変位に比例する固体摩擦力が働くばね質量系の自由振動

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For the damping of a mass-spring(m-k) system, a method using a solid friction is comparatively simple and has no problems of oil leakage and no characteristical change by temperature being different from an oil damper. However, the system with such damping has the characteristic of infinite resonance when input exceeds a critical value, and has an offset from the natural equilibrium position. A method to remove these shortcomings utilizing the friction force proportional to the displacement of the mass m was reported elsewhere, in which only the stationary vibration, i.e. the frequency characteristic was discussed. In the present paper, characteristics of the free vibration are theoretically studied, and the results are ascertained by the experiment. Conclusions obtained are summerized as follows: (1) Free vibration can be described by three parameters, α, ρ, and λ, αwhere a is the inclination of the groove, ρ the friction angle between the groove and the solid piece, λ the ratio of k_d to k.k is the spring constant of the m-k system, and k_d is that for another spring which pushes the solid piece to the mass m. (2) Value of the damping natural frequency ω_0 is given by 2ω_1ω_2/(ω_1+ω_2), where ω_1=ω_n〓{1+λtanαtan(α-ρ)}, ω_2=ω_n〓{1+λtanαtan(α+ρ)}, and ω_n=〓(k/m). (3) Damping characteristic of the amplitude is expressed by the logarithmic decrement, 2(ω_1/ω_2), or by the damping ratio, 1/〓|{2π/1n(ω_1/ω_2)}^2}2+1|. (3) Free vibration exists in a domain λ<{tanαtan(ρ-α)}^(-1) on the α-λ plane.
社団法人日本時計学会の論文
1992-09-25

変位に比例する固体摩擦力が働くばね質量系の自由振動

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