Mechanics of a front wheel on a bicycle

[bollen]

TL;DR Summary

I am working on a project where I am supposed to find some ways to get constraints on some of the components (rim, hub and spokes) to use these for parametrization.

I am working on a project where I am supposed to find some ways to get constraints on some of the components (rim, hub and spokes) to use these for parametrization. So far I have thought that the constraint for the rim is that it can't buckle from the pre tension of the spokes (here I am thinking about using tension formulas for a thin walled pipe) . The spokes are not allowed to buckle from a radial force (here I am thinking of using Eulers critcal load). For the rim I figure that I maybe can use some kind of torque constraint assuming that the wheel has a rim brake that will apply a force that will be levered as a moment from the spokes.

The problem is that I am not sure if these assumptions would be enough (or accurate either for that part). I do already see the problem of not taking the possibility of a lateral load in consideration so any suggestions of doing that are welcome. I would also be interested in how it is possible to calculate how much tension a spoke can lose before the rim buckles.

I am thankful for all help I can get

 

[jrmichler]

Start by getting a copy of Bicycling Science by David Gordon Wilson. It's an excellent resource on bicycles in general, and it has several pages on the engineering of bicycle wheels. Those pages include exactly the information you need to get started. The book references another book, The Bicycle Wheel, by Jobst Brandt. In both cases, get the third edition. The third edition of Bicycling Science has far more information than the previous editions.

Hint: You can ignore the Euler column buckling force on a spoke. Do the calculation, compare to typical loads, and you will see why.

 

[bollen]

Start by getting a copy of Bicycling Science by David Gordon Wilson. It's an excellent resource on bicycles in general, and it has several pages on the engineering of bicycle wheels. Those pages include exactly the information you need to get started. The book references another book, The Bicycle Wheel, by Jobst Brandt. In both cases, get the third edition. The third edition of Bicycling Science has far more information than the previous editions.

Hint: You can ignore the Euler column buckling force on a spoke. Do the calculation, compare to typical loads, and you will see why.

I have read some parts of the book now and I feel like I am at a loss. Now I understand the reason for ignoring the Euler force. The problem now is that I am not sure how I can put the conditions into equations. It feels difficult to do calculations from a fatigue perspective, do I have to do a Haigh-diagram for the decrease and increase of tension. I also don't still understand how I can put a constraint for the hub since it doesn't seem to receive any torque from the rim brake. Is the hub instead limited by the force from the spokes that might damage the flanges? My wish is to later on be able to decide material using the Ashby-method.

 

[berkeman]

I also don't still understand how I can put a constraint for the hub since it doesn't seem to receive any torque from the rim brake.

There's a reason for the angles that spokes are laced with in bicycle wheels...

 

[bollen]

There's a reason for the angles that spokes are laced with in bicycle wheels...

From my understanding the torsional load in a front wheel is really low since it is the rear wheel taking up torque from the pedals. I do although understand the reason for laced spokes since it both protect against torque and to some degree lateral load. Are you saying that torque actually is transferred to the hub through the spokes when braking with a rim brake?

 

[berkeman]

Are you saying that torque actually is transferred to the hub through the spokes when braking with a rim brake?

I guess I was thinking more of cases like my mountain bike (MTB), which has small disk brakes front and rear. In that configuration, the stopping torque on the rim is transferred from the hub to the rim/tire via the spokes. I haven't seen any big difference in the lacing of bicycle wheels with disk brakes versus rim brakes, but maybe there is some subtle difference?

 

[bollen]

I haven't seen any big difference in the lacing of bicycle wheels with disk brakes versus rim brakes, but maybe there is some subtle difference?

From my understanding a rim brake does not give a torsional load on the spokes as a hub brake does. The lacing doesn't differ because it is no reason for using radial spoking that is weaker for both lateral and torsional loads.

I guess that the reaction force from a rim brake must come from the hub. I also assume that there will be some kind of compression condition on the rim as well as a heat transfer. I am sadly still struggling to make these theories into equations

 

[John Archer]

Often on high end front wheels with rim brakes, the spoke lacing is much less than that of a disk brake equipped front wheel.