Wednesday, September 18, 2013

Thoughts about chassis stiffness and efficiency

As an introduction to the upcoming post about how I modelized frame compliance in the dynamical model, I would like to give a general overview about some possible links between frame compliance and efficiency.  

First of all, we shouldn't forget that the bike is controlled by a rider whose input could be modified by the mechanical properties of the frame and the components. For example, a rear end too stiff could cause excessive bouncing of the rider and have a negative effect on his power output. For this reason, we should always consider the negative effects that could have a particular design feature on the vibration in the contact points, intersegmental loads, joint torques and steering inputs and not treat the bike as an isolated system.

Leaving this influence on the rider input aside, I have identified some possible efficiency loss mechanisms due to the deformation of the chassis:

- Rolling resistance. Although the rolling resistance coefficient (Crr) has been always defined as a constant value, there is a relation between it and sinkage depth. The explanation for this is pretty simple: Rolling resistance moment is caused by the difference in normal pressure  between the leading and the trailing edge of the contact patch due to the hysteretic cycle of the material. If sinkage depth is increased, the tire deforms more, the severity of the hysteretic cycle is maximized and the losses increase. There is also second order effects like the radius of the contact point between the ground and the tire.

- Drivetrain misalignement. Both the torques perpendicular to the BB axle caused by the pedalling forces and the combination of asymmetric chain loads and symmetric rear ends produce misalignements between the BB axle and the rear wheel axle. Those misalignements could cause torsional loads on the chain and increase friction due to the contact between the side plates and the sprockets/chainrings.

- Sideslip and camber of the rear wheel. Once again, the combination of asymmetric chain loads (both in the longitudinal and horizontal planes) and symmetric rear ends produce two effects: 1) a misalignement between the bike speed and the speed of the contact point with respect to the bike and 2) a small camber angle. Dissipation increases due to the presence of a yawing moment that tends to align those two speeds and the effect of camber on rolling resistance.

- Wheel slip. Traction is a function of wheel pressure and frame/fork stiffness so an optimization of these parameters could minimize slip and, consequently, power losses.

- Losses in the frame. The harmonic excitation of the bike causes losses in the structure due to both hysteresis and viscoelaticity that can affect negatively the performance of the bike. Alternatively, a well tuned placement of materials with these characteristics can increase damping and, consequently, comfort.

As you can imagine, the analysis of such complex interactions would need a very complete system. A deformable 3D bike model controlled by a virtual rider capable of balancing the bike in a similar way an human would do would be needed. Additionally, both the effect of drivetrain misalignement and losses in the frame have to be quantified using experimental methods or complex FEA models.

In my case, I haven't gone so far. I have modelled just two of these mechanisms: rolling resistance and wheel slip. I think that these are the ones that could play a major role on efficiency.

That's all for today. Greetings

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