Evaluation of an experimental modal analysis device for micromilling tools

Stable machining conditions in the micromilling process are critical to increase the production of small components. Precise frequency response measurements are essential to generate the stability diagrams. Therefore, impact hammer application which mostly relies on operator’s skill and experience is very time-consuming and can produce imprecise results. This study aims to analyze a device developed to perform the experimental modal analysis of micromilling tools. The device facilitates the positioning of a fixed point Laser Doppler Vibrometer (LDV) as well as providing automatic and reproductive impact tests. Two mirrors supported by kinematic mounts are used to position the laser beam on the micro milling tool surface. The impact hammer is composed of a force sensor attached to a custom designed flexure-based body, in which an automated electro-magnetic releases the mechanism. A set of experiments were conducted to perform the precision positioning of the laser beam and the impact hits. The impact force repeatability in terms of the magnitude and impulse duration were also investigated. The application of the device was demonstrated through modal testing of two micromilling tools with two different diameters.

spindle speed, feed and depth of cut depends on the dynamic interaction between the tool and the workpiece.
Vibration can be minimized when the dynamic response of the micromilling system and the workpiece material properties are known. Through the Stability Lobule Diagrams (SLD), a more productive and suitable cutting conditions for material removal can be selected [1,7,9,12,13,15,17,18].
The generation of SLD for micromachining is still a challenge, as it requires the correct measurement of the Frequency Response Function (FRF) at the tip of the microtool attached to the tool holder set [23]. Experimental Modal Analysis (EMA) is the most common method of determining the tool FRF. However, due to very small tool size, the experimental methods are still difficult to be applied.
The excitation method is vital for the EMA. An excitation device must be able to excite all modes of interest. In other words, the excitation bandwidth needs to cover the frequencies of the modes of interest [10].
The dynamic analysis of micro tools by the experimental method using a mini impact hammer and laser vibrometer was reported by [19,20,27]. However, the measurements performed by Singh and Singh showed uncertainties, which were attributed to noise presented in the responses captured by the laser displacement sensor and imprecision in the positioning of the excited and the measured points [27]. The reported problems are contextualized by the image of the experiment carried out by Matuszak et al. in Fig. 1 [20]. Mascardelli et al. point out that numerous excitations with the mini impact hammer were necessary to obtain a consistent result. In addition, the difficulty in positioning the laser beam on axis of the tool was also reported [19].
Some other methods have been developed to determine the FRF in micromilling. Jin and Altintas determined the FRF using a specially designed a piezoelectric actuator to excite the micro-endmill tool tip [15]. Wiederkehr et al. [28] investigated the excitation micromilling tools using bearing balls, shot by compressed air. With the proposed approach the FRFs at different spindle speeds within a wide frequency range was obtained. The impact force magnitude, necessary to calculate the FRFs, were simulated the using finite element method [28].
Ahmadi applied the Operational Modal Analysis (OPA) method based on excitation by acoustic method to excite micromilling tool. The author used the experimental modal test with impact excitation to validate the frequency values found by the OMA method [2].
Hybrid methods combining experimental and analytical or numerical approaches has also been applied. En example is the receptance Coupling Substructure Analysis proposed by Schmitz and Donalson that has been an alternative to characterize the dynamics of micromilling systems [25]. Its has the advantage in reducing the time spent on experiments when new modal tests are required for different toolholder-spindle assemblies [8,19,22,26,27,29]. Even using hybrid processes, it is necessary to use conventional EMA.
In order to make EMA an operator-independent process and therefore more reliable, different automated devices have been developed. Taking the macro milling as example, an automatic hammer was used by Dunwoody to obtain the tool tip FRF on the machine tool. The device consists of a solenoid actuated plunger with a force sensor on the end to hit the tool, and a capacitive displacement sensor to measure the response [11].
Ganguly investigated the spindle dynamics under different rotation speeds. A first setup was designed based on a oscillating impact hammer, which translates along a linear bearing. A second device was designed, in which a force sensor was mounted on a parallelogram leaf spring flexure. In both setups, a Laser Doppler Vibrometer LDV was used to measure the response of the structure [14].
Brüggemann et al. developed an automated modal impact hammer based on the pendulum principle to obtain the FRF of the milling tools [6]. Brüggemann et al. [24] constructed an automated impulse hammer for using in a 5axis CNC milling machines. The working principle is based on an axially moving bolt, which is accelerated through a compressed spring and is pulled back by a linear actuator [24].
In relation to automatic systems for dynamic analysis of small-sized structures, Ozturk et al. developed an automated setup with impact hammer and vibrometer in order to obtain FRF of a macro milling tool dynamics [21]. A standard impact hammer is clamped on a flexible plate that is attached on to the table of the machine. The response of the tool is measured using a laser vibrometer. Bediz et al. studied an impact excitation system for modal testing of miniature structures using a flexure-based body and an automated electro-magnetic release mechanism. With this system repeatable, high-bandwidth, controlled-force modal testing of miniature structures was possible [3].
The main advantage of an automated modal analysis system is that an operator-independent process is achieved. With that, the need for a highly-skilled operator is eliminated, the repeatability of results of measurements increases, and the testing time can be reduced.
Therefore, this work aims to present and test a device capable of positioning a laser vibrometer and impact hammer, as well as the automation of the exciting process. The work is divided into description of the device, positioning test and impact force and finally its application in FRF determination.

Device description
The device consists of two systems, the first one the impact hammer and the second one the vibration measurement.
It was designed for quick and easy positioning of the laser beam and impact hammer. The device base is attached to the machine tool table using a 3R Macro clamping system from System 3R Company, which enables a high precise positioning repeatability and the performance of EMA in Xand Y-directions.
Further, the impact excitation system must not influence the measurement one, which means that the vibration energy must not be transported by the device structure in order to excite the mirrors that conduct the laser beam. Figure 2 presents the elements of the Experimental Modal Analysis Device (EMAD) according to the 1impact hammer system, 2 -laser beam positioning system, 3 -device base.

Impact hammer system
A schematic drawing of the impact system is shown in Fig. 3. This consists of an electromagnet, a force sensor mounted on flexure mechanism and the micromilling tool.
It is also possible to see in this figure the two adjustable parameters, the distance x e between electromagnet and the sensor and the distance x t between the sensor and the micromilling tool.
A miniature Integrated Circuit Piezoelectric (ICP) force sensor, from PCB Peizoetronics model 209C01 with a sensitivity of 489.9 mV /N, was used as impact hammer.
The tips are aluminum made cylindrical body with a flat end and a semi-sphere (spherical tip) or a half-cylinder In the force repeatability tests, a spherical tip was used so that contact with the flat surface was always punctual, absorbing small misalignments between the excitation mechanism and the micromilling system. In the tests using the dummy tool or the micromilling tool, a cylindrical tip was used.
The force sensor was attached to the end of a parallel-leaf spring flexure. This mechanism has the advantage of having approximate a straight displacement, hitting the tool at same incidence angle.
The electromagnet provides initial deflections and enables repeatable release of the flexure-based hammer. The initial deflection x e was adjusted varying the distance between the force sensor and the electromagnet. A carriage, on which the electromagnet, is mounted moves along the linear guides. A micrometer with a resolution of 0.01 mm was used to measure the displacement and thereby regulate the distance x e . The distance x t between the impact hammer and the tool was adjusted by controlling the positioning of the machine tool spindle. A UNO arduino was used to drive the model SRD-05VDC-3L-C relay that controls the 12 V electromagnet. The magnetization and demagnetization times of the electromagnet was programmed in the code running on UNO arduino board, which contributes to hit the structure only once at a time.

Vibration measurement system
A commercial single-point laser vibrometer Polytec PDV-100 was tripod mounted and used to provide the noncontact measurements of the tool response. It is capable to measure up to 22 kH z of frequency bandwidth with a sensibility of 8 mV /mms −1 . The vibrometer measures the velocity of the target along the direction of the laser beam. To convert to receptance, the mobility was multiplied by iω.
Since the vibrometer was mounted on a tripod relatively distant from the tool, the great challenge was to perform the EMA, positioning the laser beam spot at different points on the tool. Therefore, any small displacement in the measurement region required an even smaller displacement in the tripod head, making the adjustment process even more difficult.
As the vibrometer is a relatively large device, the alternative found was to keep it mounted on a fixed position Two broadband dielectric mirrors from Thorlabs Inc (BB1-E02) were used, which reflect > 99% of light between 700 and 1150 nm at a 45 • angle of incidence. The laser beam hit the two mirror surfaces that were mounted on kinematic mounts. The mirrors were angular adjusted in order to positioning the laser beam spot on desired target. The schematic drawing is shown in Fig. 4.
Manual adjustment of bottom mirror along the Z axis was done via graduate knob with 10 divisions, enabling the 1 mm pitch M12 feedscrew the positioning with a 0.1 mm resolution. The top mirror was fixed not moving along the z axis.
To minimize the effect of backlash, a spring was adopted to pre-tension the translation mechanism. The coarse positioning of the laser beam was carried out by rotating the support of the mirrors around the Z axis at the angles θ 1 and θ 2 . Since the mirrors were mounted on a kinematic mounting, the fine adjustment was carried out by adjusting two M3 screws, rotating the mirrors in two directions, according to the angles θ 3 and θ 4 .

Device evaluation
The objective of the automated device was to provide repeatable modal testing of the micromilling tools. This means that location of the hits and the vibration measurement, as well as the force magnitude applied to the tool could be controllable and reproducible.

Location variability analysis
Experiments were carried out in order to obtain the characteristics of the impact test and the vibration measurement location variation using the EMAD.

Impact location variability
The repeatability of the impact location was assessed by comparing the area of marks generated by the impact hammer on a flat surface. The EMAD without the vibration measurement system was attached to the machine table. A prismatic workpiece was positioned in front of the impact hammer. The workpiece surface was aligned perpendicularly to the impact hammer using a dial indicator. A thin layer of white powder was deposited on the workpiece surface in order to highlight the point of contact after the hammer impact. Ten consecutive hits were performed using the automated impact hammer. The marks left on the workpiece surface were captured with the ZEISS stereoscope model Discovery V8. Figure 5(a) shows the experimental results with the automated impact hammer. This test demonstrated that the device tends to hit at the same position when compared to the obtained results using a miniature impact hammer manually as presented by Bediz et al. and shown in Fig. 5 (b). From the tests using manual hits, it is possible to observe great variability in the impact location [3].
The impact area for manual hits obtained by Bediz et al. [3] was calculated as 10.94 mm 2 , while the impact area for the automated device was 0.07 mm 2 for a maximum impact force of 6.83 N and a tip radius of 1.0 mm.
In contrast with a manual application of a miniature impact hammer, an automated device provides a high level of impact location repeatability.

Laser spot location analysis
In this experiment, a prismatic workpiece was also used. A millimeter paper was fixed on the workpiece surface to serve as a reference. Figure 6 illustrates the experimental setup.
Images were taken with a Canon 5D Mark IV DSLR camera, 30-megapixel full-frame sensor (5.6 μm pixel size),   remotely took and saved on computer for post-processing. Measurements were made every 1 mm in the Z-direction by moving the bottom mirror, from the lower position upwards over 24 mm, totalling 25 measurement points.
The coordinate of the bright spot was offline processing using a Matlab (Mathworks Inc.) program. First the captured images were converted from RBG into grayscale. Afterthat, the brighter pixels were selected and a circle was fitted using the method of least squares. The radius and the coordinate of the laser spot were calculated and converted to mm. The algorithm used is described in [30].
The positioning repeatability in the Z-direction was calculated in relation to the first position, while in the Xdirection by the distance from the laser spot center to an adjusted line passing through the first position. Figure 7 presents the laser beam position error in the Xand Z-directions (radial and axial). The maximum position error P was calculated considering the average of the measuresŪ and standard deviation σ , according to the relationship P =Ū + 2 · σ . The maximum positioning error in the Z-direction was 0.20 mm, while in the X-direction was 0.14 mm.

Force excitation analysis
The force impact analysis were conducted with regard to the influence of the distance between impact hammer and tool, the existence of a double hit and the repeatability of the force magnitude.

Distance between tool and impact hammer
The impact momentum depends on the impact velocity and mass. For a given mass, obtaining repeatable impacts with limited force necessitates providing an accurate and repeatable impact velocity.
Tests were carried out to determine the influence of the distance between the sensor and the tool x t on the maximum impact force. The initial distance x t = 0 μm was adjusted to obtain the maximum impact force. With x t = 0 μm, the sensor reaches the maximum velocity and hence the maximum impact force (maximum impact moment) is obtained. After that point, the leaf spring acts decelerating the sensor, decreasing the impact force. The automated release mechanism provides the distance x e between the electromagnet and the sensor and hence initial deflection. It was adjusted so that the maximum force measured by the sensor does not exceed 9.8 N (the maximum allowable force).
Three impacts were performed for each distance and the result is shown in Fig. 8. The result of the maximum impact force as a function of the distance x t presented a behavior that approaches a second order curve and can be used to adjust the impact force.

Double hit effect
Double hit is a very common problem during impact tests. It occurs when there are multiple impulses after one hit due to structure rebound. When it happens, the spectrum of the excitation is distorted and force spectrum has no longer the wide band constant type. The phenomenon is influenced by the hammer tip hardness, by the dynamic characteristics of the structure and by the excitation device. Therefore, in conducting the EMA, the selection of impaction points is important to avoid the occurrence of double hit.
Two experiments were carried out to illustrate the double hit phenomena. A cylinder dummy tool (H13 tempered steel) with a diameter of 3 mm and a length of 50 mm was attached to the machine tool spindle with a 30 mm overhang. The hit points on the tool were 4 and 8 mm away from the holder face. Figure 9 illustrates the effect of the hit position on the double hit phenomenon. Exciting the structure at 4 mm, impact force without double hit is obtained (Fig. 9a), while exciting at 8 mm the effect of double hit can be observed (Fig. 9b). Figure 10 presents the result of 10 consecutive hits on a plane surface using the impact hammer device. It is possible to observe that the curves have a good reproducibility. The average maximum force was μ = 6.83 N and the standard deviation σ = 0.12 N, given the coefficient of variation σ/μ = 1.7%, which means a satisfactory value. Analyzing the interval in which the sensor is in contact with the tool, the mean time was μ = 167.15 μs with a standard deviation of σ = 6.06 μs, given approximately σ/μ = 3.6%. This data is important, since it is associated with bandwidth, showing that it is also reproducible.

Experimental validation and application
For EMAD evaluation, impact test of a dummy tool was first experimentally obtained. The results were compared against the analytical results. In a second part the dynamics of two micromilling tools with different diameter were carried out. The calculation of modal parameters like natural frequency ω n , damping ratio ζ and stiffness k n were extracted from the frequency response function FRF at the tool tip using the peak-picking method. They are required to construct, for example, the SLD, which is necessary to choice stable cutting conditions.

Experimental setup
Experiments were performed on a KERN Pyramid Nano-Machining Center with a Heidenhain Controller. Figure 11 shows the EMAD mounted on the machine table.
In this figure, it is possible to observe mirrors and the impact hammer systems. In the same figure, enlarging the cutting tool region, it is possible to observe point 1 where the tool is impacted by the hammer and points 1 and 2 where the vibration response are measured by the laser vibrometer.
The positioning of the impact hammer and laser beam spot in relation to the experimental points on the cutting tool followed the procedure described below.
First, the position of the tool in relation to the impact hammer is adjusted. The hammer tip coordinates is then obtained in relation to the machine tool coordinate system with a probe. In addition, the diameter and length of the tool is measured in a tool presetter. The tool and are calculate with respect to the machine tool coordinate system. In this way, the coordinates of the cutting tool can be computed such that the impact point on the tool coincides with the tool tip during the test.
After positioning the impact hammer, the laser beam spot must be positioned relative to the tool. For that, the bottom mirror was moved to the height corresponding to the vibration measurement point on the tool. Rotating the mirror support, a coarse angular position on the tool was achieve. Two screws were used for fine adjustment, always seeking to obtain the maximum intensity of the signal indicated on the display on the laser vibrometer.
When the process begins, the electromagnet pulls the impact hammer, thereby providing an initial deflection to the flexure-based body. When the relay is switch off by the arduino UNO, the electromagnet releases the body and the impact hammer moves along a well-described trajectory. The arduino UNO was programmed in such a way that after the impact hammer hits the sample surface, the relay switches the electromagnet on pulling back the impact hammer.
The impact and vibration response signals were acquired by a Bruel & Kjaer -Type 3160-A-024 data acquisition hardware. The software PULSE LabShop Fast Track v. 16.1.1.24 was used to obtain the experimental FRFs.
The acquisition rate was 16.4 kH z. To avoid aliasing, the acquisition rate was set to approximately 3 times the bandwidth excited by the hammer. Rectangular and exponential windows were applied to the force pulse and vibration response respectively to avoid leakage. Each FRF was obtained considering the average of five measurements. The data were transferred to a PC and the Matlab software was used for post-processing and modal parameter extraction.

Analysis with a cylindrical dummy tool
A excitation force was applied to dummy tool at 6.5 mm, and the tool vibration was measured at 6.5, 12.5, 18.5, 14.5 and 29.5 mm from the holder face.
The analytical solution of the natural frequencies and mode shapes for a cantilever beam was obtained according to [4]. The parameters used in calculation are the elastic modulus, mass, and geometry of dummy tool. In order to get a more accurate results, the Young's modulus was obtained from a tensile test and yields 164 GP a. The calculated natural frequencies were 2117, 13269 and 37152 H z. Figure 12(a) shows the signals measured during the impact test of the dummy tool where it is possible to observe the impact hammer signal, as well as the tool vibration response measured by the vibrometer. In relation to the impact hammer signal, it is to observe a impulse force with maximum level of about 5.6 N. When the impact hammer moves back, it collides with the release mechanism and therefore a small force oscillation can be observed.
These experimental results served to calculate the FRF. The existence of a dominant mode around 1995 H z was observed, which is close to the first theoretical natural frequency of circa 2117 H z, i.e., a difference of about 6%. The imaginary part of the experimental FRFs was used to determine the first vibration mode of the cylinder blank, as shown in Fig. 12(b). By normalizing the amplitude of the imaginary part by the maximum value and comparing it with the analytical result obtained according to [4], the average error between the five experienced points was around 14%.
It can be considered that an error around 6% in the natural frequency and 14% in the amplitude of the first vibration mode are satisfactory to validate the device.

FRF of micromilling tools
A significant aspect of the micromilling process dynamics is the prediction of the tool tip FRF. Due to the small dimensions and the complex geometry, the excitation cannot be applied directly on the tool tip with an impact hammer. With this regarding the modal synthesis is normally used. Tool response is measured directly at the tool tip with laser vibrometer, while excitation is applied on the tool shank with impact hammer. Another important fact is that, the dominant mode of the tool is the most important to calculate the SLD and the first mode is the dominant in general.
To demonstrate the application of the device, two microtools DIXI model 7242 with tool tip diameter of 0.2 mm and 1.0 mm were investigated. The tool holder set was attached to the machine spindle and the measurements were carried out directly at the KERN Pyramid Nano machining center.
As can be seen in Fig. 11, the impacts were performed at 4 mm from the support (point 1) and the vibration response was measured at this point and at the tool tip (points 1 and 2). In this way, the FRFs H 11 and H 21 are experimentally obtained. Five measurements per position were carried out. The coherence were also analyzed for both FRFs.
Numerical modal analysis was conducted to serve as a basis for the experimental results. Abaqus software was used to calculate the natural frequencies and mode shapes of the micromilling tools.
Solid model was meshed using linear hexahedral elements of type C3D8R (a 8-node brick element with reduced integration). The overhang length of tool is kept at 25 mm. The properties of the tungsten carbide tool are taken as density ρ = 14, 300 kg/m 2 , Young's modulus E = 580 GP a, Poisson's ratio ν = 0.28 and damping ratio of 1%. The fluted section of the end mill was modeled as a solid cylinder, considered to be 80% of the total diameter, as presented by Kops and Vo [16]. Figure 13 presents the finite element simulation of the first vibration mode for the 0.2 mm tool diameter. The first three natural frequencies were 4, 944 H z, 29, 298 H z and 42, 800 H z. The first two are bending modes and the third is a torsion mode.
The experimental FRFs of the spindle-tool structure and the coherence functions for the 0.2 mm tool diameter are presented in Fig. 14. Three resonance peaks were detected at approximately 1590 H z, 2350 H z and 4144 H z. It was observed that the closest natural frequency to that obtained from the simulation is the third one, about 4144 H z. According to the natural frequencies between the experimental and the simulated, the difference was approximately 19%.
The first and second resonance peaks can be associated with a natural frequency of the spindle, of the tool holder or even of the experimental device. In the frequency range of 0-1000 H z the FRF magnitude showed a disturbed signal that is caused typically by the integration of the noise in velocity measurement and hence was not shown.
The frequency bandwidth obtained in the tests was in the order of 5.7 kH z, which means that the device is suitable to excite the first vibration mode of the micromilling tool.
For FRF H 11 , the measurement was closer to the holder face and hence the tool was stiffer, so the vibration speed is lower, which worsens the quality of the FRF. This fact is noticed mainly in the anti-resonance regions and above 5 kH z. For the H 21 , the interval between 1000 and 6000 H z the coherence result provided evidence of an excellent performance. Coherence values were above 97% within the measured range, except when the measured response was small, including the anti-resonance and the low frequency regions. Figure 15 presents the experimental results for the 1.0 mm diameter of the cutting part of the micromilling tool. As in the previous test, three natural frequencies are also observed. The first two frequencies were close to the found in the test of 0.2 mm tool diameter. The third, of about 4878 H z was assigned to the cutting tool. The numerical result obtained in Abaqus simulation for the 1.0 mm tool diameter was 5280 H z, which means an error of 8.2% between the frequencies.
An explanation for the difference found in the first natural frequency between the simulated and the experimental results can be explained based on the work of Mascardelli et al. [19]. They pointed out that the effects of the imperfectly constrained tool holder, as well as the effects of the spindle modes on the tool mode, can significantly decrease the tool mode frequency. Table 1 shows the modal parameters extracted for the two tools. The experimental modal parameters of the system, i.e., natural frequencies, modal damping ratio and modal stiffness were obtained through the curve fitting using the peak-picking method. Comparing the results of the FRF H 11 and H 21 at the frequencies 1590 and 2530, it was observed that there was no significant difference in the parameters modal damping ratio ζ and modal stiffness k n between the cutting tools. In the third natural frequency, a change was observed in both the modal damping ratio and the modal stiffness, as expected.
In the modal damping ratio a decreased from 2.0 to 1.6 for H 11 and from 2.2 to 1.7 for H 21 was observed with the increase of the cutting tool diameter. Regarding the modal stiffness, the relative difference between the two tool diameters increases 104% and 71%, for H 11 and H 21 , respectively. Therefore, for the tool with the larger diameter of the cutting part, the stiffness increases, while the modal damping ratio decreases.
The reliable frequency range of the FRF obtained with the proposal device was between 1 and 5.7 kH z, which is satisfactory to determine the FRF of the most flexible mode of the micromilling tool. This FRFs can be used to calculate the SLD or to simulate the process dynamics in the time domain.

Conclusion
The impact hammer test of micromilling tools is a difficult task. The frequency response function accuracy relies on the operator's skill. In order to turn the process more reliable and less time-consuming, a devise that can facilitate the positioning of the laser vibrometer beam directly at certain points on micromilling tool and enable the automatic hit process of the impulse hammer was investigated. The laser beam was guided from the laser vibrometer to the micromilling tool by two mirrors. One mirror was linear displaced positioning the laser beam along the tool axial direction, while the angular adjustment moves the mirror in the radial direction of the tool. Analyzing the maximum positioning error of laser beam spot in the axial and radial directions, the results were satisfactory. Regarding the impact hammer, the tests showed that the reproducibility of the impacts location was considerably better than the manual hits, compared to those in the literature. Moreover, it could be shown that the device can provide repeatable, controlled-force, and adequate bandwidth excitations for modal testing. Using a cylindrical dummy tool the device was evaluated in terms of modal testing, showing satisfactory agreement with analytical results. Impact tests of two micromilling tools with different diameters were carried out to show the device application. The FRFs were satisfactorily obtained for both tools and the modal parameters extracted for the first vibration mode. In addition, modal parameter was effectively extracted and can be used to construct the Stability Lobes Diagram. The investigated device still requires some expert knowledge on modal testing and a technician to set it up, however due to its modularity it is easily installed in a machine tool. The laser beam and the impact hammer were easily adjusted. The results showed that the device can provide a satisfactory alternative method for manually operated impact test. Further works, provides the development of a system that can be permanently installed in the machine tool in order to conduct a fully automated experimental modal analysis without any external intervention.