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A new centerless grinding technique using a surface grinder
Journal of Materials Processing Technology 162–163 (2005) 709–717
A new centerless grinding technique using a surface grinder Y. Wu a,∗ , T. Kondo b , M. Kato a a
Department of Machine Intelligence and Systems Engineering, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Honjo-shi, Akita 015-0055, Japan b Graduate School, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Honjo-shi, Akita 015-0055, Japan
Abstract This paper proposes a new centerless grinding technique using a surface grinder. By this technique centerless grinding operations can be performed at low cost by installing a compact centerless grinding unit on the worktable of a multipurpose surface grinder and without the employment of a costly centerless grinder. The unit consists mainly of an ultrasonic elliptic-vibration shoe, a blade, and their respective holders. The shoe is produced by bonding a piezoelectric ceramic device (PZT) on a metal elastic body (stainless steel, SUS304), and an elliptic motion occurs on its end-face when two phases of AC voltage are applied to the PZT. The function of the shoe is to hold the cylindrical workpiece in conjunction with the blade, and to control the workpiece rotational speed with the elliptic motion on its end-face during grinding. The detailed structure of the unit was designed by Finite Element Method (FEM) analysis, and an actually constructed unit was installed on the worktable of a CNC surface grinder to perform tangential centerless grinding operations after its fundamental performance such as elliptic motion generation and capacity to control workpiece rotational speed had been investigated. As a result, it was clarified that the workpiece rotational speed changes linearly with variation in the applied voltage. This indicates that the workpiece rotational motion can be precisely controlled by the elliptic motion of the shoe. In addition, the workpiece roundness was clearly improved from an initial value of 23 m to a final value of 2.6 m after grinding, indicating that the constructed unit performed well in actual grinding operations. © 2005 Elsevier B.V. All rights reserved. Keywords: Centerless grinding; Regulating wheel; Ultrasonic vibration; Shoe; Machine tools; Micro parts
1. Introduction In the manufacturing industry, for high accuracy and high productivity machining of cylindrical components such as bearing raceways, silicon-ingots, and pin-gauges, centerless grinding has been widely used as an effective process. The conventional centerless grinding, in which a special machine tool (i.e., a centerless grinder) is essential, is greatly suitable for small-variety and large-volume production from the viewpoint of production cost due to the fact that the loading/unloading of parts is extremely easy and fast. However, the centerless grinder is a purpose-limited machine and is relatively costly, putting it at a disadvantage for large-variety and small-volume production, the demand for which has increased rapidly in recent years. As a solution to this problem, a centerless grinding operation that could be performed even on a multipurpose machine, such as a surface grinder (rather ∗
Corresponding author. E-mail address: [email protected] (Y. Wu).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.168
than a centerless grinder), is desirable. Thus, so far, no attempt to develop such a technique has been made. In order to carry out a centerless grinding operation on a surface grinder, it is essential to establish a centerless grinding unit for the purpose of supporting the workpiece and controlling the workpiece rotational motion, and to install it on the surface grinder worktable. Considering the functions of the regulating wheel and the blade in conventional centerless grinding, it is simple to create a centerless grinding unit equipped with a regulating wheel and a blade. In this case, however, it is difficult to build a compact unit because such a unit requires the installation of many apparatuses such as a rotary drive mechanism and a truing attachment for the regulating wheel. In the current work, a compact size centerless grinding unit is designed and constructed on the basis of the ultrasonic elliptic-vibration-shoe centerless grinding method proposed by the present authors in previous works [1–3]. This unit consists mainly of an ultrasonic shoe and a blade and their respective holders, and, thus, tangential feed centerless grinding operations [4] can be performed when it
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is installed on a CNC surface grinder worktable. In this paper, we describe the design of the unit in detail and the experimental evaluation of the performance of the unit in terms of its ability to control the rotational motion of the workpiece and its validity in actual grinding operations.
2. Processing principle of centerless grinding using surface grinder The conventional tangential feed centerless grinding using centerless grinder and the proposed new method using surface grinder are outlined in Fig. 1(a) and (b), respectively. The former employs a regulating wheel to support the cylindrical workpiece in conjunction with a blade and to control the workpiece rotation. As the blade drops downward at a speed of Vf , the workpiece is fed between the grinding wheel and the regulating wheel and ground by the counterclockwise rotating grinding wheel. The diametrical grinding allowance is given by adjusting the gap between the regulating wheel and the grinding wheel. However, there is a risk in this method that both the regulating wheel roundness error and the rotary
errors of its axis significantly affect the final roundness of the workpiece. In addition, a centerless grinder is required, leading to cost concerns especially for large-variety and smallvolume production. On the other hand, the new method (see Fig. 1(b)) employs an ultrasonic elliptic-vibration-shoe to hold the workpiece in conjunction with a blade and to control the workpiece rotational speed by its elliptic motion. Because both the shoe and the blade are fixed on the worktable of a surface grinder via their respective holders, the grinding operation is performed as the worktable feeds right-toward at a feed rate of Vf . Once the workpiece has passed from the left-side to the right-side of the grinding wheel, the grinding allowance given by adjusting the gap between the grinding wheel and the worktable is completed. It is, therefore, evident that this method not only avoids the risk of roundness errors caused by the regulating wheel or the rotary errors of its axis but also provide an alternative centerless grinding technique especially suited to large-variety and small-volume production at low cost achieved largely by installing a compact centerless grinding unit, composed mainly of an ultrasonic shoe and a blade, on a multipurpose surface grinder.
3. Design and construction of the centerless grinding unit 3.1. Outline of experimental apparatus
Fig. 1. Comparison of two centerless grinding techniques.
In the present work, an experimental apparatus has been established by designing and constructing a centerless grinding unit and attaching it to the worktable of a CNC surface grinder. Fig. 2(a) and (b) shows the schematic illustration of the apparatus and a picture of an established one, respectively. The centerless grinding unit is fixed to the worktable via a magnetic chuck. The workpiece constrained between the unit and the grinding wheel is fed right-toward with the movement of the worktable. Once the workpiece interferes with the clockwise rotating grinding wheel, actual grinding action begins, and the grinding action is completed when the ground workpiece loses contact with the grinding wheel with the successive right-toward movement of the worktable. Fig. 3 shows the detailed construction of the centerless grinding unit, composed mainly of the ultrasonic shoe, along with the power application method. The shoe is fixed on its holder via a spacer (electric isolation), and the blade on its holder directly, by means of bolt. Then they are fastened on a metal base plate so that the unit can be mounted on the worktable by means of the magnetic chuck. The shoe is constructed by bonding a piezoelectric ceramic device (PZT) having two separated electrodes onto a metal elastic body (stainless steel, SUS304). When two alternating current (AC) signals (over 20 kHz) with a phase difference of ψ to each other generated by a wave function generator are applied to the PZT after being amplified by means of power amplifiers, bending and longitu-
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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. Thus, the workpiece rotational speed can be adjusted by changing the value of parameters such as the amplitude and frequency of the voltage applied to piezoelectric ceramic device (PZT) because the shoe bending vibration speed varies with the variation of the applied voltage [5]. In addition, a pre-load is then applied to the shoe at its down end-face in its longitudinal direction using a coil spring in order to prevent the PZT from breaking due to resonance. 3.2. Design of the ultrasonic shoe 3.2.1. Vibration modes of the shoe As described above, it is essential that two vibration modes, i.e., bending vibration and longitudinal vibration, be excited simultaneously at the same frequency so that an elliptic motion is created on the shoe end-face. In determining the details of the two vibration modes, for simplicity the shoe is regarded as a plate of length l with an uniform cross section of width b and thickness t, as shown in Fig. 4(a). For this plate, formulas expressing its bending and longitudinal vibration modes are given as [6]: UB (x) = U¯ B {(cosh λl − cos λl)(cosh λx + cos λx) −(sinh λl + sin λl)(sinh λx + sin λx)} x UL (x) = U¯ L cos rπ , l
(1)
(2)
where UB (x) and UL (x) are the bending and longitudinal vibration displacements, respectively, at position x, and U¯ B and U¯ L are the amplitudes of the two modes. The parameter λl within Eq. (1) can be obtained by solving the following equation with respect to λl: Fig. 2. Experimental rig.
1 − cosh λl cos λl = 0.
dinal ultrasonic vibrations with amplitudes of several m are excited simultaneously. The synthesis of vibration displacements in the two directions creates an elliptic motion on the end-face of the metal elastic body. Consequently, the rotation of workpiece is controlled by the frictional force between the
Fig. 3. Unit structure and power application method.
Fig. 4. Shoe vibration modes and nodes.
(3)
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Fig. 6. Structure and dimensions of shoe. Fig. 5. Node distribution.
Substituting the nth solution of Eq. (3) λn l into Eq. (1) in order to calculate UB (x) yields the nth bending vibration mode, while rth longitudinal vibration mode is given by Eq. (2). For example, the bending mode of n = 2 (B2 mode) and the longitudinal mode of r = 1 (L1 mode) are described in Fig. 4(b) and (c), respectively. As shown in Fig. 4(b) and (c), the positions in the xdirection, at which UB (x) and UL (x) are zero, are the vibration nodes for bending and longitudinal vibrations, respectively. It is thus found that the B2 mode has three vibration nodes while the L1 mode has only one. Because the ultrasonic vibration of the shoe should not be restricted when it is supported and fixed on its holder, the shoe should be held at a common node of the bending mode (B-mode) and the longitudinal mode (Lmode). Fig. 5 shows the distribution of the vibration nodes for both the bending and longitudinal vibrations calculated using Eqs. (1)–(3). It is evident that only one common node exists along the shoe length for only the even-ordered B-modes (i.e., B2, B4, B6, B8, . . .) and the odd-ordered L-modes (i.e., L1, L2, L3, L7, . . .) at a central position of x = 0.5l. Therefore, it is crucial to select the combination of an even-ordered Bmode and an odd-ordered L-mode and to hold the shoe at its central location. In addition, the simpler the vibration mode, the easier the excitation of the shoe. From this viewpoint, in this work the L1B2 combination is selected for the ultrasonic elliptic-vibration-shoe. Based on the discussion above, the detailed structure and the vibration excitation method are proposed as shown in Fig. 6. A T-shaped extrusion is located at the central position of the shoe via which the shoe can be fixed on its holder. The two separated electrodes, a and b, are distributed on the PZT based on the B2-mode. The detailed dimensions of the shoe are then determined by FEM analysis followed by impedance measurement to be described in Section 3.2.3. 3.2.2. Generation of the elliptic motion In order for the shoe to vibrate ultrasonically in the bending and longitudinal directions, two AC voltages, VA and VB , are applied to the PZT at electrodes a and b, respectively (see Fig. 6). If the frequencies of VA and VB are set at the same
value of f, and their amplitude at V, in addition to the phase difference between the two voltages at ψ, VA and VB can be expressed by following equations: VA (t) = V sin 2πft VB (t) = V sin(2πft + ψ) When f is set to be the same or close to the resonant frequencies for both the L1 and B2 modes, the shoe will vibrate in the two modes simultaneously due to the transversal effect of PZT. Let the longitudinal displacement x and bending displacement y at point p on the shoe end-face (see Fig. 6) be in proportion to VA and VB , then the displacement xA in the longitudinal direction and that yA in the bending direction caused by VA , and xB and yB by VB can be obtained from Fig. 6, as shown below: xA = kxA VA (t) = kxA V sin 2πft yA = kyA VA (t) = kyA V sin 2πft xB = kxB VB (t) = kxB V sin(2πft + ψ) yB = −kyB VB (t) = −kyB V sin(2πft + ψ) where kxA , kxB , kyA , and kyB are proportional constants. Synthesizing the displacements due to VA and VB yields the resulting longitudinal and bending displacements x and y as expressed in the following equations. x = xA + xB = V [kxA sin 2πft + kxB sin(2πft + ψ)] y = yA + yB = V [kyA sin 2πft − kyB sin(2πft + ψ)]
(4)
Eq. (4) indicates that the displacements in the two directions, x and y, at point p change with time t, and thus the point p traces an ellipse having length of AL and breadth of AB with time t in X–Y plane, as shown in Fig. 7(a), where all the proportional constants kxA , kxB , kyA , and kyB were kept at 0.01 m/V and the voltage amplitude V at 100 V for simplicity. It is also known from Eq. (4) that the size of the ellipse is in proportion to the voltage V and that the ellipse will become larger with increasing value of V. Fig. 7(b) and (c) show the variation of the ellipses calculated using Eq. (4)
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Fig. 8. L1 and B2 modes obtained by FEM analysis.
L1 mode and the B2 mode of a shoe of t2 = 11.8 mm obtained by FEM analysis, indicating fL1 = fB4 to be 46.35 kHz. In order to confirm the generation of the elliptic motion on the shoe having the FEM-predicted dimension of t2 = 11.8 mm, frequency response analysis (FRA) was carried out using piezoelectric device analysis software (PIEZOplus 4.0 by Dynus Co. Ltd.). Fig. 9 shows one of the FRA results under the conditions of Vp-p = 50 V, f = 46.37 kHz, and ψ = 90◦ .
Fig. 7. Generation of elliptic motion.
under different phase differences and the different proportional constants, respectively. It can be seen in Fig. 7(b) that at ψ = 0 the bending vibration amplitude, i.e., the breadth AB of the ellipse, is zero, and therefore no elliptic motion occurs. As ψ increases, AB increases while the longitudinal vibration amplitude, i.e., the length AL of the ellipse, decreases, leading to the occurrence of a counterclockwise elliptic motion. This indicates that the shape of the ellipse is dependent on the phase difference. On other hand, the influence of the proportional constants kxA , kxB , kyA , and kyB on the ellipse is shown in Fig. 7(c), indicating that variation of the combination of kxA , kxB , kyA , and kyB results in the rotation of the ellipse around its center. 3.2.3. Dimensions of the shoe Except for the thickness t2 of the metal elastic body, all the other dimensions were determined as listed in Table 1 taking into consideration the installation space for the proposed unit on the existing surface grinder. Dimension t2 was initially predicted by Finite Element Method (FEM) analysis under the condition of fL1 (frequency of L1 mode) = fB2 (frequency of B2 mode). Fig. 8(a) and (b), respectively, show the Table 1 Shoe dimensions (mm) b t1 t3 t4 l1 l2 l3 l4
20 4 5 5 50 5 18 50
Fig. 9. Elliptic motion predicted by FRA.
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Fig. 10. Photograph of the produced shoe.
Clearly, an elliptic motion occurs on the upper end-face of the shoe. As predicted by FEM and FRA above, the dimension t2 of the shoe should have a value of t2 = 11.8 mm such that the frequency fL1 of the L1 mode is the same as that of fB2 of the B2 mode in order to generate elliptic motion on the shoe end-face. However, it is foreseen that the actual values of fL1 and fB2 would not agree with the predicted ones due to dimensional errors of the metal elastic body and the PZT used. Therefore, three shoes with different values of t2 , 11.7 mm, 11.8 mm, and 11.9 mm, were constructed based on the results of the FEM and FRA, and one of them was selected after their actual frequencies fL1 and fB2 had been obtained by measuring their impedance characteristics. Fig. 10 shows a photograph of the designed and constructed ultrasonic elliptic-vibration-shoe. For the produced shoe, a waterproof layer was applied to its surface in order to protect the grinding fluid during grinding. Further, the friction coefficient between the shoe and the workpiece should be large enough to prevent the workpiece from slipping on the shoe end-face. For this purpose, a thin rubber sheet (0.5 mm in thickness) of the same material as that of a conventional regulating wheel (A120R) was made and attached to the end-face of the shoe. An impedance analyzer (4294A by Agilent Co. Ltd.) was used for investigating the impedance characteristics of the shoe. The results obtained for the shoe of t2 = 11.8 mm are shown in Fig. 11(a) and (b) for L1 mode and B2 mode, respectively. It is obvious that the impedance for the L1 and the B2 modes reach their minimums at he frequencies of 46.34 kHz and 46.42 kHz, respectively, indicating that the respective resonant frequencies for the L1 and the B2 modes are fL1 = 46.34 kHz and fB2 = 46.42 kHz. In the meantime, the impedances for the two modes reached their maximums at 46.56 and 46.58 kHz, respectively, meaning that power consumption would be lowest when the voltages with these frequencies are applied. This is called the anti-resonance phenomenon [7,8]. The relationship between the measured fL1 , fB2 , and the t2 are plotted in Fig. 12. It can be seen that fL1 becomes equal to fB2 at t2 = 11.79 mm. Consequently, the value of t2 was determined at 11.76 mm.
Fig. 11. Frequency characteristics of shoe.
3.3. Performance of the ultrasonic elliptic-vibration shoe 3.3.1. Elliptic motion The elliptic motions of the shoe end-face under various applied voltages (amplitudes, frequencies, and phase differences) were investigated using a measuring system composed of two laser Doppler vibrometers (LV-1610 by Ono Sokki Co. Ltd.) equipped with the respective sensor heads and a vector conversion unit (Ono Sokki Co. Ltd.), as shown in Fig. 13. The conditions for shoe fixing, electric isolation, and pre-load application were the same as those described in Section 3.1 (see Fig. 3). Two AC signals generated by a wave function generator (WF1944 by NF Corporation) are applied to the PZT after being amplified by two power amplifiers (4010 by NF Corporation). During measurement, the two laser beams from the respective sensor heads are focused at the same point on the shoe end-face. The signals from the laser Doppler vibrometers are then inputted into the vector conversion unit for synthesis and recorded with a digital oscilloscope (LT364L by Iwatsu Co. Ltd.).
Fig. 12. Measured frequencies of two modes.
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Fig. 13. Method of measuring the ultrasonic elliptic motion.
Fig. 14 shows the results measured for various amplitudes, Vp-p , of the applied voltage while the frequency, the phase difference, and the pre-load were kept constant at f = 46.68 kHz, ψ = 90◦ , and P = 15 N, respectively, demonstrating that the elliptic motion actually occurred and the ellipse increases with the Vp–p . The two radii, AB and AL , of the ellipse represent the amplitude of the bending vibration and that of the longitudinal vibration, respectively. Fig. 15(a) and (b) show the influences of f and Vp–p on AB and AL , respectively. It is obvious from Fig. 15(a) that both AB and AL initially increase with the increase of frequency and then decrease after reaching their peak values at the same point of f = 46.2 kHz. The two peaks correspond to the resonant points for the B2 mode and the L1 mode, respectively. In particular, it is noted from Fig. 15(b) that both AB and AL are proportional to Vp–p . The linear relationship between AB and Vp–p indicates that the workpiece rotational speed, which is dependent on the bending vibration speed of the shoe, can be controlled by changing the value of Vp–p rather than the frequency f of the applied voltage. Fig. 16 shows the effects of the phase difference ψ on the elliptic motion. It can be seen that the shapes of the ellipses for various ψ agree with the predicted ones (see Fig. 7).
Fig. 15. Influence offrequency and voltage on vibration amplitude.
ing. Therefore, a test involving the rotational control of a cylindrical workpiece using the produced ultrasonic shoe was conducted on an apparatus, shown in Fig. 17, specially built in-house. 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 shoe is bolted on its holder and then held on a small three-axis dynamometer (9876 by Kistker Co. Ltd.) installed on a linear motion guide. 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 the wheel correspond to the normal and tangential grinding
3.3.2. Workiece rotation control test In the new centerless grinding method, it is crucial to precisely control the workpiece rotational speed via the elliptic motion of the shoe in order to achieve high-precision grind-
Fig. 14. Measured elliptic traces of the shoe end-face.
Fig. 16. Influence of the phase difference on the elliptic traces.
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Fig. 19. Relationship between the workpiece rotational speed and the applied voltage.
Fig. 17. Performance evaluation apparatus for the shoe.
forces, respectively. In the test, the dynamometer was used to set up the forces, and the same wave function generator and power amplifiers as used in the elliptic motion measurement (see Fig. 13) were employed to apply the AC voltage to the PZT. The workpiece rotational speed was obtained by recording the motion of the rotating workpiece end-face linemarked with a laser beam by using a digital video camera. The video images were stored in a computer for analysis using animated image-processing software (Swallow2001DV by Dijimo Co., Ltd.). Pin-shaped cylinders (φ5 × L15 mm) prepared from a long steel (SK4) rod were used as the workpieces. In addition, Vp–p was set in the range of 30–150 V while the voltage frequency, the phase difference, and the
pre-load were fixed at f = 46.68 kHz, ψ = 90◦ , and P = 15 N, respectively. Fig. 18 shows some of the video images of the workpiece end-face taken every 0.033 s with the camera. The workpiece rotational speed nw can be thus calcultated as follows: nw =
N nwi i=1
N
where nwi = (βi+1 −βi )/(ti +1−ti ) i = 1,2, . . ., N. Fig. 19 shows an obtained relationship between nw and Vp–p . It is obvious that nw increases linearly with the increase of Vp–p . This is in close agreement with the prediction described above, and indicates that the workpiece rotational speed can be controlled precisely by the elliptic motion of the shoe.
4. Grinding test In order to validate the proposed new method and to confirm the performance of the constructed centerless grinding unit in actual grinding operations, the unit was installed on the worktable of a CNC surface grinder (SGT-315RPA by Nagase Integrex Co. Ltd.) (see Fig. 2), and a grinding test was carried out involving the same workpiece used in the rotational control tests. During grinding operations, the preload, the amplitude, frequency, and phase difference of the applied voltage and the blade angle were set up at P = 15N, Vp–p = 120 V, f = 46.68 kHz, ψ = 90◦ , respectively. A flat indentation with a radius depth of δ = 21 m was made by surface grinding to indicate the initial roundness (see Fig. 20(a)). The other grinding conditions are listed in Table 2.
Fig. 18. Video images of the rotating workpiece.
Fig. 20. Workpieces before and after grinding.
Y. Wu et al. / Journal of Materials Processing Technology 162–163 (2005) 709–717 Table 2 Experimental conditions Grinding wheel Workpiece Coolant
SDC400N180 × 15 × 75, 1A1 SK4 5 × L15 Solution Type
Grinding parameters Input Voltage Amplitude Frequency Phase difference Grinding wheel speed Stock removal Table feed rate
Vp–p = 120 V f = 46.68 kHz ψ = 90◦ Vg = 20 m/s 0.03 mm Vf = 3 mm/min
The grinding test was performed as follows. First, the horizontal position of the worktable, on which the unit was fastened with the magnetic chuck, was adjusted carefully so that the workpiece held on the unit is located on the grinding wheel at the down-left-side. Next, the diametrical grinding allowance was given by adjusting the distance between the grinding wheel and the worktable. Further, the worktable was fed right-toward to carry the workpiece toward the grinding wheel at a feed rate of Vf = 3 mm/min, and the workpiece was ground under the grinding conditions listed in Table 2. The grinding operation was completed once the workpiece passed through and reached the grinding wheel right-side. Fig. 20(b) shows a picture of the ground workpiece and its roundness measured with a roundness measurement instrument (Rondcom55A by Tokyo Seimitsu Co. Ltd.). The roundness was clearly improved from an initial value of 21 m to a final value of 2.6 m, indicating that the constructed unit performed well even in actual grinding operations. Thus, the validity of the proposed new centerless grinding technique was confirmed. However, in order to establish this new technique completely, it is essential to clarify the influence of process parameters such as the applied voltage (amplitude, frequency, and phase difference), the worktable feed rate, the grinding allowance, and the blade angle relative to the grinding accuracy (i.e., roundness). Those details will be described in another report.
5. Conclusions A new centerless grinding technique using a surface grinder has been proposed. A compact centerless grinding unit composed mainly of an ultrasonic shoe and a blade and their respective holders has been designed and constructed and then installed on the worktable of a CNC surface grinder to perform tangential centerless grinding operations. During grinding by this method, the cylindrical workpiece is held on the ultrasonic shoe and the blade, and its rotational motion is controlled by the elliptic motion of the shoe end-face. The
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performance of the unit, including the shoe elliptic motion of the shoe, the capability to control the workpiece rotational speed, and the validity of its use in actual grinding operations has been investigated. The results can be summarized as follows. (1) The ultrasonic shoe was created by bonding a piezoelectric ceramic device (PZT) onto a stainless steel body (SUS304). When two phases of AC voltage with a phase difference between them were applied to the PZT, the shoe vibrated in longitudinal and bending directions simultaneously, and the synthesis of the vibration displacements in the two directions induced an elliptic motion on the shoe end-face. The shape and size of the ellipse were dependent on the amplitude, the frequency, and the phase difference of the applied voltage. (2) The workpiece rotational speed was in proportion to the voltage amplitude. (3) The results of the grinding test showed that the workpiece roundness was improved from an initial value of 21 m to a final value of 2.6 m after grinding. The results described above confirmed the validity of the proposed new centerless grinding technique, and demonstrated that the constructed unit performed well even in actual tangential feed centerless grinding operations. In future works we will deal with the optimization of the grinding conditions in tangential feed centerless grinding in order to easily obtain high-precision parts by the new technique, in addition to making attempts to carry out in-feed and through-feed centerless grinding using the unit on a surface grinder. The details of those attempts will be reported in subsequent papers.
References [1] Y. Wu, Y. Fan, M. Kato, J. Wang, K. Syoji, T. Kuriyagawa, A new centerless grinding technique without employing a regulating wheel, Key Eng. Mater. 238–238 (2003) 355–360. [2] Y. Fan, Y. Wu, M. Kato, T. Tachibana, K. Syoji, T. Kuriyagawa, Design of an elliptic-vibration-shoe and its performance in ultrasonic elliptic-vibration-shoe centerless grinding, JSME Int. J., Ser. C 47 (1) (2004) 43–51. [3] Y. Wu, Y. Fan, M. Kato, T. Tachibana, K. Syoji, T. Kuriyagawa, Determination of an optimum geometrical arrangement of workpiece in the ultrasonic elliptic-vibration-shoe centerless grinding, Key Eng. Mater. 257–258 (2004) 495–500. [4] H. Tsuwa, Fundamental of Mechanical Machining, Youkendou Publication, Tokyo, 1983 (In Japanese). [5] S. Ueha, Y. Tomikawa, New Ultrasonic Motor, Torikkepus Publication, Tokyo, 1991 (In Japanese). [6] M. Kunieda, Practical Vibration Theory, Rikougaku-sha Publication, Tokyo, 1988 (In Japanese). [7] N. Kenjo, S. Yubita, Primer of Ultrasonic Motor, Sougoudenshi Publication, Tokyo, 1991. [8] Piezoelectric Ceramics Technical Handbook, Fuji Ceramics, Tokyo, 1998 (In Japanese).
A new centerless grinding technique using a surface grinder Y. Wu a,∗ , T. Kondo b , M. Kato a a
Department of Machine Intelligence and Systems Engineering, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Honjo-shi, Akita 015-0055, Japan b Graduate School, Akita Prefectural University, 84-4 Tsuchiya-ebinokuchi, Honjo-shi, Akita 015-0055, Japan
Abstract This paper proposes a new centerless grinding technique using a surface grinder. By this technique centerless grinding operations can be performed at low cost by installing a compact centerless grinding unit on the worktable of a multipurpose surface grinder and without the employment of a costly centerless grinder. The unit consists mainly of an ultrasonic elliptic-vibration shoe, a blade, and their respective holders. The shoe is produced by bonding a piezoelectric ceramic device (PZT) on a metal elastic body (stainless steel, SUS304), and an elliptic motion occurs on its end-face when two phases of AC voltage are applied to the PZT. The function of the shoe is to hold the cylindrical workpiece in conjunction with the blade, and to control the workpiece rotational speed with the elliptic motion on its end-face during grinding. The detailed structure of the unit was designed by Finite Element Method (FEM) analysis, and an actually constructed unit was installed on the worktable of a CNC surface grinder to perform tangential centerless grinding operations after its fundamental performance such as elliptic motion generation and capacity to control workpiece rotational speed had been investigated. As a result, it was clarified that the workpiece rotational speed changes linearly with variation in the applied voltage. This indicates that the workpiece rotational motion can be precisely controlled by the elliptic motion of the shoe. In addition, the workpiece roundness was clearly improved from an initial value of 23 m to a final value of 2.6 m after grinding, indicating that the constructed unit performed well in actual grinding operations. © 2005 Elsevier B.V. All rights reserved. Keywords: Centerless grinding; Regulating wheel; Ultrasonic vibration; Shoe; Machine tools; Micro parts
1. Introduction In the manufacturing industry, for high accuracy and high productivity machining of cylindrical components such as bearing raceways, silicon-ingots, and pin-gauges, centerless grinding has been widely used as an effective process. The conventional centerless grinding, in which a special machine tool (i.e., a centerless grinder) is essential, is greatly suitable for small-variety and large-volume production from the viewpoint of production cost due to the fact that the loading/unloading of parts is extremely easy and fast. However, the centerless grinder is a purpose-limited machine and is relatively costly, putting it at a disadvantage for large-variety and small-volume production, the demand for which has increased rapidly in recent years. As a solution to this problem, a centerless grinding operation that could be performed even on a multipurpose machine, such as a surface grinder (rather ∗
Corresponding author. E-mail address: [email protected] (Y. Wu).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.168
than a centerless grinder), is desirable. Thus, so far, no attempt to develop such a technique has been made. In order to carry out a centerless grinding operation on a surface grinder, it is essential to establish a centerless grinding unit for the purpose of supporting the workpiece and controlling the workpiece rotational motion, and to install it on the surface grinder worktable. Considering the functions of the regulating wheel and the blade in conventional centerless grinding, it is simple to create a centerless grinding unit equipped with a regulating wheel and a blade. In this case, however, it is difficult to build a compact unit because such a unit requires the installation of many apparatuses such as a rotary drive mechanism and a truing attachment for the regulating wheel. In the current work, a compact size centerless grinding unit is designed and constructed on the basis of the ultrasonic elliptic-vibration-shoe centerless grinding method proposed by the present authors in previous works [1–3]. This unit consists mainly of an ultrasonic shoe and a blade and their respective holders, and, thus, tangential feed centerless grinding operations [4] can be performed when it
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is installed on a CNC surface grinder worktable. In this paper, we describe the design of the unit in detail and the experimental evaluation of the performance of the unit in terms of its ability to control the rotational motion of the workpiece and its validity in actual grinding operations.
2. Processing principle of centerless grinding using surface grinder The conventional tangential feed centerless grinding using centerless grinder and the proposed new method using surface grinder are outlined in Fig. 1(a) and (b), respectively. The former employs a regulating wheel to support the cylindrical workpiece in conjunction with a blade and to control the workpiece rotation. As the blade drops downward at a speed of Vf , the workpiece is fed between the grinding wheel and the regulating wheel and ground by the counterclockwise rotating grinding wheel. The diametrical grinding allowance is given by adjusting the gap between the regulating wheel and the grinding wheel. However, there is a risk in this method that both the regulating wheel roundness error and the rotary
errors of its axis significantly affect the final roundness of the workpiece. In addition, a centerless grinder is required, leading to cost concerns especially for large-variety and smallvolume production. On the other hand, the new method (see Fig. 1(b)) employs an ultrasonic elliptic-vibration-shoe to hold the workpiece in conjunction with a blade and to control the workpiece rotational speed by its elliptic motion. Because both the shoe and the blade are fixed on the worktable of a surface grinder via their respective holders, the grinding operation is performed as the worktable feeds right-toward at a feed rate of Vf . Once the workpiece has passed from the left-side to the right-side of the grinding wheel, the grinding allowance given by adjusting the gap between the grinding wheel and the worktable is completed. It is, therefore, evident that this method not only avoids the risk of roundness errors caused by the regulating wheel or the rotary errors of its axis but also provide an alternative centerless grinding technique especially suited to large-variety and small-volume production at low cost achieved largely by installing a compact centerless grinding unit, composed mainly of an ultrasonic shoe and a blade, on a multipurpose surface grinder.
3. Design and construction of the centerless grinding unit 3.1. Outline of experimental apparatus
Fig. 1. Comparison of two centerless grinding techniques.
In the present work, an experimental apparatus has been established by designing and constructing a centerless grinding unit and attaching it to the worktable of a CNC surface grinder. Fig. 2(a) and (b) shows the schematic illustration of the apparatus and a picture of an established one, respectively. The centerless grinding unit is fixed to the worktable via a magnetic chuck. The workpiece constrained between the unit and the grinding wheel is fed right-toward with the movement of the worktable. Once the workpiece interferes with the clockwise rotating grinding wheel, actual grinding action begins, and the grinding action is completed when the ground workpiece loses contact with the grinding wheel with the successive right-toward movement of the worktable. Fig. 3 shows the detailed construction of the centerless grinding unit, composed mainly of the ultrasonic shoe, along with the power application method. The shoe is fixed on its holder via a spacer (electric isolation), and the blade on its holder directly, by means of bolt. Then they are fastened on a metal base plate so that the unit can be mounted on the worktable by means of the magnetic chuck. The shoe is constructed by bonding a piezoelectric ceramic device (PZT) having two separated electrodes onto a metal elastic body (stainless steel, SUS304). When two alternating current (AC) signals (over 20 kHz) with a phase difference of ψ to each other generated by a wave function generator are applied to the PZT after being amplified by means of power amplifiers, bending and longitu-
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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. Thus, the workpiece rotational speed can be adjusted by changing the value of parameters such as the amplitude and frequency of the voltage applied to piezoelectric ceramic device (PZT) because the shoe bending vibration speed varies with the variation of the applied voltage [5]. In addition, a pre-load is then applied to the shoe at its down end-face in its longitudinal direction using a coil spring in order to prevent the PZT from breaking due to resonance. 3.2. Design of the ultrasonic shoe 3.2.1. Vibration modes of the shoe As described above, it is essential that two vibration modes, i.e., bending vibration and longitudinal vibration, be excited simultaneously at the same frequency so that an elliptic motion is created on the shoe end-face. In determining the details of the two vibration modes, for simplicity the shoe is regarded as a plate of length l with an uniform cross section of width b and thickness t, as shown in Fig. 4(a). For this plate, formulas expressing its bending and longitudinal vibration modes are given as [6]: UB (x) = U¯ B {(cosh λl − cos λl)(cosh λx + cos λx) −(sinh λl + sin λl)(sinh λx + sin λx)} x UL (x) = U¯ L cos rπ , l
(1)
(2)
where UB (x) and UL (x) are the bending and longitudinal vibration displacements, respectively, at position x, and U¯ B and U¯ L are the amplitudes of the two modes. The parameter λl within Eq. (1) can be obtained by solving the following equation with respect to λl: Fig. 2. Experimental rig.
1 − cosh λl cos λl = 0.
dinal ultrasonic vibrations with amplitudes of several m are excited simultaneously. The synthesis of vibration displacements in the two directions creates an elliptic motion on the end-face of the metal elastic body. Consequently, the rotation of workpiece is controlled by the frictional force between the
Fig. 3. Unit structure and power application method.
Fig. 4. Shoe vibration modes and nodes.
(3)
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Fig. 6. Structure and dimensions of shoe. Fig. 5. Node distribution.
Substituting the nth solution of Eq. (3) λn l into Eq. (1) in order to calculate UB (x) yields the nth bending vibration mode, while rth longitudinal vibration mode is given by Eq. (2). For example, the bending mode of n = 2 (B2 mode) and the longitudinal mode of r = 1 (L1 mode) are described in Fig. 4(b) and (c), respectively. As shown in Fig. 4(b) and (c), the positions in the xdirection, at which UB (x) and UL (x) are zero, are the vibration nodes for bending and longitudinal vibrations, respectively. It is thus found that the B2 mode has three vibration nodes while the L1 mode has only one. Because the ultrasonic vibration of the shoe should not be restricted when it is supported and fixed on its holder, the shoe should be held at a common node of the bending mode (B-mode) and the longitudinal mode (Lmode). Fig. 5 shows the distribution of the vibration nodes for both the bending and longitudinal vibrations calculated using Eqs. (1)–(3). It is evident that only one common node exists along the shoe length for only the even-ordered B-modes (i.e., B2, B4, B6, B8, . . .) and the odd-ordered L-modes (i.e., L1, L2, L3, L7, . . .) at a central position of x = 0.5l. Therefore, it is crucial to select the combination of an even-ordered Bmode and an odd-ordered L-mode and to hold the shoe at its central location. In addition, the simpler the vibration mode, the easier the excitation of the shoe. From this viewpoint, in this work the L1B2 combination is selected for the ultrasonic elliptic-vibration-shoe. Based on the discussion above, the detailed structure and the vibration excitation method are proposed as shown in Fig. 6. A T-shaped extrusion is located at the central position of the shoe via which the shoe can be fixed on its holder. The two separated electrodes, a and b, are distributed on the PZT based on the B2-mode. The detailed dimensions of the shoe are then determined by FEM analysis followed by impedance measurement to be described in Section 3.2.3. 3.2.2. Generation of the elliptic motion In order for the shoe to vibrate ultrasonically in the bending and longitudinal directions, two AC voltages, VA and VB , are applied to the PZT at electrodes a and b, respectively (see Fig. 6). If the frequencies of VA and VB are set at the same
value of f, and their amplitude at V, in addition to the phase difference between the two voltages at ψ, VA and VB can be expressed by following equations: VA (t) = V sin 2πft VB (t) = V sin(2πft + ψ) When f is set to be the same or close to the resonant frequencies for both the L1 and B2 modes, the shoe will vibrate in the two modes simultaneously due to the transversal effect of PZT. Let the longitudinal displacement x and bending displacement y at point p on the shoe end-face (see Fig. 6) be in proportion to VA and VB , then the displacement xA in the longitudinal direction and that yA in the bending direction caused by VA , and xB and yB by VB can be obtained from Fig. 6, as shown below: xA = kxA VA (t) = kxA V sin 2πft yA = kyA VA (t) = kyA V sin 2πft xB = kxB VB (t) = kxB V sin(2πft + ψ) yB = −kyB VB (t) = −kyB V sin(2πft + ψ) where kxA , kxB , kyA , and kyB are proportional constants. Synthesizing the displacements due to VA and VB yields the resulting longitudinal and bending displacements x and y as expressed in the following equations. x = xA + xB = V [kxA sin 2πft + kxB sin(2πft + ψ)] y = yA + yB = V [kyA sin 2πft − kyB sin(2πft + ψ)]
(4)
Eq. (4) indicates that the displacements in the two directions, x and y, at point p change with time t, and thus the point p traces an ellipse having length of AL and breadth of AB with time t in X–Y plane, as shown in Fig. 7(a), where all the proportional constants kxA , kxB , kyA , and kyB were kept at 0.01 m/V and the voltage amplitude V at 100 V for simplicity. It is also known from Eq. (4) that the size of the ellipse is in proportion to the voltage V and that the ellipse will become larger with increasing value of V. Fig. 7(b) and (c) show the variation of the ellipses calculated using Eq. (4)
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Fig. 8. L1 and B2 modes obtained by FEM analysis.
L1 mode and the B2 mode of a shoe of t2 = 11.8 mm obtained by FEM analysis, indicating fL1 = fB4 to be 46.35 kHz. In order to confirm the generation of the elliptic motion on the shoe having the FEM-predicted dimension of t2 = 11.8 mm, frequency response analysis (FRA) was carried out using piezoelectric device analysis software (PIEZOplus 4.0 by Dynus Co. Ltd.). Fig. 9 shows one of the FRA results under the conditions of Vp-p = 50 V, f = 46.37 kHz, and ψ = 90◦ .
Fig. 7. Generation of elliptic motion.
under different phase differences and the different proportional constants, respectively. It can be seen in Fig. 7(b) that at ψ = 0 the bending vibration amplitude, i.e., the breadth AB of the ellipse, is zero, and therefore no elliptic motion occurs. As ψ increases, AB increases while the longitudinal vibration amplitude, i.e., the length AL of the ellipse, decreases, leading to the occurrence of a counterclockwise elliptic motion. This indicates that the shape of the ellipse is dependent on the phase difference. On other hand, the influence of the proportional constants kxA , kxB , kyA , and kyB on the ellipse is shown in Fig. 7(c), indicating that variation of the combination of kxA , kxB , kyA , and kyB results in the rotation of the ellipse around its center. 3.2.3. Dimensions of the shoe Except for the thickness t2 of the metal elastic body, all the other dimensions were determined as listed in Table 1 taking into consideration the installation space for the proposed unit on the existing surface grinder. Dimension t2 was initially predicted by Finite Element Method (FEM) analysis under the condition of fL1 (frequency of L1 mode) = fB2 (frequency of B2 mode). Fig. 8(a) and (b), respectively, show the Table 1 Shoe dimensions (mm) b t1 t3 t4 l1 l2 l3 l4
20 4 5 5 50 5 18 50
Fig. 9. Elliptic motion predicted by FRA.
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Fig. 10. Photograph of the produced shoe.
Clearly, an elliptic motion occurs on the upper end-face of the shoe. As predicted by FEM and FRA above, the dimension t2 of the shoe should have a value of t2 = 11.8 mm such that the frequency fL1 of the L1 mode is the same as that of fB2 of the B2 mode in order to generate elliptic motion on the shoe end-face. However, it is foreseen that the actual values of fL1 and fB2 would not agree with the predicted ones due to dimensional errors of the metal elastic body and the PZT used. Therefore, three shoes with different values of t2 , 11.7 mm, 11.8 mm, and 11.9 mm, were constructed based on the results of the FEM and FRA, and one of them was selected after their actual frequencies fL1 and fB2 had been obtained by measuring their impedance characteristics. Fig. 10 shows a photograph of the designed and constructed ultrasonic elliptic-vibration-shoe. For the produced shoe, a waterproof layer was applied to its surface in order to protect the grinding fluid during grinding. Further, the friction coefficient between the shoe and the workpiece should be large enough to prevent the workpiece from slipping on the shoe end-face. For this purpose, a thin rubber sheet (0.5 mm in thickness) of the same material as that of a conventional regulating wheel (A120R) was made and attached to the end-face of the shoe. An impedance analyzer (4294A by Agilent Co. Ltd.) was used for investigating the impedance characteristics of the shoe. The results obtained for the shoe of t2 = 11.8 mm are shown in Fig. 11(a) and (b) for L1 mode and B2 mode, respectively. It is obvious that the impedance for the L1 and the B2 modes reach their minimums at he frequencies of 46.34 kHz and 46.42 kHz, respectively, indicating that the respective resonant frequencies for the L1 and the B2 modes are fL1 = 46.34 kHz and fB2 = 46.42 kHz. In the meantime, the impedances for the two modes reached their maximums at 46.56 and 46.58 kHz, respectively, meaning that power consumption would be lowest when the voltages with these frequencies are applied. This is called the anti-resonance phenomenon [7,8]. The relationship between the measured fL1 , fB2 , and the t2 are plotted in Fig. 12. It can be seen that fL1 becomes equal to fB2 at t2 = 11.79 mm. Consequently, the value of t2 was determined at 11.76 mm.
Fig. 11. Frequency characteristics of shoe.
3.3. Performance of the ultrasonic elliptic-vibration shoe 3.3.1. Elliptic motion The elliptic motions of the shoe end-face under various applied voltages (amplitudes, frequencies, and phase differences) were investigated using a measuring system composed of two laser Doppler vibrometers (LV-1610 by Ono Sokki Co. Ltd.) equipped with the respective sensor heads and a vector conversion unit (Ono Sokki Co. Ltd.), as shown in Fig. 13. The conditions for shoe fixing, electric isolation, and pre-load application were the same as those described in Section 3.1 (see Fig. 3). Two AC signals generated by a wave function generator (WF1944 by NF Corporation) are applied to the PZT after being amplified by two power amplifiers (4010 by NF Corporation). During measurement, the two laser beams from the respective sensor heads are focused at the same point on the shoe end-face. The signals from the laser Doppler vibrometers are then inputted into the vector conversion unit for synthesis and recorded with a digital oscilloscope (LT364L by Iwatsu Co. Ltd.).
Fig. 12. Measured frequencies of two modes.
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Fig. 13. Method of measuring the ultrasonic elliptic motion.
Fig. 14 shows the results measured for various amplitudes, Vp-p , of the applied voltage while the frequency, the phase difference, and the pre-load were kept constant at f = 46.68 kHz, ψ = 90◦ , and P = 15 N, respectively, demonstrating that the elliptic motion actually occurred and the ellipse increases with the Vp–p . The two radii, AB and AL , of the ellipse represent the amplitude of the bending vibration and that of the longitudinal vibration, respectively. Fig. 15(a) and (b) show the influences of f and Vp–p on AB and AL , respectively. It is obvious from Fig. 15(a) that both AB and AL initially increase with the increase of frequency and then decrease after reaching their peak values at the same point of f = 46.2 kHz. The two peaks correspond to the resonant points for the B2 mode and the L1 mode, respectively. In particular, it is noted from Fig. 15(b) that both AB and AL are proportional to Vp–p . The linear relationship between AB and Vp–p indicates that the workpiece rotational speed, which is dependent on the bending vibration speed of the shoe, can be controlled by changing the value of Vp–p rather than the frequency f of the applied voltage. Fig. 16 shows the effects of the phase difference ψ on the elliptic motion. It can be seen that the shapes of the ellipses for various ψ agree with the predicted ones (see Fig. 7).
Fig. 15. Influence offrequency and voltage on vibration amplitude.
ing. Therefore, a test involving the rotational control of a cylindrical workpiece using the produced ultrasonic shoe was conducted on an apparatus, shown in Fig. 17, specially built in-house. 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 shoe is bolted on its holder and then held on a small three-axis dynamometer (9876 by Kistker Co. Ltd.) installed on a linear motion guide. 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 the wheel correspond to the normal and tangential grinding
3.3.2. Workiece rotation control test In the new centerless grinding method, it is crucial to precisely control the workpiece rotational speed via the elliptic motion of the shoe in order to achieve high-precision grind-
Fig. 14. Measured elliptic traces of the shoe end-face.
Fig. 16. Influence of the phase difference on the elliptic traces.
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Fig. 19. Relationship between the workpiece rotational speed and the applied voltage.
Fig. 17. Performance evaluation apparatus for the shoe.
forces, respectively. In the test, the dynamometer was used to set up the forces, and the same wave function generator and power amplifiers as used in the elliptic motion measurement (see Fig. 13) were employed to apply the AC voltage to the PZT. The workpiece rotational speed was obtained by recording the motion of the rotating workpiece end-face linemarked with a laser beam by using a digital video camera. The video images were stored in a computer for analysis using animated image-processing software (Swallow2001DV by Dijimo Co., Ltd.). Pin-shaped cylinders (φ5 × L15 mm) prepared from a long steel (SK4) rod were used as the workpieces. In addition, Vp–p was set in the range of 30–150 V while the voltage frequency, the phase difference, and the
pre-load were fixed at f = 46.68 kHz, ψ = 90◦ , and P = 15 N, respectively. Fig. 18 shows some of the video images of the workpiece end-face taken every 0.033 s with the camera. The workpiece rotational speed nw can be thus calcultated as follows: nw =
N nwi i=1
N
where nwi = (βi+1 −βi )/(ti +1−ti ) i = 1,2, . . ., N. Fig. 19 shows an obtained relationship between nw and Vp–p . It is obvious that nw increases linearly with the increase of Vp–p . This is in close agreement with the prediction described above, and indicates that the workpiece rotational speed can be controlled precisely by the elliptic motion of the shoe.
4. Grinding test In order to validate the proposed new method and to confirm the performance of the constructed centerless grinding unit in actual grinding operations, the unit was installed on the worktable of a CNC surface grinder (SGT-315RPA by Nagase Integrex Co. Ltd.) (see Fig. 2), and a grinding test was carried out involving the same workpiece used in the rotational control tests. During grinding operations, the preload, the amplitude, frequency, and phase difference of the applied voltage and the blade angle were set up at P = 15N, Vp–p = 120 V, f = 46.68 kHz, ψ = 90◦ , respectively. A flat indentation with a radius depth of δ = 21 m was made by surface grinding to indicate the initial roundness (see Fig. 20(a)). The other grinding conditions are listed in Table 2.
Fig. 18. Video images of the rotating workpiece.
Fig. 20. Workpieces before and after grinding.
Y. Wu et al. / Journal of Materials Processing Technology 162–163 (2005) 709–717 Table 2 Experimental conditions Grinding wheel Workpiece Coolant
SDC400N180 × 15 × 75, 1A1 SK4 5 × L15 Solution Type
Grinding parameters Input Voltage Amplitude Frequency Phase difference Grinding wheel speed Stock removal Table feed rate
Vp–p = 120 V f = 46.68 kHz ψ = 90◦ Vg = 20 m/s 0.03 mm Vf = 3 mm/min
The grinding test was performed as follows. First, the horizontal position of the worktable, on which the unit was fastened with the magnetic chuck, was adjusted carefully so that the workpiece held on the unit is located on the grinding wheel at the down-left-side. Next, the diametrical grinding allowance was given by adjusting the distance between the grinding wheel and the worktable. Further, the worktable was fed right-toward to carry the workpiece toward the grinding wheel at a feed rate of Vf = 3 mm/min, and the workpiece was ground under the grinding conditions listed in Table 2. The grinding operation was completed once the workpiece passed through and reached the grinding wheel right-side. Fig. 20(b) shows a picture of the ground workpiece and its roundness measured with a roundness measurement instrument (Rondcom55A by Tokyo Seimitsu Co. Ltd.). The roundness was clearly improved from an initial value of 21 m to a final value of 2.6 m, indicating that the constructed unit performed well even in actual grinding operations. Thus, the validity of the proposed new centerless grinding technique was confirmed. However, in order to establish this new technique completely, it is essential to clarify the influence of process parameters such as the applied voltage (amplitude, frequency, and phase difference), the worktable feed rate, the grinding allowance, and the blade angle relative to the grinding accuracy (i.e., roundness). Those details will be described in another report.
5. Conclusions A new centerless grinding technique using a surface grinder has been proposed. A compact centerless grinding unit composed mainly of an ultrasonic shoe and a blade and their respective holders has been designed and constructed and then installed on the worktable of a CNC surface grinder to perform tangential centerless grinding operations. During grinding by this method, the cylindrical workpiece is held on the ultrasonic shoe and the blade, and its rotational motion is controlled by the elliptic motion of the shoe end-face. The
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performance of the unit, including the shoe elliptic motion of the shoe, the capability to control the workpiece rotational speed, and the validity of its use in actual grinding operations has been investigated. The results can be summarized as follows. (1) The ultrasonic shoe was created by bonding a piezoelectric ceramic device (PZT) onto a stainless steel body (SUS304). When two phases of AC voltage with a phase difference between them were applied to the PZT, the shoe vibrated in longitudinal and bending directions simultaneously, and the synthesis of the vibration displacements in the two directions induced an elliptic motion on the shoe end-face. The shape and size of the ellipse were dependent on the amplitude, the frequency, and the phase difference of the applied voltage. (2) The workpiece rotational speed was in proportion to the voltage amplitude. (3) The results of the grinding test showed that the workpiece roundness was improved from an initial value of 21 m to a final value of 2.6 m after grinding. The results described above confirmed the validity of the proposed new centerless grinding technique, and demonstrated that the constructed unit performed well even in actual tangential feed centerless grinding operations. In future works we will deal with the optimization of the grinding conditions in tangential feed centerless grinding in order to easily obtain high-precision parts by the new technique, in addition to making attempts to carry out in-feed and through-feed centerless grinding using the unit on a surface grinder. The details of those attempts will be reported in subsequent papers.
References [1] Y. Wu, Y. Fan, M. Kato, J. Wang, K. Syoji, T. Kuriyagawa, A new centerless grinding technique without employing a regulating wheel, Key Eng. Mater. 238–238 (2003) 355–360. [2] Y. Fan, Y. Wu, M. Kato, T. Tachibana, K. Syoji, T. Kuriyagawa, Design of an elliptic-vibration-shoe and its performance in ultrasonic elliptic-vibration-shoe centerless grinding, JSME Int. J., Ser. C 47 (1) (2004) 43–51. [3] Y. Wu, Y. Fan, M. Kato, T. Tachibana, K. Syoji, T. Kuriyagawa, Determination of an optimum geometrical arrangement of workpiece in the ultrasonic elliptic-vibration-shoe centerless grinding, Key Eng. Mater. 257–258 (2004) 495–500. [4] H. Tsuwa, Fundamental of Mechanical Machining, Youkendou Publication, Tokyo, 1983 (In Japanese). [5] S. Ueha, Y. Tomikawa, New Ultrasonic Motor, Torikkepus Publication, Tokyo, 1991 (In Japanese). [6] M. Kunieda, Practical Vibration Theory, Rikougaku-sha Publication, Tokyo, 1988 (In Japanese). [7] N. Kenjo, S. Yubita, Primer of Ultrasonic Motor, Sougoudenshi Publication, Tokyo, 1991. [8] Piezoelectric Ceramics Technical Handbook, Fuji Ceramics, Tokyo, 1998 (In Japanese).