Edited Date/Time:
It was last spring, in the beginning of this pandemic that has turned our lives upside down, when we were having heated debates in the Technical Rumours topic regarding suspension, forks, dual crowns, right-side-ups, upside-downs, axle diameters, etc., when I mentioned much of it could be checked using finite element simulation. It was a great project to get into FEA and to have a cool result, but, as is usual for a master procrastinator without a deadline, it took a while to get it done.
But get it done I did! So, in this post I will present the results of a finite element simulation comparison of a right-side-up (RSU from here on) fork and an upside-down (USD from here on) fork regarding the stiffness on a ‘level playing field’, meaning identical dimensional features on both variants. There are some assumptions and simplifications made compared to real life products for the simulation sake, but I don’t think it will influence the results in a meaningful way. Only the stiffness of different variants was evaluated, I did not check any other performance metrics (like bushing friction and the like), as that is a whole different can of worms.
This will be the mother of all long posts, so scroll to the end of it for some TL; DR punchlines.
The basis of the analysis is an RSU fork resembling a Rock Shox Lyrik. These forks are very common, but the most important reason for this choice is that I have one and could check certain dimensions to get somewhat close to real life conditions. The Lyrik was used to determine the base stanchion thickness (and length, but that doesn’t play much of a role as long as it’s overlapped with the bushings), the location and dimension (height) of the bushings, base axle clamping width on the lowers and base axle thickness. The USD version of this fork only has the bridge removed and the stanchion and outer flipped around, with outer mounted to the crown instead of the dropout ‘foot’ and vice versa for the stanchion. For the sake of comparison, the crown, the two dropout feet and the axle are exactly the same models on both the RSU and USD fork.
The models:
RSU:
USD:
Besides comparing just RSU and USD variants of a fork with the same dimensional values, I’ve also performed an analysis how different dimensions affect the stiffness. In all cases the crown and dropout shape and dimensions stayed the same, it’s essentially the same part shared across all variants. They are both also oversized, so the same part ‘accepts’ the outer tube in all diameters (one of the different dimensions affecting the stiffness, more on that later).
The crown:
The crown is actually a hollow part with a base thickness of 5 mm (the influence of thickness on stiffness was evaluated, more on that later), including the steerer tube. The steerer tube wall thickness does not have an effect given the constraints that are used, but crown thickness does. While the geometry is not ideal (the tubes are not inserted into the crown, but attach to the bottom of it), this is one of the simplifications for the sake of keeping the same component across all configurations. The fact that it is hollow can be seen in the following image featuring transparency:
The dropout:
The dropout is mirrored between both left and right side of the fork and is mostly always the same. The changes in the geometry of the part involve either a larger hole for a 20 mm axle (the outer dimensions stay the same) or the clamping width of the axle.
The bushings:
The axial position within the outer and the height of the bushings is one of the dimensions taken from my Lyrik. It was kept the same for all variants (except for the diameter of the bushings of course).
The bridge:
The bridge connecting the outer is something that is present only on the RSU fork and not on the USD fork for the obvious reason. It is crude, but it is present and that is the important thing. It is also a ‘component’ that has been kept the same dimensionally through all variants. This could be a point of analysis, as in how different dimensions influence the stiffness, but I did not go into this one at this time.
The axle:
Just a straight tube of constant diameter, thickness and the correct length to fit within the dropouts.
Both the diameter and thickness are varied depending on the configured parameters.
The axle itself is constructed from 5 parts, but only to form additional distinct surfaces to apply the loads to a defined section of the axle (roughly where the hub bearings would be).
The stanchion:
Just a straight tube of a constant diameter and thickness, but both are varied depending on the configured parameters.
The outer:
Mostly a straight tube of varying diameter with the addition of the bushings. And yes, in a Lyrik, the upper bushing has a lower height than the lower bushing. While the stanchion thickness was varied, the thickness of the outer was not. At the time I didn’t think it would be worthwhile and would now require modifications to the model. While it would affect the results of the USD fork more than the RSU, it should have less of an effect than the stanchion thickness due to larger overall diameter.
Base configuration:
As noted, the base fork configuration that every other variant will be compared to is an RSU fork with 35 mm stanchion diameter, 2 mm stanchion wall thickness, 5 mm crown thickness, 15 mm axle diameter with 3 mm wall thickness and 25 mm width of clamping in each dropout. The axle to crown was set to 572 mm, which would mean a 160 mm 29” Lyrik, but was set to 40 mm (25 %) of travel (effective ATC of 532 mm) for the base analysis. Hub spacing is 110 mm. The fork trail was set to 37,5 mm, less than the 42 mm of a 29er fork, but this is one of the assumptions and simplifications. Similarly, the crown is a relatively simple box section with a height of 40 mm, when the real crown of a Lyrik is 70 mm high and much shapelier.
The material for all components was set to aluminium 6061, T651. It doesn’t matter much which grade and temper it is as the ultimate tensile strength is what differs between grades while the stiffness characteristic (Young’s modulus of elasticity) is more or less equal across the range. And since we are dealing in relative terms, as long as the materials are the same across the variants, it doesn’t really play much of a role.
Analysis parameters:
The following parameters were checked, including the following values (bold number represents the base configuration value):
Stanchion diameter: 32, 34, 35, 36, 38, 39,99 mm (<- this is when dub goes to 11)*
Stanchion wall thickness: 1, 2, 3 mm
Crown thickness: 2,5, 5, 10, 15 mm
Travel: 0, 40, 80, 120 mm
Axle diameter: 15, 20 mm
Axle thickness: 1, 2, 2,5, 3, 4 mm
Clamping width: 15, 25, 35, 45 mm
Whenever any of the values were changed on the model, all other values were kept at the bold value, thus base value.
Finite element analysis details:
The model was assembled with all contacts using the ‘bonded’ method, which essentially makes one single part of the model. The exception is of course the stanchion-to-bushing interface where a frictional contact with a very low friction value was used (enabling any axial sliding of the two bodies caused by deformation).
The mesh applied to the models (if anyone is interested) was applied to all faces with the element size set to 3 mm. This gave a fairly quick calculation (~3 to 5 minutes per design point) with relatively low memory usage (~10 G
and good accuracy. I did run some tests going down to 0,6 mm element size and the difference in the results was 1,3 % at 0,6 mm, but that required 2,5 hours per design point (there are now 144 in total...) and ~80 GB of RAM. At 0,8 mm and up the difference was within 1 %. And in any case the error will be more or less the same in all variants, so the comparisons are still valid.
Loads and supports:
All design points were checked for their bending stiffness with the force applied perpendicularly to the axle (perpendicularly to the steerer tube) and torsional stiffness with the moment applied to the axle around the vertical axis, parallel to the steerer tube. The force that was applied was 100 N, while the torque applied was 50 Nm, mostly because the deformation on the base fork variant was similar in both cases.
For the simulation the whole outer surface of the steerer tube was fixed in all degrees of freedom (displacement and rotation), preventing any movement – shown by the blue surface, annotated with C. Ideally there would be a small band right at the crown fixed in all degrees of freedom except for rotation around the axis of the tube (enabling torsional loads to be applied to the steerer) with the upper part of the tube fixed in all direction, representing the stem and the top bearing. This would enable the steerer tube to both bend and twist in torsion. But the deformation of the tube would be similar across both RSU and USD variants, so having it fixed will not create a large error. If anything, the steerer deforming would make the calculated deformations higher and would make differences between all the variants relatively smaller. This sort of fixation would required if a comparison with a dual crown fork was made though, as it would affect the results greatly.
As mentioned when covering the axle, the loads are applied to the two bands of the axle, representing roughly the locations of bearings of a hub. Hubs mostly come with an additional axle going between the two dropouts, with the dropouts axially preloaded onto the hub surfaces and sending quite a bit of these loads towards the dropouts instead of into the axle. What this setup does though is accentuate any differences between different axle thicknesses and diameters. In practice the differences should be smaller. Applying the loads to only the two bands enables the axle to bend into a C shape under bending loads or into an S shape under torsional loads, which would be somewhat prevented with a hub covering the axle. The bending force and torsional moment are annotated with letters A and B (they cover only one of the faces, but are applied to both faces).
The deformation taken as the result was the maximal deformation value of the middle part of the axle in the bending mode and the maximal deformation value of the right dropout for the torsional mode. Both deformation modes are shown in pictures below, where the deformation was scaled by a factor of 10.
The results:
Finally, the results. The results will be normalised to the base RSU fork, so 35 mm stanchions with a wall thickness of 2 mm, 5 mm wall thickness of the crown and steerer tube, 15 mm axle with 2,5 mm wall thickness and 25 mm clamping width with the fork at 40 mm of travel. The results will be shown as a percentage of stiffness of this variant (with this variant being 100 % of course), calculated by inverting the percentage of deformation -> double the deformation gives us 200 % of deformation and 50 % of stiffness and vice versa.
To make some more sense of the graphs, the RSU vs. USD comparisons will be bar charts coloured in the following manner (the sticking point is the green bordered bar, representing the base configuration):
To hit it off, here is a straight comparison of an RSU fork to an USD fork in both bending and torsional mode:
The bending mode gives expected results with the USD fork turning out stiffer. This is expected since the highest stresses are seen right at the crown, where an USD fork has the most material – the outers at the top and the stanchions at the bottom, where they are loaded less. Torsional mode, while also giving somewhat expected results as in an USD being less torsionally stiff than an RSU fork, gave at least to me unexpectedly large difference with the USD fork experiencing almost three times as much deformation as an RSU fork. I was expecting less of a difference here if I’m honest. This story mostly repeats throughout the range of analysed parameters as well.
Stanchion diameter:
Stanchion diameter surely has a large impact on fork stiffness, confirmed by rave reviews of the new thicker stanchion forks? Well I’m not so sure.
Given these calculations 32 mm stanchions by themselves cause less than a 20-percentage point reduction in bending stiffness, while going up to 40 mm gains you roughly 30 % on an RSU fork. The differences in torsional mode are much smaller than that with roughly -5 to +10 percentage point difference in stiffness going from 35 to either 32 or 40 mm. What is interesting though is that for USD forks the main advantage in bending is at smaller diameters with an USD fork at 32 mm being almost twice as stiff as an RSU fork, while the difference at 40 mm is much smaller. This is expected as USD forks are known to be stiffer fore-aft. A 32 mm variant is roughly 10 % less stiff than a 35 mm USD variant with the 40 mm variant being almost 20 % stiffer. While RSU forks show only small differences in torsion, the gains by larger stanchion diameters are greater for USD forks, over 25 % at 40 mm compared to a 35 mm USD fork. All other things being equal this does mean an almost twice as stiff fore-aft fork than a 35 mm RSU fork.
Stanchion thickness:
Looking at stanchion wall thickness, it appears 2 mm has been chosen as it’s the sweet spot. Going down to 1 mm reduces bending stiffness of an RSU fork by roughly one third, while 3 mm doesn’t gain you as much, just shy of 20 mm. In torsion the differences are much smaller for the RSU fork, roughly -10 to +5 percentage points.
The changes for USD forks are even smaller and are actually basically the same both in bending and torsion, a thinner, 1 mm stanchion losing only ~5 percentage points, but a thicker, 3 mm stanchion gaining even less than that.
USD forks would probably benefit more from a change in outer tube thickness or even more through a tapered wall of the outer tube
Crown thickness:
Crown thickness gives by far the largest changes in bending stiffness. The 15 mm wall thickness would mean an almost billet crown for this model (not quite, but the small void in the centre of the block doesn’t play a big role in torsional stiffness) giving 50 % more stiffness compared to a 5 mm wall thickness for the RSU fork, while almost doubling the stiffness of an USD fork.
The gains are nowhere to be seen with torsional stiffness though with the ‘billet’ crown not even passing a 10 % increase. With USD fork the improvement by going to the billet’ crown from a 5 mm thick box is 20 % though, so it is a larger gain for USD forks. Still, compared to the gains in bending stiffness, the effects on torsional stiffness are again MUCH smaller.
Axle diameter:
Axle diameter has roughly diddly squat of an effect on RSU forks in bending, but an almost 20 % increase in torsional stiffness.
For USD, interestingly, the effect in bending is a few percent, but in torsion it is less than 20 % as opposed to RSU, but still over 10 %. The most important factor is that this is a ‘free’ gain, impacting torsion while hardly impacting bending stiffness.
Axle thickness:
With axle thickness there is almost no effect in bending stiffness, while there are a few percentage points of gain to be observed in torsional stiffness. Nevertheless, for RSU forks, this is an area of marginal gains.
Going to a 20 mm axle will have a much larger effect in torsion (~20 % higher stiffness for RSU forks) with virtually no effect seen in bending, given the same thickness. And the thickness, as long as it’s over 2 mm, also doesn’t play a significant role in the stiffness of the fork.
As long as the axle is at least 2 to 3 mm thick, the gains are marginal in torsion, both for 15 mm and 20 mm, when we are talking about RSU forks.
For USD forks while the gains in bending are marginal, they are larger than with RSU forks when going to a 20 mm axle. In torsion the overall gains with either a 15 mm or a 20 mm axle are smaller than with RSU forks, but nonetheless are present.
Axle clamping width:
Clamping width shows a similar situation with even more marginal gains. Once you’re at 25 mm or above, the are hardly even seen with a loss of stiffness when you are at 15 mm width. There is even a decrease observed at 45 mm in torsion, but I’d suspect it might be caused by the dropout rotating and sticking out and giving a more unrealistically high maximal value. Honestly, given the results in this category, I didn’t inspect it more thoroughly.
If anything, this category is, given the way the model was assembled, the most unrealistic. In real life you have the before mentioned hub clamped between the legs, the joint between the dropout and the axle is not ideally ‘bonded’ to the dropout hole, there is some play in the interface. You can also have pinch bolts, etc. I do remember DVO saying clamping width is important for increases stiffness, so I would gladly accept that there is an issue with my analysis here. But I can hardly imagine a world-shattering difference by clamping the axle over a longer distance compared to the results in other categories.
Travel:
To cap it off, travel. What happens at different points of travel? Quite a lot actually, but again, mostly in the bending mode, maybe not so much in torsion. This data point was added more for fun, as it doesn’t really matter that much. Nobody will go out and buy a shorter travel fork just to have it ‘10 % stiffer’ in torsion or ‘25 % stiffer’ in bending.
Conclusions:
I’m sad to say upside down forks do appear to be torsionally much more flexy, at least according to these results. They are quite a bit stiffer front-to-back, but while that stiffness can additionally be relatively easily greatly increased, there is no silver bullet when it comes to torsion. Or, to put it in a different way, all the work done to increase torsional stiffness will add quite a bit more weight and make a MUCH stiffer fork front-to-back. A quick assumption of throwing 40 mm stanchions, a billet crown and a 20 mm thick/billet axle, maybe even steel onto an upside down fork would give somewhat similar torsional stiffness to the base 35 mm stanchion, 15 mm axle right side up fork, but at roughly six times the front-to-back stiffness. Let’s rather not discuss the potential weight of this monster.
For everybody wishing 20 mm axles were brought back, there is some logic to it if you want a torsionally stiffer right side up fork. A 20 mm axle shows almost no change in bending stiffness with an almost 20 % increase in torsional stiffness. The effect of it in upside down forks is nowhere near as noticeable. And we have the bridge to thank for that. The bridge forces each outer leg to twist along the length to conform to the angle the axle is positioned at, which it doesn’t want to do. And the axle is being bent into an S shape, adding stiffness. With an upside down fork with no bridge, the stanchion and dropouts can just rotate in the bushings freely, leaving the bending stiffness of each outer to carry most of the load. That’s why I added a variant of a right side up fork without a bridge. The results are... eye opening to say the least.
So yeah, it’s the bridge that makes all the difference in torsion.
TL; DR:
-upside down forks are torsionally much more flexy than right side up forks (about three times as much)
-upside down forks are stiffer in frontal impacts than right side up forks (over 1,5-times as much)
-larger diameter of stanchions does help upside down forks in torsion
-20 mm axles help in torsion much more than in bending
-most dimensional changes impact bending stiffness more than torsional stiffness
-the bridge makes all the difference in right side up forks
Final thoughts:
These numbers shouldn’t be taken as the be all, end all or as a basis to say ‘yeah, well the Zeb is xx % stiffer than the Lyrik’ or ‘the 38 is yy % stiffer than the 36’. Real life products have different parts of their whole optimised to achieve different results, as can be seen by a much different crown and bridge on the Zeb compared to the Lyrik, by the ovalized steerer tube on the 38, etc. Hell, even steerer tube length will play a factor in torsional stiffness once mounted to the bike, even on the same fork! This analysis was meant purely as something to hold on to when there were discussions about pros and cons of upside down forks, but given that the models were designed with a parametric study in mind, I got carried away a bit and tested a few other factors.
Additionally while the geometry of both right side up and upside down variants was kept the same in this case, upside down forks open certain possibilities not available to right side up forks, like mounting a bushing much closer to the crown of a dual crown fork with the stanchion passing into the outer above the lower crown of a dual crown fork.
Given these numbers I don’t really see upside down forks becoming popular outside of niche brands. While they do have some other benefits not mentioned above (lubricated seals and bushings for example), I’m afraid the lack of torsional stiffness is too great to ignore. Plus, it’s coupled with a large increase in bending stiffness.
There was a debate (mostly between Jeff and me if I remember correctly) almost a year ago about MX equipment, where upside down forks are de rigueur. We know the stanchions arethicker, the axle diameter was debated (seemed relatively thin given the supplied data compared to MTB forks) and they are all using dual crowns. What I’ve started wondering is if the lower torsional stiffness and higher bending stiffness of an upside down fork might be a benefit for a motorcycle, both in MX and track racing? They are much heavier, so they load the fork front-to-back more, thus the benefit in stiffness in this direction. The forks can also be heavier, thus have more stiffness in any case (more material...). Then, is it possible both MX and track racing doesn’t require as much torsional stiffness? Could it be a benefit to ride the ruts with the front wheel having some more torsional compliance? Prevent unwanted sliding of the front wheel on tarmac if you put too much input into the bars? With brakes we know the holy grail of modulation is in part caused by a flexy lever and hose, giving you a distinct and noticeable correlation between lever throw and the resulting force. The stiffer the system will be, the less it will move for a given braking force increase.
On the other hand MTB usually is a bit more precise when it comes to line choice, dodging roots and rocks and the like. Could increased torsional stiffness aid here? Given a certain stiffness a right side up fork will be much lighter as well.
Or am I completely wrong here?
What we need now is either Cornelius to seed someone an Ebonite and a Hero for a comparison review or someone to put down ~4000 € to buy both of them and close the matter once and for all 
*the largest diameter being 39,99 mm is like that due to the model. Setting it to 40 mm makes the outer surface of the outer tube merge with the outer surface of the dropout, breaking the reference for the bridge creation. Thus, at 40 mm stanchion diameter, the bridge on the RSU fork is not created, which would cause an issue. Going one hundredth of a mm under that value causes no significant difference in the result, but does create a separate surface on the outer tube, giving us a working model. So, it’s not intentionally dub related, but it does set up a great joke
*also, post #1000!
) - this would widen the Crown and make it more flexy but might also improve the torsional stiffness. This could be just the ticket for USD forks (does it trade bending for torsional stiffness?). Motorbikes also have wider hubs so maybe this partly explains it.
