Reduced Weight Design of a Flexible Rotor with Ball Bearing Stiffness Characteristics Varying with Rotational Speed and Load

2000 ◽  
Vol 122 (3) ◽  
pp. 203-208 ◽  
Author(s):  
Dong-Soo Lee ◽  
Dong-Hoon Choi
Keyword(s):  
Dynamic Behavior ◽  
Rotational Speed ◽  
High Speed ◽  
Optimization Technique ◽  
System Dynamic ◽  
Design Approach ◽  
Ball Bearings ◽  
Flexible Rotor ◽  
Augmented Lagrange Multiplier ◽  
Stiffness Characteristics

This paper presents an effective design approach for reducing the weight of a flexible rotor in ball bearings with rotational speed and load dependent stiffness characteristics under constraints on the system eigenvalues and bearing fatigue life. Design variables are chosen to be the inner radii of shaft elements, the positions of ball bearings, and the preloads on the bearings. The stiffness characteristics of high speed ball bearings are completely described as functions of applied loads and spin speed, and applied to the dynamic behavior analysis of a rotor-bearing system. A transfer matrix method is used to obtain eigenvalues of the system and an augmented Lagrange multiplier (ALM) method is employed as an optimization technique. A multi-stepped rotor supported by two angular contact ball bearings is analyzed and designed to show the speed and load dependent stiffness effect on the system dynamic behavior and to demonstrate the effectiveness of the proposed optimum design approach. The results show that the effect of the stiffness on the system dynamic behavior is noticeable and that the suggested design approach is effective. [S0739-3717(00)00803-5]

scholarly journals A Dynamic Analysis of a Flexible Rotor in Ball Bearings with Nonlinear Stiffness Characteristics

1997 ◽  
Vol 3 (2) ◽  
pp. 73-80 ◽  
Author(s):  
Dong-Soo Lee ◽  
Dong-Hoon Choi
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Analysis Approach ◽  
Nonlinear Stiffness ◽  
Ball Bearings ◽  
Flexible Rotor ◽  
Combined Loads ◽  
Rotor Bearing ◽  
Stiffness Characteristics ◽  
Bearing System

This paper presents an effective analysis approach for a flexible rotor in ball bearings with nonlinear stiffness characteristics to obtain realistic dynamic behavior results. The ball bearing is modeled in five degrees of freedom and the nonlinear stiffness characteristics of the bearing are completely described as functions of combined loads and spin speed. For dynamic behavior analysis of the nonlinear rotor-bearing system, a transfer-matrix method is iteratively used until the bearing displacements and the shaft displacements at every bearing location converge to the same values. The results show that the nonlinear stiffness characteristics of ball bearings significantly influence system dynamic behaviors and the proposed analysis approach for the nonlinear rotor-bearing system is effective.

Experimental and Numerical Studies on Nonlinear Dynamic Behavior of Rotor System Supported by Ball Bearings

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Changqing Bai ◽  
Hongyan Zhang ◽  
Qingyu Xu
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
High Speed ◽  
Ball Bearing ◽  
Rotor System ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Flexible Rotor ◽  
Nonlinear Dynamic Behavior

Ball bearings are important mechanical components in high-speed turbomachinery that is liable for severe vibration and noise due to the inherent nonlinearity of ball bearings. Using experiments and the numerical approach, the nonlinear dynamic behavior of a flexible rotor supported by ball bearings is investigated in this paper. An experimental ball bearing-rotor test rig is presented in order to investigate the nonlinear dynamic performance of the rotor systems, as the speed is beyond the first synchroresonance frequency. The finite element method and two-degree-of-freedom dynamic model of a ball bearing are employed for modeling the flexible rotor system. The discrete model of a shaft is built with the aid of the finite element technique, and the ball bearing model includes the nonlinear effects of the Hertzian contact force, bearing internal clearance, and so on. The nonlinear unbalance response is observed by experimental and numerical analysis. All of the predicted results are in good agreement with experimental data, thus validating the proposed model. Numerical and experimental results show that the resonance frequency is provoked when the speed is about twice the synchroresonance frequency, while the subharmonic resonance occurs due to the nonlinearity of ball bearings and causes severe vibration and strong noise. The results show that the effect of a ball bearing on the dynamic behavior is noticeable in optimum design and failure diagnosis of high-speed turbomachinery.

scholarly journals Dynamic Performances of Foil Bearing Supporting a Jeffcot Flexible Rotor System Using FEM

Lubricants ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 14
Author(s):  
Benyebka Bou-Saïd ◽  
Mustapha Lahmar ◽  
Ahcène Mouassa ◽  
Bachir Bouchehit
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Point Of View ◽  
Flexible Rotor ◽  
Auxiliary Power ◽  
Partitioned Approach ◽  
Non Linear ◽  
Auxiliary Power Units ◽  
Dynamic Performances ◽  
Air Film

Aerodynamic bearings have received considerable attention in recent decades and are increasingly being used in applications where high speed, low loads and high precision are required. Aerodynamic applications mainly concern auxiliary power units (APU) and air-conditioning machines (ACM). From the industrial point of view, the static and dynamic characteristics of these bearings rotating at very high speed must be determined. According to the literature, studies carried out on this type of bearing consider the elastic deformations of the foils due to the pressure generated in the air film. The linear approach is from time to time adopted for the prediction of the dynamic behavior of these bearings, which is not always justified. This paper aims to present a step towards a better mastery of the non-linear dynamic behavior of a flexible rotor-air bearing system. We will focus on finite element modeling (FEM) of the non-linear isothermal elasto-aerodynamic lubrication problem in the case of a radial bearing operating in a dynamic regime. We will present the effects of rotational speed, unbalance eccentricity, and rotor mass on the non-linear response of rigid and compliant bearings. We use a partitioned approach which treats fluid and structure as two computation domains solved separately; reducing the development time needed for a monolithic code which is difficult to manage when the geometries or the physical properties of the problem to be treated become complex.

Computational-experimental research of the stiffness of high-speed spindles

2020 ◽  
pp. 33-39
Author(s):  
I.A. Zverev
Keyword(s):  
Elastic Deformation ◽  
Experimental Research ◽  
Rotational Speed ◽  
High Speed ◽  
Ball Bearing ◽  
Deformation Model ◽  
Ball Bearings ◽  
Radial Load ◽  
Angular Contact Ball Bearing ◽  
Spindle Unit

The stiffness indices of high-speed spindle units on angular contact ball bearings at high rotational speeds are investigated. It is found, that the spindle rotational speed, radial load, bearing temperature, type and magnitude of the preload in the bearings significantly affect the stiffness of the spindle unit. Keywords: high-speed spindle unit, angular contact ball bearing, elastic-deformation model. [email protected]

scholarly journals Simulation of Wellbore Drilling Energy Saving of Nanofluids Using an Experimental Taylor–Couette Flow System

2021 ◽  
Author(s):  
Masoud Rashidi ◽  
Ahmad Sedaghat ◽  
Biltayib Misbah ◽  
Mohammad Sabati ◽  
Koshy Vaidyan ◽  
...  
Keyword(s):  
Power Consumption ◽  
Energy Saving ◽  
Rotational Speed ◽  
High Speed ◽  
Optimization Technique ◽  
Power Saving ◽  
Total Power ◽  
Total Power Consumption ◽  
Taylor Couette ◽  
Correlated Parameters

AbstractPower consumption of wellbore drilling in oil and gas exploitations count for 40% of total costs, hence power saving of WBM (water-based mud) by adding different concentrations of Al2O3, TiO2 and SiO2 nanoparticles is investigated here. A high-speed Taylor–Couette system (TCS) was devised to operate at speeds 0–1600 RPM to simulate power consumption of wellbore drilling using nanofluids in laminar to turbulent flow conditions. The TCS control unit uses several sensors to record current, voltage and rotational speed and Arduino microprocessors to process outputs including rheological properties and power consumption. Total power consumption of the TCS was correlated with a second-order polynomial function of rotational speed for different nanofluids, and the correlated parameters were found using an optimization technique. For the first time, energy saving of three nanofluids at four low volume concentrations 0.05, 0.1, 0.5 and 1% is investigated in the TCS simulating wellbore drilling operation. It is interesting to observe that the lower concentration nanofluids (0.05%) have better power savings. In average, for the lower concentration nanofluids (0.05%), power was saved by 39%, 30% and 26% for TiO2, Al2O3 and SiO2 WBM nanofluids, respectively. TiO2 nanofluids have better power saving at lower concentrations of 0.05 and 0.1%, while Al2O3 nanofluids have saved more power at higher concentrations of 0.5 and 1.0% compared with their counterpart nanofluids.

Research on modeling and mechanical behaviors of matched angular contact ball bearings

2020 ◽  
pp. 095440622093703
Author(s):  
Jianguo Gu ◽  
Yimin Zhang
Keyword(s):  
Fatigue Life ◽  
High Speed ◽  
Transformation Method ◽  
Axial Position ◽  
Ball Bearings ◽  
Mechanical Behaviors ◽  
Heavy Load ◽  
Rotating Speed ◽  
Proposed Model ◽  
Stiffness Characteristics

In engineering applications, angular contact ball bearings are usually mounted in pairs to accommodate the high-speed and heavy-load conditions. The usability, security, and stability of rotating machinery systems are heavily dependent on the mechanical behaviors of matched angular contact ball bearings. However, few related works about matched bearings have been reported. Consequently, it is of great significance to investigate the mechanical properties of matched bearings. This paper presents an analysis of the stiffness and fatigue life characteristics of matched angular contact ball bearings under axial position preload. First, an improved quasi-static model is proposed by using universal coordinate transformation method to investigate the stiffness characteristics of matched bearings. On basis of this, the fatigue life of matched bearings under running condition can be calculated. Then, the validity of the proposed model is verified via comparison between calculated results with previously published experimental results. Finally, a pair of 7206B bearings is taken as a numerical example to illustrate the application of the proposed model. The effects of bearing configuration form, preload, external loads, rotating speed on the stiffness, and fatigue life of matched bearings are discussed in detail.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Dynamic Damping and Stiffness Characteristics of the Rolling Tire

2001 ◽  
Vol 29 (4) ◽  
pp. 258-268 ◽  
Author(s):  
G. Jianmin ◽  
R. Gall ◽  
W. Zuomin
Keyword(s):  
Dynamic Behavior ◽  
Variable Parameter ◽  
Low Frequency ◽  
Vertical Load ◽  
Frequency Range ◽  
Inflation Pressure ◽  
Vehicle Simulation ◽  
Dynamic Damping ◽  
Speed Range ◽  
Stiffness Characteristics

Abstract A variable parameter model to study dynamic tire responses is presented. A modified device to measure terrain roughness is used to measure dynamic damping and stiffness characteristics of rolling tires. The device was used to examine the dynamic behavior of a tire in the speed range from 0 to 10 km/h. The inflation pressure during the tests was adjusted to 160, 240, and 320 kPa. The vertical load was 5.2 kN. The results indicate that the damping and stiffness decrease with velocity. Regression formulas for the non-linear experimental damping and stiffness are obtained. These results can be used as input parameters for vehicle simulation to evaluate the vehicle's driving and comfort performance in the medium-low frequency range (0–100 Hz). This way it can be important for tire design and the forecasting of the dynamic behavior of tires.

Temperature Rise Prediction of Oil-Air Lubricated Angular Contact Ball Bearings Using Artificial Neural Network

2019 ◽  
Vol 12 (3) ◽  
pp. 248-261
Author(s):  
Baomin Wang ◽  
Xiao Chang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Temperature Rise ◽  
High Speed ◽  
Ball Bearing ◽  
Influence Factors ◽  
Ball Bearings ◽  
Ann Model ◽  
Angular Contact Ball Bearing ◽  
Artificial Neural

Background: Angular contact ball bearing is an important component of many high-speed rotating mechanical systems. Oil-air lubrication makes it possible for angular contact ball bearing to operate at high speed. So the lubrication state of angular contact ball bearing directly affects the performance of the mechanical systems. However, as bearing rotation speed increases, the temperature rise is still the dominant limiting factor for improving the performance and service life of angular contact ball bearings. Therefore, it is very necessary to predict the temperature rise of angular contact ball bearings lubricated with oil-air. Objective: The purpose of this study is to provide an overview of temperature calculation of bearing from many studies and patents, and propose a new prediction method for temperature rise of angular contact ball bearing. Methods: Based on the artificial neural network and genetic algorithm, a new prediction methodology for bearings temperature rise was proposed which capitalizes on the notion that the temperature rise of oil-air lubricated angular contact ball bearing is generally coupling. The influence factors of temperature rise in high-speed angular contact ball bearings were analyzed through grey relational analysis, and the key influence factors are determined. Combined with Genetic Algorithm (GA), the Artificial Neural Network (ANN) model based on these key influence factors was built up, two groups of experimental data were used to train and validate the ANN model. Results: Compared with the ANN model, the ANN-GA model has shorter training time, higher accuracy and better stability, the output of ANN-GA model shows a good agreement with the experimental data, above 92% of bearing temperature rise under varying conditions can be predicted using the ANNGA model. Conclusion: A new method was proposed to predict the temperature rise of oil-air lubricated angular contact ball bearings based on the artificial neural network and genetic algorithm. The results show that the prediction model has good accuracy, stability and robustness.

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