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High Performance Cutting with Abrasive Waterjets beyond 400 MPa
High Performance Cutting with Abrasive Waterjets beyond 400 MPa A.M. Hoogstrate 1, T. Susuzlu 1, B. Karpuschewski 2 (1) Precision Manufacturing and Assembly, Delft University of Technology, The Netherlands 2 Institute for Manufacturing Technology and Quality Management, University of Magdeburg, Germany 1
Abstract Abrasive waterjet (AWJ) cutting has been widely accepted by the industry after the successful introduction of 400 MPa cutting systems. This paper describes the cutting with AWJ beyond the current industrial pressure limit. Firstly, the factors that limit the water pressure are discussed. Secondly, the jet formation is considered by addressing the effects of the geometry of the upstream tube and the orifice. Finally, the AWJ cutting process is described in terms of energy transfer efficiency. There is an optimum abrasive load ratio over which the cutting ability of the jet decreases due to the less efficient power transfer from waterjet to the abrasives. Keywords: Abrasion, Cutting, Waterjet
1 INTRODUCTION Abrasive waterjet (AWJ) cutting is a technique for separating materials by means of a high-velocity slurry jet, formed as a result of injecting abrasive particles to a waterjet ejected by an orifice. The main advantages of the AWJ machining process are being able to cut versatile geometries and its ability to cut both ductile materials like aluminum, brass, steel and titanium and brittle materials like glass, stone and ceramics without any influence on their microstructure [1]. The water pressure, combined with the water flow rate defines the ability of the AWJ, since both factors define the maximum available power of the abrasive-water mixture. Since the successful introduction of pure waterjet cutting around 1970 and the introduction of abrasive waterjet cutting in 1983 [2], the maximum pressure of the industrial available systems has been limited to 400 MPa. Increasing the pressure beyond its current limit may have the following advantages: • • •
Increased cutting speeds or depths of cut. Increased efficiency. Reduced abrasive usage, reducing the cost.
This paper presents the applicability and the advantages of the AWJ cutting process beyond 400 MPa. The factors that define the possibilities of pressure increase are the endurance of the components subjected to high alternating stresses and the solidification of water at ultra high pressures. After ensuring the quality of the jet, the AWJ cutting process is described in terms of energy flow, stressing the advantages of water pressures beyond 400 MPa. 2
DEFINING THE LIMIT PRESSURE
2.1 Components under hydraulic loading In waterjet cutting systems, components subjected to the high pressure need special attention in designing and manufacturing. The failure of parts like the sealing of the intensifier is predictable while others like the high pressure (HP) cylinder, the HP tubing, the check valve and the
Annals of the CIRP Vol. 55/1/2006
upstream tube may fail suddenly and catastrophically (Figure 1). Monobloc cylinders without residual pre-stresses have limited pressure bearing capacities. Pressurized monobloc cylinders start to yield at pressures slightly higher than half of their yield strength value according to Lame’s equations, even when the cylinder has infinite thickness (Figure 2). Knowing that the yield strength of the suitable construction materials does not exceed 1100 MPa, the maximum allowable water pressure is, with some safety margin, limited to 400 MPa. Attenuator
Attenuator
HP cylinder
Water supply
Upstream tube Hydraulic pump
Check valve
Figure 1: AWJ cutting system with two double acting pressure intensifiers. Compressive residual stress imposed to the bore of the cylinder reduces the operating tensile stresses, thus increasing the pressure capacity of the cylinder. Both autofrettage and multi-layer cylinder construction are well known methods to create residual compressive stress. In autofrettage, the part is deformed plastically by applying internal pressure. When this pressure is removed, the elastic recovery of the outer sections of the cylinder causes tangential compressive residual stress in the bore. In multilayer cylinders, the inner cylinder is shrink-fitted to the jacket cylinder. The jacket exerts pressure to the outer surface of the inner cylinder, which causes tangential compressive stress at the bore. In both cases re-yielding of the bore, due to the Bauschinger effect, should be avoided since it reduces the
AISI S15500 H1100 Stainless Steel
Yielding pressure
800
pa= 1000 MPa
700 MPa
pa= 800 MPa pa= 600 MPa
600 500
pa= 0 MPa
400 300 1
2
3
4 5 6 Diameter ratio
7
8-
9
Elastic modulus = 196.5 GPa Yield strength = 793 MPa Tensile strength = 965 MPa Poisons’ ratio = 0.27 Figure 2: Pressure capacity of thick-walled cylinders. 2.2 Phase equilibrium of water Another limiting factor to increase the water pressure indefinitely is the solidification of water at room temperature at very high pressures. Ice I (Figure 3) is the natural ice which is formed at atmospheric pressure. All the other types of ice are observed at higher pressures than the atmospheric pressure. Ice VI is important for AWJ applications above 400 MPa. The equation of the boundary line for ice VI can be found in Figure 3 where pice_VI is the solidification pressure at temperature T [4].
Pressure
104 MPa
Ice V
pice_VI
2
10
p1
1
10
0
Ice I 250
Ice VII
Ice VI
Ice III
⎛ ⎛ ⎞ 4.6 ⎞ T ⎜ ⎟ = 1 − 1.07476 ⋅ ⎜1 − ⎜⎜ ⎟⎟ ⎟ ⎜ ⎝ T1 ⎠ ⎟ ⎝ ⎠
Liquid
p1= 632.4 MPa T1= 273.1 K
300 K Temperature T
400
Figure 3: Phase diagram of water. If the inlet water temperature is assumed to be 293 degrees K, it starts to solidify when the pressure exceeds 894 MPa. However, the temperature of water increases due to the adiabatic compression of the water. It is
estimated that the temperature raises 3 degrees K for every 100 MPa increase [5]. Therefore the solidification pressure at 293 degrees K increases to 1317 MPa. Furthermore, the friction in between the water and the components also causes a temperature rise, which further increases the solidification pressure of water. However, the pressurized water is stored while the cutting operation is temporarily stopped. During this period, there is a risk of solidification since the water may cool down to the room temperature. 3 TEST SETUP AND PROCEDURE The pressure unit is a two-stage double acting intensifier with a maximum design pressure of 800 MPa. The intensifier is connected to a cutting head by a series of tubing with an internal diameter of 1.6 mm and an external diameter of 9.5 mm. The final section of the tubing is spiral to allow the movements of the cutting head. The cutting head is manipulated by a SCARA robot. There are two buffer volumes in the system. The first one has a capacity of two liters and is located after the initial intensifier. The second one lies after the final intensifier and its capacity is 1 liter. They limit the pressure fluctuations to 1% for an orifice diameter do of 0.1 mm at 700 MPa [6]. Research has shown that the tube prior to the orifice affects the jet quality as well since it reduces the upstream turbulences by acting like a reservoir [7]. The diameter of the tube should be large enough to promote laminar flow and the length of the tube should be long enough to let the flow be fully developed. Therefore, all the tests were conducted with a longer (212 mm) than usual (100 ~ 150 mm) upstream tube with a large inner diameter (3.5 mm) to decrease the initial level of turbulence in the flow. The jet former is mounted to a strain-gage device to measure the reaction force or back thrust of the jet. The material that has been cut is an AISI 304 stainless steel; garnet abrasive of mesh 150, with an average grain size of 100 µm, is used throughout the experiments. 4 JET FORMATION It is important for a waterjet to maintain its kinetic energy for an appreciable distance. However, the jet breaks down in the downstream and its kinetic energy is divided among small droplets. A scattered jet generates wider cuts with wider damaged zones and rounded edges. In AWJ applications a scattered jet will accelerate the wear of the entry region of the focusing nozzle and will show a poor behavior in accelerating the abrasive particles. Most efforts to obtain coherent jets are focused on the orifice geometry [8]. The edge condition (sharp, rounded or chamfered) and the orifice geometry (cylindrical, coneup or cone-down) are key parameters. In this study, jet coherency is determined in terms of its doubling length, defined as the length of the jet until its diameter becomes twice the diameter of the orifice do. The doubling length is determined by image analysis of over-exposed photos of the jet. The over-exposure is applied to increase the contrast between the jet and its surroundings. Three different types of orifices are used (Figure 4). Doubling length
final pressure capacity of the cylinder. The residual stress improves the fatigue life of the components as well by reducing the mean stress [3]. Increasing the water pressure in two sequential steps also reduces the mean stress of the cylinder. With a two-stage intensifier, the initial intensifier boosts the pressure to an intermediate value, e.g. 400 MPa; then the water reaches its ultimate pressure by the final intensifier. A finite element analysis has been carried out to find the residual stresses due to autofrettage. A bilinear kinematic hardening material model with plane strain is applied since it is capable of handling the Bauschinger effect. Then, the new initial yielding pressure is calculated by using Lame’s equations and the Von Mises failure criterion. The results are presented in Figure 2. For constant material thickness, the process becomes less efficient with increase of the autofrettage pressure pa. The re-yielding of the bore counteracts the benefits of further pressure increase. Increase of the thickness of the cylinder is not a solution since the performance of the cylinder does not improve proportionally with the thickness. Therefore, multi-layer constructions with a combination of a hard and strong inner cylinder and a tough and lighter jacket should be implemented.
Type 1 Conical seal Sharp edge
Type 2 Flat seal Sharp edge
Type 3 Flat seal Round edge
Figure 4: Photos of a jet and of the orifices used.
10 10
Type 2
55
Type 3
00 300
350 350
4 0 0 450 450 5 0 0 MPa 550 ssu re WaterP re pressure pw
600
650 650
Figure 5: Jet coherency of different orifices. 5
AWJ CUTTING PROCESS
5.1 Energy transfer efficiency In AWJ applications, abrasive particles are entrained in the mixing chamber of the jet former and accelerated by the pure waterjet. Only a part of the available kinetic energy of the water is transferred to the particles in this mixing process [9]. The impulse balance equation is used to determine the amount of energy transfer to the abrasive particles:
(m& w + m& a + m& air ) ⋅ v awj
(
)
& w ⋅ vwj + m & a ⋅ va + m & air ⋅ v air (1) =η m
&w , m & a and m & air are the mass flow rates and vwj, where m va and vair are the initial velocities of water, abrasive and air respectively, vawj is the velocity of the abrasive jet and η is the momentum transfer efficiency. The abrasive load ratio R is defined as the ratio of mass flow rate of abrasive and water:
R=
&a & &a m m m = a = &w m q& ⋅ ρ (c d ⋅ Ao ⋅ v wj ) ⋅ ρ
(2)
where q& is the volumetric water flow rate, ρ is the density of water, cd is an orifice specific discharge coefficient and Ao is the cross sectional area of the orifice. Under the assumption that the final velocity of the abrasive particles and water is equal, which is valid when the focusing tube is sufficiently long, and by neglecting & air ; vawj can be written as: both va and m
v awj = η ⋅
1 ⋅ v wj 1+ R
(3)
The momentum transfer efficiency η expresses the momentum losses due to the interactions of the abrasives and water with the walls of the mixing chamber and focusing tube, and due to the fragmentation of the particles. The momentum transfer efficiency can be expressed as:
η=
&w + m & a ) ⋅ v awj Fawj (m = & w ⋅ v wj m Fwj
(4)
= η2 ⋅
R
(5)
(1 + R )2
where µ is the power transfer efficiency, Pa and Pwj are the power of the abrasives and the waterjet respectively. If η was independent of R, the power transfer efficiency would reach its maximum when R equals to unity. However, experiments show that the momentum transfer efficiency strongly depends on both abrasive load ratio and jet former geometry (Figure 6). Combinations of smaller orifice diameters do and focusing tube diameters df tend to have a lower momentum and power transfer efficiency which points out an alignment problem of orifice and focusing tube. As shown in Figure 6, the optimal power transfer efficiency is located around R-ratios of 0.3. Overloading of the jet by higher R-values will not only decrease the momentum transfer efficiency, but also deteriorate the abrasive jet structure itself, indicating a major change in flow conditions. Therefore the cutting theory developed is only valid up to the maximum power transfer efficiency. 0.25
ηideal μideal
1.0
0.20 -
0.8 -
0.15
ηmeasured
0.6 0.4
0.10
μmeasured
0.2
do= 0.12 mm df = 0.5 mm
0.0 0.0
0.05
do= 0.2 mm df = 0.8 -mm
0.1 0.2 0.3 0.4 Abrasive load ratio R
0.5
Power efficiency μ
Type 1
15 15
1 ⋅m & a ⋅ v 2 awj 2 1 ⋅m & w ⋅ v 2wj 2
0.00 0.6
Figure 6: Momentum and power transfer efficiencies. 5.2 Cutting With the increase of the water pressure pw from 400 MPa to 600 MPa, the cutting maximum speed increases by 48%. If, on the other hand, the cutting speed vf is kept constant, it is possible to save 52% of the abrasive consumption while maintaining the same depth of cut with the same cutting quality (Figure 7). Material thickness 10 mm 200% do = 0.2 mm pw = 400 MPa pw = 600 MPa d = 0.8 mm f 150% 4.2 g/s
100% 50% 0%
5.2 mm/s
do = 0.175 mm
Pa = Pwj
3.5 mm/s
Doubling length
Doubling length
25 25
mm 20
μ=
Momentum efficiency η
Sharp edged orifices generate more coherent jets due to the constricted jet formation. Figure 5 shows the importance of the entry region of the orifice as well. The type 1 orifice, which has a streamlined sealing has a longer doubling length than the ones with flat seals. The smoother streamlines are directed to the orifice with less turbulence due to its inclined surface of the sealing of the type 1 orifice.
where Fwj and Fawj are the measured reaction or thrust forces of the pure and the abrasive waterjet respectively, therefore their ratio gives a direct measure of the momentum transfer efficiency. The amount of power transferred to the abrasives depends on the momentum transfer efficiency and the abrasive load ratio:
Change in vf and abrasive consumption
Types 1 and 2 have sharp edges and type 3 has a rounded edge. The type 1 has an inclined sealing surface towards the orifice which promotes smoother streamlines. All orifices have cone down geometries.
Cutting speed vf 1 & a = 4.2 g/s) (m
2.0 g/s
Abrasive consumption 2 (vf = 3.5 mm/s)
Figure 7: Example of the improvement in cutting speed or reduction of abrasive usage.
The experimental power transfer efficiency showed an optimum at R-ratio’s around 0.3. The cutting results validate the existence of the optimum abrasive load ratio at around 0.3 (Figure 8) independent of the water pressure. 25
vf = 2.5 mm/s
670 MPa
Depth of cut
20 mm
580 MPa
15
470 MPa
10
do = 0.15 mm df = 0.5 mm
5 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Abrasive load ratio R Figure 8: Abrasive load ratio with respect to depth of cut. This indicates that the cutting performance of the AWJ is directly related to the power of the abrasive jet. To incorporate the feed speed of the jet former relative to the workpiece in the formulation the energy density ea is defined as:
ea =
μ ⋅ Pwj ⎛⎜ π Pa = = df ⋅ v f df ⋅ v f ⎜⎝ 2 2 ⋅ ρ
⎞ μ ⋅c ⋅ p 3 2 ⋅d 2 d w o ⎟ ⎟ df ⋅ v f ⎠
(6)
In Figure 9, the relation between the energy density and the depth of cut is shown. The regressive instead of proportional behavior at higher depths of cut can be explained by increased energy losses of the jets at longer traveling lengths through the workmaterial at higher depths of cut.
Depth of cut
50
470 MPa to 670 MPa
mm 40 30 20
do = 0.12 mm df = 0.5 mm do = 0.15 mm df = 0.5 mm do = 0.175 mm df = 0.8 mm
10 0 0.0
2
kJ/mm 0.5 1.0 Energy density ea
1.5
Figure 9: Cutting ability of AWJ as a function of energy density of the abrasive. From equation (6) it is clear that the energy density can be increased by increasing the jet diameter do, however this is against the general trend towards smaller products with intricate details. The energy density can also be increased by the reduction of the feed speed vf, which conflicts with economical considerations of maximum production, or it can be increased by increasing the pressure pw. Reducing the focusing tube diameter df seems also to be an option for increasing the energy density ea. However, experiments have shown that this will also include a reduction of the orifice diameter do, to maintain a df /do ratio between 3 and 4, resulting in an overall reduction of the energy density. Simultaneously increasing the water pressure pw can theoretically compensate this effect, creating a more efficient cutting process. Higher pressures and smaller orifices result, with the same water power Pwj, in a higher energy density. Experiments have shown however, that combinations of smaller orifices and
focusing tubes result in less power transfer efficiencies (Figure 7), so the goal of increasing the energy density by using smaller jet formers at high pressures could not be achieved at this time. 6 CONCLUSIONS AND OUTLOOK The water pressure is limited by the endurance of the components and the physical properties of water at high pressures. The components that are subjected to pressures beyond 400 MPa should be autofrettaged or produced by multilayered cylinders. Due to the Bauschinger effect, there is an optimum autofrettage pressure. Increase of pressure will increase the cutting ability of the jet. The jet becomes more powerful with equal diameter. Therefore, the depth of cut or cutting speed is improved. There is an optimum abrasive load ratio over which the cutting ability of the jet decreases due to the less efficient power transfer from waterjet to the abrasives. The optimum abrasive load ratio is independent of the pressure. The miniaturization of the jet former to smaller dimensions is currently decreasing the efficiency of the jet formation process, and thereby counterbalancing the effect of higher energy densities of the pure waterjets. The development of jet formers having more accurate alignment of the orifice and focusing tube is necessary. 7 ACKNOWLEDGMENTS This research is conducted in cooperation with Resato International b.v., with financial support of the Dutch Ministry of Economical Affairs under the BTS-program. 8 REFERENCES [1] Hoogstrate, A.M., 2000, Towards High-Definition Abrasive Waterjet Cutting. Ph. D. Thesis, Delft University of Technology, The Netherlands. [2] Hoogstrate, A.M., van Luttervelt, C.A., 1997, Opportunities in Abrasive Water-Jet Machining, Annals of the CIRP, 46/2:697-714. [3] Trieb, F.H., Schedelmaier, J., Poelzl, M., 2004, Developments on Optimized Autofrettage of High Pressure Components for Waterjet Cutting Pumps, Proceedings of the 17th Int. Conf. on Jetting Technology, 7-9 Sept., Mainz, Germany, 23-32. [4] Wagner, W., Pruß, A., 2002, The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, J. Phys. Chem. Ref. Data, 31:387535. [5] Bridgman, P.W., 1970, The Physics of High Pressure. Dover Publications, Inc., New York. [6] Susuzlu, T., Hoogstrate, A. M., Karpuschewski, B., 2004, Initial Research on the Ultra-High Pressure Waterjet up to 700 MPa. J. of Material Processing Technology, 149:30-36. [7] Hashish, M., 2004, Abrasive-waterjet (AWJ) Studies, Proceedings. of the 16th Int. Conf. on Jetting Technology, 16-18 Oct., Aix-en-Provence, France, 13-47. [8] McCarthy, M.J., Molloy N. A., 1974. Review of Stability of Liquid Jets and the Influence of Nozzle Design. The Chemical Engineering Journal, 7:1-20. [9] Hoogstrate, A.M., Karpuschewski, B., van Luttervelt, C.A., Kals, H.J.J., 2002, Modeling of High Velocity, Loose Abrasive Machining Processes, Annals of the CIRP, 51/1:263-266.
Abstract Abrasive waterjet (AWJ) cutting has been widely accepted by the industry after the successful introduction of 400 MPa cutting systems. This paper describes the cutting with AWJ beyond the current industrial pressure limit. Firstly, the factors that limit the water pressure are discussed. Secondly, the jet formation is considered by addressing the effects of the geometry of the upstream tube and the orifice. Finally, the AWJ cutting process is described in terms of energy transfer efficiency. There is an optimum abrasive load ratio over which the cutting ability of the jet decreases due to the less efficient power transfer from waterjet to the abrasives. Keywords: Abrasion, Cutting, Waterjet
1 INTRODUCTION Abrasive waterjet (AWJ) cutting is a technique for separating materials by means of a high-velocity slurry jet, formed as a result of injecting abrasive particles to a waterjet ejected by an orifice. The main advantages of the AWJ machining process are being able to cut versatile geometries and its ability to cut both ductile materials like aluminum, brass, steel and titanium and brittle materials like glass, stone and ceramics without any influence on their microstructure [1]. The water pressure, combined with the water flow rate defines the ability of the AWJ, since both factors define the maximum available power of the abrasive-water mixture. Since the successful introduction of pure waterjet cutting around 1970 and the introduction of abrasive waterjet cutting in 1983 [2], the maximum pressure of the industrial available systems has been limited to 400 MPa. Increasing the pressure beyond its current limit may have the following advantages: • • •
Increased cutting speeds or depths of cut. Increased efficiency. Reduced abrasive usage, reducing the cost.
This paper presents the applicability and the advantages of the AWJ cutting process beyond 400 MPa. The factors that define the possibilities of pressure increase are the endurance of the components subjected to high alternating stresses and the solidification of water at ultra high pressures. After ensuring the quality of the jet, the AWJ cutting process is described in terms of energy flow, stressing the advantages of water pressures beyond 400 MPa. 2
DEFINING THE LIMIT PRESSURE
2.1 Components under hydraulic loading In waterjet cutting systems, components subjected to the high pressure need special attention in designing and manufacturing. The failure of parts like the sealing of the intensifier is predictable while others like the high pressure (HP) cylinder, the HP tubing, the check valve and the
Annals of the CIRP Vol. 55/1/2006
upstream tube may fail suddenly and catastrophically (Figure 1). Monobloc cylinders without residual pre-stresses have limited pressure bearing capacities. Pressurized monobloc cylinders start to yield at pressures slightly higher than half of their yield strength value according to Lame’s equations, even when the cylinder has infinite thickness (Figure 2). Knowing that the yield strength of the suitable construction materials does not exceed 1100 MPa, the maximum allowable water pressure is, with some safety margin, limited to 400 MPa. Attenuator
Attenuator
HP cylinder
Water supply
Upstream tube Hydraulic pump
Check valve
Figure 1: AWJ cutting system with two double acting pressure intensifiers. Compressive residual stress imposed to the bore of the cylinder reduces the operating tensile stresses, thus increasing the pressure capacity of the cylinder. Both autofrettage and multi-layer cylinder construction are well known methods to create residual compressive stress. In autofrettage, the part is deformed plastically by applying internal pressure. When this pressure is removed, the elastic recovery of the outer sections of the cylinder causes tangential compressive residual stress in the bore. In multilayer cylinders, the inner cylinder is shrink-fitted to the jacket cylinder. The jacket exerts pressure to the outer surface of the inner cylinder, which causes tangential compressive stress at the bore. In both cases re-yielding of the bore, due to the Bauschinger effect, should be avoided since it reduces the
AISI S15500 H1100 Stainless Steel
Yielding pressure
800
pa= 1000 MPa
700 MPa
pa= 800 MPa pa= 600 MPa
600 500
pa= 0 MPa
400 300 1
2
3
4 5 6 Diameter ratio
7
8-
9
Elastic modulus = 196.5 GPa Yield strength = 793 MPa Tensile strength = 965 MPa Poisons’ ratio = 0.27 Figure 2: Pressure capacity of thick-walled cylinders. 2.2 Phase equilibrium of water Another limiting factor to increase the water pressure indefinitely is the solidification of water at room temperature at very high pressures. Ice I (Figure 3) is the natural ice which is formed at atmospheric pressure. All the other types of ice are observed at higher pressures than the atmospheric pressure. Ice VI is important for AWJ applications above 400 MPa. The equation of the boundary line for ice VI can be found in Figure 3 where pice_VI is the solidification pressure at temperature T [4].
Pressure
104 MPa
Ice V
pice_VI
2
10
p1
1
10
0
Ice I 250
Ice VII
Ice VI
Ice III
⎛ ⎛ ⎞ 4.6 ⎞ T ⎜ ⎟ = 1 − 1.07476 ⋅ ⎜1 − ⎜⎜ ⎟⎟ ⎟ ⎜ ⎝ T1 ⎠ ⎟ ⎝ ⎠
Liquid
p1= 632.4 MPa T1= 273.1 K
300 K Temperature T
400
Figure 3: Phase diagram of water. If the inlet water temperature is assumed to be 293 degrees K, it starts to solidify when the pressure exceeds 894 MPa. However, the temperature of water increases due to the adiabatic compression of the water. It is
estimated that the temperature raises 3 degrees K for every 100 MPa increase [5]. Therefore the solidification pressure at 293 degrees K increases to 1317 MPa. Furthermore, the friction in between the water and the components also causes a temperature rise, which further increases the solidification pressure of water. However, the pressurized water is stored while the cutting operation is temporarily stopped. During this period, there is a risk of solidification since the water may cool down to the room temperature. 3 TEST SETUP AND PROCEDURE The pressure unit is a two-stage double acting intensifier with a maximum design pressure of 800 MPa. The intensifier is connected to a cutting head by a series of tubing with an internal diameter of 1.6 mm and an external diameter of 9.5 mm. The final section of the tubing is spiral to allow the movements of the cutting head. The cutting head is manipulated by a SCARA robot. There are two buffer volumes in the system. The first one has a capacity of two liters and is located after the initial intensifier. The second one lies after the final intensifier and its capacity is 1 liter. They limit the pressure fluctuations to 1% for an orifice diameter do of 0.1 mm at 700 MPa [6]. Research has shown that the tube prior to the orifice affects the jet quality as well since it reduces the upstream turbulences by acting like a reservoir [7]. The diameter of the tube should be large enough to promote laminar flow and the length of the tube should be long enough to let the flow be fully developed. Therefore, all the tests were conducted with a longer (212 mm) than usual (100 ~ 150 mm) upstream tube with a large inner diameter (3.5 mm) to decrease the initial level of turbulence in the flow. The jet former is mounted to a strain-gage device to measure the reaction force or back thrust of the jet. The material that has been cut is an AISI 304 stainless steel; garnet abrasive of mesh 150, with an average grain size of 100 µm, is used throughout the experiments. 4 JET FORMATION It is important for a waterjet to maintain its kinetic energy for an appreciable distance. However, the jet breaks down in the downstream and its kinetic energy is divided among small droplets. A scattered jet generates wider cuts with wider damaged zones and rounded edges. In AWJ applications a scattered jet will accelerate the wear of the entry region of the focusing nozzle and will show a poor behavior in accelerating the abrasive particles. Most efforts to obtain coherent jets are focused on the orifice geometry [8]. The edge condition (sharp, rounded or chamfered) and the orifice geometry (cylindrical, coneup or cone-down) are key parameters. In this study, jet coherency is determined in terms of its doubling length, defined as the length of the jet until its diameter becomes twice the diameter of the orifice do. The doubling length is determined by image analysis of over-exposed photos of the jet. The over-exposure is applied to increase the contrast between the jet and its surroundings. Three different types of orifices are used (Figure 4). Doubling length
final pressure capacity of the cylinder. The residual stress improves the fatigue life of the components as well by reducing the mean stress [3]. Increasing the water pressure in two sequential steps also reduces the mean stress of the cylinder. With a two-stage intensifier, the initial intensifier boosts the pressure to an intermediate value, e.g. 400 MPa; then the water reaches its ultimate pressure by the final intensifier. A finite element analysis has been carried out to find the residual stresses due to autofrettage. A bilinear kinematic hardening material model with plane strain is applied since it is capable of handling the Bauschinger effect. Then, the new initial yielding pressure is calculated by using Lame’s equations and the Von Mises failure criterion. The results are presented in Figure 2. For constant material thickness, the process becomes less efficient with increase of the autofrettage pressure pa. The re-yielding of the bore counteracts the benefits of further pressure increase. Increase of the thickness of the cylinder is not a solution since the performance of the cylinder does not improve proportionally with the thickness. Therefore, multi-layer constructions with a combination of a hard and strong inner cylinder and a tough and lighter jacket should be implemented.
Type 1 Conical seal Sharp edge
Type 2 Flat seal Sharp edge
Type 3 Flat seal Round edge
Figure 4: Photos of a jet and of the orifices used.
10 10
Type 2
55
Type 3
00 300
350 350
4 0 0 450 450 5 0 0 MPa 550 ssu re WaterP re pressure pw
600
650 650
Figure 5: Jet coherency of different orifices. 5
AWJ CUTTING PROCESS
5.1 Energy transfer efficiency In AWJ applications, abrasive particles are entrained in the mixing chamber of the jet former and accelerated by the pure waterjet. Only a part of the available kinetic energy of the water is transferred to the particles in this mixing process [9]. The impulse balance equation is used to determine the amount of energy transfer to the abrasive particles:
(m& w + m& a + m& air ) ⋅ v awj
(
)
& w ⋅ vwj + m & a ⋅ va + m & air ⋅ v air (1) =η m
&w , m & a and m & air are the mass flow rates and vwj, where m va and vair are the initial velocities of water, abrasive and air respectively, vawj is the velocity of the abrasive jet and η is the momentum transfer efficiency. The abrasive load ratio R is defined as the ratio of mass flow rate of abrasive and water:
R=
&a & &a m m m = a = &w m q& ⋅ ρ (c d ⋅ Ao ⋅ v wj ) ⋅ ρ
(2)
where q& is the volumetric water flow rate, ρ is the density of water, cd is an orifice specific discharge coefficient and Ao is the cross sectional area of the orifice. Under the assumption that the final velocity of the abrasive particles and water is equal, which is valid when the focusing tube is sufficiently long, and by neglecting & air ; vawj can be written as: both va and m
v awj = η ⋅
1 ⋅ v wj 1+ R
(3)
The momentum transfer efficiency η expresses the momentum losses due to the interactions of the abrasives and water with the walls of the mixing chamber and focusing tube, and due to the fragmentation of the particles. The momentum transfer efficiency can be expressed as:
η=
&w + m & a ) ⋅ v awj Fawj (m = & w ⋅ v wj m Fwj
(4)
= η2 ⋅
R
(5)
(1 + R )2
where µ is the power transfer efficiency, Pa and Pwj are the power of the abrasives and the waterjet respectively. If η was independent of R, the power transfer efficiency would reach its maximum when R equals to unity. However, experiments show that the momentum transfer efficiency strongly depends on both abrasive load ratio and jet former geometry (Figure 6). Combinations of smaller orifice diameters do and focusing tube diameters df tend to have a lower momentum and power transfer efficiency which points out an alignment problem of orifice and focusing tube. As shown in Figure 6, the optimal power transfer efficiency is located around R-ratios of 0.3. Overloading of the jet by higher R-values will not only decrease the momentum transfer efficiency, but also deteriorate the abrasive jet structure itself, indicating a major change in flow conditions. Therefore the cutting theory developed is only valid up to the maximum power transfer efficiency. 0.25
ηideal μideal
1.0
0.20 -
0.8 -
0.15
ηmeasured
0.6 0.4
0.10
μmeasured
0.2
do= 0.12 mm df = 0.5 mm
0.0 0.0
0.05
do= 0.2 mm df = 0.8 -mm
0.1 0.2 0.3 0.4 Abrasive load ratio R
0.5
Power efficiency μ
Type 1
15 15
1 ⋅m & a ⋅ v 2 awj 2 1 ⋅m & w ⋅ v 2wj 2
0.00 0.6
Figure 6: Momentum and power transfer efficiencies. 5.2 Cutting With the increase of the water pressure pw from 400 MPa to 600 MPa, the cutting maximum speed increases by 48%. If, on the other hand, the cutting speed vf is kept constant, it is possible to save 52% of the abrasive consumption while maintaining the same depth of cut with the same cutting quality (Figure 7). Material thickness 10 mm 200% do = 0.2 mm pw = 400 MPa pw = 600 MPa d = 0.8 mm f 150% 4.2 g/s
100% 50% 0%
5.2 mm/s
do = 0.175 mm
Pa = Pwj
3.5 mm/s
Doubling length
Doubling length
25 25
mm 20
μ=
Momentum efficiency η
Sharp edged orifices generate more coherent jets due to the constricted jet formation. Figure 5 shows the importance of the entry region of the orifice as well. The type 1 orifice, which has a streamlined sealing has a longer doubling length than the ones with flat seals. The smoother streamlines are directed to the orifice with less turbulence due to its inclined surface of the sealing of the type 1 orifice.
where Fwj and Fawj are the measured reaction or thrust forces of the pure and the abrasive waterjet respectively, therefore their ratio gives a direct measure of the momentum transfer efficiency. The amount of power transferred to the abrasives depends on the momentum transfer efficiency and the abrasive load ratio:
Change in vf and abrasive consumption
Types 1 and 2 have sharp edges and type 3 has a rounded edge. The type 1 has an inclined sealing surface towards the orifice which promotes smoother streamlines. All orifices have cone down geometries.
Cutting speed vf 1 & a = 4.2 g/s) (m
2.0 g/s
Abrasive consumption 2 (vf = 3.5 mm/s)
Figure 7: Example of the improvement in cutting speed or reduction of abrasive usage.
The experimental power transfer efficiency showed an optimum at R-ratio’s around 0.3. The cutting results validate the existence of the optimum abrasive load ratio at around 0.3 (Figure 8) independent of the water pressure. 25
vf = 2.5 mm/s
670 MPa
Depth of cut
20 mm
580 MPa
15
470 MPa
10
do = 0.15 mm df = 0.5 mm
5 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Abrasive load ratio R Figure 8: Abrasive load ratio with respect to depth of cut. This indicates that the cutting performance of the AWJ is directly related to the power of the abrasive jet. To incorporate the feed speed of the jet former relative to the workpiece in the formulation the energy density ea is defined as:
ea =
μ ⋅ Pwj ⎛⎜ π Pa = = df ⋅ v f df ⋅ v f ⎜⎝ 2 2 ⋅ ρ
⎞ μ ⋅c ⋅ p 3 2 ⋅d 2 d w o ⎟ ⎟ df ⋅ v f ⎠
(6)
In Figure 9, the relation between the energy density and the depth of cut is shown. The regressive instead of proportional behavior at higher depths of cut can be explained by increased energy losses of the jets at longer traveling lengths through the workmaterial at higher depths of cut.
Depth of cut
50
470 MPa to 670 MPa
mm 40 30 20
do = 0.12 mm df = 0.5 mm do = 0.15 mm df = 0.5 mm do = 0.175 mm df = 0.8 mm
10 0 0.0
2
kJ/mm 0.5 1.0 Energy density ea
1.5
Figure 9: Cutting ability of AWJ as a function of energy density of the abrasive. From equation (6) it is clear that the energy density can be increased by increasing the jet diameter do, however this is against the general trend towards smaller products with intricate details. The energy density can also be increased by the reduction of the feed speed vf, which conflicts with economical considerations of maximum production, or it can be increased by increasing the pressure pw. Reducing the focusing tube diameter df seems also to be an option for increasing the energy density ea. However, experiments have shown that this will also include a reduction of the orifice diameter do, to maintain a df /do ratio between 3 and 4, resulting in an overall reduction of the energy density. Simultaneously increasing the water pressure pw can theoretically compensate this effect, creating a more efficient cutting process. Higher pressures and smaller orifices result, with the same water power Pwj, in a higher energy density. Experiments have shown however, that combinations of smaller orifices and
focusing tubes result in less power transfer efficiencies (Figure 7), so the goal of increasing the energy density by using smaller jet formers at high pressures could not be achieved at this time. 6 CONCLUSIONS AND OUTLOOK The water pressure is limited by the endurance of the components and the physical properties of water at high pressures. The components that are subjected to pressures beyond 400 MPa should be autofrettaged or produced by multilayered cylinders. Due to the Bauschinger effect, there is an optimum autofrettage pressure. Increase of pressure will increase the cutting ability of the jet. The jet becomes more powerful with equal diameter. Therefore, the depth of cut or cutting speed is improved. There is an optimum abrasive load ratio over which the cutting ability of the jet decreases due to the less efficient power transfer from waterjet to the abrasives. The optimum abrasive load ratio is independent of the pressure. The miniaturization of the jet former to smaller dimensions is currently decreasing the efficiency of the jet formation process, and thereby counterbalancing the effect of higher energy densities of the pure waterjets. The development of jet formers having more accurate alignment of the orifice and focusing tube is necessary. 7 ACKNOWLEDGMENTS This research is conducted in cooperation with Resato International b.v., with financial support of the Dutch Ministry of Economical Affairs under the BTS-program. 8 REFERENCES [1] Hoogstrate, A.M., 2000, Towards High-Definition Abrasive Waterjet Cutting. Ph. D. Thesis, Delft University of Technology, The Netherlands. [2] Hoogstrate, A.M., van Luttervelt, C.A., 1997, Opportunities in Abrasive Water-Jet Machining, Annals of the CIRP, 46/2:697-714. [3] Trieb, F.H., Schedelmaier, J., Poelzl, M., 2004, Developments on Optimized Autofrettage of High Pressure Components for Waterjet Cutting Pumps, Proceedings of the 17th Int. Conf. on Jetting Technology, 7-9 Sept., Mainz, Germany, 23-32. [4] Wagner, W., Pruß, A., 2002, The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, J. Phys. Chem. Ref. Data, 31:387535. [5] Bridgman, P.W., 1970, The Physics of High Pressure. Dover Publications, Inc., New York. [6] Susuzlu, T., Hoogstrate, A. M., Karpuschewski, B., 2004, Initial Research on the Ultra-High Pressure Waterjet up to 700 MPa. J. of Material Processing Technology, 149:30-36. [7] Hashish, M., 2004, Abrasive-waterjet (AWJ) Studies, Proceedings. of the 16th Int. Conf. on Jetting Technology, 16-18 Oct., Aix-en-Provence, France, 13-47. [8] McCarthy, M.J., Molloy N. A., 1974. Review of Stability of Liquid Jets and the Influence of Nozzle Design. The Chemical Engineering Journal, 7:1-20. [9] Hoogstrate, A.M., Karpuschewski, B., van Luttervelt, C.A., Kals, H.J.J., 2002, Modeling of High Velocity, Loose Abrasive Machining Processes, Annals of the CIRP, 51/1:263-266.