Vibration damping device and method for designing the same

A method for designing a vibration damping device including a support member that rotates, together with a rotary element to which torque from an engine is transferred, about a center of rotation of the rotary element, a restoring force generating member that is coupled to the support member and that is swingable as the support member rotates, and an inertial mass body that is coupled to the support member via the restoring force generating member and that swings, with motion of the restoring force generating member, about the center of rotation as the support member rotates, the method comprising

• determining moments of inertia J1, J2, mass m, and distances L3 and L4 so that torque fluctuation of an object for which vibration is to be damped, which is derived based on angular displacement δ and angles ζ and θ obtained by solving the following expressions (1) and (2), is equal to a target value
• [Expression 2]
• J1·{umlaut over (δ)}+(J2+m−L42)·({umlaut over (δ)}+{umlaut over (θ)})+m·L32·({umlaut over (δ)}+ζ′·{umlaut over (θ)}+ζ″·{dot over (θ)}2)+m·L4·L3·[2·{umlaut over (δ)}+(1+ζ′)·{umlaut over (θ)}+ζ″·{dot over (θ)}2]·cos(θ−ζ)−m·L4·L3·[2·(Ω+{dot over (δ)})+(1+ζ′)·{dot over (θ)}](1−ζ′)·{dot over (θ)}·sin(θ−ζ)+k·δ=Td·cos ω·t (4)
• (J2+m−L42)·({umlaut over (δ)}+{umlaut over (θ)})+m·L32·ζ′·({umlaut over (δ)}+ζ′·{umlaut over (θ)}+ζ″·{dot over (θ)}2)+m·L4·L3·[(1+ζ′)·{umlaut over (δ)}+2·ζ′·{umlaut over (θ)}+ζ″·{dot over (θ)}2]·cos(θ−ζ)+m·L4·L3·[(Ω+{dot over (δ)})2−ζ′·{dot over (θ)}2]·(1+ζ′)·sin(θ−ζ)=0 (5)
• where “L3” represents a distance between a center of gravity of the restoring force generating member and a fulcrum of swinging of the restoring force generating member with respect to the inertial mass body,
• “L4” represents a distance between the fulcrum and the center of rotation,
• “J1” represents a moment of inertia of the rotary element and the support member,
• “J2” represents a moment of inertia of the inertial mass body,
• “m” represents mass of the restoring force generating member,
• “k” represents stiffness of a system from the engine to the rotary element,
• “Ω” represents an angular velocity of steady rotation of the rotary element,
• “δ” represents angular displacement of the rotary element from a steady rotation state,
• “ζ” represents an angle formed by a reference line defined on the support member and extending in a radial direction of the support member through the center of rotation and a line segment from the fulcrum of swinging of the restoring force generating member with respect to the inertial mass body to the center of gravity of the restoring force generating member,
• “θ” represents an angle formed by the reference line and a line segment from the center of rotation to the fulcrum,
• “Td” represents torque that is transferred from the engine to the rotary element, and
• “ω” represents a frequency of vibration that is transmitted from the engine to the rotary element.