Research on Stability of Shafting Under Two Kinds of Impact Load

Tianran Chen

Liangxiong Dong

and Yiran Shi

ZheJiang Ocean University, ZhouShan 316022, China

Keywords: Ship shafting; rub-impact load; vibration; stability time

Abstract: The influence of rub-impact loadsupon the stability of shafting is directly related to the damage of ship

propulsion system, so the numerical simulation and experimental technology is applied to the studyon

stability of ship shafting under rub-impact load. Based on the dynamics model of stern shaft - oil film - stern

structure system, the amplitude-time response curve are obtained by the numerical simulation. On the basis

of theoretical researches, the tests of stability time under two kinds of loads are carried out. In addition, the

effective method to shorten the shafting stability time under rub-impact load is obtained that are provided

for the safe operation of shafting.

1 INTRODUCTION

Ship in the voyage, affected by the harsh

environment, the hull under external forces will

produce uneven deformation and random movement,

resulting in hull deformation, bearing oil film

whirling and the unstable state of shafting, So,

restraining or weakening ship vibration is the key to

strengthen the stability of shafting and improve

transmission performance. In this paper, by

numerical simulation and experimental, the variation

law of ship shafting stability under different load

and rotational speed is studied, the characteristics of

longitudinal vibration are analyzed, and the effective

method is found to shorten the time spent in

restoring the stability of the rear axle system. It

provides some theoretical basis for the optimization

design of ship construction and reasonable

installation of shafting, and strengthens the safety of

ship in the course of navigation.

2 STABILITY ANALYSIS OF SHIP

STERN SHAFT UNDER

EXTERNAL FORCE

In view of the complex stress state of ship shafting,

it has important theoretical significance and

application value to carry out the research of

shafting stability. There are two kinds of dynamic

load on the ship shafting, one is the impact load of

which the duration is very short and the energy

release quickly. The other is the cyclic dynamic load

of which the most common is the rub-impact load.

Under the action of Impact load some

significant changes may be made in the axis

trajectory. Therefore, through the axis trajectory can

obtain the stability of ship shafting and then judge

the rationality of the shafting parameters design.

According to the idea of discrete modeling, the

hull stern structure is discretized firstly, the discrete

stern structure is linearly elastic, and the tail shaft

system is simplified as a single disk system. So, the

corresponding mechanical model is set up

[1-3]

shown in Figure 1.

In Fig.1, the M1,M2 is the mass of the left and

right axle neck; the M5 is the mass of disc; the C1 is

the damping coefficient of the hinge at the bearing

place; the C2 is the damping coefficient of the hinge

at the disk; the C3 is the stern structure damping

coefficient; the K1 is the elastic axis rigidity; The

K3,K4,K5.is the connection stiffness of stern

structure. The values of the parameters

are:

100mkg=

，

80 ,mkg=

，

200mkg=

5000 . /cNSM=

，

510 /kNm=×

，

510 /

kNm=×

，

0.2cmm=

，

0.06rmm=

，

0.2mm

，

0.1f =

，

510k =×

，

510k

=×

Fig.1 The mechanical model of ship shafting.

The dynamic equations of the rotor system are:

()

uCGuKuF++ + =

&& &

(1)

Where in,

is the displacement array,

is the

excitation force array,

is the mass matrix,

the gyro matrix,

is the damping matrix, the

the stiffness matrix.

3 THE SIMULATION OF

STABILIZATION PROCESS

UNDER IMPACT LOAD

Under normal operating conditions, the axis

trajectory is most sensitive to the change of

rotational speed that transferred between the

convergence and the divergence state [4-7].The axis

trajectory tends to deviate from the original motion

trajectory when the disturbance occurs, and

the time it takes to stabilize are not the same under

different disturbances. Therefore, this paper mainly

analyzes the change of the axis trajectory in two

cases, one is the change of the axis trajectory under

the condition of impact load, the other is under the

condition of rubbing load.

In the course of navigation, the propeller and the

hull withstand the external forces and thus the

movement of the shafting are influenced. The impact

load acting on the axis can be described as a

rectangular pulse load shown in Fig. 2.

Fig.2Impulsive load fig.

0, <16

1, 16 18

0, 18

τπ

πτ π

τπ

⎧

⎪

=≤≤

⎨

⎪

⎩

（2）

Under the condition of impact load, with the

increase of excitation frequency, the system presents

the state of transition from stable motion to periodic

motion and chaos motion. Accordingly, the

topological structure of vibration system will be

changed correspondingly. Two kinds of shafting

working condition, i.e., periodic motion and chaotic

motion, is analyzed and simulated of which the

corresponding rotational speed is 760r/min and

800r/min. The axial-cervical vibration response is

shown in Fig. 3-1andFig. 3-2in which the arrow

segment indicates the time required to restore

stability.

1560 1580 1600 1620 1640 1660 1680

-0.68

-0.67

-0.66

-0.65

-0.64

-0.63

-0.62

-0.61

T(s )

Amplitude(mm)

stability time

Fig3-1

1540 1560 1580 1600 1620 1640 1660 1680

-0.395

-0.39

-0.385

-0.38

-0.375

-0.37

-0.365

Amplitude(mm)

T(s )

Stability time

Fig3-2

Fig.3Thevibration response at speed of 760 and 800r/min.

Fig.3 show that the impact load has a certain

disturbance effect on the axis trajectory. The more

intense the impact load become, the longer the larger

the amplitude of shafting become. As shown in

Fig.3-1, the stable time is 120 when the rotational

speed is 760r/min, but the stable time become 140 at

speed of 800r/min as shown in Fig.3-2.Therefore,

under the same impact load, choosing the

appropriate rotational speed can effectively shorten

the stabilizing time. And then, keeping the speed

constant and changing the magnitude and duration of

the impact load, the stable time under various impact

loads at speed of 760r/min is measured in table 1:

Table.1 The stability time under different impact loads.

1 2 3 4 5 6 7 8 9 10

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Emagnitude impact load(KN)

（）

Ampli t ude mm

T=0.8pi

T=1.2pi

T=1.5pi

T=2pi

Fig 4Thestability time changed with magnitude and

duration of impact load.

The curve fitting is done according to

the sheets data as shown in Figure 4, that is the

variation curve of stability time according to the

magnitude when the duration of impact load remain

constant. It can be seen that the stabilize time of

shafting is different in different impact load, and the

change speed of stabilize time is related to the

magnitude of impact load.

4 ANALYSIS OF THE STABILITY

OF THE TAIL SHAFT UNDER

RUBBING LOAD

4.1 Simulation of Stability Process Under

Rubbing Load

Rubbing load is a kind of working condition caused

by the contact each other between tail shaft and tail

bearing in the process of ship operation. When the

rub occurs, the tail shaft and the tail will bear not

only the collision force but also the circumferential

friction force. Assuming the elastic deformation

happen in the collision process, and the gap between

the tail shaft and the tail bearing is

, the rub force

can be expressed as:

()

⎧⎫

−

⎡

⎤⎧ ⎫

⎪⎪

=−

⎨

⎬⎨⎬

⎢⎥

⎪⎪

⎣

⎦⎩ ⎭

⎩⎭

（3）

Where in,

exy=+

is the radial

displacement of the shaft. When

,both the

radial force and tangential friction are zero.

In the same way, make the friction coefficient of

the rub is 0.1 and the gap

is 0.0002, meanwhile

keep the rub load and its action time constant, and

change the shafting speed. When the shafting

rotational speed is respectively760 and 800r/min, the

stability time and the vibration amplitude under

different working conditions are measured. as shown

in Fig. 5-1 and Fig. 5-2.

1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670

-0.65

-0.6

-0.55

-0.5

-0.45

stablity time

T(s )

A m plitude(m m )

Fig 5-1

1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740

-0.401

-0.4005

-0.4

-0.3995

-0.399

-0.3985

-0.398

-0.3975

-0.397

-0.3965

Amplit ude(mm)

T(s )

stabl ity time

Fig 5-2

Fig.5The vibration response at speed of 760 and 800

r/min,

It can be seen that the change of the rotational speed

of the ship shafting will affect the stability of the

axis track when the rub load is constant. With the

increase of the shafting speed, the dynamic

characteristics of the bearing oil film force are

changed, and the amplitude of the disturbance

caused by the rub load is also increased. In addition,

the changes of friction coefficient also has a certain

effect to the shafting vibration. The larger the

friction coefficient of rub become, that is, the bigger

the spring stiffness, the more intense the longitudinal

vibration of the shafting become, and the larger the

vibration amplitude of shafting. Therefore, subjected

to the same rub load, the stability time of the

shafting system can be effectively shorten by

adjusting the rotational speed and selecting the

appropriate friction coefficient .

4.2 Comparison of Shafting Stability

Between Two Kinds of Load

In order to compare the stability of the tail shaft

under variousrub load, keeping the rotational speed

unchanged and just changing the friction coefficient

and elastic coefficient of rub-impact load, the

stability time is observed and recorded in table 2.

The data from Table 2 is shown in Figure 6.

The Fig. 6 shows the change curve of the elastic

coefficient according to the increase of the friction

coefficient. It can be seen that the change speed of

stabilize time is different in different friction

coefficients, that is, the lower the friction coefficient

is, the smaller the growth rate of stabilize time is

likely to be. For example, when the elasticity

coefficient is 150, the shafting have the fastest

recovery speed. When the coefficient of friction is

less than 150, the greater the elasticity coefficient is,

the greater the time needed for the stability of the

shafting system, which is come to opposite

conclusions when the coefficient of friction is more

than 150.

Table 2TheStability time under different loads .

Fig 6The stability time changed with friction coefficient

and elasticity coefficient

5 CONCLUSIONS

In this paper, the dynamic model of the stern shaft -

oil film - stern structure system is established, and

the stability characteristics after impact and rub are

studied, which provides a theoretical reference for

the safety evaluation of the shafting.

1. The impact and rub load will disturb the

motion of ship propulsion shafting with compromise

in stability which extent is related to the axis speed.

In the non periodic moving region, the prolongation

of the load duration will lead to the amplitude

decays slowly and the ability restore the stable state

of shafting become weak. On the other hand, in the

periodic motion area the amplitude decays fast, and

the more shaft's rotational speed deviates from the

frequency area farther, the faster the amplitude

decays, and the better the stability recovery of

shafting system.

2. Compared under the influence of impact load,

the shafting under the influence of rub load can

recovered to steady state within a shorter time. By

adjusting the rotational speed of shafting, the

damage effect of rub-impact on shafting can be

weaken. Meanwhile, by increasing coefficient of

friction will shorten the stability time of the tail

shaft, and thus strengthen the stability of the ship

shafting.

ACKNOWLEDGEMENTS

This research was supported by Zhejiang Provincial

Natural Science Foundation of China under Grant

No. LY16E090003; The National Undergraduate of

China Innovation and Entrepreneurship Training

Program (NO. 201703440007).

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