Mtt-k. Mat*. 77m, cwy VoL 27. No. 4. pp. 491-505, 1992 0094-114X/92 ~Lq.00 + 0.00 Printed in Great Britain. All r io t s reserved C o ~ t G 1992 F,a,atom Prem Ltd

MODELING KNOWLEDGE-BASED SYSTEM FOR OPTIMUM MACHINE DESIGNt,~:

JERZY KOWALSKI ReMo Expert Group, WDK Ostrorop 35, 60-349 Poznan, Poland

(Received i November 1987". received for publication 5 November 1991)

Almtract--This paper describes a problem and procedure-oriented system for using modeling knowledge, to enable the increase of machine performances for different design Ionls. The system organization and operation has been outlined. The applications to solve design optimization problems for typical machine construction have been given. The perspective for complex machine modelinig and optimization has been discussed indodins system location.

INTRODUCTION

Dixon and Simmons gave a research program of expert systems for mechanical design [I]. Important applications of a knowledge-based system to a mechanical design were given by Dym [2].

Li and Papalambros have formulated an optimization knowledge-based system emphasising application of symbolic language for preprocessing of optimum design models [3]. However, the authors have not searched for the mathematical model of the design object, which would be adequate for the real design problem. The objective of this paper is to present a modeling knowledge-based system for optimum design of machine construction which facilitates the designer to create an adequate and easy solvable mathematical model of the design object. The system takes into account the degree of complexity for the design structure including a variable number. A variety of design problems and conditions, i.e. need for carrying out parametric, substructural and structural optimization which influences the model production, has been also considered in the system.

Parametric optimization

Based on the selection of an optimum set of variable values for the design object (or object series-type) with a given structure for the assumed optimization criterion by satisfying all constraints imposed on the construction.

Substructural optimization

Based on the selection of an optimum variant of design pair structure for the design object with a given structure from the set of variants for the assumed optimization criterion.

Structural optimization

Based on the selection of an optimum structure variant for the object exactly fulfilling the fixed parameters from the given set of compatible variants considering a production and operating for the assumed selection mask, i.e. a set of pairs of criteria and their scales (%) portions. In this way, the system presented is a problem and procedure-oriented system for using modeling knowledge, to aid the designer's effort in improving machine design performances.

The modeling knowledge-based system for optimum design of machine construction is based on a review of 39 expert references (Moses, Siddall, Canada; Feldbrugge, The Netherlands; Eschenauer, Fandei, Koller, Pahl, Fed. Rep. Germany; Shinno, Japan; Brandt, Golinski, Lesniak,

tBased on the author's lecture given in Stutqgart and Aachen Universities, Fed. Rep. Germany within the DAAD Professors Interchange Prolgram (1990).

~Dedictated to my mother Sabina Kowalska, 1904-1981.

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Pogorzelski, Urbaniec, Poland; Diechtiarenko, Pavlov, Savcenko, Soviet Union; Gregory, Jones, Moe, Pierson, U.K.; Alexander, Freudenstein, Johnson, Klir, Lee, Linstone, Nadler, Rao, Seireg, Wilde, Zhou, U.S.A. [4-36, 60-62] and the author's own research.

The system presented is a synthesis of the author's paper published in the period of 1981-1987. It is based on the abstraction process carried out on quantity, idea, methodology, s t r a t t~ and system levels, nnq~-tively. Figure I shows the creation process for the system. It contains 53 rules and 3 principles for the system-using listed in the paper. However, to obtain details, the author's references [37-39] are recommended.

The rules occurring in the system strongly increase the quality of the optimization model for the design object in the direction of its higher adequacy level to a real design problem and easy solution using a computer. Basically, it is obtained, utilizing the author's idea of a hierarchic two level optimization modeling system controlled according to the principles of classification of the object models as well as principles for selecting optimization criterion and constraints [37, 38, 41]. To fulfil their utility, the rules must also integrate design process, systems theory and the designer's intellect features.

It is noteworthy that the author has also made efforts to adapt Pavlov's hierarchic three level mathematical modeling system [20] to optimum design of machine construction. Because of certain defects of the system, it appeared to be, however, impossible [37].

In this way, the system presented may not be treated as any sophisticated front-ended optimization algorithm, but an effective aid to arrive at the optimized machine design.

The main application fields of the system are: static optimization based on nonlinear program- ming and determined models. However, it contains general principles for creating a possibly adequate model for optimization problems under risk and uncertainty.

Referring to dynamic optimization, the formulation of the model located at the upper level of abstraction for this problem appeared to be difficult [39]. Therefore, the dynamic optimization has been excluded from the system.

The system presented is coherent. However, the generalization degree for these considerations must be properly balanced. It would be aimless to search for much far-reaching correctness occurring in the models of design objects differing by their application.

The system presented is not a black box, but a tool which facilitates the creation of conscious product models by the designer. Therefore, it can not be treated as a panacea for all problems occurring in the design optimization of mechanical systems.

SYSTEM ORGANIZATION AND OPERATION

Let us describe the system organization and operation. The system is defined as the ordered doublet:

M g B S ffi (SSU, A S U ) , ( l)

where $$U is a STRATEGY subsystem, and ASU denotes an APPLICATION subsystem. One may treat the STRATEGY subsystem as the ordered doublet:

SSU ffi ~,K. M ) . (2)

Here K is a set of knowledge base, including inference engine, creating the heart of the system, and M is a set of methodologies for different design problem classes.

The set of knowledge base, including inference engine, is given as the ordered I 1 component set:

K ffi (P,) ; i ffi I, 2 . . . . . !! . (3)

Here PI is an information library subset including strategy skeletal idea, but the subsets P2-PII are operating subsets.

The subset P, contains the following input information: 1. Expert reference lists in the field of design optimization of mechanical sys-

tems [4-36]. 2. Strategy objective [37, 38, 41].

494 Jmz~ Kow~

3. Main application fields: static optimization based on nonlinear programming parametric, substructural and structural optimization; determined models [37, 38, 41].

4. Basic ideas outlined [37, 38, 41]. The operation subsets are arranged as follows:

p, m Subset of the rules of thumb for creating hierarchic two-level optimiTa_tion modeling system (rules 1-4).

P3 = Subset of the rules of thumb for classifying optimization models (rules 5-6). P, m Subset of the rules of thumb for selecting optimization criterion (rules 7-15). ,as =' Subset of the rules of thumb for selecting constraints (rules 16--21). /'6 = Subset of the rules of thumb for an integrating modeling idea within design

process (rules 22-25). /'7 = Subset of the rules of thumb for a connecting modeling idea within bases of

the systems theory (rules 26-28). Ps--Subset of the rules of thumb for complex product optimization (rules

29-3O). /'9 = Subset of the rules of thumb for approximate optimization of construction

shape (rule 3 I). Pm= Subset of the rules of thumb for minute detail of the modeling idea in

optimization problems under risk and uncertainty (rules 32-33). P,, = Subset of the rules of thumb for connecting the modeling idea within designer's

intellect features (rules 34-35). The rules are as follows:~"

i. Definition of the optimization model including index assessment for object reflexion in the model [37, 38, 41].

2. Brief basic pre-design for the optimization modeling system: creation ofan object kinematic diagram, structure graph and geometric models of design elements; variable identification; initial selection of optimization criterion [37, 38, 41].

3. General element specification of an analytic-structural model (upper level of abstrac- tion) [37, 38, 41] including object-system modeling [43].

4. Specification of quantity model elements (lower level of abstraction) including principles for model transformation [37, 38, 41].

5. Criteria for product model classification: means of interrelation: optimization criterion *-. object elements; effects of object structure and body complexity [37, 38, 41].

6. Basic classes and subclasses of product models [37, 38, 41]. 7. Set of machine construction features for creating optimization criteria [37, 38, 41] including

decomposition problem [43]. 8. Recommendations for selecting the optimization criterion type based on objective function,

comparative factor, scaling and preference functions including utilization assessment for fuzzy set theory [38, 41].

9. Recommendations for polyoptimization problem formulation [37, 41]. 10. Recommendations for decomposition-making based on variable number and its limitation

[37, 38, 43]. 11. Definition of additive dimensionless scaling function and preference function (scaling

function interrelated with distance function) for uniform not too large objects including geometric representation [38, 40-42].

12. Definition of the scaling function for objects-systems [37, 38, 41,43]. 13. Recommendations for scaling factor selection [38, 41]. 14. Method for series-type optimum design [37, 41,44]. 15. Assessment of direct interrelation: product .-. optimization criterion [37, 41]. 16. General classification of constraints [37, 38, 41]. 17. Recommendations for explicit constraint formulation [37, 38, 41].

tDue to limitations, structural components of particular rules have not been given.

18. Reoommendations for elastic preference of inequality constraints: their input for not too large uniform objects [37, 38, 41]; equality constraint formulation for object-systems aided by using artificial variables [37, 38, 41, 43].

19. Application of transcendental, differential and integral equations to constraint formu- lation [38, 411.

20. Constraint significance analysis [38, 41]. 21. Recommendations for optimum decision making aided by different calculation methods

for design pairs[37, 38, 41]. 22. Basic location of the modeling idea in the design process [37, 38, 41]. 23. Step sequence for object pre-design incorporating modeling idea [37, 38, 41]. 24. Recommendations for using effective numerical methods for solving models [37, 38]. 25. Modeling system revision [37, 38, 41]. 26. Subordination degree of modeling idea elements into fundamental aspects of systems

theory (model design and justification) [41]. 27. Subordination degree of modeling idea elements into fundamental operating aspects

(control and communication aspects)[41]. 28. Possibilities and limitations of modeling idea [38, 41]. 29. Three step method for complex product optimization [37, 38, 41]. 30. General recommendations for using uniform means of particular optimization problem

formulation by nonlinear programming for the manufacturing processes of optimized construc- tion [37, 38, 41].

31. General recommendations for variable selection for optimum outer contour problem of the constrnction [41].

32. General recommendations for creating product models at upper levels of abstraction for optimization problems under risk and uncertainty [37, 38].

33. General procedure for creating product models at lower levels of abstraction for optimization problems under risk [37].

34. General classification of the factors combined with a structure of designer's intellect model including elements inspiring development of his features [38, 41].

35. Subordination degree of modeling idea elements into designer's intellect features [41]. The set of methodologies for different design problem classes is given as the ordered doublet:

Here

M -. ; ,MC, M S ) . (4)

M C ,~ Subset of methodologies for creating optimization models for classes of recurrent objects in machine design (rules 36-43). It contains the following elementary subsets: M C I for the class "gears and gearboxes" and M C 2 for the class "screw construction".

M S - , Subset of methodology for selecting optimum structure for the object exactly fulfilling the fixed parameters (rules 44-47).

The rules are as follows: 36. Characteristic qualities of models for a class of recurrent objects at upper level of

abstraction for M C ! [37, 38, 47] and for M C 2 [48]. 37. Characteristic qualities of models for a class of recurrent objects at lower level of

abstraction [37, 38, 46--48]. 38. Application of methodically formulated models for a class of recurrent objects to practical

construction [37, 38, 47, 48]. 39. Procedure for creating variants of design pair structure for a class of recurrent objects

[37, 38, 47, 48]. 40. Procedure for arranging variables and parameters for a class of recurrent objects

[37, 38, 47, 48]. 41. Recommendations for selecting optimization criterion for a class of recurrent objects

[37, 38, 46-48]. 42. Recommendations for constraint formulation for a class of recurrent objects including

making rational simplification [37, 38, 47, 48].

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43. Application of methodical recommendations for model creation for a class of recurrent objects to practical design [37, 38, 47, 48].

44. Four step method of structure selection for the object [38, 45]. 45. Recommendations for selection mask-assuming [38, 45]. 46. Recommendations for point allocation for particular strucural variants and criteria [38, 45]. 47. Application ofthe method ofstructure selection to design self-loading trailer geurbox [38, 45].

The APPLICATION subsystem creates a model bank for typical machine construction. It may be treated as the ordered triplet:

ASU = <OS, CL, RE>, (5)

where OB is a set of typical design objects, CL denotes a set of optimization model classes and subclasses, and RE is a set of relations of mutual compatibility amonget elements of the sets OB and CL.

The subsystem ASU contains rules 48-53. The rules are as follows: 48. General model bank organization [38].

Block A

Objects assigned to model class of uniform objects/subclass of complete models. (Typical objects listed: screw jack, worm- and planetary geared hoists, scroll three-jaw chuck, boiler drum, two-column radiator of central heating, laboratory electromagnet, casted grid for measuring residual stresses, channel manhole: four variants of design pair structure for worm geared hoist.)

Block B

Objects a_~igned to model class of uniform objects/subclass of partial models. (Typical objects listed: double-wave gear with flexible toothed wheel rim, five-speed gearbox, four-stroke single- cylinder diesel engine of a tractor, gathering assembly of a self-loading trailer; two variants of design pair structure for the five-speed gearbox and four variants for diesel engine.)

Block C

Object assigned to model class of objects composed of subsystems/subclass of complete models. (Typical object listed: three-throw plunger pump including two variants of design pair structure.)

Block D

Objects assigned to model class of objects composed of subsystems/subclass of partial models. (Typical objects listed: two-high strip mill, forging crank press; two variants of design pair structure for strip mill.)

49. Table specification of structural relations and correlations between material parameters occurring in the models at an upper level of abstraction for the objects listed [38, 41].

50. Table specification of qualities occurring in the models at lower level of abstraction for the objects listed [38].

51. Specification of elements of the analytic-structural model and typical elements of the quantity model for the objects listed. (The author's references are recommended as follows: screw jack [37, 48], worm- and planetary seared hoists [37, 49], scroll three-jaw chuch [37, 44], boiler drum [37, 50], two-column radiator of central heating [51], laboratory electromagnet [52], casted grid for measuring residual stresses [53], channel manhole [54], double-wave gear [37, 47], five-speed gearbox [37, 55], four-stroke single-cylinder diesel engine of a tractor [37, 42], gathering assembly of a self-loading trailer [41, 56], three-throw plunger pump [37, 57], forging crank press [43].)

52. Specification of numerical calculation results or starting point determination for a computer for the objects listed [37, 38].

53. Application of modeling systems to design including level obtained of technical and economic effects [37, 38].

Figure 2 shows basic details of designer-and-system cooperation. The principles for system- using are as follows:

(A) While creating optimization models of the neutral object, i.e. not assigned to the class of recurrent objects or not located in the model bank, the designer uses the set of knowledge base

Modeling SYSTEM for optimum design I

°' machi" c°nllrucu+°n I '~ 1 STRATEGY subsystem I

~ . . * Set of Bet of melho- knowledge dologics for

base Including different design Inference engine problem classes

2 APPLICATION subsystem

Model bank for typical machine con strucl~,.~,..

Objects listed i ~ Block A

Screw jack

Worm geared hoist

Planetary geared hoist

Scroll throe-jew chuck

Boiler drum

Two-column radiator of central heating

Laboratorial electro- magnet

Casted grid for measuring residual stresses

Channel manhole

Block B

Double-wave gear

Five-speed gearbox

Four-stroke single- cylinder diesel engine ol I tractor

Gathering assembly of a self-loading triller

Block C

Three-throw plunger pump

Block O

Two-high strip mill

Forging press

Subset of information library including

strategy skeletal idea

Operation subsets

- - I I I - - - i i

I

Subset of methodologies for creating optimization

models for object classes

t Gear and gear-boxes

Screw construction

Subset of methodology for selecting optimum

structure

Possibilities for carrying out

substrural optimi- zation for object

Graph el modeling process (MPG)

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I

I I

I I

I I

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SYSTEM

I I

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t

Optimization model / formulation for ~e.

recurrent object . ~

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Screw construction J

0plimum structure L selection for object J -

1] Optimization model utilization for typical

object or model ~" formulation for

approximated object or design requirement

modification for typical object

i

I . D E S I G N E R

Fig. 2. Basic details of designer.and-system cooperation.

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including interference engine of the STRATEGY subsystem. It also covers a case of approximate selection of optimum outer contour for a construction.

(B) While creating optimization models of the object which is a$~gned to the classes listed of recurrent objects or selecting optimum structure for the object from a set of compatible structures, the designer uses the set of methodologies for different design problem classes of the STRATEGY subsystem. However, for this purpose, the utilization of chosen operation subsets of the set of knowledge base may be necessary.

(C) While creating optimization models of the object which is located in the model hank or approximated to the object listed, the designer directly uses the APPLICATION subsystem. It also covers a case of design modifying requirement in relation to the models located in the hank, e.g. transformation of a partial model for the double-wave gear [37, 47] to a complete one.

While creating an optimization model of the object, it is recommended to plot a graph of the modeling process. This directed graph is defined as the ordered triplet:

M;'G -- (V', L', R'> (6)

where V' is vertex set, L" denotes line set, but R' is relation set. The vertices are the system rules which have been chosen by the designer for the considered object and design problem type. The lines join neighboring rules used in the modeling process, according to the general sequence of rules occurring in the system. The relations show mutual compatibility of following rules and lines in particular elements of the system.

SYSTEM APPLICATIONS

The system developed in this paper has been implemented in the Faculty of Engineering at Salamanca, University of Guanajuato and the School of Engineering, Autonomous University of Zacatecas, Mexico. The research program has been included in the project entitled "'Prototype Design and Production for Small and Average Industry" supported by the OEA, American Country Organization [38].

Design optimization of a poppet cut-off valve A problem of parametric optimization for a poppet cut-off valve has not been considered in

professional literature. Also in the ASME's course of 22-23 September, 1986 entitled "'Valve selection, design and manufacture" no problem in the field of valve optimum design was presented.

Therefore, to model valves, principle (A) for system-using should be applied. According to this principle, Fig. 3 shows the graph of the modeling process for the object. It is a graphical representation of equation (6) for the considered object and design problem type.

From 35 rules located in the set of knowledge base including inference engine K, 17 rules have been used to model valves. They are combined with operation subset P2-P~. The operations have been preceded by use of the subset of information library including strategy skeletal idea Pi. However, basic operations in the modeling process of the valve are carried out, using operation subset P~-Ps.

One treats rules I and 2 as a preliminary to formulate hierarchic two-level optimization modeling system for the valve. The 1st rule contains a general definition of the optimization model for the design object [41]. It is treated as the ordered triplet:

OM = (E*, W*, R*), (7)

where E* denotes the set of design element representations, W* is the set of object feature representations and R* denotes the set of object relation representations. The optimization criterion f is also included in the W* set. In any optimization model, the part of rapresentatiom may occur in a hidden form. The Ist rule also informs one that an index of object reflection in the model is incomplete because only part of representations is homomorphous.

The 2nd rule permits us to formulate a brief basic pre-design valve modeling system [41]. First, the valve functional diagram is created (Fig. 4) and, then, the design structure graph and geometric models for particular design elements. The considered valve is composed of I I design elements, but the geometric models are created, based on the existing construction [60]. The design structure

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Ner.esslly of optimization model I formulation for a poppet cut-off

valve

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Formulation of optimization modeling system for poppet valve:22 variables,

29 inequality constraints: model-solving and evaluation

Fig. 3. Graph of modeling process for the valve.

graph permits us to systematize the process of model creation according to a working sequence of the elements in the object. Using geometric models and Re£ [60], one identifies the variables.

The thickness of the casing wall and flanges; the semiaxes of casing internal eliptic cross-section; the screw bore, number and spacing of casing-and-piping joint; the valve head full diameter and basic thickness; the valve spindle thread pitch diameter and basic length; the pitch diameter of spindle nut outside thread; the length and thickness of cover; the screw bore for easing-and-cover joint; the rectangle cross-section dimensions and depth for valve yoke; the gland tube full diameter and depth; the fork bolt thread pitch diameter and spacing, are treated as the variables. Considering valve of a general application and large-lot production, the object mass (excluding standard handwbeel) has been assumed initially as the optimization criterion.

Using the 3rd rule [41, 42], the analytic structural model for the valve is created. It is an effective means to determine structural relations such as: correlations between the components and elements of optimization criterion and variables as well as the constraints imposed on the design and variables. Moreover, it determines correlations amongst material parameters, and sets of nonma- terial parameters. The formulation of the analytic structural model also enables us to create a valve quantity model by which this model is directly systematized.

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Using the 4th rule [41], one creates a valve quantity model, in which all kinds of relations are quantified as the mathematical formulae, i.e. equalities and inequalities.

Rules 5 and 6 are a controlling modeling process of the design object, to determine the means of interrelation: optimization criterion ,-, object elements and establish a class and subclass of the object models, for which a valve model must be assigned. For the considered case, the variable number is 22. Therefore, the valve model is assigned to the model class of uniform objects, i.e. without making decomposition [41]. RefmTing to the model subclass, it is a complete one, because the assumed optimization criterion directly influences the whole object, i.e.

f . - . E* (s)

On the one hand, rules 7 and 8 permit us to take a final decision concerning selection of the optimization criterion. Particularly, using the 7th rule, the input of mechanical efficiency and/or stress equalization for casing may be considered. In this case, it is necessary to use a scaling function [41] or preference function i.e. scaling function interrelated with distance function [40]. An application of valve scat total life criterion would require experiments including theoretical specification. On the other hand, the formulation of the optimization criterion based on fuzzy set theory is difficult due to lack of certain date. Considering the valve of a general application, the object mass is fixed as the objective function. It is noteworthy that the average valve cost in Mexico is $2.50-330. Therefore, the problem of valve mass reduction is important, using optimum design.

Rules 16-18 effectively aid the process of the constraint formulation. Particularly, the 16th rule permits us to systematize constraints according to basic types. In the considered case, the number of inequality constraints in 29. One may list stress conditions for casing wall and casing-and-piping screw joint, spindle, nut, valve head, cover including yoke, casing-and-cover screw joint, gland and fork bolts: yoke stiffness condition; fluid condition limiting free choking; design and assembly conditions. To formulate certain constraints, the Polish Technical Regulations [60] are used. However, while using American or German formulae, the general structure of these constraints is not changed.

The 17th rule recommends constraint explicit formulation [41] (contrary to the view expressed in Johnson's definition of the optimum design [28]). That means, they must be mathematically formed.

According to the ! 8th rule, it is necessary to avoid using the equality constraints, which makes the solution of valve computer model more difficult. All equality constraints have been put into the optimization criterion and inequality constraints.

Rules 22 and 23 show the stage in valve design process for which the application of optimum design may give maximum economic advantages. It is the pre-design stage, because further design stages have been directed by proposals resulting from the solution obtained using exact operations made on the optimization model.

The 24th rule permits us to select an effective numerical method for valve model-solving from the set of advanced methods [9, ! 1, 15, 16, 30, 36]. One selected a Lee-Freudenstein method of heuristic combinatorial optimization. It is a nonnumerical technique, the convergence of which is essentially independent of continuity, differentiability, or the starting point of the search. The method requires less computational capacity and time than most conventional optimization techniques.

Rules 25, 26 show interrelations of the object optimization model with systems theory [41]. Particularly, from the 25th rule, it results that an optimization modeling system for the valve considered has not the capacity of automatic adaptation to conditions of the design problem, but it is susceptible to partial modification of its elements. For example, for angle valve, this modification is based on the replacement of certain elements of the objective function and certain constraints. From this rule, it also results that valve optimization model is characterized by partial modularity because certain elements of optimization criterion and certain constraints may occur in the models of other designs, e.g. elements of pipe fittings. Moreover, the rule shows that finding the discrepancy in the valve modeling system is only possible by numerical experiments.

On the other hand, from the 26th rule [41], it results that the stability aspect of valve model solution is exactly combined with the model sensitivity with a small change of input values, e.g. parameters and small change of the model structure combined, e.g. the constraint form change. For this case, only numerical experiments enable one to evaluate the degree of the model sensitivity.

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Table 1. Values of objective fuaction for exisfiall tad opeimum valws

Objective function Existing Optimum values valve valve

f(x. It) - m- k8 19.23"7 13.795

The 27th rule [41] shows the imperfect state of modeling theory applied to the valve considered. Particularly, the evident presentation of representations of particular design elements in the model is impossible. It also concerns the representations of relations to mutual compatibility for the design elements resulting from their mating. Moreover, a minute detail of valve operation model in the constraint range is combined with necessity of making certain assumptions and using the determined calculation algorithms.

Existing Polish valve with the following basic parameters [60]: • working pressure P0 = 2.5 MPa; • pressure conduit nominal diameter D,~ = 50 mm; • steam temperature T = 523 K.

which have been optimized. The quantity model has been solved by the Lee-Freudenstein method, using minicomputer

TANDY 1000 PC. CPU time was equal to 480 s (for 10 solutions). Mass reduction of 28.29% (that means 5.442 kg including 3.675 kg for casing) has been achieved compared with the existing valve. The result is given in Table I. Moreover, the optimum design is characterized by a larger valve lift at 2.258 mm that improves the steam flow. The torque at the hand wheel is also decreased at 22.4% (that means 4700 Nmm). It permits us to select the hand wheel with a full diameter of 175 mm. (For the existing valve, this diameter is 200 mm.) If necessary, a pressure conduit may he incorporated to the optimization model.

Other a~Jlications Design optimization of a tractor gearbox for manufacture in Mexico. The modeling process for

the object is based on a system using principle (B). As the objective function, the gearbox rotating element mass has been selected. The gearbox model is assigned to the model class of uniform objects/subclass of partial models including a strong housing interrelation by the assumed optimization criterion. The optimization problem is reduced to finding the minimum of the objective function in an 8-dimensional space bounded by 23 stress, stiffness, total-life, design, assembly and production engineering inequality constraints. Eight design elements have been considered in the model. Using the Lee--Freudenstein method and minicomputer APPLE ll-e, 21.9°/, rotating element mass reduction (that means 3.767 kg) has been achieved compared with the existing gearbox. The optimum design method was used to modernize existing construction.

Design optimization of a general application of a worm gear. Using principle (B) for the system is also applied to the modeling process. The gear mass and efficiency are treated as the components of the scaling function. The worm gear model is assigned to the model class of uniform objects/subclass of complete models. The optimization problem is reduced to finding the minimum of the scaling function in a 13-dimensional space bounded by 20 stress, stiffness, total-life, heating, design and assembly inequality constraints. The object is composed of 14 design ekments.

The quantity model has been solved by the Lee-Freudenstein method, using minicomputer APPLE II-e. For scaling factor relation of 0.6 : 0.4, the highest effects have been obtained. The scaling function decreasing by 12.5% has been achieved compared with existing Polish gear. It brings 20.18% mass reduction (that means 30.932 kg including 13.163 kg for housing), and a I% efftciency increase.

Design optimization of a German four-stroke ~ringle-cylinder diesel engine MWM AICD 112E for a tractor. Using principle (C') for the system has been applied to the modeling process for the object. The variant of design pair structure considered corresponds to a crank shaft monolithic with counterweights and supported in slide bearings. The scaling function is based on the crank mechanism mass and typical height and length of crankcase. The engine model is assigned to the model class of uniform objects/subcluss of partial models including strong crankcase interrelation by the mass component. However, it also participates significantly in engine mass. The optimi~tion problem is reduced to finding the minimum of the scaling function in a 24-dimensional space

502 Jiw.zv KowAt.wa

Fi 8. 4. Functional diagram of the poppet cut-off valve.

bounded by 42 stress, total-life, vibration, balance, flywheel rim effect, design and assembly inequality constraints. Ten design elements have been considered in the model. The scaling factor relation has been assumed as 0.5, 0.25, 0.25. The quantity model has been solved by the Leo- Freudenstein method, using minicomputer TANDY 1200 HD. CPU time was equal to 72,000 s (for 90 solutions). The scaling function decreasing at 20.71% has been achieved compared with the existing engine. It brings 27.37% crank mechanism mass reduction (that means 28.013 kg), 9.82% crankcase basic height decrease (36.4 ram) and 27.86% crankcase basic length decrease (108.5 ram).

The engine modeling system covers the mechanical effects. If necessary, thermodynamic effects may be incorporated in the model for simultaneous minimizing of the crank mechanism mass and specific fuel consumption.

In this case, the optimization model contains 26 variables and 43 inequality constraints. The scaling factor relation has been assumed as 0.4:0.6. CPU time was equal to 4500 s (for 15 solutions). The scaling function decreasing is 10.52%. It brings a 23.4% crank mechanism mass reduction (that means 23.946 kg) and 2.38% specific fuel consumption reduction (4.399 ffHP h).

Design optimization of a double reduction bevel/helical gear. The modeling process for the object is based on using principle (B) for the system. The components of the preference function are: rotating elements mass, equalization of pinion wear, equalization of surface rise for Onions and equalization of bearing total life. As the factor of pinion wear uniformity, the ratio of safety factor for tooth bending to safety factor for tooth pressure is assumed. These factors have been determined by Niemann's method ("old" formulae) [61]. In order to obtain uniform pinion wear, the factor values should be located in the interval 1.25-1.65 which should be secured by the suitable constraints. The equalization of surface temperature rise for pinions is based on Seireg's method [62]. It was adapted by the author to the bevel gear. The gear model is assigned to the model class of uniform objects/subelass of partial models including strong housing interrelation by the mass component. The opthnk~tion problem is reduced to finding the minimum of the preferenee function in an 18-dimensional space bounded by 40 stress, stiffness, total-life design and assembly inequality constraints. Six design elements have been considered in the model. The quantity model has been solved by the method of systematic searching. For scaling factor relation of 0.2:0.2:0.2:0.4, the highest effects have been obtained. The preference function decreasing at 41.6% has been achieved compared with the existing Polish gear. It brings a 16.19% reduction of gear rotating element mass (that means 7.66 kg), 5.59% decrease of pinion wear equalization factor

T(technologial perrpective)

Command Uanagwnrnt Uethods kciotv and /

\ 0 Papalambror’ optimization

knowledge-based system

\ q Author’s modeling knowledge- based system tar optimum dosign of machine construction

\

Cognition Intuition Exporioncr Reactions Imagination Worth systen Unit reality

/

authority

--- _-- __-

P (individual perspective)

503

Traditional, automatized and optimum dosign 01 machino l ssomblios and l lomonts

Perspective of machino complex modeling and optimization

Perfect forms for optimization criterion 0.9. based on fuzzy set theory

Perlect tosting methods

Porfoct calculation methods

Incroaso of homromorfic rrlatron number in a model

Direct intrrrrlation between product and optimization criterion

Perfect optimization algorithms

Perfect computers

Optimization algorithm classification

Direct intrrrolation befwoon product model and optimization algorithm

Complor analysis 01 machine COSIS

Fig. 5. Pcrspcctiw for complex machine modeling and optimization including system location.

(0.00724). 93.16% decrease of equalization factor of pinion surface temperature rise (48.029”F) and 46.55% decrease of total life bearing equalization factor (182,879 h).

PERSPECTIVE FOR COMPLEX MACHINE MODELING AND OPTIMIZATION

Based on Linstone’s multiple perspective concept (311, Fig. 5 shows the perspective for compkx machine modeling and optimization including system location. The cone of technological pcrspec tive is simple, but the cones of organizational and individual perspectives arc multiple.

504 Jn.zv KowAt.wa

An engineer, computer scientist and economist concentrate on different problems of optimum machine design. However, they use the technological perspective, utili~/ng mathematical modeling and making an endeavour to quantify and optimize. This activity is presented in Fig. 5 by the lining cone common for all experts. Simply speaking "how", is the same for them, however, "what" is different for various organizations or persons. Figure $ shows the steep sequence for particular experts related with the development of various scientific theorie~ to fulfil technological perspec- fives. The organizational perspective strongly interrelates with the technological perspective. It identifies forces supporting and resisting the development of complex machine modeling and optimization that permits us to evaluate its social acceptation. Moreover, the organizational perspective increases the possibility to hasten or delay its implementation and permits us to choose tactical variants in the range of the determined organization or their new coalitions.

On the other hand, individual perspectives reveal unit intuition, reactions, command abilities and motivation which may be a principal for an interaction of the technological perspective.

CONCLUSION

The level obtained of technical and economic effects of design optimization for typical machine contruction has confirmed effectiveness of the modeling knowledge-hased system for practical design. It enables better rationalization of design process of new constructions and improves their quality by transferring the design working out stage from a labour-consuming testing step to the optimum design. However, while optimizing in practical terms, the designer is aware of pouibilities and limitations of the system presented and has to employ his own design and theoretical knowledge in the field.

For further reading Refs [63-65] are recommended. Optimum electrical machine design problems have been also included in the system presented.

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Modeling knowi~l~--bm~! system SO5

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