Influence of Abrasive Flow Rate and Feed Rate on Jet Lag During Abrasive Water Jet Cutting of Beech Plywood

Abstract

Cutting beech plywood using abrasive water jet (AWJ) technology represents a significant area of research due to increasing demands for precision, quality, and environmental sustainability in manufacturing processes within the woodworking industry. AWJ technology enables non-contact cutting of materials without causing thermal deformation or mechanical damage, which is crucial for preserving the structural integrity and mechanical properties of the plywood. This article investigates cutting beech plywood using technical methods using an abrasive water jet (AWJ) at 400 MPa pressure, with Australian garnet (80 MESH) as the abrasive material. It examines how abrasive mass flow rate, traverse speed, and material thickness affect AWJ lag, which in turn influences both cutting quality and accuracy. Measurements were conducted with power abrasive mass flow rates of 250, 350, and 450 g/min and traverse speeds of 0.2, 0.4, and 0.6 m/min. Results show that increasing the abrasive mass flow rate from 250 g/min to 350 g/min slightly decreased the AWJ cut width by 0.05 mm, while further increasing to 450 g/min caused a slight increase of 0.1 mm. Changes in traverse speed significantly influenced cut width; increasing the traverse speed from 0.2 m/min to 0.4 m/min widened the AWJ by 0.21 mm, while increasing it to 0.6 m/min caused a slight increase of 0.18 mm. For practical applications, it is recommended to use an abrasive mass flow rate of around 350 g/min combined with a traverse speed between 0.2 and 0.4 m/min when cutting beech plywood with AWJ. This balance minimizes jet lag and maintains high surface quality comparable to conventional milling. For thicker plywood, reducing the traverse speed closer to 0.2 m/min and slightly increasing the abrasive flow should ensure clean cuts without compromising surface integrity.

1. Introduction

Abrasive water jet (AWJ) technology is an advanced, unconventional machining tool widely used for processing various materials, especially those that are challenging to cut by traditional methods [1,2,3]. AWJ is distinctive in its ability to create precise, cold cutting without causing thermal deformation of the materials [4], a crucial advantage when working with sensitive or multi-layered materials [5]. By combining a high-pressure water jet with abrasive particles, AWJ can effectively separate inhomogeneous materials with minimal waste, reducing both processing costs and environmental impact. Among typical materials used as abrasives are aluminium oxide, silicon carbide, garnet, diamond, glass beads, and cubic boron nitride [6]. These properties give AWJ technology an increasingly valuable alternative for applications requiring high precision, low thermal impact, and clean cuts, such as woodworking and wood composites [7,8]. Pioneers in this area, including Hashish [9], Geskin et al. [10], Zeng and Kim [11] and Bernd et al. [12], laid the foundational knowledge for AWJ technology. Their research enabled subsequent researchers, such as Chao [13], Kovacevic [14], Yong [15], and Krajný [16], to expand the understanding of the AWJ machining process, focusing on both the basic principles [17] and the practical optimization of cutting parameters across various industries. This technology is well established in fields ranging from precision component manufacturing and advanced functional materials to intelligent automotive engineering, aviation technology, renewable energy sources, and high-end medical device development [18]. In these areas, AWJ has proven to be a critical technological need, including optimized cutting parameters to increase the efficiency and quality of machining, dynamic simulations to predict material behavior under a water jet, and real-time process monitoring [19]. This technology is now essential not only in traditional industries but also in cutting-edge, high-precision applications [20]. AWJ cutting is a complex multi-parameter process in which various input factors, such as water pressure, traverse speed, abrasive concentration, and other factors, interact with each other [21]. Each input setting plays a crucial role in achieving precise, clean, and efficient cuts and in optimizing desired product properties, such as surface smoothness, dimensional accuracy, and minimal defects [22]. Among these factors, the lagging of the jet in the cutting plane is particularly significant, resulting from complex interactions between the stream of abrasive water and the material, which can influence geometry and final properties of the cut. As with other high-energy jet technologies, AW leaves surface traces known as grooves, which can impact the surface quality and dimensional accuracy of the final products [1,23]. The cutting process is initiated slightly below the surface of the material and gradually deepens, resulting in a machined surface that consists of a smooth zone followed by a grooved zone [16]. The traces reveal the trajectory of the water jet as it moves through the material, whilst the lag of the water jet also visibly affects the uniformity and quality of the cut [24].

The mass flow rate of the abrasive material has a fundamental influence on the efficiency of the AWJ cutting. As the abrasive particle content in the liquid stream increases, the depth of cut also increases [25]. This phenomenon is due to the increased kinetic energy (E_a) of the abrasive particles, a key factor in the cutting process. The kinetic energy is defined as follows:

$${\mathit{E}}_{\mathit{a}}={\displaystyle \frac{1}{2}}{\mathit{m}}_{\mathit{a}}.{{\mathit{v}}_{\mathit{a}}}^2 [\mathrm{J}/\mathrm{s}],$$

(1)

where the following is true:

• m_a—abrasive mass flow rate of the abrasive particles [kg/s];
• V_a—speed of abrasive material exiting the focusing tube [kg/s].

As the mass flow rate increases, so does the depth of cut and the quality of the machined surface. A higher concentration of abrasive particles in the jet allows more efficient material removal, resulting in a smoother and more accurate cut. However, this flow rate increase is limited by the critical mass flow rate. Beyond this threshold, the depth of cut will decrease. This decrease is because the excess particles collide with each other, leading to the loss of kinetic energy that would otherwise contribute to cutting the material [16,26]. Changing the traverse speed affects the shape and depth of the cut and, hence, its profile and quality. Slower speeds cause visible unwanted milling on the surface, affecting the surface appearance and accuracy. Conversely, higher traverse speed results in a more precise and smoother cut, though it may result in higher cost and other technological challenges. Hashis [27] and Krajný [16] have defined the required amount of particles (Equation (2)):

$$\mathit{P}\mathit{D}\mathit{D}={\displaystyle \frac{{\mathit{m}}_{\mathit{a}}}{{\mathit{v}}_{\mathit{f}}}} [\mathrm{kg}/\mathrm{m}],$$

(2)

where the following is true:

• PDD (Particle Dosing Density) is the abrasive particle density division (the amount of particles necessary to generate a groove of nominal length under specific conditions) [kg/m];
• m_a is abrasive mass flow rate [kg/s];
• v_f is the traverse speed of water jet movement against material [m/s].

Additionally, the energy density division (EDD) of abrasive particles may be defined according to Equation (3):

$$\mathit{E}\mathit{D}\mathit{D}={\displaystyle \frac{1}{2}}.\mathit{P}\mathit{D}\mathit{D}.{{\mathit{v}}_{\mathit{a}}}^2 [\mathrm{J}/\mathrm{m}],$$

(3)

where the following is true:

• EDD is the energy density division of abrasive particles (the amount of energy reverted to a unit of the generated groove length) [J/m];
• v_a is the speed of abrasive coming from the nozzle [kg/s].

These equations are essential for industrial practices, as they can be used to optimize the cutting processes for specific materials and required properties [23]. Beech plywood was chosen due to its widespread use in Eastern and Central Europe and the need to improve the machinability of this material. Cutting beech plywood using technical methods with AWJ is crucial in the furniture and construction industry, as it enables high precision and quality. This technology uses a high-pressure water stream enriched with abrasive particles, which enables precise and clean cuts in rigid materials (such as beech plywood). In this article, the focus is on optimizing the AWJ cutting parameters for technical beech plywood to minimize potential negative impacts. Despite the potential advantages of this method, there is a lack of systematic studies in the current literature analyzing the influence of AWJ cutting parameters on the long-term durability of beech plywood. This gap limits the ability to optimize cutting processes and fully exploit the technology’s potential in industrial applications. Furthermore, the growing need for environmentally friendly manufacturing technologies must be emphasized, with AWJ representing an ecological alternative to traditional cutting methods, as it does not generate thermally damaged waste or harmful emissions. For these reasons, scientific investigation into AWJ cutting of beech plywood is essential for expanding current knowledge, optimizing manufacturing processes, and supporting sustainable development in the woodworking industry. This study has the potential to fill identified gaps in the scientific literature and contribute to both technical and environmental advances in material processing. The core hypothesis of the article is whether it is possible to assume the existence of a combination of cutting parameters (traverse speed, abrasive mass flow rate, and material thickness) that minimizes AWJ lag without negatively affecting surface quality.

2. Materials and Methods

This section describes the material used in the experiments and the methodology applied to evaluate the influence of AWJ cutting parameters on jet lag and the resulting surface quality of beech plywood.

2.1. Testing of Technical Beech Plywood

Various specimens of technical beech plywood of thickness 36 mm and 54 mm were tested. For each test, the width (w) and length (l) of each specimen were 180 mm (±2.5 mm) and 500 mm (±2.5 mm), respectively. The moisture content (m_c) of the specimens was 8% (±2%). The 54 mm thick beech plywood consisted of 17 layers. The 36 mm thick plywood had 11 layers. The average density of the beech wood used for producing the plywood was approximately 690 kg/m³. Melamine glue was used to bond the individual layers, which ensured high resistance and durability of the glue lines.

2.2. Parameters of Cutting Process

The cutting of the tested samples was carried out under actual operating conditions at DEMA spol s.r.o (Zvolen, Slovakia), as shown in Figure 1. Thus, a water jet system was from PTV spol. s.r.o. (Prague, Czech Republic) was used, fitted with a high-pressure pump model PTV 37–60 Compact, throughout this study. A cutting table equipped with a WJ 20 30 D -1Z cutting head was supplied by PTV. This system is designed for precision cutting and features advanced technology for managing high-pressure water and abrasive materials, achieving accurate and efficient results in various applications. The high-pressure pump provides consistent water flow and pressure, whilst the cutting head allows precise control of the cutting process, enhancing the overall performance and reliability of the water jet cutting system.

The cutting process was conducted according to the cutting plan (shown in Figure 2), outlining the optimal method for cutting the samples. This plan included the specification of cutting paths and individual sections to be followed to achieve the desired results. During the cutting of technical beech plywood, we proceeded in a way that took into account the grain orientation in the individual layers of the material. Cuts were performed in the longitudinal direction (so-called longitudinal cut—with the cutting plane parallel to the grain of the outer layer), as well as in the transverse direction (so-called transverse cut—perpendicular to the grain of the outer layer), in order to compare the cut quality, material behavior during cutting, and the occurrence of potential edge defects. This approach allowed the observation of the influence of grain orientation on the final cut quality, providing valuable insights for optimizing the parameters of plywood cutting using the AWJ method. The input parameters of the experiment were selected based on a theoretical analysis of the issue, as well as practical experience, as follows:

• Cutting liquid pressure: 400 MPa;
• Abrasive: Australian Garnet GMA (grain composition 80 MESH);
• Abrasive jet diameter: 1 mm;
• Water jet diameter: 0.013 inches = 0.33 mm;
• Electric power input: 37 kW;
• Focusing tube distance above a work piece: 4 mm.

The traverse speeds and abrasive mass flow were chosen according to the technical capabilities of the equipment and recommendations from professionals, so that any results would be applicable in practice. The selection of experimental parameters was carried out with the aim of obtaining detailed information about the behavior of the cutting process under different levels of abrasive system loading. By including both lower and higher parameter values, it was possible to observe the material’s response under deliberately shifted boundary conditions, providing valuable insights for designing cost-effective cuts with reduced abrasive consumption or assessing the maximum performance of the equipment in demanding applications. The parameters were selected to cover the full spectrum of potential operating conditions, thus enabling an evaluation of interactions and establishing a foundation for optimizing efficient and sustainable abrasive water jet cutting. This approach enabled the quantification of the individual variables’ effects on AWJ lag. The parameters were also selected with regard to the technical limitations of the machine equipment, which restricted the range of operating conditions that could be realistically set and maintained during the cutting process.

A suitable combination of traverse speed and abrasive quantity was selected during the testing, with parameters carefully optimized and summarized in

Table 1. Combination of traverse speed and abrasive flow attributable to each cut.

Cut	Traverse Speed vf = [m/min]	Abrasive Mass Flow ma = [g/min]
A	0.6	250
B	0.6	350
C	0.6	450
D	0.4	250
E	0.4	350
F	0.4	450
G	0.2	250
H	0.2	350
I	0.2	450

.

2.3. Methodology of Water Jet Lagging Evaluation

In order to evaluate results, it is necessary to define several terms. The water jet lagging, L, shown in Figure 3, is the lagging of the jet path while cutting a material, specifically the difference in the X-coordinate of the water jet path between its entry and exit in the material. The X-Y relationship of the water jet trace represents a coordinate recording of the path—a curve left by the water jet—within a coordinate system. The origin of this system is located at the intersection point where the jet curve meets the edge of the load-bearing surface in cross-section, with the Y-axis perpendicular to this edge. This coordinate recording allows precise tracking and analysis of the jet path during the cutting process.

2.4. Working Procedure

As part of the assessment, it was necessary to create a digital photo of the surface together with a reference gauge. In order to do this, the zoom setting and focus were adjusted to ensure consistency using the Canon ZoomBrowserEX 5.0 software (Tokyo, Japan), with the default zoom value set to 25%, corresponding to a 2× magnification. A series of measurement points was then placed on the sample, as shown in Figure 4. In total, 8 repetitions were performed.

The measurement of the cutting path parameters and the degree of lagging was performed by importing the digital photograph into Autodesk AutoCAD 2020 (San Francisco, CA, USA) and then overlaying the curve onto the trace left by the abrasive water jet. This allowed a proportional measurement of the coordinates of the curve and the lag of the abrasive water jet.

In order to transfer the proportional dimensions to real dimensions, Equation (4) was used:

$$(\mathbf{X}/\mathbf{Y}/\mathbf{L})={\displaystyle \frac{({\mathit{X}}_{\mathit{P}}/{\mathit{Y}}_{\mathit{P}}/{\mathit{L}}_{\mathit{p}}).\mathit{a}}{{\mathit{a}}_{\mathit{p}}}} [\mathrm{mm}],$$

(4)

where the following is true:

• X/Y/L—Real lagging of water jet [mm];
• X_p/Y_p/L_p—Proportional dimension of water jet lagging [--];
• a—Real dimension of reference gauge unit [mm];
• a_p—proportional dimension of reference gauge unit [--].

AWJ lag has a direct impact on the resulting surface quality, particularly in the lower part of the cut, where increased roughness and deviation from the ideal cutting trajectory occur.

The quality of the surface should meet the quality obtained from flat milling. This is the requirement for any AWJ application as a final operation of the surface finishing.

During the experiments, the relevant parameter–surface abrasiveness (R_a) could be determined. Specifically, R_a represents the middle arithmetical deviation of the abrasiveness profile, which is the middle arithmetical level of absolute profile deviations within the basic length, measured on the abrasiveness profile (in the profile implied from the primary profile by the elimination of parts with long wavelength).

Samples were measured in a laser profilemeter LPM 120 (Figure 5a), oriented in such a direction that it was possible to measure roughness of a processed surface in a given track (measured place is marked by laser light, Figure 5b).

Conditions were the following:

➢

All tracks were parallel with lateral edge of a sample;

➢

The first track was 5 mm from lateral edge of the sample;

➢

Every further track was moved by 5 mm;

➢

The last track was 5 mm from opposite lateral edge of the sample;

➢

Tracks were centered in the center of sample length.

The scanned profile was focused by the vertical movement of the laser profilometer. The given profile characteristics were measured using the MEASURE >>> PROFILE PARAMETERS function (Figure 6).

2.5. Statistical Analyses

Statistical data analyses were conducted using both MS Excel and Statistica 14 (StatSoft, Palo Alto, CA, USA). The results were evaluated at a significance level of α = 0.05.

3. Results

3.1. Statistical Overview of Results

Based on the statistical evaluation, the observed parameters have a statistically significant effect, with particularly strong statistical significance observed for the $\mathit{v}$_f factors across all tested plywood thicknesses. The cutting process for technical beech plywood included two key components. Firstly, the AWJ, which carries the energy needed to split the material itself, gives resistance to the cutting force. The energy from AWJ depends on the traverse speed and the abrasive flow rate. Secondly, the material’s resistance depends upon its properties and the specific cutting conditions. A vital indicator of the interaction between these two components is the width of the kerf created by the water jet. Increasing energy supplied or reducing material resistance can decrease the width of the kerf. Conversely, reducing energy or increasing material resistance can result in increasing the width of the cutting joint. This relationship between energy and material resistance is essential for optimizing the cutting parameters to achieve the desired surface quality.

The importance of monitored factors (according to

Table 2. Summary of multivariate analysis of variance for AWJ lagging in plywood.

Lagging AWJ (mm)	Sum of Squares	Degrees of Freedom	Dispersion	F-Test	p-Level of Significance
Intercept	203.9305	1	203.9305	4995.715	0.000000
{1} thickness	29.8266	1	29.8266	730.666	0.000000
{2} cutting direction	0.0008	1	0.0008	0.020	0.888127
{3} traverse speed	1.5739	2	0.7869	19.277	0.000000
{4} abrasive flow	0.3307	2	0.1653	4.050	0.019438
thickness * cutting direction	0.2088	1	0.2088	5.114	0.025231
thickness * traverse speed	1.7062	2	0.8531	20.898	0.000000
cutting direction * traverse speed	0.1372	2	0.0686	1.680	0.189994
thickness * abrasive flow	0.9516	2	0.4758	11.656	0.000020
cutting direction * abrasive flow	1.0787	2	0.5393	13.212	0.000005
traverse speed * abrasive flow	1.0410	4	0.2603	6.376	0.000094
thickness * cutting direction * traverse speed	0.6995	2	0.3498	8.568	0.000305
thickness * cutting direction * abrasive flow	1.1396	2	0.5698	13.959	0.000003
thickness * traverse speed * abrasive flow	0.9075	4	0.2269	5.558	0.000345
cutting direction * traverse speed *abrasive flow	0.8263	4	0.2066	5.061	0.000761
1 * 2 * 3 * 4	1.3567	4	0.3392	8.309	0.000005

Note: red color highlights significant changes.

) was the following:

Material thickness: This factor has the most significant influence on the AWJ cutting process. As the plywood thickness increases, the material’s resistance to cutting also increases, which requires more energy. The material’s thickness also affects the cutting quality. Thicker materials often require finer adjustment to achieve an optimal result.

Traverse speed: The speed at which the material moves under the cutting beam dramatically affects both the quality and efficiency of the cut. A higher traverse speed can lead to lower cut quality, as the beam may not have enough time to fully cut through the material. On the other hand, too slow a traverse speed increases processing time and costs.

Abrasive flow: The amount of abrasive material supplied to the cutting process affects the depth and quality of the cut. An intense abrasive flow rate can improve cutting efficiency, but exceeding the optimum value leads to excessive equipment wear and increased consumables costs.

Cutting direction: This factor was evaluated as statistically insignificant, which means that changes in the cutting direction do not significantly affect the quality of the cut or the efficiency of the process. Nevertheless, the direction of cutting can affect certain applications, where wood grain structure or aesthetic requirements must be taken into account.

3.2. Effect of Plywood Thickness

When the thickness of the plywood was increased from 36 mm to 54 mm, there was a significant increase in the AWJ lag within the material, averaging 0.82 mm (

Table 3. AWJ lagging at current plywood thicknesses.

Thickness Material (mm)	Lagging AWJ (µm)
	Average Value (µm)	Standard Error (µm)	−95.00% (µm)	+95.00% (µm)
36	657.33	2.129	615.24	699.43
54	1471.47	2.129	1429.37	1513.56

). As the material thickness increased, the resistance to the water jet also rose, making it more difficult for the jet to penetrate the plywood. This increased resistance slowed down the jet and caused a wider spread of abrasive particles, leading to a broader cut and a potential decrease in edge quality. Increasing material thickness thus necessitated adjustments to the cutting parameters, such as traverse speed and abrasive flow, to achieve optimal results. This can lead to uneven cutting and reduced accuracy. When the focusing tube or jet lagging occurs, it means that the abrasive particles are not evenly distributed, which can cause deviations in the cut.

The material and its thickness represent the main resistance factors in the cutting process, critically affecting the efficiency of energy utilization in AWJ cutting. As material thickness increases, so does the energy required to overcome this resistance and achieve the desired cut. The results are consistent with the study of Deep Kumar and Srinivasu [28], which focused on cutting thicker materials using AWJ. They found that increasing material thickness led to greater jet lag and a wider cut. This relationship emphasizes the importance of selecting suitable material thickness for optimizing the cutting process, as an unsuitable choice can result in excessive energy consumption and reduced efficiency. Wang et al. [29], in their study modelling and analysing AWJ, concluded that it was possible to predict the course of the cut. Therefore, adjustment of cutting parameters for varying material thicknesses is important to ensure both process efficiency and quality at the lowest possible costs.

3.3. Effect of Traverse Speed in Plywood

The effect of the traverse speed on AWJ lag in plywood is shown, with supporting results, in

Table 4. Influence of traverse speed on AWJ lagging in plywood cutting.

Traverse Speed (m/min)	Lagging AWJ (µm)
	Average Value (µm)	Standard Error (µm)	−95.00% (µm)	+95.00% (µm)
0.2	933.43	2.608	881.88	984.99
0.4	1145.73	2.608	1094.18	1197.29
0.6	1114.03	2.608	1062.48	1165.59

. At higher traverse speeds, the AWJ had less time to interact with the material, resulting in a lower concentration of abrasive particles at the cutting point. This not only increased lag but also reduced cutting efficiency, which can affect cutting quality. Higher speeds may result in irregularities, such as rougher edges or less accurate cuts. Wang et al. [30] investigated the relationship between traverse speed and cutting quality of various materials, including wood composites. Similarly, Ramesh and Mani [31] showed that higher AWJ speeds result in poorer edge quality in wood and composites, aligning with our findings for plywood. Additionally, higher speeds accelerated wear on the cutting head and increased abrasive consumption, impacting the long-term process costs [32]. Therefore, appropriate traverse speed settings are essential for achieving optimal cut quality and, from an economic perspective, allowing a balance between quality, speed, and equipment operating costs.

3.4. Influence of the Mass Abrasive Flow

When the abrasive flow was increased from 250 g/min to 350 g/min, the AWJ cutting width decreased by 0.05 mm (see

Table 5. Average values of AWJ lagging for various abrasive mass flow rates.

Abrasive Flow (g/min)	AWJ Lagging (µm)
	Average Value (µm)	Standard Error (µm)	−95.00% (µm)	+95.00% (µm)
250	1067.12	2.608	1015.56	1118.67
350	1010.60	2.608	959.04	1062.16
450	1115.48	2.608	1063.93	1167.04

). This decrease was attributed to the increased cutting efficiency from the optimal number of abrasive particles in the jet. However, increasing the abrasive flow rate further, from 350 g/min to 450 g/min, resulted in a slight increase (0.1 mm) in the width of the cutting edge. This phenomenon indicated a critical abrasive flow rate, beyond which cutting efficiency began to decrease, causing a wider cutting edge.

This result can be explained by the increase in the mass flow rate of abrasive from 250 g/min to 350 g/min, where 350 g/min was the optimal rate. At this rate, abrasive particles were evenly distributed in the stream, which maximized cutting efficiency. Conversely, when the mass flow rate further increased to 450 g/min, the jet was overloaded with abrasive particles. This overload caused particles to collide with one another, reducing their individual kinetic energy, resulting in a wider notch and reduced cutting efficiency. This result is consistent with the work of Du et al. [32], Perec [33], and Perec et al. [34], where it was shown that increasing the amount of abrasive above a certain limit caused the abrasive particles to interact with each other, reducing efficiency and broadening the cut width [35]. Surface roughness was reduced by 26.7% and 27.9%. Yang et al. [36] and Zou et al. [37] both investigated scratches, with positive results using regulation AWJ. Similar conclusions were also drawn by the study of Pelit and Yaman [38], where it was shown that optimal mass flow was critical for maximizing cutting efficiency and minimizing notch width, confirming previous publications. The results show the importance of finding and maintaining the optimal abrasive mass flow rate to achieve better edge quality and energy efficiency in the AWJ cutting process.

3.5. Effect of Cutting Direction in Plywood

The effect of cutting direction on AWJ lag for plywood is shown in

Table 6. AWJ lagging regarding the cutting direction in plywood.

Cutting Direction	Lagging AWJ (µm)
	Average Value (µm)	Standard Error (µm)	−95.00% (µm)	+95.00% (µm)
longitudinal	1066.52	2.129	1024.43	1108.62
transverse	1062.28	2.129	1020.18	1104.37

. The results show no significant differences when the cutting direction was changed from longitudinal to transverse. Multivariate variance analysis also confirmed this effect as statistically insignificant. Therefore, cutting direction need not be prioritized in optimizing the AWJ cutting process for plywood. However, it is essential to note that for specific applications or materials, the cut direction could have a more substantial effect.

When optimizing cutting parameters for specific applications, it is essential to analyze individual factors separately while considering their interactions, as suggested by Valíček et al. [39]. For example, the combination of material thickness and traverse speed can significantly affect both cutting quality and the economic efficiency of the process. This study aligns with the previous study [40], confirming the significant influence of critical parameters such as abrasive mass flow rate, traverse speed, and material thickness on AWJ cutting quality. However, notable differences emerged regarding the impact of cutting direction, which was found to be insignificant for plywood. This may be due to the specific properties of this material.

Additional literature [40,41,42,43,44] highlighted that the surface quality is a crucial aspect of hydro abrasive cutting, influenced by the adjustment of parameters. The focus on surface quality and the development of topographic functions during this process is a very current and widely discussed topic. The surface quality is a crucial factor not only for cutting efficiency but also for the subsequent material processing. Various parameters, such as traverse speed, abrasive flow, or water jet pressure, significantly influence the surface quality. Therefore, optimizing these settings is essential, as well as accounting for material-specific factors that can affect the cutting surface. Current research focuses on surface topography to find optimal cutting parameters for achieving a high-quality cut while minimizing defects such as rough edges or burrs. This issue is gaining importance with the growing industry demands for precision and quality of cut products.

Approximate Cost Overview:

At an operating pressure of 400 MPa, the high-pressure pump typically requires a power input of around 30–40 kW, which, at a feed rate of 50 mm/min, results in an energy consumption of approximately 10–12 kWh per meter of cut.

Abrasive consumption (e.g., garnet) ranges from 0.2–0.4 kg/min, which equates to about 4–8 kg per meter of cut, depending on the abrasive flow rate settings. Given a market price for garnet of approximately EUR 0.8–1.2 per kg, the material costs for abrasive can reach EUR 3–8 per meter of cut.

In addition, regular maintenance costs must be considered, particularly the replacement of worn nozzles (which have a service life of several tens of operating hours) and the costs associated with recycling or disposal of used water and abrasive, which can add approximately 10–15% to the total operating costs.

3.6. Arithmetic Average Deviations R_a for Plywood

The analysis of variance demonstrated that feed rate, cutting direction, abrasive flow, and beech plywood thickness significantly influenced surface quality measured by roughness R_a (p < 0.001) (

Table 7. AWJ delay depending on roughness.

Average Arithmetical Deviations of Surface Roughness Ra (μm)	Sum of Squares	Degrees of Freedom	Variance	F Test	p-Significance Level
Intercept	64,341.63	1	64,341.63	16,232.7	0.000000
{1} Feed rate	14.45	2	2.616	8.35	0.000271
{2} Cutting direction	5.232	2	2.616	10.22	0.001453
{3} Abrasive flow	7.86	2	2.613	9.82	0.000458
{4} Thickness	6.876	1	2.617	10.08	0.000345

). Higher feed rates reduced the contact time between the abrasive and the material, which deteriorated cut quality. The cutting direction affected roughness due to the anisotropic nature of the plywood and fiber orientation. Abrasive flow regulated the amount of abrasive particles, with the flow rate being crucial for material removal. Increased material thickness led to a wider cut and greater jet lag, reducing both accuracy and surface quality.

Economic aspects refer to all parameters or inputs that may impact the cost of cutting. When evaluating the AWJ method, economic consideration has a crucial influence on choosing between this and conventional cutting methods. AWJ offers efficient, versatile cutting across various materials, reducing the need for expensive tools. Its unique process creates burr-free edges, reducing the need for post-finishing [45,46]. In addition, this process does not produce heat, minimizing the material deformation [47,48,49]. A critical economic factor to consider is the initial investment and operating costs, including the price of the machine, maintenance expenses, and consumables such as abrasives and water. These upfront costs should be weighed against long-term savings from improved efficiency and post-finishing needs. An important economic factor is the cost of possible repairs or poor-quality water jet cutting. Here, the costs of removing defects and the losses associated with the material deterioration can be reflected. Another essential aspect is the total production time, which includes the cutting itself and subsequent operations. A shorter processing time increases the productivity and efficiency of the entire production process, directly impacting customer satisfaction and the ability to respond flexibly to demand while maintaining high-quality standards. Additionally, it is necessary to consider the labor costs involved in operating and maintaining the machinery. Operators are often required for AWJ, and their wages contribute to the overall cost of production. Additionally, waste generated by AWJ is often lower than traditional cutting, which results in material savings and reduced disposal costs. Under standard cutting parameters (pressure of 3800 bar, water flow rate of 4 l/min, and feed rate of 0.4 m/min), the estimated energy consumption for cutting one meter of beech plywood with a thickness of 15 mm is approximately 1.67 kWh/m. As the material thickness increases, the energy demand also rises due to greater material resistance and more pronounced jet lag. For instance, at a thickness of 36 mm, the energy consumption increases to approximately 2.00 kWh/m, and for 54 mm plywood, it further rises to about 2.25 kWh/m, representing a 20–35% increase compared with the baseline value. These data confirm that the selection of appropriate technical and material parameters is essential not only in terms of cutting quality but also in terms of energy efficiency and operational costs.

3.7. Final Discussion

Experimental results showed that the combination of cutting parameters—abrasive mass flow rate (250–350 g/min) and traverse speed (0.2–0.4 m/min)—enabled the minimization of AWJ lag while maintaining the surface quality of beech plywood comparable to that of planar milling. Increasing the abrasive mass flow rate from 250 to 350 g/min slightly improved cutting accuracy, whereas a further increase to 450 g/min caused a slight widening of the cut, resulting in higher material removal and a decrease in surface quality. It was also confirmed that as the plywood thickness increased, the required cutting force rose, leading to a wider cut and potentially negatively affecting the quality of the cut surface. Economic factors, including high initial investments and operational costs such as machine price, maintenance, and consumables, may restrict the practical implementation of AWJ technology in certain industrial sectors. Technological limitations, such as focusing tube wear and the need for operators, can impact long-term efficiency and costs. For future research, it is recommended to expand the investigated parameters to include the effects of additional technological factors such as standoff distance, water jet pressure, and type of abrasive, which can significantly influence jet lag and cutting quality. The development of predictive models and simulations, as well as the application of automation and artificial intelligence for real-time optimization of cutting parameters, also appears promising. These approaches could substantially enhance the understanding and practical applicability of this technology.

4. Conclusions

Based on the results of this study, which focused on the effect of abrasive mass flow rate and traverse speed on the cutting quality of technical beech plywood with an AWJ, the following recommendations can be formulated:

• Optimizing the Mass Flow Rate of the Abrasive

To achieve optimal results in abrasive water jet (AWJ) cutting, it is crucial to fine-tune the abrasive mass flow rate. Based on the study’s findings, a flow rate between 250 and 350 g/min is recommended, as this range yielded the most favorable cutting width. Exceeding this range may lead to a decline in cut quality. Proper adjustment of this parameter not only enhances process efficiency but also contributes to cost savings by reducing abrasive material consumption. Similarly, the traverse speed must be carefully regulated to balance the trade-off between cut quality and productivity. Experimental results indicated that speeds between 0.2 m/min and 0.4 m/min were optimal for achieving the desired cutting width. While higher traverse speeds can shorten processing time and increase throughput, they may also compromise cut quality, potentially leading to additional post-processing costs.

• Effect on Cut Quality

Maintaining high surface quality in abrasive water jet (AWJ) cutting requires careful monitoring of process parameters to prevent the formation of unwanted scoring or surface irregularities. Key variables such as abrasive mass flow rate and traverse speed must be precisely adjusted to minimize their adverse effects on surface finish. Continuous testing and calibration are essential for ensuring consistent performance. Furthermore, real-time process control and monitoring—enabled by modern sensors and automation technologies—allow for the immediate detection of deviations in cutting parameters. This facilitates prompt adjustments, thereby optimizing cut quality and enhancing overall process reliability.

• Practical Applications

For industrial applications of abrasive water jet (AWJ) cutting, the implementation of optimal parameter settings, along with regular equipment maintenance and inspection, is essential for ensuring long service life and consistent system performance. Equally important is the monitoring and minimization of energy consumption. Companies employing AWJ technology should invest in employee training and the practical application of research findings. A thorough understanding of equipment setup and the influence of various process parameters is crucial for achieving high production quality and reducing operational costs. Well-trained personnel contribute to lower error rates and enhanced productivity over time. Additionally, minimizing waste generated during the cutting process—through optimized cutting paths and reduced material wastage—not only lowers raw material expenses but also decreases waste disposal costs. For industrial practice, it would be highly beneficial to develop a practical guide or directive that includes recommended cutting parameters for different wood species and material thicknesses. Such a document could significantly facilitate the implementation of AWJ technology in the woodworking industry and improve its efficiency in processing layered or harder wood materials.

These practical jet recommendations can guide the use of AWJ in industrial applications and can help improve cutting efficiency and quality, but also significant economic savings, which increases the overall efficiency and competitiveness of the production process. From an economic perspective, AWJ technology offers significant advantages over traditional cutting methods, particularly due to its versatility in handling a wide range of materials, producing high-quality burr-free edges, and preventing heat-related material deformation.