Bike Frame Design(www.slwotwitch.com) by Kim Blair PhD Director, Center for Sports Innovation Massachusetts Institute of Technology FRAME DESIGN 101 (4.14.00) FRAME DESIGN 101
- Stress and Strain: What happens when you put a force on a bike frame component?
- Materials Issues: Issues that result from using various frame materials
- Tube Geometry: Now that we understand the effect of applying forces on frame components of different materials, we can start playing with the geometry of the tubes to get target performance needs.
• Stress and Strain
Stress is a measure of how the intensity of an applied load is distributed over a given section of a component. Figure 1 shows an axial (along the axis of the tube) applied load (P) on a tube. For this simple case, distributing the applied load over the cross-sectional area results in a stress of The Greek letter sigma, to the left of the equation, is used to denote stress. Stress is expressed in terms of lbs/in2 (psi). As an example, let's say I stand a bike tube on end, on the ground, and I am able to perfectly balance my body weight on the tube by balancing on one foot. Furthermore, assume the tube is 1" in outside diameter, with a wall thickness of 0.1", which results in a cross sectional area of 0.283 in2. (The area of a circle is &Mac185;r2, where r is the radius of the circle.) Assume I weigh 160 lbs. Thus, the stress in the tube resulting from my balancing on it is 45 psi. Note that we have yet to mention anything about the material of the tube. At this point, it is clear that stress and strain are likely related. FIGURE 2: STRESS-STRAIN PLOT RESULTING FROM AXIAL LOADING OF A TUBE - Stress and Strain: What happens when you put a force on a bike frame component?
- Materials Issues: Issues that result from using various frame materials
- Tube Geometry: Now that we understand the effect of applying forces on frame components of different materials, we can start playing with the geometry of the tubes to target specific performance needs.
• Review of 101 - the modulus of elasticity (its "springiness"),
- the yield strength of the material (where it fails), and
- the density, which determines the weight of a tube.
The following table lists these three values for common types of frame alloys described above.
When building frames (or any component for that matter) the designer needs to work with all of the material properties to optimize the characteristics of the frame. Note that the density and modulus are nearly the same for all alloys. The yield strength, however, varies widely dependent on the alloying elements and heat treatment process. Note that a high yield strength allows one to form thinner tubes, which of course reduces weight. The trade-off is typically cost. More processes nearly always means a higher cost.
As we expect, the table shows that the steel tube is the heaviest, followed by the titanium tube and the aluminum tube. - Stress and Strain: What happens when you put a force on a bike frame component?
- Materials Issues: Issues that result from using various frame materials
- Tube Geometry: Now that we understand the effect of applying forces on frame components of different materials, we can start playing with the geometry of the tubes to target specific performance needs.
The goal of the tube designer is actually quite simple, at least in principle. Use the least amount of material possible to get the required strength of the tube set. In reality, this is actually a very difficult design optimization problem. The designer not only needs to understand the loading conditions for the bike, but also must understand a plethora of manufacturing techniques and relative costs. The perfect design may not be manufacturable at a price point that is acceptable by the consumer.
Once again, we are concerned with the stress and deflection resulting from bending the tube. The stress can be calculated by S = M*y/I where M is the applied moment, y is the distance from the center of the tube and I is the inertia. Note that this equation tells us that the maximum stress is in the outer surface of the tube (where y is the largest).
Finally, Tube Shape The following table shows the inertia, stress and curvature results for an aluminum tube, one standing upright and one lying on its side. What one observes is that you want the long side of the tube to be in line with the loading.
Consider your bike’s down tube. Where it meets the head tube, you’d imagine that the largest bending loads occur as a result of the head tube pulling on the tube in the upright direction. You’d want your square tube in the upright position as shown above. Conversely, at the bottom bracket, you’d imagine the largest bending is the result of the pedaling motion. Thus, you’d want your tube in the horizontal position. Certainly, some manufacturers have utilized this principal in their tube sets. You can find bike frames with tubes that vary from tall and thin at the head tube, to wide and fat at the bottom bracket. |
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