Thinking of this system as a dynamic mechanical system, it can be modeled as having a step input of angular velocity driving an inertia, with the stiffness of the system between the applied torque and the inertia controlling how much torque is applied to the inertia. In the limit, if the system were infinitely stiff, infinite torque would be applied, and the output would instantly come to speed.
If the system were very “soft,” the clutch spring would wind up and then start rotating that output arbor, which would result in a lower torque for the practical case. I put a new spring clutch together on a vise and cranked it tight with a torque wrench and protractor to measure its rotary stiffness.
Taking the measured rotary stiffness and the inertia of the system, the equations told me I should be expecting maybe 15 or 20 times the torque that conventional wisdom had measured. Then I looked at a used clutch from a real copier that had not yet failed and found the center coil of the clutch was all stretched out of shape.
The mechanical designer who developed the design told me not to worry -- they all did that. Really? I had not yet been introduced to the design philosophy that materials should exceed yield point during break-in. I was extremely fortunate that my boss was a PhD ME from Stanford who was a brilliant engineer.
We discussed the fact that we had never measured torque directly, that it was always inertia times angular acceleration. The input arbor of this device was driven by a roller chain sprocket. We came up with a concept that we could remove major sections of the drive sprocket, leaving radial ribs. Then, we would mount strain gages on the insides of the ribs, wire them together in a bridge, and use some slip rings to get the signal to somewhere that wasn’t spinning.
I connected it to an oscilloscope and measured the torque directly. We had to design the ribs on this sprocket so they were stiff enough to not affect the dynamics of the system, while soft enough that they would bend and have sufficient deflection for the strain gages to give us a torque measurement. At the same time, the torque sprocket had to be strong enough to withstand the torque impacts without yield.
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