Q. He, S. Su, and R. Du


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  20. [20] B. Boashash & P. Black, An efficient real-time implementation of the Wigner-Ville distribution, Processing of Acoustics, Speech, and Signal, 35, 1987, 1611–1618. Appendix A: Modal Frequencies of a Mechanical Watch Movement Finite Element Analysis (FEA) is performed to evaluate the modal frequencies of the escapement. As shown in Fig. A1(a), the escapement consists of a balance wheel, a pallet fork, and an escape wheel. SolidWorks r was used to draw the solid model of the escapement and then to conduct FEA. In the FEA, the materials of the balance wheel are set as copper and ruby, the materials of the pallet fork are alloy steel and ruby, and the material of the escape wheel is alloy steel. The boundary conditions are very important in FEA. Take the escape wheel, for example. It can only rotate in the axial direction, so a frictionless support was given to each end of the pivot (see Fig. A1(b)). The same constraints can be imposed on the balance wheel and the pallet fork. The mesh type is solid mesh. The FEA results (the modal frequencies) are summarized in Table A1. 196 Figure A1. FE model of the escapement. Table A1 Modal Frequencies of the Escapement Mechanical Parts Modal Frequencies (Hz) Balance wheel 481, 1752, 2488, 6417, 6766, 18331, 18892, 20223, 21537 Pallet fork 16779, 21150, 22212 Escape wheel 9117, 11262, 12667, 18728, 19425

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