediction is founded on a theo- retical analysis that entails certain assumptions and simplifications, namely a simplified tool description is assumed and the nature of the manufacturing conditions are sim- plified. Some work that has adopted the analytical approach has simplified the process even further by considering only simple 2D shapes (and without considering any realistic forming process), see for example [149, 169, 230]. Examples of work using the analytical approach where the forming process is taken into consideration can be found in [14, 230]. It is generally acknowledged that the analytical approach is informative even though the process is over simplified. It has also been suggested that the analytical approach can be used to provide support for modelling approaches so as to provide some understanding of the manufacturing process conditions and parameters that have an impact on the nature of springback.

Modelling approaches, as the name suggests, are directed at building a simulation environment. The most frequently used modelling approaches are based on FEM, see for example [36, 137, 153, 222]. Some researchers, such as Karafillis et al. [119], have proposed iterative FEM models where springback calculations are used to optimise the tool path. Other researchers have used FEM not only to predict but also to com- pensate for springback error (see for example [38, 150]). There has been some work

where the outcomes from FEM simulations have been analysed using Rough Set Theory (RST). Examples include [185] and [219]. In [185] RST was applied to FEM U-bending simulation results in order to identify optimal forming process parameters. In [219] a framework was proposed, based on the Knowledge Discovery in Data (KDD) process, whereby FEM simulation results could be collected and analysed using RST. Despite the sometimes successful application of FEM it requires significant resource to undertake. The limitation and drawbacks of FEM, as presented in [43, 99, 134, 150, 204], may be summarised as follows.

1. Identifying the different alternatives for each parameter required by FEM is chal- lenging and time consuming.

2. Given that FEM supports different alternatives for each parameter and that these parameters may be related, choosing a particular parameter setting may impact on the options for other parameters.

3. To generate an accurate simulation environment an extensive set of “try-out” experiments must first be undertaken with respect to the alternatives for each parameter. This is a resource intensive process. Hadoush et al. [90] estimate that the time required may vary between 16 hours to a few days.

4. To achieve a highly accurate level of prediction requires accurate identification of the forming parameters which in turn requires a degree of expertise (which may be informed using analytical work).

5. FEM cannot respond interactively when a new condition arises that was not con- sidered during the FEM design stage [56].

6. The choice of alternatives for the various parameters impact upon the simulation process with respect to: (i) the integration algorithm used (implicit or explicit), (ii) the number of integration points and (iii) the type of shape used in the simulation (shell, solid or 2D plane) [134].

7. FEM entails mathematical approximations (such as numerical integration) which in turn are a source for potential inaccuracies (sensitive to numerical tolerances). In other words, the reliability and accuracy provided by FEM, in many cases, do not satisfy industrial requirements [150].

8. Limited applications in real life as prediction using FEM is very time consuming [91, 134].

Despite the significant work that has been conducted to develop and improve FEM simulation/modelling, the accuracy of the resulting springback prediction remains in- sufficient with respect to industrial requirements [34, 157]. Therefore Artificial Neural Networks (ANNs) are often quoted as being a good alternative modelling approach to

FEM. Moreover, ANN approaches are suited to interactive simulation environments such as those described in [56, 126, 148]. The forming process parameters, such as tool ge- ometry and material properties, are input into the ANN for training purpose. Typically an ANN comprises several layers where each layer consistis of several “neurons”. The structure of an ANN is determined after several iterations of training [110]. The work presented in [92] proposed a hybrid simulation environment based on both FEM and ANN simulation to predict springback. However, the main drawback of the use of ANNs is the computational cost (time and memory) required. In addition, when using ANN techniques it is difficult to understand the internal operation due to the black box na- ture of ANNs. ANN techniques can be argued to be a data mining technique. However, there has been a very little reported work that considered the problem of springback prediction in the context of classification (as in the case of the work described in this thesis).

The final category of previous work on springback analysis considered in this review is the work based on regression analysis. The significance of this approach is that it is the most recent. A good example of the use of this approach, in the context of spring- back prediction, can be found in [17] where aMultivariate Adaptive Regression Splines (MARS) technique to support springback prediction is proposed. MARS incorporates a non-parametric1 statistical regression test [75]. Initially, two files are generated; one describing the desired shape and one the obtained shape (in other words T and T0) in terms of a small number of “features” (types of geometries, such as flat planes), along with a description of their locations, orientations and normals. A comparative analysis between the description files (before and after manufacturing) was used to generate an accuracy file that contains details about each individual point located in the T and T0 point clouds along with their springback values in the x,y, and z directions. Features of a particular type (such as flat plane features) were identified and then linked with this accuracy file. Then for each identified individual feature a separate text file was produced that contains information about all the points (vertices) within the feature with respect to certain parameters (some parameters are related to the part to be man- ufactured such as its geometry while other parameters are related to the manufacturing process such as tool diameter). Series of “try-out” experiments were conducted to deter- mine the main parameters of each relevant feature. After that, the text files were used to generate the “MARS” models which could then be employed to predict springback in the context of new shapes that contain the identified feature types. Although an improved result was reported, the usage of MARS is limited because it typically covers only a limited range of features. Another disadvantage is that the technique requires complex structures to compare features with corresponding parameters; this complexity increases as the number of features is increased and/or when the features are specified to a greater level of detail.

The approach presented in this thesis is founded on the idea of classification. The conjecture is that sufficiently robust classifiers can be learnt without the need for: (i) a detailed understanding of the effect that specific parameters have on the springback phenomena (as in the case of the experimental and analytical approaches) or (ii) a deep understanding of the process (as in the case of the modelling approaches) or (iii) restriction to a limited set of “features” (as in the case of the regression approach). To the best knowledge of the author there has been no reported work on the use of classification techniques to predict springback in the context of AISF (or sheet metal forming in general).

It should also be noted that successful springback prediction (however this is done) is only “half of the story”. For such predictions to be useful they need to be applied. The application of springback prediction, in order to produce high quality shapes, is also a research issue [10]. For example the first version of the the Displacement Adjustment (DA) algorithm, suggested by [137], was enhanced to produce the Smooth Displacement Adjustment (SDA) algorithm so as to aid the application of springback predictions. Further discussion on the application of springback, in the context of the work presented in this thesis, is described in Chapter 8.