3 SIMULATION OF THE PROCESS CHAIN

For the simulation of the processes in the production chain it is necessary to simulate first the systematic effects and in the next step to simulate the effects with a variation in a statistic way.

3.1 Systematic effects of processes

The model for the simulation is generated from the product data model and starts with a CAD-sketch of the raw part. Also the process data for the simulation comes from the data model. These process data is used in the model to simulate changings of geometric characteristics. Some of these changes will occur always, are predictable and will be summarized under the name systematic errors. Since these changes occur always and they have a direct influence on the further production on the profile they will be simulated first. Before the simulation it is necessary to split the whole process chain into its single process steps, because every step will change the geometry in a different way. Every process step will also have a direct influence of the following process steps. Therefore the generated data for a single process from the simulation will always be related to the preceding process steps.

Still there are two types of systematic errors. On the one hand there are general systematic errors and on the other hand profile specific systematic errors that need to be handled. General systematic errors are the ones that occur before the simulation of a process step. An example for a general systematic error could be the addition and subtraction of material of a profile (Fig.5).

Figure 5: Examples for systematics effects on the profile

Especially in the profiling and the process step of profile wrapping it is necessary to include this in the simulation. The CAD-sketch is in the most cases the optimal profile specification of the finished product, but to get the right process data from the model we need to have the profile geometry without the thickness of the foil or paper, which is added during the profile wrapping. The thickness of the foil or paper is stored in the material database, which is part of the product data model. Therefore it is necessary to change the geometry and subtract material from one point to another, where the foil should be added. This also leads to another problem. If for example the profile geometry has round corners with a small radius and material will be subtracted, it can happen that these corner will disappear and the model of the profile will have a sharp corner at this point. Profile specific systematic errors could be for example the positioning of the profile in a machine of a single process step. The positioning has a big influence of the following process steps because different tools can lead to a different changing of the geometry at the part of the profile they edit. The algorithm which is able to simulate the automatic positioning in a machine works in the meaning of giving the operator a suggestion. The operator will be always the last instance to crosscheck the results, since there is an infinite amount of different profiles with their own special geometrical specifications that might need to be specially handled. Also the positioning is important when it comes to the process step of profile moulding. Especially profile moulding comes with a lot of systematic errors, which comes from the fact that it includes a lot of sub-processes. Already the milling of the tools includes a systematic error because the grinding wheel, which is forming the tool has a radius at the edge. These radius will lead to round external corners of the profile because the internal corners of the tool will have at least the radius of the grinding wheel [5] (Fig.5). Another big influence of the profile moulding is the number of cutting passes. The number of cutting passes specifies which tool will edit which part of the profile. As mentioned before the algorithm which is

executing the automatic number of cutting passes is highly influenced by the positioning of the profile, since the positioning defines which part of the profile is moulded by which side of the machine. Another part of the simulation is testing the tools after the number of cutting passes are defined.

Some parts of the profile might have undercuts or the profile geometry is too deep and the desired machine can’t mould it. In some cases these errors can be erased by a different number of cutting passes or by a different positioning of the profile in the machine. Therefore testing of different positions and set ups are a big part of the simulation. But there are not only systematic changes of the profile geometry, there are a lot of influences which won’t always behave in the same way and which can’t be easily handled. In that case it is necessary to observe a process step over a long time to predict his behaviour by using statistics.

3.2 Variations of effects in production

The engineer designs the geometry of a profile for example as a CAD-Sketch. This sketch is in the most cases the ideal geometry specification of the part. Manufacturing processes are not capable of producing the part exactly as it is specified, which means they can’t produce the part without variation in his geometric characteristics. Therefore, in the most cases also tolerances will be specified, which give limits to the allowable variation [16].

Statistics are a tool with great power to handle these tolerances. Since almost every process in a well-defined process chain can be investigated, also their behaviour over a long time can be obtained. This behaviour can be transferred into the form of probability density functions. The correct estimation of the specific behaviour for single processes and sub-processes is very important since wrong probability density functions will lead to a the part will move away from the guidance element. For processes and sub-processes that cannot be investigated properly rectangular distribution are expected. Rectangular distributions are preferred because it has shown that normal distributions are not suitable for processes in a real environment [18].

[19] says that under the assumption that the probability density function fills out the whole tolerance field, the rectangular distribution has two advantages. In the first place it makes sure the result is “save” and secondly the probability density function won’t has to be verified. The probability density function for a single tolerance along a whole process chain is calculated by the convolution of the probability density functions of all sub-processes for a single process step and afterwards of the convolution of the resulted probability density functions along the whole process chain (Fig.6).

Figure 6: Consideration of statistical influences in the process chain

To simulate and integrate the functionality of statistics with probability density functions into the research project, Simulink Matlab is used. Matlab provides all the basic functionalities that are necessary to convolute distributions and to receive the desired data out of the resulted distribution.

This ability opens up another benefit of the statistical approach. With the convoluted probability density function over the whole process chain the percentage of all parts that will probably be inside the tolerances are given by quantiles [20]. These quantiles are calculated using the cumulative distribution function of the resulted probability density function. A further benefit is that for each distribution function the standard deviation can be calculated. When the standard deviations are summed up, the share of each of these values to the summed up value can be calculated, which gives us the influence of each single process and sub-process to the whole process chain.