- #1

TheCondor

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- TL;DR Summary
- Uncertainty about validity of 2 different models

I am a junior engineer tasked with modeling the dynamics of a small research UAV after landing. The UAV has 3 tires, 1 on the nose landing gear and 2 on the rear landing gear. The rear tires are equipped with disc brake calipers.

My coworker has explained that the simplified model (MODEL 1 below) is sufficient to find the horizontal deceleration on the aircraft CG caused by the brake calipers. This model assumes the tire radii are negligible and the caliper force acts at approximately the same location as the tire-runway interface. The coefficient of kinetic friction (μ_k) between the caliper and disc is then approximated from a textbook which plots μ_k decreasing with velocity.

Uncomfortable with the small radius approximation, I have attempted to model the wheel as a solid disk to find the horizontal acceleration of the wheel center (MODEL 2 below). Assuming the chassis is a rigid body, the horizontal acceleration of the wheel axle should give the acceleration of the whole aircraft.

I have difficulty understanding if either approach is correct and particularly the role and location of the frictional forces.

In MODEL 1, the maximum brake force is found directly from only the normal force and μ_k, but I don't understand why. The no slip condition and small radius approximation acting simultaneously are preventing me from understanding this clearly.

I can accept the approximation that if the tire radius is negligible, the kinetic caliper friction can be viewed as acting at the same point as the static tire friction. I also recognize that the brake force exerted by the calipers decreases at higher speeds (ie. the brake force should be a function of the kinetic friction coefficient of the caliper-disc interface).

Any help and corrections that you could provide to better intuit the physics at play would be greatly appreciated. Thank you very much for reading.

My coworker has explained that the simplified model (MODEL 1 below) is sufficient to find the horizontal deceleration on the aircraft CG caused by the brake calipers. This model assumes the tire radii are negligible and the caliper force acts at approximately the same location as the tire-runway interface. The coefficient of kinetic friction (μ_k) between the caliper and disc is then approximated from a textbook which plots μ_k decreasing with velocity.

Uncomfortable with the small radius approximation, I have attempted to model the wheel as a solid disk to find the horizontal acceleration of the wheel center (MODEL 2 below). Assuming the chassis is a rigid body, the horizontal acceleration of the wheel axle should give the acceleration of the whole aircraft.

I have difficulty understanding if either approach is correct and particularly the role and location of the frictional forces.

In MODEL 1, the maximum brake force is found directly from only the normal force and μ_k, but I don't understand why. The no slip condition and small radius approximation acting simultaneously are preventing me from understanding this clearly.

I can accept the approximation that if the tire radius is negligible, the kinetic caliper friction can be viewed as acting at the same point as the static tire friction. I also recognize that the brake force exerted by the calipers decreases at higher speeds (ie. the brake force should be a function of the kinetic friction coefficient of the caliper-disc interface).

Any help and corrections that you could provide to better intuit the physics at play would be greatly appreciated. Thank you very much for reading.

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