M. RoohnavazfarDepartment of Industrial Engineering,

Sharif University of Technology,

Tehran 11155, Iran

M. HoushmandDepartment of Industrial Engineering,

Sharif University of Technology,

Tehran 11155, Iran

R. Nasiri-Zarandi1Electrical Machines and Transformers

Research Laboratory,

Department of Electrical Engineering,

Amirkabir University of Technology,

Tehran 15916, Iran

e-mail: Rezanasiri.z@aut.ac.ir

M. MirsalimElectrical Machines and Transformers

Research Laboratory,

Department of Electrical Engineering,

Amirkabir University of Technology,

Tehran 15916, Iran;

School of Engineering,

St. Mary’s University,

San Antonio, TX 78228

Using Axiomatic DesignTheory for Selectionof the Optimum DesignSolution and ManufacturingProcess Plans of a LimitedAngle Torque MotorThe brushless dc limited angle torque motor (LATM) has been widely used in areas ofaerospace equipments, robot drives, optical scanning systems and any drive systems thatrequire limited motion, ranging from the simple ON-OFF servo valves to the accuratetracking of a reference signal. This paper presents the optimum design procedure of abrushless direct current LATM to satisfy the functional requirements (FRs) and con-straints using Independence axiom in axiomatic design (AD) approach. Also, to select thebest manufacturing process plan, we consider both cost and thermal performance as twoeffective criteria, and evaluate available alternatives by computing information contentin Information axiom. Finally, finite element method is employed to validate the resultsobtained by optimizations as well as experimental outcomes extracted from the manufac-tured prototype of the device. [DOI: 10.1115/1.4027969]

Keywords: axiomatic design theory, manufacturing process plan, limited angle torquemotor

1 Introduction

AD is a structured, rational design method generated toimprove design activities in the various design domains. Thismethodology is developed by Suh [1]. Since evaluation of engi-neering designs in the absence of an underlying science is prob-lematic, AD is especially worthwhile because the design axiomselevate engineering design to a science, governed by a few basicrules, from what has been a kind of an art integrated with engi-neering analysis [2]. When comparing the AD theory with otherdesign theories, it is clear that one of the most unique features ofAD is its requirement on clearly distinguishing design decisionsinto two different kinds with regards to the notions of domain andlayer (hence the 2D design framework). The former is called a“mapping” operation from “what” to “how” across two neighbor-ing domains, and the latter is called a “decomposition” operationfrom “what to what” (or “how to how”) across two adjacent layers[3]. Literatures offer many applications of AD methodology todesign products, systems, organizations, and software [4]. Linkeand Dornfeld [5] have reduced the gap between tool design andsustainability considerations by building an axiomatic grindingprocess model that can be used for life cycle considerations. Yuet al. [6] have designed and manufactured the sandwich endplateswhose face and core are made of carbon fiber reinforced compos-ite and honeycomb/foam, respectively. Kulak and Kahraman [7]have compared the advanced manufacturing systems using fuzzyand crisp AD. Maldonado et al. [8] have evaluated ergonomiccompatibility for the selection of computer numerical control(CNC) milling machines using fuzzy AD approach. Brown [9] hasused AD to design of the integrity of shaft surfaces for rotating lip

seals. Heo and Lee [10] have evaluated design of emergency corecooling systems. These studies show the applicability and benefitsof AD in solving industrial problems.

The LATM is an electromechanical actuator with a limitedrotation of a moving part. It produces torque through a limitedrotation angle normally less than 6180 deg. Depending on appli-cations, the several types of LATMs have been presented. Themain types of LATMs with their constructional descriptions werelisted by Nasiri-Zarandi et al. [11]. LATMs have advantages suchas higher torque/weight ratio, higher reliability, lower cost, accu-rate positioning capability, and ease of maintenance due to theelimination of mechanical commutation as well as electronicswitching over conventional motors [12]. Classic design of anLATM that was done by Nasiri-Zarandi et al. is based on mag-netic equivalent circuit (MEC) model [11]. Their performanceprediction as well as design of a wide-angle limited motion rotaryactuator has been presented in Refs. [11], [13], and [14]. An im-portant form of the LATM based on polarized reluctance principlecalled “Laws’ relay” has been constructed [15–21] in which thedesign, identification, and performance prediction have beeninvestigated. Modeling of the Laws’ relay actuator has been dis-cussed in Refs. [18] and [19]. The application of magnetic fluidsin a hydraulic servo-valve torque motor has been introduced inRefs. [20] and [21].The design and control of a two-pole toroi-dally wound armature LATM with application in fuel control ofgas-turbine engines has been presented in Ref. [12]. A brief cate-gorization of electromagnetic actuators based on operating princi-ple, design trade-offs, and material selection has been discussed inRef. [22]. The study of permanent magnets PM-assisted devicesbased upon MECis also performed in Refs. [23] and [24].

In this paper, AD methodology is applied to design and manu-facture of a radial slotless LATM. In this method, the design pa-rameters (DPs) are dependent on expert’s opinions in order toselect some design constant that have standard intervals. So wemeet a complicated design procedure. To conquer this complicity,

1Corresponding author.Contributed by the Manufacturing Engineering Division of ASME for publication

in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedSeptember 29, 2013; final manuscript received June 30, 2014; published onlineAugust 6, 2014. Assoc. Editor: Xiaoping Qian.

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the AD approach is applied to reduce the effect of designer’s opin-ions and the design computation time and to facilitate the designrecovery process.

Additionally, finite element analysis (FEA) is utilized, whoseresults closely agree with those issued from optimization out-comes as well as measurements obtained from a manufacturedprototype of the LATM, all of which satisfy the proposal motiva-tions, i.e., optimization method and manufacturing plane.

2 AD Methodology

AD is a tool for designing products and processes based on cus-tomer needs (CN). This theory is proposed and developed by Suhin 80s. According to AD every design object can be depicted infour design domains: the customer, the functional, the physical,and the process domains as depicted in Fig. 1 [25].

Each domain is characterized by set of information: CN in cus-tomer domain, FR, and constraints in functional domain, to meetthe FR, DP are determined in physical domain and process varia-bles (PVs) are defined for manufacturing in process domain.These domains are linked through several mappings as shown inFig. 1. There are three types mapping: (1) mapping between cus-tomer domain and functional domain is defined as conceptualdesign, (2) mapping between functional domain and physical do-main is defined as product design, (3) mapping between physicaldomain and process domain is defined as process design. As aresult of these mapping, two design matrices are defined. The firstmatrix defines the relations between the FRs and related DPs andthe second matrix depicts the relation between DPs and relativePVs. The elements of design matrices consist of “X” and “0” ele-ments such that “X” symbolizes the existence of relation while“0” symbolizes no relation between domains. In AD, there arethree types of design with respect to the number of FRs and DPs:(1) if the number of DPs is greater than the number of FRs, thedesign is named as redundant. (2) If the number of FRs is greaterthan the number of DPs, the design is named as coupled. (3) If the

number of DPs is equal to the number of FRs, the design can becoupled, decoupled, or uncoupled. If the design matrix is diago-nal, the design solution is uncoupled, if the design matrix is trian-gular, the design solution is decoupled. Otherwise, the designsolution is named as coupled and unacceptable [26]. AD providestwo axioms to conduce the direction of good design. The firstdesign axiom is known as the independence axiom and the secondaxiom is known as the information axiom. They are explained asfollowing [27]:

• Axiom 1: The independence axiom: maintain the independ-ence of the FR.

• Axiom 2: Information axiom: minimize the information con-tent of the design.

The independence axiom states that the independence of FRsmust always be maintained, where FRs are defined as the mini-mum set of independent requirements that characterizes the designgoals. With respect to this axiom, the uncoupled and decoupleddesigns are acceptable. The information axiom states that amongthe design concepts that satisfy the first axiom, the design conceptthat has the smallest information content is the best design [1]. In-formation is defined in terms of the information content, Ii, that isrelated in its simplest form to the probability of satisfying thegiven FRs. The information content determines that the designwith the highest probability of success is the best design. The in-formation content Ii for a given FRi is defined as [27]

Ii ¼ log2

1

pi

(1)

where Pi is the probability of achieving the FRi. In any design sit-uation, the probability of success is given by what designer wishesto achieve in terms of tolerance (i.e., design range) and what thesystem is capable of delivering (i.e., system range).

As shown in Fig. 2, the overlap between the designer-specified“area of the design range” and the system capability range “area

Fig. 1 The design process as a mapping

Fig. 2 Design, system, and common ranges and probability density function

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of the system range” is the region where the acceptable solutionexists. So the information content is equal to [27]

Ii ¼ log2

area of the system range

area of the common range

� �(2)

Where there is incomplete information about system and designranges, the fuzzy AD may be introduced. In this case, triangularfuzzy numbers (TFN) can well define these kinds of expressions.Because of the differences of expression between crisp and fuzzyAD, there is a membership function of TFN instead of probabilitydensity function in the crisp case. In order to systemically convertlinguistic terms to their corresponding fuzzy numbers, two numer-ical approximation systems for tangible and intangible factorswere used by Kulak and Kahraman [28]. So, information contentis equal to [7,27]

Ii ¼ log2

TFN of system design

common area

� �(3)

where the common area is the intersection area of TFN.

3 Definition of the Problem

This work proposes the design procedure and manufacturingplan of a LATM to meet a specified industrial application. Theconfiguration of the selected LATM is shown in Fig. 3(a).

In the current research to develop a two-pole LATM for anindustrial control application that requiring a 630 deg rotationwith a peak torque of 2.5 nm, a toroidally wound type solid corestator with rare-earth pole-tip rotor construction is selected. Thetwo DC stator windings are connected in series for single-phase exci-tation by a simple DC circuitry. The rotor carries field magnets andthe stator supports the armature windings. The interaction of thesetwo magnetic fields produces an electromagnetic torque whichcauses an attraction or repulsion force between the rotor and the sta-tor. The magnitude and direction of armature current determines themagnitude of the electromagnetic torque and rotor movement direc-tion. Manufacturers generally provide a theoretical torque versusshaft-position curve. Typically, the characteristic curve for LATMsis represented by the positive lobe of a cosine function; that is,

T ¼ Tp cos h:p

2

� �(4)

where h, p, and Tp are, respectively, the angle of rotation, thenumber of poles, and the peak torque. The general torque charac-teristic for toroidally wound motors can be represented by a simi-lar curve, but it may also have a flat portion as shown inFig. 3(b).The above equation approximates torque values only for

the roll-off portions of the curve. In particular, the curves do notreflect the effects of armature reaction, which depends on both ar-mature current level and magnet strength. The deflection range ofa LATM is generally specified in terms of a so-called excursionangle. This angle represents the difference between the rotor posi-tion that produces maximum torque and the zero-torque point onthe characteristic curve. The constant-torque region of a toroidallywound LATM that depends on the arc length of each sector of ar-mature winding and the pole arc length is derived as

h0 ¼us � ur

2(5)

where h0, us, and ur denote the constant-torque range, statorwinding arc angle, and rotor pole arc angle, respectively. The out-put torque of a LATM is directly proportional to the armature cur-rent. Hence, the torque-current characteristic is a straight line witha slope known as torque sensitivity constant kt.

A comprehensive design uses the MEC model [11]. The modelextracts the geometric parameters relations. The maximum torquerelation in MEC model at position h0 ¼ 0 is obtained as

Tp ¼pkkrsD

2i B2

0g

l0

(6)

where l0 is free space permeability, g is the length of air-gap, Di

is the inner diameter of stator core, B0 is the air-gap flux densitycorresponding to pick torque state, and k and krs are geometricconstants, which represent the ratios of w=Di and ur=us, respec-tively and w is the axial length of the LATM. The maximum tor-que is generated in a short time. By considering the maximumtorque instead of continuous torque, LATM size, weight, and costcan be reduced considerably [11]. The continuous torque is lim-ited by thermal criteria, whereas the maximum torque is usuallylimited by magnetic saturation or supply current or voltage capa-bility. Other actuator’s parameters are calculated in the step bystep design procedure. In the first step ur, us, and p are selectedaccording to the shape of motor, angular range of constant-torque,and the required maximum acceleration. The geometric constant kis usually considered as ð0:8� 1:6Þ=p for DC machines [11].Also, the average value of air-gap flux density B0 has a valuebetween 0.4 and 0.8 T [11]. According to industrial requirements,the motor axial length w, is limited between 20 mm and 80 mm.By substituting the given parameters k, B0, and w in Eq. (6), theair-gap length is calculated. An important step in LATM designprocess is determining the stator and rotor parameters. The selec-tion of an appropriate ferromagnetic material for stator and rotorcores is very important. The rotor structure is composed of tworadially magnetized PM and one cylindrical ferromagnetic magnetholder. Proper materials should have low residual magnetism, lowhysteresis loss, and a good saturation value of flux density as well

Fig. 3 (a) The configuration of designed LATM and (b) torque-rotor position characteristic ofa LATM

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as low cost. The geometric parameters of stator and rotor coresare determined after this step. By considering the continuity of themagnetic flux from PM to air-gap, the ampere’s law, and a bestlinear curve fitting for demagnetization characteristics (B-Hcurve) of PM assuming no saturation, the magnetic path length ineach PM is calculated. Next, electrical and mechanical time con-stants (TCs) of the LATM are calculated based on the dimensionsand electrical parameters of the motor [11]. Whereas, three pa-rameters k, w, and B0 vary between given upper and lower limits,for each value of these parameters in their intervals, a LATM maybe designed. The constant parameters of the design should beselected under a well knowledge of actuator system and experi-mentations. By defining k, w, B0 and changing these parameters inthe acceptable ranges, a wide variety of the design solutions maybe expected. This leads us to apply a methodology to confine andoptimize the design solutions with higher control over the DPswith respect to the industrial requirements. So, to determine thebest design solution and extract the manufacturing process plan,the AD approach has applied as an optimization tool.

4 Selection of the Best Design Solution of the LATM

A product is designed to meet an overall set of FRs and con-straints. In order to design LATM, FRs, and their correspondingDPs are selected, and the zigzagging between these two domainsis established. The minimum set of independent requirements thatcompletely characterizes the FRs of the LATM is determined asfollow. The values of the FRs are determined based on limitationsof industrial application of LATM. For example copper losses(CLs) are the main source of heat generation in the system. Theadmissible heat in the system is corresponding to 120 W of CLs.Furthermore, to track the reference signals, system needs to havean acceptable speed. The TC of LATM determines this desiredspeed. Moreover, industrial application has specific space formount an actuator with exact output torque.

• FR1 ¼ copper losses ðCLÞ must be 120 ðWÞ• FR2 ¼ time constant ðTCÞ must be 15 ðmsÞ• FR3 ¼ volume ðVÞ must be 400 ðcm3Þ• FR4 ¼ peak torque ðTÞ must be 2:5 ðnmÞConsidering the design relation in Eq. (7), in order to satisfy

CLs, the terminal resistance (R) is considered as first DP.

CL ¼ I2 � R ¼ T2

K2t

� R (7)

where Kt is torque/current sensitivity coefficient that is equal to1.11. In accordance with the design relation in Eq. (8), themoment of inertia (J) is considered as second DP to satisfying theTC.

TC ¼ R � Jkb � kt

(8)

where induced voltage coefficient kb is equal to kt [11]. Consider-ing the design relation in Eq. (9), in order to satisfy volume (V),the total air-gap (g) is considered as third DP.

V ¼ p4ðDo þ 2ðg�MCÞÞ2ðwþ 2ðg�MCÞÞ (9)

where Do is outer diameter and MC is mechanical clearance (air-gap between rotor PMs and winding surface). The design relationin Eq. (10) is extracted from Eq. (6) with substituting the krs withthe ur=us ratio. In order to satisfy peak torque (T), the air-gap fluxdensity ðB0Þ is considered as fourth DP.

T ¼ pKD2i B2

0 gur

l0uS

(10)

In order to select the independent FRs, some requirementsshould be considered as constraints. Table 1 shows the selectedconstraints in this work.

The relations between FRs and DPs are shown in the designmatrix as Eq. (11). This matrix includes two independents downtriangular sub matrices. According to AD methodology, this ma-trix is decoupled and does not violate the independence axiom.So, it is considered as a quite reasonable design. In order to designLATM, the values of the DPs have to be determined.

CL

TC

V

T

266664

377775 ¼

x11

x21

0

x22

" #0 0

0 0

0

0

0

0

x33 0

x43 x44

" #2666664

3777775

R

J

g

B0

266664

377775 (11)

The design equations of the first sub matrix are shown in Eqs.(12) and (13). Considering these equations, CL is the first FR thatshould be set by suitable R value in below equation:

CL ¼ x11 � R ¼T2

K2t

� R (12)

With respect to the values of CL and T of the actuator as twoFRs, the terminal resistance (R) is equal to 29.64 ðXÞ. By havingthe value of R, in order to adjust the TC value, it is sufficient todetermine the moment of inertia (J) in below equation:

TC ¼ x21 � Rþ x22 � J ¼R � Jkb � kt

(13)

Considering the kb and kt coefficients, J is equal to6:23� 10�4ðkgm2Þ. In accordance with the first row of the secondsub matrix, and the design relationship (9), the relation of the vol-ume (V), and total air-gap (g) are as follows:

V ¼ x33 � g ¼p4ðDo þ 2ðg�MCÞÞ2ðwþ 2ðg�MCÞÞ (14)

In order to select the LATM volume as the third FR, the totalair-gap (g) should be determined. Considering the outer diameterðDoÞ and MC, the value of g is equal to 4:325 ðmmÞ. In addition,the relation of air-gap flux density ðB0Þ, and peak torque (T) aredepicted as

T ¼ x43 � gþ x44 � B0 ¼pKD2

i B20 gur

l0uS

(15)

In order to select peak torque, it is required to determine thevalue of B0. With respect to the values of p, k, Di, and krs as con-straints, the value of B0 is equal to 0.43 T. In traditional design ofLATM, the designer should select a value for B0 from a specificinterval based on experience. However, the AD methodologyeliminates the trial and error in selection of B0 and gives a specificvalue for it.

Table 1 The industrial requirements of the LATM

Industrial requirements Value

Number of poles 2Outer diameter (mm) 100Axial length (mm) 40MC (mm) 1.5k (axial length/inner diameter) 0.55rotor pole arc angle 120 degstator winding arc angle 180 deg

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So as to manufacture LATM, it is necessary to define the PVsto satisfy each DP. In this work, wire material (WM), core mate-rial (CM), production technology (PT), and permanent magnetmaterial are considered as PVs to specify the terminal resistance,moment of inertia, total air-gap and air-gap flux density, respec-tively. The relations between DPs and PVs are shown in designmatrix as

R

J

g

B0

266664

377775 ¼

x11 0 0 0

0 x22 0 0

0 0 x33 0

0 0 0 x44

266664

377775

WM

CM

PT

PMM

266664

377775 (16)

As regards to independence axiom, this matrix is diagonal andshows an uncoupled design. There are several PV’s alternativesthat satisfy DPs. For example, in order to satisfy terminal resist-ance (R), two types of wire may be selected. They are single layerand double layer insulation wires. A most useful permanent mag-net is selected for the rotor according to their properties. For hightorque capability and energy product, NdFeB35 is chosen. Thealternatives for WM, CM, and PT are illustrated in Fig. 4.

In order to choose the best alternative for each PV, both costand thermal performance criteria are considered. The informationaxiom is used to select the optimum manufacturing process planbased on these criteria as follow.

5 Selection of the Best Manufacturing

Process Plan of the LATM

There are twelve manufacturing process plans of LATM whereselecting the PVs’ alternatives. For example, first plan consist of asingle layer wire, steel SA1010 as stator and rotor cores and wire-cut technology to manufacture the stator and rotor. Therefore,designers are faced to the problem of selecting the best manufac-turing process plan among 12 alternatives. All manufacturing pro-cess plans are depicted in Table 2. Information axiom may beused as a decision making tool to help in the process planners. Inorder to select the best alternative, the four steps are implementedas follows.

5.1 Evaluation of the Alternative of PVs Based on Costand Thermal Performance Criteria. In order to evaluate thePVs’ alternatives, both cost and thermal performance criteria areconsidered. In this study, the symbol “A” is considered as the unitof cost. Thermal performances of alternatives are expressed bylinguistic terms. The following numerical approximations systemis proposed to convert linguistic terms to their correspondingfuzzy numbers as shown in Fig. 5. This figure shows that the TFN½0; 0; 15� is very low, ½10; 20; 30� is low, ½25; 40; 55� is medium,½45; 60; 75� is high, and ½65; 100; 100� is very high. Based onexpert’s opinion, the evaluation of alternatives for WM, CM, andPT are expressed with respect to cost and thermal performance asshown in Table 3. For example, to calculate the cost of singlelayer wire, the weight of whole required length is multiplied bythe price per weight. Moreover, experts subjectively evaluate sin-gle and double layer wires with respect to thermal performancewith the linguistic terms “Medium” and “High”, respectively.

Fig. 4 The alternatives of each PV

Table 2 All the manufacturing process plans

Number of manufacturingprocess plan WMl PT CM

1 Single layer Wire cut Steel SA10102 Single layer Milling Steel SA10103 Single layer Wire cut Steel SA10204 Single layer Milling Steel SA10205 Single layer Wire cut Permendor6 Single layer Milling Permendor7 Double layer Wire cut Steel SA10108 Double layer Milling Steel SA10109 Double layer Wire cut Steel SA102010 Double layer Milling Steel SA102011 Double layer Wire cut Permendor12 Double layer Milling Permendor

Fig. 5 The numerical approximation system for thermal performance criterion

Table 3 The evaluation of the alternatives for WM, CM, and PT

Evaluation Single layer Double layer Steel SA1010 Steel SA1020 Permendor Wire cut Milling

Cost (per unit A) [29.0, 72.5] [58.0,101.5] [7.1,14.2] [14, 21] [21.9, 29.2] [150, 250] [100, 120]Thermal performance Medium High Low High Very high Medium High

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5.2 Calculation of the Information Content of Cost forEach Manufacturing Process Plan. The total cost of each manu-facturing process plan is totality of constitutive alternatives’ cost.For example, the total cost of first plan is totality of the requiredsingle layer wire cost and iron core cost and wire cut manufactur-ing cost. This value determines the system range of each manufac-turing process plan based on the cost criterion. The range120A; 250A½ � is suggested as the cost design range by designers.

Uniform probability density functions have used for the cost,since the design and system ranges have been equally probable.The design, system, and common ranges for the first manufactur-ing process plan based on the cost are illustrated in Fig. 6.

• Design range based on cost is equal to 120A; 250A½ �.• System range for first manufacturing process plan is equal to

186:1A; 336:7A½ �.• Common range that is the overlap between system and design

ranges is equal to 186:1A; 250A½ �.

IC¼ log2

system range

common range

� �¼ log2

336:7�186:1

250�186:1

� �¼ 1:236

(17)

The system ranges and the information content of the cost forall the manufacturing process plans are depicted in Table 4.

5.3 Calculation of the Information Content of ThermalPerformance for the Alternatives. Unlike the cost, the thermalperformance is a qualitative criterion. So, the thermal performan-ces of the manufacturing process plans are not equal to the aggre-gation of the values of this criterion for all the constitutivealternatives. Therefore, the information content for all the PVs’alternatives must be calculated. For example, the information con-tent of thermal performance for single layer wire is illustrated asFig. 7.

• Design range based on thermal performance for the singlelayer wire is equal to 50; 62:5; 75½ �.

• System range for the single layer wire is equal to 25; 40; 55½ �.• Common area that is intersection area of TFNs is equal to

0.454.

It¼ log2

TFN of system design

common area

� �¼ log2

15

0:454

� �¼ 5:0457

(18)

where It is the information content of thermal performancefor the single layer wire. The system and design ranges andthe information content of thermal performance for all thealternatives are depicted in Table 5.

In order to obtain the information content of thermal perform-ance for the manufacturing process plans, the values of informa-tion content of this criterion for all the constitutive alternatives

Fig. 6 Design, system and common ranges of cost for first manufacturing process plan

Table 4 System range data and information content of cost

Number of manufacturingprocess plan

Systemrange

Designrange

Information contentof cost criterion

1 [186.1,336.7] ½120; 150� 1.23682 [136.1,206.7] 03 [193.0,343.5] 1.40074 [143.0,213.5] 05 [200.9,351.7] 1.61886 [150.9,221.7] 07 [215.1,365.7] 2.10948 [165.1,235.7] 09 [222.0,372.5] 2.426310 [172.0,242.5] 011 [229.9,380.7] 2.907412 [179.9,250.7] 0.0143

Fig. 7 Design, system ranges and common area of thermal performance criterion for singlelayer wire

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should be gathered. For example, the information content of ther-mal performance for the first manufacturing process plan is total-ity of the information content of this criterion for the single layerwire, the iron core and the wire cut technology. The informationcontent of thermal performance for each manufacturing processplan is illustrated as column 2 in Table 6.

5.4 Calculation of the Total Information Content andSelection of the Best Manufacturing Process Plan. In order tocalculate the total information content for each manufacturingprocess plan, the values of information content with respect toboth cost and thermal performance criteria for each plan are gath-ered. The results are shown in Table 6.The manufacturing process

plan No. 10 has the smallest value of total information content.This plan consists of a double layer wire, steal SA1020 as statorand rotor cores and milling technology to manufacture the statorand rotor. According to the information axiom, this plan isselected as the best manufacturing process plan based on the costand thermal performance criteria.

6 FEA and Experimental Results

So as to compare the optimization outcomes of the studiedLATM, FEA is performed. Figure 8 shows the magnetic flux den-sity distributions within the designed LATM without and with sta-tor excitation, wherein it is seen that the ferromagnetic partsmagnetically operate at 1.5 T which guarantees that the CMs arenot saturated, all of which emanates from the presented designconsiderations for materials and geometrical parameters.

Based on the design data given in Table 1, a prototype LATMhas been manufactured as illustrated in Fig. 9. It is worth notingthat rotor components are glued by an “epoxy adhesive”, an adhe-sive material whose main benefits are strength and environmentalresistance. The torque-angle characteristic of the machine isextracted through the experimental test setup shown in Fig. 9(d).

The measured torque-angle characteristic of the LATM alongwith the FEA results was already depicted in Fig. 10(a). It isobserved that the measured data agrees well with those obtainedfrom FEA. The experimental position response of the prototypemotor that correlates well with the simulation result of the LATM

Table 5 System and design range data and information con-tent of thermal performance for all the alternatives

PV The alternativesof PVs

Systemrange

Designrange

Information content ofthermal performance

WMl Single layer [25,40,55] [50,62.5,75] 5.0457Double layer [45,60,75] [50,62.5,75] 0.4005

PT Wire cut [25,40,55] [45,52.5,65] 1.8754Milling [45,60,75] [45,52.5,65] 1.0445

CM Steel SA1010 [10,20,30] [25,47.5,70] 4.7082Steel SA1020 [45,60,75] [25,47.5,70] 0.5859

Permendor [65,100,100] [25,47.5,70] 5.3334

Table 6 The total information contents

Number ofmanufacturingprocess plan

Informationcontent of

thermal performance

Informationcontentof cost

Totalinformation

content

1 11.6293 1.2368 12.86612 10.7984 0 10.79843 7.5070 1.4007 8.90774 6.6761 0 6.67615 12.2545 1.6188 13.87336 11.4236 0 11.42367 6.9841 2.1094 9.09358 6.1532 0 6.15329 2.8618 2.4263 5.288110 2.0309 0 2.030911 7.6093 2.9074 10.516712 6.7784 0.0143 6.7927

Fig. 8 FEA of designed LATM (a) without stator excitation and (b) with stator excitation

Fig. 9 Pictures of the proposed LATM parts: (a) rotor, (b) arma-ture windings, (c) assembled LAT, and (d) experimental setup

Journal of Manufacturing Science and Engineering OCTOBER 2014, Vol. 136 / 051009-7

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as given in Fig. 10(b). It is seen that the rotor rotates from 0 to90 deg 250 ms which illustrates a satisfactory transient response.

7 Conclusion

In this work, a novel design process based on the AD theory fora LATM is developed. Having used the independence axiom, thetrial and error procedure in determining the main DPs are elimi-nated and the values of the DPs are calculated directly. This meth-odology explicitly extracts the design procedure from the first tothe last stages. Also, the optimum manufacturing process planwith respect to both cost and thermal performance is selectedamong several alternatives by the information axiom. Withrespect to this axiom, not only the most cost-effective manufactur-ing process plan, but also the most efficient performance criterionfor the LATM is determined. Finally, finite element method isemployed to validate the results obtained by optimizations as wellas experimental outcomes extracted from the manufactured proto-type of the device. All taken together satisfy the proposedapproach, i.e., optimization method and manufacturing process.The results of the current study were promising where using ADmethodology in an industrial case. However to get a preciseresults, the application of zigzag method on breaking down theFR, DP, and PV’s in the lower levels is suggested for furtherstudy.

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Fig. 10 (a) Torque-angle characteristic and (b) position responses of the LATM to a step input voltage obtained from finite ele-ment simulations and test

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