Flexure Pivot Oscillators for Mechanical Watches

It appears that the concerted efforts of the watchmaking industry are leading towards a limit in mechanical watch accuracy. The general consensus in horology is that the time base's quality factor, a dimensionless number that characterizes the oscillator damping, needs to be improved in order to significantly increase timekeeper accuracy. The three classical mechanical time bases all suffer from limitations for mechanical watch applications. The pendulum used in precision mechanical clocks reaches quality factors of order 100000 but is too sensitive to the orientation of gravity to be used in portable timekeepers (watches). The balance and hairspring oscillator used in classical mechanical watches sees its quality factor limited to about 300 (450 in partial vacuum) by the friction in its bearings. The tuning fork used in electronic watches can reach quality factors of order 100000 but its high frequency and very small oscillation amplitude makes it very challenging to sustain mechanically. The solution appears to be flexure-pivot oscillators in silicon. Flexure-pivot oscillators use the elastic deformation of thin beams to guide the rotational motion of an inertial body and to exert a force opposed to its displacement, thus providing all the elements for a one degree-of-freedom mechanical oscillator. The use of flexures instead of bearings eliminates contact friction and monocrystalline silicon minimizes internal friction, leading to significant improvements in quality factor in comparison to balance and hairspring oscillators. Moreover, the rotational amplitude is compatible with existing sustaining mechanisms (escapements). Accurate timekeeping requires the period of oscillation of the time base to stay as regular as possible regardless of changes in operating conditions such as amplitude of oscillation, orientation with respect to gravity, temperature and shocks. This thesis focuses on minimizing the effects of amplitude and gravity that arise from the use of flexures. First, the nonlinear elastic behavior of flexures introduces a dependence of oscillation period on amplitude called isochronism defect. Second, the weight-bearing function of the flexures and their deviation from the motion of ideal linkages result in a contribution of gravity to their effective stiffness and hence an effect on their frequency. It is assumed that the other effects, i.e., temperature and shocks, can be solved with existing techniques. The first technical contribution of this thesis is to note that the isochronism defect is a second order phenomenon, and to deal with it by modifying the second order behavior of flexure spring stiffness or inertia. The second technical contribution is a design method to reduce the effect of gravity for all orientations of the time base to within the specifications of current mechanical watches, this by ingeniously placing the flexures and exploiting the position of the center of mass. These findings are embodied in three new flexur