Estimation of valve spring surge amplitude using the variable natural frequency and the damping ratio

Abstract

Internal vibration of the valve spring is a critical factor in determining the dynamic characteristics of highspeed valve train systems. Because precise prediction of the spring surge amplitude is a difficult problem, especially for nonlinear variable-pitch springs, the development stage requires a process of trial and error. In the present study, a new method that considers the variable natural frequency and variable damping ratio is proposed to predict the spring surge amplitude. First, the change in the natural frequency and damping ratio caused by compression is predicted from the initially given pitch curve at the free height. Second, the spring surge amplitude is estimated by solving the wave equation with nonlinear variable coefficients. The surge amplitudes of typical valve springs are also measured using a motoring test rig and are compared with theoretical results predicted by the spring drawing and cam profile data. NOMENCLATURE d : spring wire diameter [mm] R : spring mean coil radius [mm] c : speed of wave propagation [m/s] k : spring stiffness [N/mm] m : mass of active coils [kg] t : time [s] x : distance along spring axis [mm] L : spring length [mm] φ : camshaft rotation angle [deg] n : order of spring natural frequency G n (φ) : dynamic component of spring internal vibration, function of camshaft angle [mm] ω n (φ) : natural frequency, function of camshaft angle [Hz] ζ (φ) : damping ratio, function of camshaft angle N α : number of active coils E : Young's modulus of spring material [Pa] G : shear modulus of spring material [Pa] ρ : density of spring material [kg/m 3 ] υ : Poisson's ratio γ : shear coefficient of wire cross section

Advanced static and dynamic analysis method for helical springs of non-linear geometries

“…By using this method, the dynamic equation is transformed from a partial differential equation to a set of ordinary differential equations. However, these equations have not considered the internal damping of the spring which plays an essential role in accurately estimating the dynamic vibration of spring [25,36]. Therefore, a viscous damping term is added into Eq.…”

“…In the vehicle suspension system, the suspension springs are usually grounded for the purpose of mounting [23,24]. In addition, valve springs are intentionally designed to have varied spring pitch for the purpose of reduction of spring surge [25]. Moreover, unique spring designs, like beehive spring, conical spring and barrel spring, are all against the assumption of a constant coil diameter [26].…”

“…These parts can considered as fixed rotational springs that are connected to the main spring body [33,34]. Another convenient way is to discount the end coils when counting the number of active coils [25]. No significant differences between the two methods have been reported.…”

Damping Impact on 1-Dimensional Ultrasonic Vibration-Assisted Turning Machining

“…The natural frequency is referred to as the frequency at which the structure will vibrate once displaced and quickly released [27]. As the damping ratio determines the size of amplitude [28], so it is a common consideration for tool designing. Therefore, this research investigated the damping impact on the 1-dimensional (1D) ultrasonic-assisted cutting tool.…”

Identification of damping ratio and its influences on wind‐ and earthquake‐induced effects for large cooling towers

“…It is also showed that amplitude‐dependent damping characteristics is based on field measurement . The fundamental natural frequency and the damping ratio decrease with acceleration amplitude . Taken as a thin rotating shell, a cooling tower has its unique configuration and material attributes, so the actual damping ratio must be smaller as compared with the high‐rise buildings.…”