© The Authors. CC-BY 4.0 Int. Licencee: SV-JME  Strojniški vestnik - Journal of Mechanical Engineering   ▪   VOL 71   ▪   NO 1-2   ▪  Y 2025
36 DOI: 10.5545/sv-jme.2024.1008
Connection Between the Dynamic Character 
of the Cutting Force and Machined Surface  
in Abrasive Waterjet Machining
Jelena Baralić
1
  – Suzana Petrović Savić
2
 – Branko Koprivica
1
 – Stefan Đurić
2
1 University of Kragujevac, Faculty of Technical Sciences Čačak, Serbia 
2 University of Kragujevac, Faculty of Engineering, Serbia
 jelena.baralic@ftn.kg.ac.rs 
Abstract This paper presents the results of research on the effect of traverse speed on cutting forces and machined surface in abrasive water jet machining. 
The results indicated that there is a significant connection between the dynamic character of the cutting force in abrasive waterjet machining, namely, peaks 
in the cutting force signal, with the appearance of irregularities and uncut parts in the machined surface. Also, the research showed that the increase of the 
traverse speed produces an increase in the mean value of the static component of the cutting force. In experiments, the vertical component of the cutting force 
has been measured for an Aluminium AlMg3 12 mm thick rod cut at traverse speeds from 900 mm/min to 1100 mm/min. Cutting with higher traverse speeds 
yields more irregularities, which are connected with the appearance of peaks in the measured cutting force.
Keywords abrasive water jet, cutting force, traverse speed, machined surface
Highlights:
 ▪ Developed experimental setup for measuring AWJ cutting force.
 ▪ Proposed a new method for calculating AWJ cutting force.
 ▪ Analysed the effect of cutting force on machined surface. 
 ▪ Analysed the effect of traverse speed on cutting force.
1  INTRODUCTION
With the development of new materials such as ceramics, reinforced 
and composite materials and heat-sensitive alloys, the problem of 
their machining has arisen. For machining of some new materials, 
high cutting forces or low clamping forces are required. Some 
materials must be machined so that high temperatures do not occur 
in the cutting zone. Hence, there has been an increasing use of an 
abrasive water jet (AWJ) in the machining of new materials. Almost 
all types of materials can be cut with AWJ [1]. It is widely used in the 
contour cutting of materials and the machining of materials that are 
difficult to process [2]. A great advantage of this machining procedure 
is that contour cutting becomes very easy, no matter how complex the 
contour [3].
The AWJ machining process consists of several complex processes 
(formation of pressurised water, mixing of pressurised water and 
abrasive, erosion of machined material and others). A short overview 
of this AWJ cutting technology, with emphasis on the cutting forces, 
will be given.
AWJ machining is an unconventional process of recent date, which 
has been the subject of much research during the last two decades. 
The output of the AWJ machining process is a machined surface. In 
order to ensure the good quality of the machined surface and detect 
errors, it is necessary to monitor and control the AWJ process. That is 
why numerous experimental studies on process monitoring, such as 
monitoring of cutting forces [4] and [5], monitoring through acoustic 
and vibration signals [6] and [7] are currently being carried out. An 
overview of these monitoring methods will also be given. When 
cutting with an AWJ at high traverse speeds, there is an increase in 
the value of the roughness parameters of the cut surface, especially 
in the zone where the AWJ exits the machined material. Increasing 
the traverse speed results in decreasing the depth of the cut [8]. 
Depending on the traverse speed, occasionally the material is not 
completely cut. However, this important subject has not yet been 
thoroughly investigated.
Previous research of cutting forces in AWJ machining have 
dealt with the development of a universal system for measuring the 
cutting force [4] and [9], using the cutting force to determine some 
parameters of the kerf geometry (mainly the maximum depth of cut) 
[10]. However, there are very few works on this subject regarding the 
modelling.
In this paper, a simple mathematical model for the calculation of 
the cutting force is proposed. The equation for calculating the cutting 
force in conventional cutting is applied to AWJ machining and the 
abrasive water jet itself is represented as a cutting tool. When there is 
an incomplete cut of the material, the cutting force increases, because 
then the jet acts on the material of the workpiece with its entire 
surface, that is, the cross-sectional area of the chip is a maximum.
For the purpose of investigation of the variation of the cutting 
force with the traverse speed also at higher traverse speeds, a specific 
system for measuring the cutting force has been developed. Thus, this 
paper presents the experimental setup for force measurement based 
on a personal computer (PC), the measurement results, along with 
their discussion and important observations.
In their research, many authors have used the vertical component 
of the cutting force as the main parameter for monitoring and 
evaluating the AWJ cutting process. Kovačević [11] measured 
the vertical force component when cutting with the AWJ. A 
three-component dynamometer was used to measure the vertical 
component force. The vertical component of the cutting force was 

SV-JME   ▪   VOL 71   ▪   NO 1-2   ▪   Y 2025   ▪   37
Production Engineering
measured for different values of the AWJ machining parameters. The 
aim of the research was to control the depth of cut based on the signal 
of the vertical force component. A precisely controlled depth of cut is 
very important when milling with the AWJ, i.e. engraving contours 
in the material. Measurements showed that the vertical component 
of the cutting force increases with increasing water pressure, nozzle 
diameter and abrasive mass flow rate. Also, it was found that it 
decreases with increasing standoff distance. Large oscillations in the 
values of the vertical force component indicated wear of the nozzle 
and that the maximum depth of cut had been reached.
In further research, Kovačević et al. [9] used the same principle 
for measuring the vertical cutting force component as in the previous 
work, with the aim of investigating the possibility of connecting 
the dynamic characteristics of the cutting force with the profile of 
the machined surface. Various parameters of the AWJ machining 
process were varied: water pressure, traverse speed, abrasive flow 
rate and standoff distance, in order to determine their effect on the 
cutting force and profile of the machined surface. It was found that 
both the abrasive flow rate and traverse speed have a slight effect 
on the vertical component of the cutting force. The influence of 
the AWJ machining parameters on the cutting force was analysed 
using stochastic modelling of the force data. Autoregressive moving 
average (ARMA) models are suitable for processing the results of 
measuring the vertical component of the cutting force for different 
values of the machining parameters. It was observed that the spectral 
density of the dynamic force ARMA model behaves in the same way 
as the measured profile of the machined surface. Based on this, they 
concluded that the signal of the vertical component of the cutting 
force can be considered as a potential parameter for the monitoring of 
the surface profile at the deformation wear zone.
Hassan et al. [10] proposed a model for monitoring the depth of 
cut during abrasive waterjet machining based on acoustic emission 
(AE) monitoring. The aim was to establish the dependence between 
these two parameters, so that the depth of the cut could be predicted 
based on the AE. Carbon steel AISI 1018 was used as a workpiece. 
The cut length of the samples was 38 mm to ensure a steady-state of 
cutting. During cutting, the working pressure values were varied from 
100 MPa to 350 MPa. The vertical component of the cutting force 
was measured for all values of the working pressure, and the AE was 
also monitored. For all cuts, the mean value of the cutting force and 
the root mean square of the acoustic emission energy (AErms) for 
steady-state of cutting were calculated. It was observed that AErms 
increases linearly with an increase in the depth of cut and could be 
used for its on-line monitoring [10]. Hlavač et al. [4] constructed a 
special device for cutting force measurements during machining with 
AWJ. They monitored the signal of the cutting force in the normal 
and tangential directions before the start of cutting and during the 
cutting of the material. The workpieces were made of different 
materials, such as steels, duralumin, copper, and brass. The cutting 
of the workpiece was done in different modes. Also, the cutting 
was performed both with and without rotation of the cutting head. 
The tangential-to-normal force ratio (TNR) was taken as the most 
appropriate indicator for monitoring the cutting force and the quality 
of the machined surface. It was observed that the TNR reaches its 
maximum value at approximately 50 % of the maximum value of the 
traverse speed. Hlavač et al. [5] used the same measuring device as in 
[4], only the obtained signal of the vertical component of the cutting 
force was used for the detection of irregularities during cutting with 
AWJ, i.e. for the detection of incomplete cutting of the material.
Orbanić et al. [12] measured the diameter of the AWJ. A hard 
metal insert was the workpiece. During machining, the cutting force 
signal was monitored. Three characteristic areas can be observed on 
the obtained diagram of the cutting force: The first one was where the 
cutting force is equal to zero - the contact of the jet and the insert has 
not yet occurred. The second one is where the force increases - the jet 
comes into contact with the insert and the contact surface increases.  
The third one is where the force has stabilised - the whole jet is on the 
insert. The Vishay Transducers 1022 load cell was used to measure 
the vertical force component. Based on the change in the value of the 
vertical component of the force and the traverse speed, the diameter 
of the jet was calculated.
Momber [13] analysed the efficiency of the energy transformation 
using measurements of the vertical component of the cutting force. A 
Kistler dynamometer, model 9273, was used to measure the vertical 
component of the force. It was shown that the forces exerted by the 
high-speed jet on the workpiece can be successfully used to analyse 
the energy dissipation process during the formation of high-speed 
water-jets and during the mixing and acceleration of solid particles 
and air by high-speed waterjet (during the formation of the AWJ).
Baralić and Nedić [14] measured the cutting force using a three-
component dynamometer for turning, KISTLER Type 9265A1, for 
samples of X5CrNi 18-10 with various thicknesses. The aim was to 
investigate the influence of the AWJ machining parameters (traverse 
speed, operating pressure, abrasive mass flow and material thickness) 
on the cutting force. It was found that an increase in the operating 
pressure leads to an increase of the cutting force. The effect of the 
abrasive mass flow on the cutting force is almost negligible, while an 
increase of the traverse speed, as well as an increase of the thickness 
of the material being machined, leads to an increase of the cutting 
force.
In the literature, there is no simple model for expressing the 
relation of the cutting force, as the significant output parameter of 
the system that can be measured, and the traverse speed as the input 
parameter that is set before the cutting of the material. Furthermore, 
the relation between these two quantities has not yet been thoroughly 
investigated for higher traverse speeds, when irregular cuts appear, 
as well as peaks in the cutting force. The present paper focuses on 
these shortcomings, with the goal of establishing a simplified F
v
(v
c
) 
model, measure accurately the cutting force at higher traverse speeds, 
analyse the peaks in the cutting force in relation to the roughness of 
the surface, and validate the F
v
(v
c
) model for the peak values of the 
cutting force. This paper contributes to the state of the art in the field 
by introducing a new F
v
(v
c
) model and its experimental validation. 
2  METHODS & MATERIALS
The main goal in today's production is to make as many products as 
possible in the shortest possible time and with as little investment 
as possible. In order to make this possible when machining with 
an AWJ, it is necessary to perform the machining with the highest 
possible traverse speeds. Machining with a high traverse speed 
results in an increase in the roughness parameters of the machined 
surface. This phenomenon is significantly expressed in the rough 
zone of the machined surface, that is, at the exit of the AWJ from 
the workpiece [15]. When the maximum traverse speed with which 
it is possible to completely cut materials of a certain thickness, is 
reached, the process of cutting with the AWJ becomes unstable and 
the material is, occasionally, not completely cut. The assumption is 
that in places where the material has not been completely cut, there is 
a sudden increase in the vertical component of the cutting force. 
In the case that material is not completely cut, in practice the 
traverse speed is most often changed (reduced). The abrasive mass 
flow rate is rarely changed, and the operating pressure is almost 
never changed. Therefore, the influence of traverse speed on cutting 
force was analysed, even though the process of machining itself is 
influenced by numerous factors.

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38   ▪   SV-JME   ▪   VOL 71   ▪   NO 1-2   ▪   Y 2025
2.1  Proposed Model for Calculation  
of Cutting Force in AWJ Machining
During its movement through the machined material, the AWJ acts on 
the material with some force. This force has the same direction as the 
speed of the AWJ, that is, it is tangent to the path of the AWJ cutting 
front line, Fig. 1.
Fig. 1.  Cutting force while machining with AWJ
The cutting force with which the AWJ acts on the workpiece can 
be divided into two components, vertical and horizontal:
 
FFF
vh
 . (1)
In general, the diagram of the change of the vertical component 
of the cutting force F
v
 with time has the form as shown in Fig. 2. 
This diagram shows that the force F
v
 has its dynamic and static 
components. Due to the dynamic character of the AWJ machining 
process, the cutting force has a distinctly dynamic character. During 
a complete cut, the dynamic character of the cutting force is a 
consequence of oscillations in the values of the working pressure and 
the number of abrasive particles that are in contact with the object of 
processing. Also, a peak in the value of the cutting force can occur 
due to inclusions in the material of the workpiece. From Fig. 2, it 
can be seen that the value of the vertical cutting force component F
v
 
increases when the AWJ starts cutting the sample.
Fig. 2.  Diagram of the vertical component of the cutting force, F
v
This value increases until the AWJ begins to cut completely 
through the entire thickness of the material. After that moment, 
there is no further increase in the value of the vertical cutting force 
component.
Abrasive particles in AWJ can be approximated by the cutting 
edge of a multi-cutting tool moving at a speed v
awj
 through the 
material being machined. At the same time, the cutting head moves at 
the traverse speed v
c 
, Fig. 3.
In a case of conventional cutting, the work W of the mechanical 
force F done along path L can be calculated in a simplified form as:
W = F L, (2)
for a constant force along a straight path and when the force has the 
direction of the path. This work, during the cutting with the AWJ, can 
be equated with the cutting energy of the water jet, E
awj
. Thus, the 
force can be determined by this energy,
F
E
L
EV
L
awj
c
= = , (3)
where E
c
 is the specific cutting energy of AWJ machining, V is the 
volume of removed material, and L is the length of the arc of the 
cutting front line. It is the length over which the cutting force acts 
(chip length).
Fig. 3.  Approximation of the abrasive water jet machining process
The volume of removed material can be calculated using Eq. (4).
VL lw
m
= . (4)
The mean width of the cut w
m
 is the mean value of w
en
 and w
ex
, the 
width of cut at the entry of the AWJ into the material being machined 
and the width of the cut at the exit of the AWJ from the material, 
respectively:
w
ww
m
en ex


2
. (5)
The path of the cutting head, while the AWJ removes the material 
along a single striation (cut the forehead through the whole material 
thickness) is l, according to Fig. 3 it is equal to:
lv tt
L
v
c
awj
= = ,. (6)
According to Eqs. (4) to (6), it follows that the volume of removed 
material V is:
VL w
v
v
m
c
awj
=
2
. (7)
By substituting the equations for calculating the volume of 
removed material into Eq. (3), the equation for calculating the cutting 
force can be written in the form:
FE Lw
v
v
cm
c
awj
= . (8)
In Eq. (8), the most influential factor is the traverse speed v
c
. 
The dependence of the cutting force on the traverse speed can be 
approximately represented as linear. It can be concluded that with 
an increase in the traverse speed, there is an increase in the value 
of the cutting force, i.e. the vertical component of the cutting force. 
The biggest peak in the cutting force occurs when the material of the 
workpiece is not completely cut, because then the AWJ acts with its 
entire surface of the machined material.
According to Fig. 1 and Eq. (1), the vertical component of the 
cutting force, F
v 
, can be calculated by:
FF ELw
v
v
ve cm
c
awj
e
 cosc os .  (9)
where α
e
 is the angle of the tangent of the cut front line.

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Production Engineering
2.2  Experimental Setup for Cutting Force Measurement
The phenomenon that when the cutting with an abrasive water jet 
does not completely cut through the material, there occur extreme 
values in the cutting force signal (peaks) and pronounced roughness 
of the obtained cut surface imposes the need for specific research.
Accordingly, the research presented in this paper has focused 
on the connection between the dynamic character of cutting forces, 
peaks in the cutting force, and the appearance of irregularities and 
uncut parts on the machined surface while machining at high traverse 
speeds. The experimental measurements of the cutting force were 
carried out for the PTV-3.8/60 abrasive water jet machine with a 
KMT cutting head. The cutting was done over the water. The cutting 
force has been measured at traverse speeds around 1000 mm/min 
(much higher than usual). The maximum value of traverse speed at 
which a complete cut can be obtained (based on the KMT calculator) 
is 900 mm/min. Traverse speeds were chosen so to obtain a regular 
cut and a combination of regular and irregular cuts, but not complete 
uncut piece. Prior to the force measurement, a set of cuts was made 
with the same sample at different traverse speeds, from lower to 
higher, to determine the range of speeds that suits the purpose of the 
planned research. Thereafter, relevant set of cuts and cutting force 
measurement were done in the range of traverse speeds of interest. 
Other parameters of the machining process were constant during 
AWJ cutting of the samples: the operating pressure was 4130 bar, 
abrasive mass flow rate 350 g/min, standoff distance x
o
 was 3 mm 
and the abrasive was garnet mesh size 80. The water nozzle (orifice) 
diameter was 0.3 mm and focusing tube diameter was 1.02 mm.
a) 
b) 
Fig. 4.  Experimental setup for cutting force measurement:  
a) photograph of the components, b) block scheme of connections
The experimental setup for measurement of cutting force is 
based on a PC. It consists of the following equipment: 1) the test 
sample, fixedly mounted to 2) the load cell CZL623B (for 10 kg, up 
to approximately 100 N), 3) the direct current (DC) power supply 
for the load cell, 4) the data acquisition card NI 9205 (placed in the 
chassis NI cDAQ 9174) and 5) a PC with LabVIEW software. The 
load cell is fixed to 6) the steel carrier profiled so it fits well one 
side of the waterjet cutting machine. Fixed mounting of the carrier 
to the machine has been made with three large screws. A photograph 
of the equipment used is shown in Fig. 4a, and a block scheme of the 
connections is given in Fig. 4b.
The test sample is a 12 mm thick aluminium rod, 50 mm wide and 
300 mm long. Aluminium is of ENAW-5754 (AlMg3) quality, the 
main alloying element is magnesium. Tensile strength of AlMg3 is in 
the range of 80 MPa to 280 MPa and Brinell Hardness (HB) from 52 
to 88. It has been screwed to the load cell at one end by two screws 
and the other end was free. The material has been selected because of 
its often used in practice. The dimensions were chosen so to have a 
significantly long cutting path, and the thickness of the sample so as 
to obtain irregular cuts at higher speeds.
The load cell contains four strain gauges connected in full bridge 
(Fig. 4b). Its sensitivity is rated by the manufacturer at 2 mV/V for the 
mass of 10 kg, or in other terms it is 2mV/kg for 10 V supplied by the 
DC power supply. Thus, the output voltage would be 10 mV for 10 
V of input voltage and 5 kilograms of the load. The data acquisition 
(DAQ) card NI 9205 is an analogue voltage input module of 16 
bits resolution and 250 kS/s maximum sample rate (in samples per 
second). Its lowest input range is 200 mV . Thus, it is suitable for the 
measurement of low voltages from the load cell and is fast enough to 
observe transients. During the measurements, the DAQ card acquired 
1200 S/s. This card has been inserted into a chassis NI cDAQ 9174 
which provides the power supply for the card and a connection with a 
PC over the USB cable.
A standard DC laboratory supply of a stable DC voltage was 
used as the power supply for the load cell. The laptop computer 
was running LabVIEW 2014. A simple program for acquisition of 
the voltage generated at the output of the load cell has been created 
for the planned measurements. The program was set to continuous 
sample acquisition and writing the data to the computer memory.
Prior the measurements of the force of the abrasive water jet 
machine, the load cell was calibrated in the laboratory using precision 
weights and by measurement of the output voltage. The calibration 
has been performed using the measurement setup presented in Fig. 
4b. The test sample 1, load cell 2 and steel carrier 6 were fixedly 
mounted to the laboratory table (similarly to Fig. 4a). Supplied DC 
voltage was set to 10 V . Laboratory weights of different masses, from 
50 g to total 5000 g (about 49 N), were positioned on the test sample 
and the output voltage was recorded using the LabVIEW application. 
The measurement results obtained are graphically presented in Fig. 5, 
together with the linear fit of these data.
Fig. 5.  Measurement data and linear fit obtained during the calibration of load cell
The slope of the linear fit is 2.001 mV/kg, which confirms the 
rated sensitivity of the load cell given by the manufacturer, which is 
2 mV/kg.
The manufacturer also stated the accuracy of the load cell 2 % 
as 0.02 % of the full scale (10 kg), which is equal to 2 g of the 
absolute error in the whole measurement range. This corresponds 
to an absolute error of 4 μV at the maximal load cell output voltage 
(20 mV). The manufacturer of the DAQ NI 9205 stated the absolute 
error of 175 μV in the range of ±0.2 V .

Production Engineering
40   ▪   SV-JME   ▪   VOL 71   ▪   NO 1-2   ▪   Y 2025
The force F has been determined from the measured load cell 
output voltage u
LC
 as:
Fg
u
S
u
S
LC
LC
LC
LC
= =9 80665 ., (10)
where S
LC
 is the load cell sensitivity. The combined uncertainty 
u
c
(F) of force F measurement is defined according to the sensitivity 
coefficients, which are calculated as partial derivatives of F, and the 
absolute uncertainties of each independent variable, as in [16]:
uF
F
u
u
F
S
u
c
LC
Bu
LC
BS
LC LC
() ,
,,


















2
2
2
2
 (11)
where u
X
 = | ∂F / ∂X | u
B,X
, X ∈{u
LC
, S
LC
} and u
B,u
LC
 , u
B,S
LC
 are Type B 
standard uncertainty calculated by dividing corresponding absolute 
errors with 3 , for a rectangular distribution with the confidence 
level of 95 %. Sensitivity coefficients are calculated for maximal 
voltage u
LC
max
 and previously calculated S
LC
. All calculated values 
are given in Table 1. 
Table 1. Type B uncertainty for load cell calibration at 49 N (5 kg)
Variable
u
LC
max
S
LC
Value 9.968 mV 2 mV/kg
Absolute error 175 μV 0.4 μV/kg
Sensitivity coefficient 4903.3 N/V −244382 kg/V
Absolute standard uncertainty u
X
 [N] 0.495 0. 056
Relative uncertainty [%] 1.014 0.115
The combined uncertainty value is 0.499 N and its relative value 
is 1.02 %. A correction factor k = 2 can be used for calculating the 
expanded uncertainty. In such a case, the confidence level is around 
95 % and expanded uncertainty is 1.00 N or 2.04 %. The calculations 
need to be repeated to obtain the uncertainty for other values of the 
force (mass).
It should be noted that the measured values of the force are not the 
real ones because the cutting force is not developing coaxially to the 
load cell. However, this issue was not considered significant, as the 
bending of the steel carrier, load cell or sample was negligible, due to 
their robustness.
3  RESULTS AND DISCUSSION
The measurements of the cutting force have been performed at higher 
traverse speed to examine the relation between irregularities in the 
machined surface and the cutting force applied to the test sample 
made by the AWJ. Cuts have been performed in the longitudinal 
direction of the sample. The cuts were 100 mm long. One transversal 
cut has been made prior to all other cuts at lower speed (600 mm/min) 
as a trial case. Other cuts have been performed at four traverse 
speeds, namely: 900 mm/min, 950 mm/min, 1000 mm/min and  
1100 mm/min. 
A comparison of the forces obtained for 600 mm/min and  
900 mm/min is presented in Fig. 6. Both traverse speeds are low 
enough that the cutting through the material is regular. 
The light grey line in Fig. 6 represents the original measured data, 
whereas the blue and orange lines represent the smoothed measured 
data (obtained using the built-in function Smooth of OriginLab 
software). The force has the same level of 5 N before and after 
the cutting and it increases up to 15 N for the transversal cut and 
up to 18 N for the longitudinal cut. Thus, both directions can be 
used for observing the cutting force and the quality of cutting. The 
longitudinal cutting contains more pronounced oscillations in the 
force and even significant peaks in the range from 30 N to 40 N. All 
that is a consequence of the higher traverse speed.  
Fig. 6.  Comparison of cutting force measured at lower (600 mm/min)  
and higher (900 mm/min) traverse speeds
Further analysis of the results will be focused on higher traverse 
speeds. The force profile for each of four cuts made will be discussed 
in detail. Photographs of the bottom and side view for each cut will 
be shown along with the force profile and their relation will also be 
discussed.
A profile of the cutting force for a traverse speed of 900 mm/
min is presented in Fig. 7. The grey dashed lines represent the lower 
(17.5 N) and upper (35 N) cutting force limits chosen so that most of 
the measured data is within those limits when the cutting is correct. In 
Fig. 7, below the cutting force signal, there are photographs of the cut 
surfaces (orange box and black arrows) and a view from the underside 
of the cut sample (magenta box and black arrow). Green arrows and 
circles indicate cutting force peaks that are within (or slightly above) 
the upper and lower limits, which correspond to normal cutting or 
with irregularities of negligible size. In this case, the bottom view 
shows no irregularities in the cutting. Small irregularities can be seen 
in the side view, where the AWJ has created several cavities of small 
sizes. Their position corresponds to the position of the force peaks.
Fig. 7.  Profile of cutting force for traverse speed of 900 mm/min,  
along with photographs of the cut
The profile of the cutting force for the next traverse speed of 
950 mm/min is presented in Fig. 8. This slight increase in the traverse 
speed results in an increase in the number of peaks in the force profile. 
Still, the cutting is regular, as can be seen from the bottom view, but 
the number of cavities is evidently larger, and again it corresponds 

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Production Engineering
well to the number of peaks. Also, the size of the cavities is larger 
than for the lower traverse speed.
Fig. 8. Profile of cutting force for traverse speed of 950 mm/min,  
along with photographs of the cut
The profile of the cutting force for the third traverse speed of 1000 
mm/min is presented in Fig. 9.
Fig. 9.  Profile of cutting force for traverse speed of 1000 mm/min,  
along with photographs of the cut
The bottom view shows that the cutting is occasionally irregular, 
as there are several smaller uncut regions and regions with material 
remaining. Almost the whole cut is covered with cavities, as can be 
seen in the side view. Many smaller peaks appear in the force profile, 
as well as two larger peaks (marked with red arrows and circles). 
These two peaks appear in the places where the material remained 
uncut. The force reaches almost 50 N in those two cases. The number 
of smaller peaks above 35 N has increased from 2 in the previous two 
cases to 8 in this case. 
Fig. 10 shows cavities on the machined surface for a traverse 
speed of 1000 mm/min. Small uncut triangles can also be observed. 
Cavities are formed when the material is not completely cut, so the 
AWJ reflects from the uncut material. AWJ, part of whose energy has 
been spent, turns into solid material, where due to insufficient energy, 
swirling of the AWJ and creation of cavities occurs. Jerman at al. [17] 
noticed this phenomenon in their study of the development of the 
cutting front in AWJ machining. This is due to the jet's redirection at 
the bottom of the cut and not a reduction in the intensity of the  AWJ.
The profile of the cutting force for the last traverse speed of 
1100 mm/min is presented in Fig. 11.
In this most extreme case, the cutting is mostly irregular (clearly 
visible in the bottom view). Some smaller or larger uncut regions 
exist, as well as regions with contiguous uncut parts. Two individual 
uncut parts in the left half have produced two individual peaks, while 
multiple uncut parts have produced multiple peaks (in the right side). 
The duration of the peak is proportional to the length of the uncut 
triangle. The force profile is such that the force is significantly higher 
than the lower limit during the whole cut. Again, force peaks reach 50 
N and more for the uncut regions. Furthermore, multiple cavities can 
be observed in the side view of the region with multiple uncut parts. 
Some of the cavities are quite large and moved from the surface to 
the inside of the material (for up to one quarter of the thickness).
Fig. 10.  Cavities on machined surface for traverse speed of 1000 mm/min
Fig. 11.  Profile of a cutting force for traverse speed of 1100 mm/min,  
along with the photographs of the cut
A summary of the characteristic data related to all four traverse 
speeds is given in Table 2. It contains the following data: the traverse 
speed v
c
, the cutting time t
c
, the number of smaller peaks N
ps
, the 
number of larger peaks N
pl
, the number of uncut parts N
u
 and the 
maximum of the vertical force F
vm
 for the whole cut. 
Table 2.  Characteristic data for four cuts 
v
c
 [mm/min] t
c
 [s] N
ps
N
pl
N
u
F
vm
 [N]
900 6.66 8 0 0 38.37
950 6.32 15 0 0 41.10
1000 6.00 18 3 2 49.78
1100 5.45 14 12 18 56.84
The results for the number of peaks and cuts and maximal force are 
related to the smoothed data. They depend slightly on the smoothing 
parameters, but without any significant changes in the nature of the 
overall force profile.

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42   ▪   SV-JME   ▪   VOL 71   ▪   NO 1-2   ▪   Y 2025
Previous research has shown that the cutting force increases 
with increase of the traverse speed in the range up to 100 mm/min 
[18], and up to 300 mm/min [19]. Also, in [5], it was shown, using 
the results of experiments on several different metals, that there is a 
connection between peaks in the value of the cutting force and uncut 
parts of the material.
 Taking the data for traverse speed and peak of cutting force given 
in Table 2 and taking into account that the peak of the cutting force 
amounted to around 15 N for the speed of 600 mm/min (see Fig. 
6), a variation of the cutting force with the traverse speed has been 
presented graphically in Fig. 12. All values of the force are reduced 
by the force made by the test sample (around 4.5 N), which exists 
before and after the cutting (Figs. 6 to 11).
The measured data (black dots) have been fitted with a linear 
function, and the result obtained is presented by a dashed blue line, 
along with the data. The result in Fig. 12 confirms linear relationship 
given by Eq. (8), when considering the cutting force peak and the 
traverse speed. The linear dependence of the cutting force on the 
cutting depth and feed also exists in conventional cutting machining 
[20]. When machining with AWJ, cutting depth and feed depend on 
traverse speed.
This simplified model could be useful for application in the 
practice. However, such a linear relation should be investigated 
experimentally also for other materials and parameters of AWJ 
process. Also, the relationship of the cutting force and other input 
parameters needs to be investigated to improve overall knowledge 
about AWJ process and obtain other useful calculation tools. This 
was out of the scope of this paper and might be a subject of a future 
research in this field.
Fig. 12.  Variation of cutting force with traverse speed
4   CONCLUSIONS
This paper presents the results obtained by experimental 
measurement of the vertical component of the cutting force, showing 
that measuring the vertical component of the cutting force makes 
it possible to observe a period when the machined material is not 
completely cut. Also, online measurements of the cutting force can be 
used for the evaluation of the quality of the machined surface.
The experimental results allow concluding that an increase of 
the traverse speed, above a certain limit, results in the appearance of 
irregularities in the cut and in an increase of the vertical component 
of the cutting force. Even when the cut is regular, such as for speeds 
of 900 mm/min and 950 mm/min, the maximum values of the vertical 
component of the cutting force can be more than two times larger than 
the lower limit. In the case of higher traverse speeds, when irregular 
cuts appear, the maximum values of the vertical component of the 
cutting force can be more than three times larger than the lower limit. 
Beside the appearance of the uncut parts, smaller or larger cavities 
are produced in the material during cutting at high traverse speeds. 
These cavities significantly increase the roughness of the machined 
surface. Such unwanted side effects would require additional 
treatment of the machined surface after cutting. It can influence the 
quality of the final product.
The results of the conducted experiment can also be used for a 
better understanding of the material cutting process performed with 
the AWJ. There can be established a relation between the duration of 
the cutting force peak and the length of the uncut part, as well as their 
frequency. Also, based on the appearance of peaks in the profile of the 
vertical component of the cutting force, the beginning of cutting with 
an unsatisfactory quality of the machined surface can be determined. 
In conventional cutting, increasing the auxiliary speed (feed) 
causes an increase in the cross-sectional area of the chip, and 
therefore the volume of the removed material, which further leads to 
an increase in the value of the cutting force. In this paper, machining 
with abrasive water jet is viewed as a classic cutting process. The 
abrasive water jet is represented as a cutting tool, while the cross-
sectional area of material removed per unit of time is represented as 
a cross-sectional area of the chip. By applying the formulas valid for 
conventional cutting procedures, a new model was obtained for the 
calculation of the cutting force during machining with an abrasive 
water jet. This model is much simpler than the models presented in 
previous research by other authors. In AWJ machining, traverse speed 
is most often varied in practice, while operating pressure and abrasive 
mass flow rate are less frequently changed. In these conditions, the 
model presented in the paper shows that there is a linear relation 
between the traverse speed and cutting force. With the increase of 
traverse speed, there is an increase in the cross-sectional area of the 
chip, and therefore the volume of the removed material. This further 
leads to an increase in the value of the cutting force. Measurements 
have shown that with an increase in the traverse speed, there is an 
increase in the value of the cutting force, which confirmed these 
assumptions. To determine the cutting force for a given material 
and machining parameters, it is necessary to determine the specific 
cutting energy, which can be the subject of further research. Also, 
future research can deal with the influence of the operating pressure 
and mass flow rate on the values of the cutting force.
AWJ requires a much larger number of input parameters than 
considered in the conducted research. However, the focus was given 
to the traverse speed as input parameter and the cutting force as the 
output parameter to validate the model under specific conditions. 
It was of a particular importance to investigate if the direct 
proportionality of the simplified model still remains valid at higher 
speeds.
To apply the conclusions presented in this paper to the current 
manufacturing of parts using abrasive water jet technology, it is 
essential to develop specialized cutting tables. These tables should 
facilitate online monitoring of cutting force values, which could also 
be a subject for further research.
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Acknowledgements  This study was supported by the Ministry of Science, 
Technological Development and Innovation of the Republic of Serbia, and 
these results are parts of the Grant No. 451-03-66/2024-03/200132 with 
University of Kragujevac - Faculty of Technical Sciences Čačak, Serbia.
Received 2024-04-02, revised 2024-08-19, accepted 2024-11-05
Original Scientific Paper
Data Availability  The data that support the findings of this study are available 
from the corresponding author upon reasonable request.
Author Contribution  Conceptualization, J.B. and B.K.; methodology, J.B., 
S.P.S. and B.K.; software, B.K. and S.Đ.; validation, J.B., S.P.S., S.Đ. and 
B.K.; formal analysis, B.K., J.B., S.P.S. and S.Đ.; investigation, J.B. and B.K.; 
resources, J.B., S.Đ. and S.P.S.; writing – original draft, J.B., B.K. and S.P.S.; 
writing – review and editing, J.B. and B.K.; visualization, J.B., B.K., S.P.S. 
and S.Đ.; supervision, J.B. and B.K. All authors have read and agreed to the 
published version of the manuscript.
Povezava med dinamičnim značajem rezalne sile in obdelano 
površino pri obdelavi z abrazivnim vodnim curkom
Povzetek V članku so predstavljeni rezultati raziskave o vplivu hitrosti 
premikanja na rezalne sile in obdelano površino pri obdelavi z abrazivnim 
vodnim curkom. Rezultati so pokazali, da obstaja pomembna povezava med 
dinamičnim značajem rezalne sile pri obdelavi z abrazivnim vodnim curkom, 
natančneje med vrhovi v signalu rezalne sile, ter pojavom nepravilnosti in 
nerazrezanih delov na obdelani površini.  Prav tako je raziskava pokazala, 
da povečanje hitrosti pomikanja povzroči povečanje srednje vrednosti 
statične komponente rezalne sile. V eksperimentih je bila izmerjena navpična 
komponenta rezalne sile za 12 mm debelo palico iz aluminija AlMg3, rezano s 
hitrostmi premikanja od 900 mm/min do 1100 mm/min. Pri rezanju z večjimi 
hitrostmi se pojavijo večje nepravilnosti, ki so povezane s pojavom vrhov v 
izmerjeni rezalni sili.
Ključne besede abrazivni vodni curek, rezalna sila, prečna hitrost, obdelana 
površina