**2. Ultrasonic vibration shoe centerless grinding method**

Fig. 1(a) illustrates the principle of ultrasonic-shoe centerless grinding where an ultrasonic shoe and a blade are used to support the workpiece and feed it toward the grinding wheel, instead of using a regulating wheel as in conventional centerless grinding (see Fig. 1(b)). In the former case (see Fig. 1(a)), an ultrasonic vibration shoe supports the workpiece and feed it towards the grinding wheel. The rotational speed of the workpiece is controlled by the elliptic motion of the shoe end face. Whereas in the latter case (see Fig. 1(b)), the conventional centerless grinding method includes three basic elements: grinding wheel, regulating wheel and blade. A regulating wheel supports the workpiece together with a blade and to feed the workpiece towards the grinding wheel. The rotational speed of the workpiece is controlled by the rotation of the regulating wheel.

**Figure 1.** Illustrations of the new centerless grinding with ultrasonic shoe (a) and conventional centerless grinding with regulating wheel (b)

The Fig.2 shows the detail principle of ultrasonic vibration shoe centerless grinding. The workpiece is supported by an ultrasonic elliptic-vibration shoe together with a blade, and it is fed towards the grinding wheel by the shoe. When two alternative current (AC) signals (over 20kHz) with a phase difference of *Ψ*, generated by a wave function generator, are applied to the PZT after being amplified by means of power amplifiers, the bending and longitudinal ultrasonic vibrations are excited simultaneously. The synthesis of vibration displacements in the two directions creates an elliptic motion on the end face of the metal elastic plate.

122 Tungsten Carbide – Processing and Applications

present authors [12–15] in microscale fabrication.

**2. Ultrasonic vibration shoe centerless grinding method** 

workpiece is controlled by the rotation of the regulating wheel.

centerless grinding with regulating wheel (b)

especially on microscale cylindrical workpieces with a large aspect ratio because of the low stiffness of the workpiece support mechanism. Fortunately, these problems can be solved if a centerless grinding technique is employed since the workpiece can then be supported along its entire length on a regulating wheel and blade. However, in microscale machining by conventional centerless grinding, an extremely thin blade is required because the blade thickness must be smaller than the workpiece diameter so that the regulating wheel does not interfere with the blade. This necessitates the installation of a costly blade and significantly reduces the stiffness of the workpiece support mechanism. In addition, because of the extremely low weight, the microscale workpiece springs from the blade easily during grinding due to the surface tension of the grinding fluid adhering to the lifting regulating wheel circumference surface. This phenomenon is called "spinning" [11], and causes the grinding operation to fail. However, as will be explained below, these problems would be overcome by employing the ultrasonic-shoe centerless grinding technique developed by the

Fig. 1(a) illustrates the principle of ultrasonic-shoe centerless grinding where an ultrasonic shoe and a blade are used to support the workpiece and feed it toward the grinding wheel, instead of using a regulating wheel as in conventional centerless grinding (see Fig. 1(b)). In the former case (see Fig. 1(a)), an ultrasonic vibration shoe supports the workpiece and feed it towards the grinding wheel. The rotational speed of the workpiece is controlled by the elliptic motion of the shoe end face. Whereas in the latter case (see Fig. 1(b)), the conventional centerless grinding method includes three basic elements: grinding wheel, regulating wheel and blade. A regulating wheel supports the workpiece together with a blade and to feed the workpiece towards the grinding wheel. The rotational speed of the

**Figure 1.** Illustrations of the new centerless grinding with ultrasonic shoe (a) and conventional

(a) (b)

Consequently, the rotation of workpiece is controlled by the friction force between the workpiece and the shoe so that the peripheral speed of the workpiece is the same as the bending vibration speed on the shoe end face. The speed varies with the variation of the voltage. In addition, the geometrical arrangements of workpiece such as the shoe tilt angle , the workpiece center height angle over the grinding wheel center, and the blade angle can be adjusted to get the optimum geometrical arrangement in order to achieve the least roundness error.

Based on the processing principle described above (see Fig.2), a grinding apparatus was built as illustrated in Fig.3. The cylindrical workpiece is constrained between the ultrasonic shoe, the blade, and the grinding wheel. The shoe and the blade are xed on their holders by using bolts. A ne feed mechanism consisting of a linear motion way, a ball screw, and the shoe holder is driven by a stepping motor to give the shoe a ne

**Figure 2.** The detail principle of ultrasonic vibration shoe centerless grinding

Motion forward and backward on to the grinding wheel during grinding. The rotational speed of the workpiece is controlled by the elliptic motion of the shoe. Once the clockwise rotating workpiece interferes with the grinding wheel that is rotating counterclockwise at high speed, the workpiece is fed forward and grinding commences. As can be seen in Fig.1 (a), the gap between the lower right edge of the shoe and the top face of the blade should be smaller than the workpiece diameter; otherwise the workpiece would fall through the gap, causing the grinding operation to fail. Therefore, when grinding a microscale workpiece less than100μm in diameter, the vertical position of the shoe must be adjusted carefully so that

the gap is sufciently small. To this end, a ne vertical position adjustment mechanism composed of a vertical motion guide, a ball screw, and a table, on which the ne feed mechanism is held, was constructed in order to adjust the gap by manipulating the ball screw. Moreover, a pre-load is applied to the shoe at its left end face along its longitudinal direction using a coil spring in order to prevent the shoe from breaking due to resonance.

Fabrication of Microscale Tungsten Carbide Workpiece by New Centerless Grinding Method 125

(1)

the common node on the shoe holder. In addition, the simpler the vibration mode is, the easier the excitation of the shoe. From this viewpoint, a combination of L1 and B2 modes is desired. However, when the shoe is treated as a plate of length l with a uniform crosssection of width b and thickness t for simplicity, the precondition that the frequency of the rth L-mode must be the same as that of nth B-mode yields the following relationship between

> <sup>2</sup> (2 1) 8 3 *n t <sup>l</sup> r*

Eq. (1) gives the relationship *l*=5.7t for the L1B2(r=1, n=2) combination, but the relationship *l*=18.4t for the L1B4(r=1, n=4) combination. This suggests that a thin type shoe, the vibration excitation of which can be more easily compared with others, can be constructed based on the L1B4 combination. Thus, the L1B4 combination was selected as the ultrasonic shoe.

**Figure 4.** Structure and operating principle of the ultrasonic elliptic vibration shoe

measurement to be described later.

Based on the discussion above, the structure proposed is shown in detail in Fig.5. A Tshaped extrusion is located at the center of the shoe via which the shoe can be xed on its holder by bolts. Four separate electrodes are distributed on the PZT based on the B4 mode. The dimensions of the shoe are then determined by FEM analysis followed by impedance

(b)Generation principle of elliptic motion

(a) Shoe structure and power application method

*l* and *t* [16]:

1.Workpiece 2.Ultrasonic shoe 3.Vertical motion guide 4.Pre-load spring 5.Ball screw for adjusting the vertical position of shoe 6.Ball screw for feeding the shoe 7.Gear head 8.Stepping motor 9.Table for holding fine feed mechanism 10.Shoe holder 11.Linear motion way 12.Bolt for fixing the shoe 13.Blade 14.Blade holder

**Figure 3.** Illustration of the new centerless grinding apparatus
