Abstract
Internal vibration of the valve spring is a critical factor in determining the dynamic characteristics of high-speed 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.
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Abbreviations
- 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
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Liu, H., Kim, D. Estimation of valve spring surge amplitude using the variable natural frequency and the damping ratio. Int.J Automot. Technol. 12, 631–638 (2011). https://doi.org/10.1007/s12239-011-0073-1
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DOI: https://doi.org/10.1007/s12239-011-0073-1