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pushrod (the next lowest spring rate) as a exible element The model then takes the shape of Fig 1125a, where the mass of the pushrod has been divided equally between the elements on either side of it, the lifter and the rocker arm (Chen, 1982; Hanachi and Freudenstein, 1986) The parameter values then become m1 = ml + 1 m pr 2 = 0270 lbm + ( 05)0114 lbm = 0327 lbm J m 2 1 2 m pr + 2 ra + mvs rra + cs rra lra , pr 2 3 0132 lbm in 2 0153 lbm 2 (17)2 = 110 lbm + 0251 lbm(17) + 3 (0875 in )2 K1 = K pr = 30 10 5 lb in K2 = Keq = 660 lb in Since this is exactly the same form as the suspension model discussed earlier, the natural frequencies of this two-mass system can be calculated and occur at 67 Hz (as predicted by the one degree of freedom model) and 3400 Hz This suggests two things First, the next natural frequency is signi cantly higher than the rst so there is ample justi cation for using a single-mass model for basic analysis Secondly, while the single mass
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= ( 05)0114 lbm +
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(b) Single mass with damping
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(a) Two-mass model
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FIGURE 1125 Other simple models of the valve-gear system
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