AXIOMATIC DESIGN OF SIGNAL ANALYSES.pdf

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machine design, Vol.4(2012) No.1, ISSN 1821-1259 pp. 53-58

*Correspondence Author’s Address: University of Niš, Faculty of Mechanical engineering, Niš, Serbia, A. Medvedeva 14, 18000 Niš

Serbia, [email protected]

Research paper

AXIOMATIC DESIGN OF SIGNAL ANALYSES

Miloš MILOVANČEVIĆ1, * - Jelena STEFANOVIĆ MARINOVIĆ2 - Boban AN ĐELKOVIĆ3 1,2,3 University of Niš, Faculty of Mechanical engineering, Niš, Serbia

Received (08.01.2012); Revised (25.01.2012); Accepted (05.02.2012)

Abstract: Axiomatic design (Suh 1990, 2001) shows that the engineering of good designs can be taught as a science.There is a simple set of underlying rules, or design axioms, on which good designs are based. The design axioms provide the opportunity for teaching design as a science, in that it is based on some simple underlying principles.Taking advantage of this opportunity a systematic approach to teaching how to engineer and critically evaluate good designs has been developed.Three steps are used in introducing axiomatic design. First is providing motivation, which is attempted by observing

that design is fundamental to all engineering. The purpose of traditional engineering analysis, which is emphasized in

engineering studies, is to support design. Second is developing the concept that there are two simple axioms,independence and information, that govern design, just as Newton's laws govern mechanics. Third is observing that inorder to apply the axioms designs must be decomposed into a hierarchical structure. This leads to stating that there arethree essential elements to engineering design: the axioms, the structure, and the process for creating that structure.

Key words: axiomatic design, signal analyses

1. INTRODUCTION

The objective of this paper is to present a simple,

straightforward approach for teaching engineers the

theory and applications of axiomatic design in less than a

full course. Axiomatic design is especially worthwhile

because the design axioms elevate engineering design to a

science, governed by a few basic rules, from what has

been a kind of an art integrated with engineering analysis.

The importance of the effectiveness of teaching essential

methods in engineering design has a broad and significant

impact on adding value to the practice of engineering.

In 1997, Campbell and Colbeck published an insightful

critical literature review on teaching and assessing

engineering design. They note that there are no articles

about how to assess students' designs and that the

literature on teaching engineering design is relatively

new, begun about 1987. Campbell and Colbeck point out

that the approach to teaching engineering involves practice solving open-ended problems, creativity,

teamwork, teaching by coaching, and experience for

offering evaluation of student work. They stress the need

for more education on teamwork.

Evaluation of engineering designs in the absence of an

underlying science is problematic. Love in 1980 showed

how design evaluation could be based on the degree of

achieving objectives, or functions. Pugh in 1991, taking a

broad view, which incorporates marketing and selling, as

well as traditional engineering design functions, also

bases evaluation on a student's level of success in

achieving design objectives [17, 18, 19, 20, 21, 22, 23].

The University of Maryland has made notablecontributions to the literature on teaching engineering

design including Dieter's book (1991) which emphasizes

an algorithmic approach to design, and discusses

evolution, iteration, trial-and-error, art and intuition in

optimization of designs. Dieter also shows a method for

evaluating designs based on the degree of achieving the

functions. Parcover and McCuen (1995) cite the need for

curricular improvements. They focused on the

constructive learning method, the content of which is

process oriented, focusing on individual problem solving.

They emphasize experience, and iteration with prototypes

and testing for evaluating designs. Zhang (1999)

discussed a product driven approach to teaching design to

hundreds of first year students, at the University of

Maryland which emphasizes experience, one-on-one

instruction, and is resource intensive.

Decomposition can be a useful approach for a variety of

engineering problems. Frindley et al. (1992) discuss the

use of a kind of lateral decomposition, or product

dissection, divided into three segments: function,

performance, and manufacture. The purpose was to

facilitate the use of benchmarking in the design process,rather than assisting the design process itself. In that

work, it was enabling the application of benchmarking

that provided the motivation for product dissection or

decomposition. Their paper focuses on development and

applications of the benchmarking process for classroom

use [10, 11, 12, 13, 14, 15, 16].

In a landmark book for advancing a scientific approach to

design, Suh (1990) put forth a proposition that good

engineering design is governed by two axioms: axiom one

-maximizing independence (or minimizing coupling), and

axiom two - minimizing information (or maximizing the

probability of success). This approach is refined and

further illustrated with expanded applications of axiomatic design in a second book (Suh 2001). In Suh's

axiomatic approach, designs are evaluated according to

their compliance with the axioms, which inherently



Miloš Milovančević, Jelena Stefanović-Marinović, Boban Anđelković: Axiomatic design in signal analyses;

Machine Design, Vol.4(2012) No.1, ISSN 1821-1259; pp. 53-58

54

incorporates the degree of achieving the functional

requirements. The design structure of lateral

decomposition into design domains and vertical

decomposition into hierarchies defines the necessary parts

of applying the axioms. Suh also defines the process of

creating the hierarchy, by zigzagging between the

domains at progressively more detailed levels of thehierarchy, as well as by a process of physical integration

of the components. These are excellent books (Suh 1990,

2001), although they may be challenging for any teaching

situation other than a graduate or advanced undergraduate

course dedicated to axiomatic design.

For teaching axiomatic design, Bathurst (2004), in a paper given at the third international conference on axiomaticdesign and intended for those already familiar withaxiomatic design, emphasizes the importance of examples

and adapting existing design practices to independenceanalysis. He cites the strength of axiomatic design in promoting a hieratical representation that facilitates

communication, documentation, and evaluation. He alsonotes that high-level restructuring of the design process inindustry is required to implement axiomatic design.

An axiomatic approach to design allows engineeringdesign to be taught as a science. As in other sciences, basic underlying principles with broad applications can betaught... These principles are applied to solving design problems and are used for evaluation. This approach hasclear and important advantages over the traditionalapproaches, which rely on compliance with sometimes

abstract algorithms to attempt to ensure good results.These approaches often include intuition, innatecreativity, and evaluation by experience, teaching by one-

on-one coaching, and a process based on time-intensiveiterations of trial-and-error work. A good design methodshould be self-consistent and could therefore be used to

design the content as well as the best approach for teaching engineering design.

2. PRODUCT DESIGN

Axiomatic design is a tool for designing products and processes exceeding customer expectations. The

axiomatic design process is axiom driven assuringtechnology neutral and innovative solutions for increased

competitive power. The customer requirements are

decomposed in trees of independent and robust productfunctions successively translated to productspecifications. Axiomatic design is widely applicable

including design of simple products, design of integratedhardware, software, man /machine processes and design

of organizations.Design of products and processes are usually performedas an iterative organic growing process based onknowledge en experience within and outside the design project organization. Design goals are usually set basedon previous designs and customer requirements as defined

by the designer.Axiomatic design (AxD) is a widely applicable method

used to achieve a well structured and efficient design process. AxD is knowledge based and focused on asystematical identification and breakdown of customer needs to product specifications resulting in products with

to the customer robust attributes.

3. MATHEMATICS

AxD is based on mathematics. Mathematical definitionsand concepts are combined and adapted to en efficient

product developement management tool. The mostimportant mathematical building blocks are domians,

functions, mapping, matrices and statistical densityfunctions.

3.1. The design process

An ongoing design process can be described as a mappingof what we want to achive (design goal) on an domainthat describes how this will be achived (design result).This model is to crude to be used as a design management

tool. Axiomatic design use standardized domains to createstructure and facilitate systematic decomposition of

customer requirements. Axiomatic design is partitioningthe design process as follows:

Design goal; (Satisfy customer needs)

Customer domain; {Customer requirements} Functional domain; {Functional requirements}

Physical domain; {Design parameters};

Process domain; {Process variables} ;

Design result; (Products that satisfies customer requirement in a robust way)

Rows in black are axiomatic design standard domains.Text in {} are domain elements. Each domain pair represent a mapping i.e. the upper represent a design goal(what) and the lower a design result (how).

3.2. Mapping and zigzagging in hierarchies

Designs with just one customer requirement are mappedwith simple mathematical functions. However, most products have more than one customer requirement

leading to mappings in martrix equation forms. Thesemapping equations are called design equations.Complex products and processes are usually of ahierachichal design e.g. sturctured in a system, machine,component hierarchy. You usually zigzag betweendomain pairs when you work your way down through this

type of hierarchy. This facilitates a creative design process without design solution preferences. Example:Mapping the functional domain onto the physical domainwe chose an overall physical solution to satisfy an overall

function and subsequently decompose the physicalsolution to functions at next hierarchical level and then

mapping these onto the physical domain to create a moredetailed solution. This is repeated until we have animplementable design [5, 6, 7, 8, 9].The above described structure can be considered thedesign process fundamental structure. It provides goodtraceability and, if the independence axiom (se below) issatisfied, good scalability characteristics.

4. AXIOM

Based on the domain structure above the design axiomsare implemented to create robust high quality productswith customer appeal.In axiomatic design two design axioms are postulated –

the independence axiom and the information axiom.





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Based on these theorems and corollaries can be derived.This presentation will only adress the axioms.

If we mapp the functional domain onto the physicaldomain the independence axiom can be defined asfollows:

1. The Independence Axiom: Maintain the independence

of the functional requirements2. The design equation can be written in matrix form as

DP A FR ⋅= where FR is a vector with functional

requirements, A is the design matrix with designcoefficients and DP is a vector with design parameters. The coefficient matrix also called designmatrix, should be either diagonal or triangular tosatisfy the independence axiom. For all other designmatrixes, the design is dependent witch, given there is

a solution, require an iterative method to find a usefuldesign solution. This is also true for other domain pair

combinations.The product should satisfy the independence axiom inall parts including the chain from customer requirements via product design to process design and

down through the hierarchical trees between thedomain pairs. This usually tests the designer’s creative

skills. The result is often unique and patentablesolutions.Designs that satisfy the independence axiom are morerobust, simplify the design work, result in a less

complex design organization, simplify operation andmaintenance and are easier to use as platforms when

developing new products on previous designgenerations.

3. The Information Axiom: Minimize the informationcontent of the design

The information content for a functional requirement is

calculated with the functional requirement tolerance limits

and the corresponding system performance density

function as inputs. When the whole denisity function is

within the tolerance limits the information function has its

minimum value 0. For designs with more than one

functional requirement, designs with independent

functional requirements have the lowest information

content [1].

The information content is used as a design quality

measurement. It is used to compare different design

concepts and solutions to select the design that satisfy the

customer requirements in the best and most robust way .

4.1. Axiomatic design and quality of design

Standardized Design For Six Sigma (DFSS) processes

have been designed with axiomatic design as one of the

key components. Axiomtic design contributes to the

design quality through the design axioms but also through

the clear and customer focused structure facilitating

coordination of other quality enhancing tools. Among

these tools are TRIZ, innovation and patent databases,

design for x, statistically designed experiments and

associated robust design tools, cost / benefit analysis, risk

management, FMEA, traceability systems and cost

analysis.

4.2. Industrial applications

Well defined and executed axiomatic design projectsusually yield good results. Some examples: MuCell – anew plastic material with lower weight while improvingtoughness and dimensional stability – resulting in an

entirely new industry; Patented connectors – high

reliability and low weight – Tribotek inc started based onthe patent; Asian vehicle manufacturer used axiomaticdesign for “Lean” and “Value add” in the production process resulting in drastic reductions in “work in progress”, cycle times and volume of transport.

5. BASIC ELEMENTS OF AXIOMATIC

DESIGN

There are three basic elements that need to be understood

to get started teaching axiomatic design; they are: the

design axioms, structures, and processes. The axioms are

decomposed into the rules or grammar that governs

design, i.e., the two axioms, already mentioned above and

the corollaries and theorems (Suh 1990, 2001). The

structures are decomposed laterally (Fig. 1) into the

design domains and vertically into the design hierarchies

(Suh 1990, 2001). The processes consist of

decomposition, by zigzagging between the design

domains (Fig. 2) down to the "leaf levels" or "nitty-

gritty," i.e., the most detailed or fundamental level of the

design hierarchy, and physical integration or composition

of the final design (Suh 1990, 2001).

Functional

domain

Physical

domain

Process

domainWhat itdose?Functionalrequirements

FR1

FR2…FRn

↔

What itlooks like?Design parameters

DP1

DP2…DPn

↔

How it ismade?Processvariables

PV1

PV2…PVn

Fig. 1 Lateral decomposition ot trie design structure intodesign domains, ine arrows represent mapping betweenthe domains. Understanding the nature of the mapping isthe objective of engineering analysis and experimentation

(Suh 1990, 2001).

The lateral decomposition (Fig. 1) has been called the

playing field for design, and the axioms, corollaries, and

theorems called the rules. While the domains are usually

presented with the customer domain (not shown in Fig. 1)

and the process domain, the design exercises concentrate

on the relationships between the Functional Requirements

(FRs) and the Design Parameters (DPs) in the functional

and physical domains. The process domain is used as a

check to see if a reasonable manufacturing process and process variables exist. This helps with concurrent or

simultaneous engineering. Manufacturing process and

tool design are recast as product design problems aligned

with the appropriate customer FRs and DPs.





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Defining the FRs properly is essential for a good design.The final design cannot be better than the FRs. Engineers

have a tendency to jump immediately to physicalembodiments, DPs, in addressing design problems. Theresult, frequently, is that the FRs are not well defined.Understanding the difference between FRs andConstraints (Cs) is also essential.

5.1. Decompositions

At each level of the hierarchy the FRs must becollectively exhaustive and mutually exclusive (CEME).This means that the required functions are coveredwithout overlap between the FRs. The overlap would

result in coupling and violate the independence axiom.Also, the decompositions must logically flow from onelevel to the next. If an FR at one level, say FR1, is toguard against mechanical impacts, then it might bedecomposed in one of several logical ways. One waywould be to decompose it into guarding against

mechanical impacts from different directions, so that, for example, FR1.1 guards against vertical impacts, FR1.2 isto guard against frontal impacts, and FR1.3 is to guardagainst lateral impacts. Another decomposition schemewould be to guard against impacts of different duration.This could substitute for the above decomposition or be

useful in the next level of decomposition. In the case of guarding against shocks from different directions, whilethree lower level FRs for guarding against impacts fromthree different orthogonal directions appears to bedecoupled, i.e., mutually exclusive, it is not clear if oblique impacts would be included; therefore, the exercise

would require some checking to be sure that these lower

level FRs are collectively exhaustive.In the initial decompositions, a common mistake is todecompose an FR into only one other FR. This results ineither an incomplete decomposition, i.e., the lower levelFR is not collectively exhaustive, or else it makes the

lower level FR redundant, just a redefinition of the higher level FR. In the FR decomposition structure each parentmust have at least two children, unlike the biologicalmetaphor.

6. OPTIMAL MICRO CONFIGURATION

Optima micro configuration for vibration monitoring is

designed based on axiomatic design regarding electroniccomponents selection.Basic idea in optimal micro configuration design is tofulfill frame conditions that are required for pumpaggregates vibration monitoring.In order to define all components of micro configuration

it is necessary to define functional requirements of systemand conditions in which system will be tested.

6.1. Functional requirement of micro system for

vibration monitoring

Considering micro systems for vibration monitoring thesignal characteristics determine system accuracy and

vibration monitoring quality in general. Selection of themicrocontroller that is base for micro system has beendone primarily considering economical aspects of newlydeveloped system that is PC (personal computer)dependant [2]. Microchip, company that is producing

microcontrollers for more then a decade, andmicrocontroller PIC16F877A has been developed as

symbioses of microprocessor (CPU), memory and periphery, there for PIC is acronym for (PeripheralInterface Controller) [3]. This microcontroller is based onCMOS technology with RISC architecture andimplemented FLASH and EEPROM memories. Thus,PIC16F877A represents best compromise between priceand technology. Main signal characteristics that have been

chosen as main requirements for design of optimal microsystem are: resolution, stability and repeatability of signal. In order to fulfill requirement of resolution an A/Dconverter is added, since microcontroller has 10-bitresolution, a MCP3204 12-bit A/D converter is connectedvia SPI connection protocol [4].

Fig.2. Diagrams of signal repeatability testing byexponential signal

6.2. Signal repeatability analyses

Analyses of main, selected signal characteristics have

significant influents in optimal micro system selection.Significant signal resolution has been obtained by





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introducing MCP3204 12-bit A/D converter and stabilityis insured by selecting leading electronic components

manufactures and implementing their components. Thus,testing signal repeatability in laboratory conditions, onsignal generators Tektronix 3102 and Tektronix dpo 4034,is method for selecting optimal micro configuration.Following diagrams represent part of intensive signalrepeatability testing of selected optimal microconfiguration.

Signal repeatability has been tested by two types of complex signals: exponential and triangle. Exponentialsignal in repeatability testing is presented in Figure 2 infollowing order, a) original signal screen shot of referenttesting signal, b) fast furrier transformation (FFT)diagram of collected signal from tested configuration, c)

collected signal from tested configuration withouttransformation.

Fig.3. Diagrams of signal repeatability testing by triangle

signal

Triangle signal in repeatability testing is presented in

Figure 3 in following order, a) original signal screen shotof referent testing signal, b) fast furrier transformation

(FFT) diagram of collected signal from testedconfiguration, c) collected signal from tested

configuration without transformation. This testing has proved that selected optimal micro configuration for vibration monitoring based on microcontroller hassuitable performance regarding signal characteristics.

7. CONCLUSIONS

Using axiomatic design requires greater investment in the

higher levels of the design than is the practice historically.Engineers are often uncomfortable with investing somuch time in design work, without producing drawings.Managers need to realize the value of design effort at thehigher levels. For example, definitions need to beformulated to facilitate exclusivity and decomposition.

The goals of the design need to be clearly and succinctlystated. Often it is clear from the homework efforts thatthere is confusion between designing the product and

creating the design process for designing the product.Both exercises can have value, but they should be distinct.Also there is sometimes confusion between designing the

process and designing the tools to accomplish the process.These kinds of confusions may be only apparent when a

clear, systematic, and scientifically rigorous designapproach is used.In addition, axiomatic design provides clear and simplerules for evaluating the results of students' work,

eliminating the need to get experienced designers tolegitimate the evaluations.

Created monitoring system has significant results infrequency vibration analyses regarding mechanical

defects detection of the pumping aggregate

REFERENCES

[1] Milovančević, M., Milenković D., Troha S.(2009).The optimization of the vibrodiagnostic method applied on turbo machines. TRANSACTIONS OFFAMENA XXXIII-3 (2009), Faculty of mechanical

engineering and naval architecture, ISSN 1333-1124 pp. 63-71, Zagreb

[2] Milovančević, M., Miltenović Đ, Banić, M. (2008).Spectral analysis of the working order conditions for the engines on pumping power units, MonographMachine design, Faculty of Technical Science, NoviSad, ISBN 978-86-7892-105-6

[3] Milovančević, Miloš, Miltenović, Đor đe, Banić,

Milan (2009). Microcontroller based method for rotary machines monitoring , Machine Design: On theoccasion of 50th anniversary of the Faculty of Technical Sciences: 1960-2009 (ISSN 1821-1259);Faculty of Technical Sciences; Novi Sad

[4] Milovančević, M., Cvetković M. (2009). Primenanove generacije mikrokontrolera za analizu stanjaradne ispravnosti pumpnih agregata. Naučno-stručničasopis „Istraživanja i projektovanja za privredu”.ISSN 1451- 4117 UDC 33. Br.23/24. pp. 35-41.





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[5] Milovančević, M., Cvetković M. (2009). Aplikativni znač aj optimizacije vibrodijagnostič kog modela kod

turbo pumpi. Naučno-stručni časopis „Istraživanja i projektovanja za privredu”. ISSN 1451- 4117 UDC33. Br.25. pp. 41-48.

[6] Milovančević, M., Anđelković B. (2009). Wind turbine condition monitoring and control , Proc. of 3nd Internat. Conference POWER TRANSMISSIONS ‘09. 25 – 26 October, 2009. pp.

85.-90. Chalkidiki, Greece[7] Nelson, D., McVaugh, J.M. (1976). The Dynamics of

Rotor-Bearing Systems Using Finite Elements,Journal of Engineering for Industry, May 1976, pp.593.- 600., Paper No. 75-WA/DE-19,

[8] Nelson, H.D., Meacham, W.L. (1981). Transient

Analysis of Rotor-Bearing System Using Component

Mode Syntesis, The Gas Turbine Conference & Products Show, pp. 1-7

[9] Nordmann, R., Massmann, H. (1984). Identification

of Dynamic Coefficients of Annular Turbulent Seals,Proceedings of Rotordynamic Instability Problems inHigh-Performance Turbomachinery, NASAConference Publication 2338, College Station, Texas,

pp. 295.-312.[10] Nordmann, R., Weber, D., Hilbrath, K., Meinel, A.

(1990). StudienArbeit 8613/90/S24, ArbeitsgruppeMaschinendynamik, Kaiserslautern.

[11] Nordmann, R., Weber, D. (1990). Dynamik Vertikaler Turbomaschinen mit Fluiddynamischen

Koppelelementen, 1.Zwischenbericht ueber dasForschungvorhaben No. 136/8-1, Kaiserslautern

[12] Osgodd, W.F. (1965). Mechanics, Dover

Publications, New York.

[13] Pestel, E.C., Leckie, F.A. (1963). Matrix Methods in Elastomechanics, McGraw-Hill Book Company,

New York [14] Rades, M.: Mixed Precession Modes of Rotor-

Bearing Systems, Schwingungen in rotierdenMaschinen III, Viewig, 1995., pp. 153.-164.

[15] Rades, M. (1997). Use of Monophase Modal Vectorsin Rotordynamics, Schwingungen in rotierdenMaschinen IV, Viewig, pp. 105.-112.

[16] Sapunar, Z., Krpan, M. (1980). Dinamika,Sveučilišna naklada Liber, Zagreb.

[17] Schaffrath, G. (1969). Ein Vervahren zum Berechnender vier Feder- und der vier Dampfungskoeffizientenvon Radialgleitlagern, Forschung imIngenieurwessen 35, Nr. 6, pp.184.-195.

[18] Simon, U., Brommund, E.t, Periodische Bewegungeneiner Pendelzentrifuge in einem mehreckigen Fanlager , Schwingungen in rotierden Maschinen IV,Viewig, pp.181-188.

[19] Smith, I.N. (1994). Programming in Fortran 90, JohnWiley, Chichester.

[20] Smith, J.M., Griffiths, D.V. (1998). Programming the

Finite Element Method , John Wiley & Sons, NewYork.

[21] Someya, T. (1989). Journal Bearing Databook ,Springer-Verlag Berlin, Heidelberg.

[22] Souza, A.F., Garg, V.K. (1984). Advanced Dynamics, Modelling and Analysis, Prentice Hall International, New Yersey.

[23] Suh, NP (2001). Axiomatic Design: Advances and Applications. Oxford University Press, New York, NY.

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