How to build your own wheel – ROTA

In this section you may find a comprehensive guide about bicycle wheels construction.
This guide is divided into two subsections: Components choice and Building the prestressed structure. The first one covers all you must know to choose the right components according to your necessities. Meanwhile, the second one is pointted to be a manual in which you may find different techniques reaching the same goal: building your wheel.

Find a guide relative to each component in the following links:

Find in this section all the steps implied in building a wheel, from how to organize the components up to lacing and truing the wheel:

Components choice

Rim

The main propperties of the rim do not depend only on the material but also on its shape, hence this shape will be discusse in the forthcoming lines.

When any object is slightly bent, there is particular locus whose length is not changed. This is often an axis or a surfece for single dimensional deformations as it is our case. This is known as the neutral axis of the deformation. the parts over it are stretched and the ones bellow it are shortened (if it is bent in one way, if it is bent in the opposite one, the parts over it are shortened and the ones bellow it are stretched).

This problem can turn into a very complex one, However, this text is aimed at providing some criteria for the selecion of a rim fit for a particular use, not at modelling a specific rim. Then, we will try to keep it as simple as possible by using the crudest and less diffcult aproximations available, the Euler Bernoulli beam theory.

We will consider our part as made of very thin (differential) layers, each one getting the same stress and the same strain (longitudinal deformation), hence each one of them shall follow hookes law:

E= stress/ strain

Where the stress is the force per unit of area and the strain is the relation between the new and the old length. E is -in our case- a number called Young modulus or elasticity modulus. In the general case which we are not dealing with, it could be a tensor.

so $strain* E =stress$ for each and every single layer.

Then, the force on each one shall be:

dF= dA* stress =\newline =dA * strain * E

And we could write the strain as a function of the bending radius, just using the basic definition of angle ( $angle=arc/radius$ , so the further from the neutral axis, the bigger the strain).

dF= dA* E *z / \rho

Then, it is important to consider the momentum since we are discussing a bending and bending always implies some kind of rotation. In this case the part which does not move is on the neutral axis,so;

dP =Fdistance= dA E z^2/ \rho

which is the equation we will discuss. In our case the radius is the difference with the intended radius, however, for the shake of clarity,take the approximation of a flat part since it is what we are doing at a differential level.

This could turn into:

P = \int E z^2 dA/ \rho = \newline =E/ (\rho) \int z^2 dA= I _yE/\rho

P = I _yE/ \rho

Where $I_y= \int z^2 dA$ which is the second moment of the area distribution for the section of this particular “beam” or rim in our case. It is a function of the cross section of the beam or rim, and bears no dependency on the material it is made of. We can use this since we assumed that the material follows Hook’s law in the same way both in tension and compression. This might not be true for every material, however can give a glimpse over the properties of different shapes without getting into complex modelling.

$P = I_y E/ \rho$ so the higher the second moment of area, the more rigid the rim turns out to be.

In the following line we will discuss different common rim profiles and give their second moments of area.

Locus: It is a set of points fulfilling a particular condition. we use it to describe the lamella not changing its length.

Hub

The hub is the part of a wheel where all the spokes meet. They often meet there an axle as wheel. They do in bicycles or in other cases they might meet a shaft or an arbour. This has sprung the imagination of many leading to a colourful imaginary of “hubs” having nothing to do with wheels or spokes. This is not unlike the case of gears and mills which rich imaginary includes ears of power or war or diploma mills waving little to do with actual gear wheels or grinding processes.

Most of the hubs offered by reputed manufacturers are up to decent quality standards, However there are some notorious exceptions to this quite general rule, The more dangerous ones are typically found at both extremes of the price range, whether for low quality and low cost whether for extreme weight savings compromising the safety of the whole assembly.
Hence the main concerns when it comes to choose the way it conveys tresses to different parts, This could be the case of the wheel trough the spokes, the transmission through the relevant system, the brake, or to an electric machine be it an alternator or a motor.

We will discuss those interfaces in the following lines.

Spokes holes

The most common case is finding them in the hub flange and parallel to the shaft.This is intended to use J bend spokes. they draught their name from recalling the shape of this letter. In some cases the holes are perpendicular to the axle instead. They tend to have a non so flange like shape- Then, a straight shape is used. in this case they are refereed as straight pull spokes. This process is aimed at reducing the stress concentration points (stress riser, diffraction points for the flow of defects in the defect gas….) that… comes at a cost: having specified spokes angles and then a specific lacing pattern some cases a more difficult insertion. it might also involve relaying on a particular manufacturer for sourcing the particular kind of spoke you might need. However obvious might it seem it is not uncommon to find people who bought a hub with a different than intended number of spokes. It is also common for some competition oriented hub to have different number of spokes in each side.

Torque transmission devices:

Brakes

Many bikes have different devices to convey torque from and to the wheels. in this case, brakes take ir from them. There are different kind of hub based brakes, from drum brakes to disc brakes. It is of utmost importance to make them match at your desire and the specification the frame or fork is designed to (drum brakes, different disc systems, and other particular specification that might be found). It is worth noting that in the case of fixed gear bikes the transmission serves a dual purpose, both as a driving mechanism and as a brake conveying torque back to the chainring.

Drive

This part conveys torque into the wheels. it attaches to the wheel in different ways. The most common ones are threaded and keyway based solutions. It goes without saying that it is of utmost importance not to mistake the necessary attachment. In many cases the shape and sizes of the grooves are brand specific, whereas the thread pitch is 24 tpi.

Load transmission

This is mainly a way to attach the wheel to the frame as well as conveying the payload onto the wheels. There are different ways in which the wheel can be attached to the bike. The most common systems are the ones where the wheel fits into a groove (as in the quick release) and the one where the bike contains a threaded nut (as in the through hole). the choice among them is dictated by the frame and fork dropouts, so there is little room for choice here if you are building a wheel for an existing bike.

Let’s introduce an slight remark about the different attaching systems to highlight the merit of the thru axle which allows for a stronger system. The axle has not only a bigger diameter which gives it a higher second moment of area, but it is also more firmly fixed to the frame since the bolt keeping it in place is fully embraced by the dropouts. This would prevent the not very likely while theoretically possible accident where the disc makes the wheel scape from its intended place.

The bearings

They are the part where the moving wheel contact the static axle. Currently a vast majority of bike bearings are ball bearings and have been so for at least a century. The most common ones will be explained in the following lines.

Radial bearings

They are intended to carry loads which are perpendicualr to the rotation. The ones commonly usef for bikes are ball bearings, In fact they can also tolerate some axial load (in the direction of the axle) but they do not excell at this.

Spokes

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Nipples

Tyre

Building the prestressed structure

Organize the components

You can tell apart different sets of spokes in every wheel (i.e. the ones coming from each side). This difference will be relevant in case they are different. We will see the possible split of different kinds of wheels.
In some other case this splitting might only be useful for reference and to keep a tidy and decent workshop (regardless its possible temporal or makeshift nature). However, I must strongly suggest you get them in separate places to help you during the building process. Whereas it is perfectly possible to build a perfect wheel without taking any of those considerations into account. It is remarkably difficult to avoid causing a mess of Homeric proportions in the process.

First case: the symmetrical radially spoked wheel.

In this case every single spoke is the same length, so we would advise to keep just each “half” of the wheel in a separate group. just count them and make two lots. This will hopefully avoid having to find the missing spoke while building as well as to have an unnoticed extra spoke.
In case you wanted to make any special pattern with the head of the spokes, please keep them in separate groups (bend, butt…).

A radially spoked wheel has no spokes crossing other spokes.

In addition, both left flange and right flange distance to the rim are equal, so we get two sets of spokes of the same length.

Asymmetrical radial spoke:

The most obvious structure is just two set of spokes (long in one side and short in the other), The two sets are going to split into four for alternating the heads. In case you were making just half radial wheel, consider it as a half of a radial wheel.

In case distance from left flange to the rim were different to right flange to rim distance, we would obtain two sets of spokes of different lengths.

Cross $n$ wheel. (with $n !=0$ )

You will have four different sets: drive side (DS) and non drive side (NDS) will have each two sets of identical spokes one of them bending to the rear and the other one leading forward. So you will have: DS front, DS rear, NDS front, NDS rear. So, all the DS spokes shall be the same length and the all the NDS shall be the same length. please, bear in mind that the only case in which both sides (DS and NDS) are of the same length is a symmetrical wheel.