The Tourbillon and How It Works IEEE Control （陀飞轮和它是如何工作的IEEE控制）.pdf

AA PP PP LL II CC ATAT II OO NN SS O O FF C C OO NN TT RR OO LL « The Tourbillon and How It Works MARK DENNY he tourbillon is a mechanical device that was invent- associated with only the best quality timepieces. See “Two ed to improve the precision of old-fashioned pocket Centuries of Tourbillons” for a discussion of the status of Twatches. These devices continually rotate the escape- tourbillon timepieces within the horological community. ment, balance wheel, and spring to compensate for bias due to gravity. To help visualize the operation of a tourbillon, ELEMENTARY ESCAPEMENT we recommend that the reader view the videos and anima- Figure 1 shows the hairspring and balance wheel of a clock tions of tourbillons that are available on YouTube [1]–[3]. escapement. The balance wheel oscillates about its center The tourbillon has always been a luxury add-on for under the influence of the hairspring. Friction acting on the pocket watches and, more recently, wristwatches. In this axle located at the center of the spring dampens wheel article we analyze the dynamics of the tourbillon, show oscillations. In a real pocket watch, the balance wheel’s how it works for pocket watches, and explain why it serves center of mass is not located at the axis of rotation; this no practical purpose in wristwatches. We model the phys- imbalance is represented by the mass m on the balance ics of the mechanical watch escapement in the simplest wheel. The escapement wheel and pallet shown in Figure 1 possible manner and then show how the tourb