A Dynamic Model for Vibration Studies of Deep Groove Ball Bearings Considering Single and Multiple Defects in Races

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
V. N. Patel ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Dynamic Model ◽  
Experimental Results ◽  
Ball Bearings ◽  
Governing Equations ◽  
Multiple Defects ◽  
Runge Kutta Method ◽  
Deep Groove ◽  
Frequency Domains ◽  
Coupled Solution ◽  
Equations Of Motions

A dynamic model is reported herein for the study of vibrations of deep groove ball bearings having single and multiple defects on surfaces of inner and outer races. Masses of shaft, housing, races, and balls are considered in the modeling. The coupled solution of governing equations of motions is obtained using Runge–Kutta method. The model provides the vibrations of shaft, balls, and housing in time and frequency domains. Computed results from the model are validated with experimental results, which are generated using healthy and defective deep groove ball bearings. Characteristic defect frequencies and its harmonics are broadly investigated using both theoretical and experimental results. Comparison of vibration spectra for the cases having single and two defects on races reveals relatively higher velocity amplitudes with two defects. Good correlations between theoretical and experimental results are observed. Authors believe that this dynamic model can be used with confidence for the study and prediction of vibrations of healthy and defective deep groove ball bearings.

Vibration Characteristics for Planetary Geared Systems with Plastic Gears

2015 ◽  
Vol 713-715 ◽  
pp. 77-84
Author(s):  
Jian Ying Li ◽  
Qing Chun Hu ◽  
Fu Hai Duan
Keyword(s):  
Dynamic Model ◽  
High Frequency ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Frequency Spectra ◽  
Gear Mesh ◽  
Runge Kutta Method ◽  
Variable Step ◽  
Planet Gear ◽  
Plastic Gears

A torsional dynamic model and testing model for planetary geared systems are established to study the effects on its vibration characteristics as substituting plastic gears for steel ones successively. The dynamic model is solved by using variable step Runge-Kutta method and the vibration testing experiments for four kinds of combined planetary geared systems are carried out under different rotation speed and load torque. The numerical and experimental results show that the high frequency spectra are suppressed effectively as substituting plastic gears for steel ones. The gear mesh dynamic load and vibration intensity caused by the meshing fundamental frequency and side-frequency reduce markedly when the plastic ring and planet gear substitute for steel ones together. The numerical simulations have a better consistency with the experimental results, which verifies the correctness of the conclusions.

scholarly journals Experimental Study for Vibration Behaviors of Locally Defective Deep Groove Ball Bearings under Dynamic Radial Load

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
V. N. Patel ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Good Health ◽  
Ball Bearings ◽  
Radial Load ◽  
Rolling Bearings ◽  
Revolute Joints ◽  
Deep Groove ◽  
Frequency Domains ◽  
Rolling Element ◽  
Vibration Responses ◽  
Local Defects

Rolling element bearings are used in many mechanical systems at the revolute joints for sustaining the dynamic loads. Thus, the reliable and efficient functioning of such systems critically depends on the good health of the employed rolling bearings. Hence, health monitoring of rolling bearings through their vibration responses is a vital issue. In this paper, an experimental investigation has been reported related to the vibration behaviours of healthy and locally defective deep groove ball bearings operating under dynamic radial load. The dynamic load on the test bearings has been applied using an electromechanical shaker. The vibration spectra of the healthy and defective deep groove ball bearings in time and frequency domains have been compared and discussed. Overall vibration increases in presence of local defects and dynamic radial load.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

A modified Runge-Kutta method

SIMULATION ◽  
1968 ◽  
Vol 10 (5) ◽  
pp. 221-223 ◽  
Author(s):  
A.S. Chai
Keyword(s):  
Error Estimate ◽  
Linear Combination ◽  
Experimental Results ◽  
The Other ◽  
New Method ◽  
Kutta Method ◽  
Starting Values ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
A Minor

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values. Experimental results are shown in verification of the for mula.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

2021 ◽  
pp. 1-29
Author(s):  
Ahmet Dindar ◽  
Amit Chimanpure ◽  
Ahmet Kahraman
Keyword(s):  
Dynamic Model ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Mechanical Power ◽  
Ball Bearings ◽  
Power Losses ◽  
Euler Parameters ◽  
Surface Shear ◽  
Axial Forces ◽  
Set Up

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces, and (ii) a singularity-free dynamics model, and establishes the two-way coupling between them that dictates power losses. The dynamic model employs a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental set-up is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared to those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

DESIGN AND DEVELOPMENT OF AN EFFICIENT COMPUTER SIMULATION MODEL FOR RESPONSE ANALYSIS OF A MOORED SEMI-SUBMERSIBLE

2021 ◽  
Vol 161 (A1) ◽  
Author(s):  
V Domala ◽  
R Sharma
Keyword(s):  
Computer Simulation ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Experimental Results ◽  
Response Analysis ◽  
Computer Simulation Model ◽  
Governing Equations ◽  
Design And Development ◽  
Mooring Lines ◽  
Steel Wires

This paper presents the design and development of an efficient modular ‘Computer Simulation Model (CSM)’ for response analysis of a moored semi-submersible. The computer simulation model is designed in two split models (i.e. computational and experimental models) and each of these models consists of various modules. The modules are developed from basic governing equations related to motion and modules are integrated and we aim for a seamless integration. The moored semi-submersible is represented mathematically as six degrees of freedom dynamic system and the coupling effects between the structure and mooring lines are considered. The basic geometric configuration of semi- submersible is modelled and analyzed for stability computations in MS-Excel*TM and then the basic governing equations related to motion are modelled mathematically in a module and solved numerically with Ansys-AQWA**TM. The computational model is validated and verified with some available experimental results. The CSM is utilized to study the surge and sway responses with respect to the horizontal range of mooring lines and our results show good validation with the existing experimental results. Our presented results show that the fibre wires have minimum steady state response in surge and sway degrees of freedom as compared with the steel wires. However, they have large drift as compared with steel wires. Finally, we show that the computer simulation model can help in detailed analysis of responses and results can be utilized for design and development of new age semi-submersibles for optimum performances for a given set of parameters.

Experimental Vibration Studies of Deep Groove Ball Bearings Having Damaged Surfaces

2018 ◽  
Vol 100 (6) ◽  
pp. 919-935 ◽  
Author(s):  
Dipen S. Shah ◽  
V. N. Patel ◽  
Pranav H. Darji
Keyword(s):  
Ball Bearings ◽  
Deep Groove
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