The empirical formulae, being able to estimate engine damping ratio and torsional vibration amplitude, are derived from the experimental results both for high-speed and for low-speed diesel engines mentioned in the previous paper, in which the torsional angular displacements were measured at the free-end of the crankshafts. The relationship between the main dimension of the diesel engines and the damping ratio is individually investigated by adopting the empirical formulae, and the obtained results are as follows:
1) Which loss is dominant in engine damping friction or hysteresis can be judged from the value given by the equation (5) in this paper: that is
Q (
n, D) ≡ (
n1.6/
R) √
D/IF kgf
-1/2 s
-1. Where,
D: cylinder bore,
n : number of equivalent masses except for a flywheel-mass in an engine system,
R =IF/IE: mass ratio,
IF : inertia moment of flywheel,
IE : sum of effective inertia moments of an engine system except for flywheel.
2) Damping ratio due to friction loss is in proportion to
Q (
n, D), so it is related to the main dimension of an engine. As the value of the proportional constant varies from 0.21×10
-2 to 0.75×10
-2kgf
1/2s, it becomes difficult to decide the value definitely.
3) Damping ratio due to hysteresis loss has nothing to do with the main dimension of an engine, and is in proportion to θ
0.310 (where, θ
10 : angular displacement in the free-end of crankshaft) . The values of θ
10 in critical engine speed are those of the order of 10
-3, so the values of engine damping due to hysteresis loss are those of the order of 10
-3.
From the above-mentioned results, it has become easy to judge which loss is dominant in engine damping, friction or hysteresis, when the main dimension of an engine is given.
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