key: cord-0331373-hd3f3nk8
authors: Eren, Bora; Sencer, Burak
title: Mechanistic Cutting Force Model and Specific Cutting Energy Prediction for Modulation Assisted Machining
date: 2020-12-31
journal: Procedia Manufacturing
DOI: 10.1016/j.promfg.2020.05.071
sha: 34cfeca9ff0d874c085e7bb232170c3a652cf30c
doc_id: 331373
cord_uid: hd3f3nk8

Abstract This paper presents a mechanistic model for analytical cutting force and specific energy prediction for modulation assisted turning. Kinematics of the process is used to analyze the cut surface topography and derive the uncut chip thickness variation for various modulation parameters. It is found that uncut chip thickness is governed by successive spindle rotations and can be represented in the form of trigonometric functions. The cut and no-cut phase durations are controlled by the modulation frequency and amplitude. Cutting (machining) forces are predicted based on the orthogonal cutting mechanics. The thin shear plane angle is predicted considering oscillations in the cutting velocity, resultant effective rake angle and by employing the well-known Minimum Energy Principle (MEP). In order to accurately predict the shear forces, length of the shear plane is estimated directly from the uncut and cut part surface geometries, which incorporates waviness of the surface. Analytical chip thickness predictions and proposed cutting force models are combined used to predict the specific cutting energy in MAM. Experimental results verify accuracy of developed force models in estimating cutting forces and energy in orthogonal modulated assisted turning of Al6061 T6511.

The long-standing practice in turning is to utilize chip breakers to assist the chip break into pieces for effective chip disposal [1] . In parallel, flood type cooling is used to cool down the cutting zone and improve tool life [2] . In today's machining; these are the well-established techniques for effective chip-control and to extend tool-life. However, altering the age-old kinematics of turning presents great potential for eliminating chip-jam, extending the tool-life and at the same time greatly improve the machinability [3] .

For instance, "turn-milling" process [4] has been proposed to enhance mechanics of turning. Instead of feeding a stationary cutting tool, a rotating milling tool is used to shear material from a rotating workpiece. Introducing milling kinematics in turning enables intermittent cutting and thereby generates discrete chip. It is natural cure for chip-jam. In addition, the intermittent tool engagement kinematics provides cool-down time for cutting edges and thereby elongates tool-life [5] . Another way to realize chip breakage is by slowly oscillating the tool in feed direction as depicted in Fig. 1 . As shown, tool is sinusoidally oscillated in the feed direction at the modulation frequency of m f and amplitude A . When these

The long-standing practice in turning is to utilize chip breakers to assist the chip break into pieces for effective chip disposal [1] . In parallel, flood type cooling is used to cool down the cutting zone and improve tool life [2] . In today's machining; these are the well-established techniques for effective chip-control and to extend tool-life. However, altering the age-old kinematics of turning presents great potential for eliminating chip-jam, extending the tool-life and at the same time greatly improve the machinability [3] .

For instance, "turn-milling" process [4] has been proposed to enhance mechanics of turning. Instead of feeding a stationary cutting tool, a rotating milling tool is used to shear material from a rotating workpiece. Introducing milling kinematics in turning enables intermittent cutting and thereby generates discrete chip. It is natural cure for chip-jam. In addition, the intermittent tool engagement kinematics provides cool-down time for cutting edges and thereby elongates tool-life [5] . Another way to realize chip breakage is by slowly oscillating the tool in feed direction as depicted in Fig. 1 . As shown, tool is sinusoidally oscillated in the feed direction at the modulation frequency of m f and amplitude A . When these

The long-standing practice in turning is to utilize chip breakers to assist the chip break into pieces for effective chip disposal [1] . In parallel, flood type cooling is used to cool down the cutting zone and improve tool life [2] . In today's machining; these are the well-established techniques for effective chip-control and to extend tool-life. However, altering the age-old kinematics of turning presents great potential for eliminating chip-jam, extending the tool-life and at the same time greatly improve the machinability [3] .

For instance, "turn-milling" process [4] has been proposed to enhance mechanics of turning. Instead of feeding a stationary cutting tool, a rotating milling tool is used to shear material from a rotating workpiece. Introducing milling kinematics in turning enables intermittent cutting and thereby generates discrete chip. It is natural cure for chip-jam. In addition, the intermittent tool engagement kinematics provides cool-down time for cutting edges and thereby elongates tool-life [5] . Another way to realize chip breakage is by slowly oscillating the tool in feed direction as depicted in Fig. 1 . As shown, tool is sinusoidally oscillated in the feed direction at the modulation frequency of m f and amplitude A . When these

The long-standing practice in turning is to utilize chip breakers to assist the chip break into pieces for effective chip disposal [1] . In parallel, flood type cooling is used to cool down the cutting zone and improve tool life [2] . In today's machining; these are the well-established techniques for effective chip-control and to extend tool-life. However, altering the age-old kinematics of turning presents great potential for eliminating chip-jam, extending the tool-life and at the same time greatly improve the machinability [3] .

For instance, "turn-milling" process [4] has been proposed to enhance mechanics of turning. Instead of feeding a stationary cutting tool, a rotating milling tool is used to shear material from a rotating workpiece. Introducing milling kinematics in turning enables intermittent cutting and thereby generates discrete chip. It is natural cure for chip-jam. In addition, the intermittent tool engagement kinematics provides cool-down time for cutting edges and thereby elongates tool-life [5] . Another way to realize chip breakage is by slowly oscillating the tool in feed direction as depicted in Fig. 1 . As shown, tool is sinusoidally oscillated in the feed direction at the modulation frequency of m f and amplitude A . When these 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to waves are generated at a certain ratio with the spindle speed frequency s f , the tool jumps out of cut as shown in Fig. 1 and generates discrete chip. This simple approach is adapted for drilling and turning processes in the past and called as the Modulation Assisted Machining (MAM) process [6, 7] .

Origins of MAM can be traced back to low frequency assisted drilling process used for chip evacuation application [8, 9] , and later applied for improving effectiveness of lubrication in turning [10] . Its effectiveness on chip breaking [11] and temperature regulation [12] are also analyzed. In fact, the biggest advantage of the MAM is on discretizing the continuous cutting process to generate discrete chip [6] , which makes its most suitable for chip control during machining of ductile materials such as low carbon steel used in automotive industry [12] .

A major drawback for MAM is the excess chip-load and large instantaneous cutting forces. When MAM is applied, resultant material removal rate is unchanged; however, since the tool undergoes air-cutting phases, the chip-load during cutting phase is increased. In fact, it is reported that the uncut chip thickness can reach up to 2x of the nominal feed rate [13, 14] . Hence, there is a demand on accurate estimation of uncut chip thickness, cutting forces and energy of the MAM process for robust tool design and better planning of the process. Past research has experimentally observed that MAM turning requires larger cutting forces but it is also reported that overall specific cutting energy is lowered [15] . Cutting forces are predicted for limited modulation parameters [13, 16] . This paper fills in this lack of knowledge by introducing analytical uncut chip thickness prediction for modulated tool kinematics. It presents prediction of maximum uncut chip thickness and proposes an orthogonal cutting force model to accurately predict cutting forces. The force model is also used to validate energy efficiency of MAM in low immersion cutting.

Kinematics of the MAM is illustrated in Fig. 1 . As shown, cutting tool is modulated (sinusoidally vibrated) in the feed direction at low frequency:

where A is the modulation amplitude and m f is the modulation frequency. Tool trajectory in the n th spindle revolution is expressed by the nominal feed rate 0 h , spindle speed s f , superimposed with modulation amplitude and frequency as:

where /

s m d f f is the wavelength that the tool generates along the periphery of the cylindrical part with diameter d, and x is the nominal cutting distance [14] . Fig. 2 shows tool trajectory during consecutive modulation cycles. In Eq. (2), donates the phase angle, which controls "completeness" of a modulation wave within a single spindle revolution and has been defined as [6] : By setting , a full tool modulation is not completed within a single spindle revolution, and hence tool can be disengaged from the workpiece in the successive revolution due to the previously generated wavy surface finish. Here, the modulation amplitude A plays a key role to ensure that the tool is disengaged from the cut. The condition to ensure discrete cutting can be solved from Eq. (2) to establish negative chip thickness in each revolution and can be derived as [6, 14] : Fig. 3 summarizes the conditions to realize discrete cutting for various phase angles and modulation amplitudes. For instance, by selecting discrete chip can be generated for the smallest modulation amplitude of A/h0 = 0.5. In practice, setting phase angle within the range of is realizable since lower modulation amplitudes are required, which can be generated by the existing servo drives of the machine tool axes [8] . Otherwise, high bandwidth actuators are required to modulate the tool [17, 18] .

Prediction of the uncut chip thickness is detrimental for accurate force prediction. This section presents uncut chip generation kinematics of modulated cutting. As shown in Fig.  4 , during modulated turning, uncut (instantaneous) chip thickness is defined as the material removed through successive modulation cycles. This work presents analytical chip-thickness formulations for 3 most well-used modulation conditions; namely, for the phase angle cases of . As observed, based on the phase angle, cutting regime resembles up and down cutting kinematics of a milling process [19] . For instance, in Fig. 4a , tool pushes the workpiece through feed direction (down) in majority of the cutting. Therefore, process can be viewed as down-cutting. On the other hand, when the phase angle is increased, process changes to up-cutting. For , a balance of up and down cutting is achieved. It must be noted that this characterization also depends on the feed rate selection which plays a key role in determining the instantaneous chip formation.

For the case, tool's modulation cycle is half incomplete within a single spindle rotation. As a result, during successive spindle rotations, surface waves are out of phase and generate discrete chip for the smallest modulation amplitude. Fig. 5 illustrates tool trajectories (surface modulations) for several successive spindle revolutions. While the light grey shaded area represents current chip generation, the purple and light pink shaded areas represent chip generation in the past (n-1) th and (n-2) th cycles.

As shown in Fig. 5 , chip thickness is controlled by 3 consecutive spindle revolutions. Analytical chip thickness can be derived by computing the surface cut from Eq. (2). For example, for t1 -t2 time interval shown in Fig. 5 , instantaneous chip thickness can be found by simply taking the difference of . Similarly, by applying same procedure to all time intervals, uncut chip-thickness can be expressed as:

where 2 m m f . 

The ratio of off-cut and in-cut periods is then evaluated from Eq. (6):

This ratio is critical for practical implementations, and it can be altered by the modulation amplitude and the feed rate. To generate robust discrete chip, larger modulation amplitudes are recommended to extend no-cutting cycle.

The uncut chip thickness for this case can be derived similar to the previous case by evaluating Eq. (2) for several spindle revolutions. However, care should be taken. In this case, modulation cycle leaves quarter (1/4) wave in the next spindle revolution to be cut. Hence, it may require 4 spindle revolutions to reach steady state discrete cutting. Kinematics is complex and analysed as follows. Fig. 6 shows the case where feed rate is greater than the modulation amplitude 0 h A . In this case, uncut chip thickness is controlled by 3 consecutive tool modulations and derived as: (8) where the corresponding time stamps are calculated as:

On the other hand, when feed rate is less than the modulation amplitude 0 h A, two different chip formations are observed. Figs. 7 and 8 illustrate those two cases. The process is sensitive to the nominal feed rate h0. As depicted in Fig. 7 , when h0 is below a critical value hcrit, tool modulation from (n-4) th cycle affects the current uncut chip thickness and it becomes 4x of the nominal feed rate, i.e. max(h(t)) = 4h0. In contrary, when the nominal feed rate is selected as , uncut chip thickness is not affected by the (n-4) th cycle. Tool trajectory and chip thickness variation are shown in Figs. 8a and b respectively for this case. To determine hcrit, time points at the intersections of (n-3) th cycle with (n-4) th and (n-1) th cycles are analysed. By utilizing Eq. (2), these time points are evaluated as: (10) For known modulation amplitude A , the 0 h value makes these time points overlap (i.e. describes crit h as:

For , uncut chip thickness is derived as: (12) with the time stamps: (14) with corresponding time stamps: 

In this case, chip formation is a time domain mirror image of the chip generation observed for the . Similar steps can be followed for analytical chip thickness prediction.

Overall, the relationship between phase angle and the maximum uncut chip thickness hmax is summarized in Fig. 9 . Note that 0 / A h ratio is critical, as shown in Fig. 3 , to achieve discrete chip formation. 

During MAM, effective cutting velocity V oscillates around the nominal cutting direction Vc due to tool modulations. As shown in Fig. 10 , fluctuations in the effective cutting direction creates an effective rake angle αeff that is defined by the angle between tool's rake face and the nominal of the instantaneous effective cutting direction. Minimum energy principle (MEP) dictates that shear angle is controlled by the rake and friction angles [20] , and thus it fluctuates with the modulation. On the other hand, friction angle is primarily controlled by the tool workpiece material pair [20] and should not change largely due to fluctuations in the effective cutting velocity direction. Hence, assuming a fixed friction angle , shear angle is modulated based on the varying rake angle, and the shear plane length is altered. As illustrated in Fig. 11 , the shear plane is constrained by the free surface. Its length is thereby influenced by the previously left surface finish (topography). As a result, in MAM, cutting forces not only dependent on the varying chip thickness h(t), which is derived analytically in the previous section, but it is also influenced by the effective cutting direction V and the surface finish generated by the previous spindle revolutions. Following paragraphs present the cutting force model for the MAM process, which considers these 3 critical characteristics. Firstly, the effective rake angle is calculated as a function of the tool position from the geometrical relationships shown as in Fig. 10 : (16) where is obtained by taking the derivative of the tool trajectory with respect to nominal cutting distance ( x ) from Eq.

(2), as: (17) Although the effective clearance angle varies with the cutting direction (see Fig. 10 ), proposed model assumes that its effect on ploughing force components is not significant. By assuming fixed friction angle, the shear angle is predicted from MEP principle as: The length of the shear plane (l) determines total shear force, F s by (19) where b is width of the cut and is the shear strength of the material. Shear plane length l is determined by the undulated surface topography and tool modulation trajectory. The angle between the shear plane and the nominal cutting direction becomes . As shown in Fig. 10 , a line is drawn from the tool tip (O) to the free surface to indicate the shear plane. The intersection of this line with the free work surface (A) determines the shear plane. Effective (instantaneous) shear plane length can then be computed as:

(20) Fig. 11 . illustrates the importance of undulated surface topography in shear plane length calculation. Note that the coordinates of O(xO, yO) is determined by the current (n th ) tool trajectory, and coordinates of A(xA, yA) is solved from the previous tool trajectories. Fig. 12 is generated to illustrate the difference between proposed shear plane length and the conventional shear plane length which does not consider undulated surface topography and the effective rake angle. Based on the predicted shear plane length, Eq. (19) is used to calculate shear force, s F . Orthogonal cutting geometry is then used to derive the principle cutting force component (21) and it is resolved to its cartesian cutting force components as: Figure 13 . Experimental setup.

The experimental setup for realizing MAM turning process is shown in Fig. 13 . HAAS TL-1 CNC lathe is used as the testbed, and a piezo actuator is mounted on the tool-post for modulating the tool in the feed direction. The piezo actuator is controlled by a PID controller implemented in an in-house designed servo control system. Positioning bandwidth is set to 300 [Hz] and the servo loop is closed at 10 [kHz] sampling which allows MAM turning for various spindle speeds. Mechanical design of the piezo actuator is presented in [21] . The actuator is equipped with a capacitive sensor with 5 [nm] resolution and 50 [micron] total stroke. The actuator can provide 16000N force. Its dynamic stiffness is limited by its 1 st resonance mode at 2.97 kHz with 370 N/μm. Assembly scheme of the piezo actuator is given in Fig. 14 [21] . Fig. 15 shows quality of the identified cutting force coefficients, and Table 1 provides the corresponding values. Next, the friction angle can be determined from the geometry:

Principle c F and shear s F components are mapped from Merchant's equations [20] ,

Finally, shear strength of the material is obtained from Eqs. (19) and (25) Predicted uncut chip thickness variation for these cases are shown in Fig. 16 . Measured feed and thrust forces were compared against the predictions through the force model presented in the previous section by adding the ploughing effect as well: Experimental results and predicted cutting forces are presented in Fig. 17 . The proposed cutting force model simulates machining forces at good fidelity. Both thrust and feed force components are accurately predicted. During the experiments, effect of static and dynamic deflections of the tool post were observed. This has altered tool's in-cut and off-cut cycle durations slightly. Note that due to the edge effect, peak cutting forces do not increase at the same rate with the uncut chip thickness. 

Specific cutting energy of the MAM is evaluated. Firstly, cutting power is calculated from both measured and predicted thrust and feed forces, and cutting velocities t V and f V . Specific cutting energy is then evaluated by their time integration and considering the volume of the material removed,

where h(x) represents instantaneous uncut chip thickness, Eq. (28) allows analytical computation of actual specific cutting energy based on only cutting force measurements. For higher accuracy, actual removed material volume was also considered. Discrete chips generated during the MAM were collected, weighted and used in evaluating the specific cutting energy. The density of the Al 6061 T6511 is taken as [22] . In addition, continuous orthogonal (tube) cutting experiment was conducted with 10 Hz spindle speed and 0.005 mm/rev feed rate. Same workpiece/tool pair is used. Specific cutting energy is computed by using both measured and predicted cutting forces. In this case, force predictions were calculated by using Eq. (23) and removed material volume was calculated from process kinematics. Table 2 and the continuous cutting case. As can be seen, MAM requires significantly less cutting energy than continuous cutting to remove same amount of material. Furthermore, MAM with and phase angles are slightly more efficient than the case with phase angle. These efficiencies are attributed to the augmentation of the maximum uncut chip thickness. For instance, during the MAM with phase angle, maximum uncut chip thickness in the in-cut period (t1 -t4) reaches 2x of the nominal uncut chip thickness observed in continuous cutting with the same cutting conditions h0 and fs. This requires larger cutting forces but at the same time larger material removal rate. Notice that the edge cutting force component does not increase with the uncut chip thickness (see Eq. (23)), and thus increase in the material removal rate becomes more dominant than the increase in the cutting forces. As a result, specific cutting energy U (See Fig.18 ) decreases in MAM as compared to continuous cutting.

This paper presented an analytical uncut chip thickness prediction for the MAM process. Uncut chip thickness is derived by tool kinematics within successive spindle revolutions. For phase angles of , maximum chip thickness becomes 2x of the nominal feed. However, if phase angles are selected as or , chip thickness can reach up to 4x of the nominal value. In addition, cutting forces and specific cutting energy are predicted accurately by the proposed mechanistic model. It is also clarified that MAM process is more energy efficient material removal process than conventional continuous cutting process for small feed rate values. It is concluded that this is due to non-linear relationship between the cutting force and uncut chip thickness.

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