単純な衝突体の反発特性
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概要
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Mechanical components in telecommunication equipments have many moving parts accompanying collision. In these equipments, rebounding after collision should be minimized for the purpose of high speed operation. Coefficient of restitution is mainly affected by two factors: the local energy loss at the impact point and the energy loss due to wave propagation. In the present paper we investigated the impact force, contact time and the coefficient of restitution when a sphere impinges upon a rod to the longitudinal direction, and obtained the rebound characteristics due to the loss of wave propagation. In the case of a sufficiently long rod in which the reflected wave does not return during the contact time, the vibration model can be expressed as series connection of s_0 and z_0 as shown in Fig. 1 where s_0 is the stiffness of local defomation at the impact point and z_0 is the characteristic impedance of the rod. In this case, the rebound characteristics are determined by a single parameter δ=mω_s/2z_0 ( m is a mass, ω_s=√<s_0/m>). In the case of a Hertz contact, if we put s_0=k^<4/5>ξ_0^<2/5>m^<1/5>, the parameter δ is equal to one half of the inelasticity parameter λ introduced by C. Zener. Stiffness s_0(=k^<4/5>ξ_0^<2/5>m^<1/5>) is regarded as the equivalent linear stiffness of the Heltz contact. Next, the coefficient of restitution (Fig. 7), contact time (Fig. 8) and peak impact force (Fig. 9) were calculated in the case where the length of rod is short and the reflected wave appears during the contact time. In this case, besides δ we have to consider the parameter S=ω_s/ω_1 (ω_1=fundamental angular frequency of the rod). δ is a parameter to represent the cross-sectional area of the rod and the parameter S represents the length of the rod. From Fig. 7 we see that, when a sphere impinges upon the end of a free-free rod, the coefficient of restitution is determined only by mass ratio M_0(=mass of the rod/mass of the sphere) so long as S<0. 3. This means tha the rod can be regarede as a concentrated mass if S<0. 3. When a mass impinges upon a free-fixed rod, the coefficient of restitution is nearely equal to 1, if S<0. 4. This means that the rod can be regarded as concentrated stiffness if S<0. 4. Comparison of the analytical results between the case where the stiffness of local deformation is linear and the case where the Heltz theory holds, shows a close agreement in the coefficient of restitution, but a slight difference in impact force.
- 社団法人日本音響学会の論文
- 1969-05-30