The international journal of advanced manufacturing technology, tập 60, số 5 8, 2012

4.1 Agility assessment at Trident The assessment of TAL value was carried out using a 30 criteria agility assessment tool.. Based on this TAL value Assessment of total agility level TAL

ORIGINAL ARTICLE

Enhancing total agility level through assessment and product

mapping: A case study in the manufacturing

of refrigeration air dryer

C G Sreenivasa&S R Devadasan&R Murugesh

Received: 10 October 2010 / Accepted: 9 September 2011 / Published online: 27 September 2011

# Springer-Verlag London Limited 2011

Abstract The world’s manufacturing community has been

questing for ways to face the onslaught of competition One

of those ways is the adoption of agile manufacturing (AM)

paradigm AM paradigm enables a company to quickly

respond to the customers’ dynamic demands In order to

implement AM paradigm, a model named “model for

enhancing total agility level” (METAL) is proposed in this

paper METAL enunciates the assessing of the total agility

level (TAL), identifying the weak AM criteria and

subsequently strengthening them The practicality of

MET-AL has been explored in an air dryer manufacturing

company During this case study, refrigeration air dryer

was considered as AM capable product After assessment,

three weak AM criteria were identified Proposals were

drawn to strengthen these three weak AM criteria These

proposals envisage the strengthening of the weak AM

criteria through the removal of nonvalue adding activities,

utilization of mathematical models, and creation of web

portal The reassessment has indicated the possibility of

enhancing the TAL value in the above company through the

implementation of these proposals The experience of

carrying out this research has revealed that the deployment

of METAL would facilitate the contemporary companies tosystematically infuse AM paradigm and enhance their TALvalues

Keywords Agile manufacturing Agility assessment Airdryer Time management Global optimization

1 Introduction

During past two decades, significant researches on “agilemanufacturing” (AM) have been reported in the literaturearena AM is a paradigm that makes a company capable ofquickly responding to the customers’ dynamic demands [1,

2] Today, the manufacturers who successfully implement

AM paradigm are able to thrive in globalized marketenvironment Companies belonging to electronic industry,particularly television and mobile phone manufacturers arefew of such examples [3] Those AM companies exhibittheir agile capabilities by producing variety of models withinnovative features within a very short period Hence, thosemanufacturers are able to sustain the competition despitethe arrival of many competitors [4] Despite the dissemina-tion of AM paradigm among researchers and practitioners,

it is applied at slower pace in the manufacturing oftraditional engineering products such as air conditioners,compressors, air dryers, generators, motors, and refrigerators

It is high time that the manufacturers of these traditionalproducts need to acquire AM characteristics at a higher pace toface the onslaught of competition

Researchers started to work on AM after the formation

of the institution called AM forum at Iacocca Institute,Lehigh University, USA in the year 1991 [5–7] A majoremphasis of these researchers is that technology andmanagement practices are required to get integrated in

C G Sreenivasa ( *)

University B.D.T College of Engineering,

Davangere 577004 Karnataka, India

Darshan Institute of Engineering and Technology,

Rajkot 363650 Gujarat, India

e-mail: drmurugesh_m@yahoo.com

DOI 10.1007/s00170-011-3636-4

proportionate form to implement AM paradigm in

compa-nies [8] These researchers have mainly viewed the

out-comes of AM from four perspectives namely cost, market,

time, and environment While viewed from these

perspec-tives, the products produced by an AM company shall

enjoy high sales in the market Also, these products shall be

ecofriendly Those products shall require minimum time

and cost to evolve new models [9–13] These enunciations

suggest that a company shall map the characteristics of the

products produced by it from these four AM perspectives

The outcome of this mapping exercise would be useful to

identify the potential products about which AM characteristics

shall be infused to enhance the agility level of the company A

survey conducted in the literature arena revealed the absence

of any model that would enable the modern companies to

enhance their agility levels by conducting such AM mapping

exercise On identifying this absence, the research being

reported in this paper was undertaken

During the research being reported in this paper, the way of

enhancing the “total agility level” (TAL) in a company

through assessment and product mapping was explored This

was accomplished in two stages In the first stage, a pneumatic

products manufacturing company was identified Then the

research was focused on the manufacturing of one of the

products produced by this company namely air dryer

Subsequently, the construction and working of air dryers were

studied In the second stage, a model for infusing agility by

strengthening the weak AM criteria was designed This model

basically envisages the assessment of TAL and identifying the

weak AM criteria which shall be strengthened to enhance the

TAL The working of this model was explored by applying it

on air dryer manufacturing

2 Literature survey

During the research being reported here, the literature was

surveyed in two directions In the first direction, the

literature was surveyed to identify agility assessment

models A search in this direction revealed the appearance

of 11 papers reporting agility assessment models The

contributions of some of these papers are briefly described

here Kumar and Motwani [14] identified 23 factors and

subfactors which influence a firm’s agility These factors

assist in the identification of strengths and weaknesses of

the firms with regard to competing on time A parameter

named“agility index” has been used for assessment The

procedure for calculating the agility index has been

explained However, this agility index has not been tested

and validated Zhang and Sharifi [15] have proposed a

conceptual model for implementing agility They have also

contributed an agility assessment model This model

facilitates the assessment of agility by gathering responses

to the questions contained in a questionnaire This naire consists of 72 questions for assessing agility needs and

question-66 questions for determining current agility level of theorganization These authors have conducted case studies in 12companies for validating this agility assessment model.Ramesh and Devadasan [8] have reported their research

on agile assessment using qualification and quantificationtools The 72 questions for assessing agility needs proposed

by Zhang and Sharifi [15] were used by these authors asqualification tool These authors have proposed a quantifi-cation tool consisting of 20 AM criteria The practicality ofthis model was explored by these authors by conducting acase study in an Indian pump manufacturing company Inline to this research work, Vinodh et al [16] haveredesigned the 20 AM criteria quantification tool proposed

by Ramesh and Devadasan [8] These authors havestatistically validated the redesigned 20 AM criteriaquantification tool and carried out a case study in an Indianelectronic switches manufacturing company An extendedversion of this research has been reported in Vinodh et al.[17] In this paper, the method of measuring agility indexusing multigrade fuzzy logic approach is presented Onanalyzing the characteristics of the agile assessment modelsand tools which have surfaced in the literature arena duringthe recent years, it was found that the 20 criteria agilityassessment tool proposed by Ramesh and Devadasan [8]which was further refined by Vinodh et al [16] was mostsimple, exhaustive, and accurate in assessing agility Yet itwas found necessary to append this tool with the newcriteria of AM reported in literature This is due to thereason that the researchers continue to work in the direction

of identifying new criteria of AM [11]

In the second direction of literature survey, the tion on the application of AM paradigm on products wasgathered This direction of literature survey revealed thatfew researches have been conducted by applying AMparadigm on products such as semiconductor, journalbearing, electronic switches, and pumps These researcheshave been conducted by adopting various technologies andmanagement models to apply AM paradigm on theseproducts Some of these technologies and managementmodels include rapid prototyping technology (RPT),computer-aided design (CAD), activity-based costing, andTabu-enhanced genetic algorithm For example, Cheng et

informa-al [18] have proposed an artificial intelligence and internettechnologies-based system for implementing design andmanufacturing agility in journal bearing In this system, thecustomer shall input the application requirements and thenthe system responds quickly to facilitate an optimumselection and offers design solutions Likewise, Vinodh et

al [3] have explored the way of infusing agility in pumpmanufacturing company These authors have consideredCAD and RPT for infusing agility The Pro/E software

package was used for building the CAD model of the

pump The GAMBIT and FLUENT software packages were

used for conducting flow analysis Then, the model was

prototyped using fused deposition modeling technique Few

qualitative and quantitative techniques were used to gather

the reactions of the practitioners As a result of this research

experience, the CAD and RPT were found to be practically

feasible for infusing agility in a traditional pump

manufac-turing company Thus although a few researchers have

started to explore the way of infusing agility in products, no

research on mapping of the characteristics of products with

AM criteria has not so far been reported

Altogether, the literature survey conducted during this

research along the two directions has revealed that no model

to enhance the agility of the company by systematically

assessing it and mapping the product characteristics with AM

criteria has been evolved In order to fill this research and

practice gap, a model named as“model for enhancing total

agility level” (METAL) was evolved during the research being

reported in this paper The conceptual features of METAL are

briefly described in the next section

3 Conceptual features of METAL

The conceptual features of METAL are depicted in Fig.1

As shown, the TAL has to be assessed using an agility

assessment tool in a product-manufacturing company If the

TAL value is less than 50%, then the path of AM journey of

the company is in disarray which cannot be easily corrected

or enhanced This principle of fixing 50% as the minimum

TAL base value has been drawn from Vinodh et al [16]

According to this principle, a company scoring less than

500 marks using the agility assessment tool would lack

management commitment This is due to the reason that, in

the agility assessment tool encompassed in METAL, 50%

of the marks are allotted under management commitment

enabler Hence, a company lacking management commitment

towards implementing AM will not be scoring more than 50%

marks when agility assessment tool is used Hence, such a

company will fail to implement AM successfully as it is an

indication that AM pathway of this company is in disarray and

cannot be corrected or improved The principle behind

choosing 50% marks as the eligibility for implementing AM

is also an impact of the grading system followed in

educational system Most universities in the world fail the

students who secure less than 50% of the marks [19,20] This

would mean that those students securing less than 50% of

the marks would be failing to exhibit the traits of the

education and skill imparted on them

If the TAL value is greater than 90%, then the AM

journey is correctly carried out on a hurdle-free path and

hence there is no need to correct or accelerate it This

inference is drawn by observing the nature of evaluation ofstudents followed in educational system It is observed that,most Universities in the world award highest grade to thestudents who secure more than 85% of the marks [19, 20].This would mean that those students securing more than85% of the marks would be capable of successfullyexecuting the knowledge and skill that are imparted on themduring their courses of study In line to this observation, inthe METAL, it is earmarked that, a company scoring morethan 90% of the marks when agility assessment tool is usedshould be already in the AM path and free from facing anyhurdles Such companies require no further actions toaccelerate AM journey along the right path

If the TAL value is equal to or greater than 50% butequal to or lesser than 90%, then there is a scope forinfusing AM in the product/s of the company to enhancethe TAL value In this case, the base value of TAL is fixed

to declare weak AM criteria which are to be strengthened

by infusing agility in the product/s of the company Forexample, if base value of TAL is fixed as 50%, then the

AM criteria whose TAL values fall below 50% shall have

to be declared as weak criteria Meanwhile, the productcharacteristics are mapped from the AM perspectives Asthe result of this exercise, the products possessing thepropensity for infusing agility are identified These arechosen as candidate product/s for infusing agility with theobjective of strengthening the weak AM criteria The TALvalue is reassessed and compared with earlier TAL value.Based on the results of this comparison, strategic decisionsare made to remove the hurdles in the pathway so that the

AM journey of the company is accelerated

4 Practicality of METAL in the manufacturing

of air dryersThe practicality of METAL was investigated in a company byname Trident Pneumatics Private Limited (hereafter referred

to as Trident) Trident is located in Coimbatore city of India.Trident was started in the year 1988 with just four employees.Today, Trident’s employee strength has increased to 51.Trident is associated with designing and manufacturing ofvarious pneumatic application supporting products such as airdryers, drain valves, and filters Among the broad classifica-tion of air dryers, Trident manufactures two types of air dryersnamely refrigeration and regenerative air dryers Till now,Trident has designed and manufactured 17 models of therefrigeration air dryer and 30 models of the regenerative airdryer These air dryers are widely applied in the fields likeautomobile, textile, medical, and cement manufacturing.Trident’s air dryers cater to the need of the applications inthese fields These air dryers are supplied to companieslocated within and outside India Besides designing and

manufacturing of pneumatic products, Trident is involved in

research and development of pneumatic products The

out-comes of Trident’s research and development activities have

resulted in filing three patents These information indicate that

Trident has been in the AM journey

4.1 Agility assessment at Trident

The assessment of TAL value was carried out using a 30

criteria agility assessment tool This assessment tool is the

extension of the 20 criteria agility assessment tool proposed

by Ramesh and Devadasan [8] As the name implies, this tool

facilitates the assessment of agility level of an organization

from the perspective of 30 AM criteria These 30 AM criteriacan be viewed in Fig 2 This tool is incorporated withquestionnaires under each AM criteria The competentpersonnel of Trident were interviewed with these question-naires A conversion table encompassed in 30 AM criteriamodel was used to convert the responses of respondents intomarks These marks were subsequently used to computeTAL of Trident The TAL value thus determined indicatedthat Trident has acquired 68.37% of agility This value fallsbetween 50% and 90% Hence, according to the METAL,the need of infusing agility in the products manufactured byTrident was realized In order to declare the weak AMcriteria, base TAL value was fixed as 50% Based on this

TAL value Assessment of total agility level (TAL)

≥ 50% and ≤ 90%

Agility needs to be infused in the product/s to increase TAL value

Fixing of base TAL value

Declaration and identification of weak AM criteria

Identification of the product/s possessing maximum propensity for applying agility

AM infusion in the candidate product/s with the objective of strengthening weak

AM criteria

Reassessment of TAL value

Comparison of TAL value before and after the infusion of AM in the candidate

product/s

Strategic decision making Fig 1 Conceptual features

of METAL

fixation of base TAL value, the weak AM criteria at Trident

were identified The weak AM criteria thus identified are

graphically shown in Fig 2 As shown, three AM criteria

namely“time management” (with agility level of 30.625%),

“global optimization” (with agility level of 37.5%), and

“production methodology” (with agility level of 45%) were

identified as weak AM criteria of Trident Due to space

limitation, the detailed explanation about the 30 AM criteria

has not fallen within the scope of this paper However, in

order to facilitate the clarity of presentation, characteristics of

the above three weak AM criteria considered for enhancingthe TAL value of Trident are briefly described in Table1.4.2 Mapping AM factors with air dryer characteristicsTheoretically, an AM company may produce all types ofproducts to meet the customers’ dynamic demands within ashort duration of time without compromising profitability[1,2] This is possible only if the company produces AMinfused products As appraised in Section 1, an AM-infused

Fig 2 Actual agility levels and

agility gaps at Trident

product will indicate its agility from the viewpoint of four

perspectives namely cost, market, time, and environment

These perspectives will be reflected in the forms of indicators

For example, the agility of a product from market perspective

will be indicated in the form of high sales These AM

perspectives with their AM indicators are required to be

mapped with the product characteristics This exercise carried

out at Trident on air dryers is explained in the next subsection

4.2.1 Mapping exercise at Trident

The exercise on mapping from the AM perspectives was

carried out at Trident on refrigeration and regenerative air

dryers which are manufactured at Trident This exercise wascarried out by interviewing the managing director (MD) ofTrident and gathering of relevant information along with hisremarks Table2 presents the results of this exercise

An analysis of the information presented in Table 2

would reveal that the refrigeration air dryers possesspropensities for implementing AM from the AM perspec-tives namely market and environment However, refrigera-tion air dryers do not possess propensities to implement

AM from the AM perspectives namely cost and timerequirements The regenerative air dryers have been found

to possess propensities to implement AM from all AMperspectives Thus, the exercise on mapping air dryer

Table 1 Weak AM criteria identified in Trident and their characteristics

Weak AM criteria identified in

Trident

Characteristics

Time management A primary capability of a company implementing AM is the ability to respond quickly against the

customers ’ dynamic demands Such quick response is possible if the time of developing the product and offering the services is totally eliminated While this task is not possible in all cases, efforts must be made to eliminate the nonvalue-adding activities in all endeavors that are required to quickly respond against customers ’ dynamic demands In order to exert these efforts, the company implementing AM is required to utilize time management tools and techniques [ 16 , 43 ]

Global optimization AM is highly enabled through the operations carried out along both internal and external supply chains

[ 16 ] Along these supply chains, the members of them have contradictory objectives [ 44 ] For example, a supplier prefers to get order for supplying huge quantity In this case, the supplier may offer discount to the company implementing AM On the other hand, this company will be attempting to enhance agility

by applying just-in-time manufacturing principles in which case small quantities are ordered by allowing least lead times In this case, the company implementing AM stands to lose profit due to the absence of price discount offered by the supplier In this context, global optimization plays an important role in AM environment by providing optimized solutions to balance the contradictory objectives of the members of supply chains [ 31 ]

Production methodology In an AM environment, the production methodology shall be efficient enough to meet the quantity and

quality requirements of customers within a short period of time In order to develop such a capability, flexible and lean manufacturing principles need to be applied in the shop floor Application of flexible manufacturing principles will allow the production of customized and innovative products by fulfilling the quality requirements On the other hand, lean manufacturing principles will allow the production of exact quantity of goods without experiencing wastages [ 45 ]

Table 2 Mapping AM perspectives with air dryer characteristics in Trident

Remarks by the MD of Trident

are equally design intensive

capabilities from AM perspectives has revealed that

regenera-tive air dryers possess maximum propensity for infusing agility

Hence, the regenerative air dryer was to be considered as the

candidate product for infusing AM with the objective of

strengthening weak AM criteria at Trident However, the

MD of Trident wanted to consider refrigeration air dryer

as the candidate product This is due to the reason that,

refrigeration air dryers are more widely used [21] than

regenerative air dryers In this context, during the research

work being reported here, refrigeration air dryer was

chosen as the candidate product for investigating the

practicality of METAL

4.3 Strengthening the AM criterion“time management”

As shown in the Fig.2, the agility level of the AM criterion

“time management” at Trident is 30.625% The remaining

69.375% of agility gap in time management AM criterion

needs to be filled In order to strengthen “time

manage-ment” AM criterion, time compression technologies such as

CAD/Computer-aided manufacturing (CAM), RPT,

simu-lation, mass customization,“removal of non-value adding

activities”, quick response strategies, “configure to produce

according to the order”, and “redesign according to

customers’ perceptions” are required to be employed

[3,22–28]

While conducting agility assessment and carrying out

subsequent analysis at Trident, two deficiencies were

identified under “time management” AM criterion The

first deficiency was that there has been no program to train

the employees about the power of time compression in

acquiring the competitiveness The second deficiency was

that there has been no deployment of time-compression

technologies at Trident The first deficiency could not be

rectified during the research being reported here as allotting

the time of employees to train them on time management is

not currently affordable at Trident In this background, the

efforts were made to rectify the second deficiency To begin

with, the steps of assembling refrigeration air dryer were

closely observed at Trident This observation indicated that,

out of the several time compression technologies listed in

the previous paragraph, the“removal of non-value adding

activity” has high potential in applying time compression in

the case of manufacturing refrigeration air dryer at Trident

Hence, efforts were made to identify the nonvalue adding

activities and the methods of removing them

At Trident, assembly of refrigeration air dryer is carried

out in an assembly cell In this assembly cell, three

components namely compressor, condenser, and heat

exchanger are assembled The activities carried out during

this assembly practice are shown in Fig.3

The time taken to carry out each of these activities is

indicated in brackets These activities were studied to

identify those that add no value while assembling the airdryer The nonvalue adding activities thus identified and theproposals drawn to eliminate them are enumerated in thefollowing subsections

4.3.1 Unloading and unpacking of outsourced components

As shown in Fig.3, the components outsourced are receivedand unpacked Since these components are heavy, thisexercise consumes as much as 10 min while assemblingone refrigeration air dryer Subsequent to this exercise, thesecomponents are unloaded and moved to a place located at adistance of 10 ft from the assembly cell Instead if thesecomponents are unloaded at the assembly cell itself, then thetime of 10 min consumed to move them to the assembly celland placing them there can be reduced to 5 min

4.3.2 Receiving compressor and condenser

as separate unitsCurrently, Trident receives compressor and condenser as anintegral unit from a manufacturer Then the compressor and

Placing the unit containing compressor and condenser away from assembly cell

Dismantling of compressor and condenser separately (25 minutes)

Assembly of compressor, condenser and heat exchanger (25 minutes)

Brazing of copper tubes (25 minutes)

Leak testing (10 minutes)

Vacuum process (20 minutes)

Gas charging (20 minutes)

No load and full load testing (20 minutes)

Final inspection and packaging (20 minutes)

Fig 3 Activities carried out in the assembly cell of refrigeration air dryer at Trident

condenser are dismantled and made as separate units.

Subsequently, the compressor and condenser are assembled

on the base plate of a component called canopy This

dismantling and fixing are necessitated as the compressor

and condenser are assembled in the refrigeration air dryer in

different orientation to suit the dimensions of the base plate

of canopy This exercise consumes as much as 25 min

while assembling one unit of the refrigeration air dryer

This exercise is pictorially depicted in Fig.4

During the research being reported here, this whole

exercise was recognized as a nonvalue adding activity

After analyzing the steps, the following two proposals were

suggested:

1 Trident may place order for procuring the compressor

and condenser separately from the same or two

different manufactures These two components may

be assembled on the base plate of the canopy at Trident

Thus, the nonvalue adding activity shown as steps 1

and 2 in Fig.4can be eliminated

2 Trident may ask the manufactures to manufacture the

base plate of the canopy in accordance with the

dimensions furnished by the Trident This manufacturer

shall assemble both compressor and condenser on this

base plate of canopy and dispatch the same to the

Trident In this case, all the three steps shown in Fig.4

can be eliminated at Trident

Trident may choose to implement any one of the above

proposals Here, it is obvious that the nonvalue-adding

activity can be totally eliminated in the case the second

proposal is implemented at Trident

4.3.3 Centralized inventory management facility

One of the assembly activities is the positioning of the

compressor, condenser, and heat exchanger according to the

canopy size of refrigeration air dryer at Trident The timetaken to carry out this activity is 25 min While carrying outthis activity, the operator is required to collect the inventorylocated at two different places One place is located inside theassembly cell and the other is located outside the assemblycell Further, these inventories are stacked in the rack whichcannot be rotated These conditions result in unnecessarymotion of operators Hence, this motion is considered as anonvalue-adding activity In order to remove this nonvalueadding activity, it is proposed that the inventory may becentrally maintained within the assembly cell Furthermore, it

is suggested that the inventory shall be stacked in a rack whichmay be rotated Implementing these proposals may reduce

10 min from the currently consumed time of 25 min incollecting the inventory

4.3.4 Reducing the time of carrying out brazing operation

In order to enhance agility level, all the components andsub-assemblies required to manufacture refrigeration airdryers are outsourced at Trident These components andsub-assemblies are assembled at Trident using few manu-facturing processes One of those manufacturing processesemployed is brazing Brazing is employed to join thecopper tubes with the compressor, condenser, and heatexchanger During this process, the copper tube is bent tothe required dimension and positioned The time taken forcarrying out this process is 25 min During this research,this process was recognized as a nonvalue-adding activity

In order to remove this nonvalue-adding activity, followingproposals were evolved:

1 Trident may outsource the bending process to bend thecopper tube to the required shape and dimension

2 A fixture may be designed and manufactured to speed

up the bending process

Base plate supplied

by the manufacturer

Step 1 : Compressor

and condenser are supplied by the manufacturer as an integral unit

Step 3 : Compressor

and condenser are fixed on the base plate of canopy

Step 2: Compressor and

condenser are dismantled separately

Base plate of canopy manufactured at Trident

Compressor CompressorCompressor

Fig 4 Steps currently followed

to assemble compressor and

condenser

Implementing either one of the above proposals would

reduce 10 min out of the currently consumed time of

25 min in bending the copper tubes

4.3.5 Time reduction through the removal of nonvalue

adding activities

An estimation indicated that, on implementing the

pro-posals evolved during this research being reported here to

strengthen the AM criterion“time management”, the time

of manufacturing a refrigeration air dryer may reduce from

a minimum of 45 min to maximum of 65 min at Trident

4.4 Strengthening the AM criterion“global optimization”

As shown in Fig.2, the agility level of the AM criterion

“global optimization” at Trident is 37.5% Hence, the AM

criterion“global optimization” needs to be strengthened to

fill 62.5% of agility gap prevailing in Trident The efforts

made to fill this agility gap are described in the following

two subsections

4.4.1 Strengthening through information technology

infrastructure

While conducting agility assessment and carrying out

subsequent analysis at Trident, two deficiencies were

identi-fied under the AM criterion“global optimization” The first

deficiency is that there has been no deployment of information

technology (IT) infrastructure to handle conflicting objectives

prevailing in global supply chain In order to overcome this

deficiency, the necessary IT infrastructure is required to be

employed at Trident The IT infrastructure such as enterprise

resource planning, electronic data interchange, internet

proto-cols, local area network, database management systems,

groupware, intranets, extranets, decision support systems,

multimedia, e-commerce, expert system, modeling, and

simulation are required to be employed [7, 29, 30] In this

background, the IT infrastructure at Trident was closely

observed

Presently at Trident, the information among the

custom-ers, supplicustom-ers, and employees are managed over telephonic

and postal communications A study in this direction

revealed that, out of the several IT infrastructure listed

above, internet technology possesses high potential for

application in the case of manufacturing refrigeration air

dryer at Trident The internet technology allows people to

interact with each other If internet technology is used in

Trident, then their employees, suppliers, and customers can

interact with each other In this context, a web portal was

designed to facilitate the Trident to overcome the

afore-mentioned first deficiency This web portal is named as

“Trident Global Optimization Platform” (Trident-GOP)

The “Trident-GOP” has been designed using the PHPversion 5.2.3 as front end, MySQL client version: 5.0.45 asback end and XAMPP 1.6.3a software as editor TheTrident-GOP can be accessed by three categories of users.The first category of users of the Trident-GOP is named as

“Trident group” These users are the top management andemployees of Trident The other two categories of Trident-GOP are suppliers and customers, Trident-GOP allow thecustomers to place the order online The web page ofTrident-GOP enabling this process is shown in Fig 5.Trident-GOP allows the Trident group users to record thecomponents to be supplied by the suppliers and the duedate of supplying them The web page of Trident-GOPenabling this process is shown in Fig.6 On the other hand,Trident-GOP allows the supplier to submit a request torevise the due date The web page enabling this process isshown in Fig.7 Now the Trident group user can view theorders placed by the customers and the request made by thesuppliers to revise the due date The web page displayingthese information is shown in Figs.8and 9 Thus Trident-GOP has been designed and developed to meet rudimentaryrequirements of globally optimizing the supply chain of theTrident More facilities can be added in the future toTrident-GOP for meeting many other globalized optimiza-tion requirements of Trident

4.4.2 Strengthening through the use of optimizationtechniques

The second deficiency identified under the AM criterion

“global optimization” at Trident was that there has been nodeployment of techniques to optimize the contradictoryobjectives of supply chain management activities In order

to overcome this deficiency, appropriate optimizationtechniques are required to be employed Several optimiza-tion techniques and mathematical models are available inthe literature to optimize the contradictory objectives ofsupply chain For example, optimal policy models forhandling temporary price reduction and price increasesituations are presented in [31] Besides these kinds ofmathematical models, other optimization techniques namelygenetic algorithm and artificial neural network are required to

be employed to enhance the efficiency and performance ofsupply chains [32–37] In this background, the contradictoryobjectives of the supply chain of Trident were closelyobserved

Presently at Trident, the components are procured fromtheir suppliers based on monthly forecasting As mentionedearlier in Section4, Trident has been in the AM journey Acompany practicing AM principles is required to follow thejust-in-time (JIT) philosophy [13] However, this companyoften has to confront the business dynamics such astemporary price discount and price increase During the

temporary price discount period, the company is tempted to

procure large quantities of components from their suppliers

Also, when the price increase is expected shortly, the

company is tempted to procure large quantities of

compo-nents before their price increase becomes effective The

company will be financially benefited by utilizing these

situations wisely In these types of situations, the

procure-ment cost is reduced when compared to that is incurred in

JIT scenario Hence out of the optimization techniques

listed above, the optimal policy models proposed by [31,

38, 39] to handle the temporary price discount and price

increase situations were found to be the most potential

models that can be applied at Trident The method of

adopting these models in practice is illustrated in the

following parts of this section

When price discount is offered by the suppliers temporarily,

the following mathematical models may be used

Qd optimal discount order quantity in case oftemporary price discount

Sd optimal cost saving in case of temporary pricediscount

D annual demand

O ordering cost

P purchasing cost per unit

H annual holding cost fraction

d reduction in the price per unit in case of temporaryprice discount

q stock position when optimal discount order quantity

is procuredModel 1 is used when no price discount is offered Inthis case, economic-ordering quantity is computed Anorder may be placed for supplying this quantity of goods Incase price discount is offered by the supplier, model2 can

be used to determine optimal discount order quantity When

Fig 5 Web page allowing the customer to place an order with Trident

this calculated optimal discount order quantity is ordered,

the cost saved is computed using the model3

When there is price increase, Trident may use the

following mathematical models4,5, and6

EOQr economic order quantity during price increase

Qr optimal price rise order quantity in case of price

increase

Sr optimal cost saving in case of price increase

D annual demand

O ordering cost

P purchasing cost per unit

H annual holding cost fraction

d reduction in the price per unit

i anticipated increase in price per unit

q stock position when optimal price rise order

quantity is procuredModel4 is used to calculate the order quantity after theprice increase is announced There are circumstances inwhich Trident may anticipate price increase ahead of time

In this situation, Trident can increase the order quantity andescape from the adverse effect of price increase to amaximum possible extent This quantity to be orderedahead of the price increase can be calculated using themodel 5 The cost saving achieved in this case may becalculated using the model 6 During these situations, thecompany may procure the exact quantities required andthus save the cost

4.5 Strengthening the AM criterion“productionmethodology”

As shown in Fig 2, the agility level of the AM criterion

“production methodology” at Trident is 45% Hence, this

Fig 6 Web page enabling the Trident group to record the order placed with supplier

AM criterion needs to be strengthened to fill 55% of agility

gap prevailing in Trident While conducting agility

assess-ment and carrying out subsequent analysis at Trident, two

deficiencies were identified under the AM criterion

“produc-tion methodology” The first deficiency is that there has been

no deployment of automated/computerized inspection at

Trident The infrastructure such as vision-based automated

inspection system [40], X-ray oblique computed tomography

[41], and reconfigurable automated inspection systems are

required to be employed to enhance agility In this

background, the infrastructure utilized to inspect the

refrig-eration air dryer at Trident was closely observed This

observation indicated that leak testing was carried out

manually This manual inspection is carried out to check

whether any leak prevails in the joints of the assembly This

manual inspection was carried out by reading the values in

pressure gauge in regular intervals Here, the entire

refriger-ation air dryer was filled with nitrogen gas and the pressure

variation if any was checked in the gauge at the specified

interval of time Drawbacks such as excessive time

con-sumption, difficulty in pinpointing the leak joint, and need

for removing the nitrogen after leak testing were observed at

Trident due to the adoption of this manual inspection

Presently at Trident, this manual leak inspection has

been replaced by semi-automated leak inspection This

semi-automated leak inspection is carried out using ahelium leak detector Here, the air dryer under inspection

is vacuumed to 0.5 mille bar and then the helium gas issupplied If there is any leak in the joints of the assembly,then this is indicated through an alarm signal This heliumleak detector overcomes the drawback of the manualinspection carried out at Trident earlier

The second deficiency is the adoption of lot-by-lotacceptance sampling practice at Trident This acceptancesampling was carried out by quality control departmentpersonnel The lot considered for sampling was one refriger-ation air dryer per day Apart from this, the quality controldepartment personnel used to inspect a particular attributebased on the customer complaints Presently at Trident, 100%inspection is followed This 100% inspection is executed byinfusing quality control check sheet at all inspection stagesduring the manufacturing of refrigeration air dryer Thus, the

AM criterion “production methodology” has now beenstrengthened by overcoming the above two deficiencies

5 Reassessment of TAL valueAccording to the METAL, the TAL value has to bereassessed after strengthening the weak AM criteria This

Fig 7 Web page enabling the supplier to make due date revision

task was carried out by explaining the proposals and

solutions derived to strengthen the weak AM criteria to

the competent personnel of Trident After clarifying their

doubts, the questionnaires contained under the weak AM

criteria were given to them As mentioned in the previous

section, Trident has strengthened“production methodology”

AM criterion However, Trident is yet to implement the

proposals evolved during the research being reported here to

strengthen the two AM criteria namely“time management”

and “global optimization” Hence, these personnel were

requested to assume that these proposals were implemented

to strengthen weak AM criteria and respond to these

questionnaires The responses of these personnel were

quantified Thus, the agility levels of weak AM criteria and

TAL value were reassessed at Trident

5.1 Comparison of TAL before and after strengthening

weak AM criteria

The agility level and TAL value determined at Trident

before and after reassessment are summarized in Table3

As shown, the reassessed TAL value at Trident was found

to be 69.43% The TAL value has enhanced by 1.06% The

reason for this meager enhancement is that only three weak

AM criteria were identified and strengthened at Trident Asshown in Table3, the reassessed agility level of AM criterion

“time management” is 46.875% This AM criterion hasenhanced its agility level by 16.25% However, the agilitygap of 53.125% still prevails in this AM criterion at Trident.The existence of this large gap is attributed to two reasons.The first reason is that the proposals for removing nonvalueadding activities for strengthening this AM criterion are onlypartially accepted by the Trident Second reason is that notraining programs on time management concepts areconducted at Trident The reassessed agility level of weak

AM criterion “global optimization” is 66.667% This AMcriterion has enhanced its agility level by 29.167%.However, the agility gap of 33.333% prevails in Tridentagainst this criterion This is due to the same reason that thesuggestions proposed to strengthen this AM criterion areonly partially accepted by the Trident The reassessed agilitylevel of weak AM criterion “production methodology” is75% This AM criterion has enhanced its agility level

by 30% However, the agility gap of 25% prevails inthis AM criterion This is due to the reason that, theinspection system adopted is semi-automated and hence,Trident has to consider adopting fully automated inspectionsystem

Fig 8 Web page enabling the Trident group to view the order placed by the customer

6 Conclusion

Numerous research papers on AM are found in the literature

arena [11,42] An overview of these research papers indicate

that researchers have explored the way of infusing agility in

the companies and products in a scattered manner However,

there has been no effort made to enhance the TAL of

companies by infusing agility through the mapping of

product characteristics from AM perspectives In order to

meet this research requirement, the model METAL is

contributed in this paper METAL facilitates the modern

companies to enhance their TAL value The practicality of

METAL was examined at Trident The METAL is initiated

by assessing of the TAL value of the company In this paper,

the adoption of an agility assessment tool consisting of

30 AM criteria is recommended to assess the TAL value ofthe company On applying this 30 AM criteria assessmenttool, the TAL value of Trident was found to be 68.37%.Simultaneously, the AM characteristics-enabled productswere identified by mapping refrigeration and regenerativeair dryer characteristics designed and manufactured atTrident from four AM perspectives At the end of thisexercise, the refrigeration air dryer was chosen for infusingagility by strengthening the AM criteria The weak AMcriteria were identified by fixing the agility base level as50% The weak AM criteria identified were studied.Subsequently, proposals were evolved to strengthen them.After that, the agility levels were reassessed It was foundthat two weak AM criteria namely“global optimization” and

“production methodology” have been strengthened by 30%

Fig 9 Web page enabling the Trident group to view the request made by the supplier

Table 3 Comparison of TAL and agility levels before and after strengthening the weak AM criteria

The weak AM criterion “time management” has been

strengthened by 16% The TAL value was reassessed and

found to be 69.43% The overall TAL value of Trident has

enhanced by 1.06%

The research reported in this paper has suffered from few

limitations One of the limitations is that the proposals

derived to strengthen the weak AM criteria have been only

partially accepted by the Trident management This is due

to the reason that the effectiveness of implementing the

suggestions proposed is required to be examined and

validated Another reason is that Trident needs to

finan-cially invest for implementing these proposals This factor

prevents the immediate implementation of the suggestions

at Trident On the whole, the experience of carrying out the

research reported in this paper has revealed that the

deployment of METAL would facilitate the contemporary

companies to systematically infuse agile characteristics and

enable to enhance their TAL values This research may be

further continued by implementing METAL in many more

companies The results of these case studies may be used to

refine METAL and enhance its practical compatibility

Acknowledgment The authors are thankful for the cooperation and

support rendered by the management and employees of Trident

Pneumatics Private Limited, Coimbatore, 641 004, India towards the

conduct of the research work reported in this paper The authors are

thankful to an anonymous referee whose two suggestions have been

used to improve the description of the research reported in this paper.

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ORIGINAL ARTICLE

Adaptation of the simulated annealing optimization

algorithm to achieve improved near-optimum objective

function values and computation times for multiple

component manufacture

Atef Afifi Afifi&Wasim Ahmed Khan&

David R Hayhurst

Received: 4 March 2011 / Accepted: 31 August 2011 / Published online: 13 October 2011

# Springer-Verlag London Limited 2011

Abstract The paper concerns the development of the

Simulated Annealing Algorithm (SAA) for the sequencing

of cutter tool movement in machine tools capable of

manufacturing many components, located on a box-like

jig/pallet, in a single setting using a multiple tool magazine

The objective of the SAA is to minimise the total machine

tool residence time The general SAA has been enhanced,

to achieve lower values of the objective function during the

iterative scheme, and hence improve solution accuracy;

and, to reduce computation time by cessation of the

iterative scheme when no further improvement in the

objective function occurs The reconfigured SAA has been

evaluated using a number of case studies The results show

that a reduction in the objective function value can be

achieved in up to 6%, with far less computational effort In

addition, it is shown that the computation time can be

reduced by a factor of between 20% and 72% The

improvement in the objective function value and the

computational speed depends on the complexity of theproblem posed to the SAA software

Keywords Simulated annealing algorithm Computationally efficient Optimization Multi-component manufacture

b Random number between 1 and 0

r and s Operational nodes on different pallet faces

q Number of tools utilised

g Number of operational segmentsi–j Two operational nodes that define a segmentACF Acceptance check factor

eT Temperature in algorithm of Metropolis

et al [6]

E Energy level in algorithm of Metropolis

et al [6]

Θ Non-productive machine time objective

functional units (s), c.f Eq.2

C Control parameter used in the optimization

process

Coand Ci Initial/original and general value of

optimization control parameter

Cf Final value of optimization control parameter

ΔC Increment of C between optimization steps

Tij Time of non-productive motion in the X–Y

plane parallel to a single pallet face

A A Afifi

German University in Cairo,

Main entrance Al Tagamoa Al Khames, Al Khames,

New Cairo, Egypt

W A Khan

Institute of Business Administration,

City Campus, Garden Road,

Tz Time of non-productive motion in the Z

direction

Tchp Time to change tool p

Ttpwfp Tool path weight factor for tool p

Tpr Total pallet rotation time

bKB Boltzmann’s constant

K Counter for iteration number

K* Freezing parameter counter

Kwi Number of iterations performed without

improvement of Θ

Q Pre-determined value of the total number of

iterations

ξo Initial solution

ξiandξi+1 Current solution at the ith and i+1th steps

ξp Potential candidate solution

ξBest Best solution in iteration

Figures 2–7

A Approach to node

E Exit from node

S Start from node

The numerical solution of large combinatorial optimization

problems associated with machining/manufacture of

multi-ple components with multimulti-ple tools, and sometimes using

several machine tools, is challenging because of the large

number of variables involved Many different techniques/

algorithms are available for the optimization of the

associated path planning, and some of these are briefly

addressed Yue-Jaw et al [1] used a generic algorithm to

obtain optimal probe travel paths for coordinate

measure-ment machine operation; Saravan et al [2] optimised

cutting conditions during profile machining using a

non-traditional optimization techniques; and, Zamani [3] used a

parallel constrained anytime procedure for manufacturing

project scheduling Whilst such non-traditional techniques

can be tailored to specific problems, and give acceptably

good results; it is the Simulated Annealing Algorithm

(SAA) that is often preferred due to its adaptability,

robustness in coping with huge numbers of variables, and

its ability to avoid the numerical difficulties associated with

local minima The SAA has been used successful in

conjunction with other techniques; for example, Wang et

al [4] have combined it with a genetic algorithm in the

optimization of multi-pass milling; and Bachlaus et al [5],

have enhanced it using chaos embedded techniques to

sequence the machining of components on multi-functionalmachining systems Although all of these techniques havetheir own merits, particularly when tailored to specificproblems, this paper addresses the use of the classical SAAapproach, and seeks to identify those conditions thatimprove both accuracy and computational speed

The SAA is comprised of a stochastic search procedurewhich seeks the minimum of a pre-defined deterministicobjective function The method systematically applies smallperturbations to the current solution whilst seeking tominimise the overall objective function The techniquealways accepts objective function decreases, but can bemade to accept objective function increases with apparentbenefits This feature is examined in this paper For verylarge combinatorial problems associated with manufactur-ing scheduling, the speed of computation can be a limitingfeature; this aspect is also addressed here

The simulated annealing technique was first developed

by Metropolis et al [6] to analyse the physical annealingprocess associated with condensed matter Thereafter, it hasbeen applied to combinatorial problems by a number ofresearchers and has been shown experimentally by Kirkpa-trick et al [7] and Cerny [8] to provide near-optimalsolutions It has also been applied to the formation andscheduling of manufacturing cells with encouraging results

by Jahangirian et al [9], Varadharajan and Rajendran [10],Liu and Wu [11], Vakharia and Change [12] and Tam [13]

In addition, Laarhoven et al [14] have employed the SAA

to solve the job shop scheduling problem, and they provedthat it converges in probability to a global minimal solution.The scheduling problem of a semiconductor circuit fabri-cation plant has been tackled by Peyrol et al [15] using theSAA method; and, Ben-Arieh and Maimon [16] havesuccessfully applied the SAA to the printed circuit boardassembly Timetabling problems have been addressed byZhang et al [17]; and, constrained optimisation problemshave been studied by Pendamallu and Ozdamar [18] usinghybrid and local search techniques In this way, it has beenclearly demonstrated that the simulated annealing approachyields global optimal solutions for large combinatorialoptimization problem

In the computer-aided manufacture of component ladenpallets in machining centres with multiple tool magazines(Fig 1), components can be bolted to four faces of thebox-like pallet which can rotate about a symmetricalvertical axis, B motion; tools, selected from a magazine,are driven in the plane of a pallet face, X–Y motion, andperpendicular to a pallet face, Z motion In this way, four-axis tool motion is achieved When the implication oflarge numbers of components and tools are taken intoaccount, it is found that non-optimal job sequences andtool selections can have a significant impact on overallprofit margins, and hence on the competitive position of

the firm However, finding the optimum sequence/solution

has proved quite difficult for manufacturing engineers due

to the large number of cutting paths, and tool

combina-tions that may be selected c.f Bard and Feo [19] In this

paper, the problem will be addressed of performing

optimization computations for the minimization of the

manufacturing times of pallets that contain multiple

components, located on several pallet faces, and

manu-factured with multiple tools The emphasis will be on the

minimization of the related objective function, and the

associated accuracy of solution, whilst keeping

computa-tion time to a minimum

The problem of minimization of pallet residence time for

multiple component, multiple tool manufacturing under

imposed constrains has been formulated as a Euclidian

Travelling Salesman Problem The constraints are, for

example, associated with the need to manufacture particular

features with individual tools at the required speeds, and

with the need to execute traverses between different

machining operations at maximum speed In addition,

optimisation constrains are imposed by component

geom-etry, clamps and fixtures and have to be taken account of;

these aspects have been addressed in detail by Afifi et al

[20] in Section 6 of their paper The SAA technique has

been used by Khan and Hayhurst [21] and Afifi and

Hayhurst [22] and further developed by Afifi et al [20,23]

to achieve optimum tool movement between different

productive contours around the pallet faces In the work

reported by Khan and Hayhurst [21], the SAA algorithm

achieved optimum solutions for most of the cases examined

due to simplicity of the problem In the work reported by

Afifi et al [20,23] the size of the problems were increased,

and a number of new parameters were included, such as a

cost function for tool changes and a penalty function for

pallet rotations In the previous work by Afifi et al [23],

and during the evaluation of the operation of the simulated

annealing method for some complex case studies, it was

found that the SAA reaches a solution which is typically a

few percent from the optimal one, and that it takes a

considerable computational time to do so It is therefore

apparent that there is a need to improve accuracy andcomputational speed of the SAA algorithm when applied tothis class of manufacturing problems

Because of the enormity of the combinatorial problem,speed of computation is a prime concern, whilst preservingcomputational accuracy, and techniques for the reduction incomputational time are a key part of this paper Two particularaspects are thought to offer significant benefits and areexamined in detail The first relates to the improvement ofsolution accuracy, and the second to reduced computersolution times Regarding the latter, the solutions due to Afifi

et al [20,23] indicate that the SAA iterative scheme can beoperated non-productively for many iterations withoutsignificant reduction in the value of the objective function

or increase in the accuracy of solution Hence, judicialtruncation of the iterative scheme is thought to be capable ofincreasing computational speed

The paper therefore focused on: (1) improvement of theaccuracy of solution of SAA algorithm by reduction of theobjective function, and (2) reduced computer solution times

by elimination of redundant SAA iterations In the nextsection, descriptions are given of the general SAA and ofthe physical problem to be addressed

2 Description of physical problem2.1 The general annealing algorithmMetropolis et al [6], in the earliest days of scientificcomputing, introduced a simple algorithm that can be used

to provide an efficient simulation of a collection of atoms inequilibrium at a given temperature In each step of thisalgorithm, an atom is given a small random displacement,and the resulting change in the energy of the system,ΔE, iscomputed IfΔE≤0, then the displacement is accepted andthe configuration with the displaced atom is used as thestarting point for the next step The case ΔE>0 is treatedprobabilistically, and the probability for acceptance of theconfiguration is:

P $Eð Þ ¼ exp $E bK . BeT; ð1Þwhere bKB is Boltzmann’s constant, and eT is temperature.Random numbers uniformly distributed in the interval (0–1)provide a convenient means of implementing the random part

of the algorithm One such number is selected and comparedwith the acceptance probability P(ΔE) If it is less than P(ΔE),the new configuration is retained; if not, the originalconfiguration is used to start the next step By repeatingthe basic step many times, the thermal motion of atoms inthermal contact with a heat sink is simulated at the temperature

eT This choice of the acceptance probability P(ΔE) has the

Fig 1 Machining on a Bridgeport 320H machining centre

consequence that the system evolves into a Boltzmann

distribution

The physical terminology used by Metropolis et al [6],

atomic configuration, energy E and the temperature eT have

been replaced in the current problem by the sequence of the

segments in the tool motion that are not associated with

manufacturing/metal cutting; the non-productive machining

objective function value, Θ, to be minimised; and, the

algorithm control parameter Ci Two types of nodes are

used to define the non-productive tool segments:

opera-tional and non-operaopera-tional nodes Operaopera-tional nodes are

points where there is either a need to move to a new

component or to change tool; and, non-operational nodes

are points such as those associated with machining the

same component with the same tool It is the operational

nodes that are used to define different machining scenarios

and to enact the optimization phase Entire part

pro-grammes are automatically segmented into discrete

ele-ments as defined by these nodes, and the sequencing of the

elements is varied untilΘ is minimised Then a new part

programme, that can drive the machine tool, is created from

the optimised sequence

The objective functionΘ defined in Eq.2is computed,

principally, as the sum of the following: (1) the time of

travel between operational nodes associated with

non-productive manufacturing/metal cutting, expressed by the

first and second terms on the right hand side; (2) the time

for tool changes involving q tools, given by the third term

on the right hand side; and, (3) the time for rotation of the

pallet that holds the multi-components under manufacture,

quantified by the last term on the right hand side Afifi et al

[23] used these quantities to define an objective function,

Θ, given by Eq 4 of their paper, which for convenience, is

where Tij is the non-productive motion in the X–Y plane

parallel to a single pallet face, Tz is the non-productive

motion in the Z direction normal to the pallet face,Tchp is the

time to change tool p,Ttpwfp is the tool path weight factor for

tool p, and Tpris the pallet rotation time defined as the time

to move the spindle from operational node r on one pallet

face to operational node s on another pallet face and given

by Eq 3 of Afifi et al [23] The summations in Eq.2 are

carried out with respect to the two operational nodes i–j

defined in the segmentation phase, which are also used to

execute the optimization phase, and the summation is

carried out over g operational segments, denoted as 1-g

An efficient tool path is one that minimises the

non-productive motion between all non-operational nodes, and

hence achieves an absolute minimum in Θ For a moredetailed statement on the definition and use of these terms,the reader is directed to the work of Khan and Hayhurst[21] and Afifi et al [23]

The annealing idea was applied to the travellingsalesman problem by Kirkpatrick et al [7] Lundy [24]has also used the simulated annealing algorithm to solve theevolutionary tree problem The general annealing algorithm

is as follows: start with an initial solutionξothat is selectedrandomly and select a suitable high initial value of thecontrol parameter Co, and a suitable final value of Cf At theith step the current solution is termed ξii The controlparameter is Ciand the objective function isΘi=Θ(ξi) Thealgorithm will repeat the following sequence until Ci≤Cf:

1 Perturb ξito form ξpas a candidate solution c.f Khanand Hayhurst, [21] The stateξpis a potential candidatefor the next stateξi+1

2 If Θp≤Θi(downhill move), setξi+1toξp

3 If Θp>Θi (uphill move), calculate the acceptanceprobability APi=exp [−(Θp−Θi)/Ci]

4 Generate a random number b from the uniformdistribution between 0 and 1

5 If b≤APithen setξi+1toξp Otherwiseξi+1=ξi

6 Update Cito Ci−ΔC, and update i to i+1

7 If Ci<Cfgo to step 1, otherwise terminate the process.The uniqueness of the annealing method is that it allowsoccasional uphill moves (i.e it accepts inferior solutions) in

an attempt to reduce the probability of becoming stuck in apoor local minimum solution However, as noted byMetropolis et al [6], the value of the acceptance probabil-ity, APi, should approach zero as the iteration limit isreached That means the probability decreases as a function

of the number of iterations

2.2 Description of the problemAlthough the simulated annealing procedure is guaranteed toconverge to optimality if the increment in control parameter,

ΔC, is sufficiently small, this usually requires a large number

of iterations, and thus a high computational requirement c.f.Afifi et al [20,23] Hence, some applications have tried torestrict the number of iterations Lundy and Mees [25]suggest a careful sequence of control parameters whichterminates the SAA arbitrarily close to the global optimum,with probability arbitrarily near to one The time totermination cannot be shown to be polynomially boundedfor a general NP-hard problem Lundy and Mees [25] gaveexamples where the time is exponentially long, and theannealing method may actually take longer than a determin-istic algorithm that simply examines all the solutions.However, as discussed in Section 1, the SAA willconverge to within a few percent of the optimal solution

for complex combinatorial optimization problems with

appropriate controls The convergence theorems developed

in the context of simulated annealing suggested that the

choice of an initial solution does not affect the probability

of attaining a global optimum solution after an infinite

number of iterations Therefore, conventional applications

of the simulated annealing algorithm use a randomly

selected initial solution Matsuo et al [26] mentioned that

the previous approach often requires a large amount of

computer time to eliminate the initial solution They

defined a new approach of using a good initial solution

instead of using a random initial solution, and showed that

this approach yields better results; and, Johnson et al [27]

have endorsed this approach Also, the same technique has

been used by Sridhar and Rajendran [28] to achieve better

results The drawback of the approach is the need for a

good initial solution As pointed out by Sridhar and

Rajendran [28], and by Matsuo et al [26], this means the

use of another algorithm to obtain a good initial solution for

the SAA This will result in a reduction of computation

time for the simulated annealing algorithm but, will add

more time to the overall computation time of the

optimi-zation process, and alternative approaches are therefore

required to reduce computation time

During the course of this research, two techniques have

been used to improve the performance of the simulated

annealing algorithm for large combinatorial problems The

first technique allows the algorithm to accept increases in

the objective functionΘ, and hence permits a wider SAA

solution search to achieve a near-optimal solution without

increase of computational effort The second technique is

directed to reducing the computational time, without

reducing the accuracy of the output, by control of the

number of iterations made without improvement in the

objective function,Θ

In the next two sections, the techniques used to improve

the accuracy of the SAA and to reduce the computation

time will be explained with the aid of some case studies

3 Improved solution optimality by acceptance

of objective function increase

3.1 Problem definition and solution strategy

The acceptance of an objective function increase with non

zero probability avoids local minimum traps, and makes

the SAA converge to a near-optimum solution The

acceptance of the objective function increase is usually

carried out (in the general SAA) by calculating the

acceptance probability, and comparing it with a random

number generated from the uniform distribution between 0

and 1

In this research, this number is termed the AcceptanceCheck Factor (ACF) The use of a random number givescomplete freedom of the SAA to find the near-optimalsolution, but it may result in acceptance of a new solutionwith very high objective function value relative to thecurrent one The acceptance of such a solution oftenrequires a large amount of computation time to eliminateits effect In this case, the approach of reducing thecomputational time by restricting the total number ofiterations will result in a solution far from the optimal one(particularly for complex combinatorial problems) Hence,there is a need to modify the SAA to give a solution veryclose to the optimal one, without increasing the computa-tional time

In this paper, a new approach is utilised of comparingthe acceptance probability with a constant value of ACF inthe range 0≤ACF≤1.0 The aim was to investigate theexistence of a range of values of ACF for which thesimulated annealing output will be improved This ap-proach has been employed and examined for three differentcase studies with different degrees of complexity

3.2 Case studiesThe first case study concerns the manufacture using a four-axis machining centre of six components of Afifi et al [20]and is presented as Figs 1, 2 and 3 of this paper Thecomponents, c.f Fig 1, are located on one pallet face andare machined using nine tools taken from an auto-selectionmulti-tool magazine Figures2and3respectively define theun-optimised and optimised problem configurations, and inaddition illustrate the complexity of the problem Thebroken lines and arrows show the direction of toolmovement, the horizontal line at the top of the figuredenotes tool changes, with the associated numbers definingthe tool number The machine tool is software driven: a tool

is automatically selected and moves in four-dimensionalspace (X, Y, Z and pallet rotation B) over a sequence ofmachining contours Each contour is characterized by startand end nodes The number of nodes involved in this casestudy is 69

In the second case study the machining of eightcomponents, around the four pallet faces with a single tool,has been chosen from Afifi et al [23] The case study ispresented in Figs 4 and 5, and involves 96 nodes In thiscase study, the components are fixed to a box-like palletwhich has four vertical faces The axis of rotation of thepallet, or fourth machine axis, is symmetrically locatedbetween the faces Figure 4 depicts the un-optimised toolpath, and Fig.5 shows the optimised tool path

The third case study involves the machining of 10components around the four pallet faces, using sevendifferent tools, as shown in Figs 6 and 7 This case

study has been taken from Afifi et al [23], and involves

194 nodes In this case study, additional nodes correspond

to the extra motions of the tool spindle associated with

tool changes Figure 6 depicts the un-optimised, or

extracted, tool path, and Fig.7 shows the optimised tool

path

3.3 Discussion of results

Comparison between the results obtained by using constant

values for the ACF and the result obtained from using a

random number generator have been made and are shown

in Figs.8,9and 10where the objective function value,Θ

(s), is plotted against ACF All three figures show results

for constant values of ACF presented as the solid diamond

symbols connected by a solid line; the computations were

carried out for increments in ACF of 0.01 Results for theother three cases with random starting values of ACF,selected between 0 and 1, have objective function valuesshown as constant values for maximum, minimum andmean values of Θ (s) To determine the maximum,minimum and mean values of Θ (s) for each case study,

11 different runs have been carried out in which the randomnumber generator has been used to dynamically select thevalue of the ACF In Figs.8,9and10for case studies 1, 2and 3, respectively, the solid line represents the mean value

of these readings The second and third broken linesrepresent the lower and upper bound for the range ofvalues ofΘ

When the SAA is used to compare the acceptanceprobability with constant values of the ACF instead ofusing random numbers between 0 and 1, better results have

Fig 2 Un-optimised tool path

for six components (case

study no 1)

been obtained for all case studies, as shown by the solid

lines connecting diamond-shaped symbols, typically when

0.4≤ACF≤1.0

The values of the objective function, obtained by

comparing the acceptance probability with randomly

selected ACF, have been reduced by factors in the range

from 1% to 6% by using constant values of ACF Figure8

ð Þ  100=661:8g relative to Θ mean for

ACF=0.98 However, to achieve this reduction inΘ, it is

necessary to perform some experimentation with 0.75≤

ACF{Constant starting value}≤1.0 It is suggested that

calculation be performed initially with ACF = 1

decreas-ing with ΔACF=0.02 until no further improvement isachieved The reduction in the objective function valuehas been achieved in the same computational time asthat for the case of using random numbers between 0and 1

The reduction in Θ, depends on the complexity of theproblem, namely the number of nodes in the cases study, i.e.,

69, 96 and 194 for case studies 1, 2 and 3; to demonstrate thismore clearly, an additional problem has been solved with 29nodes, and the results are presented in Fig.11, ΔΘ=0.43%.The figure shows that the percentage reduction in theobjective function value, ΔΘ, increases as the number ofnodes is increased This clearly shows that the methods areappropriate for complex problems, particularly those pos-sessing symmetries which may be used to judge, at a glance,the degree of optimality of the solution

Fig 3 Optimised tool path for

six components (case study

no 1)

It is important to emphasise that with the limited number

of cases presented in this paper, it is only possible to show

trends, and for more complex problems with the same, and

with larger numbers of nodes, it will be necessary to perform

sensitivity studies to confirm improved performance

4 Reduction of computation time by control of number

of iterations without improvement of objective function

4.1 Problem definition and solution strategy

In the application of the simulated annealing algorithm to

the tool path re-sequencing problem, one has to take into

account that the number of nodes is unpredictable c.f Khanand Hayhurst [21] By the use of a careful sequence ofcontrol parameters, as suggested by Lundy and Mees [25],the application of the general SAA to the tool path re-sequencing problem has been made for the three casestudies used here; and, near-optimal solutions have beenobtained However, as indicated in Section 3, the SAAtakes a considerable computation time before termination ofthe process, and it does so without improvement of theobjective function value

Although it is known that the output from the SAA is notoptimal, attempts were made to improve the objectivefunction values in two different ways during the course ofthe research reported by Afifi and Hayhurst [23] The first

Fig 4 Un-optimised tool path

for eight components (case

study no 2)

method used was to double the number of iterations to

allow a more widespread search for a better solution by the

SAA The second method used was to terminate the

SAA as usual, and then use the output from it as an

input to another independent SAA run This means that

one uses a good solution as the starting point for the

next run The latter method slightly improved the output

over that produced by the first method Although the

previous two methods improved the output by a few

percent they do however increase the computation time

sharply

Reported in this paper is a modification of the approach

that yields a new general technique which reduces the

computation time, and improves the objective function

value, or at least maintains it at the same level reached

in the previous Section 3 The technique depends on theintroduction of a new parameter to the simulated anneal-ing method The new parameter is the number ofiterations performed by the SAA without improvement

of the objective function value Kwί This parameter istermed the freezing parameter The modified SAA willthen be operated according to the following operationalsequence:

1 Set the:

Counter for the iteration number K=0;

Counter for the freezing parameter K*=0;

Fig 5 Optimised tool path for

eight components (case study

no 1)

Pre-determined value of the freezing parameter Kwi; and,

Pre-determined value of the total number of iterations Q

2 Start with the randomly selected sequence ξi, and

calculate the objective functionΘi.

3 Generate a candidate solution ξp and evaluate the

objective functionΘp

4 If Θp≤Θi.then:

Either

(a) Set the candidate solution to be the current one

(ξi+1=ξp), the iteration counter K to be K+ 1, and

the freezing parameter counter K*to be K* + 1

Or

(b) If the solution is the best so far, then:

1 Set ξBest=ξpand ΘBest=Θp

2 Reset the value of K* to 0

3 Set the iteration counter K to be K+1, and thefreezing parameter counter K* to K*+1

(c) Go to step 5

5 If Θp>Θi,(a) Calculate the acceptance probability, and compare itwith a constant value of the acceptance check factor,ACF, between 0 and 1

(b) Accept or reject the candidate solution according tothis probability

Fig 6 Un-optimised tool path

for ten components (case study

no 3)

(c) If the solution is accepted, set the iteration counter

K to be K+1, and the freezing parameter counter

K* to be K*+1

(d) Go to step 5

6 If K=Q then terminate the process

7 If K*=Kwior K*=2 Kwi,setξi+1=ξBest

8 If K*=3 Kwiterminate the process

9 Go to step 3

The benefits of using the freezing parameter, Kwi, i.e., the

number of iterations performed by SAA without

improve-ment of the objective function value, are as follows:

1 It will terminate the SAA after performing a certainnumber of iterations without improving the objectivefunction value This will reduce the computationtime

2 If the simulated annealing algorithm is capable ofimproving the objective function value, then K* will

be repeatedly reset and the procedure will neverfreeze

3 The use of the best solution so far as a currentsolution, when the value of Kwi reaches its pre-determined value or double this value, will help theSAA remove itself from the freezing effect by using a

Fig 7 Optimised tool path for

ten components (case study

no 3)

better solution as the starting one for the next step in

the procedure c.f Matsuo et al [26] and Johnson et al

[27]

It is clear from this discussion that the value of the

objective function,Θ, and the reduction in the computation

time will be affected by the pre-determined value of Kwi

So, the modified approach has been evaluated for differentvalues of Kwi.

4.2 Case studiesThe three case studies introduced in Section 3 have beenused to evaluate the performance of the modified technique

Number of nodes Fig 11 Effect of the number of nodes on the percentage reduction of the objective function, ΔΘ, for constant ACF

Acceptance Check Factor (ACF)

Fig 10 Effect of ACF on the objective function value, Θ, for case study 3

Acceptance Check Factor (ACF)

Fig 9 Effect of ACF on the objective function value, Θ, for Case Study 2

Acceptance Check Factor (ACF)

Fig 8 Effect of ACF on the objective function value, Θ, for case study 1

Fifty runs with different values of Kwihave been made for

each case study The results are now discussed The value

of ACF=1.0 has been selected as a representative value for

the reduction of the objective function value,Θ (s), and is

held constant for the cases studied

4.3 Discussion of results

The variation of the objective function values,Θ (s), with

the freezing parameter, Kwi, for the three case studies are

given in Figs 12, 13 and 14 Comparisons are made

between the values obtained using the modified SAA with a

constant acceptance check factor, ACF = 1.0, (diamond

symbols); and the target values, i.e., constant ACF=1.0

and randomly selected values of ACF (square and

triangu-lar symbols, respectively) It was found that for a certain

range of Kwithe target objective function value,Θ, can be

obtained, or slightly improved, using the new approach It

is clear that, for all three case studies, there is a range of Kwi

for which the computation time can be reduced, whilst still

achieving the target objective function value for constant

ACF For convenience, this domain is termed the safety

range Figure12for case study 1, with 69 nodes, shows a

safety range of Kwi=869–5,402; Fig.13 for case study 2,

with 96 nodes, shows a safety range of Kwi=953–2,097;

and Fig 14 for case study 3, with 194 nodes, shows a

safety range of Kwi=1,843–2,500 Clearly for case studies 1

and 2 a modest reduction in the value of the objective

function can be achieved with appropriate selection of the

value of the freezing parameter, or the number of iterationswithout improvement in the objective function, Kwi.The most important aspect of the studies is the reduction

in the computation time, CPU, (s) which can be achievedwithout deterioration in the objective function value, as

Freezing parameter (K wi ) Fig 13 Effect of freezing parameter (number of iterations done without improvement of objective function value) on objective function value, Θ, for case study 2

Freezing parameter (K wi ) Fig 12 Effect of freezing parameter {number of iterations done without

improvement of objective function value} on the objective value, Θ, for

case study 1

shown in Figs.15,16and17 The figures show the change

in the computation time, CPU (s), with the freezing

parameter Kwi The maximum reduction in CPU time, over

the safety range, relative to the values obtained using the

unmodified SAA with constant ACF=1.0 (square symbols),

are: 72% for the 69 noded case study 1, given in Fig 15

with Kwi=869; 69% for the 96 noded case study 2, given in

Fig 16 with Kwi=953; and, 20% for the 194 noded case

study 3, given in Fig.17with Kwi=1,843

To take full advantage of the CPU time reduction whilst

improving the objective functionΘ, it may be necessary to

carry out initial experiments to determine the safety range

The level of reduction in computation time, and in the

safety range, is increased by decreasing the number of

nodes A reduction of computational time between 20% and

72% (depending on the number of nodes) has been

achieved

It is important to emphasise that in the limited number of

cases presented in this paper it is only possible to show trends;

and for more complex problems with the same, and with

larger numbers of nodes it will be necessary to perform

sensitivity studies to confirm improved performance

5 Conclusions

This paper presents a new approach for the application of the

simulated annealing algorithm to the tool path re-sequencing

problems The solution acceptance criterion has been fied by comparing the acceptance probability with a constantvalue between 0 and 1 instead of using a random number Theresults show that this approach reduces the objective function

Freezing parameter (K wi )

Fig 15 Effect of freezing parameter (number of iterations done

without improvement of objective function value) on the CPU time for

case study 1

value by a significant amount (up to 6%) without increasing

the computation time The constant values of ACF are

typically in the range 0.4≤ACF≤1.0 hence requiring some

numerical optimization to achieve best results The results

show that the acceptance of a small increase in the objective

function value leads to a better solution

The introduction to the SAA of the freezing parameter,

Kwi, which is the number of iterations performed with the

SAA without improvement in the objective function value,

Θ; and, the use of the best solution as the current one, when

freezing has occurred, have reduced the computation time

without reducing the accuracy of the solution The output

from the case studies examined showed that the

improve-ment in the objective function value and the computation

speed depends on the complexity of the problem examined

Reductions in CPU time of between 20% and 72% have

been achieved For the cases studied, values of the freezing

parameter in the range Kwi=869–5,402 have defined the

Safety Range; however, for new and different classes of

problems, some numerical experimentation will be required

to define the relevant safety ranges

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manufac-ORIGINAL ARTICLE

Distribution of unit forces on the tool edge rounding

in the case of finishing turning

Borys Storch&Anna Zawada-Tomkiewicz

Received: 25 February 2011 / Accepted: 31 August 2011 / Published online: 23 September 2011

# The Author(s) 2011 This article is published with open access at Springerlink.com

Abstract An experimental investigation was conducted to

determine the effects of tool cutting edge geometry on the

cutting forces in finish turning, where the applied feed and

depth of cut are small and often comparable with the tool

edge radius If a tool with large tool edge radius is used in

finish turning, the ploughing effect begins to determine the

machined surface This paper presents the results of

analytical considerations concerning the unit forces on a

cutting edge The aim of this paper is to indicate

possibilities of modelling the unit forces and stress

distribution based on cutting resistance The forces

calcu-lated in the feed and cutting speed directions were projected

onto the tangential and normal directions of the rounded

cutting edge surface An important assumption in all the

considerations was that the thermo-mechanical properties of

the materials used remained constant The minimum

thickness of cut was defined, and some characteristic points

were identified dividing the cutting zone into three

subregions: where a chip is formed, where the machined

surface is formed and an unstable region

Keywords Cutting model Cutting force Unit force

distribution Rounded cutting edge Orthogonal turning

Nomenclature

ap Depth of cut

rn Cutting edge radius

h Thickness of cut layer

hi Thickness of cut layer in i-cross section

hmin Minimal thickness of cut layer

f Rate of feed

ф Shear angle

=i Angle in i-cross section

σ Normal stress in a cross section perpendicular to

the cutting edge

τ Tangential stress in a cross section perpendicular

to the cutting edge

Af,Ac Directional coefficients in equationsFf=f(h) and

Fc=f(h)

Ff Feed force

Fc Cutting force

FN Normal force in a cross section perpendicular to

the cutting edge

FT Tangential force in a cross section perpendicular to

the cutting edge

1 Introduction

In the fundamental machining investigations carried out byZorev [1] and continued by Hayajneh et al [2] andAstakhov [3], primary attention has been paid to modellingthe geometrically simple orthogonal cutting process involv-ing two-dimensional plastic deformation Oxley [4]explains the basics of the process of material removal for

a simple case of cutting At the same time, his researchshows that although in practice tools with more geometri-cally complex shapes are used in processing, the cuttingmechanism remains the same

In machining process models, it is assumed that the tool

is perfectly sharp (Fig 1a) The first to propose such amodel was Marchant [5] In the machining model, the toolwas infinitely sharp with a shearing plane located at theangleϕ However, cutting tools have a natural roundness of

edges (Fig.1b) For a diamond tool, the natural roundness

is less than several micrometres, while for a sintered

carbide tool, the roundness is several tens of times greater

A large radius cutting edge makes it stronger and more

resistant to chipping Nevertheless, in precision cutting

applications when the thickness of the cut layer is

comparable to the cutting edge radius, the ploughing or

rubbing action can be substantial and the accuracy of

cutting deteriorates [6] A rounded cutting edge can affect

significantly both the forces and temperatures during

cutting, especially at chip thicknesses at or below the

cutting edge radius The problem is how to assess the effect

of nose radius on the accuracy of the cutting process,

especially when cutting thin layers

In the case of orthogonal free cutting, the resulting

machined surface is formed by the active part of the tool

moving along the helix Without movement in the feed

direction, the tool's cutting comes to an end after one

revolution of the part When the thickness of the cut layer is

smaller than the thickness, below which it is unable to form

a chip, the tool's active part elastically and plastically

deforms the surface of the machined part

When the feed is switched off, the cutting force drastically

decreases until chip decay First, the cutting force remains at a

small value, then after the decay of plastic deformation, its

value decreases, and finally, it ceases completely after the

disappearance of the elastic and friction phenomena

The above reasoning is illustrated in Fig.2 This diagram

shows a field of forces on the cutting edge rounding It is

clear that if the thickness of cut is less than the minimum

thickness (Fig.2, point 1), then the tangential forces on the

edge rounding may only have a sense consistent with the

direction of the flow of the work material around the

rounding

If we assume that the tool moves, then the relativemovements influence the sense of the normal and tangentialforces on the edge rounding To allow the simultaneousmovement of both elements of cut toward the flank andrake faces, there must be a point 3 (Fig 2) of cut layerseparation The thickness of cut corresponding to this point

is called the minimum thickness

During turning, the layer located below the minimumvalue (hmin) moves under the lowest point on the edge;hence, it is subjected to strong plastic deformations Thedimension after the passing of the tool is, therefore, thedepth difference between the surface of the base and theone newly formed after the pass of the tool This dimension

is created as a composite of two elements: the residual,plastically deformed thickness of cut and deeper locatedpart of the material, which returns elastically after the toolpass It is difficult to estimate the actual value of the depth

of cut, different from the theoretical one, because its value

is largely determined by the properties of the work material.The literature on metal cutting includes several attempts

to capture the effect of tool edge geometry on themechanics of the cutting process, and particularly to explainthe phenomenon of ploughing that accompanies the processwhen a tool features a considerable edge radius

Yen et al defined the ploughing ratio as the amount ofworkpiece material that flows under the cutting edge [7].They demonstrated that the ploughing ratio depends on thepredicted cutting force ratio Fc/Ft Thiele and Melkote [8]and Kang et al [9] confirmed that the cutting edgegeometry has a significant effect on the cutting forcecomponents Karpat and Özel investigated the frictioncharacteristics of tools with curvilinear edges [10] Theydemonstrated the influence of the size of the edge radius onthe mechanics of cutting Özel, by experimental and modelinvestigations, showed the influence of cutting edgegeometry on chip formation, forces, temperatures, stressesand tool wear [11] Variable edge design was consideredbeneficial in reducing the heat generation and stressconcentration along the tool cutting edge The conclusiondrawn from the above research is that force and stress

Fig 1 Cutting edge configurations: a sharp edge, b rounded cutting

edge (images of edge rounding —Eclipse MA200×20)

Fig 2 Force field acting on the rounding of a cutting edge

distribution in the vicinity of the tool edge has its source in

the tool edge geometry

Nevertheless, the possibility of measuring force

compo-nents on the tool edge is very limited Liu et al stated that the

problem of minimum chip thickness estimation is a key factor

in the characterization of machining at reduced size scales [12]

The majority of the work has been experimental in nature and

little work can be found that deals with the thermal aspects

Guo and Chou examined the extrapolation of cutting force to

zero uncut chip thickness [13] They confirmed that the

extrapolation method may be suitable to determine the

ploughing force, which is also dependent upon cutting speed

with a possible non-linear relationship However, Ranganath et

al demonstrated that the ratio of chip thickness to ploughing

forces remains identical for materials being machined at

identical cutting speed [14] In more than 200 carefully

designed cutting experiments, Fang and Wu demonstrated that

work material properties play an important role in machining

[15] Liu et al [16] made an attempt to take account of the

temperature conditions in determining the normalized

mini-mum chip thickness Their research confirms that the thermal–

mechanical properties of the work material play an important

role in micromachining At the same time, their model is very

theoretical It can be concluded from all the above that both the

mechanical and thermal properties of work materials must be

considered when constructing a cutting model

The presented research, devoted to unit forces on the

tool edge rounding, develops the model proposed earlier by

Storch [17] In his research, a model for an analytical

solution of force distribution on the rounded cutting edge

was introduced The model was based on the assumption

that work material properties and tool material and

geometry remained the same during cutting

In this study, the assumption was reflected by maintaining

constant temperature conditions during cutting The unit force

and stress distributions in the vicinity of the cutting edge were

modelled, and were calculated based on measurement of the

components of cutting resistance For this purpose, the

increments of forces calculated in the direction of feed and

cutting speed were used, which were then projected onto the

tangential and normal directions of the rounded cutting edge

surface As a result of those transformations, nonlinearities of

unit force distribution were revealed

2 Model description

In orthogonal free cutting, the shearing phenomena

connected with chip formation operate in the same way

This is due to the fact that the thickness of the cut layer is

identical in all cross sections orthogonal to the cutting edge

In order to fully describe the shearing phenomena,

therefore, it is enough to describe it for one cross section

To be able to obtain the process of cutting, it is necessary

to use cutting forces Values of the forcesFfandFccan bemeasured on a base of cutting resistance with the use of aforce gauge The main assumption in the construction of thecutting model is that constant temperature conditions werepreserved regardless of changes in the cutting parameters.The evaluation of forces in such conditions was thenperformed when the mechanical properties of tool and chipinterface are preserved with an additional assumption ofconstant tool geometry

Under these assumptions, the stresses and mechanicalproperties in the vicinity of a rounded tool cutting edge aresteady This assumption constitutes a basis for the linearnature of the forces as a function of the thickness of the cutlayer, given as a system of equations

Assignation of forces for cut layer thicknesseshiandhi −1

allows the increments of forces to be established:

ΔFc¼ Að c hiþ BcÞ  Að c hi1þ BcÞ ¼ Ac Δh ð2Þ

ΔFf ¼ Að f  hiþ BfÞ  Að f  hi 1þ BfÞ ¼ Af Δh ð3ÞThe increments ΔFc and ΔFfcan be interpreted as unitforces acting on the thickness of the machined layer with

Δh ¼ hi1 hi(Fig 3)

It can be assumed that along the cutting edge in eachnormal cross section to the cutting edge, the increments offorceΔFciand ΔFfican be determined from Eqs.2 and3.For each part of the tool edge rounding, the unit forcesare projected on the tangential and normal directions asshown in Fig.3

The vector sum ofΔFcand ΔFfafter the transformationcan be defined as:

ΔFT¼ mΔF1 ¼ ΔFcicosyi ΔFfisinyi

¼ AcΔhicosyi AfΔhisinyi ð4Þ

ΔFN¼ ΔF1¼ ΔFcisinyiþ ΔFficosyi

¼ AcΔhisinyiþ AfΔhicosyi ð5Þ

where μΔF1 is the tangential force determined as the

product of normal forceΔF1and friction coefficientμ, =iis

a polar coordinate determining the location of the centrepart of the element on the tool edge rounding

The algebraic expression 4 determines the value of thetangential force It takes the value zero at a point wherethe machined layer is being sheared With the assumption

ΔFT= 0, the expression 4 establishes the critical value ofthe angle ===critical

AcΔh cosycritical AfΔh sin ycritical¼ 0; then ycritical¼ arc ctgAf

Ac

ð6ÞEquation 6 defines the polar coordinate of the locationwhere the thickness of the cut layer is minimal This pointdefines the favourable conditions for chip forming.The cutting edge operation is similar in each hi crosssection There can be defined a minimal thickness of the cutlayer hmin for which the conditions of conversion of the

Fig 3 Scheme of unit forces acting on a particular element of the

cutting edge rounding

Fig 4 Model and

implementa-tion of orthogonal cutting

layer into chip are limited For such conditions an

expression taking into account=criticalcan be written:

hmin¼ rnð1cosycriticalÞ ¼ rn 1cos arc ctgAf

Ac

ð7Þ

whereAfandAcare directional coefficients in the equations

ΔFf=f(h) and ΔFc=f(h), respectively This is the expression

that makes the so-far insoluble problem of the minimum cut

layer thickness hmin, a phenomenon definable in the

machining process

3 Experimental procedure

Experimental methodology was proposed to determine the

forces in the cutting zone Unit force distribution and values

were established based on force measurements in

orthog-onal cutting First, a research station was built to create the

conditions for orthogonal turning (Fig.4)

Two cutting tools were used The front tool was fastened

on the force gauge for obtaining force and temperature

characteristics The back tool was applied only to achieve

the conditions for orthogonal turning Testing was also

performed to check that turning with the use of front tool

was not affected by the heat produced by the back tool The

station made it possible to measure forces for orthogonal

turning on a workpiece with a length of 700 mm and adiameter of 200 mm

C55 steel of hardness 220 HB was used as the workmaterial Sintered carbides S10S were used as the toolmaterial The tool edge radius was measured with aspecially equipped stylus profilometer, and was equal to0.04 mm Other tool geometry parameters wereαf=6°,αp=0°, γf=0°, κr=90°, κ′r=30° and rε=0.8 mm The experi-ment was performed with a variable feed rate (0.08–0.3 mm/rev) and cutting speed (50–130 m/min) Depth ofcut was established by the cutting of the back tool and wasequal to 1 mm All the data points in the experiment (i.e.four feed rate settings and nine cutting speed settings) werecalculated based on four repetitions

Figure 5 summarizes the values of cutting forces as afunction of cutting speed and thickness of cut (for free cutting,thickness of cut is equal to feed rate) The forces are presented

on a background of constant thermocouple voltage EΘ (ofnonlinear waveform) It can be observed that the thermo-couple voltage increase is accompanied by an increase in thecutting forces Nevertheless, a constant predetermined value

of thermocouple voltage can be obtained only for a preciselydefined set of cutting parameters Hence, it is concluded thatthe most important aspect of the presented charts is that there

is a possibility of controlling the temperature conditionsknowing only the cutting parameters

Fig 5 Forces as a function of cutting parameters for constant E Θ

4 Distribution of unit forces in the cutting zone

The primary assumption throughout the research was that

fixed temperature conditions would be maintained In order

to provide conditions of constant temperature, an

experi-ment was designed in which the thermocouple voltage in

the cutting zone was measured for variable thickness of cut

and cutting speed In orthogonal free cutting, the cut layer

thickness is equal to the feed rate, which varies as shown in

Fig.5 With variable thickness of cut, the cutting speed was

changed as well The results made it possible to create a set

of constant temperature conditions Constant temperature

preserves the values of the parameters of characteristic

Eq.1at the same level

The second assumption is a result of analysis of the

orthogonal cutting principle It states that the thicker cross

section of the cut layer contains all the thinner cross

sections This is an assumption which enables the

measure-ment of cutting forces in constant temperature conditions

The above two assumptions ensure the invariance of

cutting phenomena in the vicinity of the cutting edge

rounding, and allow the forces to be plotted as a function ofthickness of cut Behaviour in such conditions allows thecutting process to ensure the linearity of the forces as afunction of thickness of cut

To each thickness of cut h can be assigned, the resultantforce F, whose componentsFcandFfcan be measured Theresultant force is not known as far as direction and value areconcerned However, its components are measurable Theincrement of thickness of cut from point 2 (Fig.6) to point

4 (Fig.6) can be estimated byΔh=h4−h2in the middle ofthe area A (Fig 6), and the unit forces ΔFc and ΔFf

assigned to the area can be determined

The dependence of the force Fc as a function of thethickness of the cut layer is linear, both when the layers aresmaller than the radius of the cutting edge rounding andwhen they are larger, and the relationship does not changegoing from one area to another It can therefore bemeasured only for two different thicknesses of cut Themeasurement in this case is reduced to determine the slope

in the equations Ff=f(h) and Fc=f(h)

A series of cutting tests were performed for fixedtemperature conditions, and then the values of cuttingforcesFfandFcwere determined as a function of thickness

of cut Next, the increases in these forces were establishedand decomposed into two directions—tangential andnormal—according to Eqs 4 and 5 The resultant unittangential and unit normal forces are presented in Fig.7.Figure7a illustrates the distribution of the unit tangentialforceΔFTand unit normal forceΔFNforces on the contour

of the cutting edge rounding Figure 7b illustrates thedevelopment of the forces in a Cartesian coordinate system.The forces act perpendicularly to the cutting edge withradius rn, so that on the cutting edge rounding, a certainpoint occurs (point 2 in Fig.7a and b) at which only a unitnormal force ΔFNcan exist, the unit tangential forceΔFT

being equal to zero The unit tangential force changes itssign in the neighbourhood of this point The location of

Fig 7 Distribution of unit forces ΔF T and ΔF N a in a cross section perpendicular to the cutting edge, b distribution of unit forces in a Cartesian coordinate system as a function of angle =

Fig 6 Variation of cut layer thickness for cutting edge radius r n

point 2 (Fig 7) at angle = was computed to be in an

interval between 60.1° and 81.1°, taking into account all the

considered conditions This point separated the cutting edge

surface rounding into two parts: attributable to the rake and

the flank faces

The point of cut layer separation (point 2 in Fig 8)

defines the unit force relation in which it has the value

of zero (stagnation point or separation point) For higher

values of=, the unit force relation changes its sign (a chip

is formed) For smaller values of=, the unit force relation

describes what is happening with the rest of the work

material Point 1 (Fig 8) represents the situation where

the tangential and normal forces are of the same value

When the tangent force is higher than the normal force,

the work material moves around the tool edge rounding

in a direction opposite to the chip In the interval

between points 1′ and 2 (Fig 8), the unit normal force

is larger than the unit tangential force In this range of

=, the work material can behave in an unstable manner

The work material can change into a chip or can move

around the cutting edge rounding and form the machined

surface

5 Distribution of shear stress in the cutting zone

To determine the unit stress on the rounded cuttingedge, the values of unit tangential and unit normalforces were divided by the field on which these forcesact As a result of the calculation, the unit tangentialand unit normal stresses were obtained, as presented inFig 9a

The established unit stress values ofτ and σ, obtained bydividing the unit forces by their field of action, exceeded2,000 MPa and showed variability like that of the unitΔFT

and ΔFNforces The highest value of unit normal stress σwas observed in the vicinity of point 3 (Fig 9a), whichindicates that the machined material, adherent to the cuttingedge surface rounding, is situated in the area of stress inwhich it reaches its strength limit

The unitτ and σ stresses are of the same value at points

1, 2 and 3 (Fig 9b) Taking into account that theconsiderations concern the same temperature conditions,one can observe that the difference of cut layer thickness ofthe unstable layer (value ofh1in Figs.8b and9b) changesdepending on the tool edge radius For a sharp tool with

Fig 9 Variation of unit τ and σ stress on the cutting edge rounding

Fig 8 Value of ‘friction coefficient’ computed as the relation ΔF T / ΔF N

edge having a radius of 4 μm, the unstable layer can be

estimated to be 2.5 μm For a blunt tool with an edge

having a radius of 40μm, the unstable layer is indicated to

be much higher, equal to 24 μm This unstable layer

depends mainly on the tool edge radius, material properties

and cutting parameters

6 Summary and conclusions

In this paper, a calculation method was proposed to

evaluate the distribution and value of unit normal and unit

tangential forces on the rounding of a cutting edge The

experiment was conducted on a specially built laboratory

station to obtain conditions of orthogonal cutting with

simultaneous measurement of temperature and force

com-ponents For constant width of cut layer cross section,

steady-state temperature conditions were achieved for

different combinations of cutting speed and feed rate The

experimental results were the basis for force calculations in

steady-state temperature conditions The developed

analyt-ical model of forces was calculated as a function of feed

rate, tool nose radius, edge radius, workpiece and tool

material

Simplification of cutting edge design by using

cham-fered edges instead of rounded ones had no influence on the

correctness of the above considerations, and can lead only

to the shortening of tool life due to change of load

distribution and, in effect, increased stress concentration

on the edge The abovedescribed model of forces concerns

all cases of single-point cutting with a cutting tool of stable

geometry

The distribution of forces along the rounded cutting edge

facilitated a more insightful analysis of unit force

distribu-tion Although the courses of determined unit forces were

very much diversified, the summation of their values

revealed that the computed components of cutting forces

were almost identical to those measured The calculated

force models in orthogonal cutting were in agreement

with the experiment The model is particularly valid for

finish turning, where the edge radius influences the

surface finish

The distribution of unit normal and tangential forces on

the rounding of the cutting edge was of the same character

independently of the cutting conditions Force and stress

distribution on the rounding of the cutting edge are

nonlinear and independent of the cutting temperature

Nevertheless, the temperature influences the value of the

forces

On the rounding of the cutting edge, a specific point can

be identified where only the normal force is non-zero and

where the unit tangential force changes its sign At this

point, the shearing conditions of the work material are

introduced Work material located above this point turnsinto a chip Work material below this point tends only to bedeformed Additionally, the value of the relation betweenunit tangential and unit normal forces motivates thedistinction of two subregions—with dominant normal forceand with dominant tangent force The first region, calledunstable in this study, introduces indefinite cutting con-ditions In the second region, the larger values of unittangential force in relation to unit normal force have abeneficial effect on the flow of material around the cuttingedge

Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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