Forces applied on the bolts in the bike's hinge

[kielbasa]

TL;DR Summary

Forces applied on the bolts in the bike's hinge in the alluminium frame. Steel grade of the bolts is needed.

Hi,
I recently bought a folding bike and it turned out over time that its weak point is the main hinge where two bolts (vertically placed) are located.
I've had the lower bolt break twice during a ride, leaving a part of it stuck inside the hinge thread. It's clear that the forces applied were too much for the low-grade steel bolt to handle. Anyway - since I don't want to spend more money on service bolts which are obviously bad quality, I'd like to use ready-made ones but higher steel grade and modify them to my needs by a turner.

My main question is, how can I estimate the maximum forces applied during a ride, for instance when getting off a 10cm curb? I think in these circumstances the hinge is most vulerable to destruction (maybe there are some others?)
I primarily use this bike for city riding, not for off-road or mountain biking and I'm trying to figure out the appropriate steel grade for the bolts that will be sturdy enough for this purpose so I can use them instead. Good quality bolts are made of 10.9 graded steel, which means they can withstand around 1000mPa / approximately 100kg per mm2 of the screw section. This translates to a yield strength of around 1600kg for an M6 bolt. This seems like a lot, but I'm not sure if it's enough. I can't quite estimate the forces acting on the hinge. Any ideas on how to do it ? It looks like the forces are still significant enough to break the service bolts that are sold in shops, and I'm certain they're not made of plasticine...
My weight is around 105kg.
Any ideas? thanks!

 

[jrmichler]

The peak load from driving off a curb can vary by an order of magnitude depending on how you drive off the curb. All you really need to know is that the factory bolts are not strong enough for your weight, road conditions, and riding style. If you replace with bolts that are sufficiently stronger than the factory bolts, the next weakest part will break.

A realistic approach is to:

1) Look at your riding style. Do you move your body so as to minimize the forces on the bicycle frame? Do you actively avoid hard bumps?

2) Change the bolts to the strongest that you can find, which would probably be metric class 12.9.

 

[jack action]

Good quality bolts are made of 10.9 graded steel, which means they can withstand around 1000mPa / approximately 100kg per mm2 of the screw section. This translates to a yield strength of around 1600kg for an M6 bolt. This seems like a lot, but I'm not sure if it's enough.

Why not use bolts of 12.9-graded steel and call it a day? They are the highest-grade bolts with 1200 MPa and probably not much more expensive than the 10.9. If they still break, nothing else will help except redesigning the bike frame or hinge.

 

[berkeman]

In addition to using the strongest bolts possible, you might look into whether there are wider tires available that will fit inside that frame. You could run them with a little less air pressure to give you a bit of a "suspension" effect (since your bike appears to be rigid). What pressure are you running in your tires right now?

If you replace with bolts that are sufficiently stronger than the factory bolts, the next weakest part will break.

^^^^this^^^^

 

[Baluncore]

I recently bought a folding bike and it turned out over time that its weak point is the main hinge where two bolts (vertically placed) are located.

You selected a bike that is not suited to your riding style and weight. If a bolt is failing in use, exceeding the design load and the safety margin now, then no higher grade bolt can make that structure safe, as it is now designed.

The folding frame you show in post #1, is designed as a single-beam that looks stylish, but you require the strength of a triangulated truss, with two hinges that share a common axis. The weak point will then move to the junction between the steering-tube and the front forks.

 

[berkeman]

You selected a bike that is not suited to your riding style

I dunno, it might be alright if the OP has a British accent. This part of the video is kind of a multi-curb test that he can perform...

 

[Baluncore]

Low-grade bolts are employed to protect the aluminium frame and hinges of a folding bicycle, in the same way that fuses are used to protect electrical wiring. The fuse should blow before the wire reaches a temperature that could melt the insulation.

Failure of one hinge bolt or pin, should result in a loss of rigidity, not in a loss of all integrity. Failure of a sacrificial bolt, should not damage the material of the frame.

 

[hutchphd]

the next weakest part will break.

I am reminded of the joke whose punchline is " I don't need to run faster than the bear: just faster than you!"
I would have some problems trusting that machine and its design team. A very crude estimate using energy conservation would be $$ F_{max}=W_{rider} \frac {h_{curb}} {d_{tire}} \frac {l_{frame}} {l_{bolt} } $$
Two factors greatly increase the force of your weight: the dynamics of the tire absorbing the shock of dropping off the curb and the small vertical size of the hinge relative to the cantilever of the rear wheel. these each add a factor of >10 to the shear force on that bolt . This design without more triangulation in the frame is at best worrisome and at worst a disaster. Perhaps the choice of fastener was a clever and deliberate safety choice.

 

[kielbasa]

Hi again,
Thank You for the replies however, there are few things You need to be aware of.
I never thought about it this way that the bolt might be protecting the frame and is the first one to be damaged.. but...
the hinge in this bike is called FBL 2 gen 1, and it has changed over the years to FBL 2 gen 2 so Tern constructors knew wery well that the first generation used to cause troubles. And what's interesting - only the pin/bolt itself has changed. Take a look at the picture below. In the second gen there is only one long pin that goes through the hinge. I also called Tern support and they admitted that 1gen had been faulty.

Getting off the curb is by no means my style of riding. I gave it as an example of a scenario when forces applied to the hinge might be the most destructive. It often happens, not only to me, that I drive on pavements and I need to get off the curb. It has nothing to do with my 'way of using this bike'

Yes, I can use 12.9 bolts but I wanted to have an idea of the approximate acting force we are talking about here first.

hutchphd, what is L frame and L bolt in Your equation? is this frame length (but what length?) and the bolt length, while d tire would be the tire diameter ?

The last resort wouldl be to drill out the hinge hole and enlarge the diameter to M7 (but after this mod there's no turning back), so the bolts used would be yet stronger. But I assume that the thickness of walls in the hinge might be insufficient to withstand the load and can break first.

 

[sophiecentaur]

1) Look at your riding style. Do you move your body so as to minimize the forces on the bicycle frame? Do you actively avoid hard bumps?

Agreed: general mechanical sympathy can always help.
I wonder where the cost of that bike comes in the hierarchy of folding bikes. I bought a folder (used) and it was like a tank. I soon stopped treating it as a delicate flower and would ride up and down curbs and through ruts in the road. It never failed. BUT it was far too heavy. I see guys running along the station platform carrying their Brompton plus other stuff; mine was really hard work just to carry on its own. Mine was not a pricy model, of course and it was the other end of the weight/cost distribution from Brompton. I wonder where the OP's bike comes in the statistics. Could it just be a matter of getting what you pay for?

 

[kielbasa]

Guys, let's not treat this thread as general advice on how I should ride a bike, please.
I'd be grateful if anyone could tell me how to estimate the forces acting on the hinge bolts during the ride, under described conditions. Dropping off the curb is the only situation I can think of, that happens sometimes to me, and when the forces might be the most destructive. Curbs are not higher than, let's say, 15cm.
I saw the Hutchphd equation but some of the data are not clear to me yet.

sophiecentaur, this bike was a 'better medium' bike in the Bickerton's range in 2017. I bought it as a used one.
But still, claimed max weight for any of their folding bike is 105kg, regardless of the price.

 

[hutchphd]

hutchphd, what is L frame and L bolt in Your equation? is this frame length (but what length?) and the bolt length, while d tire would be the tire diameter ?

Again this is very rough estimate but I was comparing: (1) the moment from the rear wheel to hinge (rear frame length) and ()2) the counter moment from the hinge (roughly the bolt shear force times the "hinge" length) As mentioned it is not a very robust design!

 

[kielbasa]

Yes, I'm aware of the fact, that folding bikes are not too robust..but still thousands of people use them. It is what it is.. ;)
Thanks for the explanation, but what does the 'd' stand for in the equation? is it the tyre thickness or rather the tyre/wheel diameter?
BTW I didn't know that bolt length can make a significant difference when calculating the shear force.

 

[Lnewqban]

I'd be grateful if anyone could tell me how to estimate the forces acting on the hinge bolts during the ride, under described conditions.

Could you show us photos of the broken bolt, as well as better detail of the side of the hinge into which those go?

The weakest point of the bolt seems to be where the threaded section meets the cylindrical section.
The load at those sections is tension from the torqued nut plus shear from weight plus dynamic loads (braking, potholes, curbs, etc.).

Measure the distance between those points when the bolts are normally installed (let's call it distance B).
Measure the distance between the contact patches of the tires-asphalt and the seat (let's call it distances Tf and Tr).

Shear force on each bolt = σ max

At the following link, in order to calculate σ max, look for:

Beam Supported at Both Ends - Eccentric Load​

https://www.engineeringtoolbox.com/beam-stress-deflection-d_1312.html

Then, consider that the resistance to shear force is about half the maximum tensile load number that you have mentioned for each material or bolt grade.

 

[kielbasa]

Could you show us photos of the broken bolt, as well as better detail of the side of the hinge into which those go?

The weakest point of the bolt seems to be where the threaded section meets the cylindrical section.

It's exactly how You described it. The bolt was broken in the place where the thread meets the cylindrical section.
But only the lower bolt was sheared, the upper was not. Since I've already taken out the bolt's broken part from the thread, I can't show You how it looks, but if You want to take a closer look at the hinge and the original bolts, I've attached a pdf file with the service instruction.

Thank You for the hints on how to calculate the shear force. I'll try to do it now :D

 

[hutchphd]

Thanks for the explanation, but what does the 'd' stand for in the equation? is it the tyre thickness or rather the tyre/wheel diameter?

It is meant to be the tire thickness
.....which is a measure of how far the bike travels vertically when the tire compresses after jumping off the curb.

 

[Lnewqban]

The diameter of the weakest cross section of that bolt is measured from bottom of a thread filet to the bottom of the opposite one.
Therefore, it is about 5 mm for a M6 thread.

That is one of the factors that make version 2 superior to 1, the increased diameter of the solid pin.
Could you find a kit to convert yours to version 2?

Also, threads are more fragile to cyclic loads (which your hinge suffers even in conservative riding due to frequent braking and irregularities of the street surface), because the bottom fillet (the thread surface) is not smooth at microscopic level, inducing micro cracks that weaken the cross section even more.

Any play between the bearing and the bolt (or factory's misalignment between the bearing and the female thread) could cause abnormal forces on that weakest cross-section of the bolt thread.

Please, see:
https://smrp.org/News/Solutions-Arc...y-Learn-to-Recognize-Mechanical-Failure-Modes

https://aeroenginesafety.tugraz.at/doku.php?id=23:233:2331:23312:23312

 

[berkeman]

Yes, I'm aware of the fact, that folding bikes are not too robust..but still thousands of people use them. It is what it is.. ;)

Yes, and that is a good thing, IMO.

Guys, let's not treat this thread as general advice on how I should ride a bike, please.

Well, sort of. You have chosen a folding bike where you are right at the upper limit of the weight range, and you are riding off some sharp bump things, as opposed to riding on smooth surfaces (where the bike company likely generated its maximum weight spec limit).

You did not reply to my post below, which I meant sincerely. Can you reply to it now please?

In addition to using the strongest bolts possible, you might look into whether there are wider tires available that will fit inside that frame. You could run them with a little less air pressure to give you a bit of a "suspension" effect (since your bike appears to be rigid). What pressure are you running in your tires right now?

I ride thousands of miles a year on my mountain bikes (MTBs), and on my hard tail (no rear suspension), I avoided jumping curbs because it puts too much of an impulse into my rear wheel and tire. I didn't want to unnecessarily flat my rear tire when I could just slow and lift over the sharp curb... With my full suspension MTB, there is no slowing...

 

[Baluncore]

The bolt was broken in the place where the thread meets the cylindrical section.
But only the lower bolt was sheared, the upper was not.

The two hinge plates are held together by the bolt and hinge pins. The pins or bolt will fail in tension because the hinge plates carry compression, through direct contact.

If you lift the hinge, the wheels will come off the ground, but if you press the hinge or frame downwards, you apply a multiplied tension to the bottom pin or bolt of the hinge.

The failure was due to excessive weight, as an impulse on the crank spindle, applied through the pedals, when riding on uneven ground.

 

[kielbasa]

You did not reply to my post below, which I meant sincerely. Can you reply to it now please?

I ride on the widest tyres possible, they were changed soon after I bought the bike. The ones I got it with were too slim, the ride was much less comfortable than it is now.

But let me ask You one more thing - I realized that the thread of the bolt could be longer, there is still some space in the hinge between these two bolts. Does the length of the threaded part of the bolt matter in this case? If this part is longer, will the screw be more durable? (I personally don't think so).
I'm asking because I found a ready-made bolt which is almost the same as the original one, but the threaded part is not 12mm but 10. So now I'm wondering if I should convert a longer one, or use the one below.

That is one of the factors that make version 2 superior to 1, the increased diameter of the solid pin.
Could you find a kit to convert yours to version 2?

I don't think converting to 2gen is possible 'just like that'. It was made in the factory as a new hinge version, and while they look the same, in the 2nd gen there's no thread in the hinge (I assume) since there's one long pin used.
I could use a smiliar solution - make a one long solid rod/pin to fit tightly across the hole in the threaded part of the hinge and thread both ends of the pin to screw in the nuts. It's just an idea that came to mind right now. edit: - nope. I won't be able to fit the socket on the nut to lock it.

 

[kielbasa]

I also made a rough sketch of the cross-section of the hinge and slid bolts. That should give You a proper idea of what the hinge looks like. What I didn't realize before, and I know now, is the fact that the shearing force is applied where the thicker cylindrical/not threaded part of the bolt is (and thats understandable and sounds logical). However, the bolts were cut in the place where the cylindrical section meets the threaded part, but that has been said already.

 

[sophiecentaur]

claimed max weight for any of their folding bike is 105kg,

I am not a porker but I often exceed 90kg so there's not a lot of headroom. Yours was clearly not a cheapo import so the breakage is surprising.

I saw the Hutchphd equation but some of the data are not clear to me yet.

That @hutchphd equation uses Energy conservation but I would think that a momentum approach would be more appropriate, based on Impulse (Force times time is change on momentum) because the time interval for any momentum change would depend on tyres and technique. The energy from the drop could be dissipated in many different ways to produce a range of brief maximum stress forces.

 

[kielbasa]

I also tried to make an estimated calculation based on what Lnewqban wrote, but I think we cannot treat this structure as a beam supported at both ends with eccentric load since the frame has the additional hinge support that changes the load distrubution

and also, it doesn't take into account the movement dynamic while getting off the curb (thus this can be calculated separately using potential energy equation, I assume)

 

[hutchphd]

The energy from the drop could be dissipated in many different ways to produce a range of brief maximum stress forces

The tacit assumption in my gross (the warning label was included!) simplification is that the acceleration force during the impulse is constant. This is obviously untrue but provides a lower bound on the instantaneous forces. Otherwise you are in the land of dynamic FEA .....a place I chose not to visit.

 

[kielbasa]

$$ F_{max}=W_{rider} \frac {h_{curb}} {d_{tire}} \frac {l_{frame}} {l_{bolt} } $$

Shouldn't it all multiplied by 'g' (gravity) ? As 'centimeters' will be reduced in the fraction, and only the 'kg' will remain.

 

[hutchphd]

No because Weight is mg. The rest are dimensionless ratios

 

[kielbasa]

No because Weight is mg. The rest are dimensionless ratios

thanks.
I did a quick calculation and came up with 105kg x (0.15m curb x 0.6m frame length to the hinge / 0.03m tire thickness x 0.04m bolt length) = 7875kg. That seems like a lot. However, I believe this calculation doesn't consider an important factor - the presence of the frame/hinge support that I mentioned in the earlier post.

 

[hutchphd]

If you wish to do a full calculation, then have fun. My purpose was to indicate that the design is not easy because of certain design choices that rapidly escalate the forces. I wouldn't ride that thing........but I am old and brittle.

 

[kielbasa]

If you wish to do a full calculation, then have fun. My purpose was to indicate that the design is not easy because of certain design choices that rapidly escalate the forces. I wouldn't ride that thing........but I am old and brittle.

heh, thanks. I know the calculation is rough and not so precise. But that frame support might be an important factor in reducing the stress on the hinge. And for sure, I'd not be able to calculate it more precisely by myself.

But if, let's say, I use a 12.9 grade m8 cylindrical solid pin, that has 50,25mm2 cross-section, its yield resistance
would be..1200mpa x 90%, say 1080mpa x 50,25mm2 = ~ 5400kg.
Significantly less than the previously calculated max force.

Can someone try to roughly estimate by how much such a frame support from the bottom can reduce the strees force on the hinge?

 

[sophiecentaur]

The tacit assumption in my gross (the warning label was included!) simplification is that the acceleration force during the impulse is constant.

Very soft suspension and sensitive riding could possibly approach that but the Impulse time would often be a small fraction of the event when the rider and bike are taken by surprise or for an unusual angle of 'disturbance'.

resistance
would be..1200mpa x 90%, say 1080mpa x 50,25mm2 = ~ 5400kg.

kg is a measure of mass not force. You should try to tidy that up (SI helps here).

 

[kielbasa]

Very soft suspension and sensitive riding could possibly approach that but the Impulse time would often be a small fraction of the event when the rider and bike are taken by surprise or for an unusual angle of 'disturbance'.

kg is a measure of mass not force. You should try to tidy that up (SI helps here).

I took a shortcut. 1080MPa x 50,25mm2 = 54250 N --> (roughly equals to a mass of 5400kg)

 

[kielbasa]

I'm just wondering, if you look at my cross-section drawing, you'll see that the shear force is applied where two parts of the frame meet and where the bolt is thicker (cylindrical, not threaded part). Why does the bolt get cut off in the threaded part if the cylindrical part of the bolt is supposed to carry all the load and it sits tight in the hole?

 

[Lnewqban]

Why does the bolt get cut off in the threaded part if the cylindrical part of the bolt is supposed to carry all the load and it sits tight in the hole?

The flaw of this design is that there is always play between the bolt and the aluminum housing (otherwise the hinge would not be easily rotated).

If the bushing is plastic, it allows some additional relative movement due to temporary deformation under cyclic load.

With time, the hole in the aluminum housing (as well as the bushing) will expand, increasing the back-and-forth flexing of the cylindrical section of the bolt respect to the fixed threaded section.

All the above transfers shearing and bending loads to the weakest point of the bolt: the treaded neck.

Note how the Generation 2 shown in post 9 has two lateral set screws (1 and 2), which combined with the cylindrical pin, eliminates that problem.

It seems that the housing has enough meat to tap two or four holes for adding similar lateral set screws and improve the assembly of your bike by restricting any lateral movement of the bolts.

 

[Tom.G]

Perhaps a better design would be a bolt that goes all the way thru the hinge, with a locking nut or cotter pin to keep the nut on. Of course it needs to be threaded only away from the load-bearing area.

You may need a custom hinge made/machined for that approach though.

Is there a chance the bike manufacturer as upgraded the design yet?

 

[kielbasa]

Perhaps a better design would be a bolt that goes all the way thru the hinge, with a locking nut or cotter pin to keep the nut on. Of course it needs to be threaded only away from the load-bearing area.

You may need a custom hinge made/machined for that approach though.

Is there a chance the bike manufacturer as upgraded the design yet?

Take a look at one of my previous posts where I attached two drawings with two different hinge generations.
They did upgrade the hinge in the way You described, however, the drilled hole where the pin slides across the hinge (I assume) must be the same diameter at full length. Mine is not. (take a look at my cross-section drawing too.