bicycle free body diagrams/analysis

Jan 2014
11
0
Hi all, I really struggle when it comes to things like this! I've designed an electric bike frame, and I want to roughly calculate the distribution of the loading just to have something to back-up my Solidworks model. I found this:

http://www.princeton.edu/~humcomp/bikes/design/desi_57.htm

Which is essentially exactly what I want to do, although my frame is a full suspension frame so I have a 'front triangle' and rear swing arm. The frame I'm trying to analyse is a '2008 Commencal Supreme DH'.
If I analyse just the front triangle, I don't have a reaction force at the rear wheel? If I analyse both frame parts, it becomes too complicated for me!

I have been reading through loads of literature, and looking at beam bending etc. but I can't seem to work it out. If anyone could give me a few pointers I would be extremely grateful! I will continue to work on this problem, and update with my progress!
 

ChipB

PHF Helper
Jun 2010
2,369
294
Morristown, NJ USA
You should be able to find the reaction forces of the wheels R1 and R2 quite easily given the distribution of the weight of the rider on the seat, pedals, and handle bars, and also the weight and center of mass of the bike itself. These reaction forces have nothing at all to do with the arrangement of tubes and struts that make up the bike itself. Is this what you're having trouble with? However, if your issue is trying to determine moments and forces within the bike structure - so you can calculate stresses - that's a much more complicated analysis, given that the bike is structurally indeterminate. Is that where you're have trouble?
 
Last edited:
Jan 2014
11
0
Hi Chipb, I'm sorry, I didn't describe it very well! I should definitely be confident doing the first part you mention, but it's been a long time since I've done anything like this! For the first part then you have the three 'weights' (one at handlebars, one at seat, and one at pedals), and two reaction forces (where the front and rear wheels mount), and you can just use horizontal distances can you? As if it were just a simple beam?

And the second part I'm completely lost on! Any help with that at all would be fantastic.

Thanks very much in advance!
 

ChipB

PHF Helper
Jun 2010
2,369
294
Morristown, NJ USA
Not sure what you mean by first part and second part. But to find the reaction forces R1 and R1 start by taking the sum of moments about either one, and set it to zero. That's what the page you linked to talks about, and gives youo the value for R2. Then use sum of all vertical forces = 0 to find the value of R1.

The rest of the analysis is done assuming all joints of the bicycle are simple pinned conenctions, which simplifies the analysis but ends up requiring the introduction of a non-existent beam AF. The technique is to look at each trangular section and assume that all forces are either tensile or compessive - i.e. no moments oat all. Using free body diagrams and resolving all force componenets into horizontal and vertical components allows you to determine the force carried by each tube. To get started - do you understand what's going on here: http://www.princeton.edu/~humcomp/bikes/design/desi_59.htm

By the way - are you attending Princeton, or just referring to their website? If the former - there's a big lacrosse game this weeknd against my alma mater.
 
Last edited:
Jan 2014
11
0
Hi Chipb, thanks so much for the response again. I think I'm alright with finding the reaction forces.

I understand the page you linked, but I'm struggling to link it to my frame. If mine was a 'simple' bike shape like theirs, I could easily swap the numbers and angles etc. but mine has a front triangle, rear swing arm, shock, and linkage. Do I need to simplify my frame?

This is mine:
http://ep1.pinkbike.org/p4pb1390475/p4pb1390475.jpg

Obviously I can simplify the front to a simple triangle, but I'm stuck with what happens with the linkage etc. In actual fact it's only the front triangle that I need to analyse, but I don't know how the loads are transmitted through the linkage/shock/swingarm pivot?

And unfortunately no, I'm studying in the UK!

Thanks very much again, Jamie
 

ChipB

PHF Helper
Jun 2010
2,369
294
Morristown, NJ USA
This requires a different approach. I would start by modelling the rear bars as a pair of cantilever beams, and use Mc/I to find the stresses in each. For the main frame you have a force and moment applied at the pedal area by those rear beams, plus a moment and force from the front wheel fork. If that was all then you could again use Mc/I to get the stresses ant any cross-section. However, I see a shock absorber under the seat - that complicates things a lot. Do you have the spring rate for that? I suggest that the best approach to working this would be to load a known weight on the bike and see how much that spring compresses - if you know the spring rate that will give you the force on the frame at its attachment points. Then again. Mc/I will give stresses at at any cross-section of the main frame.
 
Jan 2014
11
0
Thanks so much for the response again. When you say modelling the rear bars as cantilever beams, I guess you mean as if they are constrained where the rear swingarm mounts? And use the reaction force from the rear wheel? I understand your method using the spring rate, that's certainly possible.

The rear bars are a kind of V-shape. Is it possible to model them like that, or would you simplify it to straight beams?

I will try to work through this in the simplest way possible, and post up my working. I'm still quite lost at the moment though! Thanks again for all the help
 

ChipB

PHF Helper
Jun 2010
2,369
294
Morristown, NJ USA
When you say modelling the rear bars as cantilever beams, I guess you mean as if they are constrained where the rear swingarm mounts? And use the reaction force from the rear wheel?
Yes, that's what I mean.

The rear bars are a kind of V-shape. Is it possible to model them like that, or would you simplify it to straight beams?
It's possibole to model as their V-shape - just remember that the values of c and I vary along the its length, just like M does, so you will need to take that into account.
 
Jan 2014
11
0
Sorry again for being so slow, but how do I model a V-shape cantilever beam? Thanks again for the help, I really appreciate this
 

ChipB

PHF Helper
Jun 2010
2,369
294
Morristown, NJ USA
This is like calculting stres in an I beam - but here let's call it a twin-beam. At each point along the length of the twin-beam you will need to find the centroid of the twin beam, then calculate moment of inertia I and max dimension c about that centroid. You have M from the reaction force R times distance. But here's a hint to simplify things: if all you need to is find the point of the greatest stress (for example to make sure that the tubes are strong enough), that stress will occur at the cantilever end of the twin-beam, so that's really the only point you need to check.

Just so I'm in tune with what you're doing here and yuor background - I assume you are a 1st or 2nd-year engineering student and that you have taken (or are currently taking) an introductory solid mechanics class - correct?
 
Last edited: