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# Static and Dynamic Friction – Where the Rubber Meets the Road

September 6, 2016 By: Patrick Cunningham

I was recently reminded first hand of the important distinction between sticking and sliding frictional contact. I was in a bicycle race on a speedy descent when two riders in front of me rubbed shoulders and hit the pavement. If you have ever seen footage of bicycle racers crashing, you have a pretty good idea what happened next as I and my fellow racers frantically attempted to avoid the ensuing pile up. (Picture above)

So there I was, flying down the road doing everything I could to slow down and squeeze through a rapidly narrowing avenue of escape. It is commonly known among bike racers that locking up your back wheel is bad news because controlling the bike becomes much more challenging. What is less commonly known is the reason why this occurs. Not all bike racers are engineers after all.

When your wheel is rolling on the pavement there is no relative movement between the tire and the road at the point of contact. This is considered a sticking contact interface where the static coefficient of friction is in play. The tangential force on the tire which decelerates you during braking is the static coefficient of friction multiplied by the normal force from the combined weight of you and your bicycle.

When your wheel locks up there is relative movement between the tire and the road and the contact transitions from sticking to sliding. Sliding friction coefficients are typically less than their static counterparts. This is bad news when you need to decelerate because the tangential force that is slowing you down is reduced as well.

Despite the fact that these crashes occur in a few short seconds it feels like you are moving in slow motion and I found myself thinking about how I would model this effect using finite elements.  No really, it was better than obsessing about road rash. Frictional contact modeling is fairly common in today’s world and can play an important role in a design and assembly process. In a press fit scenario you are often trying to evaluate the amount of force required to complete an assembly process. If you are relying on the static coefficient of friction alone you may be overestimating the force required. Frictional contact can also make the system response path-dependent, such that the sequence in which the loads are applied can affect the end result.

Both static and sliding friction coefficients can depend on many different variables including materials, surface finish, temperature, normal pressure, sliding distance, and relative velocity. In order to simulate the friction forces correctly, some finite element codes, like ANSYS®, allow the engineer to  explicitly characterize the these dependencies. This can be in tabular form, via common models, such as exponential decay, or through user-defined friction routines. Other codes simply use a constant value, yielding results which are either too conservative, or not conservative enough. For example, in Figure 1 below, a tabular definition of frictional force as a function of sliding distance is defined in a static analysis. To relate to my bike racing analogy, the friction between the tire and the road dips as sliding occurs and then drops again when the tire wears away and I am sliding directly on the wheel. As illustrated in the picture above, it’s something I strongly suggest you avoid.

Figure 1 – Friction Coefficient as a Function of Sliding Distance

## figure 1.png

As you would expect, knowing the values of the friction coefficients is very important. Unless you can evaluate them through testing you will likely have to rely on a textbook number for starters. When that is the case it is always a good idea to evaluate the sensitivity of the response to the coefficient used. This can done in tools like ANSYS® where the friction coefficients can be defined as input parameters as part of a sensitivity or optimization study.

If you are using other options to model friction, I would welcome a discussion on the topic. Don’t be a “stickler” and feel free to comment. I might even share the end of my bike race story.