User's Manual for the Heat Seal Calculator - Induction

HSC-I

Heat sealing via Induction is hugely important for the placing of caps onto containers.

The aim is to bring the heat seal polymer within a Cap to its seal temperature, T_Seal at the interface with the Container in the shortest possible time with the minimum risk of under-heating (producing a seal that is too weak) or over-heating general degredation). The science is well-described in the standard text on heat sealing by Dr Kazuo Hishinuma, published by DesTech Heat Sealing. Technology and Engineering for Packaging, Principles and Applications.

The app allows you to set the power of the induction heater and the diameter of the cap (doubling the diameter reduces the power density by a factor of 4), the thicknes of the heat seal layer, the polymer type for the heat seal, plus the thickness of the Al, the thickness and MPt of a wax layer (designed to melt and flow into the Cap) and the properties of the Cap and Container - including the option of the container being glass. For numerical reasons thicknesses are set in units of 4μm - allowing 2μm steps slows things down by a factor of 4.

The induction process proceeds for a time t-Heat with an optional cooling time of t-Cool. The app calculates the temperature at the heatseal/container interface as well as the temperature in the Al layer. These are shown in the graph on the right.

The graph on the left shows the temperature distribution from Cap to Container, colour-coded in time from violet (short time) to red (long time). The maximum temperature of the graph is set by GMax. It is a great way to see what is happening at the different layers within your system, which are marked out in horizontal lines. Note that the calculation models 500μm of Cap and Container but only shows 12μm of each. The loss of heat into the Cap and Container is a dominant feature of Induction and explains (below) a lot of the mysteries and confusion in induction sealing.

The app does not have a "Pressure" option. This is because pressure makes no difference to heat sealing once you are above a minimum pressure that ensures perfect contact between the surfaces. A lot of failures in induction sealing are due to the wrong torque on the cap and/or junk getting in the way of perfect contact. As mentioned above, a large amount of the heat energy goes into the cap and container. So if there is imperfect contact at any point the induced heat goes into raising the temperature of the heat seal itself to alarming levels.

Peel Strength

In general we are not trying to get a very strong seal. A typical heatseal polymer might be LDPE sticking to HDPE. HDPE is relatively slow to melt and hard to intermingle so strong bonds aren't obtained unless the temperature gets very high. And, of course, onto glass there is no intermingling so no strong bonding. Even so, the nature of the heatseal layer and the temperature reached and time spent there have profound effects on the seal quality - though it's not always clear what they are. It is generally supposed that you need to get the interface to T_Seal which is somewhere around the polymer's melting point, T_m.

What is T_Seal?

In principle T_Seal and T_m the polymer's melting point should be the same. The key issue is that many heat seal polymers such as PE will, under very careful analysis, show multiple values of T_m. Therefore T_Seal is an experimental value for a given polymer that is somewhere between the lowest and the highest values of the various T_m.

To model the effects of melting we could absorb heat via two methods: heat capacity and enthalpy of fusion. But a more elegant approach is to use a variable heat capacity which increases strongly around the melting zone. For the app the heat capacity curve assumes two forms for each meltable polymer PE and PP. The N(arrow) form has a relatively sharp and large increase in heat capacity (i.e. melting is over a narrow temperature range of ~15°) and the W(ide) form has a less sharp and smaller increase in heat capacity (i.e. melting over a wide temperature range of ~30deg). The area under the curves are the same (so the enthalpy of fusion is the same), but the effects on the temperature/time curves are visibly different. It is a common observation that Wide polymers are easier to seal reliably (given normal process variations) than Narrow ones.

The summary of all this is that a polymer shown as PE:105N is a low density, controlled branching PE with an effective T_Seal of 105°C and a Narrow melting window, PE:105W has a different form of branching giving a Wide window around the same nominal melting point - and so forth for the other PE and PP entries. Future versions of the app might allow these temperatures and width to be input variables. This approach to modelling melting was suggested by Sascha Bach at Technische Universität Dresden whose help for this and the Jaws app is warmly acknowledged.

kW

Yes, I know that it is meaningless to talk about kW in Induction heating. A badly designed induction head at 2kW might provide much less sealing than a well-designed heat at 1kW. Tunnel heads, ferrites, different frequencies and so forth have profound practical consequences. And of course, 1kW applied to a cap of 60mm diameter is going to have a very different effect compared to a cap of 30mm diameter where the power density (other things being equal) is quadrupled.For this app the definition of "1kW" is a value that gives a reasonable match to common observations from the industry. Whether it's actually 0.8kW or 1.2kW is not important for the app. Real life in induction sealing is far too complicated to be captured in a simple app (though the app is complicated enough!). Just use the powers as indicative of trends. Although the absolute numbers may not match your setup, the relative numbers should be quite reasonable. If anyone from the industry can provide me with better datasets I can refine the definition of 1kW.

Optimising

A common observation is that if you can seal X containers/min at 1kW you can seal many more than 2X containers/min at 2kW. The app makes the reason for this effect very clear. Suppose we try to heat the Al very slowly. Because the Al and heatseal are thin layers and because the container is very large, most of the heat we supply will end up in the container. If we heat the Al very quickly then its temperature will rise quickly because heat hasn't had time to flow into the container. The argument is intuitively correct and the app demonstrates this clearly. Set t-Heat to 0.2s and make sure t-Cool (cooling time) is set to 0. Set the power to 0.7kW and after pressing Calculate, note the maximum temperature reached at the Al layer and at the interface between heatseal and Container. Note, too, how broad the heat distribution is, remembering that you are only seeing 12μm of the 500μm of the Cap and Container that are absorbing a lot of heat. Now repeat the calculation at 1kW then 1.4kW. The peak Al temperature will rise very much more quickly, sharpening the thermal curve and you will reach T_Seal much more quickly. As you go to even higher powers you will (a) overheat your seal and also (b) "overheat" the calculation - it has an automatic cut-off when the numerics would start to create artefacts. If the graph in your calculation terminates before the end that means that the automatic cut-off has happened.

Details of the calculation

The app uses a classic "finite difference" calculation using 4μm thick "slices" through the wax, Al and seal (as well as the 12μm each of Cap and Container), and short timesteps during which the heat flows and temperature changes are calculated. Heat flows into each slice according to the thermal conductivity of the slice and the temperature difference from the previous slice. It also, of course, flows in to the Al layers when the power is on. Heat flows out of the slice via a similar process. The net heat flow is then used to raise the temperature according to the heat capacity of that slice (which is in itself temperature dependent, especially around the melting point).

The big problem with such calculations is speed. If the timestep is very short there are no numerical artefacts but the calculation is slow. If the timestep is too long then the numerics explode. As is common, a short timestep is used near the start when there are large heat flows, with a steadily increasing timestep in later steps to give a speed boost. The temperature gradients and power flows in Induction are much larger than in Jaws so the timesteps are much shorter and the calculations much longer.