A Correlation for Predicting the Kerf Profile From Abrasive Water Jet Cutting

Experimental Thermal and Fluid Science 30 (2006) 337–343 www.elsevier.com/locate/etfs

A correlation for predicting the kerf profile from abrasive water jet cutting C. Ma, R.T. Deam

*

Industrial Research Institute Swinburne (IRIS), School of Engineering and Industrial Sciences, Swinburne University of Technology, P.O. Box 218, Hawthorn, Melbourne, Vic. 3122, Australia

Received 20 December 2004; accepted 1 August 2005

Abstract

Abrasive water jet cutting can produce tapered edges on the kerf of workpiece being cut. This can limit the potential applic abrasive water jet cutting (AWJ), if further machining of the edges is needed to achieve the engineering tolerance required fo this study, the kerf geometry has been measured using an optical microscope. Using these measurements, a simple empirical for the kerf profile shape under different traverse speed has been developed that fits the kerf shape well. The mechanisms un formation the kerf profile are discussed and the optimum speed for achieving the straightest cutting edge is presented 2005 Elsevier Inc. All rights reserved.

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Keywords: Abrasive water jet cutting; Kerf profile; Empirical correlation

Profile cutting or contouring using an abrasive water jet is a more common cutting task than cutting in a straightline. However, the tapering of the cut edge or kerf limits beAbrasive water jet (AWJ) is the fastest growing major comes more noticeable as the local radius of curvature of machine tool process in the world [1] (Flow International the contour becomes tighter. Thus, the requirement for Corporation web site 2005). Many people in manufacturmore complicated contour processing makes it is necessary ing believe the reason for this is that the water jet equipment is extremely versatile, and quite easy to operate.to improve the performance of abrasive water jet cutting in The book by Momber and Kovacevic [2] gives a clear producing cut edges to a required tolerance. The important point is that if the final shape to be cut has a fine tolerance, explanation of the many aspects of AWJ. However, as is then the manufacturer needs to know what the kerf shape the case with every machine tool process, AWJ has some is so that the cut can be made without the need for further limitations and drawbacks. One of the common requiremachining. The kerf shape is usually described by three ments in manufacturing is to produce the cut part to the reparameters, quired engineering tolerance in a single operation. Cutting using AWJ can create tapered edges on the kerf, especially when cutting at high traverse rates. This paper examinesThe kerf width. the shape of the kerf as a function of cutting speed, so that The kerf waviness (or striations), and the best speed for the required engineering tolerance can bekerf roughness. The selected for the cutting operation. Kerf roughness is a stochastic variation of the cut surface height that increases with the depth of cut, whereas kerf waviness is a regular variation in the position of centre Corresponding author. Tel.: +61 3 9214 4339; fax: +61 3 9214 5050. E-mail address: [email protected] (R.T. Deam). line of the kerf as well as the average width of the cut. Both

1. Introduction

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0894-1777/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2005.08.003

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these phenomena have been studied by a number of Table 2 AWJ process parameters kept constant researchers as reported in Ref. [2]. It appears that there Nozzle diameter 1.33 mm have been few studies of the average kerf width as a funcAbrasive mass flow rate 3.78 g/s (0.5 lbs/min) tion of depth of cut, Arola and Ramulu [3], Guo [4]. This is Water jet pressure 310 MPa (45,000 psi) partly because there are many process parameters that afStand off distance 1 mm fect the kerf width. Thus, an experimental investigation was undertaken to correlate kerf width (as a function of cut depth) with AWJ process parameters. The work here Ten different traverse speeds were used to cut the acrylic is an attempt to gather together and present experimental The robot moved the cutting head in a straight data in a concise form that may be used to test modelssamples. of line at 0.1, 0.2, 0.5, 1.0, 1.5, 1.8, 2.5, 3.0, 4.0 and 5.0 mm/s. the kerf width (as distinct from mere correlations, which is how we have chosen to summarise our data). The form of the final correlation gives an insight into the fluid 3. Analyses of the collected data mechanics and thus the wear mechanisms that cause the Fig. 1(a)–(h) shows pictures taken under the microscope kerf width to vary with depth of cut. of the cut cross-sections for different traverse speeds. The The main process parameter varied in the cutting opershown are the full 25 mm depth of the cut, so ation is the cutting speed. In this initial study only the sections cutthe magnification is about ·6, for an A4 printout. The ting speed was varied. The water jet pressure, abrasive flow top of the cut is on the left and the bottom of the cut on rate and airflow rate were kept constant. Only one material the right. was used, acrylic plastic. Acrylic plastic is usually used as a decorative material. However, it is fragile and not easy to cut by mechanical means. On the other hand, acrylic plastic was used as our experimental material because it made the measurement easy, so that the form of the correlation could be developed and the processes that shape the kerf could be better understood. 2. Experimental

A series of water jet cutting experiments were conducted using a Flow Corporation abrasive water jet cutting system located at IRIS, Swinburne University of Technology. The intensifier pump of the water jet cutting system was capable of supplying water up to a maximum pressure of 380 MPa (55,000 psi). A six-axis robot was used to position and move the nozzle to carry out the cutting. An optical microscope was used to measure the kerf width. The kerf width was measured at different depths, thus giving the taper of the cut edge, under different traverse speed. Commercial grade Garnet was used as the abrasive material. The Garnet was sieved through a 100 mesh before use. The relevant properties of the acrylic used in the experiments are listed in Table 1 and the AWJ parameters that were kept constant during the experiments are listed in Table 2.

Table 1 Properties of acrylic Density Light transmittance Tensile strength Compressive strength Elongation Rockwall hardness Specimen thickness

1.19 · 103 kg m 3 92% 55–76 MPa (8000–11,000 psi) 76–131 MPa (11,000–19,000 psi) 2–7% ME0-100 30 mm À

Fig. 1. Optical microscope images of the kerf geometry (·6): (a)

U = 0.2 mm/s, (b) U = 0.5 mm/s, (c) U = 1.5 mm/s, (d) U = 1.8 mm/s, (e) U = 2.5 mm/s, (f) U = 3.0 mm/s, (g) U = 4.0 mm/s, (h) U = 5.0 mm/s.

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As can be seen, associated with the change of traverse1.40 speed, the shape of cutting kerf cross-section changes from 1.35 divergence to convergence. The waviness of the cut is ) apparent at high cutting speeds. This waviness is not ad-1.30 dressed here, but has been the subject of a number of other 1.25 studies [2,5–9]. 1.20 Measurements were made of the kerf width at different 1.15 depths from the optical microscope images. These measurements are shown in Fig. 2. The measurements are accurate 1.10 0.0 to 0.01 mm. The kerf profile changes with cutting speed. Cuts at low traverse speed generate a bumped divergent geometry, whereas high traverse speeds generate a convergent shape. Fig. Between cutting speeds of 1 mm/s and 2 mm/s, the kerf profile changes from divergent to convergent. The waviness or roughness of the cut profiles is also apparent from the 1.0 graphs, being more obvious at the highest cutting speeds.0.9 All the kerfs are convergent for the first few millimetres. 0.8 ) After this initial convergent region, the cross-section either 0.7 0.6 diverges at low cutting speeds or converges at high cutting 0.5 speeds. Thus there appear to be two regions to the cut and this is used to develop the correlation for the kerf width. 0.4 0.3 The same procedure is used to develop a correlation for kerf width that works for all the cutting speeds used. An 0.2 0.1 example is shown in Figs. 3–5 using the kerf shape for 0.0 2 the traverse speed of 0.1 mm/s. The form of the correlation chosen for the first 2 mm (Stage 1) of the cut depth was w

¼Aþ

B

0.5

1.0

1.5

2.0

Cut Depth (mm) Measured Width

Stage 1

3. Kerf profile for 0.1 mm/s cutting speed: Stage 1 fit.

Pearson fit 99.9%

6

10

14 18 Cut Depth (mm)

Measured Width - Stage 1 Correlation

22

26

30

Stage 2

Fig. 4. Kerf profile for 0.1 mm/s cutting speed: Stage 2 fit.

ð1 Þ

ðd þ X 0 Þ

Pearson fit 98.2%

where w is the width of the cut in mm, d is the depth ofwhere the C and D are the constants to be determined. This shown in Fig. 4. cut in mm, A, B and X0 are constants to be determined. The combined correlation is shown in Fig. 5. This is shown in Fig. 3. For the width and depth data measured for the cut a The form of the correlation for depths greater than 0.1 mm/s the best-fit data is given in Table 3. 2 mm (Stage 2) was chosen as When combining the Stages 1 and 2 correlations a Pea 2 ð 2 Þ son fit coefficient of R2 = 99.8%, is obtained. The form of w ¼ Cd þ Dd

2

U=5 mm/sec U=4 mm/sec

) 1.5

U=3 mm/sec U=2.5 mm/sec U=1.8 mm/sec U=1.5 mm/sec U=1 mm/sec U=0.5 mm/sec

1

U=0.2 mm/sec U=0.1 mm/sec

0.5 0

5

10

15

20

25

30

Cut Depth (mm)

Fig. 2. Kerf width vs depth for different traverse speed.

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C. Ma, R.T. Deam / Experimental Thermal and Fluid Science 30 (2006) 337–343 2.0 1.9 ) 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0

1.15 1.1 1.05 1

A = -0.0616Ln(x) + 0.9241 R2 = 0.9305

0.95

Pearson fit 99.8%

0.9 0

5

10

15 20 Cut Depth (mm)

Measured Width

25

30

0.85 0.8

Final Correlation

1 Speed (mm/sec)

0.1

Fig. 5. Kerf profile for 0.1 mm/s cutting speed.

Data A

Stage 1 (R 98.2%)

Log. (Data A)

Fig. 6. Correlation of A against cutting speed.

Table 3 Best fit correlation at 0.1 mm/s cutting speed Value

10

Units

0.05

2

A B X0

Stage 2 (R2 99.9%) C D

1.09 0.086 0.33

mm mm2 mm

0.041 À0.0004

mm 1

0.04 0.03

y = -0.0147Ln(x) + 0.0087 R2 = 0.9892

0.02 0.01

À

0 -0.01

the correlations for the two stages was chosen so that-0.02 they could be added, without further fitting being required. 0.1 A similar method was applied for other cutting speeds, up to 5 mm/s, and the correlation coefficients are shown Fig. in Table 4. The coefficients B and X0 were chosen to give the best fit over for all values of cutting speed used in these experiments. The values of the coefficients A, C and D vary with0.0001 cutting speed. These coefficients can in turn be correlated 0 against the cutting speed. The form of correlation chosen -0.0001 was ¼ aA LnðU Þ þ bA C ¼ aC LnðU Þ þ bC A

D

1 Speed (mm/sec) Data C

Log. (Data C)

7. Correlation of C against cutting speed.

-0.0002

ð3Þ

-0.0003

¼ aD LnðU Þ þ bD

D = 0.0001Ln(x) - 0.0002 R2 = 0.9147

-0.0004

These are plotted in Figs. 6–8.

-0.0005 0.1

1 Speed (mm/sec) Data D

Table 4 Correlation coefficients for cutting speeds between 0.1 and 5.0 mm/s Speed Value A (mm/s) 0.1 0.2 0.5 1 1.5 1.8 2.5 3.0 4.0 5.0

1.09 1.01 0.93 0.925 0.9 0.89 0.89 0.89 0.82 0.81

Value B 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086

10

Value X0 Value C 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

0.041 0.034 0.0215 0.009 À0.0001 À0.002 À0.005 À0.009 À0.011 À0.012

2 Value D R (%)

À0.0004 99.8 À0.00038 99.1 À0.00036 99.2 À0.00028 94.6 À0.00009 98.0 À0.00006 98.5 À0.00005 98.2 À0.00004 99.0 0.00002 95.2 0.00005 80.2

10

Log. (Data D)

Fig. 8. Correlation of D against cutting speed.

4. Complete correlation at fixed standoff

The complete correlation of the kerf width as a function of cut depth and cutting speed is shown below in Eq. (4), which is obtained by adding Eqs. (1) and (2). The coefficients A, C and B are a function of cutting speed and are given in Eq. (4). w

¼Aþ

0086 þ Cd þ Dd 2 ðd þ 0 33Þ :

:

ð4 Þ

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Table where w is the width (mm) of the cut at depth d (mm). A¼

5 Coefficients for cutting speed U = 0.5 mm/s

À00616 LnðUÞ þ 0 9241 C ¼ À0 0147 LnðU Þ þ 0 0087 D ¼ 0 0001 LnðU Þ À 0 0002 :

:

:

ð5 Þ

:

Standoff A (mm) [Z] (mm)

1 2 where U is the cutting speed in mm/s. 3 4 a This correlation can be used to find the kerf width as 5 function of cut depth and cutting speed when cutting ac7 :

0.93 1.04 1.17 1.23 1.4 1.66

:

B (mm2)

X0 (mm)

C

D (mm 1)

0.086 0.115 0.17 0.21 0.25 0.27

0.33 0.32 0.31 0.29 0.275 0.27

0.0215 0.016 0.009 0.0065 0 À0.0092

À0.00036 À0.00031 À0.0002 À0.00015 0 0.0002

À

rylic plastic (see Table 1), under the AWJ conditions given in Table 2. Thus knowing the tolerance required for the Table 6 final cutting edge (variation in kerf width), the maximum Final correlation coefficients speed of cut could be calculated. For example, the speed Y Y Y R that gives the straightest edge (a common requirement) can be found approximately by finding the cutting speed A 0.831752 0.0675U 0.986 B 0.061925 0.032475 at which the coefficient C = 0, since D is very small. Using X 0.3393 À0.01016 Eq. (5) this yields U = 1.06 mm/s. Using the full equation, C 0.0048(Ln[U]) 0.9927 À0.0009(Ln[U]) the kerf width can be calculated, which can be used to plan + 0.0021 Ln[ U ] À 0.0032 À 0.0211 Ln[U] + 0.0089 the nesting of the cuts and so fully utilise the materialDbe- 0.000256Ln[U] À 0.000316 À0.00003Ln[U]+0.00007 0.9943 fore starting manufacturing. 2

0

m

0.6947

À

0

2

2

U is the cutting speed in mm/s.

5. Dependence of kerf shape on standoff

ð6 Þ ¼ Y 0 þ Y mZ In practice there are two main methods of changingwhere the Y is the coefficient and Z is the standoff in mm. kerf profile, once the cutting parameters have been optiX 0 ¼ X 00 þ X 0m Z A ¼ A0 þ Am Z B ¼ B 0 þ Bm Z mised for a particular material. These are by varying the cutting speed and standoff distance. The correlation that C ¼ C0 þ Cm Z and D ¼ D0 þ Dm Z has been developed so far does not account for any alterThe results are given in Table 6. ation in standoff distance. A further series of experiments Thus the final form of the width correlation is given b were carried out to examine the effect of standoff distance B0 þ Bm Z on kerf width as a function of depth. The standoff distance þ ðC 0 þ C m Z Þd w ¼ ðA0 þ Am Z Þ þ ðd þ X 00 þ X 0m Z Þ was varied from 1 mm to 7 mm, in 1 mm steps, at constant cutting speeds of 0.5 mm/s, 1.5 mm/s, 2.5 mm/s and 4 mm/þ ðD þ D Z Þd 2 ð7 Þ 0 m s. An example of the results is plotted below, where the where Z is the standoff distance in mm, U the cutting spe cutting speed was 0.5 mm/s (Fig. 9). in mm/s and d the kerf depth in mm. These results were fitted to the same form as the correlation already developed and the coefficients, A, B, X0, CThis correlation was verified against all our experimental data. Below are plotted the worst and best cases. That and D calculated as described in the previous two sections. is the cases where our correlation matched the experiment The results are shown below in Table 5. data worst and best. The correlation has been plotted with The coefficients were measured for the other cutting error bars of ±5% (Figs. 10 and 11). speeds used in the experiments and fitted to the form: Y

;

;

;

6. Erosion mechanisms

As described above, we have divided the kerf tape formation into 2 sections. The first section is correlated by Eq. (1):

2.8 2.6 2.4 2.2

w1

2 1.8

B

ðd þ X 0 Þ

which we have called the developing flow stage Whereas, the second section uses Eq. (2).:

1.6 1.4 1.2 1

¼ Aþ

w2 0

5 df=2 mm

10 df=1 mm

15 Depth (mm) df=3 mm

20

df=5 mm

25 df=7 mm

df=4 mm

30

¼ Cd þ Dd 2

which we have called the fully developed flow stage, wh w

¼ w 1 þ w2

the kerf Fig. 9. Kerf profile for different standoff distances: cutting speed w 0.5ismm/s.

width at depth d.

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the fluid flows in pipes. Usually, near the entry to the pipe the variation of velocity across the section differs from the ‘‘fully developed’’ pattern, and gradually changes until the 1.6 final form is achieved. Fig. 12 illustrates the whole develop1.4 ing process, although the details of the development of the 1.2 boundary layer will be changed by the presence of particles 1 in the liquid. At first, all the particles (except those in contact with the wall) flow with the same velocity. That is, the 0.8 velocity profile is practically uniform across the diameter as 0.6 shown at the left of the diagram. Therefore, the cutting 0 5 10 15 20 25 30 Depth (mm) width here is wider. However, the effect of friction at the data 4 mm final correlation (±5%) wall is to slow down more and more of the fluid near the wall, so forming a boundary layer which increases in thickFig. 10. Best case fit to experimental kerf profile. ness until, ultimately, it extends to the axis of the pipe. Since the total flow rate past any section of the pipe is the same, the velocity of the fluid near the axis must inWidth v Depth Cutting Speed 2.5 mm/sec, Stand off 2 mm crease to compensate for the retardation of fluid near the 1.5 walls. This is probably why at this stage the cutting width 1.4 1.3 is becoming a little bit narrower. The shape of the velocity 1.2 profile thus changes until its final form. 1.1 Chen and Siores [6] have shown that the abrasive parti1 0.9 clesÕ kinetic energy distribution in the jet, just before 0.8 impingement on the workpiece, is not even, but a can exhi0.7 bit a peak in particle kinetic energy at about 1/3 the radius 0.6 0.5 of the jet. In other words the centre of the jet has a dip in 0 5 10 15 20 25 30 the particles kinetic energy. This distribution will change in Depth (mm) data for 2 mm final correlation (±5%) the developing flow stage. So that the fluid dynamics of the developing flow will probably depend on the abrasive parFig. 11. Worst case fit to experimental kerf profile. ticle mass flow rate as well as the water mass flow rate. A correlation covering all the variables, including abrasive particle mass flow rate and water mass flow rate, would The correlation has been constructed so that the two end up being quite complicated. However, the idea of a correlations may be added, thus sections 1 and 2 blend into developing flow region and a fully developed region seems one another. intuitively reasonable. A more useful approach might be to Some researchers divide the whole kerf wall characteriscorrelate the depth of the developing flow region for range tics into three sections called: of abrasive and water mass flow rates. 1. Initial damage region (IDR), Finally the waviness or roughness of the kerf has not 2. smooth cutting region (SCR), and been addressed here, partly because the waviness or rough3. rough cutting region (RCR). ness contributes to less than 5% of the kerf width, but mainly because the subject is worthy of a much more detailed This classification is based on the roughness of the kerf. study. From our measurements it seems that there The IDR located at the top of the kerf is due to jet are two separate components. One is where the cut has expansion prior to impingement. The SCR follows theconstant width; but waggles from side to side like a flag IDR and is a region of the kerf at the top with smooth in a breeze (see Fig. 1(h)). The other is where the width the cut varies from its expected smooth value (see walls. The wall roughness increases further down theof cut and the SCR becomes the RCR. The increasing roughness with depth can be seen in Fig. 2. This classification is a good description of the kerf. However, it does not lend itself to an immediate understanding of the processes making the cut and does not necessarily correlate with the kerf width. The correlation that has been found in this work seems e to fit a fluid dynamic dominated mechanism. The first section (Eq. (1)) applies to the kerf width as the water jet Entrance length velocity profile develops when it first enters the cut groove. The second section (Eq. (2)) applies to the kerf width when the velocity profile has fully developed. This is similar to Fig. 12. Jet velocity profile developing stage (after Massey [10]). 1.8

Width v Depth Cutting Speed 2.5 mm/sec, Stand off 4 mm

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Further work will be required to measure the correlation Fig. 2, especially for high-speed cuts at depth). Part of the coefficients for other materials, such as steel. However, we waviness of the second type could be from errors introexpect the form of the correlation to be the same. duced by the measurement, but it seems that a large component must be due to an inherent waviness of the process. This could be similar to the mechanism proposed References and modelled in Ref. [9]. Since waviness occurs in the cutting direction as well for the width, it is not unreasonable [1] Flow International Corporation. Available from: . [2] W. Momber, R. Kovacevic, Principles of Abrasive Water Jet coupling needs to be investigated further.

Machining, Springer, London, New York, 1998. [3] D. Arola, M. Ramulu, A study of kerf characteristics in abrasive 7. Conclusions water jet machining of graphite/epoxy composite, Journal of Engineering Materials and Technology 118 (1996) 256–265. The correlation for the kerf width developed in this [4] N.S. Guo, Schneidprozess und Schnittqualitat beim Wasserabrasivstrahlschneiden. VDI-Fortschritt-Berichte, Reihe 2, No. 328, work has shown that there are two regions, which we have 1994. called the developing stage and the fully developed stage. [5] Y. Chung, Development of Prediction Technique for the Geometry of The first region (the developing stage), which ends after the Abrasive Water Jet Generated Kerf, Ph.D. thesis, New Jersey about 2 mm of the cutting depth, is due to the velocity proInstitute of Technology, 1992. file of the jet changing from a uniform profile to a fully [6] F.L. Chen, E. Siores, The effect of cutting jet variation on striation developed flow in a groove. This is similar to the way the formation in abrasive water jet cutting, Journal of Materials velocity profile develops when flow enters a pipe from a Processing Technology 35 (1) (2003). [7] R. Balasubramaniam, J. Krishnan, N. Ramakrishnan, A study on the large tank. shape of the surface generated by abrasive jet machining, Journal of In the second section (the fully developed stage) which Materials Processing Technology 196 (1996). starts after about 2 mm of the cutting depth, the cutting [8] L. Chen, E. Siores, Y. Morsi, W. Yang, A study of surface striation formation mechanisms applied to abrasive water jet process, Annals width can become wider or narrower with depth, depending on the cutting speed. The kerf width opens out at lowof the CIRP (1997). [9] R.T. Deam, E. Lemma, D.H. Ahmed, Modelling of the abrasive cutting speeds and narrows down at high cutting speeds. water jet cutting process, Wear 257 (9–10) (2004) 877–891. The correlation can be used to identify the cutting[10] speed B.S. Massey, Mechanics of Fluids, Chapman & Hall, London, that produces the straightest edge. 1989.