Looking for calculations I could apply to a vacuum-forming machine

[SaldanaKS]

Homework Statement

Designing a vacuum forming machine and stuck on creating calculations to supplement the project and aid in proof of design and feasibility. I have done some basic vacuum calculations such as determining the evacuation time as well as a heat transfer calc however I'm not fully confident in their correctness and was hoping to get some advice on any calculations that could be done relating to the vacuum system, heating element, and thermodynamics or the machine in general?

The machine is a simple vacuum forming machine where an aplastic sheet is heated and then drawn over a mold, the vacuum is applied through a platen, and the sheet forms around the mold. Im creating the CAD model however I need to illustrate some calculations based off the design and considering the critical parts.

Any input, suggestions or advice would be much appreciated.

Relevant Equations

Forming area = 300 mm^2 = size of the sheet

Using a diaphragm vacuum pump

volume to be evacuated = 0.015 m^3

Using a steel rod heating element:

Power = mass x specific heat capacity x change in temp x time
P= 300 W

Rate of heat transfer, Q = 8 J/s

So far I have determined the evacuation time, a basic heat transfer between the heating element and plastic sheet, and a hold down force of the forming bed.

 

[berkeman]

Welcome to PF.

Could you please define the variables in your "Relevant Equations"? I'm guessing that T is Temperature (in K) and t is time?

Also, could you please provide a lot more details on your question, including sketches or pictures of your mold and workpiece (including dimensions) and the material that you are forming? Can you post links to the reading that you've been doing so far about vacuum forming?

Finally, just wanting to verify that this is for a schoolwork question and not for your work? I can move it to the ME forum if it is for your work. Thanks.

 

[SaldanaKS]

Welcome to PF.

Could you please define the variables in your "Relevant Equations"? I'm guessing that T is Temperature (in K) and t is time?

Also, could you please provide a lot more details on your question, including sketches or pictures of your mold and workpiece (including dimensions) and the material that you are forming? Can you post links to the reading that you've been doing so far about vacuum forming?

Finally, just wanting to verify that this is for a schoolwork question and not for your work? I can move it to the ME forum if it is for your work. Thanks.

Thank you, I will update those and try to provide more information and some of my work completed thus far. Its for a university mechanical design project, I wasn't sure which topic that would fall under?

 

[berkeman]

You are posting in the correct forum here at PF if it is for a school project. If we need to page in some ME experts at some point who have seen your thread, we can certainly do that.

 

[Baluncore]

I have done some basic vacuum calculations such as determining the evacuation time as well as a heat transfer calc however I'm not fully confident in their correctness and was hoping to get some advice on any calculations that could be done relating to the vacuum system, heating element, and thermodynamics or the machine in general?

How do you apply the heat from the rod to the plastic ?
Maybe use a hot air gun ?
Does the pump need a big capacity, or do you have a vacuum reservoir ?

 

[SaldanaKS]

How do you apply the heat from the rod to the plastic ?
Maybe use a hot air gun ?
Does the pump need a big capacity, or do you have a vacuum reservoir ?

Using a 220V rod element to heat the plastic, therefore heat would be applied via radiation.

Not sure if a hot air gun would be as effective as a heating element, i have considered quartz and ceramic however.

lastly, the pump is to be as small as possible while being able to have enough suction for the vacuum. Its for a desktop application. So there won't be a reservoir.

 

[erobz]

Using a 220V rod element to heat the plastic, therefore heat would be applied via radiation.

Usually the heating elements are rated with wattage? Is it like a $10 \, \rm{kW}$ or a $1 \, \rm{kW}$ heater?

 

[pbuk]

Its for a desktop application.

Is it like a $10 \, \rm{kW}$ heater?

Toasty!

 

[erobz]

Toasty!

 

[erobz]

After reading the OP more carefully. Apparently its rated as $0.3 \, \rm{kW}$.

 

[erobz]

Have you taken a course in Heat Transfer? I ask because heat transfer by radiation is a bit more involved than what you have seemingly computed. There is (at least) the temperature of the emitter to consider (simplest to assume the emitter is a blackbody), the View Factor between the emitter and the absorber (which depends on a number of characteristics pertaining to the physical setup), the emissivity of the absorber (simplest to assume total absorption, not necessarily most accurate), and the thermal characteristics of the absorber to consider. With some (perhaps arguably) reasonable assumptions, I think you are going to end up solving something like following differential equation for the time it takes to heat the plastic sheet to its forming temperature.

$$ \alpha \frac{dT}{dt} = -\beta T^4 + \kappa $$

If you are interested, the details can be filled in.