Right, in this case assuming that the pin is rigid shouldn’t have a negative impact on the results while allowing for an easier definition of BCs and thus bigger freedom of movement of the pin.
I applied the rigid body constraint to the pin while leaving the rest unchanged (load is 500 N in this case since I use a quarter model) and the deflection is 12.76 mm. Definitely better than before (7.672 mm) but still too stiff. I’ve noticed that the leaf below the master one partially separates from it:
It seems that no separation contact is actually closer to reality (or at least to the assumptions of analytical solution) than regular contact. Even though the latter is, generally speaking, a more complete representation of the behavior of a contact interface. From what I know, in real life leaves are not bonded but clamps hold them together.
They are taken mostly from 3 Polish books whose authors are marked in the subscript of each deflection variable’s name. The last equation is from the YouTube video that you’ve shared some time ago. I assumed that it’s the one that’s correct since it was in the closest agreement with the results of your tests involving orthotropic layers. It also agrees with one of the previous equations. But maybe the other formulas are also correct and just involve slightly different assumptions (it’s hard to say because the said assumptions are not explicitly mentioned in the books).
None of the formulas seems to involve the initial radius of the leaves. Tension and compression are linear functions of the force in linear Static but I’m not sure that the deflection value does too in this particular case. Take into consideration that a bending beam do not develop a circumferential shape. I mean, your Leaf spring is not as a flat one in which a force has been applied. Formula is not 100% applicable if there is a radious. As you said it is hard to compare.
This is what has bothered me since the beginning of these tests. The analytical solution also does not take into account the length of individual leaves. However, when it comes to the curvature issue, here’s what one of the Polish books (the one dealing entirely with leaf springs and written by Zukowski) says:
One can easily determine any deflection of a curved leaf spring by having the deflection curve of a second straight leaf spring.
The book also provides a diagram that shows the deflection curve as function of load for straight (I) and curved (II) leaf spring (p - arc height, f - deflection, P - force):
It can be easily noticed that curve II is symmetrical about point A of curve I. For example, segment AB of line BC is equal to segment AC of that line and so on. Thus, after rotating curve II by 180 degrees it will overlap with curve I.
If I understand it correctly, I can use the formula for a straight leaf spring to get its deflection as a function of force and then work my way back to calculate the displacement that will occur when already curved spring is subjected to given force. After all, in this analysis the load does not further increase the spring’s initial deflection but straightens it.
For example, let’s say that a force of 600 N is necessary to deflect the initially straight spring by 6 mm and that 400 N will deflect it only by 4 mm (the numbers are made up here). Then the initially curved spring, the deflection of which is 6 mm, will be straightened by 2 mm if an opposite force of 200 N will be applied to it. I could be wrong, but this approach seems to make sense.
I don’t want to over engage and bore you with this topic but the issue seems interesting to me and it would be great to solve it. After all the tests, I do realize that a very good agreement between the simulation and analytical solution can’t be obtained here since analytical solutions are too approximate but maybe it’s possible to get a better match. The best result so far is still almost twice too low (unless the formulas that give the value of 15 mm are correct) and it seems that the difference shouldn’t be that large even when various simplifications are considered. This case might serve as an interesting educational example and that’s what I want to use it for.
I would first try to obtain some reference model with known deflection. Real life tested spring and then check against the analytical solution provided in the book.
If both agree I would then go to model the spring to see how close the straight model is.
That’s a good idea, thanks. So far I haven’t found such data on the internet but I will keep looking and I plan to run some further simulations too.
So you’ve managed to model contact with no separation and just sliding allowed in CalculiX ? That’s great. Can you share the contents of the *Surface interaction block ?
So it’s tied contact. I will give it a try (so far I’ve used it only for the connection between eye and pin, not for the interfaces between leaves). But doesn’t it block the relative sliding of the surfaces as well ? From what I’ve read in the documentation, the friction coefficient value is irrelevant in the case of this type of contact. If it works this way then the model will likely be overstiffened like it was with tie constraint since sliding between the leaves won’t be possible.
i read again the documentation from Jaro Hokkanen (2014). setting friction and stick slope to highest values could give similar result with ‘areampc 123’ in CalculiX GraphiX (CGX). in opposite, set to lowest value is comparable to ‘areampc slide’ commands. so, i corrected my previous comment.
i will took a time to study if any simple example (problem described and result shown) solved by Abaqus no separation features or CGX/CCX areampc is available.
i have a little bit confused for long discussion and many pictures. reading Abaqus documentation, it’s only an approach to glued of two surfaces without over stiffening the models. did Abaqus can glued surfaces but with sliding allowed?
The highlighted sentence refers to a combination of no separation and rough friction behavior in Abaqus. The latter blocks sliding as if the friction between the surfaces was infinite. So it’s basically another way to model tied contact. Pure no separation contact in Abaqus prevents relative motion only in the normal direction, sliding is still possible.
Maybe tied contact in CalculiX works differently. I will try to make a simple example in order to see if the CalculiX’s tied contact can allow for sliding with proper settings.
I did some additional tests on this leaf spring model. In Abaqus, with the same settings but using no separation contact between the leaves, I got the deflection of 17.197 mm. Looks pretty good but I’m still not sure which analytical solution is correct. I also tried the approach proposed by @xyont and defined tied contact in CalculiX with both friction coefficient and stick slope set to 1e-7. Unfortunately, the result is too low: 8.63 mm. I’m afraid that this workaround cannot represent the no separation contact accurately.
i’m not familiar with leafspring behavior seems it’s complex enough: prestressed due clamping, contact in rebond clip, rotational of the eye, etc. could you simplified a model with simple enough e.g flat layered parts with point loading test? add general penalty contact analysis in study also can give an insight.
p.s setting friction & stick slope values are not my proposed, it based on the author of CCX code implementation. here i’m only a user took a quick test and verify, it seems the code implementation is working properly. as can be seen in above picture updates i’ve been posted. the movement of each part clearly shown the sliding mechanism.
I just realized that in the book that I cited before (“Resory” - “Leaf springs” by Zukowski - in Polish) there’s also an example where measured deflection of a particular initially curved leaf spring is compared with analytical calculations. The agreement is very good there even with simplified analytical approach and thanks to that example I could verify the formulas that I use in my case. It turned out that the equation from YT video (f_YT) is correct. It’s likely that I misunderstood the other formulas due to their insufficient descriptions and mistakes in books (I’ve noticed some of them). Anyway, the deflection of my spring should be 22.95 mm.
Interestingly, the exemplary spring discussed in that book also has leaves with different spans (but the distances between their ends are equal). However, they have triangular tips to fit the assumption of a beam with uniform strength. I will try to modify the geometry of my spring - maybe equalizing the distances between the leaf ends will help. Another idea that I have is to model the clamp so that the leaves don’t separate because of the lack of no separation contact.
I’ve also noticed that the results I presented in one of the previous posts (with the attached picture showing separation between the master leaf and the leaf below it) are somewhat incorrect since the load should be applied upwards to straighten the spring, not further increase its curvature. The deflection with correctly applied force is 10.9 mm in this case (a bit lower than before).
thank you @Calc_em for some explanation, but sorry i got no point regarding to the original topics as firstly you posted. Abaqus feature in contact with no separation options, with rough friction (comparable to “areampc 123” or Tied Contact) and without friction/sliding (comparable to “areampc slide” or Tied Contact excluded friction).
even a simple one from many picture and example above, there’s none shown an Abaqus result display about the features you mentions also. unfortunately, for me or maybe anyone as CalculiX user has no gain lesson learned from the discussion.
I agree with xyont.
After this long post I would appreciate some abstract once you finish the study to know which could be the right FEA approach to Leaf Springs and the correct analytical formulation.
I understand you will use the model presented in the book “Resory” - “Leaf springs” by Zukowskiwith.
@xyont I don’t want to focus on Abaqus too much since it’s a CalculiX forum. Besides, in Abaqus it’s all clear - there’s no separation contact that prevents separation of surfaces, rough friction contact that prevents their relative sliding and tied contact that blocks both forms of movement. There are doubts only about the equivalents of these contact models in CalculiX.
I think that this long discussion may already be helpful for other users if they are interested in leaf spring modeling or no separation contact workarounds in CalculiX.
Anyway, I prepared a simple benchmark and solved it in both Abaqus and CalculiX. The settings were:
Abaqus:
*Surface Behavior, no separation, pressure-overclosure=HARD
*Friction
0
And here are the results (step 1 - press the small block a bit towards the large one, step 2 - fix this position in Y axis and slide in the X direction on the large block):
It seems that the workaround with very low friction and stick slope values in tied contact is effective. This makes me wonder why I got too stiff results for my leaf spring model with this approach since in Abaqus the values were much better with no separation contact that should be equivalent. Maybe there are some differences between these approaches that I haven’t noticed yet.
@Disla Sure, I will let you know when I get any closer to the reference solution that I now established. I always share the results if I manage to solve a problem I asked about on a forum.
