An Approximate Analysis of the Temperature Conditions in a Journal Bearing. Part I: Theory

1984 ◽  
Vol 106 (2) ◽  
pp. 228-236 ◽  
Author(s):  
J. W. Lund ◽  
P. K. Hansen
Keyword(s):  
Heat Conduction Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Computer Time ◽  
Fourier Series Expansion ◽  
Approximate Analysis ◽  
Order Polynomial ◽  
Bearing Sleeve ◽  
Fourth Order Polynomial ◽  
Bearing Part

An analysis is presented for solving the energy equation for a journal bearing film, coupled with the heat conduction equation for the bearing sleeve. The analysis approximates the temperature profile across the film thickness by a fourth order polynomial while the circumferential temperature variation is expressed in terms of a Fourier series expansion. The solution gives the temperatures of the journal, the bearing sleeve, and the lubricant film from which the viscosity distribution can be obtained for use in solving Reynold’s equation. Because the method is quite economic in computer time it should prove useful in practical calculations of journal bearing performance.

An Approximate Analysis of the Temperature Conditions in a Journal Bearing. Part II: Application

1984 ◽  
Vol 106 (2) ◽  
pp. 237-244 ◽  
Author(s):  
J. W. Lund ◽  
J. Tonnesen
Keyword(s):  
Temperature Distribution ◽  
Heat Balance ◽  
Journal Bearing ◽  
Pressure Profile ◽  
Design Parameters ◽  
Experimental Measurements ◽  
Approximate Analysis ◽  
Bearing Sleeve ◽  
The Heat Balance ◽  
Bearing Part

To test the validity of the theory, described in Part I of this investigation, calculations are performed for a cylindrical, two-axial groove journal bearing over a range of loads and speeds. The results give the temperature distribution in the lubricant film and in the bearing sleeve, the journal surface temperature, the heat balance for the bearing, the journal center eccentricity, and the film pressure profile. The calculated results are compared with experimental measurements, and although significant discrepancies are observed, the overall agreement is satisfactory, considering the usual tolerance effects and the uncertainties in defining some of the design parameters

A study of a journal bearing lubricated by couple stress fluids considering thermal and cavitation effects

2002 ◽  
Vol 216 (5) ◽  
pp. 293-305 ◽  
Author(s):  
X-L Wang ◽  
K-Q Zhu ◽  
C-L Gui
Keyword(s):  
Couple Stress ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Fluid Model ◽  
Load Capacity ◽  
Modified Reynolds Equation ◽  
Couple Stress Fluids

A theoretical study of a finite grooved journal bearing lubricated with couple stress fluids is made considering both thermal and cavitation effects. On the basis of the Stokes couple stress fluid model, the modified Reynolds equation and the energy equation are derived and then numerically solved together with the heat conduction equation. The solution to the modified Reynolds equation is determined using the Elrod cavitation algorithm. The effects of couple stress on the performance of a journal bearing are investigated. It is observed that the lubricants with couple stress, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in coefficient of friction but also produce a slight increase in the temperature of lubricants and bush and a slight decrease in the side leakage flow.

Performance characteristics of two-axial groove journal bearing for different groove angles

2018 ◽  
Vol 70 (2) ◽  
pp. 432-443
Author(s):  
K.R. Kadam ◽  
S.S. Banwait
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Pressure Distribution ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Content Type

Purpose Different groove angles are used to study performance characteristics of two-axial groove journal bearing. In this study two grooves are located at ±90º to the load line. The various angles of grooves have been taken as 10° to 40° in the interval of 5°. Different equations such as Reynolds equation, three-dimensional energy equation and heat conduction equation have been solved using finite element method and finite difference method. Pressure distribution in fluid is found by using Reynolds equation. The three-dimensional energy equation is used for temperature distribution in the fluid film and bush. One-dimensional heat conduction equation is used for finding temperature in axial direction for journal. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. There is a drastic change in attitude angle and side flow. Result shows that there is maximum power loss at large groove angle. So the smaller groove angle is recommended for two-axial groove journal bearing. Design/methodology/approach The finite element method is used for solving Reynolds equation for pressure distribution in fluid. The finite difference method is adopted for finding temperature distribution in bush, fluid and journal. Findings Pressure distribution in fluid is found out. Temperature distribution in bush, fluid and journal is found out. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. Research limitations/implications The groove angle used is from 10 to 40 degree. The power loss is more when angle of groove increases, so smaller groove angle is recommended for this study. Practical implications The location of groove angle predicts the distribution of pressure and temperature in journal bearing. It will show the performance characteristics. ±90° angle we will prefer that will get before manufacturing of bearing. Social implications Due to this study, we will get predict how the pressure and temperature distribute in the journal. It will give the running condition of bearing as to at what speed and load we will get the maximum temperature and pressure in the bearing. Originality/value The finite element method is used for solving the Reynolds equation. Three-dimensional energy equation is solved using the finite difference method. Heat conduction equation is also solved for journal. The C language is used. The code is developed in C language. There are different equations which depend on each other. The temperature is dependent on pressure viscosity of fluid, etc. so C code is preferred.

Measured Performance of a Highly Preloaded Three-Lobe Journal Bearing–-Part I: Static Characteristics

1995 ◽  
Vol 38 (3) ◽  
pp. 507-516 ◽  
Author(s):  
David V. Taylor ◽  
Gregory J. Kostrzewsky ◽  
Ronald D. Flack ◽  
Lloyd E. Barrett
Keyword(s):  
Journal Bearing ◽  
Static Characteristics ◽  
Bearing Part

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

Explicit solutions to nonlinear Chen–Lee–Liu equation

2021 ◽  
pp. 2150438
Author(s):  
Lanre Akinyemi ◽  
Najib Ullah ◽  
Yasir Akbar ◽  
Mir Sajjad Hashemi ◽  
Arzu Akbulut ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Phenomena ◽  
Explicit Solutions ◽  
Mathematical Algorithm ◽  
New Exact Solutions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

In this work, a generalized [Formula: see text]-expansion method has been used for solving the nonlinear Chen–Lee–Liu equation. This method is a more common, general, and powerful mathematical algorithm for finding the exact solutions of nonlinear partial differential equations (NPDEs), where [Formula: see text] follows the Jacobi elliptic equation [Formula: see text], and we let [Formula: see text] be a fourth-order polynomial. Many new exact solutions such as the hyperbolic, rational, and trigonometric solutions with different parameters in terms of the Jacobi elliptic functions are obtained. The distinct solutions obtained in this paper clearly explain the importance of some physical structures in the field of nonlinear phenomena. Also, this method deals very well with higher-order nonlinear equations in the field of science. The numerical results described in the plots were obtained by using Maple.

Sign in / Sign up

Export Citation Format

Share Document