Mechanics of Hairspring in Mehanical Watch Movement

Abstract

Hairspring is a fine spiral spring, which is the key component in mechanical watch movement for timekeeping. According to literatures, there are only few studies on hairsprings or spiral springs. Using the Castiliago’s method, the mechanics of hairspring is studied in details. And Computer simulation with Matlab® and experimental validation are also conducted to show the spring frequency. Experiment shows that the theoretical analysis and computer simulation can be used to guide and facilitate the design of hairspring or spiral spring.

Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study

“…Respecting and regarding Castigliano's theorem, the authors developed a mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque and conducted a computer simulation with the MATLAB application. They accomplished the experimental validations of this simulation and proved that the analytical method 5,6 can be used to guide the hairspring design. Fu at al.…”

“…Their research results can provide a valuable reference for structure design and dynamics analysis. Xie et al 5,6 analyzed the mechanical characteristics of hairsprings in detail and studied their dynamic performance in mechanical watch movements. Respecting and regarding Castigliano's theorem, the authors developed a mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque and conducted a computer simulation with the MATLAB application.…”

“…Applying and accomplishing the static study simulation of the model M deformation in the assembly S; part R is excluded from the study declaring the part R as rigid 6…”

The combination of structure and material distribution ensures functionality of the honeybee wing-coupling mechanism

“…According to Castigliano's theorem, [22][23][24] the change in U under F A , dU/dF A , is equivalent to the displacement d of point A of the PRM, such that…”

Electromechanics of suspended spiral capacitors and inductors

“…For spiral capacitors, the motion mass m is roughly 2/3 of the total mass. One can here estimate Ω from a 1D cantilever equivalent [8][9][10][11] with the identical b, h, and curve length. However, the result is normally off the correct value by two orders of magnitude, or even more.…”