ijmet 06 08_005

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 6, Issue 8, Aug 2015, pp. 46-58, Article ID: IJMET_06_08_005

Available online at

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ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

___________________________________________________________________________

EXPERT KNOWLEDGE-BASE SYSTEM FOR

COMPUTER AIDED DESIGN OF FULL

HYDRODYNAMIC JOURNAL BEARING

Anand Kalani

Mechanical Engineering Department,

Government Engineering College Palanpur, India

Sandeep Soni


Sardar Vallabhbhai National Institute of Technology, Surat, India

Rita Jani


Shantilal Shah Engineering College, Bhavnagar, India

ABSTRACT

The design process of hydrodynamic journal bearing involves reading of

various charts and tables of numerical values, causing time consuming and

less accurate results. A program is developed for computer aided design of

hydrodynamic journal bearing.

This program is based on Raimondi and Boyd chart and tables, it is

developed using an integrated methodology for designing of full (360°)

hydrodynamic journal bearings. A database containing the design variables of

load per unit of projected area and bearing clearance in industrial

applications, needed in the bearing design is derived. The performance

parameters including temperature rise, clearance, minimum film thickness and

stability indicate how well the bearing is performing.

The architecture of the software uses a rule based production system, so

certain limitations on their values are imposed, using empirical guidelines, to

assure satisfactory performance. Design optimization is based on maximum

load and minimum friction.

Key words: Expert Knowledge base system, full hydrodynamic journal

bearing, lubricant, Raimondi and Boyd.

Cite this Article: Anand Kalani, Sandeep Soni and Rita Jani, Expert

Knowledge-Base System For Computer Aided Design of Full Hydrodynamic

Journal Bearing. International Journal of Mechanical Engineering and

Expert Knowledge-Base System For Computer Aided Design of Full Hydrodynamic Journal

Bearing


Technology, 6(8), 2015, pp. 46-58.

http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=8

_______________________________________________________________

1. INTRODUCTION

The design of journal bearings is of considerable importance to the development of

rotating machinery. Journal bearings are essential machine components for

compressors, pumps, turbines, internal-combustion engines, motors, generators, etc.

In a journal bearing a shaft or journal rotates or oscillates within a close-fitting

cylindrical sleeve (the bearing) and the relative motion is sliding. The journal and

bearing surfaces are separated by a film of lubricant (liquid or gas) that is supplied to

the clearance space between the surfaces. The clearance space permits assembly of

the journal and bearing, provides space for the lubricant, accommodates unavoidable

thermal expansions and tolerates any shaft misalignment or deflection. The basic

purpose of a journal bearing is to provide radial support to a rotating shaft. Under

load, the centre of the journal and the bearing are separated by a distance called

eccentricity. This eccentric arrangement establishes a converging wedge geometry,

which is conjunction with the relative motion of the journal and the bearing permits a

pressure to be developed by viscous effects within the thin fill of lubricant and thus

produces a load carrying capability. [1]

Journal bearings are termed full bearings when the bearing surface completely

surrounds the journal (Figure 1). As they are inexpensive and easy to manufacture,

full journal bearings are the most commonly used bearings.

Figure 1 Full Journal Bearing

Hydrodynamic or fluid film bearing is having load carrying surfaces separated by

a relatively thick film of lubricant, so as to prevent metal-to-metal contact, and that

the stability thus obtained can be explained by the laws of the fluid mechanics. This

lubrication does not depend upon the introduction of the lubricant under pressure,

though that never occurs; but it does require existence of an adequate supply of oil at

all times. The film pressure is created by the moving surface itself pulling the

lubricant into a wedge-shaped zone at a velocity sufficiently high to create the

pressure necessary to separate the surfaces against the load on the bearing.

Hydrodynamic journal bearings are so called self-acting bearings.

The mathematical theory of hydrodynamic lubrication is based upon Reynolds

work [2]. Therefore, the differential equation governing the pressure in the lubricating

film is called the Reynolds equation.

The Reynolds equation for most machine design applications for a steadily

running bearing is given by [Equation 1]

http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=7

Anand Kalani, Sandeep Soni and Rita Jani


(Equation 1)

Generally, three types of circumferential boundary conditions are applied in

solving the Reynolds equation. They are Sommerfield, Gumbel and Swift-Stieber

conditions [3].

In case of long bearings, here L/D > 2, the pressure does not change in the axial

direction (z-axis), i.e. there is no side leakage. Therefore, neglecting the axial pressure

flow term, Equation 1) reduces to

(Equation 2)

which is the classical Reynolds equation for one-dimensional flow. This equation

has been solved by Sommerfield and Gumbel.

In case of short bearings (L/D < 1/4), all of the entering lubricant is diverted to

side leakage. Under this condition the axial pressure flow in the z-direction will

dominate over the circumferential flow in the x – direction. Also ‘h’ is usually not a

function of z (only a function of x). Therefore the Reynolds equation may be written

as

(Equation 3)

This is known as Ocvirk equation. If the boundary conditions are taken as (i) at z

= 0, dp/dz=0 (symmetry about z = 0) and (ii) at z = ± L/2, p = 0, then Equation 1) may

be expressed as

(Equation 4)

The notations used in Equation 1 – 4 are:

p = film pressure

U = surface speed of the shaft

h = variable film thickness

x = co-ordinate in the direction of motion

z = co-ordinate in the axial direction

µ = absolute viscosity of the lubricant

L = axial bearing length

For finite-length of bearings (1/4 ≤ L/D ≤2) has been solved by many researchers.

Reason and Narang [6, 7] proposed an approximate technique to design steadily

loaded journal bearings on hand held calculator that makes use of both and short

bearings theories. They consider the film pressure ‘p’ as the harmonic mean of the

short-bearing pressure PS and the long-bearing pressure PL i.e.

(Equation 5)

The pressure and various performance parameters obtained with the help of this

combined solution approximation [3]. These parameters are written in terms of IS and

IC.

However, common practice is to use design charts for representing bearing

performance data. The most commonly used set of design charts was constructed by

Raimondi and Boyd [1, 4, 5]. The present work makes use of the charts and tables

given by them [1,4, 5] in developing the required knowledge for designing journal


Bearing


bearings. Film rupture has been considered in preparing these charts. An attempt is

made to present the knowledge in proper form to be used as knowledge bases in the

present expert system.

2. EXPERT SYSTEM

Expert systems (ES) are a branch of applied artificial intelligence (AI), and were

develop by the AI community in the mid-1960s. The basic idea behind ES is simply

that expertise, which is the vast body of task-specific knowledge, is transferred from a

human to a computer. This knowledge is then stored in the computer and users call

upon the computer for specific advice as needed. The computer can make inferences

and arrive at a specific conclusion. Then like a human consultant, it gives advices and

explains, if necessary, the logic behind the advice. ES provide powerful and flexible

means for obtaining solutions to a variety of problems that often cannot be dealt with

by other, more traditional and orthodox methods. Thus, their use are proliferating too

many sectors of our social and technological life, where their applications are proving

to be critical in the process of decision support and problem solving [6]. Since an

expert system (ES) uses domain specific knowledge bases, it is often called a

knowledge based expert system (KBES). Since KBES uses a search-inference

framework to solve a problem, it thinks like a domain specific expert. A KBES

consists of domain specific knowledge bases, an inference engine and a user interface.

The user interface provides necessary explanation of the actions of KBES if asked by

a non-expert user. It the program is designed to help an expert, it is called a design

assistant (DA) where the users interface need not be as elaborate as that of KBES.

A Rule-based ES is defined as one, which contains information obtained from a

human expert, and represents that information in the form of rules, such as IF–THEN.

The rule can then be used to perform operations on data to inference in order to reach

appropriate conclusion.

3. PRESCRIPTIVE AND FUNCTIONAL SPECIFICATIONS

The basic form of a journal bearing is shown in Figure 2. While designing journal

bearings, one may distinguish between two groups of variables [6].

Figure 2 Basic Form of a Journal Bearing



The first group consists of dependent variables:

The load per unit of projected bearing area P (= W/LD),

Bearing industrial-application for selecting the allowable range of the clearance,

lubricant inlet temperature,

L/D ratio,

SAE grade of the lubricant,

viscosity µ, and

Bearing dimensions (diameter D, length L, clearance C, and bearing arc β).

They are prescriptive variables and may be controlled by the designer.

The second group consists of dependent variables:

Load W

Speed N

Sommerfield number (bearing characteristics number) S

Coefficient of friction f

Temperature rise ΔT

Minimum film thickness hm

Eccentricity ratio ε

Attitude angle Φ

Oil flow Q

Side leakage QS

Maximum pressure Pmax

Position of maximum film pressure θ Pmax

Position at which film terminates θ P0

Angle from line of centre to start of film θ A

Torque required or power lost.

These variables may be regarded as functional specifications. The designer cannot

control these except indirectly by changing one or more of the first group, but must

impose certain limitations to assure satisfactory performance.

The fundamental problem in bearing design, therefore, is to define satisfactory

limits for the second group of variables and then to decide upon values for the first

group such that these limitations are not exceeded, then the design is complete.

4. RAIMONDI AND BOYD METHOD

The objective knowledge required for designing full journal bearings for the

maximum load (W) and the minimum friction (f) is collected from the following

sources: Raimondi and Boyd, Standard Handbook of Machine design- Shigley,

Orthewein, Juvinall and Design data book – PSG. The values of h0/C taking film

rupture into account for full journal bearings at L/D = 0.25, 0.5, 1 and are given by

Raimondi and Boyd [4, 5] or can be obtained from Shigley’s Chart as shown in Figure

3. The data here is taken from Design Data book PSG [7].

The desired values of all the performance variables can be found by applying it in

Equation 6 given by Raimondi and Boyd:


Bearing


Figure 3 Chart for minimum film-thickness variable and eccentricity ratio

(Equation 6)

Where, y = desired performance variable and the subscript of y is the L/D ratio at

which the variable is being evaluated.

The values of the performance variables are shown in Table 5.1 for at L/D = 0.25,

0.5, 1 and .

The performance variables found are as follows:

Sommerfield number (bearing characteristics number) S

Minimum film thickness ratio h0/C

Attitude Angle i.e. angle at which minimum film thickness is attained Φ

Friction coefficient variable f(r/C)

Total bearing flow rate variable Q/rCNL

The ratio of side flow rate (in z-direction) to the total flow rate QS/Q

Average to maximum pressure ratio P/Pmax

Position of maximum pressure(in degree) θpmax

Termination of pressure wave angle (in degree) θp0

Dimensionless temperature rise variable ρCΔT/P

Table 1 Values of the Performance Variables for L/D = 0.25, 0.5, 1 And .

L/D S h0/C f(r/C) Φ Q/rCNL QS/Q P/Pmax θpmax θp0 ρCΔT/P

Corresponding values to Max. W condition

0.08 0.66 1.75 63 2.53 0 0 0 113 9.5

1 0.21 0.53 4.9 59 4.1 0.56 0.47 17.4 86 20

0.5 0.345 0.43 9.0 48.8 4.8 0.718 0.374 17.5 66 36

0.25 0.5 0.27 13.8 36.4 5.3 0.848 0.272 13.7 45.3 40

Corresponding values to Min. f condition

0.0389 0.6 1 54.31 1.56 0 0 0 86 9.73

1 0.08 0.3 2.35 43.7 4.48 0.76 0.365 18.9 64 11

0.5 0.04 0.12 1.875 25.2 5.65 0.932 0.21 11.7 35 37

0.25 0.01 0.03 0.91 12.6 6.12 0.99 0.11 4.4 18 3.73



4.1 VISCOSITY – TEMPERATURE RELATIONSHIPS

For computer applications, the viscosity-temperature function for lubricants is given

by the Reynolds equation [8].

(Equation 7)

Different stages of the program for designing full journal bearings for the

maximum load W and the minimum friction f are described below.

4.2. STAGE – I

The stage – 1 is divided in two parts as shown in Figure 4.

Design Criteria

Maximum Load W

Minimum Friction f

Types of journal bearing

Full Journal bearing ( 0 )

Partial ournal bearing ( 1 0 )

Partial ournal bearing ( 120 )

Partial ournal bearing ( 0 )

4.3. STAGE – II

The 2nd

stage contains

Allowable bearing pressure values according to the application of the bearing.

Figure 5 Stage – II

The values of allowable bearing pressure of the bearing are to be selected from the

menu or the user can feed the required data as per his requirement by clicking on the

‘ADD’ button as shown in figure – 6 & 7.

Diametrical clearance as per the application of the bearing.

The values of diametrical clearance of the bearing are to be selected from the

menu or the user can feed the required data as per his requirement by clicking on the

‘ADD’ button as shown in figure – 7.


Bearing


Figure 6 Data entering window for Allowable Bearing Pressure

Figure 7 Data entering window for Diametrical Clearance

4.4. STAGE – III

In this stage the basic data of the bearing is to be entered as shown in figure – 8.

Figure 8 Stage - III

1. Bearing Load [kN]

2. Speed [RPM]

3. nlet Temperature of lubricant C]

4. The type of lubricant is to be selected from the menu of lubricant. The user can enter

own data other than the data that is in the database of software by clicking the ‘ADD’

button as shown in figure – 8.

Figure 9 Data entering window for Lubricants



The L/D ratio of the bearing is set according to the application selected for

allowable bearing pressure in stage – 2, but the range values of L/D can be edited as

per the requirement. The increment value of L/D for solution is prefixed at 0.1 which

is also editable as per the requirement.

By clicking the solve button the software generates the result as per the data

entered.

The performance parameters of the journal bearing are calculated.

4.5. STAGE – IV

The output of the data entered is shown in this stage on the basis of the L/D ratios.

The output is all the performance variables:

Sommerfield number (bearing characteristics number) S.

Minimum film thickness ratio h0/C.

Attitude Angle i.e. angle at which minimum film thickness is attained Φ.

Friction coefficient variable f(r/C).

Total bearing flow rate variable Q/rCNL.

The ratio of side flow rate (in z-direction) to the total flow rate QS/Q.

Average to maximum pressure ratio P/Pmax.

Position of maximum pressure (in degree) θpmax.

Termination of pressure wave angle (in degree) θp0.

Dimensionless temperature rise variable ρCΔT/P.

The feasibility criteria are checked in this stage.

Temperature Criteria

The goal is to obtain all partial feasible solutions which fulfill the outlet temperature

condition that is Tout ≤120° C. Each partial feasible solution of this stage consists of

L/D ratio, length, diameter, all ten performance variables.

Figure 10 Stage – IV

To achieve this goal following sets of rules and database are used:

A knowledge base consisting of all the performance variables corresponding to L/D

ratio (1/4 ≤ L/D ≤ ) rest of the L/D ratios are obtained by Raimondi interpolation

equation.

A set of rules to check whether or not the calculated outlet temperature in each case is

below 120° C.


Bearing


If no partial solutions within the desired outlet temperature limit is obtained this

condition may be modified to act as a failure handler. The value of output temperature

is prefixed at 120 C, but it can edit according to the working environment of the

journal bearing. The solution which has output temperature less than the required

temperature are retained and other solution are discarded and

Clearance Check

The value of clearance is set according to the application set for diametrical

clearance in stage – 2.

The final goal is to determine the clearance and check whether this in the

prescribed range for each partial solution.

The clearance is determined from c/r = 1000 +0 .4 V1/2

, where v is in m/s.

Values of the clearance can be edited as per the requirement of the user which acts as

a failure handler when no partial solution is within the range.

Minimum Film thickness Check

The goal is to determine whether or not each of the partial solutions satisfies the

minimum film thickness criterion given by Juvinall [9] that is, for a factor of safety of

2, h0 ≥ 0.005 + 0.00004D (h0 and D are in mm).

The check is done for h0 whether it is in the acceptable range.

Stability check

The final goal is to determine whether or not each of the remaining partial solutions is

stable.

A set of rules to check whether the design solution lies in the stable range i.e. either ε

≥ 0. or ωs ≤ 2. ( , ω = 2πN)

At this time all the database of the partial solutions are erased and a new set of

database is written which have passed all the constraint giving a final solution.

The final solutions of the in the data base can be export to excel sheet which aids

for further analysis and charting.

4.6. STAGE – V

At this stage report is generated in tabulated form of the all the final feasible solutions

which can be exported in following formats:

Pdf

Word

Figure 11 Stage – V



4.7. STAGE – VI

This is the visual stage where the output values calculated from the performance

parameters of the all the feasible solution is visualized and this data can be exported

to excel sheet for further analysis and charting.

Figure 12 Stage – VI

The output of the performance parameters:

Minimum Film Thickness h0 = C x Minimum film thickness ratio h0/C

Coefficient of friction f = (C/r) x Friction coefficient variable f(r/C)

Flow Rate Q = nRCL x Total bearing flow rate variable Q/rCNL

Side Leakage QS = Q x ( QS/Q)

Maximum Pressure Pmax = P x Average to maximum pressure ratio P/Pmax

4.8. STAGE – VII

This is the final stage of the software where report of all the feasible solution along

with the calculated output is generated and can be exported for further reference.

Figure 13 Stage – VII

4.9. EXAMPLE

The following data is given for a 0 hydrodynamic journal bearing. [7]

(Uses Raimondi and Boyd Method)


Bearing


Radial load = 3.2kN; Journal speed = 1490 rpm; Unit Load P = 1.28 Mpa; Inlet

temperature = 22 C

Density of lubricant = 860 kg/m3 pecific heat of lubricant = 1 0 /kg C.

The output of the software under optimized condition of maximum load W and

minimum friction f is as shown in table 2:

Table 2 Comparison of output of full journal bearing

Parameters

Calculated

output of

book

Software output

Maximum Load

Condition

Minimum

Friction

Condition

Diameter of bearing 50mm 50mm 50mm

Length of bearing 50mm 50mm 50mm

L/D ratio 1 1 1

Radial Clearance 0.05mm 0.07mm 0.126mm

Sommerfield No. S 0.121 0.21 0.08

Eccentricity ratio ε 0.6 0.47 0.7

Friction Variable [f (R/C)] 3.22 4.9 2.35

Flow Rate Variable [Q/RCNL] 4.33 4.1 4.48

Side Flow to Total Flow Rate

[Qs/Q] 0.68 0.56 0.76

Minimum oil thickness h0 0.02 mm 0.0418mm 0.0383mm

Coefficient of friction f 0.00644 0.0154 0.0120

Power lost in friction Pf 0.0804 kW 0.1928 kW 0.1498 kW

Total flow rate of lubricant 0.4032 l/min

0.601 l/min

10027.1152

mm3/sec

1.065 l/min

17751.490

mm3/sec

Side leakage 0.2742 l/min

0.337 l/min

5615.1845

mm3/sec

0.809 l/min

13491.1325

mm3/sec

Temperature rise 11. C 1 . 1 C . 0 C

5. CONCULSIONS

Expert knowledge base systems for designing full hydrodynamic ournal bearings

and a system for designing partial arcs ournal bearings 1 0 , 120 and 0 using an

integrated and dependable design methodology is successfully developed. The

relevant knowledge bases are collected or derived using the established facts. All the

data bases obtained are represented in appropriate forms and found to be efficiently

used by the expert system.

The expert system employs rule based production system and the architecture

consists of several stages. The rules and the data bases of each stage are properly

grouped. At any stage, if there is no design solution, proper failure handler may be

devised. The expert system software uses the computer efficiently.

The time and error for designing journal bearing is considerably reduced by this

expert system.



6. FUTURE SCOPE

The following recommendations are made for future research work in this area:

The knowledge base used for finding stiffness and damping coefficients is only for

full journal bearings; therefore an adequate knowledge base is to be generated for

partial bearings.

From the manufacturing point of view, tolerances on bearing diameter and may also

be specified.

If an expert is available for developing a real time monitoring software which can be

synchronized with an operating journal bearing along with the sensors than it can act

as an Artificial Intelligent system.

7. REFERENCES

[1] E. Shigley and C.R. Mischke, Journal Bearings, in Standard Handbook of

Machine Design, 2nd

edition , J. McGraw-Hill, Inc., New York, 1986.

[2] Avrahom Harnoy, Bearing Design in Machinery: Engineering Tribology and

Lubrication, Marcel Dekker, Inc. New York, 2003.

[3] Raimondi A.A. and Boyd J., A Solution for the Finite Journal Bearing and its

Application to analysis and Design: II, ASLE Transactions, 1(1), 1958, pp 175 –

193.

[4] Raimondi A.A. and Boyd J., A Solution for the Finite Journal Bearing and its

Application to analysis and Design: III, ASLE Transactions, 1(1), 1958, pp 194 -

209.

[5] Shu-Hsien Liao, Expert system methodologies and applications—a decade

review from 1995 to 2004, Expert system with application, Issue 28, 2005, pp 93

– 103.

[6] E. Shigley and C.R. Mischke, Lubrication and Journal Bearings, in Mechanical

Engineering Design, 6th edition, Tata McGraw-Hill, Inc., New Delhi, 2003.

[7] Design Data – Data Book of Engineers, PSG College of Technology, Coimbatore.

[8] Darko Knezevic and Vladimir Savic, Mathematical Modeling of Changing of

Dynamic Viscosity, as a Function of Temperature and Pressure, of Mineral Oils

for Hydraulic Systems, Facta Universitatis, Mechanical Engineering, 4(1), 2006,

pp 27-34.

[9] Juvinall Robert C. and Marshek Kurt M., Fundamentals of Machine Component

Design, John Wiley and Sons, Inc., 4th edition, 2005.

[10] Anand Kalani and Rita Jani, Novel Double Roller Bearing Fe Analysis And

Comparison With Conventional Double Row Cylindrical Roller Bearing.

International Journal of Design and Manufacturing Technology, 6(2), 2015, pp.

19-29.