Suppression of chatter vibration of boring tools using impact dampers

Transcription

1 International Journal of Machine Tools & Manufacture 40 (2000) Suppression of chatter vibration of boring tools using impact dampers Satoshi Ema a,*, Etsuo Marui b a Faculty of Education, Gifu University, 1-1 Yanagido, Gifu-shi , Japan b Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu-shi , Japan Received 7 July 1999; accepted 16 November 1999 Abstract In this study, improvement of the damping capability of boring tools and suppression of chatter vibration were attempted using impact dampers. Bending tests, impact tests and cutting tests were carried out, whilst widely varying the method of applying an impact damper to a boring tool. The effects of the amount of free mass and clearance, the overhang length of boring tools and their cutting condition were investigated. As a result, the following points were clarified. (i) (ii) (iii) (iv) The damping capability of boring tools is considerably improved using impact dampers. All three types of impact dampers used in the experiment can considerably suppress the vibration of boring tools in the vertical direction (principal force direction), but hardly suppress it in the horizontal direction (thrust force direction) where the amplitude is extremely small. In practical use, the method of equipping an impact damper on the flank face of a boring tool is desirable. Using an impact damper, it is possible to bore deeper holes in comparison with boring tools now on the market and to improve the efficiency of boring operations Elsevier Science Ltd. All rights reserved. Keywords: Boring tool; Impact damper; Damping capacity; Improvement; Chatter vibration * Corresponding author. address: sema@tech.ed.gifu-u.ac.jp (S. Ema) /00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S (99)

2 1142 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Nomenclature A x A y C L f n f x f y K L M m N g g 0 amplitude of boring tool in horizontal direction amplitude of boring tool in vertical direction clearance (range of free mass motion) natural frequency of boring tool without impact damper frequency of chatter vibration in horizontal direction frequency of chatter vibration in vertical direction equivalent spring constant of boring tool overhang length of boring tool main mass (equivalent mass of boring tool) free mass (equivalent mass of impact damper) spindle rotation of lathe corresponding logarithmic decrement of boring tool with free mass logarithmic decrement of boring tool without free mass 1. Introduction For the suppression of chatter vibration and improvement of cutting stability, studies on a Lanchester damper and a viscoelastic damper for boring bars or turning tools have been carried out for many years with beneficial results [1 7]. On the other hand, drills or boring tools with great ratios of overhang lengths to diameters often lead to chatter vibration due to their extremely low damping capability [8]. However, it is next to impossible from a construction standpoint to equip long, thin cutting tools such as drills or boring tools with an absorber. In order to improve the damping capability of such cutting tools, the authors [9,10] developed an impact damper consisting of a free mass and a clearance as shown in Fig. 1. The impact damper has the following features: (i) small and simple in construction; (ii) easy to mount on the main vibratory systems; and (iii) no need to adjust parameters of an impact damper to the vibratory characteristics of the main vibratory systems. Furthermore, it was clarified that by applying this impact damper to a drill, chatter vibration could be suppressed effectively [11]. Thus, in the present study, the improvement of the damping capability of boring tools and suppression of chatter vibration using the impact damper were tested. In addition, the impact damper used in this study allows a free mass to be equipped on the outside of the main vibratory system. In the vibratory system presented in Fig. 1, the free mass exists inside the main mass. 2. Experimental method 2.1. Impact dampers and boring tools Various methods of equipping a boring tool with an impact damper were examined. As a result, the following two ways were adopted in this study. One is to equip a ring-shaped free mass on

3 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 1. Impact damper. the flank face or the top face of a boring tool using a bolt and a supplementary sleeve shown in the lower part of Fig. 2. The other is to equip the ring-shaped free mass along the center axis of a boring tool shank. The impact damper on the flank face of a boring tool is marked D A, the impact damper on the top face D B, and the impact damper along the center axis D C. The three boring tools shown in the figure (marked BT A,BT B and BT C ) are equipped with impact dampers D A,D B, and D C, respectively. Every boring tool can accommodate an impact damper at a position 40 mm from the cutting edge. The amount of free mass of the impact dampers D A and D B was controlled by varying the diameter of the free mass D1 indicated in the figure. The size of the clearance was controlled by varying the diameter of the supplementary sleeve d1. This clearance C L =9 d1 is a range of free mass motion. In this manner, the free mass of the impact dampers D A and D B can move in the radial direction of the machined hole. Namely, the impact damper D A is supposed to improve the damping capability of boring tools in the vertical direction (principal force direction), and the impact damper D B is supposed to improve the damping capability of boring tools in the horizontal direction (thrust force direction). In addition, as the length of the supplementary sleeve is 0.4 mm longer than the length of the free mass (21 mm), the free mass can move not only in the radial direction of the machined hole but also in the axis direction. The amount of free mass of the impact damper D C was controlled by varying the diameter of the free mass D2 indicated in the figure. The size of the clearance (C L =d2 10) was controlled by varying the diameter of the hole machined in the free mass d2. The free mass of the impact damper D C can move in both vertical and horizontal directions. The boring tools used in this experiment are specially manufactured and have a section of mm and an overall length of 325 mm as shown in Fig. 2. On the other hand, in many boring tools on the market, when dimensions of a section are about mm, the overall length could be about 180 mm (overhang length mm). However, in order to investigate the

4 1144 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 2. Impact dampers and boring tools. relationships between the overhang length of boring tools and vibration suppression effects of the impact dampers, boring tools with a fairly long overall length were used in this experiment and compared with boring tools on the market. All dimensions of these boring tools are identical. However, the boring tools BT A and BT B differ in terms of the direction of the screw hole drilled to install the impact damper. The boring tool BT C is so constructed that the end and the shank can be separated to accommodate the impact damper D C along the shank axis as shown in Fig. 2. The end of the boring tool is fixed to the shank using three bolts Experimental method Fig. 3 shows the experimental apparatus, and Table 1 shows the experimental conditions. A boring tool was mounted on the tool post of the lathe. The overhang length of the boring tool varied from 120, 160, 200 to 240 mm as indicated in the figure. Displacements of the cutting edge of the boring tool were measured using four strain gauges attached to the shank near the tool post. Bending tests were carried out on a boring tool without an impact damper and an equivalent spring constant K was obtained. Furthermore, impact tests were carried out, and the natural frequency of the boring tool f n was obtained from free damped vibration waves. Since the amplitude of the boring tool at this time decreased almost according to an exponential function, a logarithmic decrement g 0 was obtained. The impact tests were performed under such conditions that an initial displacement of the cutting edge fell within a certain range.

5 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 3. Experimental setup. Table 1 Experimental conditions Designation Damping test Boring tool BT A BT B BT C Overhang length L (mm) Impact damper D A D B D C Vibrational direction Vertical Horizontal Free mass m (kg) Clearance C L (mm) Cutting test Boring tool BT A BT B BT C Overhang length L (mm) Impact damper D A D B D C Free mass m (kg) Clearance C L (mm) 0.8 Spindle rotation N (rpm) Feed rate S (mm/rev) Depth of cut t (mm) 0.2 Impact tests were carried out on a boring tool with an impact damper. However, the amplitude reduction of the boring tool with an impact damper significantly differed from that of the boring tool without one. Therefore, an amount corresponding to the logarithmic decrement (called corresponding logarithmic decrement g) was obtained in the same manner as in previous reports [9,10]. Furthermore, in order to investigate the effects of the free mass m and the clearance C L on the damping capability of impact dampers, m and C L were varied widely as listed in Table 1. In the bending and impact tests described above, six experiments were repeated under the same conditions. Furthermore, cutting tests were carried out using a pipe-shaped work mounted on a three-jaw

6 1146 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) chuck of the lathe spindle as shown in Fig. 3. The work had a diameter of 140 mm, a width of 60 mm and a thickness of 5 mm. Preliminary cuttings were repeated by a commercial boring tool until the value of the surface roughness in the feed direction reached about 10 µmr max. The commercial boring tool had a section of mm and an overall length of 180 mm. The overhang length was 80 mm. In the cutting tests, the free mass m=0.025 and kg and the clearance C L =0.8 mm were chosen by considering the results of the impact tests. In order to investigate the relationship between vibration suppression effects of impact dampers and cutting conditions, the spindle rotation of the lathe N was varied as listed in Table 1. In the cutting tests, eight experiments were repeated under the same conditions. The displacements of the cutting edge in the horizontal and vertical directions were measured at a 1000 points in a cutting experiment. The free mass used in the experiment was made of brass (70% Cu and 30% Zn), the works were made of carbon steel for general structural use (s B =400 MPa) and the cutting tools were made of tungsten carbide (92% WC, 6% Co, HV=1650). 3. Experimental results 3.1. Results of bending and impact tests The vibratory characteristics of boring tools without an impact damper are described below. Table 2 shows the logarithmic decrement g 0, the equivalent spring constant K and the natural frequency f n of the boring tools. The equivalent mass of the boring tools M calculated from f n and K is also shown in the table. In addition, although experimental results are not shown, vibratory characteristics of boring tool BT A in the horizontal direction are similar to those of boring tool Table 2 Vibratory characteristics of boring tools Boring tool Direction L (mm) M (kg) g 0 K (kn/m) f n (Hz) BT A Vertical BT B Horizontal BT C Vertical Horizontal

7 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) BT B in the horizontal direction, and vibratory characteristics of boring tool BT B in the vertical direction are similar to those of boring tool BT A in the vertical direction. It is clear from Table 2 that as the overhang length L for all boring tools increases, the logarithmic decrement g 0, the equivalent spring constant K and the natural frequency f n decrease, while the equivalent mass M increases. The equivalent spring constant K of boring tool BT C is smaller than those of boring tools BT A and BT B. This can be explained by the fact that the end of this boring tool can be separated from the shank as described in the previous section (Fig. 2). In boring tool BT C, the logarithmic decrement g 0, the equivalent spring constant K and the natural frequency f n in the horizontal direction are slightly smaller than those in the vertical direction. In boring tools BT A and BT B, although they are not the same tool, the logarithmic decrement g 0, the equivalent spring constant K and the natural frequency f n in the horizontal direction are slightly smaller than those in the vertical direction. These can be explained as follows. The tool shank in the vertical vibration is directly restrained by the tool post and the clamping bolts. The tool shank in the horizontal vibration is indirectly restrained by the frictional force induced due to the above. Accordingly, a corresponding overhang length in the horizontal vibration becomes longer than that in the vertical vibration. A corresponding equivalent mass in the horizontal vibration becomes greater than that in the vertical vibration. The vibratory characteristics of boring tools with an impact damper, particularly the effects of improved damping capability due to such a damper, are described in the following. Fig. 4 shows the corresponding logarithmic decrement g obtained when boring tool BT A, overhang length L=200 mm, impact damper D A and vertical vibration were used. Although the values of corresponding logarithmic decrement g vary due to the free mass m and the clearance C L, their obvious effects are not shown. The values of the corresponding logarithmic decrement g are much greater than the logarithmic decrement g 0 =0.131 indicated by a solid line. Thus, the following discussions are predicated on using the amounts of the corresponding logarithmic decrement g divided by the logarithmic decrement of each boring tool g 0 as shown in Table 2. Table 3 shows corresponding logarithmic decrement ratios g/g 0. The marks in the table Fig. 4. Corresponding logarithmic decrement (boring tool BT A, L=200 mm, vertical vibration).

8 1148 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Table 3 Corresponding logarithmic decrement ratio Boring Impact Direction L (mm) Corresponding logarithmic decrement ration g/g 0 tool damper m=0.025 kg kg kg C L = mm mm mm BT A D A Vertical BT B D B Horizontal BT C D C Vertical Horizontal show that no test was carried out under these conditions. It is clear that the damping capability of boring tools is markedly improved using impact dampers. Although the type of impact dampers, the vibrational direction of the boring tools or the overhang length varies, the similar effects of damping capability improvement are evident. Furthermore, although the free mass m and the clearance C L vary, significant differences in improved damping capability are not recognized. Accordingly, the free mass of m=0.025 and kg and the clearance of C L =0.8 mm were used in the cutting tests Results of cutting tests When boring tools with an overhang length of L=240 mm were used, boring operations (chip removal operations) were very difficult. This can be explained by the fact that the equivalent spring constants of boring tools with this overhang length, i.e. the bending stiffnesses, are extremely small as evidenced in Table 2. Fig. 5 shows the frequencies of chatter vibration f x and f y which are obtained from vibration waves in the horizontal and vertical directions, respectively. The boring tool used was BT C, and the overhang length used was L=120 mm. It is obvious from the cutting method used in this experiment that this chatter vibration is a regenerative one occurring in the boring tools. The frequency f x in the horizontal direction and the frequency f y in the vertical direction are almost equal and maintain an almost constant value, though the spindle rotation N is varied. Furthermore, the frequencies f x and f y are almost equal to the natural frequency of boring tool BT C in the

9 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 5. Frequency of chatter vibration (boring tool BT C, L=120 mm). vertical direction f ny =775 Hz. Similar tendencies to those shown in Fig. 5 are observed for other boring tools and overhang lengths. The amplitude of chatter vibration is described as follows. When an impact damper was not used, steady chatter vibrations occurred which maintained almost constant amplitudes. However, when an impact damper was used, such chatter vibrations were often observed in which the amplitude changed periodically like a humming phenomenon or fluctuated irregularly. Therefore, in order to estimate precisely the intensity of chatter vibration due to the existence of an impact damper, a mean displacement amplitude (simply called amplitude) was obtained using the following equations. A x is an amplitude in the horizontal direction and A y is an amplitude in the vertical direction. A x A y n i 1 n i 1 x i x 0 n y i y 0 n x 0 y 0 n i 1 n x i n y i i 1 n Here, x i and x 0 are a displacement of the cutting edge and a fluctuation center of the cutting edge (1) (2)

10 1150 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) in the horizontal direction, respectively. y i and y 0 are a displacement of the cutting edge and a fluctuation center of the cutting edge in the vertical direction, respectively. n(1000) is the number of sampling times in a cutting test. Fig. 6 shows amplitude A x in the horizontal direction obtained when boring tools with an overhang length of L=160 mm were used. The upper, middle and lower parts in the figure show the results when boring tools BT A,BT B and BT C were used, respectively. Figs. 7 9 show amplitude A y in the vertical direction and the results obtained when boring tools BT A,BT B and BT C were used, respectively. The upper, middle and lower parts in each figure show the results obtained when the overhang length was L=120, 160 and 200 mm, respectively. The longitudinal bar appended to the experimental values in the figures denotes a standard deviation. Amplitude A x in the horizontal direction is described as follows. In every boring tool, amplitude A x increases with an increase in the spindle rotation N. Amplitude A x when an impact damper was used is similar to amplitude A x when an impact damper was not used. Furthermore, although Fig. 6. Amplitude of boring tool in horizontal direction (L=160 mm).

11 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 7. Amplitude of boring tool in vertical direction (boring tool BT A ). the experimental results for the overhang lengths L=120 and 200 mm are not presented, the change in amplitude A x due to the existence of an impact damper was not seen. It is evident from these results that the vibration of boring tools in the horizontal direction cannot be suppressed by the use of impact dampers. The amplitude A y in the vertical direction is described as follows. When the spindle rotation is N=80 rpm, amplitude A y is quite small and the change in amplitude A y due to the existence of an impact damper is not seen. As the spindle rotation N or the overhang length L increases, amplitude A y when an impact damper was not used increases. However, when an impact damper was used amplitude A y decreases by about 50% in comparison with amplitude A y when an impact damper was not used. Such a reduction tendency in amplitude A y due to the impact damper is recognized for all variations in the types of impact dampers or the overhang lengths. It is clear from these results that the vibration of boring tools in the vertical direction can be effectively

12 1152 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 8. Amplitude of boring tool in vertical direction (boring tool BT B ). suppressed by the use of any impact damper. In addition, the effects of the free mass m on the amplitude A y are hardly detectable. Furthermore, as is clearly shown in Figs. 7 9, although it is impossible to completely restrict chatter vibration, it is possible to make the overhang length longer than that in commercial tools using an impact damper. It is also possible to makes the spindle rotation fast using an impact damper, i.e. it is possible to bore deeper holes in comparison with commercial boring tools and also to improve the efficiency of boring operations Discussion As described in the experimental method, impact damper D A was supposed to improve the damping capability of boring tools in the vertical direction, impact damper D B was supposed to improve the damping capability in the horizontal direction, and impact damper D C was supposed

13 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Fig. 9. Amplitude of boring tool in vertical direction (boring tool BT C ). to improve the damping capability in both vertical and horizontal directions. On the other hand, it was clear from the experimental results that all three impact dampers can suppress the vertical vibration of boring tools, but can barely suppress the horizontal vibration. These findings are discussed in what follows. As mentioned in the experimental method, the length of the supplementary sleeve illustrated in Fig. 2 is 0.4 mm longer than the length of the free mass (21 mm). Accordingly, the free mass can move not only in the radial direction of a hole machined in the free mass but also slightly in the axis of the hole. That is to say, impact damper D A can move not only in the vertical but also in the horizontal direction, and impact damper D B can move not only in the horizontal but also in the vertical direction. The damping capability of impact dampers results from the fact that the vibratory energy is consumed by a collision between a free mass and a main mass (boring tool). The amount of energy consumed by the collision is related to the amount of amplitude. As shown in Figs. 7 9,

14 1154 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) when an impact damper is not used, and the spindle rotation is N=130 and 200 rpm, amplitude A y in the vertical direction is markedly great. Thus, the energy consumed by the collision is assumed to be also markedly great when the amplitude is great. On the other hand, as is clear from a comparison of Figs. 6 9, amplitude A x in the horizontal direction is about one tenth of the vertical amplitude A y and is extremely small. The vertical amplitude A y when the spindle rotation N=80 rpm is extremely small. Thus, the energy consumed by the collision is assumed to be extremely small when the amplitude is small. For these reasons, all impact dampers used in this experiment are considered to be effective for the suppression of vertical vibration in boring tools. Since no impact damper was able to fully exert its functions in the horizontal vibration, the results shown in Fig. 6 could be obtained. Consequently, although the boundary is not so clear, it is evident that impact dampers can display their functions when the amplitude of boring tools becomes greater than a certain value. A discussion of the interference between an impact damper and a work now follows. Fig. 10 shows the state that boring tools, equipped with the three types of impact dampers used in the experiment, are cutting a work with an inside diameter of 130 mm. The amount of the free mass in the figure is m=0.045 kg. As clearly shown in the figure, as the inside diameter of the work decreases, the boring operation becomes impossible, because the impact damper interferes with the inner surface of the work. The inside diameter of a work in which such interference does not occur is about 60 mm for impact damper D A, about 130 mm for D B and about 40 mm for D C. Fig. 10. Interference between impact damper and work.

15 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) Therefore, regarding the inside diameter of a work possible to be bored, there is a severe limitation in the use of impact damper D B, but no limitation in the use of impact damper D C. On the other hand, to equip boring tools with impact damper D C, their ends must be separated from the shanks from the construction standpoint as described in the experimental method. Accordingly, a reduction in the bending stiffness of the boring tools is unavoidable as shown in Table 2. Summarizing the features of each impact damper described above and their comparative vibration suppression effects, it is clear that impact damper D A is superior for practical use. Thus, the method of equipping an impact damper on the flank face of a boring tool is desirable. 4. Conclusions Bending, impact and cutting tests were carried out in order to investigate improvements in the damping capability of boring tools and suppression of chatter vibration using impact dampers. The following points were clarified. 1. The damping capability of boring tools is considerably improved using impact dampers. 2. All three types of impact dampers used in the experiment can suppress considerably the vibration of boring tools in the vertical direction (principal force direction), but hardly at all in the horizontal direction (thrust force direction) where the amplitude is extremely small. 3. In practical use, the method of equipping an impact damper on the flank face of a boring tool is desirable. 4. Using an impact damper, it is possible to bore deeper holes in comparison with boring tools now on the market and to improve the efficiency of boring operations. Acknowledgements The authors would like to express their appreciation in carrying out this study to Mr K. Yamada, Mr A. Yamada, Miss M. Tanimura and Mr S. Kawai, graduate students of the Faculty of Education, Gifu University. References [1] S.A. Tobias, Machine Tool Vibration, Blackie, London, [2] R.S. Hahn, Design of Lanchester damper for elimination of metal-cutting chatter, Transactions of ASME 73 (1951) 331. [3] S. Kato, E. Marui, H. Kurita, Some considerations on prevention of chatter vibration in boring operations, ASME Journal of Engineering for Industry 91 (1969) 717. [4] K.J. Kim, J.Y. Ha, Suppression of machine tool chatter using a viscoelastic dynamic damper, ASME Journal of Engineering for Industry 109 (1987) 58.

16 1156 S. Ema, E. Marui / International Journal of Machine Tools & Manufacture 40 (2000) [5] S.F. Masri, T.K. Caughey, On the stability of the impact damper, ASME Journal of Applied Mechanics 33 (1966) 586. [6] M.M. Sadek, B. Mills, Effect of gravity on the performance of an impact damper: Part 1. Steady-state motion, Journal of Mechanical Engineering Science 12 (1970) 268. [7] M.D. Thomas, W.A. Knight, M.M. Sadek, The impact damper as a method of improving cantilever boring bars, ASME Journal of Engineering for Industry 97 (1975) 859. [8] S. Ema, H. Fujii, E. Marui, Chatter vibration in drilling, ASME Journal of Engineering for Industry 110 (1988) 309. [9] S. Ema, E. Marui, A fundamental study on impact dampers, International Journal of Machine Tools and Manufacture 34 (1994) 407. [10] S. Ema, E. Marui, Damping characteristics of an impact damper and its application, International Journal of Machine Tools and Manufacture 36 (1996) 293. [11] S. Ema, E. Marui, Suppression of chatter vibration in drilling, ASME Journal of Manufacturing Science and Engineering 120 (1998) 201.