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Design & Manufacturing

ciousuring

odeling

it

Environmentally Conscious Date: 3/22/00 1

Environmentally ConsDesign & Manufact

Class 8: Cutting Fluid M

Prof. S. M. Pand


nerating hugeery significant the earth;

e Great Lakesits ecosystemg raw sewage

f problems likerain, reduced

g., ore, mineral


Motivation

• Manufacturing processes are geamount of waste that has a vinfluence on the living conditions on

• Intense industrial development of thregion has wrought vast changes toby contamination through dischargininto the Lakes [EPA, 1994];

• Thirty years ago scientists aware oglobal warming issues, acidavailability of natural resources (e.oil, drinking water).


ere consumedas not treatedthe use stage

ing the cuttingto develop a

its life.

ting fluid itse lessen byed.


Objectives

• 92 Million Gallons of cutting fluids win 1990, and almost 50% of it wproperly after reaching the end of[EPA, 1991].

• This work is focused on investigatfluid system dynamics in ordermaintenance policy that will extend

• By extending the life of cutenvironmental impact would breducing the amount of fluid dispos


only used for

uid involved inrameters.

t can maintainsed limits andiendly.


Approaches

Two approaches are most commreducing the cutting fluid usage:

• Decreasing the amount of cutting flthe process by changing process pa

• Investigating different additives thafluid properties between the propomake them more environmentally fr


achining

gion, wearl face).

id:

n,


Cutting Fluids Role in the MProcesses

• Primary functions of a cutting fluid:

-- Heat conduction from the cutting re-- Lubrication (reduction of friction and

between machine chips and the too

• Secondary functions of a cutting flu

-- Chip removal from the cutting regio-- Corrosion protection,-- Cleaning.


tion


Cutting Fluid Classifica

• Synthetic cutting fluids,

• Soluble oils,

• Semi-synthetic fluids, and

• Straight cutting and grinding oils.


Cutting

n,


Desired Characteristics ofFluids

• Corrosion Prevention,

• Foam Resistance,

• Extreme Pressure Characteristics,

• Resistance to Microbial Degradatio

• Health and Safety,

• Recyclability and Disposability.


nce

systems and

t are monitoredto perform its

tion,


Cutting Fluid Maintena

• Characteristics of metal cutting fluidchange over time due to their usageenvironment.

• The most important parameters thain order to preserve the fluid’s abilityrole in machining are:

- Oil Concentration,- pH Level,- Microbial Contamina- Corrosion Inhibition.


thodology

ntal

odels

ntial equation

s & Interpretationterizationechanism

Design, etc.ability


Data Dependent Systems Me

DataOperational or experime

Determination ofStatistically adequate m

Difference equation

SystemPrediction & Control

Differe

System Analysi Charac Basic M

Improved St


(DDS):

at

1at 1–


Data Dependent Systems(ME4660/5660)

AR(1) Model

AR(2) Model

ARMA(2,1) Model

Xt φ1Xt 1– at+=

Xt φ1Xt 1– φ2Xt 2–– +=

Xt φ1Xt 1– φ2Xt 2–– a+t

θ–=


r

t j–

t

1B)at


Backshift Operato, or

AR(1) Model:

AR(2) Model:

ARMA(2,1) Model:

BXt Xt 1–= BjXt X=

1 φ1B–( )Xt at=

1 φ1B– φ2B2

– Xt a=

1 φ1B– φ2B2

– Xt 1 θ–(=


c polynomial

depends on itsefficients:

1– gnλnj+

)… 1 λnB–( ) 0=

θm)

1)… λi λn–( )--------------------------------


Green’s Function• Green’s function:

• λ’s are the roots of the characteristi

• Dominance of a root in the systempower that is defined by the g i co

Xt Gjat j–j 0=

t∑=

Gj g1λ1j g2λ2

j … gn 1– λnj+ + +=

1 Φ1B– Φ2B2

– …– ΦnBn

– 1 λ1B–( ) 1 λ2B–(=

gi

λin 1– θiλi

n 2–– …– –(λi λ1–( )… λi λi 1––( ) λi λi +–(

-------------------------------------------------------------------------------=


rkRMA (n,m):

troducing the

t n–

t m–

1nBn

22nBn--------------X1t

θ22mBm–

φ22nBn–----------------------a2t

+


Modeling Framewo• Auto Regressive Moving Average A

• Transfer function form by inbackshift operator:

Xt φ1Xt 1– φ2Xt 2– … φnXat θ1at 1–– θ2at 2–– …– θma–

+ + +

+

=

BXt Xt 1–=

X2t

φ211B φ212B2 … φ2+ + +

1 φ221B– φ222B2– … φ––

------------------------------------------------------------------

1 θ221B θ222B2 …–––

1 φ221B– φ222B2– …–

------------------------------------------------------------+

=


ling

the output X 2:

cripts - φabc:eledses, and

utput X2

φ22nX2t n–φ21nX1t n–

m

++


Multiple Series Mode

• General EARMA(n,n,n-1) model for

• All parameters now have three subsa: Series which is being modb: Series on which φ regresc: Time lag of series b.

Input X1 OTRANSFERFUNCTION

X2t φ221X2t 1– φ222X2t 2– …φ211X1t 1– φ212X1t 2– …a2t θ221a2t 1–– … θ22ma2t –––

+ + ++ + +

=


Diagram

θ22n 1– Bn 1–

–

… φ22nBn

–------------------------------------

t

X2t

n-


Feed-Forward Model Block

φ211B φ212B2 … φ21nB

n+ + +

1 φ221B– φ222B2

– … φ22nBn

––--------------------------------------------------------------------------------

1 θ221B θ222B2 …–––

1 φ221B– φ222B2

– –----------------------------------------------------------

a2

X1tφ121B φ122B

2 … φ12nBn

+ + +

1 φ111B– φ112B2

– … φ11nB––-------------------------------------------------------------------------------

1 θ111B θ112B2 … θ11n 1– B

n 1–––––

1 φ111B– φ112B2

– … φ11nBn

––----------------------------------------------------------------------------------------------

a2t


ng Fluid

asurements, Oil Conc.,...)


Block Diagram of the CuttiSystem

SystemDynamics

ManualFeedback

Additives(Caustic, Oil Additions,...)

Me(pH


s

cutting fluid tominum turbine

cutting fluid tobodies,

cutting fluid toanel, and

cutting fluid to support.


Analyzed System

• system “A” - 2,040 gal, suppliesmachine tools manufacturing alushafts,

• system “B” - 5,060 gal, suppliesmachine tools manufacturing valve

• system “C” - 20,000 gal, suppliesmachine tools manufacturing front p

• system “D” - 24,000 gal, suppliesmachine tools manufacturing stator


: Added(2)

(X 2)=5.249gal

100 150 200 250

f Added Oil to the cutting fluid system (real values)

DaysDays


Cutting Fluid System InputsCaustic (1) and Oil

(real values)mean(X1)=0.0892gal mean

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

Simulation of Added Caustic to the cutting fluid system (real values)

Days

Add

ed C

aust

ic

0 500

10

20

30

40

50

60

Simulation o

Add

ed O

il

Cau

stic

Add

ition

s (g

al)

Days

Oil

Add

ition

s (g

al)


rements:tion (2)

4)=3.86%

100 150 200 250

il Concentration of the cutting fluid system (real values)

DaysDays


Cutting Fluid System MeasupH (1) and Oil Concentra

(real values)mean(X3)=8.8846 mean(X

0 50 100 150 200 2508

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

10Simulation of pH value of the cutting fluid system (real values)

Days

pH

0 50

1

2

3

4

5

6

Simulation of O

Oil

Con

cent

ratio

n (%

)

Days

pH

Oil

Con

cent

ratio

n (%

)


ults


Notation Used in ResRepresentation

• X1 - caustic added,

• X2 - soluble oil added,

• X3 - pH measured, and

• X4 - measured oil concentration.


Addedonl for pH - Added

odel for Addedack)

Model:

DampingRatio

0.9023

-


Adequate Models for theCaustic - pH Relati

• EARMA(3,3,2) is an adequate modeCaustic relation (system dynamics)

• EARMA(4,4,3) is an adequate mCaustic - pH relation (system feedb

Auto-regressive Roots of the

Discrete Roots NaturalFrequencyReal Imaginary

0.1447 0.1394 0.2831

0.9737 -


ic - pH

25B3 0.064784B4+

0.0070485B4–------------------------------------------------

.81121B 0.0177B2+

0.32206B2 0.039298B3+ +-------------------------------------------------------------------

a3t

X3t


Block Diagram for CaustTransfer Function

0.49099– 0.35309B 0.45234B2– 0.177+ +

1 0.93744B– 1.1084B2 0.60779B3–+

-----------------------------------------------------------------------------------------------------------

1 0.55015B– 1.0992B2 0.19358B3+ +

1 0.93744B– 1.1084B2 0.6078B3– 0.0070485B4

–+----------------------------------------------------------------------------------------------------------------------------------

a1t

X1t - Caustic added to the cutting fluid systemX3t - pH value of the cutting fluid system

a3t - Noise incorporated in system pH measurementsa1t - Noise incorporated in added caustic measurements

0.26915B 0.43019B2– 0.19714B3+

1 1.263B– 0.32206B2 0.039298B3+ +-----------------------------------------------------------------------------------------------

1 0–

1 1.263B–----------------------------

X1t


ration

el for Oilsystem

l for Added Oil -eedback)Model:

DampingRatio

-

0.03495

-


Added Oil - Oil ConcentRelation

• EARMA(4,4,3) is an adequate modConcentration - Added Oil relation (dynamics)

• EARMA(2,2,1) is an adequate modeOil Concentration relation (system f

Auto-regressive Roots of the

Discrete Roots NaturalFrequencyReal Imaginary

0.2301 -

0.3661 0.8870 0.1878

0.9923 -


Oil - Oilunction

2

--

1.4445B2 0.55097B3–

42B2 1.2928B3– 0.21023B4+

---------------------------------------------------------------------------

a4t

X4t


Block Diagram for Added Concentration Transfer F

5.9598– 3.9815B 0.3437B+ +

1 0.25183B– 0.086716B2+----------------------------------------------------------------------------

1 0.1847B–

1 0.25183B– 0.086716B2+--------------------------------------------------------------------

a2t

X2t - Oil added to the cutting fluid systemX4t - Oil concentration of the cutting fluid system

a4t - Noise incorporated in oil concentration

0.044183B 0.045193B2– 0.047433B3 0.012994B4

–+

1 1.9546B– 2.0442B2 1.2928B3– 0.21023B4+ +

-------------------------------------------------------------------------------------------------------------------------------------

1 1.311B +–

1 1.9546B– 2.04+-----------------------------------------------

X2t

a2t - Noise incorporated in added oil meas.

measurements


d Oilstem “A”

80 90 100

y

il concentrationh


Comparison of pH anConcentration Decay for Sy

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

j

G(j)

op

Time (day)

G(j)


ation andting Fluid

0 2 4 6 8 10 12 14 16 18 20−0.2

0

0.2

0.4

0.6

0.8

Comparison plot for ph and oil concentration for sys352

ph oil concentration

(system D)

Time (day)


Comparison of Oil ConcentrpH Decay for Additional Cut

Systems

0 2 4 6 8 10 12 14 16 18 20−0.2

0

0.2

0.4

0.6

0.8

1


pH oil concentration

0 2 4 6 8 10 12 14 16 18 20−0.2

0

0.2

0.4

0.6

0.8


ph oil concentration

(system B) (system C)

Time (day) Time (day)

G (

j)

G (

j)

G (

j)


Rate forstems

40 45 50

sys (A)sys (B)sys (C)sys (D)


Comparison of pH Decay Different Cutting Fluid Sy

0 5 10 15 20 25 30 35−0.2

0

0.2

0.4

0.6

0.8

1

1.2g y

G (

j)

Time (day)


ntrationystems

40 45 50

sys (A)sys (B)sys (C)sys (D)


Comparison of Oil ConceDecay Rate for Different S

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (day)

G (

j)


ions

odels and twohe cutting fluid

ated systemwell as decaycteristics in a


Summary and Conclus

• One input - one output EARMA minput - two output ARV models for tsystem dynamics were developed

• Decay rates for investigcharacteristics in one system asrates of the same system charadifferent systems were compared

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