My first job as a mechanical engineer was with the office products division of a huge corporation. I was assigned to fix the design of a spring clutch that failed prematurely on a copier. The spring clutch design worked for hundreds of millions of cycles in an application in another office product the company made. On this particular copier, the clutch consistently failed at around 20K cycles. Conventional wisdom suggested that the torque was the same between the copier and the other product, and thus the application was almost the same.
This spring clutch transmitted torque from an input arbor to an output arbor, through a helical clutch spring, all mounted concentric on a shaft. When the input end of the clutch spring is held off of the input arbor, the input arbor spins freely, as there is no contact with the inside diameter of the spring. When the input end of the spring is released, the helical spring wraps down around the arbor. Friction between the input arbor and the spring starts the spring spinning with the arbor, like the “rope around the tree” concept for transmitting torque.
The clutch spring is clamped to the output arbor, so when the spinning input arbor gets that spring wrapped around it, all three components are rotating at the same angular velocity in short order. In this application, the load the output arbor drove had a significant inertia. The conventional-wisdom data was collected by multiple sets of previous engineers who worked on this clutch.
The process they all used was similar. They estimated the torque by multiplying the calculated rotary moment of inertia of the load being accelerated by the angular acceleration. Even back in the stone ages, we had DC tachometers that gave a dynamic angular velocity output with a reasonable frequency response that we fed into our storage scopes and took Polaroid pictures of. Theta dot vs. time –- lay a ruler down, and you can figure out acceleration. But something wasn’t right in this picture. Why would the same load yield only 1/10,000 the life in a new application? Sherlock Ohms, help?