Analysis of aerostatic spindle radial vibration error based on microscale nonlinear dynamic characteristics

This paper presents a method of predicting the radial rotary error of an aerostatic spindle based on the microscale-effect to investigate the influence of gas film fluctuation on the rotation accuracy of the aerostatic spindle. First, the gas bearing of the spindle is simplified as a spring-damping system with two degrees of freedom perpendicular to each other. Additionally, the aerostatic spindle bearing-rotor system is established by considering the forced vibration and deflection vibration of the rotor. Subsequently, the microscale-effect is introduced into the dynamic model of the gas film flow, and the dynamic Reynolds equation of the gas film is established in the microscale. Moreover, the nonlinear dynamic stiffness and dynamic damping coefficient are obtained by the perturbation method. The nonlinear dynamic parameters in the microscale are introduced into the dynamic model of the bearing-rotor system and all the vibration errors are obtained. By comparison with the conventional case, it is found that the spindle gyration error increased and that the response delay occurred when the microscale-effect is considered. Moreover, the influence of the supply pressure and speed on the vibration of the spindle is also analyzed. An experiment measuring the spindle rotation error is carried out. The experimental results reveal that the prediction method of the nonlinear spindle rotation error in the microscale is more accurate, and that the errors are 5.8% and 9.6%.

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Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.148-149.141 ◽

2010 ◽

Vol 148-149 ◽

pp. 141-146

Author(s):

Di Hei ◽

Yong Fang Zhang ◽

Mei Ru Zheng ◽

Liang Jia ◽

Yan Jun Lu

Keyword(s):

Nonlinear Dynamic ◽

Degrees Of Freedom ◽

Rotor System ◽

Dynamic Responses ◽

Flexible Rotor ◽

Runge Kutta Method ◽

Stability And Bifurcation ◽

Single Disk ◽

The Stability ◽

Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

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Nonlinear Dynamic of a Geared Rotor System With Nonlinear Oil Film Force and Nonlinear Mesh Force

Journal of Vibration and Acoustics ◽

10.1115/1.4005032 ◽

2012 ◽

Vol 134 (4) ◽

Cited By ~ 14

Author(s):

Yahui Cui ◽

Zhansheng Liu ◽

Yongliang Wang ◽

Jianhuai Ye

Keyword(s):

Numerical Integration ◽

Dynamic Model ◽

Rotational Speed ◽

Nonlinear Dynamic ◽

Journal Bearing ◽

Rotational Frequency ◽

Rotor System ◽

Dynamic Responses ◽

Oil Film ◽

Gear Mesh

To investigate the effect of oil film force on a geared rotor system, a short journal bearing model was applied to represent nonlinear oil film force. A dynamic model of the geared rotor oil journal bearing system was presented. The nonlinear gear mesh force and nonlinear oil film force were considered in the model. The nonlinear dynamic responses of the system were investigated by numerical integration method. This article shows that when the rotational speed is relatively low, the vibration of the system is mainly affected by nonlinear mesh force. With the increase of rotational speed, the influence of nonlinear oil film force also increases gradually, and the subsynchronous forward precession phenomena appear. When the speed increases to a certain value, the amplitude of the subsynchronous forward precession exceeds the amplitude of the rotational frequency, and the nonlinear mesh force is greatly affected by the nonlinear oil film force. However, the linear oil film force does not affect the nonlinear mesh force. The subsynchronous forward precession is difficult to be predicted by linear oil film force which was previously applied. This experiment is performed to validate the correctness of the dynamic model presented, and the numerical integration results of low speeds are validated by the experimental data.

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Modeling and Control of a Six Degrees of Freedom Maglev Vibration Isolation System

Sensors ◽

10.3390/s19163608 ◽

2019 ◽

Vol 19 (16) ◽

pp. 3608 ◽

Cited By ~ 1

Author(s):

Qianqian Wu ◽

Ning Cui ◽

Sifang Zhao ◽

Hongbo Zhang ◽

Bilong Liu

Keyword(s):

Dynamic Model ◽

Nonlinear Dynamic ◽

Degrees Of Freedom ◽

Vibration Isolation ◽

Nonlinear Dynamic Model ◽

Isolation System ◽

Vibration Isolation System ◽

Modeling And Control ◽

And Control ◽

Isolation Performance

The environment in space provides favorable conditions for space missions. However, low frequency vibration poses a great challenge to high sensitivity equipment, resulting in performance degradation of sensitive systems. Due to the ever-increasing requirements to protect sensitive payloads, there is a pressing need for micro-vibration suppression. This paper deals with the modeling and control of a maglev vibration isolation system. A high-precision nonlinear dynamic model with six degrees of freedom was derived, which contains the mathematical model of Lorentz actuators and umbilical cables. Regarding the system performance, a double closed-loop control strategy was proposed, and a sliding mode control algorithm was adopted to improve the vibration isolation performance. A simulation program of the system was developed in a MATLAB environment. A vibration isolation performance in the frequency range of 0.01–100 Hz and a tracking performance below 0.01 Hz were obtained. In order to verify the nonlinear dynamic model and the isolation performance, a principle prototype of the maglev isolation system equipped with accelerometers and position sensors was developed for the experiments. By comparing the simulation results and the experiment results, the nonlinear dynamic model of the maglev vibration isolation system was verified and the control strategy of the system was proved to be highly effective.

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Influence of microscale effect on the radial rotation error of aerostatic spindle

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650119870397 ◽

2019 ◽

Vol 234 (7) ◽

pp. 1131-1142

Author(s):

Chunqing Zha ◽

Tianbao Li ◽

You Zhao ◽

Dongju Chen

Keyword(s):

Aerostatic Bearing ◽

Rotating Shaft ◽

Design And Optimization ◽

Effect Factor ◽

Rotation Error ◽

Static Performance ◽

Microscale Effect ◽

Stiffness And Damping ◽

Aerostatic Spindle ◽

Test Table

This paper presents the influence of the microscale effect on the radial rotation error of aerostatic spindle, which is determined by the corresponding stiffness, damping, and unbalance mass. A microscale gas film flow model is used to simulate the static performance of the aerostatic bearing by introducing the microscale effect factor Q in this paper. Firstly, the radial stiffness and damping coefficients of aerostatic bearing were calculated considering microscale effect factor Q, therefore, the position of the rotating shaft in radial plane was deduced, and the corresponding rotation error was obtained. Finally, the simulation results of the stiffness and radial rotation error were verified by the experiment on the shaft test table, and the motion orbit was measured by a displace sensor with a high precision standard ball. The experimental results indicated that the simulated result considering the microscale effect factor Q was more consistent with the actual experimental value, which provided a reference for the design and optimization of the aerostatic spindle.

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Multi-harmonic motions of bearing cage affected by rotor unbalance

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406217722380 ◽

2017 ◽

Vol 232 (15) ◽

pp. 2610-2625

Author(s):

Baogang Wen ◽

Meiling Wang ◽

Xianwen Zhou ◽

Hongjun Ren ◽

Qingkai Han

Keyword(s):

Dynamic Model ◽

Degrees Of Freedom ◽

Rotor System ◽

Test Rig ◽

Theoretical Predictions ◽

Reaction Forces ◽

Harmonic Components ◽

Aero Engines ◽

Insight Into ◽

Combination Frequencies

The motion of bearing cage in the rotor system displays very complicated behavior affected by rotor unbalance. In order to gain an insight into the complex cage motions due to rotor unbalance, a scaled rotor test rig is designed and developed that is made to be dynamically similar to the actual rotor system in aero-engines. Eddy transducers are used to measure the cage motions and monitor the rotor vibrations. Based on the test rig, a dynamic model of its rotor system with four degrees-of-freedom is developed to determine the reaction forces due to rotor unbalance, which are introduced as boundary conditions for the bearing dynamic analysis. And then, a three degrees-of-freedom dynamic model of bearing cage taking the obtained reaction forces into account is also proposed. Finally, the experiment and simulation of the cage motions are carried out and compared at different rotating speeds and rotor unbalances. The experimental results of the cage motions agree with the theoretical predictions and reveal that the cage motions generally contain the multiple harmonic components, such as the cage rotating frequency and its multi-frequency, the inner ring rotating frequency, and also some combination frequencies due to rotor unbalance. The amplitudes of the inner ring rotating frequency and combination frequencies of the cage motions increase with the increment of the rotor unbalance values. Besides, the trajectories of cage are affected by the rotor unbalances.

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Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Complexity ◽

10.1155/2019/4536012 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17

Author(s):

Shupeng Sun ◽

Lun Liu

Keyword(s):

Model Reduction ◽

Dynamic Model ◽

Dynamic Modeling ◽

Nonlinear Dynamic ◽

Degrees Of Freedom ◽

Flexural Vibration ◽

Nonlinear Dynamic Model ◽

Thin Cylindrical Shell ◽

Reduction Strategy ◽

Nonlinear Dynamic Modeling

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in-plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in-plane vibrations. Meanwhile, for the reduced-order model, the in-plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude-frequency responses under different excitation levels.

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Nonlinear Dynamic Behaviors of Rotor System with Misaligned Journal Bearings

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.271-272.1032 ◽

2012 ◽

Vol 271-272 ◽

pp. 1032-1038 ◽

Cited By ~ 1

Author(s):

Ming Li ◽

Zi Gang Li ◽

Ping Xue

Keyword(s):

Nonlinear Dynamic ◽

Degrees Of Freedom ◽

Journal Bearings ◽

Rotor System ◽

Lateral Direction ◽

Dynamic Behaviors ◽

Rotating Speed ◽

Mass Unbalance ◽

Bifurcation Phenomena ◽

Steady State Responses

The dynamic modeling of a rotor system on misaligned journal bearings is discussed and its nonlinear dynamic behaviors are considered in this paper. Firstly, a dynamic model of six degrees of freedom system is established under the conditions of the long bearings, small bearing misalignment and mass unbalance. Then, the nonlinear dynamics of the rotor-bearing system, such as the displacement response and its frequency spectrum, rotor orbit and its Poincare map are analyzed by the Runge-Kutta method. The results show that at low speed the steady-state responses of the rotor system in lateral direction is synchronous, as the speed increases a serious of bifurcation phenomena and chaotic oscillations occur. In many cases, there exist the integer multiples components of the rotating speed except the synchronous one in displacement responses.

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