Pad Design for Heat Release and Direct Print


	Plate Shape

	In order to obtain the exact geometry of the plate to be decorated we have to get the cross section of the plate. The plate hast to be cut in the center. The so obtained cross section is scanned with the data M COPRA®Template Checker. The measurement system is based on a scanner. A special image processing software calculates the vectorized outline of the plate and saves it to a file in DXF format. *fig2: Scanned outline of a typical plate obtained from the COPRA®TemplateChecker*


	Pad Shapes

	For an existing pad we need the exact contour. If you do not have any drawing of the pad you can use the COPRA®Rollscanner for determining the exact contour of an entire pad. This machine calculates the vectorized contour of the pad and save this geometry to DXF files too. *fig3: data M COPRA®Rollscanner for measuring the pad geometry* *fig4: Pad Drawing from the data M COPRA®Rollscanner*


	Description of the FEM Model

	The numerical simulation procedure is based on the finite element method (FEM). The finite element analysis cycle involves five distinct steps CONCEPTUALIZATION MODELING -> Preprocessing ANALYSIS INTERPRETATION -> Postprocessing ACCEPTANCE This process may be traversed more than once for a particular design; that is, if the results do no meet the design criteria, you can return to either the conceptualization (Step 1) or modeling (Step 2) phase to redefine or modify the process. We focus our attention on two steps of the finite element analysis cycle: Step 2, the model generation phase, and Step 4, results interpretation phase. The modelling consists in different steps. The first step is the discretisation of the pad continuum in small finite elements. In our case we simulate a axis symmetric pad, so we have to consider only one half of the pad. The contour is based on the contour we obtained from the COPRA®Rollscanner. We create for this closed contour a finite element mesh using the advancing front algorithm for triangles *fig5: Finite element mesh of a printing pad with symmetry boundary condition* Next we have to choose the appropriate material law for the employed material. In this case we use a linear elastic material law and consider the material as nearly incompressible. The next modelling issue is the contact problem between the pad and respectively the plate or the table. We consider the pad as elastic and the plate/table as rigid. This includes representing the friction between surfaces of the bodies. We have based our calculation on the Coulomb friction law. This leads to a non linear solution procedure. fig6: Extracted outline of a scanned plate describing the contact surface As we have a axis symmetric problem we can use a triangular axis symmetric solid element. In order to define completely the mechanical problem we need to apply the boundary conditions. First we apply the symmetry condition and second we define the boundary condition describing the compression procedure. fig7: Finite element mesh of a printing pad with compression boundary condition In the case of non axis-symmetric shapes we have to modify the model. We cannot use any more a 2 dimensional geometry but we fully 3D element model .


	Simulation Cycle

	In order to evaluate the quality of printing pad we need to consider not only the transfer of the decal to the plate, but also the picking up of the decal from the table. The kinematics of both processes is quite different as the table is straight and the plate consists in different zones with different curvatures. So it is absolutely not sufficient to consider just on phase. In our procedure one complete simulation cycle consists in 2 phases: 1) picking up the decal from the heating table 2) printing the decal at the dinner plate It is worthwhile to point out that the friction coefficients in both phases are quite different. On table we have a very low friction coefficient due to the melted wax. Whereas in the transfer phase of the decal on the plate we have a very high friction coefficient as the decal sticks on the plate surface and a relative movement is only possible between the decal and the pad. The following figure illustrates the finite element representation of the printing pad and both contact bodies the plate and the table. Also the main direction of the compression movement is shown. fig8: Finite element mesh of a printing pad with both contact bodies the plate and the table


	Results

	The following figures illustrate the multitude of possible results obtained from the finite element analysis. Each increment correspond to a incremental displacement in x-direction of 0.05mm. *fig9: Sequence of the compression process – Deformed Mesh (pad) + contact body (plate). Scalar plot of Strain Component e _xx* *fig10: Deformed Mesh (pad) + contact body (plate). Scalar plot of contact normal force* *fig11: Deformed Mesh (pad) + contact body (plate). Scalar plot of contact friction force* *fig12: Deformed Mesh (pad) + contact body (plate). Scalar plot of stress component s_xx*at the end of the simulation


	Part II – Analysis and Design Optimisation of Printing Pads

	Introduction

	Design optimisation of printing pads refers to the process of attempting to arrive at certain ideal design parameters, which, when used within the model, satisfy prescribed conditions regarding the performance of the design and at the same time minimize (or maximize) a measurable aspect of the design. So we have to develop some pad quality criteria. These criteria can be used later in an optimisation but also for the analysis and evaluation of existing pads. Furthermore we need to define the design parameters describing the geometry of the pad.


	Pad Quality Criteria

	In general we observe 2 principal problems in the heat release transfer process: air inclusions and wrinkles. Other aspects deal with the overall necessary force for compressing the pad, higher life time due to reduced deformations, insensitivity with respect to geometrical variations of the plates. In fig.13 and 14 we have compared 2 different geometrical shapes of the pad. In fig.13 the outer contour of the pad does not respect the necessary kinematics imposed by the plate. In order to obtain a better “rolling” the shape of the pad must be modified in the transition zone between the horizontal and conical part of the pad. *fig13: Air inclusion during printing due to a poor pad shape* After some optimisation we obtained a new shape whose behaviour is presented in fig.14. We can see that the area of air inclusion is significantly reduced. Moreover the cinematic rolling is enhanced. The risk of air inclusions is reduced. *fig14: Optimized pad shape for minimized air inclusion during printing* We can state that the area of air inclusions is an objective value for quality of the transfer process. Of course this is just on partial aspect which needs to be weighted with respect to all the other aspects. Another important aspect is the reduction of the tangential contact forces. High values lead to high relative movements between the pad and the plate. The consequence is wrinkling of the decal especially on the flange.

Generic Pad Shapes

The geometry of the pad depends on the geometry of the plate and on the type of decal you want to apply. In empirical pad development one knows more or less which generic type of pad corresponds to the combination of plate and decal. In our optimisation procedure we use the same approach for the definition of the initial pad geometry. According to the problem we start from an empirically good generic pad shape.

The following table illustrates some possible combinations of decal and plate types.

	Deep plate	Flat plate	Relief plate	X-Large plates > 280 mm Æ
Full surface decals
Ring decals
Intermediate decals

tab14: Possible combinations of decal and plate types

The goal of our optimisation is an optimal geometry of our pad. For this procedure we need to define so called design variables. If we change one of these entities we observe a direct impact on our optimisation criterion. Analysing common plate geometries shows us that a typical plate geometry can be divided in 3 regions A to C, where A is the centre, C the border and B the transition region from A to C.

fig15: Geometrical regions A to B of a typical plate

Part [A] of the printing pad is constructed with a specific radius, in order to ensure a correct picking up and printing of the decal at the mirror-part of the plate and to avoid pressure problems.

The main problem that is implied by printing a full-surface-decal is the condition that no air-enclosures are allowed between the printing pad and the plate during printing. This puts some specific restrictions concerning the shape of part [B] (and to some extent also [C] and [D]) of the printing pad. A poor printing pad concerning this point is shown in the following row of pictures at the left:

We have subdivided the shape of the printing pad in 4 regions where the geometries of regions A to C of the pad depend on the geometries of regions A to C of the plate.

fig16:Examples of generic pad types

fig17: Examples of generic pad types (cont.)


	Iterative Optimization Procedure

	In a first step we started from a generic pad shape. Then we performed a complete simulation cycle. After each simulation cycle we evaluate the different partial optimisation criteria. Each partial optimisation criterion is related to one or more design variables which are modified accordingly. In a first optimisation pahse we focused on the minimization of the air inclusions during printing. We had to reduce the radius in the transition zone form the flat to the cone zone of the pad. In following figure we present a excerpt of some optimisation steps. *fig18: Evolution of the pad shapes during the iterative optimisation procedure* After minimizing the air inclusion in the transition zone from the flat part of the plate to the border zone, we encountered the following problem. Due to the relative sharp edge of the printing pad (required to print the sharp and deep inside edge of the plate), we observed high relative movement in this area (fig 20). *fig19: Deformed pad while flange printing with high relative movement* During further optimisation steps we reduced the contact friction forces but we were confronted to a reduction of the angle between the plate and the pad. A small angle can lead to a poor cinematic behaviour (fig.19). *fig20: Deformed pad while flange printing after relative movement minimization* Because both plate and printing pad are concave during printing, the angle between the pad and the plate small and air inclusions may occur provoked by an imperfect geometry of the plate. Some more iterations have been performed to optimise the rolling on the flange. We can conclude that the pad shape should be concave in the flange printing zone. The pad’s contact zone front should be convex in order to minimize the necessary deformation of the pad to get in contact with the plate. It should be noted that the pickup phase of the decal from the heating table has the same importance than the printing phase. The relative movement of the pad with respect to the table must be minimized too. If this movement is too high, the decal wrinkles already when it sticks on the pad. Figures: critical situations: included air, relative movement of one node from contact to end of simulation Movie of the simulations


	Discussion of the final shape

	After about 20 iterations we obtained the following optimised pad shape. *fig 21: Model of the final shape* The optimised pad has a good cinematic behaviour which corresponds to a unrolling movement of the pad’s contact front along the plate. The following figures show the deformed pad for 3 different times during the printing process. The first figure demonstrates how good fits the pad into the corner between the flat part of the plat and the flange. *fig22: Contact status for deformed pad when the contact front is in the plate’s bottom corner* The next 2 figures represent the contact status in a more advanced state when the pad come in contact with the plate flange. We observe no air inclusions, nevertheless there might be a small risk of inclusions due to the small angel between the plate flange and the pad. *fig 23: Contact status for the plate flange at 2 different times.* We have also studied the decal pick up process from the flat table. The radial strain does not show a very homogenous distribution (fig.24). This is caused by the sharp edge in zone [B] of the pad, required to transfer the decal into the plate’s bottom. We observe also high friction contact forces in this area leading to high relative movements which might lead to a wrinkling of the decal on the pad. Also the normal contact forces of the pad show a high value in the area where the sharp edge is located (fig.25). *fig 24:Radial strain distribution in the printing pad* *fig 25: Normal contact force*


	Conclusion

	A non linear finite element model for heat release transfer process of decals was developed. Optimisation criteria and design variables had been defined. A iterative optimisation procedure had been used to optimise the following aspects: minimum relative movement between the pad and the plate, minimum air inclusion in the corner of the flat bottom and the flange good cinematic behaviour during the flange printing phase. Enhanced life time of the pad Reduced compression forces of the pad This method has been successfully applied to optimise the design of pads for different plate and decal types. Some work has also been done on analysing existing pad. The finite element simulations described above were accomplished with MSC.MARC. 2003, data M Engineering


	Part I – The Simulation Model

	For analysing existing printing pads in a first step we need exact geometrical data of both the pad and the plate. For both types of measurements we use special machines and software. Then we develop a Finite Element Model for the heat release transfer process. *fig1: Example of a versatile printing pad*


	Conclusion

	We have presented a method based on finite elements to simulate the heat release transfer process of decals to plates with silicone pads. We have now a powerful tool which can be extended to analyse and develop pads. This method can also be applied to direct print with different friction factors.