A Study for an Optimization of Cutting Fluids in Machining Operations

by TOPSIS and Shannon Entropy Methods

PANKAJ PRASAD DWIVEDI1*, DILIP KUMAR SHARMA2

1Department of Mathematics,

Oriental Institute of Science & Technology, Bhopal, 462022,

INDIA

2 Department of Mathematics,

Jaypee University of Engineering and Technology, Guna, 473226,

INDIA

*Corresponding Author

Abstract: - Cutting fluids are used in machining processes to increase the quality of machined surfaces, extend

the life of tools, and lessen the effect of friction and heat on contact surfaces. The least costly, least hazardous

to the environment, and least poisonous lubricant would be the perfect choice. It should also be resistant to low

temperatures, have high lubricating qualities, be recyclable, and have stability against oxidation, hydrolysis,

and heat. Its viscosity should also fall between the ideal range and not exceed it. Taking the needed properties

of the cutting fluids into consideration, for the machining process choosing the best cutting fluid is essential.

Five types of cutting fluids are examined in this paper that are often used in machining operations: canola oil,

mineral oil, synthetic ester, PAG (Polyalkylene Glycol), and TMPTO (trimethylolpropane trioleate). In this

study, the Multicriteria decision-making (MCDM) techniques were used to identify the best choice of cutting

fluids based on several parameters, such as low temperature, toxicity, lubricating ability, hydrolytic stability,

thermal stability, viscosity index, oxidative stability, and cost. The most popular TOPSIS methods and

Shannon's Entropy were utilized to choose these cutting fluids optimally. The TOPSIS approach is used to

calculate the final ranking, and Shannon’s entropy method is utilized to calculate the weight of the criterion.

According to the result with the more lucid rating, PAG cutting fluid was shown to be the most effective,

followed by synthetic ester in second place, as well as last place achieved by vegetable-based canola oil.

Key-Words: - Multi-criteria decision making, TOPSIS Method, Shannon’s Entropy, Normalization, Material

selection, lubricants, PAG (Polyalkylene Glycol).

Received: February 15, 2023. Revised: November 29, 2023. Accepted: December 28, 2023. Published: February 29, 2024.

1 Introduction

Minimizing resistance on surfaces that contact is

largely dependent on the cutting fluids or lubricants

used in machining operations, [1], [2]. Additionally,

they lessen heat generation and enhance the quality

of machined surfaces, extending tool life, [3], [4],

[5], [6]. To attain these advantages while lowering

expenses and the degree of toxicity connected with

the fluids, choosing the right cutting fluid is crucial,

[7], [8], [9]. Several studies have been conducted in

the literature that use MCDM techniques to

optimize the parameters of the machining process,

[10], [11], [12], [13], [14]. Additionally, studies are

carried out using MCDM approaches to examine the

lubricants or cutting fluids utilized in machining

processes across a range of parameters. Papers that

add to this body of work are given in the appropriate

order. The study by [15], used the AHP approach in

conjunction with a system of fuzzy decision-making

of two orders to identify the best-cutting fluid out of

three possibilities. An MCDM approach for

choosing cutting fluids that take into account factors

including quality, cost, and environmental

implications was covered by [16]. To provide the

best cutting fluid based on the characteristics of the

cutting tool in machining operations, [17] reviewed

the studies and selection criteria. Applying the

PROMETHEE technique, [18], chose cutting fluids

based on criteria that included the lubricant's unique

technical features as w ell as some material

properties that vary. To determine the best lubricant

based on factors including surface

roughness, cutting force, tool wear, and temperature

at which the chip-tool interface occurs, [19],

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employed the combined AHP-TOPSIS technique.

The study by [20], looked into how well the

WASPAS method worked with the cutting fluid

selection problem. They also assessed how this

method's parameter affected the ranking. The

research conducted by [21], presents a new method

for data-driven neural network-based compressible

turbulent flow field prediction.

The MOOSRA approach, a novel MCDM

method, was employed for cutting fluid selection by

[22]. The resulting ranking has been compared with

the results of the AHP and DMF methodologies.

Using the PSI approach, one of the MCDM

methodologies, [23], provided a methodical and

easily comprehensible method for cutting fluid.

They located that the effects aligned with preceding

studies after they applied the strategy to 2 actual-

international troubles. The study by [24], used the

ROV technique to pick out the cutting fluid in four

specific case situations. They as compared the

rankings produced through their implemented

technique with the results of the case research. They

gave an instance of the way their approach produced

consequences with a h igh degree of correlation

while being realistic and smooth to use.

Using the QFD approach, by [25], created a

choice-making version for choosing the first-class

reducing fluid among multiple options. They used

sensitivity analysis to show how this strategy works

in two distinct scenarios and to illustrate how well it

solves MCDM difficulties. The ELECTRE III,

VIKOR, and PROMETHEE techniques were used

by [26], to choose green cutting fluids that are

favorable to the environment. The study by [27],

used the Taguchi approach to adjust the cutting

fluid's concentration, cooling pressure, and flow

rate. To choose different cutting fluids, [28],

presented a novel decision-making model and

hybrid criterion weighting technique. To find the

optimal answer, he used fifteen distinct approaches

and four different normalizing techniques. To

analyze the ranks and show their consistency, he did

correlation tests. The COPRAS approach was

employed by [29], to ascertain the perfect cutting

parameters that yield the desired surface roughness

during machining operations. In the study, they

assessed several cooling techniques (cryogenic,

flood, and MQL). In their investigation, the hybrid

cooling technique produced the best outcome. To

lessen environmental contamination, [30], employed

the ARAS and COPRAS methodologies to

determine which of the three green cutting fluids

would be best. They discovered that in both

approaches, the traditional cutting fluid gave the

lowest results. A hybrid MCDM methodology, such

as the AHP-MARCOS method, was used by [31], to

identify cutting fluids. They noticed a rating that

was comparable to the TOPSIS approach when they

compared the rankings acquired with the rankings

from the VIKOR and TOPSIS procedures.

During the procedure of machining, several

cutting fluids are used to improve surface quality

and cool the material. Certain requirements,

including lubricating qualities, stability, viscosity,

and price, must be met by these cutting fluids. For

this reason, choosing the best cutting fluid is

essential to guarantee the quality of the final output.

Selection criteria in the literature frequently include

machining parameters and output reactions such as

temperature, force, wear, and surface roughness.

Using the output answers as a criterion might result

in mistakes if they are not acquired as a

consequence of processing following the ideal

process parameters. Consequently, selecting cutting

fluids based on their basic characteristics produces

more precise outcomes. Furthermore, critical

properties of cutting fluids that are frequently

disregarded in literature studies include resilience

to thermal stability, hydrolytic stability, low

temperatures, toxicity, oxidative stability, and

affordability. This study contrasts MCDM

approaches with an innovative methodology and

includes original aspects, which sets it apart from

previous studies. The criteria for inclusion in the

literature were the cutting fluids' toxicity qualities,

pricing, tolerance to low temperatures, and stability.

The study also highlights the significance of using

cutting fluids' fundamental characteristics as criteria

during machining rather than depending exclusively

on reaction parameters. Nonetheless, a lot of

literature reviews employ many MCDM techniques.

It is noted that different MCDM techniques provide

different ranks when preference rankings are

evaluated. This discrepancy results from variations

in the multi-criteria decision-making method's

mathematical methodology. As a result, it is

essential to remove these disparities in ranking and

to make the ranks produced by the methodologies

clear and consistent. In response to previous issues,

the following cutting fluid factors were taken into

consideration as decision criteria in this study: low

temperature, toxicity, lubricating ability, hydrolytic

stability, oxidative stability, thermal stability,

viscosity index, and cost.

These criteria's worth for information was

gathered from sources in the literature, [1], [32] and

[33]. The TOPSIS and Entropy techniques were

used to choose the cutting fluids. The entropy

approach was applied to establish the weights of the

criterion. Ultimately, the TOPSIS technique

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provided clarification on the cutting fluid selection

rankings. The study's conclusions increase the

likelihood of choosing the best cutting fluid for

industrial machining operations in a way that is

affordable, long-lasting, sustainable, and highly

beneficial. For the material selection, a comparative

analysis of MCDM techniques has been provided by

[34].

The rest of the article is structured as follows:

Section 2 provides the material and method. Section

3 provides the results and discussion. Finally,

section 4 describes the conclusion of the study.

2 Materials and Methods

2.1 Selection Criteria and Materials

Inadequate use of cutting fluids during machining

operations might result in challenges as well as

surface and dimensional issues, [35], [36]. In

machining operations, cutting fluids is crucial to

counteract these unwanted consequences. Five

distinct alternative cutting fluids were considered

for the selection procedure in this material selection

research. Furthermore, the selection of cutting fluids

was based on eight criteria: low temperature,

toxicity, lubricating ability, viscosity index, thermal

stability, hydrolytic stability, oxidative stability, and

cost. References in the literature were used to get

data on the cutting fluid statistics and substitute

cutting fluids [1], [32], [33].

First up is canola oil, which is derived from

vegetables. Vegetable-based oils consist of

triglyceride molecules with long-chain fatty acids

connected to hydroxyl groups through ester bonds.

The structure of the lubricating coating's long chain

fatty acids interacts with the surface to reduce wear

and friction effects, [37], [38]. The second is

TMPTO (trimethylolpropane trioleate), a substitute

cutting fluid made of oleic acid that is produced

using vegetable oil and polyol ester. Because of its

biodegradability, it is referred to as "green cutting

fluid", [39]. The third type of cutting substance is a

synthesized ester, which is made up of fatty acid and

alcohol and is created as a cutting fluid with two or

more carboxylate groups, [40]. Polyalkylene Glycol

(PAG), a copolymer of propylene and ethylene

oxide, is the fourth cutting fluid, [41]. Which is

Mineral oil, a petroleum-based product made from

crude oils by vacuum distillation, is the best sort of

replacement cutting fluid. Cutting fluids are selected

using the hierarchical model (Figure 1) under the

specified parameters. The relationships between the

several factors considered while choosing a cutting

fluid are displayed in this hierarchical model. The

relative weighting factors of the criteria employed in

the decision-making process are gradually

established when the hierarchical model is built. A

list of substitute fluids and their definitions may be

found below:

 Vegetable oil (Canola A1): Cutting fluids are

increasingly using canola oil as a sustainable

substitute. Canola oil has inherent lubricating

qualities and is renewable and biodegradable. It

offers green cooling and lubrication at some

point of metalworking operations while

combined with slicing fluids. Because it is

biobased, it has much less of a destructive impact

on the surroundings and poses fewer fitness

dangers than standard reducing fluids. The

intrinsic traits of canola oil, such as its excessive

flash factor and coffee volatility, make the place

of work more secure. Canola oil is a feasible

choice for efficient and sustainable metal-cutting

packages due to its renewability and availability,

which coincide with the increasing

consciousness of environmentally responsible

sports.

 TMPTO (Trimethyl propane trioleate A2):

Trimethylolpropane and oleic acid are blended to

produce trimethyl propane trioleate (TMPTO), a

synthetic ester. This substance is prized for its

many uses of, mainly as an additive for

lubricants. TMPTO minimizes friction, boosts

oxidative balance, and promotes lubricity in a

number of formulations, making it best to be

used in metalworking fluids and business

lubricants. Its low volatility and high viscosity

index contribute to its effectiveness at very low

temperatures. Because of its molecular makeup,

TMPTO may also paintings as a plasticizer and a

surface-lively agent in precise programs. This

versatility makes it useful for enhancing

lubricating oil's overall performance and

prolonging its lifespan in quite a few sectors,

along with commercial, automobile, and

chemical processing.

 Synthetic ester (A3): Combining natural acids

with alcohols results in the chemical compounds

referred to as artificial esters, which might be

used to make several purposeful materials and

artificial lubricants. These esters are more

lubricating, thermally solid, and immune to

oxidation than conventional mineral oils.

Synthetic esters are regularly utilized in

hydraulic fluids, metalworking programs, and

business lubricants due to their excellent overall

performance in tough situations and excessive

temperatures. Because of their exactly

customizable chemical and bodily qualities due

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to their specific molecular architectures, they're

best for precise packages in the automobile,

aviation, and other sectors. Extended service

intervals, much less wear, and advanced

equipment efficiency are all facilitated through

artificial esters.

 PAG (Polyalkylene Glycol A4): Polyalkylene

Glycols (PAGs) are synthetic lubricants from the

polyglycol own family this is extensively

employed in many industrial packages. Alkylene

oxides go through polymerization to create those

polymers. PAGs can face up to harsh

environments such as h igh temperatures and

massive masses due to their super lubricity,

thermal, and oxidative balance. In the car,

production, and aerospace industries, they're

frequently used as co mpressor lubricants,

hydraulic fluids, and tool oils. PAGs are useful

as lubricants in vital machinery because of their

low volatility and compatibility with a variety of

materials, which are crucial for improved

performance and longer equipment life.

 Mineral oil (A5): Mineral oil is a clear, colorless

liquid with a petroleum base that has no smell. It

is a kind of oil consisting of complex

hydrocarbon mixtures with a hydrocarbon

foundation. Mineral oil has several applications

in the industrial, cosmetic, and medical fields as

an insulator, coolant, and lubricant. It may be

found in skincare products like lotions and baby

oil in the cosmetics industry because of its

moisturizing properties. Medical professionals

use mineral oil as a laxative. Its versatility is

derived from its ability to provide a smooth,

firm, and inert foundation for several products,

even in the face of a growing demand for more

ecologically friendly and natural alternatives.

The MCDM involves making decisions in the

presence of multiple and often conflicting criteria.

The term "criteria" in mixed-criteria decision-

making refers to the range of variables or aspects

that are taken into account while assessing and

contrasting distinct options. These standards, which

are selected following the particular circumstances

of the choice issue, are crucial for evaluating the

effectiveness or attractiveness of options. The goals,

principles, and inclinations of the decision-makers

and other stakeholders are taken into consideration

while choosing the criteria. Both qualitative and

quantitative criteria may be used, and they may

cover topics including social concerns, risk, quality,

cost, and time. The decision-making process cannot

succeed unless specific, pertinent criteria are

identified and defined. For better organizing and

structuring the choice issue, criteria are frequently

divided into various groups or dimensions. To

represent each criterion's relative significance

throughout the decision-making process, weighting

may also be used.

We have determined the following criteria for

cutting fluids in machining operations based on a

survey of the literature.

 Low temperature (C1): Cutting fluids with low-

temperature performance for machining

operations has several advantages. First of all, it

aids in preventing workpieces and cutting tools

from overheating during machining processes.

Lower temperatures are maintained to minimize

tool wear and increase tool life, which saves

money. Lower temperatures can improve the

dimensional accuracy of machined products by

lowering thermal expansion. Cooling also

encourages chip evacuation and lessens the

possibility of formed built-up edges. It also

improves surface polish and overall machining

efficiency. To ensure precision, maximize

machining efficiency, and make bigger the life of

reducing gear, choose slicing fluids with

incredible low-temperature houses.

 Toxicity (C2): The phrase "toxicity" refers back

to the doubtlessly disastrous consequences that

cutting fluids may additionally have on bot h

human health and the environment. Cutting

fluids can incorporate a wide variety of chemical

substances, in addition to biocides, corrosion

inhibitors, and lubricants. Cutting fluids are

utilized in metalworking activities further to

grinding and machining. Skin touch, inhalation,

or ingestion of these materials can also result in

pores and skin infections, respiration problems,

and other critical side effects. When spent

reducing fluids are disposed of, the surroundings

are likewise put in danger. Manufacturers are

stimulated to deliver fewer, less harmful fluids

which will defend employee fitness, lessen

environmental effects, and market greater

constant and ecologically pleasant metalworking

operations.

 Lubricating potential (C3): This refers to the

capacity of reducing fluids to reduce put on and

friction on the bulk of the workpiece and the

decreasing tool on the quit of machining

processes. Appropriate lubrication is crucial for

metalworking to ensure reducing accuracy,

remove defects from the ground, and develop

device lifespans. Cutting fluids with brilliant

lubricating homes creates a defensive layer

between the tool and the workpiece, reducing

frictional forces and warmth technology. By

reducing put on, t his complements widespread

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machining performance, allows chip evacuation,

and will increase device life. Proper cutting fluid

lubrication will increase workpiece notable,

reduce electricity intake, and increase

productivity in many machining procedures.

 Hydrolytic stability (C4): Fluids with slicing

houses that are hydrolytically resistant are those

that don't break down as quickly as they come

into touch with water. In metalworking

operations, water-based absolute coolants and

unintentional water touch are frequent

occurrences. By use of hydrolytic stability, the

cutting fluid's ability to preserve its standard

performance traits and withstand degradation in

the presence of water is guaranteed. High

hydrolytic stability fluids inhibit the

manufacturing of undesirable byproducts, such

as acids, that can corrode steel surfaces and

reduce the efficacy of the decreasing fluid.

Advanced hydrolytic balance in reducing fluids

allows to make sure the sturdiness of

metalworking systems and gadgets. It

additionally offers a longer fluid existence,

appreciably less safety, and maintains overall

overall performance.

 Oxidative balance (C5): Oxidative stability is the

ability of cutting fluids to withstand degradation

brought on using exposure to oxygen inside the

air. Throughout metalworking operations,

reducing fluids are subjected to excessive

temperatures, and oxidation can be due to

oxygen. Oxidative stability ensures that the fluid

continues its chemical balance by preventing the

manufacturing of dangerous byproducts that

might compromise the decreasing fluid's

capability. Reducer fluids with high oxidative

stability have longer company lifetimes even as

still capable of lubricating and unfasten. This

choice is critical for reducing working charges,

minimizing the need for routine fluid refills, and

galvanizing dependable and green machining

tactics in industries where metalworking is

popular.

 Thermal balancing (C6): Thermal balance is the

capability of lowering fluids to go through and

keep function effectively at excessive

temperatures inside the route of metalworking

techniques. Because cutting sports generates a

number of heat, the fluid desires with a purpose

to withstand thermal breakdown for you to

preserve ordinary average performance. High

warmness stability decreasing fluids withstand

degradation and show off small viscosity

variations, which prevent the formation of

deposits and breakdown products. This function

preserves the fluid's cooling and lubricating

properties, which finally lengthens the tool's

lifespan and complements the workpiece's

fantastic high quality. Thermal stability plays a

widespread position in extending the life of the

reducing system and the lowering fluid itself in

slight-name for machining applications, which

enables to increase productivity and decrease

downtime.

 Viscosity index (C7): The viscosity index of a

reducing fluid is used to measure how resistant it

is to modifications in viscosity because of

temperature versions. Temperature variations

have some distance much less of an impact on

the fluid's viscosity thanks to an extra viscosity

index. Because of the warm temperature

generated during cutting operations, reducing

fluids enjoy temperature versions in

metalworking tactics. With the help of retaining

an extra steady viscosity across a w ide

temperature variety, high-viscosity slicing fluids

provide dependable lubricating and cooling

tendencies. This is essential for maintaining

proper fluid flow and lubrication under a variety

of working circumstances, which enhances tool

performance and workpiece quality and helps

maximize machining efficiency.

 Cost (C8). Cutting fluid costs encompass

acquisition, upkeep, and disposal costs. High-

performance fluids may be more expensive up

front, but by prolonging tool life and decreasing

downtime, they may save money over time.

Costs are also affected by proper fluid

management techniques, which take waste

disposal, recycling, and filtering into account.

Even while they may cost very little initially,

high-quality fluids for cutting can save money

over time by reducing the need for more frequent

tool changes and enhancing machining

productivity. Finding the sweet spot between

initial costs and continuing advantages is

necessary to maximize the benefits of cutting

fluid selections in machining operations.

To maximize the potential output and optimize

processes for both useful and non-beneficial factors,

trade-offs need to be balanced. MCDM uses

methods such as the AHP and PROMETHEE. The

objective is to maximize usable criteria, i.e., to look

for solutions with high ratings for good aspects.

Minimization, which attempts to lessen adverse

effects, is one of the non-beneficial criteria.

Decision-makers can select options that perform

well in positive features while reducing negative

consequences by weighting and ranking these

characteristics.

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Table 1. Alternatives for cutting fluids in machining operations

Alternative 

Criteria



–

A thorough assessment of the optimization

process is necessary, taking into account the

proportional weight of each criterion as well as the

particular objectives and limitations of the choice

issue. The optimization for beneficial criteria is

represented as ‘+’ and non-beneficial criteria

represented as ‘–’. Table 1 presents the selection

criteria, relevant data, and alternatives utilized in

this work for the MCDM techniques of cutting fluid

selection. The data are derived from [1], [32], [33].

Based on eight selection criteria, the best cutting

fluid is selected among five different cutting fluids

in this study.

2.2 Methods

The MCDM methods are employed in situations

where a single best choice or alternative must be

selected from a set of available options, and these

options need to be evaluated against various criteria

that may have different importance levels or

preferences. MCDM approaches are employed in

this work to select and compare different cutting

fluids utilized in the machining operations. In this

study, offering a tool for those involved in industrial

manufacturing industries is the goal. For

assessment, the widely-used and computationally

effective MCDM methods, TOPSIS and Entropy,

are used. To avoid taking into account the decision

maker's viewpoint, the entropy approach is used to

compute the weighting factors for the criterion in

the chosen method. Next, the TOPSIS MCDM

approach steps are applied to establish the cutting

fluid selection rankings. Lastly, the flowchart of the

procedures used in this study to choose other cutting

fluids is displayed in Figure 2. Cutting fluids are

chosen using the MCDM methodologies' processing

stages.

Fig. 1: The hierarchical model for selection of cutting fluid

Selection of Cutting Fluid

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Fig. 2: The flowchart of the selection of cutting fluid

2.2.1 TOPSIS Method

The TOPSIS method is particularly useful when

making decisions involving conflicting criteria and

trade-offs. It allows decision-makers to quantify and

balance the impact of different criteria in the

selection process. However, it's important to

carefully define criteria, normalize data, and assign

appropriate weights to ensure the reliability of the

results. Hwang and Yoon developed it, [42], [43]. In

this process, various choice criteria are evaluated

using both positive and negative ideal solutions. The

optimal decision is determined by the maximization

of the distance from the negative ideal solution and

the minimization of the distance from the positive

ideal solution.

The decision-makers preferences and the

particulars of the decision issue will determine

which of the several MCDM methods—of which

TOPSIS is just one—are used. It is a tool for

decision assistance that is often used in many

different sectors, such as economics, business,

engineering, and environmental management. The

TOPSIS approach takes into account several

different criteria or qualities to assist decision-

makers in choosing the best choice from a range of

possibilities. TOPSIS may be used to evaluate and

rank some cutting fluid options based on several

criteria when selecting cutting fluids for machining

processes.

This is a co mprehensive guide to selecting,

cutting fluids for machining processes utilizing

TOPSIS: First, determine the key parameters that

will be used in the cutting fluid selection procedure.

This step is necessary to compare different

parameters equitably. Two formulas that may be

used to normalize the decision matrix are min-max

normalization and z-score normalization. Every

criterion is given a weight based on how important

they are concerning one another. The weight given

to each criterion is reflected in the decision-making

process. All weight must add up t o one. First,

construct the decision matrix with a criterion in each

column and a cutting fluid option in each row. Each

criterion's normalized values are included in the

matrix. For every parameter, the ideal and anti-ideal

solutions are computed. For every criterion, the anti-

ideal solution represents the lowest value, and the

ideal solution, the largest value. Each alternative's

Euclidean distances to the ideal and anti-ideal

solutions are computed. A metric for similarity or

dissimilarity is the Euclidean distance. The relative

closeness of each option to the optimal solution is

computed using the computed distances. The

ranking of alternatives is determined by how close

they are to the best possible answer. The best option

is the one with the highest TOPSIS score.

Applying the TOPSIS method in machining

processes to the selection of cutting fluids requires

careful consideration of the criteria, their

normalization, weight assignment, and the actual

calculation steps. Keep in mind that the success of

the TOPSIS method depends on the accuracy of the

parameters, weights, and normalization process. The

popularity, ease o f use, and mathematical

computations of this TOPSIS approach make it the

recommended one. The method's application phases

are listed below, [44].

Start

Review of literature

Determining the alternatives and criteria for cutting fluids

Calculate the criteria weight by Entropy method

Apply TOPSIS method for closeness coefficients

Rank the cutting fluids by closeness coefficients

End

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Step 1: A decision matrix (DM) is produced

during this stage. The following criteria, which were

established at the outset, yield this matrix.

 =







11 12 13 …1

21 22 23 …2

31

…

1

32

…

2

33 …31

… … …

3…







(1)

In the following equation, the performance of

alternative = 1,2,3, …  in = 1,2,3, …  criterion

is indicated by . The original decision matrix has

 criteria and  alternatives.

Step 2: Each value of the Decision matrix is

normalized as the following equation:



=

2



=1

(2)

Step 3: A weighted decision matrix (WDM) is

developed. The weight values of the assessment

criteria's relevance are used to determine this matrix.

The normalized decision matrix's elements are

multiplied by the weight () values, which are

determined as follows to generate the WDM.

 =

 (3)

Step 4: The values of the optimum solution, both

positive and negative, are found. The biggest value

in each column of the matrix  represents the

positive ideal solution, while the smallest value in

each column represents the negative ideal solution.

+= {1

+,2

+, … … . , 

+} is the

definition of the positive ideal solution set, while

= {1

,2

, … … . , 

} is the

definition of the negative ideal solution set.

Step 5: In this step the equations (4) and (5),

which relate the distance values (+,) to the

positive and negative ideal solution, are used to

compute the distance value as well as the number of

possible decisions.

+= +2



=1 (4)

= 2



=1 (5)

Step 6: In this step, the equation (6) is used to

determine the relative closeness coefficients () of

each decision alternative to the ideal solution. There

are observed to be distances from both positive and

negative ideal solution values.

=

++ (6)

Step 7: Finally, the calculation of the closeness

coefficients that were obtained which fall within the

range of 0< 1. Sorting based on values bigger

than the established closeness coefficients is how

the selection procedure is carried out.

2.2.2 Shannon’s Entropy Method

Weighing the factors is one of the most crucial

procedures in selecting a different cutting fluid. The

Shannon entropy, [45], method is used to generate

the criterion's weighting elements. As stated in [46],

this method measures the amount of uncertainty in

the data that is given in probability theory.

Claude Shannon proposed the idea of

information entropy, commonly known as Shannon

entropy, in his 1948 work "A Mathematical Theory

of Communication". Three components make up a

data communication system, according to Shannon's

theory: a data source, a communication channel, and

a receiver. According to Shannon, the "fundamental

problem of communication" is the receiver's ability

to determine, from the signal it gets over the

channel, what data originated from the source. In his

renowned source coding theory, Shannon

demonstrated that the entropy reflects an absolute

mathematical limit on how effectively data from the

source can be losslessly compressed onto a t otally

noiseless channel. Shannon took into account

various methods of encoding, compressing, and

transmitting messages from a data source. Shannon's

noisy-channel coding theorem significantly

reinforced this outcome for noisy channels.

Information theory entropy and statistical

thermodynamics entropy are exactly comparable.

Gibbs' formula for entropy is technically equal to

Shannon's formula when the values of the random

variable denote the energies of microstates, as is the

case in this comparison. Other branches of

mathematics, like combinatorics and machine

learning, are related to entropy. A series of axioms

showing that entropy should be a measure of the

average result of a v ariable's informativeness may

be used to construct the definition. Differential

entropy is equivalent to entropy for a continuous

random variable. Shannon's entropy, a fundamental

concept in information theory, has several

applications in fields where determining uncertainty

and information content is essential. It provides a

scientific and rigorous way to measure the

information or randomness included in a dataset or

system. [47], provide information measures with

data illustration.

The entropy approach's phases, [48], [49], [50],

are listed below and were utilized to establish the

weights of the criterion.

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Step 1: The decision matrix (DM) is generated

using the values of the criteria and alternatives in

Table 1. It is obtained, as equation (1) shows.

 =







11 12 13 …1

21 22 23 …2

31

…

1

32

…

2

33 …31

… … …

3…







(7)

Step 2: The following equation (8) is used to

convert the values of the choice matrix presented in

expression (7) to their normalized values. Where 

represents the normalized value of the  alternative

for the  criteria:

 =





=1

(8)

Step 3: The following equation (9) is used to

determine each criterion's entropy value ():

=



=1 log 2

log  (9)

Step 4: Finally, the entropy weight values ()

for each criteria are computed using equation (10).

The weighting of each criterion must equal one, i.e.,





=1 = 1:

=1

(1)



=1

(10)

2.3 Direction of Future Study

With further investigation on s tabbing fluids in

MCDM-based machining transactions, metal-cutting

processes may become more aesthetically pleasing,

more businesslike, and more sustainable. Efficient

fluids may be selected and evaluated by applying

MCDM techniques such as entropy to calculate the

TOPSIS, ELECTRE (Expelling and Prize

Expressing Realism), and unit criteria.

More aspects, such as environmental change,

agency account, aboveground smoothness, cost-

effectiveness, and methods vivification, may be

taken into consideration at the outset of an

investigation into knifelike liquid pick

improvement. This ecumenical meeting ensures a

far more complete presentation of the trade-offs

involved in making compliant judgments.

Furthermore, by enabling real-time machining

process modifications, the combination of cutting-

edge analytics and tool acquisition may alter the

predictive state of MCDM.

A closer look at innovative sustainable knife-like

changing possibilities, such as bio-based or

environmentally friendly fluids, inside the MCDM

potential may also lead to improved, more

environmentally friendly production techniques.

Further research should be done to improve iron

mind models that predict projectile machining

conditions and changing environmental restrictions.

This will assist in striking a balance between the

performance, cost, and environmental effects of

metal-cutting processes.

3 Results and Discussion

The corresponding weighting variables associated

with eight parameters in the selection of cutting

fluids used in machining processes have been

established in this study using the entropy

technique. Following that, the weighting factors for

the criterion are computed using the study's

equations (8) – (10). The entropy weight of the

decision matrix and criterion utilized in the MCDM

approach are shown in Table 2, equation (2) is used

to calculate the normalized value of the decision

matrix. The graphical representation of criterion

weight is presented in Figure 3.

Table 2. Normalize the decision matrix for cutting fluids

Alternative 

Criteria

–

0.164

0.312

0.552

0.160

0.292

0.485

0.232

0.493

0.312

0.442

0.320

0.438

0.485

0.465

0.493 0.312 0.442 0.480 0.641 0.583 0.485 0.814

0.493

0.312

0.442

0.480

0.438

0.485

0.232

0.493

0.781

0.331

0.641

0.480

0.438

0.243

0.116

Entropy

0.964

0.944

0.992

0.947

0.986

0.982

0.871

Weight 

0.036

0.056

0.008

0.053

0.014

0.018

0.129

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Fig. 3: Graphical representation of criterion weight for selection of cutting fluid

Table 3. Weighted normalized decision matrix for cutting fluids

Table 2 displays the weighting factors that

were determined using the entropy approach. With a

weight of 0.353, the cost criteria are the most

weighted, followed by the toxicity criterion (0.153).

Conversely, the capacity to lubricate has the lowest

weight value (0.021). It is significant to remember

that the use of water in cutting fluids can have

detrimental outcomes in machining operations,

including wear and corrosion [51]. As a result, it is

customary to rank the cost criteria as the most

significant one. Furthermore, toxicity is frequently a

key factor that many customers take into account. It

makes sense that the lubrication criteria have the

lowest weighting coefficient because the chosen

cutting fluids have comparable characteristics.

The TOPSIS approach is used to pick cutting

fluids once the entropy method has determined the

criterion weights. For this, the decision matrix from

Table 1 is used. The ranking system for cutting fluid

selection is derived by utilizing the procedures

specified in equations (3) – (5). Table 3 contains the

weighted normalized decision matrix values as well

as the ideal solution sets (+, ) that

were produced using the TOPSIS approach. These

numbers stand for each criterion's maximum and

minimum values.

After the creation of the weighted decision

matrix, step 4 is the process of allocating the

best ideal values and worst ideal values for each

criterion based on w hether or not they are

advantageous. It is also noteworthy that criteria 2

and 8 are non-beneficial criteria while the

remaining criteria are beneficial. The ideal values

that are best and worst, respectively, are shown in

Figure 4 a s += {0.049, 0.048, 0.012, 0.092,

0.022, 0.023, 0.041} and = {0.016, 0.119,

0.007, 0.023, 0.023, 0.011, 0.012, 0.287}.

0,099

0,153

0,021

0,144

0,038

0,048

0,353

Cost Viscosity index Thermal stability Oxidative stability

Hydrolytic stability

Lubricating ability

Toxicity

Low temperature

Alternative 

Criteria

–

0.016

0.048

0.012

0.023

0.011

0.023

0.082

0.049 0.048 0.009 0.046 0.046 0.017 0.023 0.164

0.049

0.048

0.009

0.069

0.092

0.022

0.023

0.287

0.049 0.048 0.009 0.069 0.069 0.017 0.023 0.082

0.049 0.119 0.007 0.092 0.069 0.017 0.012 0.041

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Fig. 4: Illustration of variation between best ideal and worst ideal values

The best ideal value represents the most

favorable values for each criterion. For

maximization criteria, the best ideal value would

have the highest possible values for all criteria,

while for minimization criteria, it would have the

lowest possible values.

Conversely, the worst ideal value represents the

least favorable value for each criterion. For

maximization criteria, the worst ideal value would

have the lowest possible values, and for

minimization criteria, it w ould have the highest

possible values. The difference between these two

sets of optimal solutions indicates how well the

alternatives perform across the board. It aids in

evaluating how well each option stacks up a gainst

the decision space's performance extremes.

Practically speaking, the more variations there are,

the more varied the range of options is about how

well they meet the specified requirements. To

choose solutions that fit their objectives and

preferences, decision-makers must analyze this

variance to comprehend the compromises and trade-

offs involved with each option. This variation's

computation is frequently used to assess how close

or comparable each alternative is to the best options.

Additionally, Table 4 di splays the rankings for

the cutting fluid as well as t he relative closeness

coefficients () and distance values (+, ) to the

positive and negative solution sets. The PAG

(Polyalkylene Glycol) cutting fluid is ranked first

and has the highest closeness coefficient ()

according to the rankings produced by the TOPSIS

approach. Mineral oil is shown to be the second-best

cutting fluid.

Table 4. Final ranking for cutting fluids based on , + ,and closeness score

0,000

0,050

0,100

0,150

0,200

0,250

0,300

Worst ideal value

Best ideal value

Alternative 

+





Ranking

0.111

0.218

0.661

0.139

0.150

0.519

0.247 0.115 0.318 5

0.053

0.229

0.813

0.076

0.262

0.774

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Fig. 5: Graphical representation of closeness scores with positive and negative ideal solutions

Through the evaluation of eight criteria, five

distinct cutting fluids utilized in machining

operations are to be chosen for this study. The

TOPSIS and Entropy approaches are used in the

selection process. Figure 5 displays the rankings

derived from the TOPSIS technique. Out of all the

cutting fluids that were assessed, the TOPSIS

approach ranks the PAG cutting fluid as the best. By

[52] favored the PAG cutting fluid exclusively in

their study due to its superiority over other cutting

fluids due to its high-quality surfaces.

According to [53], PAG cutting fluids'

recyclability allows them to display better qualities.

Based on the outcomes of the TOPSIS and entropy

techniques, it can be stated that the PAG cutting

fluid could be the best option. In both the TOPSIS

and entropy approaches, mineral oil ranks second.

However, when it comes to cutting fluids, synthetic

ester comes in last when using the TOPSIS and

Entropy methodologies. Some of the drawbacks of

vegetable-based oils are their susceptibility to fire,

less stability, and diminished performance at high

temperatures and fast processing speeds [54],[55].

Therefore, out of the five cutting fluids examined in

this study, it shouldn't be chosen.

The clarifying technique is a u seful strategy to

use in selecting applications and multi-criteria

decision-making processes. The suggested method

has many benefits. First off, it may be a very useful

tool for solving selection issues. Secondly, it

remains effective regardless of the number of

methods employed to evaluate possibilities. Thirdly,

it provides a reliable method of eliminating rank

discrepancies resulting from different approaches.

Despite these advantages, it's crucial to keep in

mind that the specific multi-criteria decision-making

methods employed can result in negligible

variations in the rankings in the end. By performing

more investigation and analysis within the corpus of

existing literature, the limitations of this approach

might be made even more apparent.

Using the TOPSIS skyway, selecting and

stemming fluids for machining activities may be

done with precision. TOPSIS gives less weight to

additional variables in this masking to activity

decision-makers analysis and bodily possibilities for

fluid laxation. Knifelike fluids are highly valued for

many reasons, such as t heir durability, lubricating

qualities, cooling effectiveness, environmental

friendliness, and amazing and assured features. To

provide a rigorous make-in care, TOPSIS analyses

every contrastive dilution available with the best

and worst ideal solutions for these parameters. For

instance, the apotheosis piercing discard may also

blackball the depression toll, the smallest possession

of an environmental mate, and the initial combining

criteria. In addition to providing decision-makers

with an unparalleled option for the small, elegant

method of figuring out liquid, TOPSIS's

comprehensive evaluation may also help them

surpass the fine-reducing discard. A humorous e-

book tracheophyte's decision-making processes are

fundamentally compacted using the TOPSIS move.

By bridging the gap between the prejudiced non-

solvent and the compensated set, TOPSIS provides a

clear framework for sorting. Examine and finance

prospects in a comic that overlaps with strategy

series. In complicated decision scenarios, the

approach improves objectivity, efficiency, and

transparency in decision-making, empowering

stakeholders to make informed decisions and

perform better overall.

0,000

0,100

0,200

0,300

0,400

0,500

0,600

0,700

0,800

0,900

Positive Ideal Solution

Negative Ideal Solution

Closeness

Rank

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4 Conclusion

This study explores cutting liquid determination for

machining processes utilizing the TOPSIS and

Entropy MCDM methods. Various details were

acquired from distributed hotspots for cutting

liquids that contained mineral oil, manufactured

ester, PAG, canola, and TMPTO. While making

decisions, the accompanying highlights of the

cutting liquid were considered: low temperature,

low poisonousness, greasing up capacity, hydrolytic

security, consistency record, oxidative steadiness,

and warm dependability. The determination

rankings were obtained by following the procedural

periods of the strategies. The areas beneath show the

review's outcomes:

 The PAG cutting fluid approach that produced

the greatest rating was TOPSIS and Entropy.

Mineral oil secured the second position. On the

other hand, synthetic ester performed the worst

out of all the MCDM approaches used.

 Cutting fluid options are carefully evaluated by

TOPSIS based on how close they are to the

best ideal solution and how different from the

worst ideal solution they are from.

 Cost, safety, cooling effectiveness, lubricating

characteristics, and environmental effects are

only a few of the variables taken into

consideration.

 Using this method permits decision-makers to

check a few matters and choose the slicing

fluid that satisfactorily fits their wishes. The

effects, which offer a wonderful and properly-

organized ranking, provide a knowledgeable

choice based totally on precise targets and

choices.

Furthermore, TOPSIS assists in figuring out

criterion change-offs by using emphasizing the

concessions made using every answer. Through a

system that ensures the selected slicing fluid

satisfies performance standards and is in keeping

with more preferred goals like economics and

environmental obligation.

With the use of TOPSIS, choice-makers may

also carefully weigh and recall several reducing

fluid-associated standards, together with fee, and

protection, which have an effect on the

environment, lubricating features, and cooling

effectiveness. Its capacity to address both

quantitative and qualitative facts is a further gain.

Quantitative components like cost or cooling prices

can be efficaciously controlled by way of TOPSIS

similar to qualitative ones like safety rules and

environmental consequences. In precis, the

consequences of the TOPSIS and entropy technique

offer a stable basis for choosing a cutting fluid,

making it simpler to decide which fluid quality fits

the tricky and sundry requirements of machining

tactics.

References:

[1] Abdelrazek A H, Choudhury I A, Nukman Y

and Kazi S N, Metal cutting lubricants and

cutting tools: a review on the performance

improvement and sustainability assessment.

J. Adv. Manuf. Technol. 106, 2020, pp.

4221–4245

[2] Said Z, Gupta M, Hegab H, Arora N, Khan A

M, Jamil M, and Bellos E, A comprehensive

review on minimum quantity lubrication

(MQL) in machining processes using nano-

cutting fluids. J. Adv. Manuf. Technol. 105,

2019, pp. 2057–2086.

[3] Liew P J, Shaaroni A, Sidik N A C and Yan

J, An overview of current status of cutting

fluids and cooling techniques of turning hard

steel. Int. J. Heat. Mass Transf. 114, 2017,

pp. 380–394.

[4] Shokoohi Y, Khosrojerdi E and Shiadhi B R,

Machining and ecological effects of a new

developed cutting fluid in combination with

different cooling techniques on turning

operation. J. Clean Prod. 94, 2015, pp. 330–

339.

[5] Wickramasinghe K C, Sasahara H, Abd

Rahim E and Perera G I P. Green

metalworking fluids for sustainable

machining applications: a review. J. Clean

Prod. 257, 2020, 120552.

[6] Yan P, Rong Y and Wang G, The effect of

cutting fluids applied in metal cutting

process. Proc. Inst. Mech. Eng. B J. Eng.

Manuf. 230, 2016, pp. 19–37.

[7] Lee C W an d Kwak N K, Information

resource planning for a health-care system

using an AHP-based goal programming

method. J. Oper. Res. Soc. 50, 1999, pp.

1191–1198.

[8] Meciarova J and Stanovsky M, Cutting fluids

evaluation based on oc cupational health and

environmental hazards. Eng. Rural Dev. 10,

2011, pp. 418–422.

[9] Sofuoglu M A, A new hybrid decision-

making strategy of cutting fluid selection for

manufacturing environment. Sadhana, 46,

2021, pp. 1–9.

[10] Yan P, Rong Y and Wang G, The effect of

cutting fluids applied in metal cutting

WSEAS TRANSACTIONS on FLUID MECHANICS

DOI: 10.37394/232013.2024.19.9

Pankaj Prasad Dwivedi, Dilip Kumar Sharma

E-ISSN: 2224-347X

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process. Proc. Inst. Mech. Eng. B J. Eng.

Manuf. 230, 2016, pp. 19–37.

[11] Khan A and Maity K, Application of

MCDM-based TOPSIS method for the

selection of optimal process parameter in

turning of pure titanium. Benchmarking Int.

J. 24, 2017, pp. 2009–2021.

[12] Lukic D, Cep R, Vukman J, Antic A,

Djurdjev M and Milosevic M, Multi-criteria

selection of the optimal parameters for high-

speed machining of aluminum alloy Al7075

thin-walled parts. Metals, 10, 2020, 1570.

[13] Niu J, Huang C, Li C, Zou B, Xu L, Wang J,

and Liu Z, A comprehensive method for

selecting cutting tool materials. J. Adv.

Manuf. Technol. 110, 2020, pp. 229–240.

[14] Pathapalli V R, Basam V R, Gudimetta S K,

and Koppula M R, Optimization of

machining parameters using WASPAS and

MOORA. World J. Eng. 17, 2020, pp. 237–

246.

[15] Sun J, Ge P and Liu Z, Two-grade fuzzy

synthetic decision-making system with the

use of an analytic hierarchy process for

performance evaluation of grinding fluids.

Tribol. Int. 34, 2001, pp. 683–688.

[16] Tan X C, Liu F, Cao H J and Zhang H, A

decisionmaking framework model of cutting

fluid selection for green manufacturing and a

case study. J. Mater. Process. Technol. 129,

2002, pp. 467–470.

[17] Cakir O, Yardimeden A, Ozben T, and

Kilickap E, Selection of cutting fluids in

machining processes. J. Achiev. Mater.

Manuf. Eng. 25, 2007, pp. 99–102.

[18] Venkata Rao R and Patel B K, Decision

making in the manufacturing environment

using an improved PROMETHEE method.

Int. J. Prod. Res. 48, 2010, pp. 4665–4682.

[19] Abhang L B and Hameedullah M, Selection

of lubricant using combined multiple

attribute decision-making method. Adv.

Prod. Eng. Manag. 7, 2012, pp. 39–50

[20] Chakraborty S and Zavadskas E K,

Applications of WASPAS method in

manufacturing decision making. Informatica

25, 2014, pp. 1–20.

[21] Nemati, M., & Jahangirian, A. A Da ta-

Driven Machine Learning Approach for

Turbulent Flow Field Prediction Based on

Direct Computational Fluid Dynamics

Database. Journal of Applied Fluid

Mechanics, 17(1), 2023, pp. 60 -74. doi:

10.47176/jafm.17.1.2109.

[22] Jagadish R A and Ray A, Green cutting fluid

selection using MOOSRA method. Int. J.

Res. Eng. Technol. 3, 2014, 559–563.

[23] Attri R, Dev N, Kumar K and Rana A,

Selection of cutting fluids using a novel,

decision-making method: preference

selection index method. Int. J. Inf. Decis. Sci.

6, 2014, pp. 393–410.

[24] Madic M, Radovanovic M, and Manic M,

Application of the ROV method for the

selection of cutting fluids. Decis. Sci. Lett. 5,

2016, pp. 245–254.

[25] Prasad K and Chakraborty S, A quality

function deployment-based model for cutting

fluid selection. Adv. Tribol. 2016, 3978102.

[26] Jayant A, Chaudry N, and Singh P, A

decision-making framework model of cutting

fluid selection for green manufacturing: a

synthesis of 3 MCDM approaches. Int. Conf.

Adv. Eng. Technol. 2018, pp. 1–7.

[27] Tu H X, Jun G, Hien B T, Hung L X, Tung L

A, and Pi V N, Determining optimum

parameters of cutting fluid in external

grinding of 9CrSi steel using Taguchi

technique. SSRG Int. J. Mech. Eng. 5, 2018,

pp. 1–5.

[28] Sofuoglu M A, A new hybrid decision-

making strategy of cutting fluid selection for

manufacturing environment. Sadhana, 46,

2021, pp. 1–9.

[29] Ross N S, Mia M, Anwar S, Manimaran G,

Saleh M, and Ahmad S, A hybrid approach

of cooling lubrication for sustainable and

optimized machining of Ni-based industrial

alloy. J. Clean. Prod. 321, 2021, 128987.

[30] Goswami S S and Behera D K,

Implementation of COPRAS and ARAS

MCDM Approach for the Proper Selection of

Green Cutting Fluid. In: Current Advances in

Mechanical Engineering, 2021, pp. 975–987.

[31] Varghese B and Karande P, AHP-MARCOS,

a hybrid model for selecting gears and

cutting fluids. Mater. Today: Proc. 52, 2022,

pp. 1397–1405.

[32] Benedicto E, Carou D and Rubio E M,

Technical, economic and environmental

review of the lubrication/cooling systems

used in machining processes. Procedia Eng.

184, 2017, pp. 99–116.

[33] Madic M, Radovanovic M, and Manic M,

Application of the ROV method for the

selection of cutting fluids. Decis. Sci. Lett. 5,

2016, pp. 245–254.

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E-ISSN: 2224-347X

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[34] Moradian M, Modanloo V, and Aghaiee S,

Comparative analysis of multi criteria

decision making techniques for material

selection of brake booster valve body. J.

Traffic Transp. Eng. 6, 2019, pp. 526–534.

[35] Pearson K VII. Note on regression and

inheritance in the case of two parents. Proc.

R. Soc. Lond. 58, 1895, pp. 240–242

[36] Petkovic D, Madic M an d Radenkovic G,

Selection of the most suitable non-

conventional machining processes for

ceramics machining by using MCDMs. Sci.

Sinter. 47, 2015, pp. 229–235.

[37] Fernando Martinez, Marina Cauhape, Luis

Zorzutti, Silvia Angelone, Validation of a

Mathematical-Based Model for the

Rheological Characterization of Asphalt

Mixtures, WSEAS Transactions on Fluid

Mechanics, vol. 18, 2023, pp. 135 -145,

DOI:10.37394/232013.2023.18.14.

[38] Ozcelik B, Kuram E, Demirbas E, and S¸ ik

E, Effects of vegetable-based cutting fluids

on the wear in drilling. Sadhana, 38, 2013,

pp. 687–706.

[39] Qiao S, Shi Y, Wang X, Lin Z, and Jiang Y,

Synthesis of biolubricant trimethylolpropane

trioleate and its lubricant base oil properties.

Energy Fuels, 31, 2017, pp. 7185–7190.

[40] Pettersso A, High-performance base fluids

for environmentally adapted lubricants.

Tribol. Int. 40, 2007, pp. 638–645.

[41] Tsai T H and Shih Y P, Recovering low-

turbidity cutting liquid from silicon slurry

waste. J. Hazard. Mater. 271, 2014, pp. 252–

257.

[42] Madanhire I and Mbohwa C, Environment

and the economics of long drain interval. In:

Mitigating environmental impact of

petroleum lubricants, 2016, Springer, Berlin,

pp. 149–164.

[43] Hwang C L and Yoon K, Methods for

multiple attribute decision making. In:

Multiple Attribute Decision Making, 1981,

Springer, Berlin, pp. 58–191.

[44] Dwivedi, P.P. & Sharma, D.K, Evaluation

and ranking of battery electric vehicles by

Shannon’s entropy and TOPSIS methods.

Mathematics and Computers in Simulation.

212, 2023,

https://doi.org/10.1016/j.matcom.2023.05.01

[45] Shannon C E, A mathematical theory of

communication. Bell Syst. Tech. J. 27, 1948,

pp. 379–423.

[46] Kumar R and Ray A, Selection of material

for optimal design using multi-criteria

decision making. Procedia Mater. Sci. 6,

2014, pp. 590–596.

[47] Dwivedi, P.P. & Sharma, D.K, Generalized

‘Useful’ Converse Jensen’s Inequality with

Data Illustration. WSEAS Transactions on

Systems. 2022;21:62-67.

https://doi.org/10.37394/23202.2022.21.7

[48] Dwivedi, P.P. & Sharma, D.K., Selection of

Combat Aircraft by Using Shannon Entropy

and VIKOR Method. Defence Science

Journal, 73, 2023, pp. 411 -419.

https://doi.org/10.14429/dsj.73.17996.

[49] Dwivedi, P.P. & Sharma, D.K., Application

of Shannon Entropy and CoCoSo Methods in

Selection of the Most Appropriate

Engineering Sustainability Components.

Cleaner Materials. 5, 2022, 100118.

https://doi.org/10.1016/j.clema.2022.100118.

[50] Dwivedi, P.P. & Sharma, D.K., Assessment

of Appropriate Renewable Energy Resources

for India using Entropy and WASPAS

Techniques. Renewable Energy Research

and Applications, 5, 2 023, pp. 51-61.

https://doi.org/10.22044/rera.2023.12960.121

[51] Gautam S, Guria C and Rajak V K, A state

of the art review on the performance of high-

pressure and high temperature drilling fluids:

Towards understanding the structure-

property relationship of drilling fluid

additives. J. Pet. Sci. Eng. 213, 2022, pp .

110318

[52] Born D K and Goodman W A, An empirical

survey on t he influence of machining

parameters on tool wear in diamond turning

of large single-crystal silicon optics. Precis.

Eng. 25, 2001, pp. 247–257.

[53] Tsai T H and Shih Y P, Recovering low-

turbidity cutting liquid from silicon slurry

waste. J. Hazard. Mater. 271, 2014, pp. 252–

257.

[54] Kuram E, Ozcelik B, Bayramoglu M,

Demirbas E, and Simsek B T, Optimization

of cutting fluids and cutting parameters

during end milling by using D-optimal

design of experiments. J. Clean Prod. 42,

2013, pp. 159–166.

[55] Shokrani A, Dhokia V, and Newman S T,

Environmentally conscious machining of

difficult-to-machine materials with regard to

cutting fluids. Int. J. Mach. Tools Manuf. 57,

2012, pp. 83–101.

WSEAS TRANSACTIONS on FLUID MECHANICS

DOI: 10.37394/232013.2024.19.9

Pankaj Prasad Dwivedi, Dilip Kumar Sharma

E-ISSN: 2224-347X

Volume 19, 2024

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Pankaj Prasad Dwivedi: Performed the

measurements, Wrote the original paper also

planning and supervising the work. He was

involved in all stages from the formulation of the

problem to the final findings and solution.

- Dilip Kumar Sharma: Processed the experimental

data, performed the analysis, and supervised the

work. Developed the theoretical formalism,

performed the analytic calculations, and

performed the numerical simulations.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

The authors did not receive support from any

organization for the submitted work.

Conflict of Interest

The authors have no conflict of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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WSEAS TRANSACTIONS on FLUID MECHANICS

DOI: 10.37394/232013.2024.19.9

Pankaj Prasad Dwivedi, Dilip Kumar Sharma

E-ISSN: 2224-347X

Volume 19, 2024