Investigation on the Cutting Force and Surface Quality in Harmonically Vibrated Broaching (HVB)

. Tis paper investigates the broaching process of phosphor-bronze (C54400) under diferent cutting conditions, and the infuential factors on cutting force and surface quality are studied. Te simulated cutting force implementing the force model based on the energy components also agrees with the results of experiments. In the frst part, diferent cutting velocities of V C � 5, 10, 15, and 20 m/min are studied. In the second part, harmonic vibrations in the form of a sine wave with precise amplitude ( A � 1m/min) and frequencies ( F � 55, 65, 85, and 95Hz) are added in the direction of the cutting velocity. Te results revealed that an increase in the cutting velocity from 5 to 20m/min results in a 40% enhancement in surface quality and a 20% decrease in the cutting force. Additionally, harmonic vibrations of higher frequencies can also contribute to a 35% higher surface quality and a 20% lower cutting force. Tis study will ultimately improve productivity in industries where broaching is considered the main manufacturing approach, such as automotive and aerospace, in which precision and accuracy are of paramount importance.


Introduction
Broaching is one of the cutting processes, similar to sawing, which allows the production of diferent shapes on the machined surface, e.g., fat, grooved, or even formed surfaces.It is a single-path operation and is commonly carried out as a postturning/postmilling process.Broaching is economical, particularly in mass production, and can produce surfaces with the desired roughness and high geometrical accuracy [1].
Broaching is commonly used in high-tech industries such as automotive and aerospace, where precision and accuracy are important [2].It is a process in which complex shapes can be produced with a high surface fnish, where the use of lubrication is common [3,4].Te broaching tool typically consists of three sections: roughing, fnishing, and calibration."Rise per tooth" is the parameter by which the material removal rate is decided.Other infuential geometrical features include depth of cut (f z ), rake angle (c), clearance angle (α), and width of the land (b fa ), which may difer depending on the section of the tool [5] (roughing, fnishing, or calibration) and mechanical properties of the workpiece material (Figure 1).
One problem with the broaching process is tool wear, which mostly afects edge fank surfaces (fank wear).However, it can also manifest as crater wear on the rake face.Multiple wear reasons can take place at once.However, abrasion is the most typical.A small degree of plastic deformation can also be seen at the tips of the teeth.Additionally, unexpected vibrations may cause edge chipping.Other processes that depend more on temperature are uncommon since coolant oils regulate process temperature [7].
Forst [8] experimentally defned broaching and investigated the efective causes and parameters of the process in detail.Although it was published in 1932, it has never been considered outdated.Terry and Cutright [9] introduced a CAD (computer-aided design) process for determining both the optimal values and operating conditions for the broaching process.Kishawy et al. [10] surveyed the mechanics of cutting and the efects of broaching tool teeth on the surface roughness of the workpiece material through an energy-based analysis, and Teti et al. [11] reviewed the monitoring of machining operation approaches and signal-processing strategies as well as their industrial applications.
Hosseini and Kishawy [12] presented a force model for predicting cutting forces and chip load in orthogonal and oblique broaching processes by introducing the cutting edge as a parametric B-spline curve.Axinte et al. [13] studied the relationship between the quality of the machined surface and the output signals of cutting force, vibration, and acoustics sensors.Tey implemented surface roughness and optical and scanning electron microscopy to evaluate surface quality parameters such as profle deviation, chatter marks, and burr formation.Özelkan et al. [14] studied a methodology to design a broaching tool, considering geometrical and physical limitations optimally.Complementary research was carried out by Ozturk and Budak [15], where they studied a broaching tool optimization method implementing cutting models and fnite element analysis (FEA) and abridged the outcome of the research into analytical forms that can be used in industrial applications.Axinte and Gindy [16] monitored the tool condition in diferent broaching conditions using the output signals extracted from some sensors in diferent tool conditions.Tey concluded that acoustic emission, vibration, and cutting force sensors are sensitive to broaching tool conditions.
Meng et al. [17] did thorough research on modelling and analysis of the broaching process enhanced by a forced vibration on cutting velocity created by a single harmonic motion.Tey also considered three important notes: the cutting force of a single tooth, the number of teeth engaged, and the infuence of simple harmonic motion.Ten, they presented two single-tooth and two multiteeth models for broaching based on the empirical approach and shear angle theory.Finally, they verifed the results with experimental tests.
In a recent study, Orouji et al. [18] studied the infuence of cutting velocity on surface quality in the broaching process on the workpiece material of Al-7075, resulting in observations of enhanced surface quality and reduced cutting force with the increase of cutting velocity.Later, Bajestani et al. [19] studied the efect of vibrations in cutting velocity on the cutting force and surface roughness in Al7075-T6 broaching.Tey concluded that increasing cutting velocity will lead to lower cutting force and increased surface quality.
In this paper, we propose the concept of harmonically vibrated broaching (HVB) with diferent frequencies to reduce the cutting force and improve the surface roughness of the process.We implemented the numerical force model using the energy balance and performed the experiment with phosphor-bronze (C54400) material to verify the results.

Force Model Using Energy Balance
According to the model proposed by Kishawy et al. [10], the cutting force can be quantifed as a function of power components as where P C (N.m/min) is the power consumed for the cutting process, P fF and P fR are the power consumption at the toolworkpiece and tool-chip interface, respectively, P pd is the consumed power for the plastic deformation of the workpiece for material removal, P ch is the power used for the formation of the new surface, and P mn-ce is the power consumed due to the combined infuence of the minor cutting edge, and V C (m/min) is the cutting velocity.
2.1.Tool Workpiece Interface.Te consumed power due to friction between the workpiece and the tool is calculated as [20] where V (m/min) is the chip velocity and F fF is the friction force between the tool and workpiece, which can be calculated through.
where Br is the Briks similarity criterion: where t 1T (m) is the uncut chip thickness and t 2T (m) is the formed chip thickness.Substituting (3)-( 5) in (2) results in 2.2.Tool-Chip Interface.Te power consumed at the toolchip interface originating from the friction between tool and chip on the rake face P fR is calculated as where τ c � 0.28 σ R (N/m 2 ) is the average shear stress at the tool-chip contact zone, σ R (N/m 2 ) is the ultimate tensile strength of the workpiece material, b 1T (m) is the chip width, and l c (m) is tool-chip contact length and is calculated as where k � 1.5 when ξ < 4 and k � 1.3 for ξ ≥ 4. In this research, experiments show that chip compression ratio is approximately 5, which will be discussed in the following sections.Substituting ( 5) and ( 8) in ( 7), we will have

Formation of New Surfaces and the Efect of Minor Cutting
Edge.Te power consumed for the formation of new surfaces is calculated as where f cf is the frequency of chip formation and E fr is the energy of fracture.P ch is negligible in the broaching process due to the low cutting velocity and, consequently, the low frequency of chip formation [10].Based on the numerical calculations considering the low cutting velocities employed in this study (5, 10, and 15 m/min), this parameter is in a scale of 10 −5 , which can be neglected compared to other power elements.Besides, as far as broaching does not have a minor cutting edge, the parameter P mn-ce is equal to zero [10].

Plastic Deformation.
Te layer being removed from the workpiece consumes power calculated as [20] where K (N/m 2 ) is the strength coefcient, n is the hardening exponent of the workpiece material, and A ω (m 2 ) is the uncut chip cross-sectional area.Substituting( 6), (9), and ( 11) in ( 1) results in a straightforward equation for measuring cutting force per tooth in the broaching process ( ( 12)).
Te cutting force for a single tooth in the broaching process is calculated using (12).To determine the total cutting force, it has to be multiplied by the number of teeth simultaneously engaged in the workpiece.
In the simulations, broaching is assumed as a plain strain process; therefore, the chip width before and after cutting is considered equal.Consequently, b T1 would be the length of the cutting edge (l ac � b T1 ), and the true uncut chip thickness, t 1T , is also considered to be equal to rise per tooth (t 1T �f z ).
Consequently, as illustrated in (5), where ξ is defned as the ratio of the formed chip thickness and uncut chip thickness, dividing the measured thickness of the formed chip resulting from the experimental broaching process, shown in Table 1, by the value of already known uncut chip thickness, the mean value of chip compression ratio is determined.
Other required parameters to determine the cutting force using (12) are related to the geometrical features of the broaching tool and mechanical properties of the workpiece material, which will be discussed in the following section.

Experimental Setup
Te experimental setup for verifying the force model using energy balance consists of the broaching tool, hydraulic cylinder, valves, accumulators, load cell, linear scale, and fxture, which will be discussed in detail in the following sections.Te overall specifcations of the servohydraulic system are tabulated in Table 2.
In Figure 2, the position and arrangement of each component of the experimental setup and the direction of the broaching process are shown.
Figure 3 also demonstrates the hydraulic circuit of the experimental setup.
Te tool implemented for this research is designed and manufactured for these specifc setup confgurations and research series.Te RENISHAW cyclone digitizer, with an accuracy of 1 µm, is utilized to extract accurate geometrical features of the broaching tool.Te broaching tool specifcations are mentioned in Table 3.

Advances in Tribology
In Figure 4, the broaching tool, as well as its dimensional characteristics extracted from the digitizer, can be seen.It consists of three main parts, the roughing teeth, where the rise per tooth is higher.Tey have the highest contribution to the material removal rate.Ten, there are the fnishing teeth, where the rise per tooth is lower, and they aim to improve the precision and surface roughness of the workpiece.Finally, the calibration teeth are responsible for ensuring the intended material is removed as expected.
Besides, there is a thorough hole at the end of the tool used for pulling the broaching tool through the guide in the broaching direction.
Te workpiece material used for this study is phosphorbronze in the shape of blocks with dimensions of 30 × 40 × 40 mm.Te machined workpiece can be seen in Figure 5.
Each block is used for two diferent tests for materialsaving issues.Besides, Table 4 shows the mechanical properties of the workpiece material.
Te fxture of the setup is made of Mo40 alloy steel and is designed and manufactured in our lab.
Te relief valve is used for setting, decreasing, or maintaining outlet pressure constant in fuid transfer lines.
Relief valves control the system pressure by bypassing pressured fuid from a secondary line.Tese valves are designed to act at a particular preset pressure and protect the pressured equipment and tank from overload.In the current study, considering other system demands and the hardware specifcations implemented for the research, the relief valve preset pressure is set to 250 bars.
Besides the relief valve, the cylinder movement and speed are controlled by a servo solenoid hydraulic valve with electrical position feedback.Te characteristics of hydraulic cylinders and valves are tabulated in Table 5.
Te digital linear scale reads the position data with 5 µm precision.In addition, to carry out cutting force tests, the Dacell CX101-T30 high-precision load cell measures the cutting force in each test.
Before running the tests, the load cell was calibrated using diferent gauge blocks of already known weights.Taylor Hobson Surtronic 25 proflometer with the accuracy of 1 μm was implemented to measure the roughness parameter (R z ) of the broached workpiece.Table 6 illustrates the detailed specifcations of the sensors implemented in the research.
Te power unit includes an electric motor and pump, supplying oil with appropriate pressure and temperature for the servohydraulic valve.To stabilize the oil pressure, two accumulators are also installed in the pressure and return lines of the hydraulic circuit.Te specifcations of the motor and pump are listed in Table 7.
PID controller is one of the most common controllers used in industry and academic research.In the design of any controller, the aim is to create a logical balance between three characteristics: overshoot (M p ), settling time (t s ), and delay time (t d ).In PID controllers, this balance is reached through the value of three parameters: proportional (K P ), integral (K I ), and derivative (K D ).
Te Ziegler-Nichols [23] heuristic method is implemented to acquire these parameters.At frst, K I and K D are considered to be zero.Ten, K P is gradually increased until the system reaches a steady oscillating state.Tis value is 4 Advances in Tribology known as the ultimate coefcient (K u ), and the period of this steady oscillation is (T u ).Using K u and T u , K P , K I , and K D are calculated.Having a rough yet educated estimation for PID parameters, experimental tests were carried out to narrow down these parameters to the optimum values presented in Table 8.Two PID controllers are required to provide operational freedom on the position and speed of the cylinder, the cutting velocity, and harmonic vibrations.Te frst PID controller is designed to control the valve spool position and, accordingly, the position of the broaching tool.To determine the optimum K's for the "spool PID" shown in Figure 6, ffteen diferent experiments were conducted and carried out through which M p , t s , and t d were simultaneously minimized.As shown in Figure 7, the PID block "Linear PID" is simulated in MATLAB 2019b and a SIMULINK circuit to enable speed control of the broaching process.
Te optimum results of the experiments are given in Table 8.Te second PID controller is designed to control the valve speed and enables us to add harmonic vibrations of the desired characteristics to the cutting velocity.

Procedure
Empirical tests for this research can be divided into two series.In the frst series of experiments, phosphor-bronze block is broached (without vibration) at diferent cutting velocities of V C � 5, 10, 15, and 20 m/min, then the cutting force and the workpiece surface roughness are measured and compared with the model.
In the second series of experiments, harmonic vibrations are applied to the cutting tool in the direction of the cutting velocity in the form of a sine wave with a constant amplitude of A � 1 m/min and frequencies of F � 55, 65, 85, and 95 Hz.To obtain interpretable results for the relationship between the cutting force, surface quality, and harmonic vibrations, the cutting velocity during every single test has to be constant.To ensure this along the cutting stroke, the desired speed must be obtained quickly (in this research, during the frst 0.01 seconds of the process) by applying the maximum pressure of 200 bars.It has to be mentioned that higher frequencies were not chosen due to the limitations of the experimental setup; however, the results with the chosen frequencies were already promising.Test results were then analyzed to investigate the infuence of cutting velocity and forced vibrations on the cutting force and surface quality.

Cutting Force and Cutting Velocity.
Te average force in the roughing section of the tool is considered the cutting force for each cutting velocity.Te cutting force-time graph for V C � 10 m/min is plotted in Figure 8, which can verify the analytical model.
Te graph is divided into three segments.Tere are three peaks in segment 1, each representing the engagement of a new tooth with the workpiece.Nevertheless, they are not considered in force analysis since the process had reached the steady phase just after segment 1.In segment 2, there are fve peaks, each of which stands for the initiation of engagement in the roughing section of the tool, preceded by segment 3, which contains three peaks resulting from three fnishing teeth of the broaching tool.As the engagement of the tool workpiece initiates, the cutting force gradually increases until the maximum number of teeth is involved, i.e., three teeth.
Afterwards, the cutting force fuctuates in a specifc range, reaching the end of the stroke, where the cutting force magnitude drops to zero after the last tooth leaves the workpiece.Figure 8 also shows the agreement between the experimental results and the simulated data.
Te increase in cutting velocity has positive efects on the chip formation process and lowers the shearing coefcient of the workpiece, which consequently results in a lower cutting  Advances in Tribology force.A case in point is the increase in cutting velocity from V C � 5 to 20 m/min, where the average cutting force encounters a decrease of at least 20% from 4600 to 3600 N, respectively.Figure 9 shows the comparison of cutting force at diferent cutting velocities.
Figure 10 shows the engagement and disengagement of the tool tooth with the workpiece.At the start of the engagement, three teeth are responsible for material removal, causing a peak in the force diagram, while with the disengagement of a tooth, the magnitude of the force falls dramatically.Te rise and fall of the force are strongly dependent on "rise per tooth," which is obviously higher in the roughing section, causing higher peaks in that area.
Te increase in the cutting force for each engagement of a new tooth at diferent cutting velocities varies depending on the value of the cutting velocity with an  531 MPa Ultimate strength (σ R ) [21] 548 MPa Strength coefcient (K) 0.51 GPa Strain hardening exponent (n) 0.29 Chip compression ratio (ξ) 5 Shear strength (τ y ) [22] 0.65 σ R Average shear stress (τ c ) 497 MPa 6 Advances in Tribology inverse relationship.At the cutting velocity of V C � 5 m/ min, per engagement of a new tooth in the roughing section of the process, an increase of 1400 N in the cutting force was observed, where the amount was reduced to 1100 N and 500 N at cutting velocities of 10 and 20 m/min, respectively.
It can be seen that when the cutting velocity is 20 m/min, the increase in cutting force per new engagement is around 700 N, while this amount is almost twice as much at 10 m/ min, reaching F C � 1300 N per engagement.

Cutting Force and Harmonic Vibrations.
Te next phase is to add intentional sine waves of predetermined amplitude and frequency to the cutting velocity to lower the cutting force.Te sine wave has an amplitude of A � 1 m/min and frequencies of F � 55, 65, 85, and 95 Hz.
Te general pattern of force diagrams is to some extent similar in both HVB and conventional broaching.
Notwithstanding, the results of the experiments show the hammering efect of the tool teeth on the workpiece.Te sinusoidal cutting movement considerably diferentiates the broaching motion in the conventional process and HVB.Te intermittent contact between the tool and the workpiece in the direction of cutting velocity results in fuctuations in the corresponding cutting force and consequently leads to a reduction in its magnitude.Harmonic vibrations of the tool created kinetic energy improved the chip formation process and enhanced the material removal rate.
Figure 11 shows the force-time graph for V C � 10 m/min and the harmonic vibrations of F � 95 Hz.
It can explicitly show that the analytical model can be verifed with the experimental procedure.Adding harmonic vibrations, depending on the magnitude of the frequency, lowers the cutting force by almost 20% at diferent cutting velocities.For instance, the average cutting force in the roughing section at V C � 10 m/min is 4236 N, whereas, in the presence of harmonic vibrations of 95 Hz, this value decreases to 3180 N. Figure 9 shows the comparison of the magnitude of the cutting force in diferent cutting conditions.
Te increase in cutting velocity and frequency of harmonic vibrations decrease the cutting force.By increasing cutting velocity, the chip formation process is enhanced, and the shearing coefcient between the workpiece material and the broaching tool tends to decrease, leading to a stable broaching process, and accordingly, the cutting force decreases.Besides, an increase in the frequency of harmonic vibrations has similar efects and causes a favorable decrease in cutting force by creating intentional interruptions in the broaching process.

Surface Quality and Cutting Velocity.
A comparison of surface quality measurements in diferent cutting conditions is shown in Figure 12.In the frst phase of the research, which is conventional broaching, an increase in cutting velocity from 5 to 20 m/min enhances the surface quality by up to 40%, reducing Ra from 3.2 to 1.8 μm.
In the second phase, which is harmonically vibrated broaching, the increase in vibration frequency from F � 0 to 95 Hz leads to a 35% reduction in surface roughness, reducing R a from 3.2 to 2 μm in the cutting velocity of V C � 5 m/min.
In comparison to conventional broaching at 5 m/min, adding a 95 Hz sine wave and increasing cutting velocity to 20 m/min enhances surface quality by up to 80%.Advances in Tribology

Conclusion
In this research, workpieces of phosphor-bronze material were broached under diferent cutting conditions.
(i) Te experiments are signifcantly in agreement with the force model based on the components of the energy consumed in the broaching process.(ii) Te increase in cutting velocity from V C � 5 m/min to 20 m/min causes a 40% reduction in surface roughness.(iii) In addition to surface roughness enhancement, higher cutting velocity leads to lower cutting force, such that experiments revealed that the cutting force at V C � 20 m/min is almost 20% lower in comparison to V C � 5 m/min.(iv) HVB at a higher vibration frequency leads to an elevated surface quality of 20% when a sine wave of F � 95 Hz is intentionally added to the broaching process compared to conventional broaching.(v) Besides, HVB at F � 95 Hz, causes a 20% reduction in cutting force.(vi) Per engagement of a tooth of the broaching tool, the cutting force magnitude increases sharply up to a peak, then falls gradually until a new engagement has occurred.(vii) Based on the numerical approach and the experiments, for cutting velocities higher than 10 m/min, it is assumed that the cutting force will decrease, and the surface roughness will increase.

Figure 4 :Figure 5 :
Figure 4: Extracted information from the digitizer for broaching tool.

Figure 9 :
Figure 9: Comparison of the cutting force under diferent cutting conditions.

Figure 10 :
Figure 10: Engagement (a) and disengagement (b) of broaching tool teeth with the workpiece.

Table 1 :
Formed and uncut chip thickness for diferent cutting velocities.

Table 3 :
Specifcations of the broaching tool.

Table 4 :
Mechanical properties of the workpiece material.

Table 8 :
Optimum PID parameters.Figure 6: SIMULINK circuit for position control.