The international journal of advanced manufacturing technology, tập 59, số 5 8, 2012

In this way, the design parameters are organized in terms of how they can be obtained by the manufacturing processes that will form part of the chain, which is important to establish pro

ORIGINAL ARTICLE

A model to build manufacturing process chains

during embodiment design phases

Robert Blanch&Ines Ferrer&

Maria Luisa Garcia-Romeu

Received: 1 February 2011 / Accepted: 4 July 2011 / Published online: 22 July 2011

# Springer-Verlag London Limited 2011

Abstract The methods for manufacturing process selection

from early design phases avoid later mistakes and ensure

the success during product manufacturing Currently, the

majority of the products need more than one manufacturing

process to become finished parts This is known as a

manufacturing processes chain, and it is important that this

manufacturing chain is well designed This paper presents

the bases and the activity model (IDEFØ) to develop a

decision-support system that helps designers and

manufac-turing engineers to configure manufacmanufac-turing process chains

while the product is being designed The model

schema-tizes all the activities and information involved in obtaining

reliable manufacturing process chains The support system

has been applied to an air-bending die design process to be

used to perform either air-bending or bottoming

Keywords Manufacturing process Process selection

Activity model Decision-support system

1 Introduction

In a context of profound changes in industrial markets—in

relation to globalization and delocalization—the main

challenge for all industries is to remain competitive [1] Inthis context, companies need to focus on satisfying as much

as possible the product requirements demanded by themarket During the first stage of product development—thedesign process—many decisions are made to meet theserequirements; however, such decisions also affect on otherissues, such as process planning, manufacturing, assembly

or recycling of the product Considering these issues duringthe design stage is important because wrong decisions canhave serious effects on development time, cost, and productquality [2, 3] Given that manufacturing issues must betaken into account at the initial stages of design [3,4], thedesigner should know the manufacturing processes orsequence of processes (i.e., the manufacturing processchain) that may be used to manufacture what they aredesigning This, however, is not an easy task First, there is

a large variety of manufacturing processes; second, theknowledge associated with each process is abundant; and,finally, the increasing trend towards relocating andseparating manufacturing and design centers from eachother has led to a decline in designers’ understanding ofmanufacturing processes by making them less accessible

To solve this problem, several methods and tools havebeen developed to help designers select suitable manufac-turing processes during product design

Manufacturing process selection tools help designerschoose the most technically and economically suitablemanufacturing process to obtain a product [3,5] Most ofthe work developed is based on quantitative analysis Inmanufacturing process selection-based on quantitativeanalysis (MPS-BQA), the choice is made by comparingthe design parameters or specifications with the attributes ofthe manufacturing process Process attributes describe thecapabilities of the process in terms of material, shape, size,

R Blanch:I Ferrer ( *):M L Garcia-Romeu

Department of Mechanical Engineering and Industrial

Construction, University of Girona,

Campus Montilivi P-II,

tolerances, production rate, cost, and environmental impact,

allowing direct, objective comparisons to be made [5], for

example, of the tolerance or roughness each process is able

to obtain in a part Some relevant examples of these

research studies are: CES [6], MAS 2.0 [7], WiSeProM [8],

and WebMCSS [9] These tools may be applied from the

preliminary design stages, in which there is already a

rough idea of design parameters, such as shape, material

and weight, as well as of product restrictions, such as

production volume or cost limit The tools result is a list

of manufacturing processes which are able to achieve the

basic product form but designer have to chose only one

manufacturing process option (a, b, c, d, and e in Fig.1)

without combining more than one process as a chain

derivation allows To obtain manufacturing process chain,

two basic requirements have to be considered First, how

much and in what way a product is modified during each

process in the manufacturing process chain needs to be

considered, thus revealing what remains to be done in the

following processes Second, the compatibility of different

manufacturing processes needs to be considered to develop

manufacturing process chains that are technically feasible

This means ensuring that a particular process is compatible

with the subsequent process

The process chain can be defined from early design

using a selection process or during detail design using a

configuration process (Fig.1) The manufacturing process

chain selection comprises all the manufacturing processes—

taken as a sequence of processes—that meet all the product

requirements [10] For example, chains I and II in Fig 1

On the other hand, configuring the manufacturing process

chain means choosing the machinery, tools, and other

production parameters that will meet the product quality

requirements [10] (see chains III and IV in Fig 1.)Therefore, the configuration takes place at the processplanning level

This research is intended to develop a decision-supportsystem to help designers or manufacturer engineers knowthe sets of manufacturing process chains that could be used

to manufacture the products being designed during earlydesign It is assumed that each chain is able to manufacturethe product in its entirety However, the paper presents thefirst stages in the development of this system First of all,the framework approach on which the system is based isdescribed Second, the IDEFØ activity model, in which allthe activities, information, and knowledge involved inobtaining a set of viable manufacturing process chains aregathered, is presented to help select manufacturing processchains Finally, an example that shows the application of themodel is explained in detail

There are three main advantages of such a method First,the design parameters are better adapted to the manufac-turing requirements and there is a better validation of themanufacturability of the design for all the processesinvolved in its manufacture; second, any problems duringthe manufacturing phase arising from an unsuitable designare reduced since these problems are detected duringthe design process; and, finally, production costs can becalculated and compared for various manufacturingprocess chains

2 Framework approachThe manufacturing process chain is defined as a processmap that describes how the initial product blank is

Fig 1 Manufacturing

process chain related to the

design process

transformed into the final product To get a manufacturing

process chain capable of producing a product, a

manufac-turing process chain derivation method is used, which is

the core of the method described in this research study

(Fig 2) The derivation method which will be presented

next is based on both design information and the

capabilities of the processes for transforming the products,

and provides as a result the set of viable manufacturing

process chains that will produce the product It is focused

on mechanical products

As shown in Fig 2, the manufacturing process chain

must begin to take shape during the embodiment design

phase [9,11], when the requirements and the functionality

are defined, and a preliminary draft is written All this

design information has to be compiled in the product design

parameters, which are a qualitative description of the

designed product Basically, these parameters have been

extracted from research works related to MPS-BQA [6,7,

12], but they have been classified into three lists: required,

optional, and feature design parameters, which are

explained in detail in section3

The manufacturing process chain derivation method

requires concise information about the manufacturing

processes, especially regarding their capacity to modifythe product with respect to the design parameters Thisinformation has to be comparable with the productinformation in order to create viable manufacturing processchains from a technological point of view The manufac-turing process description is divided into three parts(Fig 2):

& The manufacturing process information concerns facturing process data related to product design and isdivided into manufacturing process constraints andmanufacturing process transformation capabilities.– The manufacturing process constraints are attrib-utes that describe the manufacturing processes andtheir ability to meet the product design parameters.These constraints include process capabilities related

manu-to material, shape, geometrical dimensions (e.g.,thickness or tolerance), roughness, geometrical fea-tures, and production rates, which also define theproduct, allowing direct and objective comparisons to

be made between design and manufacturing tion They are, therefore, the same as processattributes defined by Lovatt and Shercliff [5]

informa-Fig 2 Manufacturing process chain derivation

– The manufacturing process transformation

capabil-ities represent the capability of each manufacturing

process to modify the product design parameters

from the initial stage or to modify the product design

parameters that have been modified by previous

manufacturing processes These capabilities are

defined using maximum values of transformation,

which quantify how much a manufacturing process

can change a product parameter Furthermore, the

differences regarding manufacturing process

con-straints will be discussed further

& The manufacturing process sequencing rules define

technological constraints among different

manufactur-ing processes so that it is possible to distmanufactur-inguish

between viable and non-viable manufacturing process

chains, because not all process combinations are viable

as a manufacturing process chain [11] Therefore, for

each manufacturing process, it needs to specify all the

other compatible manufacturing processes that can be

carried out before it, after it, or both (Fig.3) Figure3

shows an example of the sequencing rules for the

milling process It shows that during the manufacturing

of a part, the processes of casting and powder

metallurgy must always take place before milling,

whereas bending or drilling processes (labeled “both”

in the figure) can take place either before or after

milling The polishing process, however, must take

place after milling

& The manufacturing process classification classifies

manufacturing processes that vary according to the

objective pursued with this classification The

manu-facturing process classification proposed by Lovatt and

Shercliff [5] is used in this work The processes are

classified according to the extent to which they can

transform the part and are classified as [5]: primary,

secondary, and tertiary The “primary processes” take

unshaped material (liquid metal, or a powder, or a solid

ingot) and give it shape Thus, molding, casting or

machining processes are primary The “secondary

processes” modify, add, or refine features to an

already-shaped body, such as fine machining and

polishing And finally, the “tertiary processes” addquality either to the bulk or to the surface of acomponent, for example, shot-peening of surfaces.Although this classification is not absolute, since aparticular process, such as machining, may belong tomore than one group, the use of this process classifi-cation reduces the complexity of the problem and limitsthe number of candidate processes for manufacturing

at each level of the product design Therefore, it limitsthe number of processes that need to be analyzed inorder to configure each step of the manufacturingprocess chain

3 Process chain derivation modelModeling knowledge and information used to integratedesign information with manufacturing information hasbeen extensively studied and is still a very active field, asconfirmed by the following studies Skander et al [1]modeled all the product information, the manufacturingconstraints related to design, and the required rules toimplement a method that integrated process selection andmanufacturing constraints into the design Ferrer et al [13]proposed a method to formalize the most relevant designinformation related to manufacturing that should be madeavailable to the designer to design for manufacturing ofnew designs Ciurana et al [14] modeled the processplanning activities in sheet metal processes and the modelwas implemented in a computer-aided tool Guerra-Zubiagaand Young [15] show different ways to model manufactur-ing knowledge and how to make it available when needed.Thibault et al [16] propose an integrated product–processapproach to evaluate its consistency and is useful inselecting suitable forging process and product designparameters Yuh-Jen Chen [17] modeled the process forconventional molding product design and process develop-ment by using the process modeling technique IDEFØ Andfinally, Mauchanda et al [18] model the knowledge andinformation to develop a tool to calculate the manufacturingcost from conceptual design

Fig 3 Example of milling

process sequencing rules

In accordance with the framework approach presented in

Section 2, an activities model using IDEFØ methodology

has been developed as skeleton of a decision-support

system to obtain a process chain The purpose is to

schematize all the activities involved in obtaining the viable

manufacturing process chains to manufacture a given

design from the designer’s point of view, i.e., to derive

the process chain (Fig.4)

The inputs required to carry out the main activity are the

computer-aided design (CAD) part sketch and the

manu-facturing process pool, whereas the output will be the set of

viable manufacturing process chains Manufacturing

pro-cess information, manufacturing propro-cess sequencing rules,

and manufacturing process classification act as controls

The manufacturing process pool represents the whole set of

manufacturing processes that are considered for the

selection It may be wider or narrower depending on the

scope This main activity, A0, is broken down into four

specific activities, A1, A2, A3, and A4, shown in Fig.4,

which will now be described in detail

Activity A1 “Analyze the product”

In this activity, the designer has to analyzethe product information from the CAD part

sketch and classify it into three lists of

design parameters (see Fig 5): required,

optional, and feature design parameters In

this way, the design parameters are organized

in terms of how they can be obtained by the

manufacturing processes that will form part

of the chain, which is important to establish

process chains The first list consists of the

required design parameters, which are those

that all the manufacturing processes in the

process chain have to be able to deal with

These parameters are exclusive, which

means that a process is excluded when it is

not able to process with this property, for any

step of the process chain The second list is

the optional design parameters, which are

product parameters that may be transformed

by various manufacturing processes until thefinal optional design parameter is reached.Finally, the third list is the feature designparameters, where a feature refers to thesignificant processing of portions of thegeometric shape of a part or assembly.Neither optional nor features are exclusivebecause they can be obtained along theprocess chain

Activity A2 “Analyze and select manufacturing process

level 1”

The goal of this activity is to analyze andselect the first manufacturing process in theprocess chain from the manufacturing pro-cess pool, using the required, optional andfeature design parameters as inputs, andboth manufacturing process information andmanufacturing process classification as con-trols (Fig.5) Two outputs are obtained: a set

of manufacturing processes ranked ing to which should occupy the first position

accord-of the process chain, called manufacturingprocess ranking for level 1, and a list ofresolved/unresolved design parameters Theresolved design parameters are those whichwill have been completely transformed orchanged by the selected process whereas theunresolved design parameters are thosewhich will require further manufacturingprocesses Activity A2 is further brokendown into four sub-activities, shown inFig 6

A2.1 “Select manufacturing processes compatiblewith the material”

The inputs for this sub-activity are themanufacturing process pool and the materialdesign parameter The material of the product iscompared to the set of materials with which

Fig 4 The basic derivation

of the process chain A0

each process is able to work, thus the result

obtained is a list of manufacturing processes

compatible with the material The material for

required design parameters was chosen as the

first discriminatory step because this parameter

is the most restrictive in terms of selecting

manufacturing processes and it reduces the

search range for the next steps [5,9] It means

that choosing the material for the first step a lot

of processes can be excluded since the product

cannot be obtained

A2.2 “Check required parameters”

This sub-activity checks whether or not the

processes in the list of manufacturing processes

compatible with the material (from activity

A2.1) are able to manufacture the other required

design parameters These parameters are

com-pared to the manufacturing process constraints

of each process When the process is able to

obtain all the parameters from the list of

required design parameters then the process is

kept on the list; otherwise it is excluded The

result is the list of manufacturing processes

satisfying required properties

A2.3 “Check optional and feature parameters”

In this activity the lists of optional and

feature design parameters are checked The

result is the viable manufacturing process list

and a first version of the list of resolved/

unresolved design parameters indicating which

processes are able to transform the part

accord-ing to those parameters and which ones are not

A2.4 “Evaluate the manufacturing process

transformation”

As stated in Section2, transformation is thecapability of each manufacturing process tomodify the parameters of the product eitherfrom the initial stage or after a previousmanufacturing process has already modifiedthem It means that achieving the values of agiven parameter depends on the starting value

of this parameter on the part To evaluate themanufacturing process transformation, themethod needs to calculate the transformationrequired in the product parameters by compar-ing the status of these parameters from onemanufacturing process to the next Subsequently,the values obtained for the required producttransformation must be compared with thetransformation capabilities of the particularmanufacturing process When the calculatedvalues are less than or equal to the manufacturingprocess transformation capabilities, the manu-facturing process is deemed able to transform allthe“resolved design parameters” of the part andtherefore there is no need to update the list ofresolved/unresolved design parameters Other-wise, when the calculated values are greaterthan the manufacturing process transformationcapability, the list of resolved/unresolved designparameters will be updated accordingly.A2.5 “Estimate the manufacturing cost”

In the fifth and last sub-activity of A2, theviable manufacturing processes are ranked

Fig 5 Detailed derivation of the process chain

according to economical criterion Several

methods have been developed for

manufactur-ing cost estimation from early design stages, for

example CES [6] and Swift and Booker [19]

method These methods are based on three main

elements: material and consumables, tooling

and equipments, and investment, where the

batch size becomes a key factor Depending on

the value of the batch size the manufacturing

cost changes considerably In addition, some

processes that may be viable from a

technolog-ical point of view become non-viable from an

economical point of view depending on the

batch size

When A2 activity is complete, it might be

that a single manufacturing process can make

the entire part or, in contrast, that it is necessary

to continue building the chain of manufacturingprocesses This decision is determined by thelist of resolved/unresolved design parameters Ifall design parameters are resolved, the chain ofmanufacturing processes is complete and activityA4 will be implemented, showing the firstresult If they are “unresolved” and there arestill some parameters that have not beenachieved or only partly achieved, activity A3continues the elaboration of the chain ofmanufacturing processes until all the designparameters are resolved

Activity A3 “Analyze and select process level n (A3)”

In this activity, the manufacturing cess ranking for level 1 from the activity(A2) is used to evaluate new manufacturingprocesses for the next step in the process chain

pro-Fig 6 Details of Activity A2 —analysis and selection of manufacturing process level 1

In addition, a new control is used:

manufactur-ing process sequencmanufactur-ing rules These rules

validate the technological feasibility of each

combination of manufacturing processes

Al-though the procedure of this activity is similar

to that of the previous activity (A2), there are

two main differences The first change is the

starting point, since now it has the list of

resolved and unresolved parameters from the

previous activity, representing the design

prop-erties carried out by the previous process and

those pending in the next one This list will be

updated until the manufacturing process chain

resolves all the unresolved parameters The

second difference is that the transformation

calculation is carried out using the lists of

resolved and unresolved parameters from the

previous manufacturing process as well as theprocess currently being checked

Activity A4 “View final process chain (A4)”

This activity provides a list detailing theselected manufacturing processes that make

up the process chain

4 Application of the proposed modelThe developed model was applied to a selected set ofmechanical parts However, in this work the design process

of an air-bending die (Fig 7) to be used to perform eitherair-bending or bottoming is discussed in detail Themanufacturing processes are reduced in this sample to

“powder metallurgy”, “machining”, “polishing”, “hotclosed die forging”, and “roll forming” Nevertheless, the

Fig 7 CAD sketch of the die used in the case study

model developed is also applicable for other mechanical

parts than this sample and whole manufacturing processes

feasible for mechanical parts being manufactured

Follow-ing the proposed IDEFØ diagram and based on the current

version of the“CAD part sketch” (Fig 7), the designer or

manufacturing engineer has to extract the design parameters

and classify them into required, optional and feature design

parameters Table1shows these three lists and the values of

the parameters for the case study The lists are produced

during activity A1, as shown in Fig.5

In activity A2 (Fig 5), the lists of product design

parameters from Table 1 and the manufacturing process

pool are used to produce two outputs The first one is the list

of processes that can be used as the first manufacturing

process of the process chain which will initiate production of

the part, i.e.,“hot closed die forging”, “powder metallurgy”,

and“machining” The second output is the list of resolved/

unresolved parameters, which it will be explained later

Nevertheless, to achieve these outputs, the A2 sub-activities

must first be carried out Figure8shows in detail the results

of these A2 sub-activities for the die case study

Initially, the A2.1 sub-activity gives a list of all the

manufacturing processes capable of working with the

material of the product in question, comparing the product

material with the set of materials that each process is able

to manufacture “Hot closed die forging”, “powder

metallurgy”, “machining”, and “roll-forming” make up

the list of manufacturing processes compatible with the

material Subsequently, these processes are further filtered

by sub-activities A2.2 and A2.3 Activity A2.2 checks thelist of manufacturing processes compatible with thematerial to see which ones satisfy the other requiredparameters, which in the example are weight and height.Both are numeric parameters and it is checked that its value

is included in the range of values that each process is able

to achieve, according to its manufacturing process straint The“hot closed die forging”, “powder metallurgy”,and“machining” processes meet these requirements and aretherefore allowed to continue as input for the next activity,A2.3, In contrast, the“roll forming” process cannot achievethe required height and is removed from the list Now,activity A2.3 checks the list to see if these processes arecapable of manufacturing the optional and feature designparameters, which in this case include general roughness,specific roughness, and hole

con-As shown in Fig.8, the process“hot closed die forging”can meet the material, weight, general roughness andheight requirements, but not the specific roughness andhole requirements Choosing this process would require asubsequent manufacturing process to complete the part

In contrast, “machining” is able to resolve all the designparameters, which suggests that, for this case study, thisprocess would be sufficient to produce the part However,following the model proposed here, it is necessary toanalyze whether each process can transform the objec-tives set out in the list of design parameters (sub-activityA2.4)

At this point, the method has evaluated the capacity ofthe processes to meet the product design parameters takinginto account the manufacturing process constraints How-ever, activity A2.4 assesses the capability of the manufac-turing processes to transform the parameters from theoutput list of activity A2.3 Figure 9 shows the results ofactivity A2.4 for the process“hot closed die forging” Fig.9.The process “hot closed die forging” has to transform theparameters of weight, height, and general roughness from

an initial status (previous step) to a final status (next step)

In that case, the initial status corresponds to the materialblank, which is considered as the volumetric space of thepart Therefore, the values for weight and height take it intoaccount The final values of these parameters appear in thenext step The parameters are quantified with a numericalvalue—as the weight—or using a range that shows themaximum and minimum values the parameter takes in thepart—as the height dimension The result of this transfor-mation is described in the product transformation neededcolumn in the product transformation table The resultingvalues must then be compared with the range of transfor-mation values found for“hot closed die forging” in the list

of manufacturing process transformation capabilities The

Table 1 Product design parameters of the case study

Product design parameters

result of this comparison is shown in the transformation

result table, which notes whether or not the process “hot

closed die forging” can sufficiently modify the parameters

of the product If a parameter cannot be transformed by the

manufacturing process, such as height in this case, its value

is adapted in relation to the transformation capacity of theprocess In this case, the “hot closed die forging process”cannot reduce the height of the part from an initial 55 mm

Fig 8 Flow chart of Activity A2

to a final 24 mm because the maximum process

transfor-mation capability for height is 25 mm Therefore, after this

process the height of the part will be 30 instead of 24 mm

Thus, this parameter, which seemed to be resolved at the

beginning of activity A2.4, in resolved/unresolved design

parameters, version 1 (Fig.9), is classified as unresolved at

the end of it When a parameter such as roughness can be

transformed by the process, it is kept as “resolved” in the

list The weight parameter is not affected by this

manufac-turing process capability The outputs of Activity A2.4 are,

first, an update that gives us resolved/unresolved design

parameters (version 2) for each manufacturing process and,

second, the list of selected manufacturing processes, as

shown in Fig.8

Next the manufacturing cost is estimated according to

the batch size Considering the Swift and Booker cost

method [19] when the batch size is lower than 1,000 units

only manual machining is viable and the estimated cost is

21€ per part Neither “hot closed die forging” nor “powder

metallurgy” are viable from economical point of view

Otherwise when is higher than 1,000 units“hot closed die

forging”, “powder metallurgy”, and “automated machining”

continuing being viable The estimated costs for 10,000

units are 30, 97.6, and 13.7€ per part, respectively, whereas

for 50,000 units the cost is 12, 27.6, and 7.9 € per part,

respectively Figure8shows the processes ranked according

to this result

At this point, the first manufacturing process chain for

the manufacture of the die, consisting simply of

“machin-ing”, is achieved However, for the manufacturing processes

with unresolved parameters, the manufacturing process

chain must continue to be constructed This means

carrying out Activity A3 which, in the case of “powder

metallurgy” produces the chain “powder metallurgy–

machining–polishing” and in the case of “hot closed die

forging” produces the chain “hot closed die forging–

machining–polishing”

5 ConclusionThis paper presents the bases for developing a decision-support system that would help designers and manufactur-ing engineers know which manufacturing process chainscan be used to manufacture a product The main researchcontribution of this work is to help designers to define theset of useful manufacturing processes chains thus thedesigner could select for manufacturing a mechanical partbased on cost estimation and technical feasibility Thenresult is based on showing all the activities, information,and knowledge involved in obtaining a set of viablemanufacturing process chains to manufacture a productthrough the method by utilizing IDEFØ To reach thispurpose detailed novelties are:

& The model makes it possible to control the propertiesmodified in each step of the process chain and to know

if the properties are partially or completely obtained

& New classification of design properties identifyingthose which are exclusive (required properties) andthose which are not (optional and feature properties),and a procedure to assess the manufacturing processtransformation capability have been proposed

& Definition of manufacturing sequencing rules to sider the compatibility among manufacturing pro-cesses to obtain viable manufacturing process chains

Fig 9 Evaluating the manufacturing process transformation capability (A2.4)

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ORIGINAL ARTICLE

A feasibility study using simulation-based optimization

and Taguchi experimental design method for material

Kemal Subulan&Mehmet Cakmakci

Received: 8 November 2010 / Accepted: 4 July 2011 / Published online: 28 July 2011

# Springer-Verlag London Limited 2011

Abstract Nowadays, so as to adapt to the global market,

where competition is getting tougher, firms producing through

the modern production approach need to bring not the only

performance of the system designed both during the research

and development phase and the production phase but also the

performance of the product to be developed as well as the

process to be improved to the highest level The Taguchi

method is an experimental design technique seeking to

minimize the effect of uncontrollable factors, using orthogonal

arrays It can also be designed as a set of plans showing the way

data are collected through experiments Experiments are carried

out using factors defined at different levels and a solution model

generated in ARENA 3.0 program using SIMAN, which is a

simulation language Many experimental investigations reveal

that the speed and capacity of automated-guided vehicle, the

capacities of local depots, and the mean time between shipping

from the main depot are the major influential parameters that

affect the performance criteria of the storage system For the

evaluation of experiment results and effects of related factors,

variance analysis and signal/noise ratio are used and the

experiments are carried out in MINITAB15 according to

Taguchi L16 scheme The purpose of this study is to prove

that experimental design is an utilizable method not only for

product development and process improvement but it can also

be used effectively in the design of material handling–transfer

systems and performance optimization of automation

technol-ogies, which are to be integrated to the firms

Keywords Taguchi experimental design Material handling

and transfer systems Performance optimization Process

improvement

1 Introduction

In order to improve the process in production and optimize theresults obtained from production, it is required to increase theproduction performance To present the conditions for whichthe optimum results are obtained in the design phase,primarily, properties determining the performance level arespecified and factors affecting these properties are examined.Following that, experiments are carried out in order todetermine the effects of these factors on properties settingthe performance and find the optimum combination (by alsoobserving the uncontrolled factors) [1]

Considering the basic production resources, the tion of experiment design techniques becomes extremelyefficient for carrying out these experiments with the highestefficiency pursuing the economical and time constraints aswell as interpreting the results accurately (so as todetermine the relationship between controllable–uncontrol-lable factors and outputs and to realize the optimization).Besides, it has a supportive and directive role on all othermethods applied to increase quality and efficiency.With the material handling–transfer equipment, perfor-mance increase is achieved in storage systems withautomation Thus, long-term execution of material han-dling–transfer equipment within the system affects theperformance with respect to various storage system criteriahence the performance increases in this respect (increasingthe amount of utilization rate of material handling–transferequipment and the minimization of average number ofproducts awaiting to be carried by the material handling–transfer equipment and the average latency time) costreduction and optimum storage management [2]

applica-The purpose of this study is to prove that the experimentaldesign is a method that can be used effectively in not onlyproduct development and process improvement studies butalso in the designing of material handling–transfer systems

K Subulan:M Cakmakci ( *)

Engineering Faculty Industrial Engineering Department,

Dokuz Eylül University,

Buca 35160 Izmir, Turkey

e-mail: mehmet.cakmakci@deu.edu.tr

DOI 10.1007/s00170-011-3514-0

and performance optimization of automation technologies,

which are to be integrated into the operation

2 Taguchi method and experimental design

Experimental design, which is used in the design phase before

manufacturing in production, is not only a statistical approach

but it is also a technique that can be used in research and

development activities and support and complete all other

quality techniques while minimizing the cost, enhancing the

quality, and reinforcing the reliability of the results [1,2] With

the application of this technique in production, severaladvantages are provided such as improvement of perfor-mance and quality, efficient use of the sources, acceleration

of the research and development activities, making process

or products less susceptible to factors, which are costly, hard

to control or uncontrollable, and affect quality properties.Taguchi method is a technique for designing andperforming experiments to investigate processes where theoutput depends on many factors (variables, inputs) withouthaving tediously and uneconomically run of the processusing all possible combinations of values Thanks tosystematically chosen certain combinations of variables, it

Fig 1 The 3-D layout of storage system

Table 1 From/to chart depicting

the distances between local

depots and main depot

inlet–outlet

is possible to separate their individual effects [3,4] It can

be also defined as a set of plans describing the data

collection types with experiments In designing an

exper-iment, the general purpose of the problem, the input

variables to be examined and their levels, the reaction of

the experiment, the walkthrough of the experiment, and

appropriate analysis methods should be determined

Dr Genichi Taguchi is regarded as the foremost

proponent of robust parameter design, which is an

engineering method for product or process design that

focuses on minimizing variation and/or sensitivity to noise

When used properly, Taguchi designs provide a powerful

and efficient method for designing products that operate

consistently and optimally over a variety of conditions In

Taguchi’s methodology, all factors affecting the process

quality can be divided into two types: control factors and

noise factors Control factors are those set by themanufacturer and are easily adjustable These factors aremost important in determining the quality of productcharacteristics [5,6]

Table 2 Loading and offloading times of AGV according to product

types (in seconds)

Fig 2 Simulation model that developed for the storage system – ARENA 3.0

Fig 3 AGV-Automated guided vehicle [ 19 ]

This technique is a technique that is used for determining

the variable values affecting the process performance by

systematically manipulating the controllable variables,

which affect the related quality characteristics [7-9]

Genichi Taguchi came up with a solution which

increases the efficiency of the evaluation and realization

of experiments with the help of the approach called with his

name [10] Besides being only an experimental design

technique, Taguchi method is an extremely beneficial

technique for high-quality system design On the other

hand, the reduction in the number of experiments stems

from ignoring the interaction between factors to some

extent The experiment results obtained through Taguchi

experimental design method are converted into signal/noise

(S/N) ratio for evaluation The value of signal/noise ratio is

calculated and analyzed in different ways such as low value

being good or high value being good or nominal value

being good, according to the targeted quality value

Whichever S/N ratio value is used in evaluation, as a resultthe higher S/N ratio value expresses the better experimentresult Thus, the case with the highest S/N ratio among allthe factors examined within the experiment would give thebest performance [11,12] The standard designs of Taguchiare built on this system It is required that a model beconstructed for the variation of data on the targeted value.For that purpose, loss function to calculate the deviationbetween the experimental and the desired value is modelled

as below:

In this function, L(y) is the loss function, k isproportional constant, T is target value, and y is observedvalue The data obtained through loss function, a formu-lation, which is expressed as S/N ratio, is developed byTaguchi With the help of S/N ratio, which is alsoexpressed as the variation of the process, optimum processconditions which are used for the optimization of theprocess are obtained Factor levels with the highest S/Nratios are the factor combinations providing the optimumconditions [13]

For S/N ratio, there are three different approaches Theseare smaller is better, larger is better, and target value isbetter For each approach, a different calculation scheme isdeveloped

Table 3 Experimental factors and factor levels

D/the mean time between shippings from the main depot (in seconds)

The average waiting time of products

in the input area (in seconds)

For smallest is better characteristic, function is defined as

Ly ¼ y12 þ y22 þ y32 þ yn2ð Þ=n ð3Þ

For target value is better characteristic, function is

defined as

Ly ¼ y1  mðð Þ2 þ y2  mð Þ2 þ yn  mð Þ2Þ=n ð4Þ

For largest is better characteristic, function is defined as

Ly ¼ 1=y12ðð Þ þ 1=y22ð Þ þ 1=y32ð Þ þ 1=yn2ð ÞÞ=n ð5Þ

In the experimental design, orthogonality is defined asthe calculability of a factor without being dependent onanother factor The effect of a factor does not have aninfluence on the estimation of the effect of another factor.The first rule of orthogonal series is that they are balancedexperiments In other words, they include equal number oftrials for different trial conditions

3 Definition of the problem and dataThere are six different product types of ABC firm,which produces in automotive industry There arespecific locations within the main store where theseproducts are stored In other words, there are sixdifferent locations (local depots) for six differentproducts (Fig 1) All products are moved to the maindepot entrance by the help of an overhead line In themain depot, products are stored in an automation-basedstorage system, automated storage/retrieval systems (AS/RS) which are called local depots For the moment, in thestorage system, handling is realized using manualhandling cars and forklifts In the direction of executives’support, the feasibility studies are carried out fortransition of the manual storage system to automatedsystem

The unit arrival percentages of six different producttypes to the main depot entrance from overhead lines wherethe final products are handled are as follows Fifteenpercent of them is X-type, 20% is Y-type, 20% is Z-type,15% is T-type, 20% is Q-type, and 10% is P-type Similarly,the unit outlet percentages are as follows respectively: 15%

is X-type, 20% is Y-type, 20% is Z-type, 15% is T-type,20% is Q-type, and 10% is P-type The automation to be

Fig 4 The main factor effects

obtained from statistical analysis

for the average utilization rate of

The average number of

waiting products for

AGV (dB)

The average waiting time

of products in the input area (dB)

applied to the material handling–transfer system is to be

designed according to the performance optimization of the

automated-guided vehicle (AGV) system, which would

provide the computer control of the handling operation

between the locations of differently packed products The

designed AGV system is responsible for two types of

handling movements

The first one is the handling of parts, which have

arrived at the main depot, to different locations; and

the other one is the handling of products, which will

be let out from the main depot, to the outlet of the

main depot All of these data are obtained through aninput analysis carried out in the ARENA program Thenumber of AGVs and the number of products carried

by these vehicles at a time is taken as 1 Followingthat, in the experimental design phase, the extent towhich these values have an effect on performancecriteria will be dealt with The carrier goes to thetarget location following the shortest path within themain depot This information provides us with theconstruction of from/to chart for the main depot whoselayout is given in Fig 1 The speed of AGV is specified

Fig 5 Two-factor interaction

effects obtained from statistical

analysis for the average

utiliza-tion rate of AGV

Fig 6 The main factor effects

obtained from statistical analysis

for the average number of

wait-ing products for AGV

as 3 m/s The AS/RS system, where every product is

stored, has a capacity of 40 products/unit and at the

starting moment it is assumed that the stock level on

these system is 0

In Table 1, distance matrix (meter) which consists of

local depots, inlet, and outlets of the main depot regarding

the routes that AVG should follow using the layout of main

depot, and from/to chart can be seen AGV times differ due

to the weights of products being transferred The loading

and offloading of heavier products are executed slower due

to product sensitivity (Table2) For the problem described

above, a simulation model, which simulates ABC firm

working three shifts, is run for 24 h and the obtainedperformance criteria values are used as data in theexperiment design

4 Experimental procedures and resultsSimulation model developed in problem-specific ARENA3.0 simulation program can be seen in Fig.2 The values ofvariables, which are determined as controllable factors,within the model, are altered according to the determinedfactor levels, and the model is run In this way, the related

Fig 7 Two-factor interaction

effects obtained from statistical

analysis for the average number

of waiting products for AGV

Fig 8 The main factor effects

obtained from statistical analysis

for the average waiting time

of products in the input area

performance criteria values are obtained as response

variables within the experimental design

Generally, the total response number is dependent on

the number of factors, factor levels, number of

con-strained factors, and number of experiment repetitions

Especially, in multifactored experiments, the response

number may be very high This situation increases the

cost as well as the time spent for experiments For this

reason, in order to reduce the number of experiments and

cost, the number of responses is reduced However, the

reduction of the response number may cause insufficient

data collection for the inspected event Hence, responses

should be reduced without affecting the data collection

procedure

In the consideration of all this information, in order to

specify the number of repetitions, the interval estimation

of the basically related performance criterion, beneficial

use ratio of AGV, is performed in ARENA program by

taking repetition number as 5 and following that, after

the desired half-interval level is specified, the necessary

observation number is determined using the following

equation [14]

n»¼ n  h=h »2

ð6Þ

Under these circumstances, the total observation number

is specified as 20 As a result of the brainstorming sessions

held and the cause–effect matrices constructed in the firm,

several performance criteria such as average utilization rate

of AGV (see in Fig 3), the average number of products

awaiting in the main depot’ input area to be transferred to

the local depots and average idle time of these parts are set

as the performance criteria used for specifying the activity

of the automation

It is observed that these performance criteria are affected

by AGV speed, AGV capacity, local depots’ capacities, andthe intervals between the product transfers at the maindepot outlet (Table3)

Before the application of the experiment, it is required that

a“receipt” table should be prepared for the team who will runthe experiment The receipt table is constructed according tothe factor values which should be adjusted for everyobservation and“+” and “−” signs of L16 design matrix [7,8].The experiment will be run by taking the repetition number

as 20 due to the facts explained before For the repeatedexperiments, response variables are assigned using theaverage of results and point estimation Hence, the reliability

of the results is provided statistically by repeating theexperiments for 20 times and averaging the results

In Table4, point estimation values for the average utilizationrate of AGV, average number of products awaiting for AGVhandling and average idle time for the awaiting product can beseen These values will be used in the calculation of signal/noiseratio and variation analysis operations

5 Evaluation of results5.1 Taguchi method results

In Taguchi experimental design method, the criterionused for measurement and evaluation of quality charac-teristics is the ratio of signal (S) to be measured to thenoise factor (N) Signal value is the actual value that thesystem gives and desired to be measured, while noise

Fig 9 Two-factor interaction

effects obtained from statistical

analysis for the average

waiting time of products

in the input area

factor is the undesired factor portion within the measured

signal value

In the calculation of signal/noise ratio, the target quality

value which is desired to be reached at the end of the

experiment, is also important At this point, three important

categories are available [1,15-18]:

& Lower value is better (target is to reach the lowest

ANOVA results for the average utilization rate of AGV

Table 6 ANOVA results for the

average utilization rate of AGV,

ANOVA results for the average

number of waiting products for

AGV, ANOVA results for the

average waiting time of products

in the input area

depicted At the end of all these calculations, the highest

signal/value ratio value refers to the best experimental

results In other words, it refers to the experimental

results where AGV utilization rate is maximum, minimum

number of awaiting products, and idle time of the

products are minimum For finalizing the optimization

phase, variation analysis is performed using the calculated

signal/noise ratios

Later on, in order to clarify how these factors affect each

performance criterion, the statistical analysis was carried out

These main-factor effects are plotted in Figs.4,5, and6 Also,

Figs.7,8, and9show the two-factor interaction effects

5.2 ANOVA results

Analysis of variance (ANOVA) was conducted to identify

significant factors in an automated storage system process

ANOVA can be used to divide the total variation in the data

into variation resulting from main effects, interaction

effects, and error (Table6)

6 Conclusion

The main factor levels A1–B1–C2–D1 are specified as the

factor levels increasing the average utilization rate of AGV,

while main factor levels A2–B2–C2/1–D2 are specified as

the factor levels reducing the awaiting average product

number Moreover, main factor levels A2–B2–C1–D2 are

observed as the factor levels reducing the average idle time

of the awaiting parts It is obviously seen that, the main

factor effects, two-factor interaction effects and the S/N

ratios supported the same optimal factor levels (Table7)

As a result of this study, it has been proven that the Taguchi

experimental design is a method that can be used effectively in

not only product development and process improvement

studies but also in the designing of material handling–transfer

systems and performance optimization of automation

tech-nologies, which are to be integrated into the operation It can

be seen that the simulation-based optimization technique can

be effectively used in a feasibility study as an experimentaltool with the advantages of cost reduction and the property oftime compression also

References

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Table 7 Confirmation runs and optimal setting showing results for the performance criterion

Optimal factor levels for the average utilization rate

if AGV

Optimal factor levels for the average number of waiting products for AGV

Optimal factor levels for the average waiting times of products in the input area

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simulation using SIMAN McGraw-Hill, Inc., NY

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as analysed by Taguchi methods Int J Adv Manuf Technol

25:420–426

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19 AGV–automated guided vehicle JBT Corporation http://www fmcsgvs.com/content/sales/auto.htm Accessed 16 June 2011

ORIGINAL ARTICLE

Modeling, measurement, and evaluation of spindle radial

errors in a miniaturized machine tool

S Denis Ashok&G L Samuel

Received: 5 July 2010 / Accepted: 4 July 2011 / Published online: 22 July 2011

# Springer-Verlag London Limited 2011

Abstract Miniaturized machine tools have been established

as a promising technology for machining the miniature

components in wider range of materials Spindle of a

miniaturized machine tool needs to provide extremely high

rotational speed, while maintaining the accuracy In this work,

a capacitive sensor-based measurement technique is followed

for assessing radial errors of a miniaturized machine tool

spindle Accuracy of spindle error measurement is affected by

inherent error sources such as sensor offset, thermal drift of

spindle, centering error, and form error of the target surface

installed in the spindle In the present work, a model-based

curve-fitting method is proposed for accurate interpretation

and analysis of spindle error measurement data in time

domain Experimental results of the proposed method are

presented and compared with the commonly followed discrete

Fourier transform-based frequency domain-filtering method

Proposed method provides higher resolution for the

estima-tion of fundamental frequency of spindle error data

Synchro-nous and asynchroSynchro-nous radial error values are evaluated in

accordance with ANSI/ASME B89.3.4M [9] standard at

various spindle speeds and number of spindle revolutions It

is found that the spindle speed and number of spindle

revolutions does not have much influence on synchronous

radial error of the spindle On the other hand, asynchronous

radial error motion exhibits a significant speed-dependant

behavior with respect to the number of spindle revolutions

Keywords Spindle radial errors Modeling Curve fitting

Analysis

NomenclatureSymbol Description

Ch Magnitude of harmonic components of spindle

error measurement data

D Basis matrix containing the mathematical

functions of the proposed model

Ej Sum of squared residual value for the given

mci Contribution of centering error of artifact at the

given sampling time

msi Contribution of synchronous components at the

given sampling time

mti Contribution of sensor offset and thermal drift at

the given sampling time

p0 Contribution of sensor offset

p1,p2 Coefficients of second order polynomial

Manufacturing Engineering Section, Department of Mechanical

Engineering, Indian Institute of Technology Madras,

Chennai 600-036, India

e-mail: samuelgl@iitm.ac.in

DOI 10.1007/s00170-011-3519-8

θi Angular position of spindle at discrete sampling

time (ti)

1 Introduction

The global trend towards the miniaturization of products

has created tremendous needs for micro/mesoscale

compo-nents in diverse application fields such as aerospace,

automobile, defense, electronics, optics, and biotechnology

[1] Research and technological development in this field is

encouraged by the increased demand on micromotion

devices such as microactuators, manipulators, and

compli-ant mechanisms [2] Micromachining is one of the key

technologies for enabling the manufacturing of

miniatur-ized components with desired accuracy Over the past

decades, micromachining has evolved greatly to include

various techniques such as laser beam machining,

ultrason-ic machining, ion beam machining, electrodischarge

ma-chining, etc [3] However, these methods are limited to few

silicon-based materials and planer geometries Recently,

there has been strong interest for building miniature

machine tools to fabricate microsize components [4]

Mechanical micromachining using miniature machine tools

provides the unique advantage of producing 3-D

micro-structures on various materials [5]

Spindle is a key component of a miniaturized machine

tool for providing accurate rotation to micro cutting tools

or work pieces Rotation accuracy of the spindle is a

critical concern for achieving the desired form accuracy

and surface roughness of machined components [6] In

practice, manufacturing imperfections, misalignment, wear,

and aging of the bearing elements affect the rotation

accuracy of spindle These error sources introduce

unwant-ed error motions to the axis of rotation of the spindle such

as radial, axial, and tilt error motions [7] Radial error of

the spindle is identified as a significant source of error that

affects the accuracy of the miniaturized machine tool [8]

Out of roundness of bearing elements causes synchronous

radial error, which repeats in each spindle revolution

Recirculation of the balls in the bearings causes

non-repeatable motions in each spindle revolution and it is

called as asynchronous radial error [9] Consequently,

measurement and evaluation of spindle radial errors is

essential to ensure the machining accuracy of miniaturized

machine tool

ANSI/ASME B89.3.4M standard laid the modern

foundation for understanding, specifying and testing axes

of rotation errors of machine tool [9] As the rotation

speed of a typical miniaturized machine tool spindle is in

the order of 1,00,000 rpm, high-frequency response

sensing methods are required for spindle error

measure-ment An optical measurement system consisting of laser

diode, position-sensitive detectors is used for measuringspindle error motions at high-speed conditions [10] Laserinterferometer is used for measuring the spindle rotationerrors such radial error motion and axial error motion in alathe [11] An optical measurement system consisting ofrod lens, ball lens, laser beam, and photodiode isdeveloped for measuring rotation errors of a microspindle[12] Fujimaki and Mitsui developed an optical measure-ment system consisting of laser diode, quadrant photodetector, and beam splitter for measuring spindle radialrunout of a miniaturized machine tool [13] Laser-basedmeasurement techniques require extensive experimentalarrangements and more setup time for aligning the path ofthe laser with the optics This method requires precisecalibration methods as the output characteristics of thelaser beam is nonlinear with respect the displacement ofspindle due to the reflectivity of the target surface installed

in the spindle

Capacitive sensors exactly meet the high speed and highaccuracy requirements of spindle error measurement [14]

In most of the cases, accuracy of spindle error measurement

is affected by inherent error sources such as sensor offset,thermal drift of spindle, centering error, and form error ofthe target surface installed in the spindle [15] Variousprocessing methods were suggested by the researchers toeliminate the unwanted contributions in spindle errordata Thermal drift is caused due to the change in thetemperature distribution of the spindle [9] Differentmodeling techniques were classified for analyzing theeffect of thermal errors in machine tools [16] The trenddue to the thermal drift of the spindle is approximatedusing a second order-polynomial function [17] Digitalnotch filter tuned to spindle rotational frequency wasproposed for removing the contribution of centering errorfrom the measurement data [18] Reversal method,multistep method, and multiprobe method are commonlyfollowed for separating the form error of the artifact [19].These methods require measurement setup consisting ofmultiple numbers of sensors and instrumentations such asangular index table, fixtures, etc It is difficult to implementthese methods in a miniaturized machine tool due to spacelimitations and high speed conditions

A new approach has been developed for form errorseparation suitable for implementing in the miniaturizedmachine tool [20] In this method, a harmonic cutoff value

is specified for filtering the contribution of form error of theartifact in frequency domain using discrete Fourier trans-form (DFT) method However, accuracy of DFT is affected

by spectral leakage problem when it is applied to thespindle error data containing incomplete spindle revolution[17] In order to overcome this difficulty, a mathematicalmodel consisting of constant term and sum of sinusoidalfunction is used for interpreting the periodic components of

spindle error data [21] However, this method is inadequate

in identifying the contribution of thermal drift of the

spindle

It has been found that very few attempts have been done

for spindle error measurement in a miniaturized machine

tool Preprocessing of spindle error data is an essential step

to remove the unwanted contributions such as sensor offset,

thermal drift of spindle, centering error, and form error of

the artifact Existing methods follow processing steps

involving DFT-based frequency domain analysis In the

present work, a new method is proposed for simultaneous

separation of different contributions of spindle error data in

time domain using a mathematical model consisting of a

second-order polynomial and Fourier series function

Improved performance of the proposed method as

com-pared to the commonly followed DFT-based filtering

method is explained with experimental results

Experimen-tal results for evaluation of synchronous and asynchronous

radial errors of the miniaturized machine tool spindle are

also presented at various spindle speeds and number of

spindle revolutions

2 Fixed sensitive radial error motion test

for the miniature spindle

In accordance with ANSI/ASME B89.3.4M standard [9],

fixed sensitive radial error motion test is conducted for

evaluating synchronous and asynchronous radial errors of a

miniature spindle A capacitive sensor-based measurement

technique is followed for spindle radial error measurement

Table1shows the technical details of the capacitive sensor

used for measuring spindle radial errors in the miniaturized

machine tool It has been mentioned that the capacitive

sensor is factory calibrated to provide a linear output for the

given target displacement [22] Figure 1 shows the

calibrated values of the capacitive sensor for the given

target displacement of ±125 μm In the present work,

spindle error measurements were carried out within a

measuring range of ±15 μm in a temperature controlled

environment of 25°C

2.1 Experimental arrangementMiniaturized spindle considered under this study is manu-factured by Alfred Jager, GmbH, Germany The spindle ispowered by a high-frequency electric motor and it issupported by hybrid ceramic ball bearings A cylindricalartifact is used as a target for measuring radial errors in theminiaturized machine tool spindle Target size needs to beselected at least 30% higher than the size of sensingelement of the capacitive sensor [22] Hence, diameter ofthe cylindrical artifact is selected as 12.62 mm and its shankdiameter is maintained to be 3 mm for mounting in theminiature spindle Capacitive sensor is placed in the probeholder and firmly clamped on theX-axis linear stage of theminiaturized machine tool as shown Fig 2a In order toverify the sensor and target alignment, high spot of thetarget is identified by carefully moving the linear stages in

X and Z directions [22] A closer view of the cylindricalartifact and miniature spindle is shown in Fig.2b

A computer-aided data acquisition system is used forsampling the analog signal of the capacitive sensor at discretetime intervals According to Nyquist criteria, samplingfrequency for spindle radial error measurement is calculated

as the twice the spindle rotation frequency and the number ofharmonic components considered for analysis [9] Measure-ment data is obtained for multiple spindle revolutions andstored in the computer using LABVIEW software (Ver 8.1).Noise of the sensor is identified and filtered during spindleradial error measurement Measurement data is acquired atdifferent spindle speeds in the range of 10,000–70,000 rpm

in steps of 10,000 rpm It is difficult to maintain a constantspindle speed during measurement of spindle radial errorsand a speed loss of 150–300 rpm is observed at differentspindle speeds

2.2 Interpretation of measurement dataFigure 3 shows the discrete time samples of radial errormeasurement data obtained at the spindle speed of

Table 1 Technical details of capacitive sensor

Fig 1 Calibrated output of the capacitive sensor

30,000 rpm In most of the cases, measurement data includes

the contributions of thermal drift, sensor offset, centering

error, and form error of the artifact along with spindle radial

errors Contribution of centering error can be easily identified

as it causes a once per revolution sinusoidal component in the

measurement data as shown in Fig.3 It is also found that

there is a deviation between the zero level and mean of the

measurement data, which is due to the offset between the

range center of the sensor and the mean position of the

artifact [15] Measurement data also includes the repeatable

components due to the contribution of form error of the

artifact and synchronous radial error of the spindle and they

are termed as synchronous components Hence, further

processing of measurement data is required for the accurate

interpretation of different components of measurement data

3 Proposed method for processing measurement data

In the present work, a new method is proposed for processing

the measurement data using a mathematical model consisting

of a second-order polynomial function and Fourier series

function This method is useful for simultaneous separation of

sensor offset, thermal drift, synchronous, and asynchronous

components of the measurement data Mathematical

formu-lations of the proposed method are explained in the followingsubsections

3.1 Description of proposed mathematical modelProposed mathematical model for interpreting the measure-ment data is given by Eq.1

mi¼ p0þ p1tiþ p2t2

i þXHh¼1

coef-In Eq 1, ti corresponds to the sampling time for themeasured data; f0 refers to the fundamental frequency ofmeasurement data H is the number of harmonic compo-nents considered for analysis

3.2 Fitting the mathematical model to the measurement data

In order to interpret the different contributions of ment data, proposed model is fitted to the samples ofmeasurement data and it requires estimation of modelparameters In the present work, matrix method is followedfor determining the least squares solution of the modelparameters [23] It can be seen from Eq 1 that the modelparametersp0,p1,p2,ah,bhare the linear parameters andf0

measure-is the nonlinear parameter in the model As the proposedmodel contains a nonlinear term (f0), an iterative method isfollowed for estimating the model parameters In practice,fundamental frequency of measurement data needs to bearound the rotation frequency of the spindle Hence, a set ofdiscrete frequency valuesfj=[f1,f2,….,fk],j=1, 2, 3,….,k is

Fig 3 Discrete time samples of measurement data obtained at the

spindle speed of 30,000 rpm

Capacitive sensor Artifact Spindle

Linear stage -Y

Linear stage -X

Fig 2 Fixed sensitive radial

error motion test for the

miniaturized machine tool; a

experimental arrangement, b

close-up view

selected around the spindle rotation frequency for

deter-mining f0 Samples of spindle measurement data and the

corresponding sampling time are denoted by the following

equations in matrix form

Samples of measurement datam0

i¼ m0

1; m0

2; ; m0 m

ð2Þ

Sampling timeti¼ t½1; t2; ; tmT ð3ÞThe proposed model becomes linear for the given value

of discrete frequency (fj) and its interpretation for the givensamples of measurement data can be expressed by thefollowing Eq.4

37777775ð4Þ

The above equation can be represented in the simplified

form as given below

ð6Þ

Equation 4 leads to an over determined system of

simultaneous linear equations (i.e.,m>2H+3) In this case,

there exist residuals between the measurement data and the

estimated value as given by

Assuming the residuals to follow normal probability

distribution, solution for the unknown model parameters

can be obtained by minimizing sum of squared residuals as

3.3 Decomposition of measurement dataEstimated values of model parameters given in Eq 9 areused for decomposing different contributions of measure-ment data

Contribution of sensor offset and thermal drift is

Here, the first harmonic component (h=1) represents the

contribution of centering error of artifact and it can be

removed from the measurement data as given by the

following equation

bmci ¼ ba1cos 2ð pf0tiÞ þ bb1sin 2ð pf0tiÞ ð12Þ

However, it is difficult to interpret the contribution of

form error of the artifact In the present work, a suitable

cutoff value is selected based on the dominant magnitude of

the harmonic components in the form profile of the artifact

and it has been explained in Section 4.3 Magnitude of

harmonic components of measurement data can be mined using the following Eq.13

deter-bCh¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiba2

hþ bb2 h

q

ð13ÞProposed model does not include the contribution ofasynchronous components and it is considered as theresiduals between the estimated values and the measure-ment data Asynchronous components of measurement datacan be determined by

Synchronous and asynchronous components of ment data is commonly displayed in polar plot [9] In thepresent work, angular position of the spindle for the givensampling time is determined using the estimated value offundamental frequency of measurement data and it is given

measure-by the following equation

The above equation can be used for displaying thesynchronous and asynchronous components of measurementdata in polar plots for an arbitrary radius of plotting circle

(b) Asynchronous components

Fig 5 Decomposed components for the samples of measured data using DFT method; a filtered synchronous components in time domain, b asynchronous components

(a) Five spindle revolutions

(b) Ten spindle revolutions

Fig 4 Frequency spectrum for different number of spindle

revolu-tions of the measurement data obtained at the spindle speed of

30,000 rpm; a five spindle revolutions, b ten spindle revolutions

4 Results and discussion

In this section, experimental results of the proposed method

are presented for the measurement data obtained at the

spindle speed of 30,000 rpm Performance of the proposedmethod for processing the measurement data is comparedwith commonly followed DFT-based frequency domainfiltering method

4.1 DFT-based frequency domain-filtering methodBefore applying DFT-based frequency domain-filteringmethod, the trend due to the thermal drift of the spindle iseliminated by fitting a second-order polynomial to themeasurement data [17] Figure 4a shows the frequencycontent of the measurement data containing five spindlerevolutions DC component at 0 Hz is found to have amagnitude of 0.482μm and it represents the mean value ofthe measurement data The magnitude of frequency com-ponent is found to have a maximum value of 6.144μm at492.31 Hz This is referred as the fundamental frequencycomponent of the measurement data and corresponds to thecontribution of centering error of the artifact Frequencycomponents which are at the integer multiples of funda-

(a) Comparision of estimated values using the proposed method and DFT method

(b) Residuals of the measurement data (c) Histogram plot of residuals

Bell curve

Range of residuals (µm) Fig 7 Fitting accuracy and validation of the proposed method; a comparision of estimated values using the proposed method and DFT method, b residuals of the measurement data, and c histogram plot of residuals

Fig 6 Determination of fundamental frequency using the proposed

method for the measurement data obtained at the spindle speed of

30,000 rpm

mental frequency of measurement data are referred as the

synchronous components and they are shown as square

markers Frequency resolution is an important consideration

for the accurate estimation of frequency content of

measurement data and in this case, the frequency resolution

is found to be 82.05 Hz

In order to analyze in a finer frequency resolution, the

number of samples of measurement data is increased to

contain ten spindle revolutions and the frequency content of

the measurement data is shown in Fig.4b In this case, the

frequency resolution is 41.025 Hz and fundamental

frequen-cy of the measurement data is found to be at 491.62 Hz with

a magnitude of 6.041μm The increase in number of spindlerevolutions increases the effect of speed variations in themeasurement data Consequently, it leads to spectral leakage

of the fundamental frequency component to the adjacentfrequency bins as shown in Fig 4b This is an inherentproblem of DFT method when it is applied to the discretetime samples of measurement data obtained in presence ofspeed variations

Synchronous components are filtered in the frequencydomain and inverse discrete Fourier transform is applied for

Table 3 Samples values for the decomposed components of measurement data obtained at the spindle speed of 30,000 rpm

S no Sampling time×10−3(s) Measured data ( μm) Decomposed components

Sensor offset and thermal drift error (μm) Centeringerror (μm) Synchronouscomponents (μm) Asynchronouscomponents (μm)

Harmonic number ( h) Fourier coefficients ( μm) Magnitude of harmonic components ( C h ) μm

Table 2 Estimated values of

Fourier coefficients and

funda-mental frequency for the

samples of measurement data

obtained at the spindle speed

of 30,000 rpm

analyzing them in time domain Figure 5a shows thesynchronous components for the samples of measurementdata in time domain Due to the spectral leakage offundamental frequency component, there is a deviation inmagnitude of the synchronous components as compared tothe measurement data Synchronous components are sub-tracted from the measurement data for estimating theasynchronous components and they are shown in Fig 5b.Asynchronous components show the periodic variations,which is due to the inaccurate estimation of synchronouscomponents of measurement data From these results, it can

be concluded that the accuracy of DFT-based filteringmethod is limited due to frequency resolution and thespectral leakage of frequency components Different wid-owing techniques such as Hanning, Poisson, Cauchy, etc.,can be used for minimizing the effect of spectral leakage inthe frequency domain filtering method However, it affectsmany attributes such detectability, frequency resolution, andease of implementation [24]

4.2 Proposed method for simultaneous separation

of measurement dataProposed method requires estimation of model parameters forthe simultaneous separation of different contributions such asthermal drift, synchronous, and asynchronous components ofmeasurement data in time domain A harmonic cutoff value of

30 cpr is selected for estimating the synchronous components

of measurement data Fundamental frequency of ment data needs to be around 500 Hz for the spindle speed of30,000 rpm However, there was a speed loss of 150–300 rpmduring spindle error measurement; hence, a range of 494–

measure-498 Hz is selected for estimating the fundamental frequency

of measurement data A set of frequency values such as [494,494.01, 494.02… 497.99, 498] is chosen with a resolution of0.01 Hz Linear least squares solution for the modelparameters are obtained by minimizing the residuals between

Fig 9 Polar profiles for the

decomposed components of

measurement data obtained at

the spindle speed of 30,000 rpm;

a synchronous components, b

asynchronous components

(a) Sensor offset and thermal drift

(b) Centering error of the artifact

(c) Synchronous components after removal of centering erorr of artifact

Fig 8 Decomposed components of measurement data obtained at the

spindle speed of 30,000 rpm; a sensor offset and thermal drift, b

centering error of the artifact, and c synchronous components after

removal of centering eror of artifact

the estimated values and the measurement data as explained in

Section 3.3 Figure 6 shows the values of sum squared

residual at the given discrete frequency values for different

number of spindle revolutions It is found that fundamental

frequency of the measurement data is estimated to be 496.76

and 496.72 Hz for five and ten spindle revolutions,

respectively This method overcomes the speed variations

by estimating the best-fit frequency that minimizes the sum

squared residuals between the estimated values and the

measurement data Also, the discrete frequency values are

analyzed at a finer resolution of 0.01 Hz; hence, the

proposed method provides an improved estimation for the

fundamental frequency of measurement data as compared to

the DFT-based filtering method

Figure 7a shows the fitted curve using the proposed

method for the samples of measurement data containing

two spindle revolutions It can be seen that fitted curvemore closely follows the periodic pattern of the measure-ment data than the DFT method It is also found that thefitted curve have a correlation coefficient of 0.987 with themeasurement data Estimated values using the fitted curveare removed from the measurement data and the residualsare shown in Fig.7b In order to verify the assumption onnormal probability distribution, residuals are analyzedgraphically using the histogram plot as shown in Fig 7c.The count values are found to be high around zero and thespread of the residuals clearly resemble the bell curve.These results validate the proposed method for processingthe measurement data

Table 2 shows the estimated values for the Fouriercoefficients of the measurement data using the proposedmethod and they are compared with DFT method It can be

(a) Form profile of artifact surface in the base circle radius of 50µm

(b) Spectral plot for the form profile of the artifact surface

Fundamental component (3 cpr)

base circle with radius of 25 µm

Form profile of artifact surface

Fig 10 Form profile of artifact

surface and its spectral plot; a

form profile of artifact surface in

the base circle radius of 50 μm,

b spectral plot for the form

profile of the artifact surface

noted that the magnitude of Fourier coefficients are in

comparable magnitude with the estimated values using DFT

method However, estimations of fundamental frequency

are found to have higher variations, due to lesser

frequency resolution and spectral leakage problem of

the DFT method Magnitude for the coefficients of

second order polynomial is found to be p0= 0.7109μm,

p1=−0.1357 μm/s, p2=−14.2981 μm/s2

Estimated modelparameters using the proposed method are used for decom-

posing the contributions of sensor offset and thermal drift,

synchronous components, and asynchronous components of

measurement data Sample values for the decomposed

components of measurement data are given in Table3 The

combined contribution of sensor offset and thermal drift is

shown in Fig.8a Estimated values do not show the trend

due to the lesser contribution of thermal drift of the spindle

Contribution of centering error of the artifact is determinedusing the Fourier coefficients for the first harmoniccomponent and it is shown in Fig.8b After removing thecontribution of centering error of artifact, synchronouscomponents of measurement data are calculated using theestimated Fourier coefficients and it is shown in Fig 8c.Asynchronous components are calculated as the residualsbetween the fitted curve and the measurement data as given

in Fig.7b Among the different contributions, synchronous,and asynchronous components need to be analyzed furtherfor evaluating the radial errors of the spindle

Polar plot is the convenient way of displaying thesynchronous and asynchronous components of measure-ment data [6] Plotting circle radius is selected appropriately

as the three times the peak to peak value of the synchronousand asynchronous components of measurement data

Figure9a shows the synchronous components of

measure-ment data for the plotting circle radius of 15 μm Polar

profile shows the periodic variation with respect to the

plotting circle as it includes the contribution of form error

of the artifact along with synchronous radial error of the

spindle Hence, synchronous components of measurement

data requires further analysis for the separating the

contribution of form error of the artifact and it is explained

in section4.3 Asynchronous components of the

measure-ment data are displayed in polar plot for the plotting circle

radius of 5 μm as shown in Fig 9b It represents thenonrepeatable components due to recirculation of balls inthe bearings and the structural motion of the machine tool.4.3 Separation of form error of the artifact

In practice, form error of the artifact is due to the surfacedeviations which are low frequency in nature as compared

to spindle error [23] Form deviations in the surface profile

of the artifact causes a harmonic components which are

Fig 12 Polar profiles for the

synchronous radial error of

the spindle at different

spindle speeds

integer multiples of fundamental frequency of measurement

data [15] Hence, a suitable cutoff frequency can be selected

for removing the contribution of form error of the artifact in

spindle error measurement data [20] In the present work,

surface of the artifact is inspected separately in the

coordinate measuring machine and the form profile of the

artifact is identified as shown in Fig 10a Harmonic

components in the form profile of artifact is estimated and

shown in Fig 10b It can be seen that magnitude of

harmonic component at 3 cpr is higher than the other

frequency components, hence the form profile of the

artifact shows a significant three-lobe feature as shown in

Fig 10a The magnitude of harmonic components in

spindle error measurement data is determined using the

Fourier coefficients as given in Table2 It can be seen that

the magnitude of third harmonic component is higher than

the other harmonic components due its dominant magnitude

in the surface profile of the artifact as identified in Fig.10b

Though the magnitudes of sixth and ninth harmonic

components in the surface profile of the artifact are also

significant, their magnitude is much less as compared to the

fifth and seventh harmonic components in spindle error

measurement data as noticed in Table2 Hence, in this case,

the cutoff value is selected as 3 cpr, which is the dominant

harmonic component in the spindle error measurement data

and the surface profile of the artifact

As the contribution of form error of the artifact is

independent of the spindle speed, the specified cutoff value

needs to be verified at different spindle speeds Figure11

shows the magnitude of harmonic components for the

measurement data obtained at different spindle speeds It is

observed that the magnitude of third harmonic component

is high in all spindle speeds and its variation is found to be

in the order of 0.06 μm These results prove that the

specified cutoff value is not influenced by spindle speed

and it is suitable for filtering the contribution of form error

of the artifact After removing the contribution of third

harmonic component, the synchronous components of

measurement data is given in Fig.12 These polar profiles

are further analyzed for evaluating the synchronous radial

error of the spindle

4.4 Evaluation of spindle radial errors

In accordance with ANSI/ASME B89.3.4M standard [9],

least squares circle center for the polar profiles are

determined to assess the synchronous radial error of the

spindle Inscribing circle and circumscribing circles were

drawn from the least square center Radial width between

the circles is determined as the synchronous radial error of

the spindle Figure13a shows the least squares center for

the polar profile of the synchronous radial error obtained at

the spindle speed of 30,000 rpm and evaluated value is

found to be 1.713μm Figure 9b shows the asynchronouscomponents of measurement data obtained for the spindlespeed of 30,000 rpm and it is further analyzed forevaluating the asynchronous radial error of the spindle.Asynchronous radial error value is evaluated as themaximum radial width of the asynchronous components

in the polar plot at any angular position Figure13b showsthe evaluation of asynchronous radial error of the spindlefor the spindle speed of 30,000 rpm and its valuedetermined to be 2.132μm

4.5 Effect of spindle speed and number of spindlerevolutions

There are no guidelines to select the number of revolutionsconsidered for the evaluation of spindle radial errors [9].Hence, spindle error values are evaluated at differentspindle speed and number of spindle revolution Figure14shows the evaluation of synchronous radial error of thespindle at different spindle speeds and given number ofspindle revolutions Radius of the plotting circle is taken as

15μm Evaluated values for the synchronous radial error at

(a) Synchronous radial error

(b) Asynchronous radial error

Least squares circle center

0.477µm

Inscribing circle

Circumscribing circle

2.132µm

Fig 13 Evaluation of spindle radial errors for the measurement data obtained at spindle speed of 30,000 rpm; a synchronous radial error, b asynchronous radial error

S no Spindle speed (rpm) Evaluated values of synchronous radial error ( μm)

Number of spindle revolutions

Table 4 Evaluated values for

synchronous radial error at

different spindle speeds and

number of spindle revolutions

(a) 10,000 rpm, 8 revolutions (b) 20,000 rpm, 16 revolutions

Fig 14 Evaluation of

synchro-nous radial error at different

spindle speeds and number

of spindle revolutions

S no Spindle speed (rpm) Evaluated values of asynchronous radial error ( μm)

Number of spindle revolutions

Table 5 Evaluated values of

asynchronous radial error at

different spindle speeds and

number of spindle revolutions

5

10

15

(b) 20,000 rpm, 16 revolutions (a) 10,000 rpm, 8 revolutions

Fig 15 Evaluation of

synchro-nous radial error at different

spindle speeds and number

of spindle revolutions

different spindle speeds as given Table4 It can be seen that

the radial width enclosing the polar profile of the

synchronous radial error is decreasing, when the spindle

speed increases Synchronous radial error is caused due to

the out of roundness of the ball and the guide in the built-in

bearings When the spindle speed increases, contact point

of the balls is flattened by the increase of centrifugal force

or because the rotor of the spindle cannot mechanically

respond to a vibration source of high frequency such as the

radial run-out of the built-in bearings [13] Consequently, it

leads to the smoothing of the polar profiles and the

reduction in the evaluated value of synchronous radial

errors of the miniature spindle

Figure15 shows the evaluation of asynchronous radial

error of the spindle at different spindle speeds and given

number of spindle revolutions Plotting circle radius is

taken as 10μm Table5summarizes the evaluated values of

asynchronous radial error of the spindle at different spindle

speeds and number of spindle revolutions It can be

observed that there is an increase in asynchronous radial

error value when spindle speed and number of revolution

increases Asynchronous radial error is caused by

imper-fections and defects in the ball bearings and ball races [9]

At high spindle speed, the recirculation of balls increases

the magnitude of asynchronous radial error of the spindle

and it also includes the structural motion of the machine

tool When the number of spindle revolutions is increased,

the nonrepeatability of the spindle also increases due to the

recirculation of balls in the bearings Hence, the magnitude

of asynchronous radial error increases with increase in

spindle speed and spindle revolutions

5 Conclusions

In the present work, fixed sensitive radial error motion test

is carried out for evaluating spindle radial errors of a

miniaturized machine tool Spindle error measurement is

found to be affected by different error sources such as

sensor offset, thermal drift of the spindle, centering error,

and form error of the artifact along with speed variations

DFT-based frequency domain filtering method provides a

fixed resolution for resolving frequency components and its

accuracy is found to be limited by the spectral leakage due

to speed variations Alternatively, proposed model-based

fitting method provides frequency estimation with a higher

resolution and it leads to accurate interpretation of spindle

error data Proposed method effectively handles the speed

variations and it simultaneously separates the different

contributions of spindle error data Effect of spindle speed

and number of spindle revolutions was analyzed on the

evaluation of spindle radial error values Magnitude of

synchronous radial error is found to be in the order of

1.517–1.766 μm It does not show significant variations forthe given spindle speeds and number of spindle revolutionand it represents the repeatable behavior of the miniaturespindle However, the magnitude of asynchronous radialerror is found to vary in a broader range of 2.1029–4.595 μm An increasing trend is observed for theasynchronous radial errors for the increase in spindle speedand number of spindle revolutions This behavior is due tothe contribution of structural motion of the machine tooland the nonrepeatable motion of the balls in the bearings.Higher magnitude of asynchronous radial error ascompared to the synchronous radial error of the spindle

is the characteristic nature of rolling element bearingspindles The proposed method is distinct in analyzingthe spindle error data in time domain and it can beapplied for online monitoring of spindle performance athigh speed conditions

Acknowledgement The authors sincerely thank Prof MS Shunmugam, Department of Mechanical Engineering for providing the mechanical micromachining setup for conducting the experiments The authors also thank the reviewers for their encouraging comments and valuable suggestions.

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