topic Re: Auger flight sections into flat pattern? in Fusion Design, Validate & Document Forum

Auger flight sections into flat pattern?

harry.doldersum — Tue, 15 Mar 2022 18:44:38 GMT

I've found some posts on auger flight creation and that's working out quite well - I think, at least... the results look alright, so far. But in these earlier posts was mentioned that converting sections of the flight into a flat pattern is not possible yet - apart from 1 post, that proposed using an external program to flatten the geometry (I think, Meshmixer was proposed).

When trying to convert my results into sheetmetal, I'm also getting the error "can't calculate body thickness", as stated here earlier.

Is there a work-around in Fusion by now, that I might have missed?

(I've looked at meshmixer.com and read that Fusion 360 should gradually take that market over from Meshmixer?).

Re: Auger flight sections into flat pattern?

jodom4 — Tue, 15 Mar 2022 23:41:40 GMT

Hey harry.doldersum,

Fusion doesn't have this capability at this time. Exactflat would make short work of this though: https://apps.autodesk.com/FUSION/en/Detail/Index?id=3499335255055878377

Re: Auger flight sections into flat pattern?

harry.doldersum — Wed, 16 Mar 2022 10:28:07 GMT

I've just had me a look at ExactFlat, but it's quite clearly stated that it cannot handle solids, only surfaces - unless I misunderstood the website video?

So, I'd need to convert a design into a surface (or re-design it as a surface), before being able to use ExactFlat....? That doesn't really fit into my workflow: most often, I model as I go. Quite honestly, I don't recall ever having used surfaces at all.... 🙂

Thanks for the suggestion, but I don't think ExactFlat is suitable for me.

Re: Auger flight sections into flat pattern?

TrippyLighting — Wed, 16 Mar 2022 11:12:13 GMT

I am not advocating for ExatFlat, but if working with surfaces is not part of your workflow, then it's time to reconsider, and upgrade your workflow.

Re: Auger flight sections into flat pattern?

harry.doldersum — Wed, 16 Mar 2022 12:32:20 GMT

Fair point, I guess. 🙂

Quite honestly, I never saw added value in working with surfaces - I could well have been wrong in that. I'll have a look at surfaces, one of these days....

Meanwhile, if someone would know about the issue at hand, that would be great. ^^

Re: Auger flight sections into flat pattern?

jeff_strater — Wed, 16 Mar 2022 14:12:58 GMT

@harry.doldersum - I am not an expert in ExactFlat. However, if it is true that it only works with surfaces (which actually makes sense, because the goal is a flat pattern, which is inherently 2D), why not just create a zero-offset surface from the auger geometry, and send that to ExactFlat? You don't need to change your design at all, just have an extra surface body in it for unwrapping.

Re: Auger flight sections into flat pattern?

harry.doldersum — Wed, 16 Mar 2022 15:35:00 GMT

I just checked & found the license fee for a SolidWorks license for ExactFlat: maybe their pricing is a bit different for Fusion, I don't know, but you can buy a good 2nd hand car for that price - won't be a hybrid, probably, but still....

ExactFlat can't be the solution I'll be going for.

I'm doing this work since the early '80's - on & off - and I never needed a tool like that before & I'm 61, which means there's a fair chance I'll never need it again, so - there's no return on investment in it for me - not at those prices.

If ExactFlat is the only way to proceed here, I'll just pass on this one. 🙂

Re: Auger flight sections into flat pattern?

MichaelT_123 — Fri, 18 Mar 2022 10:54:33 GMT

Hi Mr. Harry Doldersum,

AUGER tool is based on simple topology objects: cylinder and helical surface.

Let us skip the cylinder and concentrate on the helical part. I assume that we are talking here about a classical auger (not, e.g., one designed for removing vax from ear cavity … images of which pop-up profusely everywhere on media in my jurisdiction). Considering the diversity of the F360 Forum, I am sure that there will be time for this one also.😏

The equation of helical surface can be drawn as follows:

x = <r>*sin(φ) r ∈ <R1,R2> Eq.1

y = <r>*cos(φ) r ∈ <R1,R2> Eq.2

z = <φ>*h φ ∈ < Φ0=0,Φ> Eq.3

Compel ourselves to do a simple mental exercise. What will happen if we squeeze (stretch) out a helical auger.

A carpenter's intuition will deduce that inner, outer arc perimeter lengths and the surface area will be preserved (sort off). At the same time, R1, R2 and Φ will change … slightly.

The helix inner & outer arc lengths can be derived from the equations:

L1 = Φ*sqrt(R1^2 + H^2) Eq.4

L2 = Φ*sqrt(R2^2 + H^2) Eq.5

and after the squeeze:

L1_ = Φ_*sqrt(R1_^2 + H_^2) Eq.6

L2_ = Φ_*sqrt(R2_^2 + H_^2) Eq.7

… but why stop … just flatten-out this thing!!!

_L1 = _Φ*sqrt(_R1^2) = _Φ * _R1 Eq.8

_L2 = _Φ*sqrt(_R2^2) = _Φ * _R2 Eq.9

If our carpenter's intuition is at least close to the target, then:

L1 = L1_ = _L1 Eq.10

L2 = L2_ = _L2 Eq.11

What about the surface area? The simple integration yields:

S = ∫ (L, r, dr) r ∈ <R1,R2> Eq.12

S = ∫Φ* sqrt (r^2 + H^2)dr r ∈ <R1,R2> Eq.13

Which gives:

S = Φ*(r*sqrt(H^2 + r^2))/2 + (H^2*Log(r + sqrt(H^2 + r^2)))/2 |R1, |R2 Eq.14a

S = Φ*(R2*sqrt(H^2+R2^2))/2 + (H^2*Log(R2 + sqrt(H^2+R2^2)))/2 –

Φ*(R1*sqrt(H^2+R1^2))/2 + (H^2*Log(R1 + sqrt(H^2+R1^2)))/2 Eq.14b

and for the flattened helical surface where lim H ⇒ 0

_S = Φ*(R2*sqrt(R2^2))/2 + (0*Log(R2 + sqrt(R2^2)))/2 –

Φ*(R1*sqrt(R1^2))/2 + (0*Log(R1 + sqrt(R1^2)))/2 Eq.15

_S = _Φ*(_R2^2 – _R1^2)/2 Eq.16

… so finally … surprise … surprise … we have got three equations with three variables.

_L1 = _Φ * _R1 Eq.17

_L2 = _Φ * _R2 Eq.18

_S = _Φ*(_R2^2 – _R1^2)/2 Eq.19

It's time to solve them!

Observe that:

_L1/_L2 = _R1/_R2 = L1/L2 = R1/R2 Eq.20

So,

_R1 = _R2*R1/R2 Eq.21

_S = _Φ*_R2^2*(1 – (R1/R2)^2)/2 Eq.22

_S = _L2 *_R2*(1 – (R1/R2)^2)/2 Eq.23

S = L2 *_R2*(1 – (R1/R2)^2)/2 Eq.24

Thus,

_R2 = 2*S/(L2*(1 – (R1/R2)^2)) …. Bingo Eq.25

_R1 = _R2*R1/R2 …. Bingo Eq.26

_Φ = 2*S/*(_R2^2 – _R1^2) …. Bingo Eq.27

The solution of R2_, R2_,Φ_ for arbitrary ‘squeeze phase’ as per Eq.1,2,3

would be challenging as the nasty Eq.14 is on the way. However, considering dependence of R2_, R2_, Φ_ on the squeeze deformation, by knowing the boundary condition one can resort to the simple linear approximation approach where:

R1(h) = R1 + (_R1 – R1)*_H/H_0 Eq.28

R2(h) = R2 + (_R2 – R2)*_H/H_0 Eq.29

Φ (h) = Φ + (_Φ – Φ)*_H/H_0 Eq.30

The simulation presented in the attached videos has adopted such a path.

The accuracy seems to be better than half a finger carpenter's gauge, and as measured by the standard deviation of the calculated area of helical surface, it is about -0.012.

The purely theoretical approach will not address many physical phenomena when shaping metal plates to helical forms… although in some instances … the method might be good enough.

One significant benefit is … it is inexpensive (not even the cost of a second-hand diesel car). So don't worry, mate. I will charge a small interest rate and afterlife only, … but forever.😐

Attached files:

FlattenTheAuger_mono.png 4K_mono (0.2MB) https://a360.co/3ubewZO

FlattenTheAuger _mono.mp4 4K_mono ( 6MB) https://a360.co/3IgiO7b

FlattenTheAuger _arcd.png 4K_stereo ( 4MB) https://a360.co/3JtXay0

FlattenTheAuger _arcd.mp4 4K_stereo ( 20MB) https://a360.co/3CTKrC1

FlattenTheAuger _al.mp4 4K_stereo ( 12MB) https://a360.co/34QRr64

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for an active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Regards

MichaelT

NOTE To TF360

There is still a deficiency (and bipolar craziness) in managing user parameter units. Also, as many probably agree, the whole interface/input method is very inefficient and cumbersome. In this example, I have had to resort to implementing a surface area parameter as unitless. The other only choices were acres and circular_mil (whatever this means). Here is my earlier … well … I know … the sarcastic post.

Units in 21st century - Autodesk Community - Fusion 360

Re: Auger flight sections into flat pattern?

harry.doldersum — Fri, 18 Mar 2022 12:45:12 GMT

Thanks for the effort, much appreciated - it's all sorted, though. I passed it on to someone else: he used an additional step, available in his CAD program, after which he could create the flat pattern as required. 🙂

Re: Auger flight sections into flat pattern?

TheCADWhisperer — Fri, 18 Mar 2022 13:33:12 GMT

@harry.doldersum

Can you File>Export your *.f3d file to your local drive and then Attach it here to a Reply?

And also the result from other CAD program?

- You might be able to use FREE Autodesk MeshMixer for this - with the files I could do a comparison check.

Re: Auger flight sections into flat pattern?

harry.doldersum — Fri, 18 Mar 2022 14:05:55 GMT

Thanks for responding - I can't share the files here, but I'll certainly have a me a look at Meshmixer.

I'm just wondering, though: would flattening a pattern from an external application, such as Meshmixer (or ExactFlat, for that matter) need to track of bending rules & k-factors?

Re: Auger flight sections into flat pattern?

MichaelT_123 — Sun, 20 Mar 2022 11:41:35 GMT

Hi Fellows,

I have found the problem with some formulae/assumptions in my earlier post. I will send, I hope, the correct version in about two-three days. In the meantime, if someone discovers the problem, I will be happier than Pirx and Pirxess after conceiving the successive πnfant.

Greetings from Hon. Pirxess and Pirx - Autodesk Community - Fusion 360

Regards

MichaelT

Re: Auger flight sections into flat pattern?

MichaelT_123 — Wed, 23 Mar 2022 01:02:59 GMT

Hi Fellows,

So, … what is the problem …?

We have arrived at the set of equations:

_L1 = _Φ * _R1 Eq.17

_L2 = _Φ * _R2 Eq.18

_S = _Φ*(_R2^2 – _R1^2)/2 Eq.19

… and at this point, the issue emerged!

The following equation implemented the constrain condition on R1 & R2

In the form:

_L1/_L2 = _R1/_R2 = L1/L2 = R1/R2 Eq.20

It was a weak condition!

When we look at Eq.17 and Eq.18 in the context of it and perform based on this constraint, the substitution:

_R1/_R2 = _L1/_L2

_R2 = _R1*_L2/_L1

Then:

_L2 = _Φ * R1*_L2/_L1 Eq.18 .. sub

After div by _L2 and mul by _L1 becomes Eq.17.

It means that we have got not three but only two independent equations with three variables.

They still can be solved in funiverse, giving a legit infinite number of solution pairs ( Φ, (R1, R2)) we are after.

The problem is that we live in the universe (aka. reality, …. really?), so we need to find out only one definite and deterministic, unavoidable guidance imposed on us by the law of physics.

To discover it, we need to reject the weak condition and replace it with the strong conviction, which is …

W = R2 – R1 = const

Where W is a radial width of a helical surface (auger spiral). It is perhaps very obvious to any rational carpenter. Therefore, I must repent … I was fallacious … believing in … R1/R2=const although … well it is still could be true, … but only in the weak sense.

After improving on truthiness of the truth … let's correct the equation's flow to get the only proper answer. Replace Eq.20 with the new one.

W = _R2 - _R1 = R2 - R1 = const Eq.20_n

Thus,

_L1 = _Φ * _R1 = L1 = Φ*sqrt(R1^2 + H^2) Eq.18,4 recall

_L2 = _Φ * (R2 - R1 + _R1) = L2 = Φ*sqrt(R2^2 + H^2) Eq.21_n,5 recall

_L1/_L2 = _R1/(R2 - R1 + _R1) Eq.22_n

L1/L2 = sqrt((R1^2 + H^2)/ (R2^2 + H^2)) Eq.23_n

_L1/_L2 = L1/L2

_R1/(R2 - R1 + _R1) = sqrt((R1^2 + H^2)/ (R2^2 + H^2)) Eq.24a_n

_R1 = (R2 - R1 + _R1) *sqrt((R1^2 + H^2)/(R2^2 + H^2) Eq.24b_n

_R1*(1-_sqrt((R1^2+H^2)/(R2^2+H^2))=(R2-R1)*sqrt((R1^2+H^2)/(R2^2+H^2) Eq.24c_n

_R1=(R2-R1)*sqrt((R1^2+H^2)/(R2^2+H^2))/(1-sqrt((R1^2+H^2)/(R2^2+H^2)) Eq.24d_n

Finally ( I hope so)…

_R1 = (R2-R1)*sqrt((R1^2+H^2)/(R2^2+H^2))/(1-sqrt((R1^2+H^2)/(R2^2+H^2))) Eq.25_n

_R2 = (R2-R1)*sqrt((R2^2+H^2)/(R1^2+H^2))/(1-sqrt((R2^2+H^2)/(R1^2+H^2))) Eq.26_n

_Φ = _L1/_R1 = _L2/_R2 Eq.27a_n

_Φ = Φ *sqrt(R1^2 + H^2)/_R1 = Φ *sqrt(R2^2 + H^2)/_R2 Eq.27b_n

If we look at the previous answer, it is not difficult to discover that the new one is much neater, and thanks … there is no reference to the helical surface area in them, … hence no need for the strenuous gymnastic in dealing with its userParameter representations.

The last step is to rebuild the auger's F360 model file. For the sake of clarity, rehearse:

Input data:

_F – ‘squeeze’ phase factor, <0,1>=<flattened, at rest>

_H – helical surface vertical span (auger flight height)

_T – auger flight plate thickness

R1 – inner helical surface radius (auger pole radius)

R2 – outer helical surface radius (auger external radius)

Φ – helical surface angular span (auger flight span angle)

Intermediary:

H_ – HR/(2*π), helical surface vertical span 2π normalized, Eq.3 parameter

Output data:

R1F – inner radius of the flattened helical surface

R2F – outer radius of the flattened helical surface

Φ.F – flattened helical surface angular span (flattened ager’s plate angular span)

L1 – theoretical length of inner helical arc

L2 – theoretical length of outer helical arc

ST – theoretical helical surface area (auger flight plate area)

Φx – maximum helical surface angular span (auger flight span angle) ) when ΦF=360 °

Hx – maximum helical surface vertical span (auger flight height) when ΦF=360 °

Sx – maximum theoretical helical surface area (auger flight plate area)

Add one important note here. In order to avoid falling into F360 userParameters units’ grinding machinery … both input and output values will be represented as unitless. Angles will be assumed to be in radians and lengths/distances in millimeters (I have allergy to inches, … hope that this long-lasting viral imposition will be cured … mercilessly & soon. Don’t wary … if you have one, after three i-shots you will remember nothing, you shouldn’t). Units will be applied post-factum directly on the modelled objects (aka. model’s units’ tattooed skin) giving it … customized identity.

Attached files:

FlattenTheAuger_mono.png 4K_mono (0.2MB) https://a360.co/3qtaD1f

FlattenTheAuger _mono.mp4 4K_mono ( 6MB) https://a360.co/37LQBsl

FlattenTheAuger _arcd.png 4K_stereo ( 4MB) https://a360.co/3IrQ8rX

FlattenTheAuger _arcd.mp4 4K_stereo ( 20MB) https://a360.co/3tutUS4

FlattenTheAuger _al.mp4 4K_stereo ( 12MB) https://a360.co/3ipGxrg

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for an active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Regards

MichaelT

Re: Auger flight sections into flat pattern?

MichaelT_123 — Wed, 23 Mar 2022 11:46:02 GMT

Hi Fellows,

It seems that the Auger_B.f3d file is corrupted. The coil features are unhealthy! although no warning on the timeLine is present. It is difficult to say how it has happened.

Please find attached the replacement file Auger_C.f3d

Regards

MichaelT

Re: Auger flight sections into flat pattern?

harry.doldersum — Thu, 24 Mar 2022 19:10:29 GMT

I compared the outcome of @MichaelT_123 's model with information received from third parties - and the flat pattern provided with this method seems quite accurate. Again, we can't do this as a Fusion CAD based solution as yet - but as a work-around, this could provide a result that one could apply to a next project.

It would be better still, if Fusion would have a function similar to "Lofted Bend" - I'm told, that this function was used in the alternative CAD application to create a flight in a sheetmetal form that is recognizable for the "flat pattern" function. But maybe we'll get that lateron...

Thanks for your input, everyone - much appreciated. 🙂

Re: Auger flight sections into flat pattern?

MichaelT_123 — Fri, 25 Mar 2022 08:04:41 GMT

Hi Mr. Harry Doldersum,

I am glad that you were able to validate the model somehow. All the best with your project.

As per your question from PM:

"The flat pattern in your model wasn't derived / sketched / modelled in some way from the modeled flight, was it? You drew the flat pattern as a result from your calculation?"

The answer is YES. All model objects/geometries (with minor exceptions) are in sync with the values of userParmeters. The flat pattern is represented by the sketch < Auger_F>< project_xy_f>.

With Regards

MichaelT