Parameters research on time-varying stiffness of the ball bearing system without race control hypothesis

2021 ◽  
pp. 095440622110179
Author(s):  
Yongzhen Liu ◽  
Yimin Zhang
Keyword(s):  
Ball Bearing ◽  
Combined Loading ◽  
Time Varying ◽  
Noticeable Effect ◽  
Rotating Speed ◽  
Bearing Stiffness ◽  
Vibration Mechanism ◽  
Control Hypothesis ◽  
Full Consideration ◽  
Bearing System

When the ball bearing serving under the combined loading conditions, the ball will roll in and out of the loaded zone periodically. Therefore the bearing stiffness will vary with the position of the ball, which will cause vibration. In order to reveal the vibration mechanism, the quasi static model without raceway control hypothesis is modeled. A two-layer nested iterative algorithm based on Newton–Raphson (N-R) method with dynamic declined factors is presented. The effect of the dispersion of bearing parameters and the installation errors on the time-varying carrying characteristics of the ball-raceway contact and the bearing stiffness are investigated. Numerical simulation illustrates that besides the load and the rotating speed, the dispersion of bearing parameters and the installation errors have noticeable effect on the ball-raceway contact load, ball-inner raceway contact state and bearing stiffness, which should be given full consideration during the process of design and fault diagnosis for the rotor-bearing system.

The Radial Stiffness and Application of Double-Decker Ball Bearing

2010 ◽  
Vol 450 ◽  
pp. 353-356 ◽  
Author(s):  
Yi Li Zhu ◽  
Long Xiang Xu
Keyword(s):  
Ball Bearing ◽  
Contact Angles ◽  
Initial Contact ◽  
Rotating Speed ◽  
Unbalance Response ◽  
Double Decker ◽  
Rotor Bearing ◽  
Nature Frequency ◽  
Bearing Stiffness ◽  
Bearing System

Single Decker Ball Bearing (SDBB) is widely used in Rotor-Bearing system. A new method using DDBB composed of two ball bearings as support bearings is proposed. The mechanical model of the DDBB based on the quasi-dynamic method is established and the corresponding calculating program compiled in Matlab is developed after considering the radial load, axial load, centrifugal force as well as gyroscopic moment acted on the bearing simultaneously. And then a simple Rotor-DDBB model is adopted to analyze the rotor unbalance response with different parameters. The simulation results show that shaft rotating speed, ball materials, axial preload and the initial contact angles to some extent impact the bearing stiffness while have little affects on system nature frequency and the rotor unbalance response which greatly affected by the system base stiffness. The results provide a theoretical basis for the design of DDBB and application in a Rotor-Bearing system.

The Non-Uniform Preloading Effect on Stiffness Behaviour of Angular Contact Ball Bearings

2012 ◽  
Author(s):  
Wenwu Wu ◽  
Jun Hong ◽  
Xiaohu Li ◽  
Yang Li ◽  
Baotong Li
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Operating Conditions ◽  
Structural Performance ◽  
Angular Contact Ball Bearing ◽  
Actual Operating ◽  
Bearing Life ◽  
Bearing Stiffness ◽  
Increasing Demand ◽  
Bearing System

With the increasing demand of higher operating speed for bearing system, more challenges have been exposed on the maintaining of the bearing performance. Preloading is an effective method to handle these challenges. Traditionally, the preloading of bearing system has been applied by uniform approaches such as rigid preload and constant preload. However, this treatment may hardly deal with the optimization of preloading problem due to the non-uniformity of the bearing stiffness becomes more apparent under high-speed operating conditions. A novel and practical approach is therefore presented in this paper to incorporate the non-uniformity effect to improve the structural performance of bearing under actual operating conditions. Firstly, the critical relationship between the stiffness behaviour and the non-uniform preload is evaluated for bearing system. The stiffness problem of angular contact ball bearing system is then formulated analytically by Jones’ model. With this approach, boundary conditions are achieved to solve the local contact deformation and predict the bearing life under non-uniform preload. Finally, both the uniform preload and the non-uniform preload cases for bearing system are simulated under various operating conditions. Comparing with traditional methods, the proposed method can provide a better solution in both stiffness and life that will enable a designer to obtain a deep insight on the optimization of bearing system.

On the Bifurcation of Periodic Motion of Rotor Ball Bearing System Considering Five Degrees of Freedom

2014 ◽  
Vol 945-949 ◽  
pp. 707-710
Author(s):  
Li Cui ◽  
Qing Sheng Wang
Keyword(s):  
Periodic Motion ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Dynamic Equations ◽  
Radial Clearance ◽  
Rotating Speed ◽  
Under Five ◽  
Bifurcation And Stability ◽  
Shooting Algorithm ◽  
Bearing System

Nonlinear bearing forces of ball bearing under five-dimensional loads are given, and five-DOF dynamic equations of rotor ball bearing system are constructed. Bifurcation of periodic motion of rotor ball bearing system in unbalance-rotating speed and radial clearance-rotating speed parametric domains are studied by use of continuation-shooting algorithm. Results show that the way of bifurcation and stability of period-1 motion vary with radial clearance and unbalance.

scholarly journals A New Model for Studying Nonlinear Vibration Behaviors of Gear-Bearing System

2021 ◽  
Author(s):  
Zi Wang ◽  
Caichao Zhu
Keyword(s):  
Nonlinear Vibration ◽  
Load Transfer ◽  
Force Model ◽  
Time Varying ◽  
New Model ◽  
Dynamic Eccentricity ◽  
Bearing Stiffness ◽  
Bearing Force ◽  
Excitation Model ◽  
Bearing System

Abstract A new model for nonlinear vibration behaviors of gear-bearing system is proposed in this work. For presenting the nonlinear excitation from bearing compliance, the enhanced bearing force excitation model containing two kinds of bearing stiffnesses, which are mean stiffness for the load transfer capacity and alternating stiffness for the disturbance resisting ability, is developed. Considering other dynamic excitations including mesh stiffness, contact pressure angle, center distance, unbalance force caused by static and dynamic eccentricity, an advanced iterative numerical method is introduced, which can timely and accurately update the excitations caused by load-dependent and time-varying nonlinearities inside of the system. The constant bearing stiffness and time-varying bearing alternating stiffness models are introduced and compared with the enhanced bearing excitation force model. The parametric resonant regions and system nonlinear periodic motion states are studied and compared for different bearing supporting models. The effects from internal and external excitations on the system nonlinear vibration behaviors are investigated.

Research on the Influence of Clearance Variation on the Stiffness Fluctuation of Ball Bearing Under Different Operating Conditions

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Bin Fang ◽  
Shaoke Wan ◽  
Jinhua Zhang ◽  
Jun Hong
Keyword(s):  
Ball Bearing ◽  
Dynamic Performance ◽  
Research Work ◽  
Mathematic Model ◽  
Rotor System ◽  
Operating Conditions ◽  
Exploratory Research ◽  
Proposed Model ◽  
Bearing Stiffness ◽  
Control Hypothesis

Abstract The vibration induced by the varying compliance (VC) or the stiffness fluctuation of ball bearing plays a key role in the dynamic performance of the rotor system. The aim of this article is to study the stiffness fluctuation behaviors of ball bearing under different operating conditions. This article presents an improved mathematic model for ball bearing with wider applicability based on the new initial/reference position assumption and the ball-raceway contact/separation determination. The proposed model not only gets rid of the limitations of the raceway control hypothesis but also considers the space constraints of the cage on the balls. The advantages of the proposed model are presented through the typical working condition analysis, and the influences of the internal clearance on the stiffness and stiffness fluctuation of ball bearing under different operating conditions are given and discussed. The results show that bearing stiffness and stiffness fluctuation are determined by the external loads, rotating speeds, and internal clearances together, and properly increasing the axial load can effectively reduce the amplitudes and frequency components of the stiffness fluctuation. As an exploratory research work on the excitation source for the VC vibration of the bearing-rotor system, this article not only explains the complexity and diversity of the rotor VC vibration behavior from another side but also provides new ideas and important supplements for the rotor nonlinear analysis.

Numerical analysis on the static–dynamic coupling influences of parallelism flaw in disc-rod rotor ball bearing system

2017 ◽  
Vol 232 (1) ◽  
pp. 103-112
Author(s):  
Yi Liu ◽  
Heng Liu ◽  
Bowen Fan
Keyword(s):  
Numerical Analysis ◽  
High Speed ◽  
Dynamic Stress ◽  
Ball Bearing ◽  
Three Dimensional ◽  
Dynamic Features ◽  
Dynamic Coupling ◽  
Rotating Speed ◽  
Nonlinear Complexity ◽  
Bearing System

The static–dynamic coupling influences of parallelism flaw are investigated in the disc-rod rotor ball bearing system. Three-dimensional finite element method and a contact solving method are combined to analyze the statics of flawed disc-rod rotor. This analysis shows that parallelism flaw causes mass eccentric and rotation-dependent rotor bow. When these dynamic factors are involved, parallelism flaw promotes the nonlinear complexity in high speed and reduces global stability areas for the flawed disc-rod rotor. Unstable motions are more likely to happen when rotating speed exceeds the critical speed when rotor has a parallelism flaw. The spectrums of flawed rotor are composed of rotating frequency, subharmonic frequency, and their linear combinations. Flawed rotor has a larger bow deformation and orbit size than the ideal rotor. Dynamic stress performs the same property with vibration curves which enables rotors to have the first-order bow deformation. Dynamic stress of flawed rotor is much higher than that of ideal rotor. This paper presents a numerical analysis method to study the static-dynamic features of disc-rod rotor ball bearing system with parallelism flaw.

A New Model for the Relationship Between Vibration Characteristics Caused by the Time-Varying Contact Stiffness of a Deep Groove Ball Bearing and Defect Sizes

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Jing Liu ◽  
Yimin Shao ◽  
W. D. Zhu
Keyword(s):  
Surface Defect ◽  
Ball Bearing ◽  
Contact Stiffness ◽  
Vibration Characteristics ◽  
Time Varying ◽  
Defect Depth ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Length Width ◽  
The Relationship

Vibration characteristics of a deep groove ball bearing caused by a localized surface defect are greatly affected by defect sizes, such as the length, width, and depth. However, effects of the defect depth, the time-varying contact stiffness between the ball and defect, and the relationship between the time-varying contact stiffness and defect sizes have not been considered in previous defect models. In this work, a new defect model considering a new force–deflection relationship is presented to replace the Hertzian force–deflection relationship to describe the ball-line contact between the ball and defect edge. Both the time-varying displacement impulse and time-varying contact stiffness are considered. The relationship between the time-varying contact stiffness and defect sizes is obtained. Effects of defect sizes on the vibrations of the deep groove ball bearing, especially the defect depth that cannot be described by previous defect models, are investigated. The simulation results are compared with those from the previous defect models. The results show that the model developed can predict a more realistic impulse caused by a localized surface defect for dynamic simulation of the deep groove ball bearing. An experimental investigation is also presented to validate the proposed model.

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