Engineering

In this article we would like to tell about the approach we used to develop our fatbike rim, Naran 80.

The first step was to understand how does the rim work, what loads and how frequently act on it. At this stage we closely collaborate with the product manager. Product manager is a person with basic engineering knowledge who can speak the same language with the engineers. But more importantly he is that person with the vision of what the product should look like, how it should behave, and what requirements should be set. Also, the product manager largely determines the required weight criteria as well as some other physical properties of the product. For example, can a wheel collide with an obstacle? Of course! At what speed? What is the biker’s weight, and how is it distributed between the front and rear wheels? From what height can a bike fall and remain undamaged? Obviously, there is a limit beyond which it makes no sense to consider. If a cyclist falls to the ground from the height of three meters, the wheel safety will be his/her least worry. Other matters to be taken into account are spokes tension, the setting procedure, the maximum difference in tension between two adjacent spokes. How it should - or should not - affect the wheel geometry, i.e. egg shape or wobby-wheel?
At the first stage there are continuous questions arising, and we need to compose the whole mosaic in our heads to create the vision of the future wheel, to feel its strong and weak points, weight and stiffness. And, of course, to ride a fat-bike by ourselves!
  
At the same time there is engineering work being done, that is, researching materials and types of existing rims.

Choice of design

When developing any new product it is useful to look at any past experience so that not to reinvent what already exists. Even though at the time of initial development the carbon fiber rims for fatbikes were not yet present in the market, it is still a good idea to learn the experience of existing metal rims.
And immediately it becomes clear that there are two main approaches, a closed profile with a high torsional and bending rigidity but relatively more massive due to additional shelves, or an open profile design with less rigidity, but potentially less heavy.

As you can see on the figure, the stiffness of the open profile is supported by small closed tubes in the corners of the profile. This design helps to resist forces imposed by a tire trying to stretch / unbend the rim aside. 

There was also an idea to make all-composite three-spoke wheel like this:

but at this stage it was decided to choose the classical shape.
To understand which of profile options is better we have analyzed both, as composite materials behave quite differently from metal.
Special aspects of the composite rim manufacturing as compared to aluminium.
Needless to say, the laboriousness of the composite rim manufacturing is a lot higher as compared to a metal rim. The main point of carbon fiber part production process is molding the part under certain temperature and pressure in a specially constructed tooling.
The process can be described as follows. The carbon fabric layers pre-impregnated by epoxy resin (so called prepregs) are stacked in a certain sequence on the silicone core. This preform is placed into a metal mould and pressed.

The mould is heated to about 180 ºC with the pressurized air supply inside the core. During this process, carbon fibers compact, air bubbles are expelled, and resin cures and consolidates the part. At the end, the part is cooled, removed from the mould and goes for further processing. The accuracy of layer stacking and fiber direction, cleanliness inside the shop, storage conditions of raw materials, temperature and pressure conditions inside the mould affect the part quality.

Properties of aluminium and carbon rims

With sufficient approximation an aluminium extrusion profile can be considered isotropic because its properties are the same in all directions. Depending on the shape of the dye, through which the profile is extruded, single-wall or multi-wall rims are produced. Then holes are drilled to install spokes or to reduce the rim weight.

However, drilling holes is not applicable to the composite rim.
Composite material is anisotropic, i.e. its properties are different in various directions. It gives a great advantage. By varying the layers' number and orientation we can use more fibers in the direction of the highest load in order to increase the local strength. Due to this ability, as well as to the excellent torsional rigidity, carbon fiber rims allow to avoid the wing effect  when offset lacing is used.
However, there are also serious limitations. Carbon fibers can not be bent at sharp angles because it would cause their breaking and creating a weak point.

In a composite part the maximum load (tension or compression) should be applied to carbon fibers, and in a case of a sharp angle mostly resin works to resist the loading, but its strength and rigidity its substantially less than that of carbon fibers. Furthermore, a corner is always a stress riser, i.e. a point with increased tension which entails the formation and distribution of cracks in the material. Therefore, all possible corners in a composite part must be rounded. That is why a profile like, for example, Surly’s Clownshoe design, can not be used as a pattern for a composite rim:

Its too sharp corners do not allow producing a good carbon fiber part of the same design.
The second limitation of carbon fiber rims are holes made to reduce the weight and to prevent a tube from rolling inside a tire.

The composite material strength is determined by fibers, and cutting huge amounts of them will affect the strength and durability of the structure.

Bicycle rims and “rocket science” modeling

So, the principles of loading, technological features, and key limitations have been set, let’s proceed to working out the first sketches. 

For our design work we used 3D modeling software with the strength analysis of Finite Element pack. Finite element method is widely used in the automotive and aerospace industries for solving tasks related to the stress and strength problems of parts and structures.

The pursuit of low weight and high strength brings cycling to a field of serious calculations and extensive testing. For the analysis of loaded composite parts of bicycle we have taken approaches used, for example, in aviation industry for plane parts design. Similar software was used in America in the 60’s for the aerospace program. It was called Nastran (NASA STRucture Analysis). Later its code was opened for public use, and several competing companies which took it then as a basis to create their own modules, and companies that created their own programs continue developing the finite element analysis software to present days.
Approaching solving the task of strength, it is necessary to choose the type of elements, their size and number on the basis of the results we need to obtain. In our case, the main objective was to optimize the carbon layers stacking based on the stress-strain state of the rim at various types of its loading. For the basic model we used flat quad 4 nodes elements. Spoke holes were not included to the model since they are loaded locally. It was decided to create for that task an individual finite element model. So, spokes are connected straight to the rim, node to node.  First it was necessary to create the approximation to determine the geometric position of the walls and spokes, and then to prepare this geometry to create the finite element model. We limited the composite rim weight by the value of its metal analogues. If the carbon fiber rim is heavier, it will be useless. Thus, knowing the carbon fiber composite density (appr. 1.5 g/cm3 of the finished product) we can obtain the approximate shelf thickness for our calculations.

a) Fillets and holes eliminated

b) medial surfaces built 

c) finite element mesh built on medial surfaces

The obtained model is still a hollow “skeleton” to which the following data should be added: thickness values, layups, elasticity modules, composite failure criteria and allowable stresses and strains. And, of course, to apply various loads to our model.
Because the model contains a small number of elements we can quite quickly change various parameters and recalculate the analysis.
Now we encounter the task of correct load transfer from real life to a virtual model. For example, the rim hits an obstacle.

Depending on the speed and weight, i.e. the inertia forces, the obstacle height and the wheel diameter, we can calculate the reaction forces affecting the rim. 

Safety factor

There are many factors that affect the strength of the final product, and it is hardly possible to eliminate all of them. Storage conditions, prepreg properties which may vary from batch to batch, layer stacking orientation precision (its limits are set in the range from -3º to +3º), deviations from the correct moulding process, not careful post-processing, etc. Then, during its life, the rim will be absorbing moisture, exposed to high or low temperatures, receiving small damages that will affect its strength. It is impossible to account for all factors, therefore we add a factor of safety to be confident in successful passing of laboratory and field tests. Time and results of these tests will show whether this factor of safety is too high or not, and in which sections of the rim the layers should be added for higher strength, or excluded for less weight.
The analysis below shows how does the rim sags when the wheel hits the ground


 
Next picture shows buckling mode of the rim. If safety factor is too low, walls will start to bend out and all the rim can collapse. So buckling is a necessary analysis

Of course, finite element modelling is not all we did to create our rim. But this method allows us to reduce the number of iterations and expenditures on mould and test samples manufacturing.

Testing

The photo shows how the first rim was tested in our laboratory.

The type of loading was selected intentionally. Clearly, in real life rim will not be subjected to exactly this load, but it allows us to apply the same load to any number of samples. The same loading is very important because after spokes installation each wheel is loaded a bit differently. Spokes may have more or less tension, or a hole may be drilled not ideally. These deviations will not show themselves during normal use, but we produce a certain number of samples with a purpose to break them under supervision and find out their strength limits and permissible loads. During any critical load, even the slightest deviation from the design documentation will change the strength of the whole structure. Only through a series of identical loading tests we can be confident in the reproducibility of the rims and, respectably, in their quality.
After the rim destruction on the testing machine, its undamaged sections are selected for spoke pulling-out test:

In the course of mass production a certain number of rims from each batch will also be tested to ensure rigidity and strength properties. However, the optimization process will be continuous.
Analytical approach enables to save a large amount of efforts and money invested in the product development and manufacturing. The main problems related to the rim strength and design are solved analytically before the first prototype is made, and then engineering calculations are confirmed by various tests. Of course, little surprises also happen, but in this case the cost of a mistake is smaller, and these problems can usually be solved without remanufacturing of the mould. By gaining experience and receiving feedback from testers, we will be coming back to the design of every detail, trying to find the best solution to make our product lighter and stronger.
- The weight of our rim, Naran 80, is about 650 grams. Calculations and tests proved this is the optimal weight/strength ratio while the rim boasts adequate rigidity to minimize the wing effect  when offset lacing is used.

Closed profile enables the use of tubeless tires which are lately becoming popular due to the benefits like high puncture resistance, lower rolling resistance, and lower weight. In particular, we used a bead lock on our rim, which allows to install a tubeless tire.

So this is how an idea to create a lightweight and durable composite bicycle grew into aspiring work of a team of professionals in different fields, and gave birth to a new rim, which we know from the inside and which we trust.