On the Mechanism Generating Unstable Phenomena of the Propulsion Shafting with a Reduction Gear
Masayasu MATSUDA* and Minoru KAMATA**
ABSTRACT
There often occurs an extraordinary torsional vibration influenced by the combination of the excessive external torque, the gear backlash and the oil film characteristics of the bearing in the propulsive shafting with the reduction gear when the gear load is light. In order to clarify the conditions and the mechanism of this extraordinary vibration, the torsional vibration model considering self-exciting vibration of the bearing oil film is proposed and analyzed by the characteristic equations and also the computer simulation. As the result, it is concluded that the extraordinary vibration is caused by the instability of the self-exciting vibration of the bearing coupled with the torsional vibration and that the existence of the gear backlash makes the stable area changed.
And the simple design criterion that pinion rpm should be below 2 times of the natural circular frequency of the torsional vibration of the shafting to prevent the extraordinary coupled vibration can be obtained by assuming the steady oil whirl of the journal. It is also noted that this kind of extraordinary vibration generally occurs for such propulsive shafting as has idling reduction gears including a diesel engine propulsion shafting.
Key Words: Torsional Vibration, Self-exciting vibration, Tribology, Shafting, Reduction Gear
NOMENCLATURE
Cij: non-dimensional damping coefficient of oil film
c: clearance of bearing (m)
cij: damping coefficient of shaft (Nms/rad)
Fe: oil film force in eccentricity direction (N)
FH: oil film force perpendicular to eccentricity direction (N)
Ji: moment of inertia (kgm2)
Kij: non-dimensional spring constant of oil film
kl: torsional spring constant of shaft (Nm/rad)
kij: spring constant of oil film (N/m)
l: bearing length (m)
M: mass of pinion (kg)
r: bearing radius (m)
rp: pitch circle radius of pinion (m)
S: Sommerfeld No.
u: reduction ratio
x,y: displacement of pinion (m)
ε: eccentricity ratio of pinion bearing
φi: angular displacement (rad)
△φ: half backlash (rad).
1. INTRODUCTION
There often occurs a peculiar chattering phenomena caused by the torsional vibration [1], [2], [3] influenced by the excessive external exciting torque and the existence of the gear backlash in such low gear load on the propulsive shafting with the reduction gear trains.
And it is also reported [4] that there occurred an extraordinary torsional vibration caused not only by the excessive external exciting torque and the gear backlash but also by the self-exciting vibration of the oil film characteristics of the bearing coupled with the torsional vibration in the propulsive shafting with the reduction gear having light load.
It is very difficult to solve analytically the non-linear equations of motion, therefore, the computer simulation has been usually used. But it is hard to make causes clear by the computer simulation because of so many cases of calculation required. In view of these disadvantages of the computer simulation, it is the purpose of this paper to describe the alternative approach in which the simplified vibration model considering the coupled vibration of the self-exciting vibration of the bearing oil film and torsional vibration is proposed and analyzed by the characteristic equations. As the result, it is concluded that the extraordinary vibration is caused by the instability of the self-exciting vibration of the bearing oil film coupled with the torsional vibration in light gear load and that the existence of the gear backlash makes the stable area changed. The design criterion to prevent the extraordinary vibration can be obtained by assuming the steady oil whirl of the journal. And it is noted that this extraordinary vibration could generally occur in referring to such a diesel engine plant as has the reduction gear.
2. SIMPLIFIED VIBRATION MODEL
2.1 Modeling philosophy and equations of motion
The simplified vibration model is proposed for investigating the causes of the extraordinary coupled vibration of self-exciting vibration and torsional vibration as shown in Fig. 1. The model consists of basic components such as a prime mover, a pinion and a wheel, each of which has a moment of inertia J1, J2 and J3 respectively, and also a shaft with torsional spring constant k1 and a pair of bearing. In addition, a gear backlash and the lateral movement of the pinion caused by the self-exciting vibration of the oil film is considered for the model.
