On Force–Displacement Characteristics and Surface Deformation in Piezo Vibration Striking Treatment

Because friction, wear, corrosion, and fatigue usually intensify on the surface, the performance, and service life of engineering components are strongly dependent on their surface attributes, such as surface roughness, hardness, microstructure, and residual stress [1]. Modifying these surface attributes is an effective and economical way of improving the overall performance of engineering components and products.

A common method to modify surface attributes is by surface plastic deformation imposed by striking the surface with hard tool indenters. The most notable example is shot peening (SP) [2,3]. In SP, a myriad of small hard balls made of steel or ceramic is impacted onto the surface by compressed air, resulting in randomly distributed strikes on the targeted surface. The process will generate compressive residual stresses on the surface and thereby improve the fatigue strength of critical components and the overall fatigue life of a structure [4,5]. Surface mechanical attrition treatment (SMAT) is another striking-based surface modification process [6]. In SMAT, hard steel balls (used as tool indenters) and the workpiece are all confined inside a vibrating chamber. The workpiece is fixed with the chamber while the steel balls are free to bounce between the workpiece surface and the chamber walls, leading to repeated strikes on the workpiece surface. This process emphasizes inducing severe plastic deformation which transforms the surfaces into a nanocrystalline microstructure [7,8]. In both SP and SMAT, the surface is struck by numerous free indenters whose kinematics is not directly controlled. The striking location, striking angle, and striking force associated with each indenter are random variables to a large extent. The accumulated effect from these strikes is therefore of stochastic nature, which makes it difficult to control the treatment quantitatively. In addition, since the exact locations of these random strikes cannot be strictly controlled, these processes suffer from poor reliability.

Alternatively, surface striking can be also realized while controlling the striking location by a single vibrating tool indenter(s) driven by either a pneumatic or ultrasonic actuator. This is demonstrated by high-frequency mechanical impact (HFMI) treatment which is mainly used to treat weld joints [9]. The HFMI equipment is usually made as a hand-held impact device connecting to an external power source, which enables the treatment to be carried out manually for weldments of large sizes or complex geometries. The impact device is usually directed to strike the weld toe to modify its geometry, induce compressive residual stress, and close subsurface micro-cracks, which can significantly enhance the fatigue strength of the weld joints [10,11]. Although it is possible to treat the weld joints manually with hand-held equipment, the manual operation is apparently not ideal for treating component surfaces generally. Machine hammer peening (MHP) treatment [12,13] and ultrasonic nanocrystal surface modification (UNSM) treatment [14,15] are examples of such devices integrated onto a computer numerical control (CNC) machine or robotic arm. MHP has been shown to be effective for reducing surface roughness and increasing surface hardness for machined molds and dies [16,17]. As indicated by its name, UNSM employs ultrasonic tool vibration which enables generating nanocrystalline surfaces and improving tribological and fatigue properties [14,18]. From the process control point of view, the main advantage of MHP and UNSM is that the scanning path of the vibrating tool over the surface can be precisely controlled by the CNC machine, which implies that the strikes on the surface can be much better controlled compared to SP, SMAT, and HFMI.

While a CNC machine enables more precise positioning of the strikes, the control of each strike still depends on the striking device. In MHP, the striking device can be pneumatically or ultrasonically driven [10,13,19]. The indenter held in the front of the device is usually not rigidly connected to the actuator. While the actuator repeatedly impacts the indenter, the relative motion between indenter and actuator cannot be strictly controlled. Therefore, the impact on the surface may be only energy controlled similar to SP but cannot be delivered in consistent intensity [20]. In UNSM, the motion of the indenter is fully driven by the rigidly connected ultrasonic actuator, leading to more uniform strikes on the surface [14]. However, ultrasonic vibration depends on the resonance of the vibrating structure, and thus, its frequency and amplitude cannot be controlled [21]. Technically, the vibration displacement and the striking force are difficult to measure in the ultrasonic frequency regime. This makes it difficult to monitor or control surface deformation imposed by each individual strike, and the overall surface deformation resulting from the treatment then cannot be quantitatively controlled. Note that imposing controllable surface deformation is a critical step toward understanding and controlling the modified surface attributes [22].

Comparing with ultrasonic vibration, the non-resonant vibration directly driven by piezo stack actuation is more convenient to control. This has been demonstrated in its applications in vibration-assisted turning and drilling processes [23–25]. The non-resonant piezo vibration often has a lower vibration frequency but can achieve a higher vibration amplitude (up to 200-µm stroke piezo stack is commercially available). The frequency and amplitude can be independently controlled with the piezo stack actuation. Monitoring the vibration displacement and striking force within each vibration cycle also becomes possible. These characteristics make non-resonant piezo vibration more suitable for imposing controlled strikes and deformation on the surface.

In this study, a vibration striking device enabled by non-resonant mode piezo stack actuation is developed. Using this device integrated into a CNC machine, piezo vibration striking experiments are conducted to investigate the striking force, tool vibration displacement, and the resulting surface deformation. The study reveals the feasibility and the promising capability of piezo vibration striking treatment (PVST) in inducing controllable surface plastic deformation. This is the first step toward developing PVST as a more efficient process for enabling deformation-based surface modification including finish, residual stress, hardness, microstructure, and hence enhancing components’ performance such as fatigue life and wear resistance.

Figure 1 shows the experimental setup of PVST. The developed piezo vibration striking device (Fig. 1(b)) is mounted onto the spindle of a CNC vertical milling machine (Hass VF-4) through a standard CAT 40 tool holder. The spindle rotation function in the machine is locked to provide only the vertical motion of the striking device along the Z-axis, which is capable to control the striking distance between striking tool and workpiece surface. The workpiece is mounted on the machine table which provides the horizontal motion of the workpiece in both X and Y axes for the striking location.

The piezo vibration striking device is realized using non-resonant mode piezo stack actuation. Figure 1(c) shows the schematic of the striking device assembly. Inside the device body, a piezo stack actuator is assembled with a spline shaft along the axial direction. The piezo stack is compressed by the shaft through an internal pre-loaded spring. A ball spline bearing is mounted on the spline shaft and fixed with the device body, which allows the linear motion of the shaft in the axial direction while restricting the bending and rotation of the shaft. The striking tool indenter, in the form of a small cylinder with a hemispherical end, is rigidly connected to the end of the shaft. The tool indenter is made of M2 high-speed steel with a tip diameter of 3 mm. The vibration of the indenter is actuated by the extension and contraction of the piezo stack which is controlled by the driving voltage from a waveform generator and a power amplifier.

To monitor the striking process, the vibration displacement of the indenter tool is measured using a capacitance displacement probe (Capacitec HPC-40). As shown in Figs. 1(b) and 1(c), the probe is clamped on the device body and facing the flat surface of a flange that is part of the vibrating shaft. The displacement is measured based on the change in the gap between the probe and the flange. The striking force is measured using a dynamometer plate (Kistler 9527B) mounted on the CNC machine table. The measured displacement and force signals are recorded using a data acquisition system (NI USB 6361 + LabView). The sampling rate for both signals is 4000 per second which is at least 40 times higher than the tool vibration frequencies used in the study; therefore, the displacement and force signals during each vibration or striking cycle can be sufficiently captured.

The frequency and amplitude of tool vibration are controlled by varying the frequency and amplitude of the sinusoidal driving voltage. The lower bound of the driving voltage is always set at zero, and thus, the upper bound of the driving voltage is equal to the peak-to-peak amplitude (V_pp) of the voltage oscillation. The maximum driving voltage allowed for the piezo stack is 150 V. The nominal stroke of the piezo stack is 100 µm. Figure 2 shows the calibrated tool vibration of the device assembly without striking at the driving voltage frequency (f) of 10 and 100 Hz and the driving voltage amplitude (V_pp) of 60, 90, 120, and 150 V. Figures 2(a) and 2(b) show that the vibration displacement of the tool (u) closely follows the sinusoidal driving voltage (V). The tool vibration frequency is the same as the driving voltage frequency. The tool vibration amplitude without striking (u⁰_pp) is proportional to the driving voltage amplitude (V_pp) and is not significantly affected by the vibration frequency (Fig. 2(c)). The maximum vibration amplitude achieved at V_pp = 150 V is about 90 µm, which is 10% lower than the nominal stroke (100 µm). The calibration results indicate the frequency and amplitude of tool vibration can be conveniently and independently controlled. Note that the driving voltage conditions calibrated here are used to conduct the vibration striking experiments in this study.

Figure 3 gives an overview of the four basic experiments conducted in this study. The first experiment (Fig. 3(a)) investigates the tool-surface approaching process in which the vibrating tool is fed vertically toward the workpiece surface. The second experiment (Fig. 3(b)) investigates the single-spot striking process in which the vibrating tool repeatedly strikes the same location on the workpiece surface from a fixed tool vertical position. The third experiment (Fig. 3(c)) investigates the one-dimensional (1D) scan vibration striking process in which the vibrating tool strikes the workpiece surface while it is continuously moving along a linear path. We will refer to the horizontal tool feed motion as the tool scan motion in this study. The fourth experiment (Fig. 3(d)) investigates the two-dimensional (2D) scan vibration striking process which is the extension of the 1D scan striking to treat a 2D surface area using the vibrating tool with parallel scan path lines. These experiments are designed for better understanding the relationships among tool displacement, striking force, and surface deformation in PVST.

For all experiments, the workpiece material is mild steel ASTM A572GR50 with a dimension of 120 mm × 40 mm × 20 mm. The initial surface of the workpiece is prepared by grinding to have the roughness (Sa) of 0.32 μm. Note that the uniform initial smooth surface is necessary to characterize and understand the deformed surface resulting from the striking. Three-dimensional (3D) surface profiles are characterized using Keyence Digital Microscope.

In the tool-surface approaching experiment (Fig. 3(a)), the initial vertical (Z) position of the tool is set to 120 µm, i.e., Z = 120 µm with the reference from the workpiece surface. The vibration of the tool is turned on and fed onto the surface at a speed of 1 µm/s. Figure 4 shows the measured force (F_z) and tool vibration displacement (u) plotted against the tool position (Z) as the vibrating tool is fed toward the workpiece at f = 100 Hz and V_pp = 150 V. Note u refers to the displacement of the vibrating tool while Z refers to the tool position during the feed motion. In regime A of the tool position (from Z = 120 µm to Z = 105 µm), the tool has no contact with the workpiece surface without any load on the vibrating tool. The vibration of the tool has the calibrated amplitude. Entering regime B (from Z = 105 µm to Z = −55 µm), the vibrating tool begins to engage and disengage the workpiece in each vibration cycle leading to the repeated strikes on the surface. The peak force of each successive strike increases steadily because the indentation depth reached by each successive strike increases as the tool position Z decreases. At the same time, the reduction in the vibration displacement of the tool is evident due to the elastic compression of the vibration device by the striking force. The higher the striking force, the lower the vibration displacement. Therefore, the maximum displacement of the tool in each successive vibration cycle (or striking cycle) decreases steadily with the decrease of tool position Z. However, the minimum displacement of the tool remains unchanged because the tool is disengaged at this moment, and hence, there is no force to compress the piezo stack. Entering regime C (Z < −55 µm), the vibrating tool becomes continuously engaged with the workpiece during its vibration. As a result, the minimum force in each vibration cycle is no longer zero; it increases steadily with the decrease of tool position Z. Correspondingly, the minimum vibration displacement of the tool decreases with the tool position Z.

In the approaching experiment, the vibration striking occurs in the regime B which includes the tool position both above (Z > 0) and below (Z < 0) the initial workpiece surface. For practical application of vibration striking treatment, the vibrating tool also needs to move horizontally (in the X − Y plane) to impose the strike at any location on the surface. When considering the horizontal tool motion, the tool vertical position below the initial surface (Z < 0) will result in the continuous engagement between the tool and the workpiece, which will generate significant sliding-type deformation on the surface. To minimize the sliding deformation, the tool position for inducing vibration striking should be limited to Z ≥ 0. The upper bound of the tool position is equal to the maximum vibration displacement under no-load condition (u⁰_max) since no striking occurs when Z > u⁰_max.

As noted already, the maximum vibration displacement (u_max) during the striking process is dependent on the striking force. Figures 5(a) and 5(b) show the relationship between the reduction in maximum vibration displacement (Δu_max = u⁰_max − u_max) and the peak force of the strike (F_max) at f = 10 and 100 Hz, respectively. The relationship is based on the force and displacement data corresponding to the tool position range 0 < Z < u⁰_max in the approaching experiment. Note in this Z range, the reduction in maximum vibration displacement is the same as the reduction in vibration amplitude (Δu_pp = u⁰_pp − u_pp). The relationship between F_max and Δu_max (or equivalently Δu_pp) is clearly linear, which gives a stiffness value of 11.1 N/µm at f = 10 Hz (Fig. 5(a)) and 11.4 N/µm at f = 100 Hz (Fig. 5(b)). The axial stiffness of the vibration device assembly is nearly identical at 11.7 N/µm (Fig. 5(c)) confirmed by a static compression test on the device (with no vibration). Therefore, the reduction in vibration displacement is due to the elastic compression of the device assembly under the striking force, which means the reduction in vibration displacement can be calculated from the striking force given the stiffness of the vibration device.

The single-spot vibration striking experiment (Fig. 3(b)) is conducted on a single surface spot with a fixed tool position Z = 0. With the initial tool position Z set to zero, the vibration is turned on for a duration of 3 s to induce repeated strikes on the same surface spot. It is expected the plastic deformation is imposed only within the first few strikes. After reaching a steady-state, the repeated strikes only involve elastic deformation of the deformed surface. This is confirmed by Fig. 6 which shows the measured force and vibration displacement during the repeated strikes at the vibration condition f = 10 Hz and V_pp = 150 V. It is observed both the force and displacement signals reach the steady-state oscillations nearly right after the starting of the tool vibration. The peak force (F_max) and the maximum vibration displacement (u_max) then remain constant. For other vibration conditions, the measured force and vibration displacement signals show similar steady-state oscillations except that F_max and u_max are different. Figure 7 summarizes the measured F_max and u_max at various vibration conditions (V_pp = 60, 90, 120, 150 V, f = 10 and 100 Hz). It is observed that both F_max and u_max increase with V_pp which is expected since higher V_pp means higher vibration amplitude. It is also observed that higher f results in higher F_max but lower u_max for a given V_pp. The higher F_max may be partially attributed to the increased inertial force which the tool needs to overcome to accelerate the workpiece material when it strikes the surface. Higher frequency leads to higher acceleration during each strike and hence higher striking force. The lower u_max is consistent with the higher F_max since there is more reduction in vibration displacement due to the elastic compression of the vibration device (Fig. 5).

Figure 8(a) shows the resulting permanent indentation on the surface at each vibration condition. Figures 8(b) and 8(c) show the cross-sectional profiles of these indentations grouped at f = 10 and 100 Hz, respectively. It is observed that the depth (h) and diameter (D) of the indentation increase with V_pp. For a given V_pp, higher f results in higher h and D. As noted earlier, a higher f results in a lower u_max (Fig. 7(b)). Since the tool position is at Z = 0, u_max is equal to the maximum indentation depth reached by the strike, which represents the total plastic and elastic deformation. In contrast, h represents only the plastic deformation. Then it can be deduced that a higher f leads to a larger plastic deformation (Fig. 7(c)) despite a smaller total deformation (Fig. 7(b)). The higher plastic deformation leads to more strain hardening of the material which can also contribute to the higher F_max for higher f (Fig. 7(a)). It should be noted the comparison of F_max is at the steady-state striking stage where the plastic deformation has already been completed and only elastic deformation is taking place, so the observed difference in F_max for different f is not attributed to the strain rate effect which occurs only during plastic deformation.

Figure 9 shows how F_max is related with h and D, respectively. It is found that the size of the permanent indentation generated on the surface is linearly dependent on the peak force of the strike. This indicates the force signal can be used to monitor the plastic deformation imposed by each strike.

Figure 11(a) shows the longitudinal section profiles of these grooves. The indentation spacing d_s can be measured from these profiles as 516 ± 8, 392 ± 12, 269 ± 13 and 131 ± 8 μm for r_o = 0, 0.25, 0.5, and 0.75, respectively. The measured d^′_s values agree well with the calculated ones using Eq. (1). This indicates the vibration striking with tool scan motion can be accurately controlled. Furthermore, the measured peak-to-valley height (R_z) for the longitudinal section profiles are 17.0, 10.5, 7.6, and 1.6 μm, respectively, which indicates again higher r_o leads to smoother surface in the groove.

Figure 11(b) shows the transverse section profiles of these grooves (perpendicular to the tool scan direction) taken at the center of each indentation which corresponds to the maximum depth location in the groove. As readily observed, the transverse section profile is not much affected by r_o. The profile appears nearly the same for different r_o. The groove depth (h) measured from the undeformed surface is about 24 μm. The groove width measured by the distance between the two ridges is about 645 μm. The two ridges are formed by displacing material within the groove. The ridge size increases slightly with r_o as more material tends to be displaced, which also creates a smoother surface in the groove. Note the left ridge is slightly higher than the right ridge for all cases, which is likely caused by the imperfect mounting of the workpiece in the experiment that results in slight tilting of the initial surface.

Figure 12 shows the measured forces corresponding to creating these grooves. There are two force components during 1D scan vibration striking: the striking force (F_z) in the Z direction and the sliding force (F_x) in the X direction. Both forces are highly repetitive in the successive striking cycles, which indicates the process is quite stable. The primary force is the striking force which is not significantly affected by r_o. The peak of the striking force is around 550 N for all cases. The secondary force is the sliding force which is much smaller than the striking force. The sliding force is generated due to the horizontal scan motion of the tool. Unlike the striking force, which has symmetrical profile and nearly independent of r_o, the sliding force decreases with increasing r_o, and the force profile also becomes more asymmetrical. The asymmetrical profile indicates the sliding force increases even when the tool is pulling from the surface after it reaches the maximum vibration displacement. This is likely caused by the generation of pileup material in front of the tool due to sliding. The sliding force is dependent on the effective engagement depth between the tool and workpiece surface during sliding. Besides the tool vibration displacement, the effective engagement depth is also affected by the amount of pileup material in front of the tool. While the tool is retracting from its maximum vibration displacement which tends to reduce the effective engagement depth, the continuous sliding action keeps generating pileup material in front of the tool which tends to increase the effective engagement depth. As a result, the occurrence of the maximum engagement depth (corresponding to the sliding force peak) lags the maximum vibration displacement (corresponding to the striking force peak) which then results in the asymmetrical profile of the sliding force.

Besides varying r_o, the 1D scan vibration striking experiment has also been conducted while varying V_pp. Figure 13 summarizes the measured groove depth (h) and width (W) for all cases. It shows that the groove depth and width are primarily dependent on V_pp (i.e., vibration amplitude) and less on r_o. Moreover, it is found again the depth and width of the groove are linearly dependent on the striking peak force (Fig. 14) though the linear relationships are different from those found in single-spot vibration striking experiment (see Fig. 9). Therefore, the indentation deformation resulting from each individual strike with tool scan motion can be also monitored using the force signal.

In this experiment, a 5 mm × 5 mm area of the workpiece surface is treated by the vibrating tool following parallel line scan paths. For all cases, the spacing (d_p) between the path lines is set to be the same as the offset distance (d_s) between two successive striking locations along the scan path (see Fig. 15(a)). This results in approximately the same striking overlap ratio r_o in both the scan direction and the transverse direction with respect to the scan path lines. The effects of V_pp and r_o on the topography of the treated surface are investigated.

Figure 15 shows the surface topography obtained at various V_pp and r_o. The upper row is for different r_o (0, 0.25, 0.5, and 0.75) with fixed V_pp (120 V) while the lower row is for different V_pp (60, 90, 120, and 150 V) with fixed r_o (0.75). For each condition, the generated surface texture is uniform throughout the treated area, which reflects the uniform spacing and intensity of the strikes during the treatment. The r_o significantly affects the generated surface texture. With the small r_o (Figs. 15(a) and 15(b)), the surfaces have a dimple texture that reflects each indentation on the surface. It shows that the material is displaced to form circular ridges. However, more material is displaced to the two lateral sides compared to the front and back sides with respect to the tool scan path. As r_o increases, the dimple size decreases. When r_o is increased to 0.75, the individual dimple is no longer visible (Fig. 15(d)). When the surfaces generated at r_o = 0.75 are examined at a higher resolution (Figs. 15(e)–15(h)), line ridges parallel to the tool scan path can be observed on the surfaces at higher V_pp. These line ridges are formed mainly by the lateral displacement of the material from inside the tool paths. The height of these line ridges decreases with decreasing V_pp. At r_o = 0.75 and V_pp = 60 V (Fig. 15(e)), the line ridges are no longer visible. The surface texture appears to have no significant difference along the scan direction and its transverse direction, leading to a more isotropic texture.

Figure 16 summarizes the quantified roughness parameters (S_a, R_a, and R_z) for these surfaces. The 1D roughness parameters R_a and R_z are measured along both the scan and the transverse directions. It shows that all roughness parameters decrease with the increase in r_o and decrease in V_pp. For r_o < 0.75, R_a and R_z are significantly higher in the transverse direction than the scan direction, and S_a is very close to the R_a in the scan direction (Figs. 16(a) and 16(b)). For r_o = 0.75, the roughness difference in the two directions is significantly reduced, and the difference is further reduced with decreasing V_pp (Figs. 16(c) and 16(d)). These changes are consistent with the transition of surface texture from the dimple type to the line type and eventually to the isotropic type.

Note the roughness of the treated surfaces is all higher than the initial roughness for the ground surface. The smoothly ground surface was used to minimize the influence of initial surface roughness and texture such that the generated surface roughness and texture can be easily related to the processing parameters of the vibration striking treatment. Furthermore, these measured roughness values represent the achievable surface roughness using the corresponding treatment parameters. Among all the surfaces shown in Fig. 15, the smoothest surface is obtained with V_pp = 60 V and r_o = 0.75 at S_a = 0.44 µm, which is only slightly higher than the initial S_a value of 0.32 µm for the ground surface.

The results from the four experiments demonstrate the feasibility and excellent controllability of piezo vibration striking treatment (PVST) in terms of force and vibration displacement monitoring and surface deformation control. The important process parameters for PVST are tool vertical position Z, tool vibration frequency f, vibration amplitude u_pp, striking overlap ratio r_o, and tool scan path. By combining piezo stack actuated vibration device with CNC machine, these process parameters can be directly or indirectly controlled as well as monitored in real time. In general, the piezo stack vibration device enables the control of tool vibration frequency and amplitude while the CNC machine enables the control of tool position Z and tool scan motion (speed and path). The control of tool vibration and tool vertical position is critical for controlling the local surface deformation imposed by each individual strike while the control of tool scan motion is critical for controlling the locations and layout of the successive strikes. Such combined process controllability will lead to enhanced controllable surface deformation which is beyond the capability of current striking-based treatment processes, such as SP, SMAT, MHP, and UNSM. Therefore, PVST has the potential to realize more efficient deformation-based surface engineering including finish, residual stress, hardness, and microstructure for enhancing components’ performance such as fatigue life and wear resistance.

The 2D vibration striking experiment has shown surface finish can be improved by increasing r_o and/or decreasing V_pp. The trade-offs in different combinations of r_o and V_pp which can achieve the same level of surface finish are worth further discussion. In general, the same level of surface finish may be achieved by the combination of higher r_o and higher V_pp or the combination of lower r_o and lower V_pp. Higher r_o can be achieved by reducing the tool scan speed which will increase the treatment time. It can be also achieved by increasing tool vibration frequency which will increase the power consumption for piezo stack actuation. Higher V_pp leads to higher plastic strain and thicker deformed layer due to higher vibration amplitude. In contrast, the combination of lower r_o and lower V_pp results in faster treatment and less vibration power consumption. However, the induced plastic strain and strained layer thickness are smaller. Based on these trade-offs, the higher r_o–higher V_pp setting is more suitable for surface microstructure refinement purpose while the lower r_o–lower V_pp setting is more suitable for surface residual stress modification purposes.

The second linear force relationship is found between the striking force and the resulting indentation size (Figs. 9 and 14). This relationship should depend on the workpiece material and the striking tool tip geometry since both affect the plastic deformation induced on the surface. For the workpiece material (mild steel) and striking tip (d = 3 mm) used in this study, the force–indentation size relationship can be well approximated as being linear. Theoretically, this relationship is nonlinear for a spherical-shaped indenter [26]. However, the indentation depth range of PVST is usually very small (e.g., ∼30 µm in Figs. 9 and 14) compared to the striking tool tip diameter (3 mm). It is this small indentation depth range that enables a good approximation of the linear relationship between the striking force and indentation size. The quality of this linear approximation can be considered to depend on the ratio of the indentation depth range to the diameter of the striking tool tip (h/d). The smaller this ratio, the better quality has the linear approximation. It can be expected that the linear force relationship is better approximated for a harder material than for a softer material because h becomes smaller for the harder material and better for a larger striking tool tip than for a smaller tool tip.

In practice, the h/d ratio may still be very small despite the changes of workpiece material or tool tip size, so the linear force–indentation size relationship may be generally acceptable in PVST. The linear equation describing the relationship, however, will change with the workpiece material and the striking tool tip diameter. For a given combination of workpiece material and tool tip diameter, the linear force–indentation size relationship should be fixed, based on which the indentation size or plastic deformation level induced by each individual strike can be monitored using the measured force signal.

The two linear force relationships provide a basis for realizing real-time monitoring and force-based feedback control of PVST which can greatly enhance the treatment efficiency and capability. For practical implementation, the force sensor eventually needs to be integrated into the vibration device. This type of integration has been demonstrated feasible although for implementation of modulation-assisted drilling process [23,24]. In this study, PVST is only performed on a flat workpiece surface. The force-based feedback control capability will be very useful for performing the treatment on a freeform surface. In this case, the tool's vertical position and vibration amplitude can be controlled in real time based on the striking force signal to accommodate the change of surface height during the tool scan. This capability will greatly enhance the automation and efficiency of the treatment process.

This study has experimentally investigated the non-resonant piezo vibration striking surface treatment (PVST) process with an emphasis on the striking force, vibration displacement, resulting surface deformation, and their relationships. From this study, the following can be concluded:

1. It is feasible to implement PVST using a piezo stack actuated vibration device installed on a CNC machine platform. PVST can induce strikes with consistent intensity in each cycle of tool vibration. Both the striking intensity and striking location can be well controlled leading to improved control of surface plastic deformation induced by the treatment.

2. In PVST, the tool vibration amplitude during striking is always reduced from the amplitude without striking. This reduction in vibration amplitude is due to the elastic deformation of the vibration device assembly and is linearly dependent on the striking force. The linear force–amplitude reduction relationship reflects the stiffness of the device assembly.

3. In PVST, the depth of the permanent indentation resulting from each strike is, to a first approximation, linearly dependent on the striking peak force. This linear force relationship offers the opportunity to directly monitor and control the surface deformation induced by each strike using the force signal.

4. The texture and roughness of the treated surface are primarily affected by the striking overlap ratio and tool vibration amplitude in PVST. The finish of the treated surface can be improved by increasing the striking overlap ratio and/or decreasing the vibration amplitude.

The present study has demonstrated the promising capability of PVST in inducing controllable surface deformation. Future studies will focus on how to utilize this capability to realize deformation-based engineering of surface attributes for enhancing components’ performance such as wear-resistance and fatigue life.

This work is supported in part by NSF CMMI (Grant Nos. 2019320 and 2102015).

There are no conflicts of interest.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper. No data, models, or code were generated or used for this paper.

f =

driving voltage frequency or vibration frequency

h =

depth of permanent indentation

u =

tool vibration displacement

D =

diameter of permanent indentation

V =

Piezo stack driving voltage

d_p =

spacing between parallel scan lines

d_s =

spacing between two successive strikes

r_o =

striking overlap ratio

u_max =

maximum vibration displacement w/ striking

u_pp =

peak-to-peak vibration amplitude w/ striking

v_s =

speed of horizontal tool scan (or feed) motion

F_z =

striking force

F_max =

striking peak force

F_x =

sliding force

V_pp =

peak-to-peak driving voltage amplitude

$umax0$ =

maximum vibration displacement w/o striking

$upp0$ =

peak-to-peak vibration amplitude w/o striking