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Rimpact Tuned Mass Damper Development Blog Part 2 – Math

After analysing the problem and coming up with a conceptual solution for reducing front-end vibrations and forces on mountain bikes, the next step was to further develop our prototype so that it could fit inside the limited space of the headtube of an average Enduro or DH bike and provide greater change over the system. In the last post we discussed why it needed to be fixed to the main frame of the bike, and as there is a perfect hollow tube on almost all bikes we opted for this location as our target mounting point. We gathered data on the dimensions of headtubes on a range of frame sizes and fork brands to get the maximum available space to work with. The dimensions of the headtube presented a major constraint that required us to come up with a compact design that could exert enough change over the bike to be useful whilst still fitting in this handy space up inside the headtube. Next, we needed to calculate the mass, spring rate and damping coefficient required for the system.


We used our vibration sensors to gather data on both the natural frequency of the bike and a range of G-forces that occur on a number of hard rides. We conducted a Fourier Transform on this data to help us identify the ‘correct’ frequency in hertz. We then had to do some complex math to calculate the required Mass, Stiffness and Damping Coefficient we needed As the reality of mountain biking is that every rider is different, every trail and bike and suspension set up is also different and we don’t ride at one static speed, we needed to make informed decisions on what ranges of frequencies we were going to target with this system. We used MATLAB to do this.


The stiffness was calculated based on the materials and geometry of the damper. We knew the maximum available space we had to work with, the Mass we had to squeeze into the damper and the rough design we were going to go with so finding the spring rate was based off of this knowledge, a range of prototypes we tested and some field testing. We planned to design the damper to work in various locations for various amplitudes of force so we had planned a range of real word tests to feel out the best spring rates so having the math help provide a ball park was key in speeding this process up.


In order to ensure that the damper would work out of phase with the frequency of the system, we needed to ensure that the damping coefficient was correct to prevent the damper from oscillating at the wrong frequency. To be clear, the system oscillating at the wrong frequency should still provide benefits to the rider, however it would not be as potent as a correctly tuned system. The aim was to achieve a critical damping ratio above ‘1’ where the system is helped and not hindered by the presence of a mass moving out of phase with the vibrational forces passing through the system. Once all the values for the damper design prototype were dialled in, we verified our final choices with some extra math and ran it by a couple of different engineers to verify we weren’t barking up the wrong tree.

The vast majority of this work was to ball park the design so that we could move on to feild testing. Due to the variable nature of the intended appliction, we knew dialling the TMD in by a mixture of feel and data analysis would be the most effective solution to achieving the goal.

In the next post we will discuss the design and how we arrived at the particular configuration we did.


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