Lateral strength of bicycle wheels

Discussion in 'Cycling Equipment' started by lukeevans, Oct 9, 2013.

  1. lukeevans

    lukeevans New Member

    Joined:
    Mar 22, 2013
    Messages:
    8
    Likes Received:
    0
    Hi all,

    I know there was a bit of discussion about this regarding a 20" recumbent bicycle wheel a while back, but I am wondering if anybody out there could help me out.

    I am a final year student of an integrated masters of engineering program and am going to investigate the lateral behaviour of a bicycle wheel when held in the upright position.

    The reason why I think this is important is because I think there will be an increase in human powered load carriers which have either three or four wheels which cannot lean like the conventional bicycle. Last year I attempted to design a human powered log delivery vehicle, but got stuck on the specification of the wheels. I contacted hub manufacturers, spoke manufacturers, and wheel manufacturers who could not give me any quantifiable data and all said that if their components failed they would replace them for free. It was great to hear such confidence in their products but I would like to know a safe limit to use wheels.

    I would just like to appeal to the expertise on this forum to see if anybody would like to offer ideas of how to do this. My current plan is to model a wheel in Pro Engineer and run some finite element analysis, then compare the results with hanging weights on the wheel whilst attaching strain gauges to the spokes, much like the tests people have posted on the internet to understand the stiffness of wheels. Im also interested in seeing at which point if fails and understanding where it fails, whether the spokes pull through the rim, the rim deforms, or the spokes pull through the hubs.

    I'm also after some advice on some wheel manufacturers who may be interested in giving/selling me some cheap wheels to use for testing.

    Cheers

    Luke
     
    Tags:


  2. CAMPYBOB

    CAMPYBOB Well-Known Member

    Joined:
    Sep 12, 2005
    Messages:
    11,945
    Likes Received:
    1,036
    "Last year I attempted to design a human powered log delivery vehicle, but got stuck on the specification of the wheels."

    Logs?

    Thank God you didn't get to the brake specifications!

    I suppose you could get FEA node points from this fellow...

    [​IMG]

    This chap has never heard of Unigraphics or Solidworks.

    [​IMG]

    Good luck with the wheel loading models! It sounds like a fun project.
     
  3. Volnix

    Volnix Well-Known Member

    Joined:
    Feb 19, 2011
    Messages:
    2,883
    Likes Received:
    139
    Ok basically you are not designing a bicycle, so I dont think that you would necessarely need to use bicycle wheels, or stanards for them whilst designing your vehicle.

    You can read the EN standards for road, mountain and city bicycles on line. Just google them they are there in .pdf files. They are a normal limit for defining design load cases, but if you read it you might also find that its not that "strict". They just require a 100,000cycle fatigue strength for the frame for example. Thats what? A weeks use?

    Designing something gets as much complicated as the more load cases you are desiging for.

    If you are designing something for more then a 100kg load, I think you dont need to bother with bicycle design. Actually, by the sounds of it you might get some better ideas if you look into wheelchair design, or cart design.

    If you are just designing for a vertical load of 200kg you will get one set of dimensions. If you also include some other load cases, like side winds etc, you will get another. There is no limit to how many load cases you can design for, but you should definately cover the requirements of for example EN standards, or BS standards or your local standards. I dont know if this is required by law but most of the companies do that for their stuff.

    as far as the FEM model, I think that you should probably have the whole thing there to use your load cases, not just one wheel.

    Are you actually going to built the wheel?

    This might be some good reading for bicycle design:
    "Bicycling science"
    http://mitpress.mit.edu/books/bicycling-science
     
  4. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Hi lukeevans, Lateral stiffness is essentially governed by Bracing Angle, Rim depth and width, number of spokes, spoke lacing, and spoke tension.

    Bracing Angle... essentially spoke angle of around 6 degrees is sufficient.
    Rim depth and width... this depends on material and desired rim weight.
    Number of spokes... to carry a large weight I would suggest at least 36 spokes and preferably 48 spokes.
    Spoke Lacing... the higher number of crossings the better. I would suggest at least a 4 cross spoke lacing.
    Spoke Tension... >90kgf and preferably at least 100kgf, which should avoid nipple loosening occurring.
    Nipples... Brass nipples for this application would be best.

    A hub that could be used for this application are Track hubs, although if gears are required then MTB hubs should be ok.

    thanks KL [​IMG]
     
  5. alienator

    alienator Well-Known Member

    Joined:
    Jun 10, 2004
    Messages:
    12,596
    Likes Received:
    160
    Wrong. So long as spokes have enough tension to not lose tension as the wheel rolls, spoke tension has nothing to do with wheel stiffness. Number of spokes, diameter of spokes, spoke material, spoke length, lacing pattern, bracing angle, and rim cross section parameters (shape, wall thickness, and etc) affect wheel stiffness. A simple understanding of Hooke's Law will you that tension has no impact on stiffness (except when spokes go slack).
     
  6. CAMPYBOB

    CAMPYBOB Well-Known Member

    Joined:
    Sep 12, 2005
    Messages:
    11,945
    Likes Received:
    1,036
    "Wrong."

    Says the man with spoke tension so low he sucked his rear derailleur into them.
     
  7. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Quote: Originally Posted by alienator .

    ... So long as spokes have enough tension to not lose tension as the wheel rolls...
    Hi alienator, this bit is correct, which indicates that spoke tension does play a part in Lateral Stiffness. The rest is just rhetoric ... perhaps Alfeng is correct [​IMG]

    If you would like to indicate what is the ideal "enough tension" every single hub, rim, and spoke type combination to clarify your statement (if possible) that would be wonderful.

    thanks KL [​IMG]
     
  8. alienator

    alienator Well-Known Member

    Joined:
    Jun 10, 2004
    Messages:
    12,596
    Likes Received:
    160
    As I wrote before, tension has to be enough that the spoke does not go slack. It's not rhetoric. It's physics and engineering. The only stiffness a spoke can add to the lateral stiffness of a wheel is its own stiffness. You won't believe this because for some reason you, like a few others, refuse to accept the physics and engineering principles because you apparently harbor some belief that some as yet undiscovered physics applies to bicycles. Yet somehow you and your ilk cannot justify your "beliefs", i.e. you have zero proof of anything. In the off chance that you actually have some intellectual curiosity about why a wheel's lateral wheel stiffness is not a function of spoke tension, here's the equation for the stiffness of a straight gauge spoke: [IMG ALT=""]http://www.cyclingforums.com/content/type/61/id/291619/width/200/height/400[/IMG] "k" is the stiffness, i.e. spring constant; "E" is Young's Modulus; "A0" is the cross-sectional area of the untensioned spoke; and "L0" is the unstretched length of the spoke. Okay, here's a quiz: where's the spoke tension in that equation? (Hint: it's not there) Here's the equation for a double butted spoke: [IMG ALT=""]http://www.cyclingforums.com/content/type/61/id/291620/width/200/height/400[/IMG] "keq" is the overall stiffness of the spoke; "k1" is the stiffness of the end sections of the spoke; and "k2" is the stiffness of the middle section. If you still crave knowledge, here's the equation of a spoke with "n" different diameters: [IMG ALT=""]http://www.cyclingforums.com/content/type/61/id/291621/width/200/height/400[/IMG] If you can't figure out how equation 2 came from equation 3, well, I'm sorry because that means algebra isn't your strong suit. Now I know you're about to reflexively say, "But Alfeng said..." or "....in the real world"..... Well, Klabs, physics and engineering principles (the product of physics) apply in the real world. The reason that the spoke has to be tensioned enough that it doesn't go slack is that if the spoke goes slack, spoke stiffness is contributing nothing to wheel stiffness at that point. If for example a spoke tension of 50KgF keeps a spoke from going slack, then cranking tension up to 130KgF is not going to make a laterally stiffer wheel. There might be other benefits, but that increase won't increase lateral wheel stiffness. As for what the minimum spoke tension needed is for every hub, spoke, and rim combination out there, I suggest you either buy everyone and try all the combinations or your created solid models of all the different pieces and then build solid models of every combination possible and test them with FEA at every bike/rider system weight possible, from the lightest possible rider to the heaviest possible rider. Also be sure to test them at every speed possible and every road condition possible. Since no one in history has done that, make sure to leave a lot of room in your schedule over the next year or two or three or four.
     
  9. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Hi alienator, if you had read the post correctly, it says "The rest is just rhetoric"...

    Actually, what is the exact value of "enough tension to not lose tension as the wheel rolls".
    I can't see anything in those equations re pot holes, rough roads, and load... perhaps I missed it or perhaps it needs more maths proof [​IMG]

    Perhaps your would like the OP to PM you so that you can directly assist them (Please do not PM me ... thanks) [​IMG]

    thanks KL [​IMG]
     
  10. alienator

    alienator Well-Known Member

    Joined:
    Jun 10, 2004
    Messages:
    12,596
    Likes Received:
    160
    Re-read my post, Klabs. Your answer is in there. Of course, I'm not assuming you've got an open mind or are actually interested in the physical facts. Feel free to maintain whatever wheel mythology you need to kling to. I suspect the OP already understands the equations and principles above. Did you notice that he's building models in Pro/E and is running them through some FEA?
     
  11. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Hi alienator, the answer is not for me, it is for the OP. After all, the focus of this thread is not me it is the OP...

    So perhaps, if you would like to, you could point to the areas in the formulas which point to pot holes, rough roads, and load, re "enough tension to not lose tension as the wheel rolls" [​IMG]

    thanks KL [​IMG]
     
  12. alienator

    alienator Well-Known Member

    Joined:
    Jun 10, 2004
    Messages:
    12,596
    Likes Received:
    160
    I don't want to confuse you with "science and stuff", about how forces generated from the impact with bumps and holes effect spoke tension (hint: review "Hooke's Law", Klabs).:smile: Note that it was you that said that spoke tension was important to wheel stiffness, even though you didn't understand the actual science behind lateral wheel stiffness. :smile: What principle form the basis of your statement? :smile: I think you need to lay your thoughts and reasoning out for the OP, i.e. give him the fruit of your physics and engineering knowledge. :smile: It will be interesting to hear you explain as much. :smile: I think we all look forward to learning a lot from you, KL. :smile: Thanks, KL. :smile:
     
  13. Volnix

    Volnix Well-Known Member

    Joined:
    Feb 19, 2011
    Messages:
    2,883
    Likes Received:
    139
    Quote: Originally Posted by KLabs .

    I can't see anything in those equations re pot holes, rough roads, and load... perhaps I missed it or perhaps it needs more maths proof [​IMG]


    Yeah, dont forget to design for blast loads from nearby explosions and the return trajectory loads in case the cart needs to be launched from Ukraine to the Philipines for "emergency use" too... [​IMG]

    There is really no limit to how many load cases... If you find a standard to stick with and over design a bit (some standards even define how much to over-design) you should be fine. But... check with your supervisor for those, allthough some academic supervisors tend to say "yeah thats an excellent idea, so now design me a standard for these carts too! [​IMG]"

    Standards are an on-going work that have alot of theoritical and experimental knowledge that you can use to design stuff. If you find a combination of those to use then it should be simple afterwards with defining dimensions etc. Materials availability is important too. Basically if you define what you are designing in fine detail then you probably got a good start point to start checking standards etc.

    But for that application maybe bicycle standards are not enough I think... maybe just use parts of a car design standard or a cart or wheelbarrow design standard (if such a standard exists). There are also sometimes some "additional" guidelines for designing stuff. I checked one once and it was starting with something like "after you have created a "something" that complies with the EN-standards, you should also consider..." and then were another 60 pages of guidelines for design. Not as much for loads etc but manufacturing processes etc...
     
  14. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Hi alienator, [​IMG], but the OP might be, so perhaps lukeevans can PM you (directly) because it would appear that you know everything! ... and yes, Alfeng is correct [​IMG]

    Hi lukeevans please let us know if you would only like to communicate solely with alienator or that you are happy to communicate with the rest of us via this thread [​IMG]

    thanks KL [​IMG]
    (@alienator, please do not PM me!)

    Hi All, is there an ignore list on this forum ... thanks KL [​IMG]
     
  15. Eichers

    Eichers New Member

    Joined:
    Sep 17, 2010
    Messages:
    541
    Likes Received:
    4
    Hi alienator, you had to PM me, didn't you, and be insulting in the PM. Please know that it has been reported... thanks KL [​IMG]
     
  16. CAMPYBOB

    CAMPYBOB Well-Known Member

    Joined:
    Sep 12, 2005
    Messages:
    11,945
    Likes Received:
    1,036
    Damn! I NEVER get PM's from the little douche nozzle!

    Remember, KLabs, he's the assclown that admitted that he had a wheel with low spoke tension that resulted in him sucking his Campy Record derailleur right into those "ideally tensioned" spokes as the wheel flexed laterally!

    All his rhetoric and formulae went flying right out the government shutdown window as his expensive gear changer wound itself up in his expensive, but not properly tensioned, wheel. The wheel he claimed pro racers couldn't tell if it was stiff or flexible in double-blind 'scientific' tests. The wheel you could loosen all the spoke nipples up 2-1/4 turns without affecting lateral stiffness according to 'Da Chart'â„¢.

    Union of Unconcerned Scientists! Unconcerned with reality and common sense.

    C'mon, nookums! Post us up some pikchars of your destroyed derailleur and spokes! Show us your scientific literacy!

    Whadda nimrod!
     
  17. lukeevans

    lukeevans New Member

    Joined:
    Mar 22, 2013
    Messages:
    8
    Likes Received:
    0
    Hi All,

    Thanks for the responses!

    I've actually got all of the BS documents for the bicycle and there are no specific documents on wheels, there is a BS for rims, and another for spokes, but nothing for the hubs other than the screw thread to be used for the free hub. In fact, the spokes have the same british standards for motor cycles as they do for cars as they do for bicycles.

    Vertical loading on a bicycle wheel can carry a ridiculous amount of weight, each spoke has a tension of around 1000N/1200N. In a static model you could say that the forces are shared between four to 8 spokes, that gives approx 400 to 800kg per wheel! of course a wheel is moving so the forces are dynamic and that is part of the problem with modeling a wheel.

    I don't think I was clear enough for my original post, I have already attempted to design a vehicle, and failed as I couldn't get past understanding the bicycle wheel.

    There is very little scientific data out there on bicycle wheels, other than the excellent Jobst Brandt "The Bicycle Wheel", MIT's "Bicycling Science", or going back to the 1896 when Archibald Sharp explains the physics of the bicycle in his book "Bicycles & Tricycles: A Classic Treatise on Their Design and Construction" there is not much out there.

    When searching research papers through the university search system reveals very little out there, but I am sure there must be something.

    Alienator appears to have either read something on stiffness not being related to the lateral strength of a wheel (or maybe calculating that from first principles?) but, the spokes tension is acting at an angle, so surely the overall stiffness of the wheel will be affected as there will be a greater holding force on keeping the wheel rim in place? Does that stiffness equation not only apply to a material in one plane? whereas we are talking about a number of objects working together in a dynamic way. If it was something you read could you point me in the direction? as that is what I am fishing for here, ideas and leads :)

    I agree that to be able to design an actual wheel that can hold more weight it will no longer be a bicycle wheel, but the question is where does it fail? bicycle wheel manufacturers do not have this data in the public, and the few which I contacted last year could not tell me how much lateral force it could take. I was asking bmx wheel manufacturers as I thought that they would be by far the strongest, but they could not tell me where the failure would occur, would it be the hub, the spokes or the rim?

    I want to create a first point where I could say here's a basic model of the wheel which shows how a wheel behaves under lateral loading, which somebody could then use and take forward for further understanding. This could then be added to Jobst Brandts calculations of radial (including bump), breaking, torsional, and dynamic loads, for people to design lightweight spoke wheels for human powered vehicles.

    If I could prove one model of one wheel with a known hub size and known spoke size/angle, and specific rim I would be a very happy man!

    Thanks!
     
  18. Volnix

    Volnix Well-Known Member

    Joined:
    Feb 19, 2011
    Messages:
    2,883
    Likes Received:
    139
    Quote: Originally Posted by lukeevans .
    Hi All,

    Thanks for the responses!

    I've actually got all of the BS documents for the bicycle and there are no specific documents on wheels, there is a BS for rims, and another for spokes, but nothing for the hubs other than the screw thread to be used for the free hub. In fact, the spokes have the same british standards for motor cycles as they do for cars as they do for bicycles.

    Vertical loading on a bicycle wheel can carry a ridiculous amount of weight, each spoke has a tension of around 1000N/1200N. In a static model you could say that the forces are shared between four to 8 spokes, that gives approx 400 to 800kg per wheel! of course a wheel is moving so the forces are dynamic and that is part of the problem with modeling a wheel.

    I don't think I was clear enough for my original post, I have already attempted to design a vehicle, and failed as I couldn't get past understanding the bicycle wheel.

    There is very little scientific data out there on bicycle wheels, other than the excellent Jobst Brandt "The Bicycle Wheel", MIT's "Bicycling Science", or going back to the 1896 when Archibald Sharp explains the physics of the bicycle in his book "Bicycles & Tricycles: A Classic Treatise on Their Design and Construction" there is not much out there.


    I want to create a first point where I could say here's a basic model of the wheel which shows how a wheel behaves under lateral loading, which somebody could then use and take forward for further understanding. This could then be added to Jobst Brandts calculations of radial (including bump), breaking, torsional, and dynamic loads, for people to design lightweight spoke wheels for human powered vehicles.



    I could not help noticing the BS citation in your thread.

    Plain and simple:

    1. What do you have to build? Is it a "crazy" project or do you actually have to built it? If you have to build it and you dont have access to the right machinery (Carbon fiber molds, aluminium hydroforming machinery etc...) dont bother making a very fine FEM model... You are probably gonna be fine with linear design. Unless you get some butted spokes and stuff...

    2. Do you have a clear design specification? Check for one... [​IMG]

    Bicycle wheel spokes btw "support" the load towards the rim and then it ends to the ground...
     
  19. alienator

    alienator Well-Known Member

    Joined:
    Jun 10, 2004
    Messages:
    12,596
    Likes Received:
    160
    Lukeevans: imagine you have two wheels. The wheels are laced at different tension, the first wheel at A KgF and the second wheel at B KgF. The wheels are otherwise identical: same spokes, lacing pattern, number of spokes, rims, and hubs. If you apply the same lateral force at the same point on both rims, you will get the same deflection. If you don't understand why this, look at hooks law: imagine you have two springs with identical k but loaded with two different forces (5N on one and 10N on the other), say the force on one spring is twice the other. Now increase the force on each spring by 5. What will be the additional displacement of each spring. Let's see: F/k=x Spring 1: New spring length minus original spring length: (5N + 5N)/k - 5/k = 5/k = xdisplace Spring 2: (10 + 5)/k - 5/k = 5/k = xdisplace As for bracing angles, greater bracing angles provide greater lateral stiffness because the lateral component of stiffness contributed by the spoke (k=EA0/L0) is greater. So what does great spoke tension add? Well, one thing to consider is that a lateral forces on a wheel are dynamic, not static. As such you have to find the solution to this 2nd order differential equation: F = kx + γ(dx/dt) + m(d2x/dt2) The form of that solution is going to depend on how you model the system (do you model the wheel in contact with the ground, or do you model it as if the wheel is in a stand, in contact with nothing but its axle?) and some assumptions you make, such as those about damping (is the system critically damped, over damped, or under damped; do you consider the damping viscous, Coulomb, or both?). Nevertheless you should see that since F is partially dependent on spoke tension, differences in spoke tension will affect the dynamics of rim displacement and the resultant motion once/as the displacement force goes to zero. Also keep in mind that lateral displacement is not strictly linear. That is to say applying a lateral force does not just move the rim laterally. The actual rim will deflect along a curve, so with every incremental lateral force applied, the wheel's component of lateral displacement will decrease, and the wheel's vertical component of displacement will increase. All of the above neglects the effect of the rider's weight on the shape of the rim and the subsequent changes in loading. It also neglects any effects on damping and lateral displacement resulting from a mounted tire. You can see a model can get pretty complicated quickly. You have to determine how complete you want your model to be and what assumptions you'll make and/or are willing to live with.
     
    dhk2 likes this.
  20. Tnark

    Tnark New Member

    Joined:
    Sep 27, 2009
    Messages:
    29
    Likes Received:
    2
    Lukeevans,

    I strongly suggest you read the book "The Bicycle Wheel" by Jobst Brandt. Much of what you are planning to do is discussed in this. He also did Finite Element Analysis of a wheel under various loads.

    Cheers

    Tony
     
Loading...
Loading...