Étude des engrenages de microtechnique

The research presented in this thesis addresses the design of gear drives for micro engineering applications, and was performed in collaboration with a watch manufacturer. Gears have long been found in many fields of mechanical engineering. Their use in watches satisfy specific constraints: small dimensions, little or no lubrication and unusual performance specifications. A literature review allows us to establish a catalogue of existing gear profiles, and a synthesis of profile analysis and generation methods. On the basis of this assessment, we define knowledge gaps which we propose to bridge in the present work by reaching the following objectives: 1. Characterize the behavior of existing gear profiles used in the watchmaking industry (nominal profiles, but also profiles affected by shape errors and axes misalignment errors); determine their kinematic and static performances, and their transmission efficiency. Use these results to compare various profiles on an objective and rigorous basis. 2. Formulate the equations necessary to calculate the tooth profiles using conjugate conditions differing from the tradition-al kinematic conditions ( i.e. imposing the transmission ratio) 3. Work out a design methodology for gear profiles relying on the results obtained while working on the first two objectives To reach those objectives, we develop a computer code allowing us to evaluate the performances of the profiles. The diversity of existing profiles led us to formulate a generic geometrical representation applicable to all profiles, while allowing us to use the same analysis code. The developed tool is then validated by simulating profiles, the behavior of which is known analytically. To calculate conjugate tooth profiles respecting a static criterion, we use the classical theory again, adding a new equation to it, which we derive from a balance of power. We present this equation for the three dimensional case, and the planar case. The resolution method for this equation, valid for static conjugated cams (i.e. a unique pair of teeth), must satisfy a supplementary condition that ensures that the imposed torque ratio leads to an average kinematic ratio compatible with the desired number of teeth. A numerical method was developed for the planar gears case that establishes the range of torque ratios satisfying the imposed average transmission ratio. The lower and upper bounds of the range of solutions are defined in terms of geometric and efficiency considerations, respectively. The proposed approach is illustrated and validated by some profiles computations. In parallel to those theoretical developments, we designed and built a test bench to characterize experimentally the performances of gear profiles, (altered or not by various shape or misalignment errors) under operating conditions similar to those prevailing in a watch. The last part of the thesis provides a critical discussion of these developments places them in a broader context and comments how