Stopping rotation is calculated from elastic stiffness, not selected in advance. I model a rigid rotor stopped by one initially unloaded, equivalent circular cantilever. The baseline assumes small-deflection linear elasticity, negligible bolt inertia, and no dissipation or additional driving work during compression.
Treating the 2.75-inch bending arm as unsupported span is an additional idealization. Computation uses unrounded inch/psi conversions and SI governing equations.
With rotor mass moment \(J\) distinguished from bolt area moment \(I_b\), the tip stiffness is:
\[
I_b=\frac{\pi d^4}{64},\qquad
k_b=\frac{3EI_b}{L_b^3}=46.9\ \mathrm{N/mm}.
\]
For \(\omega_0=2\pi N/60\), where \(N\) is numerical pre-contact speed in rpm, incoming energy becomes maximum elastic compression. The angle is in radians before conversion to degrees; elastic storage does not prevent rebound.
\[
\begin{aligned}
\tfrac12J\omega_0^2&=\tfrac12k_b\delta_{\max}^2,&
F_{\max}&=\omega_0\sqrt{Jk_b},\\
\delta_{\max}&=\frac{F_{\max}}{k_b},&
\theta_{\max}&\simeq\frac{\delta_{\max}}{r_c}.
\end{aligned}
\]
Nominal bending stress scales linearly with speed for this fixed-stiffness model. The 4.27 rpm result is a nominal bending screen under the stated model, not a validated operating limit.
\[
\begin{aligned}
\sigma_{b,\mathrm{nom}}&=\frac{32F_{\max}L_b}{\pi d^3}
=(6.674\ \mathrm{ksi/rpm})N,\\
N_{\mathrm{screen}}&\approx4.27\ \mathrm{rpm}
\quad\left(\sigma_{b,\mathrm{nom}}=\frac{S_y}{2}\right).
\end{aligned}
\]
Mechanical results use speed immediately before contact. Independently, constant-speed travel through angle \(\Delta\phi\) gives:
\[
\dot\phi=(6N)\ ^\circ/\mathrm{s},\qquad
t_{\mathrm{travel}}=\frac{\Delta\phi\ [^\circ]}{6N}\ \mathrm{s},
\qquad t_{180^\circ}=\frac{30}{N}\ \mathrm{s}.
\]
This nominal boundary corresponds to about 7.03 seconds for the rig’s 180° transfer at constant speed (approximately 4.27 rpm).
The analysis highlighted why the final approach matters: impact loading depends on speed at contact, not average transfer speed. The 7.03-second result is a constant-speed equivalent—not a measured transfer or compression duration—and remains separate from the thermal-test timestamps.
The nominal \(n=2\) result provided a bending benchmark for the design. At that boundary, additional cable/bungee work during compression would raise calculated stress above the criterion. The installed bolt’s free span, support/shank geometry, grade, thread stresses and preload remain unverified; the nominal factor of two does not validate those details.
