DOE with dependent factores

[#1]

I'm designing a DOE and decided to use the software. My DOE is made up of 6 factors defined as:

1. layer thickness -> 0,03 and 0,06 mm
2. Laser power -> from 100 to 400 W
3. Scanning speed -> from 400 to 1000 mm/s
4. Distance scanning -> from 0,05 to 0,2 mm
5. Temperature -> 0 and 200 ºC
6. Strategy type -> chess and stripes

However, factor 1, 2, 3 and 4 are by related by the following equation:

Ev = 2/(1*3*4) and the variation in values cannot be random but related, always respecting a constant value resulting from equation.

Have two question:

First - is it possible to transcribe this into the software when formulating a DOE?

Second -  if is possible, is it still possible to add a condition such as if the layer thickness is equal to 0.03 the result of the equation is X, but if it is equal to 0.06 the result is Y?

[#2]

Hi @StandardOkapi62,

Welcome in the Community !

I'm not sure to have fully understand your constraint, as I don't understand what is Ev in your experimental design and if Ev should be fixed and only factors 1, 2, 3 and 4 can vary, or can Ev and the factors vary according to this constraint ?

Depending on the situation, you may have at least two options :

1. Using the Custom Design platform, you can use the "Specify Linear Constraints" option in the "Define Factor Constraints" panel to include your equation linking the different factors together. This option works if Ev is a fixed value, or related to one of the remaining factors. See the article from @Jed_Campbell about Factors constraints and how to use this option in his great article Demystifying Factor Constraints 
2. If Ev is not fixed and not related to another factor (it is just limiting the repartition of levels between the 4 factors but Ev can have a large variety of values), then you could create a large datatable for your 4 factors, involving all possible combinations respecting the constraints and possible values of Ev, and use this table as Candidate Set in the Custom Design platform. This will force the DoE creation to only use runs from your table respecting your constraint/equation.
   Several topics in this community have been linked to the use of Candidate Set :
   Using the Disallowed Combination Script to define factor constraints in DOE 
   Factor Constraints: Multiplication 
   Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-784) 

For your second question, using a Candidate Set approach enable to fit any number of complex constraints directly in the runs that can be chosen by the algorithm behind the design generation. So you could create a datatable of runs with your two constraints, and use the Custom Design platform to load the candidate runs to create your Custom DoE.

I hope this answer will help you,

[#3]

I see bellow my explanition please.

Thank you very much.

[#4]

OK, this sounds like a theoretical equation.  You might want to confirm this equation works in your situation as the theoretical equation was not created using your inference.  I suggest, first, not worrying about constraints.  Develop models for both Ev and residual stress (2 Y's).  Also look for correlation between this Y's.  Once you have those equations, then you can iterate the design space to meet your constraints.

[#5]

Completely agree with @statman.
Unless your experimental runs are physically unfeasible or dangerous to run, I would start the design with a broad experimental space without constraints (or as little as possible).
Starting with a broad experimental space has a lot of benefits in a screening/preliminary stage regarding your context :

• Empirical validation of the theoritical equation
• Research or confirmation of optimal values for Ev
• Better and more representative assessment of the relative importance of factors on a broad experimental space (with the possibility to focus on optimal area, fit another model with augmented design points, and see if this changes the relative importance of the factors studied).

Starting from this initial screening/exploration design, you can then iterate to focus on the area of interest, hopefully the one where the constraint is respected and the obtained optimal values for Ev close from the ones you describe.

Hope this answer will help you,

[#6]

Similar to Victor's question.  What is Ev and how did you create that equation?  Is this theoretical or empirically derived?  If you already know their effects and have an equation, why are you experimenting on them?

[#7]

The equation in question, Volumetric Energy Density, given by the formula Ev = P / e.v.h, where P is the power of laser, "e" the layer thickness, v the scanning speed and h the distance between scans. This equation quantifies the amount of energy per mm3 that is put into the material to be melted.

There are optimal values for Ev,  in the case of thicknesses of 0.03 mm the value is around 77 J/mm3 and in the case og 0.06 mm it is around 77 J/mm3. Varying this energy when manufacturing a component will induce defects in the part.

My DOE intends to evaluate which process parameters have the most influence on the formation of residual stresses. In the literature, laser power, scanning speed, layer thickness, distance between scans, temeprature and scanning strategy are the parameters that most contribute to the formation of residual stresses.

Now, if i need values to be generated, but that consider the dependence described by the equation. For example, if i reduce the laser power, i will have to porportionally reduce any other factor in the equation.

Thank for your help.

[#8]

PS. for 0.06 mm the value is around 50 J/mm3.