Dynamic Models for Rigid Memory Mechanisms

Abstract

The paper presents a dynamic model that works with variable internal damping, applicable directly to rigid memory mechanisms. If the problem of elasticity is generally solved, the problem of system damping is not clear and well-established. It is usually considered a constant "c" value for the internal damping of the system and sometimes the same value c and for the damping of the elastic spring supporting the valve. However, the approximation is much forced, as the elastic spring damping is variable and for the conventional cylindrical spring with constant elasticity parameter (k) with linear displacement with force, the damping is small and can be considered zero. It should be specified that damping does not necessarily mean stopping (or opposition) movement, but damping means energy consumption to brake the motion (rubber elastic elements have considerable damping, as are hydraulic dampers). Metal helical springs generally have a low (negligible) damping. The braking effect of these springs increases with the elastic constant (the k-stiffness of the spring) and the force of the spring (P₀ or F₀) of the spring (in other words with the arc static arrow, x₀ = P₀/k). Energy is constantly changing but does not dissipate (for this reason, the yield of these springs is generally higher). The paper presents a dynamic model with a degree of freedom, considering internal damping of the system (c), damping for which it is considered a special function. More precisely, the cushioning coefficient of the system (c) is defined as a variable parameter depending on the reduced mass of the mechanism (m* or J reduced) and the time, i.e., c depends on the derivative of m reduced in time. The equation of the differential movement of the mechanism is written as the movement of the valve as a dynamic response.