**4.1. Method of measuring the ultrasonic elliptic vibration**

The elliptic motion of the shoe end face under various applied voltages (amplitudes, frequencies and phase differences) is investigated using a measuring system composed of two laser Doppler vibrometers (Ono Sokki Co., Ltd., LV-1610) equipped with the respective sensor heads, a vector conversion unit (Ono Sokki Co., Ltd.,), and a multi-purpose FFT(Fast Fourier Transform) analyzer (Ono Sokki Co., Ltd., CF-5220), as shown in Fig.11.

The shoe is bolted at its center (the common node for L1 and B4 mode) on the holder in order not to restrict the ultrasonic vibration. A preload is then applied to the shoe using a coil spring in order to prevent the PZT from breaking due to resonance. Two AC signals generated by a wave function generator (NF Corporation, WF1994) are applied to the PZT after being amplified by two power amplifiers (NF Corporation, 4010). During measurement, the two laser beams from the respective heads are focused at the same point near the shoe end face. The signals from the laser Doppler vibrometers are then input to the vector conversion unit for synthesis and are recorder with a digital oscilloscope (Iwatsu Co., Ltd., LT364L). The AC signal is changed by various voltages, phase differences and frequencies. From the digital oscilloscope, the trace of ultrasonic vibration will be obtained based on the different input parameters, and the relationship between the input parameters and the vibration will be clarified.

**Figure 11.** Method of measuring the ultrasonic elliptic vibration

The shoe is bolted at its center (the common node for L1 and B4 mode) on the holder in order not to restrict the ultrasonic vibration. A preload is then applied to the shoe using a coil spring in order to prevent the PZT from breaking due to resonance.

Two AC signals generated by a wave function generator (NF Corporation, WF1994) are applied to the PZT after being amplified by two power amplifiers (NF Corporation, 4010). During measurement, the two laser beams from the respective heads are focused at the same point near the shoe end face. The signals from the laser Doppler vibrometers are then input to the vector conversion unit for synthesis and are recorder with a digital oscilloscope (Iwatsu Co., Ltd., LT364L). The AC signal is changed by various voltages, phase differences and frequencies. From the digital oscilloscope, the trace of ultrasonic vibration will be obtained based on the different input parameters, and the relationship between the input parameters and the vibration will be clarified.

Fabrication of Microscale Tungsten Carbide Workpiece by New Centerless Grinding Method 131

In the apparatus, a wheel mounted on a spindle is driven rotationally by a motor and plays the role of the grinding wheel. The ultrasonic vibration shoe is bolted on its holder and then held on a small 2-axis dynamometer (Kistler Co., Ltd., 9876) installed on a linear motion guide. A thin rubber sheet (0.5mm in thickness) of the same material as that of a conventional regulating wheel (A120R) was made and attached to the shoe end face so that the friction coefficient between the shoe and the workpiece is large enough to prevent the workpiece from slipping on the shoe end face. The workpiece is fed toward the wheel by the shoe, which is carried forward by manipulating the shoe feed bolt. The normal contact force and the friction force between the rotating workpiece and wheel correspond to the normal and tangential grinding forces, respectively. In the test, the dynamometer was used to set up the force, and the same wave function generator and power amplifiers as used in the elliptic motion measurement were employed to apply the AC voltage to the PZT. The workpiece rotational speed is obtained by recording the motion of the rotating workpiece end face, on which a circular mark was created, suing a digital video camera. The video images are then stored in a computer for analysis using animated image processing software (Deigimo Co., Ltd., Swallow2001 DV). Pin-shaped rods (SK4) of 5mm in diameter and 15mm in length were used as the workpieces. In addition, *Vp-p* was set in the range of 20-200V while the voltage frequency and the phase difference were fixed at *f*=24.3kHz and *ψ*=90°, respectively.

Fig.14 shows a series of video images of the workpiece end face taken every 0.033s with a camera capable of taking 30 pictures per second. The workpiece rotational speed *nw* can thus

**Figure 13.** Evaluation apparatus for the shoe

be calculated as follows:

Fig.12 shows the measured results of the point on the end face with various parameters.

**Figure 12.** Measured results of the point on the end face with various parameters

### **4.2. Rotational motion control tests of the workpiece**

In the ultrasonic vibration shoe centerless grinding method, it is crucial to precisely control the workpiece rotational speed by the elliptic motion of the end face of shoe in order to achieve high-precision grinding. Therefore, a evaluating involving the rotational control of a cylindrical workpiece using the produced ultrasonic vibration shoe was conducted on an apparatus specially built in house, as shown in Fig.13.

In the apparatus, a wheel mounted on a spindle is driven rotationally by a motor and plays the role of the grinding wheel. The ultrasonic vibration shoe is bolted on its holder and then held on a small 2-axis dynamometer (Kistler Co., Ltd., 9876) installed on a linear motion guide. A thin rubber sheet (0.5mm in thickness) of the same material as that of a conventional regulating wheel (A120R) was made and attached to the shoe end face so that the friction coefficient between the shoe and the workpiece is large enough to prevent the workpiece from slipping on the shoe end face. The workpiece is fed toward the wheel by the shoe, which is carried forward by manipulating the shoe feed bolt. The normal contact force and the friction force between the rotating workpiece and wheel correspond to the normal and tangential grinding forces, respectively. In the test, the dynamometer was used to set up the force, and the same wave function generator and power amplifiers as used in the elliptic motion measurement were employed to apply the AC voltage to the PZT. The workpiece rotational speed is obtained by recording the motion of the rotating workpiece end face, on which a circular mark was created, suing a digital video camera. The video images are then stored in a computer for analysis using animated image processing software (Deigimo Co., Ltd., Swallow2001 DV). Pin-shaped rods (SK4) of 5mm in diameter and 15mm in length were used as the workpieces. In addition, *Vp-p* was set in the range of 20-200V while the voltage frequency and the phase difference were fixed at *f*=24.3kHz and *ψ*=90°, respectively.

**Figure 13.** Evaluation apparatus for the shoe

130 Tungsten Carbide – Processing and Applications

parameters and the vibration will be clarified.

point near the shoe end face. The signals from the laser Doppler vibrometers are then input to the vector conversion unit for synthesis and are recorder with a digital oscilloscope (Iwatsu Co., Ltd., LT364L). The AC signal is changed by various voltages, phase differences and frequencies. From the digital oscilloscope, the trace of ultrasonic vibration will be obtained based on the different input parameters, and the relationship between the input

Fig.12 shows the measured results of the point on the end face with various parameters.

 *f*=24.2kHz *f*=24.3kHz *f*=24.4kHz *f*=24.5kHz *f*=24.6kHz

(a) Elliptic vibration for various frequencies (*Vp-p*=100V, *ψ*=90°)

Vp-p=50V Vp-p=100V Vp-p=150V Vp-p=200V

(b) Elliptic vibration for various applied voltages (*f*=24.3kHz, *ψ*=90°)

**Figure 12.** Measured results of the point on the end face with various parameters

In the ultrasonic vibration shoe centerless grinding method, it is crucial to precisely control the workpiece rotational speed by the elliptic motion of the end face of shoe in order to achieve high-precision grinding. Therefore, a evaluating involving the rotational control of a cylindrical workpiece using the produced ultrasonic vibration shoe was conducted on an

(c) Elliptic vibration for various phase differences (*Vp-p*=100V, *f*=24.3kHz)

 *ψ*=0° *ψ*=45° *ψ*=90° *ψ*=135° *ψ*=180°

**4.2. Rotational motion control tests of the workpiece** 

apparatus specially built in house, as shown in Fig.13.

Fig.14 shows a series of video images of the workpiece end face taken every 0.033s with a camera capable of taking 30 pictures per second. The workpiece rotational speed *nw* can thus be calculated as follows:

$$m\_w = \frac{\Sigma\_{i=1}^N n\_{wi}}{N} \tag{2}$$

Fabrication of Microscale Tungsten Carbide Workpiece by New Centerless Grinding Method 133

In order to confirm the validity of the proposed new method, fabrication of micro-part of tungsten carbide will be carried out. The grinder is modified by the conventional grinder of μ micron grinder MIC-150, the product of μ micron Corp. The regulating wheel unit will be uninstalled and a fine feed unit, which is composed of a fine feed table and stepping motor, will be installed. In the experimental grinder, for the finish grinding of micro parts with sizes of less than 1mm in diameter, the depth of cut must be less than 1μm in order to make the grinding force small. The fine feed and fine adjustment unit is shown in Fig.16 (a and b). The shoe can be fine adjusted in Z direction by handing the fine adjustment screw. The adjustment component can be locked when the height of shoe is adjusted to an appreciable position by operating the lock handle on the back of the unit, as shown in Fig.16 (b). The fine feed and fine adjustment unit can be rotated in XY by surrounding the rotating pin, and then fixed the unit by locking other three fixed screw bolts. A fine feed unit composed of a shoe holder, a linear guide, a ball screw and a stepping motor has been designed and produced that carries the shoe toward the grinding wheel at a feed rate of less than 1μm. A pre-load is then applied to the shoe at its left end face in its longitudinal direction using a coil spring in order to prevent the shoe from breaking due to resonance and is fixed by the

The grinder installed fine feed and adjustment mechanisms was used to grinding microscale cylindrical workpiece, its aim is to verify the feasibility of micro-scale fabrication by ultrasonic-shoe centerless grinding technique, and to confirm the performance of the constructed experimental apparatus in actual grinding operations. The tungsten carbide steel cylindrical workpiece used in grinding is shown in Fig.17, 0.6mm in diameter and 15mm in length. The photo of grinder is shown in Fig.18 and Fig.19 shows a main portion of

(a) (b)

the experimental setup. The experimental conditions are listed as in Table 2.

**5. Fabrication of micro-part of tungsten carbide** 

**5.1. The modification of experimental grinder** 

screw at its right face of shoe foot.

**Figure 16.** Fine feed and fine adjustment unit

**5.2 Grinding experiments** 

where nwi =(*βi+1*−*βi*)/(*ti+1−ti*), i =1,2, ..., N.

Fig.15 shows the relationship obtained between *nw* and *Vp–p*. Clearly, *nw* increases linearly with *Vp–p*. This is in close agreement with the prediction described above, and indicates that the workpiece rotation speed can be precisely controlled by the elliptic motion of the shoe.

**Figure 14.** Video images of the rotating workpiece

**Figure 15.** Relationship between the workpiece rotational speed and the applied voltage
