Help with scaling dimensions of model to match change of material properties.

About the development of the FEM module/workbench.

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HarryvL
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Re: Help with scaling dimensions of model to match change of material properties.

Postby HarryvL » Fri Jun 15, 2018 4:56 am

Mark, that is indeed very confusing. I had another close look at the paper and see that I was referring to Table 1, whereas you were referring to "nomenclature" at the end. You are right. The paper contains an error in that part. The description for "I" is simply wrong and the explanation of the author does not help. I is the second moment of inertia of the cross section of the hairspring and the unit is m^4
Mark Szlazak
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Re: Help with scaling dimensions of model to match change of material properties.

Postby Mark Szlazak » Fri Jun 15, 2018 6:44 am

HarryvL wrote:
Fri Jun 15, 2018 4:56 am
Mark, that is indeed very confusing. I had another close look at the paper and see that I was referring to Table 1, whereas you were referring to "nomenclature" at the end. You are right. The paper contains an error in that part. The description for "I" is simply wrong and the explanation of the author does not help. I is the second moment of inertia of the cross section of the hairspring and the unit is m^4
Yeah I was suspecting something similar but since I do not have the required knowledge in this area I differed to Dr. Ru's authority. Maybe he just did not take my query seriously and forgot what was written??

In anycase, thanks a lot for the help :) :) :) :) :)

BTW, I see that high end manufactures of watches are going to silicon hairsprings.

phpBB [video]


http://www.woundforlife.com/2014/04/23/ ... airspring/

https://patents.google.com/patent/EP3056948A1/en

I do not know yet if this is some special, secret type of silicon, or whether i can 3D-print it in an effective manner to the size I plan to scale my spring. I can scale up to 75mm diameter to the stud. In any case your ceramic suggestion is something to look at. An example of the steel spring size i will scale up is a metal band of 0.1 mm thickness, 0.6mm width, and about 603mm length. The number of turns is 12, inner diameter is 4mm (size of collet) and a pitch of 1mm.

The collet/balance-wheel rotates +/- 270 degrees (+/- 2pi/3 radians) with each swing (i.e. +/-1.5 turns to each side of it's equilibrium position).

In 3D-printing, a rule of thumb for say SLS and vat-pho is that feature thickness should be not less than 1mm. So I cannot go below 1mm for the thickness of the band.
Mark Szlazak
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Re: Help with scaling dimensions of model to match change of material properties.

Postby Mark Szlazak » Fri Jun 29, 2018 9:28 pm

HarryvL wrote:
Fri Jun 15, 2018 4:56 am
Mark, that is indeed very confusing. I had another close look at the paper and see that I was referring to Table 1, whereas you were referring to "nomenclature" at the end. You are right. The paper contains an error in that part. The description for "I" is simply wrong and the explanation of the author does not help. I is the second moment of inertia of the cross section of the hairspring and the unit is m^4
Hello again HarryvL. I got back to that paper again, “The Mechanics of Spiral Springs and It's Application in Timekeeping" and have another concern. I am having trouble understanding how they get their equations for the moment of force at point P(r, theta) on the spring. These equations have Fcx and Fcy multiplied by the shortest distance of point P to their line of action. So the moment of these forces at point P is accounted for. These equations also add the term for torque Tc at point C (center of the collet) directly into the equation for the moment about P. Shouldn’t this be scaled since the perpendicular distance to the force that generates Tc from point C is not the same as the perpendicular distance from point P? The diagram does not indicate they are purposely picking a point P on the spiral with the same distance that C has from the line of the force generating Tc. So these equations make no sense to me at this point?
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HarryvL
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Re: Help with scaling dimensions of model to match change of material properties.

Postby HarryvL » Fri Jun 29, 2018 9:47 pm

Hi Mark, I had a quick look, but I believe the formula is right. It perhaps helps if you imagine the central torque being generated by two equal but opposite forces spearated by a fixed distance d, working on an imaginary lever connecting them to the point at which you want to know the total moment. You will then see that it doesn't matter how far or how close this couple is from the point of interest or even in which direction the force pair points. This explains why you can simply add couples to the moment equilibrium equation without considering their point of application. Try to draw it !!

I hope this helps.
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HarryvL
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Re: Help with scaling dimensions of model to match change of material properties.

Postby HarryvL » Fri Jun 29, 2018 10:15 pm

PS: I don't think Tc is generated by the spring action on the collet. I think it is from an external source, like the inertia of the balance wheel? In any event, think of a couple as a "couple or pair" of forces as described above and it will become clear that point of applications does not matter.
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Re: Help with scaling dimensions of model to match change of material properties.

Postby Mark Szlazak » Fri Jun 29, 2018 10:25 pm

HarryvL wrote:
Fri Jun 29, 2018 9:47 pm
Hi Mark, I had a quick look, but I believe the formula is right. It perhaps helps if you imagine the central torque being generated by two equal but opposite forces spearated by a fixed distance d, working on an imaginary lever connecting them to the point at which you want to know the total moment. You will then see that it doesn't matter how far or how close this couple is from the point of interest or even in which direction the force pair points. This explains why you can simply add couples to the moment equilibrium equation without considering their point of application. Try to draw it !!

I hope this helps.
I tried doing that and I do get a torque Tp but it isn’t Tc.

If I look at Fcx and Fcy and the perpendicular distances that their lines of action are from point C then I get moments Fcx*Rc*sin(theta_c) and Fcy*Rc*cos(theta_c) and not the more complex ones for the perpendicular distances to P as the paper has in its equations. But when it comes to Tc then they just directly use it without modifications. I just don’t get it.

Also, the way I see it is the force generating Tc acts along a line perpendicular to vector Rc which is the radius of the collet directed from its center C to the point of application of the torquing force. So point P must be some perpendicular distance to this line of action. Which also means this distance runs parallel to Rc but nothing suggests to me that it is the same length as Rc.
Last edited by Mark Szlazak on Sat Jun 30, 2018 4:21 am, edited 1 time in total.
Mark Szlazak
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Re: Help with scaling dimensions of model to match change of material properties.

Postby Mark Szlazak » Sat Jun 30, 2018 12:37 am

HarryvL wrote:
Fri Jun 29, 2018 10:15 pm
PS: I don't think Tc is generated by the spring action on the collet. I think it is from an external source, like the inertia of the balance wheel? In any event, think of a couple as a "couple or pair" of forces as described above and it will become clear that point of applications does not matter.
Sorry, I just noticed this post. I take it you mean https://en.wikipedia.org/wiki/Couple_(mechanics) and independence of reference point. OK, so there exists a couple called Tc but forces Fcx and Fcy are still needed to keep things in static equilibrium?
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HarryvL
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Re: Help with scaling dimensions of model to match change of material properties.

Postby HarryvL » Sat Jun 30, 2018 4:03 am

Correct.
Mark Szlazak
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Re: Help with scaling dimensions of model to match change of material properties.

Postby Mark Szlazak » Sat Jun 30, 2018 4:17 am

HarryvL wrote:
Sat Jun 30, 2018 4:03 am
Correct.
OK thank you. However, I am still missing something because that article I linked to says a coupled-pair has equal but opposite and parallel but non-collinear forces (vectors), which to me means the system is in static equilibrium. So why is Fcx and Fcy present or what are they there for?
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HarryvL
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Re: Help with scaling dimensions of model to match change of material properties.

Postby HarryvL » Sat Jun 30, 2018 6:20 am

I don't have the article at hand Mark, but from memory Fcx and Fcy are support reactions of the spring, whereas Tc is a moment (couple) excerted by a system (balance wheel?) external to the spring. The support reactions should be in equilibrium with al external and inertial loads. The support reactions are not necessarily in equilibrium with each other (analogous to a simply supported beam with an external load).