氏名　エパッサカ　ディユドン　ベルナール
学位の種類　博士（工学）
学位記番号　博乙第137号
学位授与の日付　平成11年6月16日
学位論文題目　Whirling of a Vertical Rotor Contacting with Annular Guard during Passage through Critical Speed（危険速度通過時振れ止めと接触する立形ロータのふれまわり）
論文審査委員
　主査　教授　矢鍋　重夫
　副査　教授　久曽神　煌
　副査　助教授　永澤　茂
　副査　助教授　太田　浩之
　副査　埼玉大学　教授　佐藤　勇一

• 論文目次
• 論文要旨

［平成11（1999）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

1. INTRODUCTION
1.1 Brief review of rotordynamics problems　p.1
1.2 Review of transient vibration problems during passage through critical speed　p.2
1.3 Review of rotor-stator rub,contact and collision problems　p.3
1.4 Scope of the present study　p.4
1.5 Nomenclature　p.10

2. EXPERIMENTS ON TRANSIENT VIBRATIONS OF A ROTOR CONTACTING WITH ANNULAR GUARD DURING ACCELERATION BY POWER LIMITED MOTOR
2.1 Experimental apparatus　p.12
2.2 Measuring system and whirl velocity estimation　p.12
2.2.1 Measuring system　p.12
2.2.2 Whirl velocity estimation　p.25
2.3 Experimental setup and results of Motor torque characteristics（Motor T-N curve）　p.28
2.4 Natural frequency and damping ratio of the experimental rotor-bearing system　p.28
2.5 Rotor eccentricity　p.30
2.6 Transient vibration responses and discussions　p.33
［A］For small rotor eccentricity（Passing through critical speed）　p.33
［B］For medium eccentricity（Backward whirl occurs）　p.34
［C］For large eccentricity（Contacting forward whirl occurs）　p.34
2.7 Summary　p.45

3. SIMULATION OF TRANSIENT VIBRATION RESPONSES
3.1 Analytical model　p.46
3.2 Equations of motion　p.46
3.2.1 Equations of motion　p.46
3.2.2 Nondimensional equations of motion　p.47
3.3 Motor torque characteristics　p.48
3.4 Nondimensional parameters and standard values　p.49
3.5 Calculation method　p.50
3.6 Simulation results and discussions　p.51
3.7 Development of Backward whirl　p.55
3.7.1 Transition from forward whirl to backward whirl　p.55
3.7.2 Effects of friction force on the whirl orbit　p.56
3.8 Checking accuracy of Numerical Integration　p.57
3.9 Summary　p.75

4. EFFECTS OF MAIN PARAMETERS ON THE CHARACTERISTICS OF THE TRANSIENT RESPONSES
4.1 Eccentricity　p.76
4.2 Coefficient of friction　p.79
4.3 Mass ratio　p.79
4.4 Frequency ratio　p.80
4.5 Contact damping　p.80
4.6 Contact stiffness　p.81
4.7 Summary table　p.82
4.8 Summary　p.104

5. EQUILIBRIUM OF FORCES IN TYPICAL WHIRL PATTERNS
5.1 Unbalanced forward whirl　p.105
5.2 Contacting forward whirl　p.106
5.3 Backward whirl of contact type　p.107
5.4 Backward whirl of collision type　p.108
5.5 Comments on force equilibrium in previous studies　p.109
5.6 Summary　p.115

6. METHODS OF SUPPRESSING BACKWARD WHIRL
6.1 Overview of methods　p.116
6.2 Experiments　p.116
6.2.1 Experimental apparatus　p.116
6.2.2 Ball bearing type of guard　p.116
6.2.3 Ball bearing type of guard with additional mass　p.117
6.3 Experimental method　p.117
6.4 Results and discussions　p.118
6.5 Mechanism of preventing the backward whirl by inner race rotation　p.119
6.6 Theoretical predictions　p.120
6.3.1 Analytical of model　p.120
6.3.2 Equations of motion　p.121
6.3.3 Simulation results and discussions　p.123
6.7 Comparison between experimental and numerical simulation results　p.124
6.8 Summary　p.159

7.CONCLUSIONS　p.160

APPENDIX　p.162

BIBLIOGRAPHY　p.165

Rotating machines have several types of clearance and backlash. Rotors in these machines often contact or collide with stationary elements during passage through a critical speed or at machine trouble and in some cases rotors execute a violent backward whirl due to friction force.And then the machines may suffer serious damages.
This thesis deals with transient vibrations of a vertical Jeffcott rotor contacting with an annular guard during acceleration by a power limited motor to pass through a critical speed.
The objectives of this study are to clarify what kinds of whirl occur in the transient process, how the backward whirl will develop and how to suppress the whirl.
The present thesis is constructed in seven chapters.
In Chapter I,“Introduction”,fundamental problems of rotordynamics,previous studies on passage through critical speed and on rotor-stator contact/collision problems are overviewed,and the background and objectives of the present study are stated.
In Chapter II,“Experiments of the transient vibrations”,T-N curves of the motor used here were measured first. Then rotor acceleration tests were carried out by changing rotor eccentricity.
Three different whirl patterns were observed.
（1）For small eccentricity,the rotor passes through the critical speed after several collisions or without any collisions and approaches the steady unbalance whirl.
（2）For medium eccentricity,the rotor executes the backward whirl of contact type after a contacting forward whirl. The whirl amplitude,frictional torque and contact force become extremely large.
（3）For large eccentricity, the contacting forward whirl continues and the backward whirl never occurs. The whirl amplitude almost equals the clearance between the rotor and guard.
In Chapter III,“Simulation of the transient vibrations”,numerical simulation of the transient vibrations is performed. The calculation model is composed of a vertical Jeffcott rotor, an annular guard supported by springs and dampers and a motor with torque
characteristics.
Considering a contact force and friction force associated with collision and the motor torque, equations of motion concerning translational motions of the rotor and guard and rotational motion of the rotor and motor are derived. Nondimensional equations of motion are solved by the Runge-Kutta method under standard parameter values to obtain the transient vibration responses.
The simulation results are in good agreement with the experimental ones qualitatively.
Further, The development process of the backward whirl is precisely investigated and the process can be explained by the change of the reflected angle of the rotor at the collision against the guard.
In Chapter IV,“Effects of main parameters on the transient vibrations”,effects of main parameters on the transient responses are clarified.
The increase in the coefficient of friction, mass and stiffness of the guard system and the contact damping promotes the occurrence of the backward whirl.While the increase in the eccentricity and contact stiffness has the opposite effect.When the contact damping is large, the backward of collision type occurs. In case of small contact stiffness, the backward whirl shows characteristics of the contact type and collision type.
In Chapter V,“Equilibrium of forces in typical whirl patterns”, the balance of forces in some whirl patterns is investigated.In the contacting forward whirl, the contact force and friction force are very small and force balance is the same as that of steady unbalance whirl. In the backward whirl of contact type,the inertial force almost balances with the resultant of the contact and friction forces and the other forces are extremely small.
Further, the relative velocity between the rotor and guard is almost zero but fluctuates between plus and minus.According to this,the friction force points forward and backward whirl. But the whirl motion seems to be in almost steady state.
In Chapter VI,“Ways of suppressing backward whirl”,effects of a ball bearing type of guard on the transient vibrations are investigated.
The ball bearing type of guard with additional mass is effective to suppress the backward whirl. The reason is that the relative velocity between the rotor and the guard inner surface is likely to be negative. For negative relative velocity,the friction force acts on a such way not to encourage the backward whirl.
In Chapter VII,“Conclusions”, conclusions of this study are summarized.