Central composite design - an aid to weld optimisation

TWI Bulletin, March - April 1998

Ian is a senior project leader in the Plastics Joining Group at TWI. He has gained a wide knowledge of plastics joining processes and equipment and is responsible for running research projects and supplying training in plastics joining.

Welding processes, like most manufacturing processes, involve the setting of many machine parameters. Determining the optimum setting for each parameter can involve many experiments. If a non structured approach is taken, often the outcome can be unsatisfactory to the users and valuable time can be wasted. The use of designed experiments can allow an overall view to be taken of a welding process using a limited number of experiments whilst still retaining the ability to examine each individual parameter. Here Ian Froment describes the use of central composite design to examine the ultrasonic welding of nylon.

Background

There are more than fifteen separately identifiable processes for welding thermoplastic materials ^[1]. It is important to select the welding process parameters for each technique to ensure that optimum performance can be achieved in the weld. In ultrasonic welding of thermoplastics, for example, there are six separately identifiable welding parameters for the process. These are weld time or weld energy, cool time, weld force, amplitude, down-speed, and ultrasonic trigger. This work was undertaken to demonstrate the use of Central Composite Design experimentation for use in setting up the ultrasonic welding process. These experimental techniques enable insights into the complex interactions between process variables and therefore allow users of the welding techniques to use the welding processes more effectively.

Ultrasonic welding

Ultrasonic welding was chosen for this investigation because of the wide range of welding parameters that have an effect on the process. Ultrasonic welding involves the use of high frequency (20-40kHz) mechanical vibrations to heat and melt the thermoplastic component being welded. A vibrating welding sonotrode or horn is first brought into contact with the thermoplastic component. The energy produced by the vibrations is transferred into heating at the joint line by intermolecular friction ^[2]. Typically, the welding horn is in contact with the component to perform the weld for 0.5 to 1 sec. Selection of the correct welding parameters is important to the integrity of the welded joint. For example, when welding semicrystalline materials, such as nylon, it is important to use high energy. This ensures that the thermoplastic is heated to the high melting point, typical of these materials. This is generally achieved by using a horn tip amplitude in the region of 100-120µm (peak to peak) and a relatively low welding force. Once the amplitude and force are selected, the trigger parameter must be set followed by down-speed, weld time or energy and cooling time. If one of these parameters is not correctly set, then the process will not function at its optimum. Typical applications of this welding process include automotive components, domestic appliance products and medical products.

Central composite design experiments

The basic concepts of the statistical design of experiments and data analysis were developed in the early part of the 20th Century as a cost effective research design tool to help improve yields in farming ^[3]. Since then, many types of designed experiment and analysis techniques have been developed to meet the diverse needs of researchers and engineers. The simplest form of experimental plan is the 2x2 factorial design. In this design four experiments are conducted consisting of all possible combinations of two factors at two levels or process parameters ie at -1, +1 denoting each of the two values in each factor.

Experimental designs for optimisation are often augmented by extending the basic 2x2 matrix by adding points around the design and at the centre, eg at 0, -1.682 and +1.682. The concept is shown in Fig1. These type of experimental matrix are known as Central Composite Design and are invaluable for determining the interactions between process parameters.

Welding trials and results

Materials

For the welding trials, nylon 6 was welded in a projection joint configuration. The sample geometry is shown in Fig 2. This material and configuration was chosen because, as a semicrystalline material, it is generally considered to be difficult to weld by ultrasonic welding particularly in the projection joint configuration.

It was anticipated that it would give maximum variation in weld strengths for the range of welding parameters under investigation and therefore better demonstrate the capabilities of the experimental design process.

Prior to welding all samples were dried in a vacuum oven for 24hrs at 90°C.

Experimental approach - central composite design

The central composite design was selected for this study. This is a response surface methodology, which is most frequently used for process optimisation. The method specifies parameter settings to be used for a two level factorial design (with levels represented by +1, -1) plus replicated tests at the centre point (0), plus axial points (+1.682, -1.682).

Actual values of weld time, cooling time, and weld force were assigned to the matrix of test levels based on a few preliminary welds which defined the limits of the conditions. The values assigned to the matrix are given in Table 1. The matrix was designed to ensure that all welds, except the outliers, were repeated at least three times, ie to minimise the error in the experiments. The centre of the matrix (0) was repeated six times. In order to analyse a statistical designed experiment, it is necessary to have a quality factor which can be measured quantitatively. For this work failure force was used in the analysis, along with recorded parameters from the machine. These were material displacement, weld energy, down-speed and peak power. The spread of welding parameters was intended to show a large variation in weld quality without including results which produced no weld strength or welds with excessive material placement.

Results

The detailed statistical analysis of the results was conducted using the Design Expert Software.

Weld strength

A selection of the software output results are shown in Fig 3 to Fig 8. The results show that the weld strength Response Surface Model (RSM) is linear and could be fitted to all experimental values with a high level of confidence (>99.99%). Further statistical tests, the most significant of which is the lack of fit test, show that the model is reliable. If there is significant lack of fit, between points in the experiment and the model, it is shown by a low probability value (prob>F). It would be difficult to use such a model as a response predictor. In the case of weld strength the prob>F value is much greater than 0.1 and is therefore desirable in the model response.

In order to evaluate the model, a number of other tests can be carried out on the data produced by the model and the experiments. Fig 3. shows the normal probability plot of studentized residuals. This isthe most important diagnostic test on the data. The plot shows that there is linearity in the error term which is desirable. Secondly, the studentized residuals versus the predicted values are examined. These are shown in Fig 4. The plot shows random scatter in the results, which is a desirable effect. The final test on the data, is examination of the run number versus the studentized residuals. As with the predicted values, there shouldbe a good scatter of the results and no trends. This is shown in the plot in Fig 5.

Fig 6. shows the perturbation plot for all three factors, weld time, cooling time, and force, examined in this study. The plot allows an overview of how each factor affects the model outcome, in this casethe weld strength, within the ranges examined (-1,0,+1). The results show that as the weld time and cooling time are increased, the weld strength increases. As the weld force is increased, the weld strength decreases.

Figure 7 shows the response surface plot for the weld strength versus weld time and weld force at a constant cooling time of 1.20sec. The plot shows that at low force (249N) the weld strength increased from 2090N to 2490N and that at high force (378N) the weld force increased from 1930N to 2340N. Therefore at any given weld time the weld strength decreases as the weld force is increased.

Machine outputs

The machine outputs were examined in a similar manner to the weld strength analysis. The lack of fit, the normal probability plot of studentized residuals, the studentized residuals versus the predicted values, and the run number versus the studentized residuals were examined in order to check the model responses and predict the reliability of each model.

For the down-speed and distance models, the lack of fit test showed a prob>F value to be much smaller than 0.05. This means that the model can not be used to predict reliably the outcome of future welding experiments within the limits of these experiments.

The models for the peak power, and energy were found to be reliable models for predicting the outcome of future tests.

The most significant results are seen by examining the perturbation plots for each of the test outcome factors, ie energy, peak power, distance, and down speed. Figure 8 shows the perturbation plot for the weld energy. The plot shows that the weld time has the most significant effect on the weld energy, closely followed by the weld force, both parameters increasing the weld energy as they increase. The plot also shows that the cooling time has had an effect on the outcome of the model for weld energy, although the effect is small.

The perturbation plots (not shown) for the other output parameters show that weld time has the most significant effect on distance, with force and cooling time having less effect. Force alone has an effect on welding head down-speed and peak power.

Discussion

Experimental design

The results of the welding trials and the designed experiment show that using these design tools to construct experiments and evaluate the outcome of welding trials, provides a powerful method for understanding the welding process. The simple set of experiments conducted in these trials confirmed the effects that each of the welding parameters has on the overall process.

In order to use successfully the experimental design, and keep the number of experiments to a minimum, it is important to review the welding parameters to determine which ones can remain constant throughout the trials. In the experiment conducted for these trials, three of the six welding parameters were preselected and not included in the experimental design. This was initially to cut down the overall number of experiments. For example, it is recognised that for semicrystalline materials, such as nylon, the amount of amplitude required would be high and therefore this was selected as a constant for all the experiments. In practice, no parameter should be left out of the design, to ensure that all effects are analysed but this will lead to further trials within the experimental matrix.

Selection of the experimental limits are also an important factor in ensuring adequate models are produced for the welding process. In these experiments, all models suggested that the output parameter, for example weld strength, would carry on increasing infinitely. In practice, experience tells us that this cannot be the true case and therefore we can conclude that the upper limits of the experiments could have been better selected.

It is important for the user of designed experiments to have at least a basic understanding of the welding process under examination. There may be effects shown in the results which cannot possibly happen in practice. For example, the results of the model used to predict the weld energy, showed cooling time had an effect on the weld energy. In practice, energy is only used during the period when the ultrasonic vibrations are applied to the component being welded. Therefore the effect can either not be real, and should be disregarded, or evaluated with further experiments to ensure that there is no definite effect.

The use of designed experiments is particularly useful as a diagnostic tool for problem solving in welding processes. If a component is experiencing regular failure in service, it is possible to use this approach first to establish the optimum welding conditions and then determine the effects of each of the parameters on the process outcome or failure. Most importantly the relative effects of each parameter are shown by the model and therefore can be more precisely controlled during the welding operation.

Welding process

The results of the design experiments confirmed a number of the basic principles surrounding the ultrasonic process, thus confirming that the design of experiment methodology works. It is important to note that designed experiments could be used for analysing the effects of all welding processes.

The results showed that the weld strength was a function of the weld time, weld force and cooling time. The results also showed that in order to produce the strongest weld, within the limits of the designed experiment, the weld time and cooling time should be maximum (1sec and 1.2sec respectively), with the weld force at minimum (249N). When welding semicrystalline materials, high amplitudes are selected and it is therefore important to use minimum weld force to prevent stresses being locked into the joint and prevent stalling of the machine during the horn start up phase.

Conclusions

The following conclusions can be drawn from this work investigating the use of central composite design experiments for investigating the ultrasonic welding process.

• Central Composite design experimentation provides a powerful tool for analysing the effects of the process parameters in ultrasonic welding.
• The techniques can easily be used to examine any plastics welding process.
• It is important when selecting the limits of the experiment, that sufficient range is selected to ensure that trends are identified within the process.
• It is important to have a basic understanding of the welding process under examination to ensure that the trends are understood and that effects are real.
• The model should be fully tested to ensure that errors in the model cannot lead to incorrect results and conclusions.

References