WATER JET CONFERENCE - Waterjet Technology Association

identifying a general trend for the shape of depth-of-cut-versus-particle-size curves. A decreasing
h-versus-d p curve, with d p as the average abrasive particle diameter, may be convex or concave for
the same material being cut, depending on other parameters. The role of particle size in the area of
erosion mechanics needs to be identified (Ruff and Wiederhorn, 1979). No studies exist that
provide an explanation of the optimum particle size. However, in abrasive-waterjet cutting, this
optimum particle size could be related to the efficiency of the mixing process, if the material
removal rate is directly proportional to the abrasive flow rate, as classical erosion theories and
experiments indicate. In other words, for a given mixing chamber configuration, there exists an
optimum particle size for the maximum transfer of the momentum of the water to abrasives.
Consequently, changing the particle size would require a different mixing chamber, so that
comparisons of the effects of particle size could be more accurate and relate only to the material
being cut.
Effect of Abrasive Flow Rate
The approximately linear, initial relationship between the depth of cut and the abrasive flow
rate has been observed to be as shown in Figure 6. However, additional data (Hashish, 1983)
showed a trend for decreasing depths of cut at higher abrasive flow rates beyond a critical one. This
trend is expected because, with an increase in the abrasive flow rate for a fixed water flow rate,
particle velocities will decrease faster than the number of impacts will increase. This
critical abrasive flow rate, at which a maximum depth of cut occurs, is generally less than the water
flow rate, which is less than 1 for a loading ratio, R. However, for ideal conditions, it can be shown
mathematically that this critical abrasive flow rate occurs when the loading ratio equals 1. Based on
simple erosion theories (Fannie, 1958), the depth of cut can be expressed as proportional to the
particles' kinetic power mV 2 , where V is the particle's exit velocity and can be related to the
waterjet velocity, V j, as V ~ Vj/(l + R), leading to
h = m V ⎡
j
⎣ ( 1 + R)
⎢
⎤
⎥
⎢ ⎦ ⎥
The condition δh/δR =0 occurs when R equals 1, as can be determined from the above
equation. The discrepancy between experimental and theoretical values for the critical value of R is
attributed to mixing losses, which result in particle velocities less than what the simple momentum
equation yields. Also, the use of the simplified erosion equation (h α V 2 ) may be inaccurate.
Notice that the lines in Figure 6 pass through the origin, as no depth will be obtained for
zero abrasive flow rate. However, this is true only for hard materials that cannot be cut with a plain
waterjet using a nozzle as shown in Figure 1. Research is needed to determine whether the rate of
impacts per unit time or the total number of impacts is more directly related to the cutting process.
If the former proves to be the case, then a material fatigue property must be among the material
parameters that affect cutting. Erosion theories (Crow, 1973) show a relationship between material
removal and the total number of impacts, but the effect of the rate of impacts was not discussed.
Also, research is needed to determine whether the abrasive particles are reentrained in the jet after
initial impacts at the top of the kerf to cause further cutting at lower portions of the kerf.
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