4. C OST A NALYSIS

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4. C OST A NALYSIS

4.1 - Introduction

In the literature there are many studies on cost calculation for abrasive water jet cutting.

In order to make a prediction of the abrasive water jet cutting cost per unit length J.Zeng and T.Kim [32] developed a model that using the machinability number of materials as a parameter predicts the cutting speed as well as other process parameters.

The predicted cutting speed is then applied in a cost analysis procedure to make a cost comparison. D.A. Summers et al. [33] investigate the relative merits of different nozzle designs and compared the cutting cost when cutting with or without recycled abrasives.

M. Hashish [34] compared the cutting cost in the case of cutting with pressure of 400 and 600 Mpa taking into account many cost components such abrasives, machine maintenance, water, power and the nozzle wear. Hashish found that cutting with the pressure of 600 Mpa can save from 10 to 25 % on the cutting cost because of the reduction in abrasive consumption despite the possible increase in maintenance cost.

M.A. Hoogstrate, Vu Ngoc Pi, B. Karpuschewski [35] carried out a comprehensive study on cost optimization when cutting with multiple head: by giving a model for cost calculation the optimal values of the nozzle-exchanged diameter were found. This method is used to minimize the cutting cost; by using this approach, both the cutting cost and the cutting time can be reduced significantly. In the literature there is a lack of research on the cutting cost when cutting with recycled abrasives. Moreover, there is still no studies on the cost prediction when cutting with recycled GMA garnet.

Vu Ngoc Pi, M.A. Hoogstrate [4] carried out a comprehensive study on calculation of the cost of recycled abrasives and the total cost when cutting with new and recycled abrasives in AWJ machining. Many cost components were taken into account for both calculations. Some designing suggestions for a new effective recycling system were introduced and a procedure for comparison between recycled and new abrasives as well as between two new abrasives was proposed.

4.2 - Cost Analysis for abrasive recycling

In order to calculate the cost per mass unit of recycled abrasive the total hourly cost of the recycling process has to be taken into account. The recycling process is analyzed

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with two recycling systems from WARDjet® Inc., the WARD1© [36] and WARD2©

[37], and one recycling system from Jet Edge® [38]. The final cost of the recycled abrasive strongly depends on the reusability of the garnet abrasive. More than one AWJC setup will be taken into account for the application of all the recycling systems.

Multiplying the hourly cost by the recycling time per unit of abrasive mass (1 kilogram) we can get the cost per kilogram of recycled abrasive. From Karpuschewski [39] this cost can be defined as:

,

(

, , ,

rcl m ma h wag h w h s

C = C + C + C ) t ⋅

(4.1)

Where:

Crcl,m [€/kg] = recycled abrasive cost per unit mass;

Cma,h [€/h] = recycling machine hourly cost;

Cwag,h [€/h] = wages including overhead per hour;

Cw,h [€/h] = water hourly costs;

ts [h/kg] = recycling time per kg of abrasive;

Usually the recycling systems manufacturers furnish the recycling capability per hour:

the recycling time per kilogram of abrasive can be determined by inverting this value.

Consequently, we have:

1

s dc

t =G (4.2)

Where Gdc is the hourly recycling capability (kg/h) of the system.

To take into account the fact that sometimes there could be less abrasive to recycle than the maximum hourly capability, a working coefficient kw (≤1) have to be included.

Since it increases the cost of the recycled abrasive because the recycling machine works at the same power consumption regime, it must multiply the recycling capability. With this coefficient the cost of recycled abrasive, from 4.1 and 4.2, can be written as:

, ,

,

ma h wag h w

rcl m

w dc

C C C

C k G

+ +

= ⋅

,h (4.3)

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4.2.1 Recycling machine hourly cost

From Karpuschewski notes, the hourly fixed costs for a machine are:

, , , ,

,

de y in y ro y ma y en y

ma h

use

C C C C C

C T

+ + + +

=

^, _(4.4)

Where:

Cde,y [€/y] = annual cost of depreciation;

Cin,y [€/y] = annual cost of interest;

Cro,y [€/y] = annual cost of the occupied room;

Cma,y [€/y] = annual cost of maintenance;

Cen,y [€/y] = annual cost of energy;

Tuse [h/y] = annual time of use.

Analyzing each cost component separately:

• C_{de y}_, =C_rpl/T_tot where Crpl is the recycling system’s replacement cost (€) and Ttot the number of years of depreciation (y);

• _, ^int

in y rpl 2

C =C ⋅x where xint the annual rate of interest (1/y);

• C_{ro y}_, =C_sqm⋅A_mt where Csqm the annual room cost per squared meter (€/(m²y)) and Amt the occupied area of the machine tool in the room (m²);

• C_{ma y}_, =x_ma⋅C_rplwhere xma the annual maintenance rate (usually about 3-8 % of the replacement cost);

• where xsh the number of shifts per day, tsh the duration of one shift (h/d), dwor the number of working days per year (d/y) and xut the utilization rate (usually is about 0.7÷0.8 [39] to take into account maintenance and unwanted interruptions; for this systems a value of 0.9 can be taken into account);

use sh sh wor ut

T =x t⋅ ⋅d ⋅x

• C_{en y}_, = ⋅e P d_tot⋅ _op⋅T_use where e is the energy cost (€/KWh), Ptot (KW) the installed machine power and dop the operation duration rate that for this kind of machine is equal to 1.

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4.2.2 Wages hourly cost

This kind of machine doesn’t need a constant supervision by the operator during the recycling operation because it’s filled automatically by the patented abrasive removal system [36], which is buried on the bottom of the waterjet tank. The only operation to make is to collect the dried abrasive ready to cut, but even this operation can be easily automated. The labor and overhead costs to account to the recycling operation can be a part of the AWJC labor cost since with the recycling system there are additional savings for the AWJ cutting cost:

• Savings on labor and overhead cost since there is no need to spend a lot of time to remove the abrasive from the waterjet tank catcher. The cleaning operation can be done much less frequently and is faster;

• Savings on the utilization rate because there are less stops of the machine to clean the tank. Indeed, the recycling machine can work even while the AWJ system is working;

To consider the fraction of the wages cost to attribute to the recycling process we introduce the supervision coefficient k_{man rec}_, ≤1.

Consequently, the wages including overhead cost per hour for recycling system can be calculated as:

, , , , , ,

,

( ) ( )

wa y man rec la h ov h sh sh wor man rec la h ov h

wag h

use sh sh wor ut ut

C k C C x t d k C C

C T x t d x x

⋅ + ⋅ ⋅ ⋅ ⋅ +

= = =

⋅ ⋅ ⋅

,

c

,

(4.5)

Where:

Cla,h is the labor cost per hour (€/h) Cov,h the overhead cost per hour (€/h)

4.2.3 Water hourly cost

The cost of the water can be calculated with the following (4.6):

,

3600

w

w h w m

C = ⋅ m

ⁱ

⋅

(4.6)

Where:

mⁱ w is the water mass flow rate required (kg/s) cw,m is the cost of 1 kg of water (€/kg)

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4.2.4 Abrasive Recharging

f the brasive recycled and of the new abrasive. The following expression can be used:

The abrasive recharging is the addition of fresh abrasive to the recycled one in order to restore the same abrasive mass after the screening of smaller particles. The reusability of the abrasive is the mass fraction of the input mass that can be recycled for cutting.

The abrasive cost per unit of mass (€/kg) can be expressed as the sum of the cost o a

a m rcl a

m new m

a C r C r

C _, = _, ⋅(1− )+ _, ⋅ (4.7)

Where

w,m l cost

Crcl,m [€/kg] = cost of recycled abrasive, including recycling system’s cost

.2.5 Cost of recycled abrasive

of the machines are vailable from the website of Wardjet [36,37] and Jet Edge [38].

ARD1© system :

Cne [€/kg] = cost of new abrasive, including disposa ra [ ] = reusability of abrasive (mass fraction)

4

The cost is calculated for the recycling systems from Wardjet and JetEdge. The supervision coefficient kman,rec is very low since these machines are almost completely automatic and is estimated as the 10% of the labor and overhead cost for the AWJC system. For the WARD2©, which recycling capacity is much less than the other systems, the supervision coefficient is reduced to the 5%. The data for replacement cost of the Ward systems are taken from [4]. The other technical data

a

W

5;

=1 a Cl =

€/KWh; cw,m = 0.004 €/kg; = 0.051 kg/s; Ptot = 33 KW;

dc=81.65 Kg/h; kw = 1;

d hourly cost Input data:

Crpl = 45480 €; Ttot = 5 years; xint = 0.10; Csqm = 50 €/m²y; Amt = 8 m²; xma=0.0 xsh nd 2; tsh = 8 h/d; dwor = 250 d/y; xut = 0.9; dop=1; a,h = 20 €/h; Cov,h 15 €/h;

kman,rec = 0.10; e = 0.06 mⁱ_w

G

From equation 4.4, 4.5,4.6 we get :

Cma,h = 9.78 €/h Recycling Machine hourly cost

Cwag,h = 3.88 €/h Wages and overhea

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Cw,h = 0.73 €/h Water hourly cost

rcl,m = 0.14 €/kg Cost of 1 Kg of recycled abrasive (2 shifts) ARD2© system

From equation 4.3:

C_rcl,m = 0.18 €/kg Cost of 1 Kg of recycled abrasive (1 shift) C

W

kma ; kw = 1; e = 0.06 €/KWh; cw,m = 0.004 €/kg;

i =0.032kg/s; Ptot = 13.2 KW.

d hourly cost

w,h = 0.45 €/h Water hourly cost

rcl,m = 0.29 €/kg Cost of 1 Kg of recycled abrasive (2 shifts) et Edge system

Input data:

Crpl = 34000 €; Ttot = 5 years; xint = 0.10; Csqm = 50 €/m²y; Amt = 5 m²; xma = 0.05;

xsh=2; tsh = 8 h/d; dwor = 250 d/y; xut = 0.90; dop = 1; Cla,h=20 €/h; Cov,h = 15 €/h;

n,rec=0.05; Gdc = 22.67 Kg/h mw

From equation 4.4, 4.5,4.6 we get :

Cma,h = 4.17 €/h Recycling Machine hourly cost

Cwag,h =1.94 €/h Wages and overhea

C

From equation 4.3:

C

J

icient is reduced to 0.9 since the recycling capacity is uite high and couldn’t be filled.

0.06 €/KWh; Ptot = 33 KW; dop = 1; Cla,h=20 €/h; Cov,h = 15 €/h;

dc = 90 Kg/h; kw = 0.9;

ost Input data:

For this system the data furnished by the manufacturer are less than for the other systems but an economical comparison is still possible. The Jet Edge company furnish just the hourly cost of the machine [38], which converted in euro from dollars is about 4

€/h. In this case the working coeff q

Cma,h = 4 €/h; xsh=2; e = xut = 0.9; kman,rec = 0.10;

G

From equation 4.4, 4.5 we get :

Cma,h = 4 €/h Recycling Machine hourly cost

Cwag,h = 3.88 €/h Wages and overhead hourly c

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Cw,h = 0.8 €/kg Water hourly cost (estimate)

rcl,m = 0.11 €/kg Cost of 1 Kg of recycled abrasive (1 shift)

ed from the company is laimed to be even conservative, so should be quite reliable.

arameter’s influence From equation 4.3:

C

From the previous analysis the most effective system seems to be the one from Jet Edge, which hourly machine cost is a half of the WARD1© with a drying capability that is even more. The data of the hourly machine cost furnish

c P

e same company,

and the influence of this parameter can be seen in e graph below for all the systems.

From company to company and even just for different set-ups in th there are some data the can change and is not possible to generalize.

One of the most important for the recycled abrasive cost is the hourly wages and overhead cost and, by choosing a range from 2 to 12 €/h, the variation of the cost of 1 kg of recycled abrasive is calculated

th

Wages influence on recycled abrasive cost

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40

2 3 4 5 6 7 8 9 10 11 12

(€/kg)

Ward1 - 1 shift Ward 1 - 2 shifts Ward 2 - 2 shifts Wages & overhead cost (€/h)

Jet Edge - 1 shift

Fig 4.1: Influence of wages and overhead cost on the recycled abrasive cost

shifts; the WARD2© system must be used on two shifts to get profit from the recycling.

As we can see, the recycling cost of the WARD1© is always lower than WARD2©.

From this analysis seems that the recycling capability of WARD2© is not enough for its replacement cost and the recycled abrasive cost is too high with that system, even with low wages costs. For both systems the cost is reduced if the machine works on two daily

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As expected, the Jet Edge system is the most effective recycling system from this comparison.

Another important parameter that affects the effectiveness of recycling is the working coefficient kw, that is the ratio between the abrasive that is actually dried and the maximum drying hourly capacity. This kind of machine should be used on its maximum recycling capability to get profit from the abrasive recycling. The influence of this parameter is hyperbolic on the cost and is shown in the next graph.

Influence of working coefficient on recycled abrasive cost

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

0,5 0,6 0,7 0,8 0,9 1

Working Coefficient

(€/Kg)

Ward1 -1 shift Ward 1 - 2 shifts Ward 2 - 2 shifts Jet Edge - 1 shift

Fig 4.2: Influence of working coefficient on the cost of recycled abrasive

As we can see the influence of the working coefficient is strong even for small changes and for this reason it is very important for the recycling system to work at its maximum hourly capacity. This is particularly true for the Ward2 system that needs very high working coefficients to allow money savings.

Of the same importance of the working coefficient is the influence of the hourly recycling capability that must be high compared to the replacement cost of the machine.

4.2.6 Cost of recharged abrasive

We consider a cost of 0.4 €/kg for the new garnet abrasive including disposal.

Obviously the cost of recharged abrasive strongly depends on the reusability of abrasive after cutting. The relationship, as we can guess from the equation 4.7, is linear.

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Recharged Abrasive Cost (€/kg)

0,15 0,20 0,25 0,30 0,35 0,40

10 20 30 40 50 60 70 80

Reusability (%)

€/kg

Ward1 Ward1 (2 shifts) Ward2 (2 shifts) Jet Edge

Fig 4.3: Influence of abrasive reusability on the cost of recharged abrasive

As we can see from the picture 4.3 the Ward2 must work on 2 shifts to be effective (otherwise the cost of recharged abrasive is 0.4) while for the Ward1 the influence of the number of shifts is quite weak. With an expected value of reusability of about 40%

at least the 25% on abrasive cost can be saved.

4.3 - Cost analysis for Abrasive Water Jet cutting

4.3.1 Cost Model

To prove the effectiveness of the abrasive recycling the overall abrasive water jet cutting cost have to be calculated. From [..] and [..] a cost model has been developed to calculate the hourly cost of the process. The manufacturing single cost per piece is defined as:

sin _s

(

_{mt h}, _{wag h}, var,_h

)

C = ⋅ t C + C + C

(4.8)

Where the symbols means:

Cmt,h [€/h] = machine tool hourly cost

Cwag,h [€/h] = wages including overhead per hour

Cvar,h [€/h] = variable hourly costs (tool wear, energy, water,abrasive) ts [h] = manufacturing time

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To have the hourly cost of the abrasive water jet cutting we have to divide the (4.8) by the manufacturing time, obtaining:

(4.9)

, , va

h

(

mt h wag h

C = C + C + C

_r,_h

)

Machine Tool hourly cost

As already defined in (4.4), the machine tool cost is defined as:

, , , ,

,

de y in y ro y ma y en y

mt h

use

C C C C C

C T

+ + + +

=

^, _(4.10)

Where Cde,y is the annual cost of depreciation (€/h); Cin,y is the annual cost of interest (€/y); Cro,y is the annual cost of the occupied room (€/y); Cma,y is the annual cost of maintenance (€/y) and Tuse the annual time of use (h/y). Analyzing each single cost component:

C_{de y}_, =C_rpl/T_tot with Crpl is the AWJ system’s replacement cost (€) and Ttot the number of years of depreciation (y);

_, ^int

in y rpl 2

C =C ⋅x with xint the annual rate of interest (1/y);

C_{ro y}_, =C_sqm⋅A_mt with Csqm the annual room cost per squared meter (€/(m²y)) and Amt the occupied area of the machine tool in the room (m²);

C_{ma y}_, =x_ma⋅C_rplwith xma the annual maintenance rate (usually about 3-8 % of the replacement cost);

with xsh the number of shifts per day, tsh the duration of one shift (h/d), dwor the number of working days per year (d/y) and xut the utilization rate (usually is about 0.7÷0.8). When cutting with multiple heads it decrease because of the increasing of the time for changing nozzles. It can be calculated with the following equation:

T =x t⋅ ⋅d ⋅x

(0.7 0.8) ^f

ut cn

f

x n

= ÷ −t ⋅L (4.11)

with tcn the time for changing a nozzle (h), the number of jet formers (cutting heads) and Lf the nozzle lifetime (h). Since there is a increase in the utilization

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rate due to the less frequent need to clean the AWJ tank catcher, the value to choose in order to calculate the xut can be 0.85.

C_{en y}_, =T_use⋅ ⋅e P d_tot⋅ _opwith e the energy cost (€/KWh), Ptot (KW) the installed machine power and dop the operation duration rate (from [35] for AWJC 0.3).

Wages including overhead cost per hour

Since the AWJ cutting system and the recycling system share this kind of costs, the labor costs for AWJC are reduced (as explained in par.4.2.2), and to consider the fraction of the wages cost to attribute to the AWJC system we introduce the coefficient

. To include even the opportunity of completely unmanned shifts, another coefficient must be included:

, 1

man awjc man rec

k = −k _,

msh msh

sh

k x

= x (4.12)

where xmsh is the number of manned shifts per day.

Consequently, the wages including overhead cost per hour can be calculated:

, , , ,

,

, , ,

( )

wa y msh man awjc la h ov h sh sh wor

wag h

msh man awjc la h ov h

ut

C k k C C x t d

C T x t d x

k k C C

x

⋅ ⋅ + ⋅ ⋅ ⋅

= =

⋅ ⋅ ⋅

⋅ ⋅ +

=

h

(4.13)

Where:

Cla,h [€/h] is the labor cost per hour;

Cov,h [€/h] the overhead costs per hour;

Variable hourly costs

The variable costs depend directly from the specified manufacturing task and influence just it:

var,h or h, f h, w h, a,

C = C + C + C + C

(4.14)

Where:

Cor,h [€/h] = cost of orifices per hour Cf,h [€/h] = cost of nozzles per hour Cw,h [€/h] = cost of water per hour Ca,h [€/h] = cost of abrasive per hour

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C_{or h}_, =n C_f ⋅ _{or p}_, /L_or with Cor,p is the orifice cost per piece (€) and Lor the orifice lifetime;

_{f h}_, ^f ^{f p}^,

f

C n C L

= ⋅ with Cf,p the nozzle cost per piece (€) and Lf the nozzle lifetime

(h);

w _W_mwith m^•w abrasive mass flow rate (Kg/s/jet former) and CW,m the water cost per kg (€/kg). By using the Bernoulli’s equation is possible to calculate the water mass flow rate as:

f h

w n m C

C _, =3600⋅ ⋅ ^• ⋅ _,

w d w

w or

w p

d c

m ρ

ρ π⋅ ⋅ ⋅ ^⋅

⋅

• = 2

4

2

(Kg/s) with pw is the waterjet pressure, dor is the orifice diameter, ρw the water density and cd an experimentally determined discharge coefficient (cd ≈ 0.6÷0.8).

⋅ ⋅m Cⁱ_a _{a m}_, with Ca,m abrasive cost per unit mass (€/Kg) and abrasive mass flow rate (Kg/s).

, 3600

a h f

C = ⋅n mⁱ a

4.3.2 Specific cutting cost

In order to compare the cutting cost for different tasks and cutting speeds, usually the specific cutting cost (the cost per squared meter of material cut) is used. It is defined as:

2

60

max h m

c

C C

v h k

= ⋅ ⋅ ⋅

(4.15)

When cutting with multiple cutting heads, the formula must include even the number of cutting head:

2

60

max

h m

c f

C C

v h k n

= ⋅ ⋅ ⋅ ⋅

(4.16)

Where:

Ch [€/h] = hourly cost of AWJC from (4.9) v [m/min] = feed rate;

hmax [m] = maximum depth of cut achievable with new abrasives;

kc [ ] = cutting performance coefficient of recycled abrasive;

nf [ ] = number of cutting head of the machine.

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kc is a coefficient which take into account the different performance of recycled abrasive respect to the new one. By means of this coefficient the cutting cost per squared meter take into account even the cutting performance of the abrasive. For this cost analysis the value taken into account, from [2], is 0.95 for recharged abrasives, with a reusability of 50%.

4.3.3 Recycling comparison

If we want to compare the effectiveness of abrasive recycling on different AWJC set- ups we have to calculate the maximum allowable cost for the recycled abrasive, given a constant specific cutting cost. We can define the “other costs” as:

*

, , va

oth mt h wa h h

C =C +C +C _r,

h

(4.17)

Where the symbols have the same meaning of (4.9) except for the variable costs that for this aim are defined as:

*

var,h or h, f h, w,

C = C + C + C

(4.18)

In this way, the specific cost can be rewritten separating the abrasive cost from the other costs:

2

,

60

max

oth a h

m

c f

C C

C v h k n

= +

⋅ ⋅ ⋅ ⋅

(4.19)

From (4.19) we can directly extract the abrasive hourly cost:

, 2 60 max

a h m c f oth

C =C ⋅ ⋅ ⋅v h ⋅ ⋅k n −C (4.20)

The more interesting recharged abrasive cost per kilogram is deduced from the following expression:

,

, 3600

a h a m

f a

C C

n m^•

=

⋅ ⋅ (4.21)

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This is the cost of abrasive per unit mass, doesn’t matter if new or recharged. Since we want to look to the maximum recycled abrasive cost, it comes from the inversion of the (4.7):

a

m new a

m a m

rcl r

C r

C _, C ^, +( −1)⋅ ^,

= (4.22)

Combining (4.22),(4.21) and (4.20) we get the equation to calculate the maximum allowable recycled abrasive cost:

2 max

, ,

60 ( 1)

3600

c f oth

m

a ne

f a rcl m

a

C v h k n C

r C

C n m

r

• w m

⋅ ⋅ ⋅ ⋅ ⋅ −

+ − ⋅

⋅ ⋅

= _(4.23)

The important parameters of this analysis are the number of focusing nozzles nf, the cost of new abrasive (including disposal) Cnew,m, the reusability of abrasive ra and the performance coefficient of recharged abrasives kc.

4.3.4 Results and discussion

4.3.4.1 AWJC specific cost

The cutting parameters included in this analysis have been chosen with the program from Resato BV [40]. Two systems are considered, related to the recycling machine used:

Crpl = 300000 €; Ttot = 5 y; xint = 0.10; Csqm = 50 €/m²y; Amt = 35 m²; xma = 0.06; xsh = 2;

tsh = 8 h/d; dwor = 250 d/y; xut = 0.841; e = 0.06 €/KWh; Ptot = 90 KW; dop = 0.3; tcn = 0.15 h; nf = 4.

From (4.10) Cmth,h = 29.77 €/h Wages and overhead Cost:

Cla,h = 20 €/h; Cov,h = 15 €/h; kman,awjc = 1- kman,rcl = 0.90; kmsh = 1.

From (4.13) Cwa,h = 37.44 €/h

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Variable Costs:

Cor,p = 12 €; Lor = 40 h; Cf,p = 70 €; Lf = 70 h; Cw,m = 0,004 €/kg; ρw = 1000 Kg/m³; dor = 0.255 mm; cd = 0.7; pw = 360 Mpa; mⁱ_a= 7 g/s;

Taking into account an average reusability of 50% for this cutting regime, from 4.7 or Fig.4.3 we get the following results for the abrasive cost:

Jet Edge ® system on 1 shift Ca,m = 0.26 €/Kg From (4.14) Cvar,h = 28.01 €/h

From (4.9) the total hourly cost is:

Crpl = 200000 €; Ttot = 5 y; xint = 0.10; Csqm = 50 €/m²y; Amt = 25 m²; xma = 0.06; xsh = 2;

tsh = 8 h/d; dwor = 250 d/y; xut = 0.846; e = 0.06 €/KWh; Ptot = 38 KW; dop = 0.3; tcn = 0.15 h; nf = 2.

From (4.10) Cmth,h = 19.38 €/h Wages and overhead Cost:

Cla,h = 20 €/h; Cov,h = 15 €/h; kman,awjc = 1- kman,rcl = 0.95; kmsh = 1.

From (4.13) Cwa,h = 39.32 €/h Variable Costs:

Cor,p = 12 €; Lor = 40 h; Cf,p = 70 €; Lf = 70 h; Cw,m = 0,004 €/kg; ρw = 1000 Kg/m³; dor = 0.255 mm; cd = 0.7; pw = 360 Mpa; mⁱ_a= 7 g/s;

Taking into account an average reusability of 50% for this cutting regime, from (4.7) or Fig.4.3 we get the following results for the abrasive cost:

From (4.9) the total hourly cost is:

In order to make a comparison between the systems (not possible by comparing the hourly cost) the cutting parameters are the same for both:

v = 100 mm/min; hmax = 56.3 mm; kc = 0.95;

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The results of the AWJC specific cost calculation with (4.19) are in the graph below:

AWJC specific cost - Reusability 50 %

83,74

76,66

120,24

74,24

50 60 70 80 90 100 110 120 130

NO RCL WARD1 WARD2 JETEDGE

Recycling Sys

€/m^2

Fig 4.4: AWJC specific cost with and without abrasive recycling

As we can see, with this set-ups, a reusability of 50% and a cutting performance coefficient of 0.95 for the recharged abrasives, the abrasive recycling seems economically effective just with the WARD1© and Jet Edge system. In fact, the percentage of saving on AWJC specific cost is 8.4 % with WARD1© and 11.3 % with JetEdge system. The fact that the WARD2© system results not effective on the specific cost comparison is due to the fact that the saving on the abrasive cost (12%) is not enough to make up for the decrease of cutting performance of the recharged abrasive respect to the new one. Another reason is that with a system of 2 cutting head the influence of the abrasive cost on the overall AWJC cost is much less than with 4 cutting heads and the savings on abrasive have less influence on the total cost. In the two following graph we can see the percentage of each cost component for the two set-ups taken into account.

Influence on overall AWJC cost - 4 heads

ABRASIVE 35,2%

WAGES 32,7%

MACHINE 26,0%

WATER COMP. 1,5%

4,5%

Influence on overall AWJC cost - 2 heads

ABRASIVE 24,5%

WAGES 47,8%

MACHINE 23,6%

WATER 1,0%

COMP.

3,2%

Fig 4.5 – The influence of each cost component on the total cost, for 2 set-ups

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The reusability and the cutting performance are very important data to know since, as we can see in the following graph the effect is linear for the reusability and is a vertical translation for the performance coefficient that affects the specific cost very much.

AWJC specific cost with WARD1

60 65 70 75 80 85 90 95

20 25 30 35 40 45 50 55 60 65 70 75 80

Reusability (% mass)

(€/m^2)

Kc=1.1 Kc=1.05 Kc =1 Kc=0.98 Kc=0.95 Kc=0.90 Kc=0.85

Fig4.6: AWJC specific cost (per squared meter)

4.3.4.2 Influence of abrasive cost on AWJC cost

Another important aspect to take into account is the new abrasive cost: as told before, the GMA garnet is widely used across Europe for its low cost, about 0.2 ÷ 0.4 €/Kg.

Instead, across US, the Barton garnet is more released, even for its cutting performance that it’s claimed to be better than GMA. The cost of Barton garnet vary from 0.7 up to 1

€/Kg and this leads to the importance of abrasive recycling. As we can see in the graph from Fig. 4.7, the influence of the abrasive cost on overall AWJC hourly cost can reach values of almost 60% with more expensive abrasives. When the abrasive cost reach so high values the savings are much more since the cost of recycled abrasive is always the same; for instance, recycling with WARD1© system on a 4 cutting heads set-up, the saving on overall AWJC specific cost is about 18% instead of just 8% with the GMA price.

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% of influence of abrasive on overall AWJC cost

0 10 20 30 40 50 60 70

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Abrasive Cost (€/kg) 2 cutting heads

4 cutting heads

Fig4.7: Influence of abrasive cost on overall hourly cost

4.3.4.3 Influence of set-up costs

A way to show the influence of different set-ups (with different hourly cost) is to calculate the maximum allowable recycled abrasive cost given a certain value of the other costs (4.17) by keeping constant the specific cost (cost per squared meter). If the recycled abrasive costs more than the value in the graph, the company can’t get any profit from recycling. This values is the threshold to evaluate the effectiveness of abrasive recycling. The specific cost taken as reference is the one calculated with the same parameters but without recycling. The parameters of the analysis are:

Nf - number of cutting heads

Ca,new – cost for 1 kg of new abrasive Ra – average reusability of abrasive

Kc – cutting performance coefficient for recharged abrasive

Some meaningful, for GMA garnet recycling, examples of calculations with the equation (4.23) of the maximum allowable recycled abrasive cost are shown in the figures below:

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Maximum recycled abrasive cost

Cutting Heads: 4, Reusability: 40%, Ca,new= 0.4 €/kg

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00

40 45 50 55 60 65 70 75 80 85 90 95 100

Other Costs (€)

Max.Recyled Abr.Cost (€/kg)

Kc=1.1 Kc=1.05 Kc=1 Kc=0.98 Kc=0.95 Kc=0.90 Kc=0.85

Fig4.8: Maximum recycled abrasive cost: 4 cutting heads, Ca=0.4 €/kg, ra = 40%

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

40 45 50 55 60 65 70 75 80 85 90 95

Kc=1.1 Kc=1.05 Kc=1 Kc=0.98 Kc=0.95 Kc=0.90 Kc=0.85

Fig.4.9: Maximum recycled abrasive cost for 4 cutting heads, Ca=0.4 €/kg, ra = 50%

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0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00

40 45 50 55 60 65 70 75 80 85 90 95 100

Kc=1.1 Kc=1.05 Kc=1 Kc=0.98 Kc=0.95 Kc=0.90 Kc=0.85

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00

40 45 50 55 60 65 70 75 80 85 90 95 100

Kc=1.1 Kc=1.05 Kc=1 Kc=0.98 Kc=0.95 Kc=0.90 Kc=0.85

As we could expect, the influence of machine, consumables and wages costs (other costs) is very strong in the case of 2 cutting heads setup and in fact the slope of the lines is much more than in the graphs for 4 cutting heads. As we can see from all the graph the cutting performance coefficient is very important.