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An intelligent design system for recessed hydrostatic journal bearings
Wear, 159 (1992) 95-105
95
An intelligent design system for recessed hydrostatic journal bearings W. B. Rowe, School
of Engineering
(Received
December
K. Cheng and
and D. Ives
Technology
Management,
9, 1991; revised and accepted
The Liverpool
Polytechnic,
Byrom
Street, Liverpool
L3 3AF
(UK)
April 24, 1992)
Abstract This paper is intended to demonstrate the power of HYPERCARD for intelligent knowledge-based design applications. The system is also educational and is a practical aid to basic design of recessed hydrostatic journal bearings. The system is built with a new design method which integrates an artificial intelligence (AI) technique
with a conventional bearing design technique. The AI technique is used to assist with numerical and also qualitative decisions. The system primarily consists of three intelligent design modules: a basic design module; a singleconstraint optimal design module; and a multi-constraint optimal design module. Any one of these three modules can be used to complete the bearing design work. The system is implemented on the HYPERCARD software of the Macintosh computer. Operation of the system shows that an appropriate recessed hydrostatic journal bearing design can easily be achieved with the system.
1. Introduction Hydrostatic journal bearings have been extensively studied during the last thirty years and many papers on operation and design principles have been published. Broadly speaking, design methods may be classified as manual or computer aided. The manual method uses design rules and graphic data or equations. Computer aided design allows greater sophistication in the optimization process [14]. The development of personal computers has accelerated the trend towards use of computer programs to aid bearing design, especially to aid the computation and optimization of the values of bearing parameters. However, effective design of a hydrostatic journal bearing is still not a simple task for many design and manufacturing engineers. With the first method, many complicated functions have to be considered in the decision making process of the design, and these functions are normally available in the form of multi-dimensional graphs and equations. The second method, which can free the designer from complicated design computation, focuses on the numerical requirements of optimizing the parameters of a proposed hydrostatic journal bearing. Computer-aided bearing design programs typically use general purpose scientific languages such as FORTRAN or PASCAL. It is hard for the programs written in these languages to consider qualitative issues, such as determining the most suitable type or configuration of bearing, evaluating the compatibility of the proposed solutions during the
0043-1648/92/$5.00
design procedure and providing suggestions, etc. It is therefore of practical relevance to develop a bearing design system using artificial intelligence (AI) which considers both numerical and qualitative issues. AI is a branch of computer science concerned with the design and implementation of software which is capable of emulating human cognitive skills such as problem solving, visual perception and language understanding. AI-based software falls into three basic categories: expert (or knowledge-based) systems; perception systems; and natural language systems. Expert systems, or more generally, knowledge-based systems, are more commonly employed in engineering [5]. This paper presents an intelligent system for the design of recessed hydrostatic journal bearings. The system is built with a new design method which integrates AI with conventional bearing design methods. The system makes it possible for the bearing design to take into account numerical and qualitative issues. The system includes three intelligent design modules: a basic design module, a single-constraint optimal design module; and a multi-constraint optimal design module. The designer can choose any one of them to do the bearing design. The system combines AI with each module and the AI covers the whole design procedure for a bearing. The system is implemented on the HYPERCARD software tool of the Macintosh computer. With this system, an appropriate recessed hydrostatic journal bearing design can easily be achieved. The system
0 1992 - Elsevier Sequoia. All rights reserved
W. B. Rowe et al. I Intelligent design Jystem for hydrostatic journal bearings
96
described is one part of a larger knowledge-based bearing design package which is being developed on an experimental basis at The Liverpool Polytechnic.
2. Recessed
hydrostatic
journal
bearings
Of the hydrostatic bearing configurations for spindle applications, the recessed hydrostatic journal bearing configuration is probably the most commonly employed. Two typical configurations are shown in Fig. 1. One configuration is with axial drain slots between the recesses, the other is without axial drain slots. The axial drain slots in a non-rotating bearing allow the recesses to operate independently of the neighbouring recesses. For the same clearance, flow rate is increased compared to a bearing without axial slots, a feature which is often considered undesirable. Inappropriate axial slot design may seriously detract from the bearing’s load carrying capacity. Axial slots also increase the complexity of bearing manufacture. The bearing configuration with axial drain slots is therefore less commonly employed for higher speed applications. The design strategy is made up of several stages. A general design strategy for the bearings is described as follows [6]: (i) Choose the bearing configuration, i.e., a bearing configuration with axial drain slots or without.
(ii) Determine the basic bearing parameters constrained by the machine design, for example load W, diameter D, length L, shaft rotation speed N. (iii) Determine the basic bearing parameters which are, if possible, selected according to rules where these are available for optimal design or ease of manufacture; for example number of recesses n; land/width ratio al L; inter-recess land/width ratio b/u; length/diameter ratio L/D; radial bearing clearance h,; concentric pressure ratio j3; concentric power ratio K; axial drain slot width c, if axial drain slots are to be used. (iv) Determine the basic bearing parameters which must be calculated; for example, supply pressure P,, from P,= W/(0’@, where J&’is provided as computed data; viscosity q,
(v) Calculate the bearing performance data; for example, stiffness A; flow rate q; pumping power HP; total power H,; maximum temperature rise AT. In addition, the relevant control device and its dimensions have to be determined. The control device governs bearing stiffness and will commonly be one of the following types: capillary control; slot control; orifice control; and diaphragm valve control. Capillaries are an example of simple laminar-flow restrictors. Compared with other types, capillary restrictors have the advantages of manufacturing simplicity and also that the bearing load and stiffness are independent of fluid viscosity and hence of temperature rise. For this reason, capillary tube control has become popular for recessed hydrostatic journal bearings. The general design strategy of a recessed hydrostatic journal bearing.can also be illustrated in the form of a flow chart as shown in Fig. 2. The intelligent system has been developed to complete the design work following the basic strategy outlined in this chart but with alternative algorithms to undertake the computation of calculated parameters depending on which optimization routines has been adopted.
3. Description
Fig. 1. Two typical configurations bearings. (a) Without axial slots axial slots.
of recessed hydrostatic between recesses and
journal (b) with
of the system
The intelligent design system includes three intelligent design modules as illustrated on the system menu card in Fig. 3. The first is the basic design module, based on the general design procedure of a recessed hydrostatic journal bearing described in the previous section. The second is the single-constraint optimal bearing design module. The third is the multiconstraint optimal bearing design module. Both of the optimal design modules are developed on the same basis as the first and take the maximum stiffness, the minimum power dissipation
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
Determine
DetermIne
reStriCtOrS:
(a) Capillary tube (b) Slot (c) Orifice (d) Diaphragm
Calculate
valve
+bearing parameters
p., rl bearing dimension
Modify
t
parameters:
a, b, c, D, L No
Calculate
bearing performance
the bearing configuration
-3
Calculate
2. Flow
Fig.
a
chart
based on‘
and reStriCtOr:
1
restrictorparameters
of the bearing
general
design
liquid film journal (Click
Orthographic
Technical
Fig.
3. The
procedure.
of recessed cylindrical
Design
required
icons,
Projection
Drawing
system
menu
buttons
97
with a mouse. The system is one part of a larger knowledge-based bearing package which includes other parts such as intelligent selection of bearing configuration and its controlling device type, bearing database, general description of bearing, and designer’s on-line help, etc. The different parts within the package are connected to each other in an organic way. The larger bearing design package can be operated on all types of Apple Macintosh computers, but needs 1.8 Mb of memory for the system as designed so far.
bearing parameters.
one of following
bearings
and character
bearing titles)
I
l Single-constraint optimization based on minimum power dissipation. * 2. nulti-constraint optimization based on minimum power, maximum stiffness and yinimum temperature Vse.
card.
and the minimum temperature rise as the bearing optimization objectives. In each module, AI is incorporated into the procedure for bearing design defined by Fig. 2. The icons, buttons and character titles on the menu card are selected by the user as required. A designer can enter any module by just clicking it
3.1. Sojhare tool selection There are two principal classes of software tool used to develop intelligent systems with AI. Class 1 uses a general purpose AI language such as LISP or PROLOG. These languages are the most frequently used for logic programming. The other class is based on the use of an expert system shell. The latter approach is becoming popular in knowledge engineering. With a shell, it is possible to build a working system very quickly. However, both classes of software tool have limitations in their ability to cope with complicated numerical computations [71* HYPERCARD is not an application program, such as a word processing package, a spreadsheet package or a database package; nor is it an expert system shell. It is, rather, a software engine, a hypermedia toolkit [8]. HYPERCARD is now available as a standard software and is provided with every Macintosh computer. The key to HYPERCARD’s authoring environment is HYPERTALK, a programming language built into HYPERCARD and designed around a natural sounding English language. Like traditional programming language, such as C or PASCAL, HYPERTALK contains features such as looping structure, variables, if-then statements, and input-output ability. Moreover, HYPERTALK can create symbolic manipulation programs with the scripts attached to HYPERCARD objects such as buttons, fields, cards, backgrounds and stacks. Programs written in HYPERTALK can cope with quite complicated numerical computation and also logic operations. For this reason HYPERCARD may be conveniently employed to construct various informationbased application programs. Other features which are useful in constructing a powerful intelligent system with HYPERCARD are its painting tools, its ability to alternatively hide and display information, and its Macintosh user-friendly WIMP interface. (WIMP is derived from windows, icons, menus and pointing, and is a radical step forward in designing intelligent computer system [9].) 3.2. Basic design module The basic design module is based on a general design procedure for a recessed hydrostatic journal bearing.
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
98
resign I) From the input data, decide diameter D IO J(W/O 17Ps)~~~mm 2) For optimum, land wdth B should be lal= L/4=mmm 3) Under the condltlon of s/L=0 25, CIrcumferentlal-flow
Please input values of the beanng p~mmeter~ Dunn! Input, the system Will gI”e adwe When fvwhed, please chck ‘Design’ to enter the deslg” procedure 1. Basic parameters constrained by machine design: Beanng d,ameter D=j90jmm Extreme load W.=mN Beanng length L.~mm Shaft ntatlon speed N=mi~m 2 Selected basic parametersAxial-flow land wdth 8=118rnrn Recess number n=m Powerrst~o K:k Axial slot wdth C=jOImm Radial beanng cleamnce ho:~mm Pressure rat10 0x1061 Crcumferentlal-flow land width b=[18lmrn 3. Calculated basic parameters: M,n,mum film thlck”ess hm,“= 0 05 mm Lubrlcsnt vlscoslty Vls=mCP t-wsqm fl~nrrwm supply pressure Psmlnz?!!!!I5 4 Calculated performance Temperature nse ATzj6oI”C Flow rate qozloL/s Total power Ht:116KW
4) 5) 6) 71
data Fll”l stiffness (,.,i,,\P:z
xo=l
Ml/m
tiP;E”K:,i&
bearings
8) &
land width
m: (nD)/(3n)=v]mm With exlal slots, the slot width Ic (nDv(En)Jo]mm With axial slots, the B” le IB)= n/n-(b+c)/D= 30 0 degree? p1 Clrcumferentlal flow factor a : “*e*(L-s)/(n*D*b) = 10912 With 8x181 slots, coefficient K /K) : sl”a~slna/0+rcossi zm Calculate dlmensloniess stiffness xo @j= 3 820(
I -0)/CI +r(1-O)): m 00
m
(b)
(4
17) Flow rate m= (Ps*ho”3/Vls)“fiB’ 18) Mlmmum pumping power
=mL/s
,9JF;lP;;;;r=mKW
(I
mz Hp+Hf = +K)Hp =mKW 20) Temperature r,se mar 0 0000012Ps =16(degrees C****l******t**************~********~
ratefactor
12) Flow 8’ m: (n*D)/(6*a*n) :jo] 13) Slldlng speed of bearing surface I= nDN/60 =m m/s 14) Recess orea for one pad i~r (nD/n-b)(L-2s) z/1846Ei8I‘qmm 15) Frlctlo” area I= (nDL/“)-(3Ar/4) =1415661Izqrnrl-, 16) viscosity m: ((Ps*ho**2)/U)J(iOB’)/Af) From the viscosity value.
m
=~~lNs/sqr.n=~/rP you are recommended--SAE
0_ *“tolt.ratlo”
D: Please B: Please b: Please c: Please
5(X light)
celslus
use use use use
the the the the
value value value value
given given given given
bu the bq the bq the bq the
sqstem. sustem. sqstem. sqstem.
(4
cm
&l5UC l&5lQw lml@~m
(OutputCardl
Plesseusefollow~ngbeanngparametersg~venbythesystem I. Basic parameters constrained by machine design: Beanng dwwter D=1840rnm Extreme load W.=(6000N Beanng length L.-mm 5haft mtstlonspeed N:/2400/rpm 2. Selected basic parameters: Axial-flow land width a:mmm Recess number n=m Powermtlo K=E Axial slot wdth c=mmm Rsdlal beanng clearance ho=~/mm Pressure rat10 oz(o6 Circumferential-flow land width b=jmrr 3. Calculated basic parameters: M~n~murnfilm thickness hml”:~mm Lubncant viscosity V15=~cP M~nwwn supply pressure Psmln=mMN/sqm 4. Calculated performance data: Film st,r,ness xo.~rPIwm Temperature nse AT=mI”C Flow rate qc:joL/s Total power Ht:mKW ,‘npcinn
(e)
Fig. 4. A bearing
design
procedure
with the basic design
module.
However, the incorporation of the AI technique with in the module makes the bearing design process both flexible and effective. Figure 4 demonstrates the use of the module for the design of the spindle bearings of a precision turning machine. The selected bearing configuration and its controlling restrictor type are suggested by the intelligent selection part of the bearing
design package. In Fig. 4, card (a) is employed for both the input and the output functions. Before entering the design procedure, card (a) is an input card. When a run through the design procedure has been completed, it changes into an output card, as shown as card (e). On card (a) there are various bearing parameters and their value fields. The designer can input selected
W. B. Rowe et al. / Intelligent design system for hydrostatic journal bearings
values to the parameter fields. Meanwhile, the system responds to the input, makes suggestions to the designer and provides an evaluation of the input. For instance, when the designer moves the mouse to the power ratio field and clicks it prior to typing a value in the field, the system responds to the click first by making a suggestion for the input value inside the upper rectangular field, as shown in Fig. 5. If the designer’s typed value is outside the normal range, the system will give an intelligent evaluation inside the rectangular field with a warning sound. The controlling intelligence for the input to the field is rule based. The rules for the power ratio field are written in HYPERTALK as follows: on mouseEnter put “(Input Card)” into card field iocard Put “ K is the ratio of friction power Hf and pumping power Hp. A suitable range is 1 3 then put “ Please input according to the system suggestion!” into card field Rectangular play “being” wait 30 else Put “ Your input may be suitable.” into card field Rectangular end if put “ Please input values of the bearing parameters. During input, the system will give advice. When finished, please click ‘Design’ to enter the design procedure.” into card field Rectangular end mouseLeave The process for other bearing parameter fields operates in a similar mode. The intelligence is rule based even
99
though there may be a different number of rules for different bearing parameters. The designer can click the “About” button to enter another card shown in Fig. 6 to find out more about the selection of bearing parameters. The text inside the left field of this card is a concise description of the rule-based knowledge concerning the bearing parameters selection. The designer can read the text by scrolling the page or directly clicking at the parameters in the right field of the card. During the bearing design procedure, the system can intelligently regulate the design formulae and coefficients with the changes of bearing configuration, number of recesses and restrictor type, which have great effect on the bearing design. For example, if the number of recesses and the configuration are changed on the input card of the design procedure, the system intelligently responds to the change and gives the procedure with some different design formulae, and hence different results, as shown in Fig. 7. When one design procedure is finished, the system puts all the designed bearing parameter values on to card (a) shown in Fig. 4. Card (a) changes into an output card which is indicated on the card by the system. On card (a), there is a “Devices” button. When
Fig. 6. A description
card about
the bearing
parameters
selection.
2) For optimum.
land width B should be &I: L/4=mImm 3) Under the condition of a/L=O25, clrcumferentlal-flow m: (nDV(3nk~Jmm 4) With axlo slots, the slot width I= (nDV(8nk~mm 5) With ax181 slot$. the 8” le LB= n/n-(b+cVD: 16 2 rfdegrees 6) Clrcumferentlal flow factor IrI.na(L-a)/(b(nD-nC-nb))=4344 7) With 8x,8, slots. coefflclent K m = sln0[sln0/0+rcosal =I 8) Calculate dlmenslonless stiffness xo’ a: 9 OOKD(
Beanng diameter
D= Shaft rutatlon speed
land width
I-0M I +r(,-0))~~ an
Fig. 5. A suggestion card.
inside
the
upper
rectangular
field
of the
Fig. 7. A typical card in the design axial slots having six recesses.
procedure
for a bearing
with
W. B. Rowe et al. / Intelligent design system for hydrostatic journal bearings
100
the designer clicks it, the system will guide the designer to the controlling device design cards. The system will assist the designer to design the controlling device by reference to the restrictor type suggested by the system and the bearing design output on the output card. Figure 8 shows the design procedure for the capillary restrictors for the spindle bearings. When the bearing design procedure is completed, the designer can click the “Expert’s analysis” icon on card (d) in Fig. 4, to obtain the system’s intelligent analysis of the design results. The system will tell the designer whether the calculated parameter values are suitable or not. If the values are unsuitable, the system will give the designer the reason and suggest ways of making these values suitable. The “expert” analysis and evaluation are listed in the “expert’s analysis” field on this card. On this card there is an “Autoiteration” icon; the designer can click it to make iterative computations of the bearing parameters. The iteration process achieves the bearing design computations automatically. The iteration process is based on achieving a bearing with maximum stiffness, minimum power dissipation and minimum
Co”,Dared 10 other types of restrIctor, csplllary WstrlCtors have Several dvantages which make them B popular chmce (1) manufacture 15 simple (‘2) capillary control gives the greatest tolerance to manufacturing v~rlances 1” bearing clearance (3) with capillary control the bearing load snd stifrness 8~ lndepende” 0r rluld vlscoslty and hence 0r temperature rl*e Four possible methods or maklng caplllsry restrlctors or-e a hypodermic tubing (commercially awlable), b glass capillary (commercially available), c drllllng. d spark machlmng Melhods c end d do not usually produce pure caplllsry actjon since the ?ngth-to-dlameterratio obtalnable 1s lnsufflclent Flow through a aplllary should be loml”8r, It IS therefore necessary to check that the eunolds number 15 less than ZOOOh A
temperature rise in a predefined computational accuracy range. On each card of the system, there are various kinds of browsing button such as the “home”, “return”, “last” and “next” buttons which allow the designer to move conveniently from one card to another and to move within the same stack or among different stacks. The results of the design process may be printed either by clicking the “Results output” icon on the card or by using the standard pull-down menu. 3.3 Single-constraint optimal design module The aim of bearing optimization is the achievement of maximum load support for minimum power. A number of variables make up the bearing design process and the designer has to decide the best value for each one. In this design module it was decided to follow the criterion that maximum load support should be achieved for minimum power expended. The designer can easily vary this criterion to achieve other objectives such as low temperature rise (high power dissipation tends to result in high temperature rise, large oil viscosity variation and large thermal distortion in the machine structure). In a hydrostatic journal bearing, the total power is the sum of the pumping power and the friction power under concentric operating conditions: H,=H,t-H, Pumping power H, illustrates the rate at which energy must be expended to force the liquid through the bearing. Friction power Hf illustrates the rate at which energy must be expended to move the bearing. Expressions for H,, and Hf are as follows: Hp=Psq=
P,2@h3 ___ 77
(1)
so that from eqns. (1) and (2): (1) (2) (3) (4)
L,qwd density c =[jKg/Cublc Capillary diameter dc =mIrn Capillary ratlo of length-lo-diameter Capillary length I =l-im
0_
The flu,d
DH>(” Ml
Desian
comwtstion
Ht=H,+Hf=p~ + y
m I/de
77
=m
System I/O Board 1s in the larnlnar flow
flqw
condltlo”
procedure
(‘),y;cdgyKg,c”b,c m
(2) From
know”
,3,7$!rl~m (4) Reynolds
KC and i/de,
number
rnrj [=
cao,llary
diameter
4Cqo/(n
m dc Vls)
dc can be detarrnlned
.r]
(3)
If the bearing operates at zero or very slow speed the power ratio will be much less than 1 and it is only necessary to take into consideration the pumping power loss H,. In most applications, however, the working speed is not negligible. The total power may be minimized for any variable by partially differentiating eqn. (3) and setting to zero.
h
(b) Fig. 8. Design
procedure
of a capillary
restrictor
3.3.1. Optimum viscosity The designer may minimize the total power by choosing the optimum viscosity value. The way to find the
M B. Rowe et al. / Intellig&t design system for hydrostatic journal bearings
optimum viscosity is to vary the value of viscosity while maintaining all other design parameters fixed at the constant value appropriated for the design requirements, i.e.
(S--c-rrnb)(l
I ‘1
t-r) with axial slots
TJD without axial slots
so that
Ps2@h3 aH,=_-+ arl
A,U2 --_=-h
v2
Hf
Hg
K=
rl~
so that aH,l&q = 0 when H, =H,. power ratio is K=H,IH, = 1.
The corresponding
3.3.2. Optimum clearance As explained when considering the optimum viscosity, the optimum clearance can be found by partial differentiation when
aHt_ 3Ps2@h2 ah-
rl
r&U2 --=
3Hp
Hf
h
h
h2
so that aHJ3h = 0 when 3H, =H,. The corresponding power ratio is K=H,IH,=3. 3.3.3. Optimum power ratio
From an extension of the foregoing techniques, it may be shown that the optimum value of power ratio for a recessed hydrostatic journal bearing with a certain working speed always lies in the range 1
The ratio of total power to applied load is H, -=
B= -&C=
101
W
(I+K)H,
i2 and is proportional
to c
~
L2
6an (L-a)2
An optimum for 3 may be determined by partial differentiation of H, with respect to a and equating to zero. It is found that the optimal value of a is Ll 3. At increasing eccentricity the optimum value of land width a shifts to L/4 [ll]. The single-constraint optimal design module is developed from the basic design module with the optimization technique described above. When the designer clicks the single-constraint optimal design title on the menu card, the system replaces the menu with a new submenu as shown in Fig. 9. The designer can select any one from the submenu by clicking with the mouse. The system will then automatically guide the designer to enter the design procedure. Each of the four design procedures has its own defined optimization condition, i.e. K= 1 for optimum viscosity, K= 3 for optimum clearance, 1 ~K63 for optimum power ratio and a/ L = l/4 for optimum landwidth ratio. The four optimization conditions are also called single-constraint conditions; they are defined by the system. Except for these predefined single-constraint conditions, the single-constraint optimal design module is exactly the same as the basic design module. 3.4. Multi-constraint optimal design module There are tens of parameters for a recessed hydrostatic journal bearing. These parameters interact with each other and on their value selections. The singleconstraint optimization technique mentioned above is in principle insufficient to design a proper bearing even though it is essential for the bearing optimization.
W
(Click
required 1~0”s.
buttons aid character
tlties)
This may be written
The maximum load for the minimum power is achieved for the bearing shape which makes K a minimum. For a recessed hydrostatic journal bearing: total projected area A =LD; effective area A,=& is proportional to D(L -a). Hence k is proportional to (L-a)/L. Flow shape factor
Orthographic
Technical
(1) (2) (3) (4)
Projection
Orawing
Optimum Optimal Optimal Optimum
viscosity clearance power ratio land width ratio
n
Fig. 9. Submenu card.
for single-constraint
optimal
design
on the menu
W. B. Rowe
102
et al. / Intelligent design system for hydrostatic journal bearings
Ideally, it is necessary to use the multi-constraint optimization technique for the bearing optimal design. When designing a hydrostatic journal bearing, there are six essential design parameters which require detailed consideration [12]. These are: (i) the length to diameter ratio L/D; (ii) land/width ratio a/L; (iii) concentric pressure ratio p; (iv) radical clearance h,; (v) power ratio K; (vi) supply pressure P,. In a general design procedure, the supply pressure P, is the most essential parameter, since it must be sufficient to support the load. Other parameter values depend on the relationship to supply pressure. Therefore, the system searches for the optimum value of supply pressure P, as the first step of bearing parameter optimization. The system gives the six bearing parameters, with constraint conditions which can be defined by the designer. During the optimization search, the system takes the bearing performance requirements of maximum stiffness, mininum power dissipation and minimum temperature rise as the optimization objectives. The designer can also define the performance requirements as constraint conditions for the bearing optimization. In this module, the system combines a single variable search with multiconstraint conditions by AI techniques. This avoids the complexity of multivariable search, while the module can still perform the operation of optimizing multiple bearing parameters. Figure 10 shows the input card of this module; the designer can directly define the constraint conditions on the card. For a single-variable search, three basic search methods are the bisection search, the Fibonacci search and the golden-section search. Compared with the other two methods, the golden-section search has the advantages of simplicity and efficiency 1131. The system described here uses the golden-section search method. Figure 11 illustrates the algorithm of the system de-
-
%
Nulti-constraint
optimization
module (Input Card)
fl-
Please input the followmg parameters Dunng input, the system will give advlce When flnlshed, chck the ‘Opt~mlzat~on’ button to enter the OptlmlZ~tlO” procedure I. Basic parameters constrained by machine design: Besnng dwneter 170% D(mm) 5 IO0 Extreme load w’ :mN Shaft mtatlo” speed N 1CT 2000 rpm Beanng length 170~ L(mm) 5 iloo !. Selected basic parameters: Recess “umber n=@ Powerratlo mrKr/3 Axial slot wdth c=mrnm Axlal-flow land wdth a=~(mm Radial clearance mr ho(mm) % 0 09 Pressure rat10 j04lini 0 7 Crcumferentlal-flow land width bzmrnm IF? I. Calculated basic parameters: Lubncont “lscaslty VISZ~CP Mnlmum film thickness hmlnz(0 rim Supply pressure (4 5 PslMN/sqml r/7 ,. Calculated performance data. Temperaturense ATT~~I”C Fll”l stiffness x0 zm MN/In Pumping pqwer HP%= KW Flow rate qozloL/s Total power Htr mKW
Fig. 10. The module.
input
card
of the
multi-constraint
optimal
design
Put P.,+.+
Fig. 11. The pressure.
Calculated
Fig.
algorithm
Ps is
12. A warning
P,(Y,,+,) Onto output card
employed
outside
the
to search
for optimum
supply
required
demonstration
window
given
by the system.
veloped to search for the optimum value range of the supply pressure. As well as the intelligence described in the former two modules, in this module the system has the intelligence to supervise the optimal design procedure. The designer can click the “optimization” button on the input card to enter the optimization procedure. When the designer enters the procedure, the system first shows a dialogue window asking the designer to input the number of iterations. The system will carry out the optimization iteration cycle according to the number of times indicated by the input value. During the iteration, if a computer parameter value is outside the range limited by the constraint conditions, the system will pause the iteration and give a warning demonstration window with a warning sound. Figure 12 shows a warning demonstration window during the optimization process. The system tells the designer which calculated parameter value is outside the constraint range, and asks the designer whether to continue the optimization process or to stop it. It is possible that the designer’s constraints on the parameters values may not be suitable. The designer can click the “Continue” button to continue the optimization process. If the designer clicks the “Stop” button, the system will stop the process and shows a reasoning demonstration window on which the system shows its reasoning on the modification of the constraint conditions or other input values. A reasoning window is shown in Fig. 13. When the optimization accuracy is achieved, the system
W. B. Rowe et al. / Intellige‘nt design system for hydrostatic journal bearings
Increase the range Of
Fig. 13. A reasoning
supply
pressure
PS.
demonstration
window given by the system.
stops the iteration and gives a notice window with a short burst of light music. The designer can obtain all the optimization values from the output card. The intelligence demonstrated during the optimization is rule based and programmed in HYPERTALK. The program consists of tens of discrete scripts each one attached to its own object which may be a card, a field or a button. Their operations are monitored by the “Optimization” button. This also illustrates a characteristic of HYPERTALK programming.
103
multi-constraint optimal design module of the system be used. The other two modules can be used as auxiliary tools for the designer. Figure 14 shows a bearing design procedure with the multi-constraint optimal design module. The design bearing is to support the spindle of a precision turning machine. In this figure the data on card (d) is the designer’s input, the data on card (h) is the system bearing design output. In practice, cards (d) and (h) are one card with input-output double functions. They are separately demonstrated here for the convenience of description. Card (i) and (j) show the design procedure of a controlling restrictor for the bearing. Compared to the design output with the basic design module (see Figs. 4 and S), it is found that the results are significantly improved. The optimized bearing parameters and performance are quite appropriate for the precision turning machine application.
4. System operation and an example 5. Concluding remarks Although each of the three modules can provide a satisfactory design situation for a recessed hydrostatic journal bearing, it is usually recommended that the
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BEARING:
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In this paper, an intelligent system has been presented for the design of recessed hydrostatic journal bearings.
Cardg$!$J*****
1. 2. 3. 4. 5. 6.
Conical journal bearing Partial ]our”al bearing Spherical bearing Recessed cylindrical journal bearing Plain journal bearing Combined ioumal and thrust beannqs (the Vateszbeari”g) SYSTEM: Which type, (liquid) “rm ?
In&x
******************************************** ’ i. Circuit and flow c”ntrnl devices ii. Tank, pump and supply system Bor=?
Intelligent System for Fluid Film Journal Bearings Design ***********************************************
I 07
m
24 urn
Design of recessed
Wednesdaq,
April
Liqpid or Gas Caoillaru
8, 1992
tlulti-constraint
Cy!i,ndrical.
optimization
Oriiice
Press&
valve
Slot
module (Input Card)
liquidfilm journal bearing (Cl,ck
requrred
,co”s,
l
Orthographic
Projection l
Technical
ac) f:ig. 14
Orawing
buttons
end charecter
titles)
Basic parameters constrained by machine design: ‘Extreme load w’.mN Beanng diameter 170~ D(mm) 5195 Shaft mtatlon speed N rm rpm Beanng length [7o-)i L(mm) rm Selected basic parameters: Recess number n=a Powerratlo miKr(3 Ax181slot wdth c=mJmm Axial-flow land width e=~rnm Rsdlsl clearance m07 ho(mm) $10 Cuwmferentlal-flow land wdfh b:mmm PressureratIo ali)rm Calculated basic parameters: nlnlmum film thickness hmln=m mm Lubncant vlscoslty V,S=mcP Supply pressure )5 i PslMN/saml r= Calculated perfornmnce data: -Temperature “se ATT~~‘C Film stiffness x0 2 150 Flow rate qo= 0 15 L/s Pump,ngpower Hpr. 0 5 Total power Htr %KW 1nntimi7atinn\ mrnw.. 6?!?i
1. Single-constraint optimization based on minimum power dissipation. 2. tlulti-constraint optimization based on minimum power, maximum stiffness and minimum temperature rise. ,,,-
I6
(4 (continued)
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
104
a: /(W/O 17Ps)=[83666m :2) For aptlmum, land wdth e should be lxi = L/4:1209 mm ,3) Under the condltlon of a/L=0 ‘25, circumferential-flow m = (nD)/(3n):[r]mm 4) With exlal slots, the slot width I= (nD)/(Bn)=[OoImm .S) With axial slots, the 8” le degrees a= n/n-(b*c)/D= 30 0 c5l
bearings
(9) Calculate supply pressure m=(3W )/(xo’D(L-a)) =mMN/sqm IO) Calculate Stiffness
, ,,~~~~~~(~,r~:o,~~~“~*~mN/m ,,)~@ho, ;~~$$ciT-l’“”
land width
@J-J:
(n*D)/(6*a*“) :(oj 13) Slldlng speed of bearing surface m; 7fDN/60 zmrn/s 14) Recess orea for one pid mar (nD/n-b)(L-28) =[-jsqmm 15) Frlctlon we8 nDL/“)-(3Ar/4) =[449449Jsqrnrn 16~~:ds,ty (UirJ= ((P,*ho’*Z)/U)J((DB’l/Af) =[0017017]Ns/Sqm=\~IcP From the vlscoslty value, you are recommended--SAE 5(X ilght)
6) C~rcumferentlal flow factor a = “*a*(L-a)/(n*D*b) = 11076 :7) With axleI slots, coefllclent K m : s~“s[sl”e/a+rcosel =(o 8) Calculate dtmenslanless stiffness x0’ IHo’l= 3 82D(
I -DU(I +r(1-D))2pE?rl
(e)
rlow rare ,?j& (Ps*ho**3/ViS)“DB’ 18) M~mmum oummno oower
n
I I,
Multi-constraint
=10106/S
optimization
Please use followng
module
beanng pammeterr
(Output
Card)
a
given by the system I
20) Temperature ~,se a= 0 0000012Ps :mdegrees ****************************************************.
[xl
Basic parameters constrained by machine design: .Extreme load W :mlN Beanng dw”eter~’ D(mm) ~183 Beanng length m$ L(mm) I 183 Shaft mtatlon speed N i(rpm Selected basic parameters Powermt~o OrKra Ax101slot wdth c=/OOmm Recess number n=m Rsdlal clearance m$ ho(mm) ~(0105 Axlal-flow land wdth a=mImm Clrumferentlal-flow land wdth bz(21mm Pressure rat10 arorloil Celculeted basic parameters. Muwnum lllm thickness him”== mm Lubncant wscoslty V,s=mcP Supply pressure 1456 ! PslMN/sqm] rm Calculated per,o”,,ance data. -Temperature “se AT$m’I’c F~lr” stiffness xo :mMN/m Flow rate qo=(ous i=U”lpl”Q pOwe,Hpi(048 KW
cel~lus
Ix)
[ii!%-]
Exemusis: 0: Pleese use the velue given bq the sustem. _p: Pleas~qiven bu the sustem. Plea bditheegiven bq the system. c: Please use the velue given bq the sustem.
:
Design procedure parameters:
:nown Compared to other types of restrlctor, capillary restrlctors have several ldwntages which make them a popular chwce (1) manufacture I* ample (2) capillary control QIves the greatest tolerance to manufacturing “er~ences I” bearing clearance (3) with cawllary control the bearing load end stiffness are lndepende” Of flud wscoslty end hence of temperature rise Four Possible methods of makIng csp~llsry restrlctors are e hypodermic tubing (commercially awlable). b glass capillary (commercially available), c drllllng, d spark mnctuning nethods C and d do not usually produce pure capillary action since the ength-to-dlameterratlo ObtaInable IS Insufflclent Flow through B splllary should be lamlnar, it IS therefore necessary to check that the !eu”Oids “umber 1s less than 2000 ,G A
1) 2) 3) 4)
of
Llquld density c :1780]Kg/cublc Ca~lllary dlsmeter dc =mm Ceplllary ratlo of length-to-dlametrr Capillary length 1 :7/m
0
The fluld
flow
a capillary
restrictor
QJ
m l/de
=m
System I/O Board IS I” the Ismlnarflow
condltlon
PIIDISlsn lesign
computation
procedure-
“~:d,~,Kg,cub,c 2) From known
4)Reynolds
m Kc and I/de,
capillary
diameter
dc con be determlned
“umber
(9 Fig.
14. A bearing
design
procedure
with
the multi-constraint
The system is implemented on HYPERCARD on a Macintosh computer and is hence very user friendly. The system employs a new design method which incorporates AI techniques with conventional numerical design techniques. The incorporation of AI techniques integrates numerical and qualitative issues. Using the
optimal
design
module
system, a bearing design can easily be achieved. The system package can be obtained for just a small charge by contacting the authors. The system is currently in the process of further development. The authors intended to expand this system to include additional abilities such as intelligently
W. B. Rowe
et al. I Intelligent
design system for hydrostatic
learning from the experienced designer and being more flexible. These features will make the system more powerful.
6. Acknowledgements The authors wish to express their gratitude to Mr. Paul Wright and Mr. Peter Moran of the Liverpool Polytechnic for their help and assistance with this research work.
References J. P. O’Donoghue and W. B. Rowe, Hydrostatic bearing design, Tribal. Int., 2 (1) (1969) 2, 25-71. N. N. S. Chen and Y. S. Ho, Computer-aided design of hydrostatic journal bearings including shaft bending effect, Tribol. Int., IO (4) (1977) 221-228. M. K. Ghosh and B. C. Majumdar, Design of multirecess hydrostatic oil journal bearings, Tribal. ht., 13 (2) (1980) 73-78.
journal
bearings
105
4 M. A. Dumbrava, Review of principles and methods applied to the optimum calculation and design of externally-pressurized bearings. Part 1: Low/moderate speed bearings, TriboZ. ht., 18(3) (1985) 149-156. 5 P. Jackson, Introduction to Expert Systems, Addison-Wesley, Wokingham, UK, 2nd edn., 1990. 6 W. B. Rowe, Hydrostatic and Hybrid Bearing Design, Butterworths, London, 1983. 7 A. Bahrami, Designing Artificial Intelligence Based Software, Sigma Press, Wilmslow, UK, 1988. 8 Danny Goodman, T&eComplete HyperCard handbook, Bantam Books, New York, 2nd edn., 1988. 9 I. Sommerville, Software Engineering, Addison-Wesley, London, 3rd edn., 1989. 10 H. Opitz, Pressure pad bearings, Proc. Inst. Mech. Eng., 182 Part 3A, (1967-1968) lO&llS. 11 W. B. Rowe, J. P. O’Donoghue and A. Cameron, Optimization of externally pressurized bearings for minimum power and low temperature rise, Tribal. Int., 3 (4) (1970) 153-157. 12 K. J. Stout and W. B. Rowe, Externally pressurized bearingsdesign for manufacture. Part 3: design of liquid externally pressurized bearings for manufacture including tolerancing procedures, Tribal. Int., 7 (5) (1974) 195-212. 13 P. R. Adbyand M. A. H. Dempster, Introduction to Optimization Methods, Chapman and Hall, London, 1974.
95
An intelligent design system for recessed hydrostatic journal bearings W. B. Rowe, School
of Engineering
(Received
December
K. Cheng and
and D. Ives
Technology
Management,
9, 1991; revised and accepted
The Liverpool
Polytechnic,
Byrom
Street, Liverpool
L3 3AF
(UK)
April 24, 1992)
Abstract This paper is intended to demonstrate the power of HYPERCARD for intelligent knowledge-based design applications. The system is also educational and is a practical aid to basic design of recessed hydrostatic journal bearings. The system is built with a new design method which integrates an artificial intelligence (AI) technique
with a conventional bearing design technique. The AI technique is used to assist with numerical and also qualitative decisions. The system primarily consists of three intelligent design modules: a basic design module; a singleconstraint optimal design module; and a multi-constraint optimal design module. Any one of these three modules can be used to complete the bearing design work. The system is implemented on the HYPERCARD software of the Macintosh computer. Operation of the system shows that an appropriate recessed hydrostatic journal bearing design can easily be achieved with the system.
1. Introduction Hydrostatic journal bearings have been extensively studied during the last thirty years and many papers on operation and design principles have been published. Broadly speaking, design methods may be classified as manual or computer aided. The manual method uses design rules and graphic data or equations. Computer aided design allows greater sophistication in the optimization process [14]. The development of personal computers has accelerated the trend towards use of computer programs to aid bearing design, especially to aid the computation and optimization of the values of bearing parameters. However, effective design of a hydrostatic journal bearing is still not a simple task for many design and manufacturing engineers. With the first method, many complicated functions have to be considered in the decision making process of the design, and these functions are normally available in the form of multi-dimensional graphs and equations. The second method, which can free the designer from complicated design computation, focuses on the numerical requirements of optimizing the parameters of a proposed hydrostatic journal bearing. Computer-aided bearing design programs typically use general purpose scientific languages such as FORTRAN or PASCAL. It is hard for the programs written in these languages to consider qualitative issues, such as determining the most suitable type or configuration of bearing, evaluating the compatibility of the proposed solutions during the
0043-1648/92/$5.00
design procedure and providing suggestions, etc. It is therefore of practical relevance to develop a bearing design system using artificial intelligence (AI) which considers both numerical and qualitative issues. AI is a branch of computer science concerned with the design and implementation of software which is capable of emulating human cognitive skills such as problem solving, visual perception and language understanding. AI-based software falls into three basic categories: expert (or knowledge-based) systems; perception systems; and natural language systems. Expert systems, or more generally, knowledge-based systems, are more commonly employed in engineering [5]. This paper presents an intelligent system for the design of recessed hydrostatic journal bearings. The system is built with a new design method which integrates AI with conventional bearing design methods. The system makes it possible for the bearing design to take into account numerical and qualitative issues. The system includes three intelligent design modules: a basic design module, a single-constraint optimal design module; and a multi-constraint optimal design module. The designer can choose any one of them to do the bearing design. The system combines AI with each module and the AI covers the whole design procedure for a bearing. The system is implemented on the HYPERCARD software tool of the Macintosh computer. With this system, an appropriate recessed hydrostatic journal bearing design can easily be achieved. The system
0 1992 - Elsevier Sequoia. All rights reserved
W. B. Rowe et al. I Intelligent design Jystem for hydrostatic journal bearings
96
described is one part of a larger knowledge-based bearing design package which is being developed on an experimental basis at The Liverpool Polytechnic.
2. Recessed
hydrostatic
journal
bearings
Of the hydrostatic bearing configurations for spindle applications, the recessed hydrostatic journal bearing configuration is probably the most commonly employed. Two typical configurations are shown in Fig. 1. One configuration is with axial drain slots between the recesses, the other is without axial drain slots. The axial drain slots in a non-rotating bearing allow the recesses to operate independently of the neighbouring recesses. For the same clearance, flow rate is increased compared to a bearing without axial slots, a feature which is often considered undesirable. Inappropriate axial slot design may seriously detract from the bearing’s load carrying capacity. Axial slots also increase the complexity of bearing manufacture. The bearing configuration with axial drain slots is therefore less commonly employed for higher speed applications. The design strategy is made up of several stages. A general design strategy for the bearings is described as follows [6]: (i) Choose the bearing configuration, i.e., a bearing configuration with axial drain slots or without.
(ii) Determine the basic bearing parameters constrained by the machine design, for example load W, diameter D, length L, shaft rotation speed N. (iii) Determine the basic bearing parameters which are, if possible, selected according to rules where these are available for optimal design or ease of manufacture; for example number of recesses n; land/width ratio al L; inter-recess land/width ratio b/u; length/diameter ratio L/D; radial bearing clearance h,; concentric pressure ratio j3; concentric power ratio K; axial drain slot width c, if axial drain slots are to be used. (iv) Determine the basic bearing parameters which must be calculated; for example, supply pressure P,, from P,= W/(0’@, where J&’is provided as computed data; viscosity q,
(v) Calculate the bearing performance data; for example, stiffness A; flow rate q; pumping power HP; total power H,; maximum temperature rise AT. In addition, the relevant control device and its dimensions have to be determined. The control device governs bearing stiffness and will commonly be one of the following types: capillary control; slot control; orifice control; and diaphragm valve control. Capillaries are an example of simple laminar-flow restrictors. Compared with other types, capillary restrictors have the advantages of manufacturing simplicity and also that the bearing load and stiffness are independent of fluid viscosity and hence of temperature rise. For this reason, capillary tube control has become popular for recessed hydrostatic journal bearings. The general design strategy of a recessed hydrostatic journal bearing.can also be illustrated in the form of a flow chart as shown in Fig. 2. The intelligent system has been developed to complete the design work following the basic strategy outlined in this chart but with alternative algorithms to undertake the computation of calculated parameters depending on which optimization routines has been adopted.
3. Description
Fig. 1. Two typical configurations bearings. (a) Without axial slots axial slots.
of recessed hydrostatic between recesses and
journal (b) with
of the system
The intelligent design system includes three intelligent design modules as illustrated on the system menu card in Fig. 3. The first is the basic design module, based on the general design procedure of a recessed hydrostatic journal bearing described in the previous section. The second is the single-constraint optimal bearing design module. The third is the multiconstraint optimal bearing design module. Both of the optimal design modules are developed on the same basis as the first and take the maximum stiffness, the minimum power dissipation
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
Determine
DetermIne
reStriCtOrS:
(a) Capillary tube (b) Slot (c) Orifice (d) Diaphragm
Calculate
valve
+bearing parameters
p., rl bearing dimension
Modify
t
parameters:
a, b, c, D, L No
Calculate
bearing performance
the bearing configuration
-3
Calculate
2. Flow
Fig.
a
chart
based on‘
and reStriCtOr:
1
restrictorparameters
of the bearing
general
design
liquid film journal (Click
Orthographic
Technical
Fig.
3. The
procedure.
of recessed cylindrical
Design
required
icons,
Projection
Drawing
system
menu
buttons
97
with a mouse. The system is one part of a larger knowledge-based bearing package which includes other parts such as intelligent selection of bearing configuration and its controlling device type, bearing database, general description of bearing, and designer’s on-line help, etc. The different parts within the package are connected to each other in an organic way. The larger bearing design package can be operated on all types of Apple Macintosh computers, but needs 1.8 Mb of memory for the system as designed so far.
bearing parameters.
one of following
bearings
and character
bearing titles)
I
l Single-constraint optimization based on minimum power dissipation. * 2. nulti-constraint optimization based on minimum power, maximum stiffness and yinimum temperature Vse.
card.
and the minimum temperature rise as the bearing optimization objectives. In each module, AI is incorporated into the procedure for bearing design defined by Fig. 2. The icons, buttons and character titles on the menu card are selected by the user as required. A designer can enter any module by just clicking it
3.1. Sojhare tool selection There are two principal classes of software tool used to develop intelligent systems with AI. Class 1 uses a general purpose AI language such as LISP or PROLOG. These languages are the most frequently used for logic programming. The other class is based on the use of an expert system shell. The latter approach is becoming popular in knowledge engineering. With a shell, it is possible to build a working system very quickly. However, both classes of software tool have limitations in their ability to cope with complicated numerical computations [71* HYPERCARD is not an application program, such as a word processing package, a spreadsheet package or a database package; nor is it an expert system shell. It is, rather, a software engine, a hypermedia toolkit [8]. HYPERCARD is now available as a standard software and is provided with every Macintosh computer. The key to HYPERCARD’s authoring environment is HYPERTALK, a programming language built into HYPERCARD and designed around a natural sounding English language. Like traditional programming language, such as C or PASCAL, HYPERTALK contains features such as looping structure, variables, if-then statements, and input-output ability. Moreover, HYPERTALK can create symbolic manipulation programs with the scripts attached to HYPERCARD objects such as buttons, fields, cards, backgrounds and stacks. Programs written in HYPERTALK can cope with quite complicated numerical computation and also logic operations. For this reason HYPERCARD may be conveniently employed to construct various informationbased application programs. Other features which are useful in constructing a powerful intelligent system with HYPERCARD are its painting tools, its ability to alternatively hide and display information, and its Macintosh user-friendly WIMP interface. (WIMP is derived from windows, icons, menus and pointing, and is a radical step forward in designing intelligent computer system [9].) 3.2. Basic design module The basic design module is based on a general design procedure for a recessed hydrostatic journal bearing.
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
98
resign I) From the input data, decide diameter D IO J(W/O 17Ps)~~~mm 2) For optimum, land wdth B should be lal= L/4=mmm 3) Under the condltlon of s/L=0 25, CIrcumferentlal-flow
Please input values of the beanng p~mmeter~ Dunn! Input, the system Will gI”e adwe When fvwhed, please chck ‘Design’ to enter the deslg” procedure 1. Basic parameters constrained by machine design: Beanng d,ameter D=j90jmm Extreme load W.=mN Beanng length L.~mm Shaft ntatlon speed N=mi~m 2 Selected basic parametersAxial-flow land wdth 8=118rnrn Recess number n=m Powerrst~o K:k Axial slot wdth C=jOImm Radial beanng cleamnce ho:~mm Pressure rat10 0x1061 Crcumferentlal-flow land width b=[18lmrn 3. Calculated basic parameters: M,n,mum film thlck”ess hm,“= 0 05 mm Lubrlcsnt vlscoslty Vls=mCP t-wsqm fl~nrrwm supply pressure Psmlnz?!!!!I5 4 Calculated performance Temperature nse ATzj6oI”C Flow rate qozloL/s Total power Ht:116KW
4) 5) 6) 71
data Fll”l stiffness (,.,i,,\P:z
xo=l
Ml/m
tiP;E”K:,i&
bearings
8) &
land width
m: (nD)/(3n)=v]mm With exlal slots, the slot width Ic (nDv(En)Jo]mm With axial slots, the B” le IB)= n/n-(b+c)/D= 30 0 degree? p1 Clrcumferentlal flow factor a : “*e*(L-s)/(n*D*b) = 10912 With 8x181 slots, coefficient K /K) : sl”a~slna/0+rcossi zm Calculate dlmensloniess stiffness xo @j= 3 820(
I -0)/CI +r(1-O)): m 00
m
(b)
(4
17) Flow rate m= (Ps*ho”3/Vls)“fiB’ 18) Mlmmum pumping power
=mL/s
,9JF;lP;;;;r=mKW
(I
mz Hp+Hf = +K)Hp =mKW 20) Temperature r,se mar 0 0000012Ps =16(degrees C****l******t**************~********~
ratefactor
12) Flow 8’ m: (n*D)/(6*a*n) :jo] 13) Slldlng speed of bearing surface I= nDN/60 =m m/s 14) Recess orea for one pad i~r (nD/n-b)(L-2s) z/1846Ei8I‘qmm 15) Frlctlo” area I= (nDL/“)-(3Ar/4) =1415661Izqrnrl-, 16) viscosity m: ((Ps*ho**2)/U)J(iOB’)/Af) From the viscosity value.
m
=~~lNs/sqr.n=~/rP you are recommended--SAE
0_ *“tolt.ratlo”
D: Please B: Please b: Please c: Please
5(X light)
celslus
use use use use
the the the the
value value value value
given given given given
bu the bq the bq the bq the
sqstem. sustem. sqstem. sqstem.
(4
cm
&l5UC l&5lQw lml@~m
(OutputCardl
Plesseusefollow~ngbeanngparametersg~venbythesystem I. Basic parameters constrained by machine design: Beanng dwwter D=1840rnm Extreme load W.=(6000N Beanng length L.-mm 5haft mtstlonspeed N:/2400/rpm 2. Selected basic parameters: Axial-flow land width a:mmm Recess number n=m Powermtlo K=E Axial slot wdth c=mmm Rsdlal beanng clearance ho=~/mm Pressure rat10 oz(o6 Circumferential-flow land width b=jmrr 3. Calculated basic parameters: M~n~murnfilm thickness hml”:~mm Lubncant viscosity V15=~cP M~nwwn supply pressure Psmln=mMN/sqm 4. Calculated performance data: Film st,r,ness xo.~rPIwm Temperature nse AT=mI”C Flow rate qc:joL/s Total power Ht:mKW ,‘npcinn
(e)
Fig. 4. A bearing
design
procedure
with the basic design
module.
However, the incorporation of the AI technique with in the module makes the bearing design process both flexible and effective. Figure 4 demonstrates the use of the module for the design of the spindle bearings of a precision turning machine. The selected bearing configuration and its controlling restrictor type are suggested by the intelligent selection part of the bearing
design package. In Fig. 4, card (a) is employed for both the input and the output functions. Before entering the design procedure, card (a) is an input card. When a run through the design procedure has been completed, it changes into an output card, as shown as card (e). On card (a) there are various bearing parameters and their value fields. The designer can input selected
W. B. Rowe et al. / Intelligent design system for hydrostatic journal bearings
values to the parameter fields. Meanwhile, the system responds to the input, makes suggestions to the designer and provides an evaluation of the input. For instance, when the designer moves the mouse to the power ratio field and clicks it prior to typing a value in the field, the system responds to the click first by making a suggestion for the input value inside the upper rectangular field, as shown in Fig. 5. If the designer’s typed value is outside the normal range, the system will give an intelligent evaluation inside the rectangular field with a warning sound. The controlling intelligence for the input to the field is rule based. The rules for the power ratio field are written in HYPERTALK as follows: on mouseEnter put “(Input Card)” into card field iocard Put “ K is the ratio of friction power Hf and pumping power Hp. A suitable range is 1
99
though there may be a different number of rules for different bearing parameters. The designer can click the “About” button to enter another card shown in Fig. 6 to find out more about the selection of bearing parameters. The text inside the left field of this card is a concise description of the rule-based knowledge concerning the bearing parameters selection. The designer can read the text by scrolling the page or directly clicking at the parameters in the right field of the card. During the bearing design procedure, the system can intelligently regulate the design formulae and coefficients with the changes of bearing configuration, number of recesses and restrictor type, which have great effect on the bearing design. For example, if the number of recesses and the configuration are changed on the input card of the design procedure, the system intelligently responds to the change and gives the procedure with some different design formulae, and hence different results, as shown in Fig. 7. When one design procedure is finished, the system puts all the designed bearing parameter values on to card (a) shown in Fig. 4. Card (a) changes into an output card which is indicated on the card by the system. On card (a), there is a “Devices” button. When
Fig. 6. A description
card about
the bearing
parameters
selection.
2) For optimum.
land width B should be &I: L/4=mImm 3) Under the condition of a/L=O25, clrcumferentlal-flow m: (nDV(3nk~Jmm 4) With axlo slots, the slot width I= (nDV(8nk~mm 5) With ax181 slot$. the 8” le LB= n/n-(b+cVD: 16 2 rfdegrees 6) Clrcumferentlal flow factor IrI.na(L-a)/(b(nD-nC-nb))=4344 7) With 8x,8, slots. coefflclent K m = sln0[sln0/0+rcosal =I 8) Calculate dlmenslonless stiffness xo’ a: 9 OOKD(
Beanng diameter
D= Shaft rutatlon speed
land width
I-0M I +r(,-0))~~ an
Fig. 5. A suggestion card.
inside
the
upper
rectangular
field
of the
Fig. 7. A typical card in the design axial slots having six recesses.
procedure
for a bearing
with
W. B. Rowe et al. / Intelligent design system for hydrostatic journal bearings
100
the designer clicks it, the system will guide the designer to the controlling device design cards. The system will assist the designer to design the controlling device by reference to the restrictor type suggested by the system and the bearing design output on the output card. Figure 8 shows the design procedure for the capillary restrictors for the spindle bearings. When the bearing design procedure is completed, the designer can click the “Expert’s analysis” icon on card (d) in Fig. 4, to obtain the system’s intelligent analysis of the design results. The system will tell the designer whether the calculated parameter values are suitable or not. If the values are unsuitable, the system will give the designer the reason and suggest ways of making these values suitable. The “expert” analysis and evaluation are listed in the “expert’s analysis” field on this card. On this card there is an “Autoiteration” icon; the designer can click it to make iterative computations of the bearing parameters. The iteration process achieves the bearing design computations automatically. The iteration process is based on achieving a bearing with maximum stiffness, minimum power dissipation and minimum
Co”,Dared 10 other types of restrIctor, csplllary WstrlCtors have Several dvantages which make them B popular chmce (1) manufacture 15 simple (‘2) capillary control gives the greatest tolerance to manufacturing v~rlances 1” bearing clearance (3) with capillary control the bearing load snd stifrness 8~ lndepende” 0r rluld vlscoslty and hence 0r temperature rl*e Four possible methods or maklng caplllsry restrlctors or-e a hypodermic tubing (commercially awlable), b glass capillary (commercially available), c drllllng. d spark machlmng Melhods c end d do not usually produce pure caplllsry actjon since the ?ngth-to-dlameterratio obtalnable 1s lnsufflclent Flow through a aplllary should be loml”8r, It IS therefore necessary to check that the eunolds number 15 less than ZOOOh A
temperature rise in a predefined computational accuracy range. On each card of the system, there are various kinds of browsing button such as the “home”, “return”, “last” and “next” buttons which allow the designer to move conveniently from one card to another and to move within the same stack or among different stacks. The results of the design process may be printed either by clicking the “Results output” icon on the card or by using the standard pull-down menu. 3.3 Single-constraint optimal design module The aim of bearing optimization is the achievement of maximum load support for minimum power. A number of variables make up the bearing design process and the designer has to decide the best value for each one. In this design module it was decided to follow the criterion that maximum load support should be achieved for minimum power expended. The designer can easily vary this criterion to achieve other objectives such as low temperature rise (high power dissipation tends to result in high temperature rise, large oil viscosity variation and large thermal distortion in the machine structure). In a hydrostatic journal bearing, the total power is the sum of the pumping power and the friction power under concentric operating conditions: H,=H,t-H, Pumping power H, illustrates the rate at which energy must be expended to force the liquid through the bearing. Friction power Hf illustrates the rate at which energy must be expended to move the bearing. Expressions for H,, and Hf are as follows: Hp=Psq=
P,2@h3 ___ 77
(1)
so that from eqns. (1) and (2): (1) (2) (3) (4)
L,qwd density c =[jKg/Cublc Capillary diameter dc =mIrn Capillary ratlo of length-lo-diameter Capillary length I =l-im
0_
The flu,d
DH>(” Ml
Desian
comwtstion
Ht=H,+Hf=p~ + y
m I/de
77
=m
System I/O Board 1s in the larnlnar flow
flqw
condltlo”
procedure
(‘),y;cdgyKg,c”b,c m
(2) From
know”
,3,7$!rl~m (4) Reynolds
KC and i/de,
number
rnrj [=
cao,llary
diameter
4Cqo/(n
m dc Vls)
dc can be detarrnlned
.r]
(3)
If the bearing operates at zero or very slow speed the power ratio will be much less than 1 and it is only necessary to take into consideration the pumping power loss H,. In most applications, however, the working speed is not negligible. The total power may be minimized for any variable by partially differentiating eqn. (3) and setting to zero.
h
(b) Fig. 8. Design
procedure
of a capillary
restrictor
3.3.1. Optimum viscosity The designer may minimize the total power by choosing the optimum viscosity value. The way to find the
M B. Rowe et al. / Intellig&t design system for hydrostatic journal bearings
optimum viscosity is to vary the value of viscosity while maintaining all other design parameters fixed at the constant value appropriated for the design requirements, i.e.
(S--c-rrnb)(l
I ‘1
t-r) with axial slots
TJD without axial slots
so that
Ps2@h3 aH,=_-+ arl
A,U2 --_=-h
v2
Hf
Hg
K=
rl~
so that aH,l&q = 0 when H, =H,. power ratio is K=H,IH, = 1.
The corresponding
3.3.2. Optimum clearance As explained when considering the optimum viscosity, the optimum clearance can be found by partial differentiation when
aHt_ 3Ps2@h2 ah-
rl
r&U2 --=
3Hp
Hf
h
h
h2
so that aHJ3h = 0 when 3H, =H,. The corresponding power ratio is K=H,IH,=3. 3.3.3. Optimum power ratio
From an extension of the foregoing techniques, it may be shown that the optimum value of power ratio for a recessed hydrostatic journal bearing with a certain working speed always lies in the range 1
The ratio of total power to applied load is H, -=
B= -&C=
101
W
(I+K)H,
i2 and is proportional
to c
~
L2
6an (L-a)2
An optimum for 3 may be determined by partial differentiation of H, with respect to a and equating to zero. It is found that the optimal value of a is Ll 3. At increasing eccentricity the optimum value of land width a shifts to L/4 [ll]. The single-constraint optimal design module is developed from the basic design module with the optimization technique described above. When the designer clicks the single-constraint optimal design title on the menu card, the system replaces the menu with a new submenu as shown in Fig. 9. The designer can select any one from the submenu by clicking with the mouse. The system will then automatically guide the designer to enter the design procedure. Each of the four design procedures has its own defined optimization condition, i.e. K= 1 for optimum viscosity, K= 3 for optimum clearance, 1 ~K63 for optimum power ratio and a/ L = l/4 for optimum landwidth ratio. The four optimization conditions are also called single-constraint conditions; they are defined by the system. Except for these predefined single-constraint conditions, the single-constraint optimal design module is exactly the same as the basic design module. 3.4. Multi-constraint optimal design module There are tens of parameters for a recessed hydrostatic journal bearing. These parameters interact with each other and on their value selections. The singleconstraint optimization technique mentioned above is in principle insufficient to design a proper bearing even though it is essential for the bearing optimization.
W
(Click
required 1~0”s.
buttons aid character
tlties)
This may be written
The maximum load for the minimum power is achieved for the bearing shape which makes K a minimum. For a recessed hydrostatic journal bearing: total projected area A =LD; effective area A,=& is proportional to D(L -a). Hence k is proportional to (L-a)/L. Flow shape factor
Orthographic
Technical
(1) (2) (3) (4)
Projection
Orawing
Optimum Optimal Optimal Optimum
viscosity clearance power ratio land width ratio
n
Fig. 9. Submenu card.
for single-constraint
optimal
design
on the menu
W. B. Rowe
102
et al. / Intelligent design system for hydrostatic journal bearings
Ideally, it is necessary to use the multi-constraint optimization technique for the bearing optimal design. When designing a hydrostatic journal bearing, there are six essential design parameters which require detailed consideration [12]. These are: (i) the length to diameter ratio L/D; (ii) land/width ratio a/L; (iii) concentric pressure ratio p; (iv) radical clearance h,; (v) power ratio K; (vi) supply pressure P,. In a general design procedure, the supply pressure P, is the most essential parameter, since it must be sufficient to support the load. Other parameter values depend on the relationship to supply pressure. Therefore, the system searches for the optimum value of supply pressure P, as the first step of bearing parameter optimization. The system gives the six bearing parameters, with constraint conditions which can be defined by the designer. During the optimization search, the system takes the bearing performance requirements of maximum stiffness, mininum power dissipation and minimum temperature rise as the optimization objectives. The designer can also define the performance requirements as constraint conditions for the bearing optimization. In this module, the system combines a single variable search with multiconstraint conditions by AI techniques. This avoids the complexity of multivariable search, while the module can still perform the operation of optimizing multiple bearing parameters. Figure 10 shows the input card of this module; the designer can directly define the constraint conditions on the card. For a single-variable search, three basic search methods are the bisection search, the Fibonacci search and the golden-section search. Compared with the other two methods, the golden-section search has the advantages of simplicity and efficiency 1131. The system described here uses the golden-section search method. Figure 11 illustrates the algorithm of the system de-
-
%
Nulti-constraint
optimization
module (Input Card)
fl-
Please input the followmg parameters Dunng input, the system will give advlce When flnlshed, chck the ‘Opt~mlzat~on’ button to enter the OptlmlZ~tlO” procedure I. Basic parameters constrained by machine design: Besnng dwneter 170% D(mm) 5 IO0 Extreme load w’ :mN Shaft mtatlo” speed N 1CT 2000 rpm Beanng length 170~ L(mm) 5 iloo !. Selected basic parameters: Recess “umber n=@ Powerratlo mrKr/3 Axial slot wdth c=mrnm Axlal-flow land wdth a=~(mm Radial clearance mr ho(mm) % 0 09 Pressure rat10 j04lini 0 7 Crcumferentlal-flow land width bzmrnm IF? I. Calculated basic parameters: Lubncont “lscaslty VISZ~CP Mnlmum film thickness hmlnz(0 rim Supply pressure (4 5 PslMN/sqml r/7 ,. Calculated performance data. Temperaturense ATT~~I”C Fll”l stiffness x0 zm MN/In Pumping pqwer HP%= KW Flow rate qozloL/s Total power Htr mKW
Fig. 10. The module.
input
card
of the
multi-constraint
optimal
design
Put P.,+.+
Fig. 11. The pressure.
Calculated
Fig.
algorithm
Ps is
12. A warning
P,(Y,,+,) Onto output card
employed
outside
the
to search
for optimum
supply
required
demonstration
window
given
by the system.
veloped to search for the optimum value range of the supply pressure. As well as the intelligence described in the former two modules, in this module the system has the intelligence to supervise the optimal design procedure. The designer can click the “optimization” button on the input card to enter the optimization procedure. When the designer enters the procedure, the system first shows a dialogue window asking the designer to input the number of iterations. The system will carry out the optimization iteration cycle according to the number of times indicated by the input value. During the iteration, if a computer parameter value is outside the range limited by the constraint conditions, the system will pause the iteration and give a warning demonstration window with a warning sound. Figure 12 shows a warning demonstration window during the optimization process. The system tells the designer which calculated parameter value is outside the constraint range, and asks the designer whether to continue the optimization process or to stop it. It is possible that the designer’s constraints on the parameters values may not be suitable. The designer can click the “Continue” button to continue the optimization process. If the designer clicks the “Stop” button, the system will stop the process and shows a reasoning demonstration window on which the system shows its reasoning on the modification of the constraint conditions or other input values. A reasoning window is shown in Fig. 13. When the optimization accuracy is achieved, the system
W. B. Rowe et al. / Intellige‘nt design system for hydrostatic journal bearings
Increase the range Of
Fig. 13. A reasoning
supply
pressure
PS.
demonstration
window given by the system.
stops the iteration and gives a notice window with a short burst of light music. The designer can obtain all the optimization values from the output card. The intelligence demonstrated during the optimization is rule based and programmed in HYPERTALK. The program consists of tens of discrete scripts each one attached to its own object which may be a card, a field or a button. Their operations are monitored by the “Optimization” button. This also illustrates a characteristic of HYPERTALK programming.
103
multi-constraint optimal design module of the system be used. The other two modules can be used as auxiliary tools for the designer. Figure 14 shows a bearing design procedure with the multi-constraint optimal design module. The design bearing is to support the spindle of a precision turning machine. In this figure the data on card (d) is the designer’s input, the data on card (h) is the system bearing design output. In practice, cards (d) and (h) are one card with input-output double functions. They are separately demonstrated here for the convenience of description. Card (i) and (j) show the design procedure of a controlling restrictor for the bearing. Compared to the design output with the basic design module (see Figs. 4 and S), it is found that the results are significantly improved. The optimized bearing parameters and performance are quite appropriate for the precision turning machine application.
4. System operation and an example 5. Concluding remarks Although each of the three modules can provide a satisfactory design situation for a recessed hydrostatic journal bearing, it is usually recommended that the
**t**
@
BEARING:
Home
In this paper, an intelligent system has been presented for the design of recessed hydrostatic journal bearings.
Cardg$!$J*****
1. 2. 3. 4. 5. 6.
Conical journal bearing Partial ]our”al bearing Spherical bearing Recessed cylindrical journal bearing Plain journal bearing Combined ioumal and thrust beannqs (the Vateszbeari”g) SYSTEM: Which type, (liquid) “rm ?
In&x
******************************************** ’ i. Circuit and flow c”ntrnl devices ii. Tank, pump and supply system Bor=?
Intelligent System for Fluid Film Journal Bearings Design ***********************************************
I 07
m
24 urn
Design of recessed
Wednesdaq,
April
Liqpid or Gas Caoillaru
8, 1992
tlulti-constraint
Cy!i,ndrical.
optimization
Oriiice
Press&
valve
Slot
module (Input Card)
liquidfilm journal bearing (Cl,ck
requrred
,co”s,
l
Orthographic
Projection l
Technical
ac) f:ig. 14
Orawing
buttons
end charecter
titles)
Basic parameters constrained by machine design: ‘Extreme load w’.mN Beanng diameter 170~ D(mm) 5195 Shaft mtatlon speed N rm rpm Beanng length [7o-)i L(mm) rm Selected basic parameters: Recess number n=a Powerratlo miKr(3 Ax181slot wdth c=mJmm Axial-flow land width e=~rnm Rsdlsl clearance m07 ho(mm) $10 Cuwmferentlal-flow land wdfh b:mmm PressureratIo ali)rm Calculated basic parameters: nlnlmum film thickness hmln=m mm Lubncant vlscoslty V,S=mcP Supply pressure )5 i PslMN/saml r= Calculated perfornmnce data: -Temperature “se ATT~~‘C Film stiffness x0 2 150 Flow rate qo= 0 15 L/s Pump,ngpower Hpr. 0 5 Total power Htr %KW 1nntimi7atinn\ mrnw.. 6?!?i
1. Single-constraint optimization based on minimum power dissipation. 2. tlulti-constraint optimization based on minimum power, maximum stiffness and minimum temperature rise. ,,,-
I6
(4 (continued)
W. B. Rowe et al. I Intelligent design system for hydrostatic journal
104
a: /(W/O 17Ps)=[83666m :2) For aptlmum, land wdth e should be lxi = L/4:1209 mm ,3) Under the condltlon of a/L=0 ‘25, circumferential-flow m = (nD)/(3n):[r]mm 4) With exlal slots, the slot width I= (nD)/(Bn)=[OoImm .S) With axial slots, the 8” le degrees a= n/n-(b*c)/D= 30 0 c5l
bearings
(9) Calculate supply pressure m=(3W )/(xo’D(L-a)) =mMN/sqm IO) Calculate Stiffness
, ,,~~~~~~(~,r~:o,~~~“~*~mN/m ,,)~@ho, ;~~$$ciT-l’“”
land width
@J-J:
(n*D)/(6*a*“) :(oj 13) Slldlng speed of bearing surface m; 7fDN/60 zmrn/s 14) Recess orea for one pid mar (nD/n-b)(L-28) =[-jsqmm 15) Frlctlon we8 nDL/“)-(3Ar/4) =[449449Jsqrnrn 16~~:ds,ty (UirJ= ((P,*ho’*Z)/U)J((DB’l/Af) =[0017017]Ns/Sqm=\~IcP From the vlscoslty value, you are recommended--SAE 5(X ilght)
6) C~rcumferentlal flow factor a = “*a*(L-a)/(n*D*b) = 11076 :7) With axleI slots, coefllclent K m : s~“s[sl”e/a+rcosel =(o 8) Calculate dtmenslanless stiffness x0’ IHo’l= 3 82D(
I -DU(I +r(1-D))2pE?rl
(e)
rlow rare ,?j& (Ps*ho**3/ViS)“DB’ 18) M~mmum oummno oower
n
I I,
Multi-constraint
=10106/S
optimization
Please use followng
module
beanng pammeterr
(Output
Card)
a
given by the system I
20) Temperature ~,se a= 0 0000012Ps :mdegrees ****************************************************.
[xl
Basic parameters constrained by machine design: .Extreme load W :mlN Beanng dw”eter~’ D(mm) ~183 Beanng length m$ L(mm) I 183 Shaft mtatlon speed N i(rpm Selected basic parameters Powermt~o OrKra Ax101slot wdth c=/OOmm Recess number n=m Rsdlal clearance m$ ho(mm) ~(0105 Axlal-flow land wdth a=mImm Clrumferentlal-flow land wdth bz(21mm Pressure rat10 arorloil Celculeted basic parameters. Muwnum lllm thickness him”== mm Lubncant wscoslty V,s=mcP Supply pressure 1456 ! PslMN/sqm] rm Calculated per,o”,,ance data. -Temperature “se AT$m’I’c F~lr” stiffness xo :mMN/m Flow rate qo=(ous i=U”lpl”Q pOwe,Hpi(048 KW
cel~lus
Ix)
[ii!%-]
Exemusis: 0: Pleese use the velue given bq the sustem. _p: Pleas~qiven bu the sustem. Plea bditheegiven bq the system. c: Please use the velue given bq the sustem.
:
Design procedure parameters:
:nown Compared to other types of restrlctor, capillary restrlctors have several ldwntages which make them a popular chwce (1) manufacture I* ample (2) capillary control QIves the greatest tolerance to manufacturing “er~ences I” bearing clearance (3) with cawllary control the bearing load end stiffness are lndepende” Of flud wscoslty end hence of temperature rise Four Possible methods of makIng csp~llsry restrlctors are e hypodermic tubing (commercially awlable). b glass capillary (commercially available), c drllllng, d spark mnctuning nethods C and d do not usually produce pure capillary action since the ength-to-dlameterratlo ObtaInable IS Insufflclent Flow through B splllary should be lamlnar, it IS therefore necessary to check that the !eu”Oids “umber 1s less than 2000 ,G A
1) 2) 3) 4)
of
Llquld density c :1780]Kg/cublc Ca~lllary dlsmeter dc =mm Ceplllary ratlo of length-to-dlametrr Capillary length 1 :7/m
0
The fluld
flow
a capillary
restrictor
QJ
m l/de
=m
System I/O Board IS I” the Ismlnarflow
condltlon
PIIDISlsn lesign
computation
procedure-
“~:d,~,Kg,cub,c 2) From known
4)Reynolds
m Kc and I/de,
capillary
diameter
dc con be determlned
“umber
(9 Fig.
14. A bearing
design
procedure
with
the multi-constraint
The system is implemented on HYPERCARD on a Macintosh computer and is hence very user friendly. The system employs a new design method which incorporates AI techniques with conventional numerical design techniques. The incorporation of AI techniques integrates numerical and qualitative issues. Using the
optimal
design
module
system, a bearing design can easily be achieved. The system package can be obtained for just a small charge by contacting the authors. The system is currently in the process of further development. The authors intended to expand this system to include additional abilities such as intelligently
W. B. Rowe
et al. I Intelligent
design system for hydrostatic
learning from the experienced designer and being more flexible. These features will make the system more powerful.
6. Acknowledgements The authors wish to express their gratitude to Mr. Paul Wright and Mr. Peter Moran of the Liverpool Polytechnic for their help and assistance with this research work.
References J. P. O’Donoghue and W. B. Rowe, Hydrostatic bearing design, Tribal. Int., 2 (1) (1969) 2, 25-71. N. N. S. Chen and Y. S. Ho, Computer-aided design of hydrostatic journal bearings including shaft bending effect, Tribol. Int., IO (4) (1977) 221-228. M. K. Ghosh and B. C. Majumdar, Design of multirecess hydrostatic oil journal bearings, Tribal. ht., 13 (2) (1980) 73-78.
journal
bearings
105
4 M. A. Dumbrava, Review of principles and methods applied to the optimum calculation and design of externally-pressurized bearings. Part 1: Low/moderate speed bearings, TriboZ. ht., 18(3) (1985) 149-156. 5 P. Jackson, Introduction to Expert Systems, Addison-Wesley, Wokingham, UK, 2nd edn., 1990. 6 W. B. Rowe, Hydrostatic and Hybrid Bearing Design, Butterworths, London, 1983. 7 A. Bahrami, Designing Artificial Intelligence Based Software, Sigma Press, Wilmslow, UK, 1988. 8 Danny Goodman, T&eComplete HyperCard handbook, Bantam Books, New York, 2nd edn., 1988. 9 I. Sommerville, Software Engineering, Addison-Wesley, London, 3rd edn., 1989. 10 H. Opitz, Pressure pad bearings, Proc. Inst. Mech. Eng., 182 Part 3A, (1967-1968) lO&llS. 11 W. B. Rowe, J. P. O’Donoghue and A. Cameron, Optimization of externally pressurized bearings for minimum power and low temperature rise, Tribal. Int., 3 (4) (1970) 153-157. 12 K. J. Stout and W. B. Rowe, Externally pressurized bearingsdesign for manufacture. Part 3: design of liquid externally pressurized bearings for manufacture including tolerancing procedures, Tribal. Int., 7 (5) (1974) 195-212. 13 P. R. Adbyand M. A. H. Dempster, Introduction to Optimization Methods, Chapman and Hall, London, 1974.