2004 Wakasawa Ball Packing Damping Test

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International Journal of Machine Tools & Manufacture 44 (2004) 1527–1536

www.elsevier.com/locate/ijmactool

The damping capacity improvement of machine tool structuresby balls packing

Yasunori Wakasawa a,Ã, Masatoshi Hashimoto a, Etsuo Marui b

a Department of Mechanical Engineering, Toyota National College of Technology, 2-1 Eisei-cho, Toyota-shi 471-8525, Japanb Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu-shi 501-1193, Japan

Received 20 November 2003; received in revised form 7 April 2004; accepted 6 May 2004

Abstract

Efficient manufacturing is achieved by the damping capacity improvement of machine tool structure. The purpose of this studyis to clarify the parameters influencing the damping capacity of machine tool structures packed with balls. In structures closelypacked with balls, various damping characteristics appear in correspondence with the ball size and other conditions. The effect of ball size is the most significant factor in these structures. Excitation of structure is necessary for close packing, however, this pro-cess is troublesome. Excitation of structure is required to achieve an optimum packing ratio where the maximum dampingcapacity is obtained. For a 50% packing ratio, this excitation process is not necessary to obtain a stable damping capacity. There-fore, the effects of magnitude of impulse, packed ball material, and structure size on the damping capacity are investigated at a50% packing ratio. Finally, actual machine tool structure models are constructed, and the effectiveness of the balls packing for thedamping capacity improvement is investigated.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Damping capacity; Packing condition; Vibration; Machine structure packed with balls; Machine tool structure; Specific gravity;Friction coefficient; Repulsion coefficient; Structure size

1. Introduction

In forging machines, high-speed press machines and

plain milling machines, a transient vibration generates

in the operation and it exerts a bad influence on

efficient manufacturing. Also, in cantilever tools as bor-

ing bars, damping capacity is low and various dampers

have been suggested for efficient manufacturing.One of these proposals is a damper (impact damper)

that uses a collision of solids. This type of damper is

simple in structure and has wide flexibility in machine

structure applications. The impact damper packed with

granular materials has been reported by Yokomichi

et al. [1] There are also many other interesting studies

on impact dampers [2–6]. However, the damping

capacity of such structures packed with granular mate-

rials or balls is induced from various energy consump-

tion mechanisms creating many parameters that affect

the damping characteristics. It is also difficult to cor-

rectly understand the behavior of the individual balls.

As a result, the generation mechanism of the damping

capacity is not necessarily clear.The authors have investigated the damping capacity

improvement of machine tool structures utilizing clo-

sely packed glass balls [7]. The effects of ball size, ball

arrangement and excitation direction on damping char-acteristics were examined in an experiment of impulsive

excitation. However, it was found that in the case of

close packing, the degree of freedom of the packed

balls is small, and sufficient and stable improvement of

the damping capacity cannot be obtained for some ball

sizes. Therefore, it is important to examine the effects

of other packing methods and to find a structure

packed with balls which has a more effective damping

capacity.Furthermore, for the damping capacity improvement

of machine tool, the studies on the epoxy resin concrete

Ã Corresponding author. Fax: +81-565-36-5924.E-mail address: [email protected] (Y. Wakasawa).

0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijmachtools.2004.05.001



machine tool bed [8] and the ferrocement machine toolbed [9] have been reported.

In the present study, we first examined the effect of packing ratios to obtain stable damping capacity. Sec-ondly, at the packing ratio where a stable dampingcapacity is obtained, the effects of impulsive force,

structure size and specific gravity of the packed ballson damping capacity were examined experimentally.Furthermore, to understand the damping capacity of structures packed with balls in more detail, the effect of waveform in impulsive excitation, friction and repul-sion coefficients of packed balls, and ball behavior dur-ing damping vibration were investigated. Finally,actual machine tool structure models are constructed,and the effectiveness of the balls packing for the damp-ing capacity improvement was investigated.

2. Experimental apparatus and method

The main elements of the machine tool structures arebed, support, column, head, and so on. Vibration gen-eration in these machine tool structures and cuttingtools is troublesome. Therefore in this paper, machinetool structures are represented by simple square pipemodels. And the damping characteristics of these struc-tures are examined by balls packing.

Fig. 1 shows the experimental apparatus of thisstudy. The fundamental structure of this apparatus isthe same as that of a previous study [7]. Model struc-tures were suspended by stainless steel wires at the pos-

ition of nodes of the fundamental vibration mode, andthe center was impacted by an impulsive hammer. Theimpulsive force and the output signal from a small andlight accelerometer bonded at a position 10 mm fromthe end were transmitted to an FFT analyzer through acharge amplifier and bandpass filter. Utilizing the timehistory of impulsive force and acceleration, the damp-ing ratios obtained from the frequency response curvewere examined.

The model structures are drawn square pipes of stainless steel (SUS 304 in JIS) with an outer side of 25–50 mm, wall thickness of 1.5 mm (inner sideb ¼ 22 47 mm) and length L ¼ 500 mm. Seven kindsof balls of different materials of equal diameter (5 mm)are used in the experiment. Ball materials are poly-

propylene, glass, aluminum, alumina, ferrite, steel andbrass. The magnitude of the impulsive force was F ¼ 150 N due to the convenience of excitation.

3. Characteristics of the damping waveform

and vibration dissipation time in impulsive excitation

A typical diagram of the damping wave in impulsiveexcitation is shown in Fig. 2. Here, characteristicvalues, which give the features of the damping wave-form, are explained. The largest amplitude immediatelyafter the impulsive excitation is called the initial ampli-

tude. In the case when there is space between thepacked balls and the structure, the amplitude does notvary for a few vibration periods. This time span iscalled the non-damping time span. After this timespan, the amplitude decreases until the residual ampli-tude becomes infinitesimally small. This time span iscalled the damping time span. Moreover, the timebetween the initial amplitude and the infinitesimallysmall residual amplitude is called the vibration dissi-pation time T . This feature T is used as one of themain characterizing factors of the damping capacity.

4. Effect of various parameters on damping capacity

4.1. Effect of packing ratio and impulsive force

In a previous study [7], it was found that dampingcapacity was not sufficiently improved at some ballsizes in close packing. Excitation of structure is neces-sary for close packing, however, this process is trouble-some. Therefore, the effect of packing ratio ondamping capacity is examined to determine an optimal

Fig. 1. Experimental apparatus. Fig. 2. Schematic drawing of damping wave.

1528 Y. Wakasawa et al. / International Journal of Machine Tools & Manufacture 44 (2004) 1527–1536



packing method other than close packing. The damp-ing capacity of the model structure was estimated bythe above-mentioned vibration dissipation time.

Packing ratio b is the ratio of packed balls volume tostructure cavity volume. The effect of packing ratio b

on the vibration dissipation time in cases of glass andsteel balls is shown in Fig. 3. Packed ball size isd ¼ 3 mm. In the packing of glass balls, the vibrationdissipation time becomes short with the increase in thepacking ratio. Vibration dissipation time T is shortestat a slightly smaller packing ratio than the close pack-ing state. At close packing, the vibration dissipationtime becomes extremely long and the damping capacitydeclines rapidly. In comparison, in steel ball packing,the vibration dissipation time is almost constantbeyond a packing ratio of 40%. The vibration dissi-pation time is shortest at a slightly smaller packingratio than close packing, as in the case of glass ballpacking. Therefore, the damping capacity is maximizedat the packing ratio immediately before close packing.However, it is well known that the maximum packingratio is influenced by the shape accuracy and the fric-tion coefficient of the balls [10]. The packing ratiowhere the maximum damping capacity is obtained dif-fers depending on the size and the material of the balls.

The damping capacity and the packing condition at

the optimal packing ratio are shown in Table 1. Inclose packing, excitation of structure is necessary anddamping capacity is low. Although the maximum

damping capacity can be obtained at the packing ratio

slightly less than close packing, excitation is required to

achieve this packing ratio. Furthermore, a delicate

adjustment of the packing ratio is required. On the

other hand, the incremental improvement of the damp-

ing capacity is not good at extremely small packing

ratios. Therefore, the 50% packing ratio is the mostpractical where the troublesome excitation process is

unnecessary and a stable damping capacity is obtained.Here, we examine the case of the 50% packing ratio

in detail. Packed ball size is d ¼ 5 mm. At a 50% pack-

ing ratio, the damping characteristics are expected to

differ depending on the magnitude of the impulsive

force because a space of approximately several milli-

meters exists between the packed balls and the inner

surface of the structure. The damping waveform in the

cases of 50 and 150 N impulsive forces and 50% glass

ball packing are shown in Fig. 4a,b.

The damping waveform differs according to the mag-nitude of impulsive force. In the case of the 50 N

impulsive force, the amplitude decreases linearly with

time. In the 150 N impulsive force case, after a non-

damping time span, in which the initial amplitude con-

tinues, the amplitude decreases rapidly, then decreases

gradually. From these results, it can be considered that

all packed balls are not necessarily in a moving state

when the impulsive force is small. There are two beha-

viors in the packed ball movement. In the first beha-

vior, the packed balls contact the structure wall and

induce a friction force. In the second behavior, the

Fig. 3. Effect of packing ratio on vibration dissipation time.

Table 1Packing condition and damping capacity

Packing ratio Damping capacity Packing condition

>60% Â Â (With excitation)660% Â (With excitation)50% v v (Without excitation)0–40% Â v (Without excitation) Fig. 4. Free vibration response (packing ratio 50%). (a) Impulsive

force 50 N; (b) Impulsive force 150 N.

Y. Wakasawa et al. / International Journal of Machine Tools & Manufacture 44 (2004) 1527–1536 1529



packed balls are in a moving state owing to the trans-mission of the impulsive force.

The effect of the impulsive force F on the damping

ratio f is shown in Fig. 5. In the case of close packing,the damping ratio f increases slightly with the increasein the impulsive force F , as seen in the figure. At the50% packing ratio, the damping ratio f changes drasti-cally when F 150 N, and is almost constant whenF ! 150 N.

The damping ratio of the structures with packedballs is approximately larger than 0.02, as shown inFig. 5. This value is larger than the damping ratio inthe case of the epoxy resin concrete machine tool bedgiven by Kim et al. [8]. Therefore, the dampingcapacity improvement of machine tool bed may be rea-

lized by the balls packing.

4.2. Effect of structure size and specific gravityof packed ball

The 50% packing ratio reaches a stable dampingcapacity from a simple packing process. At the 50%packing ratio, the damping capacity varies with themagnitude of the impulsive force, but the dampingratio remains approximately constant when F ! 150 N.These findings are obtained in the case of several struc-ture sizes. When the structure size is changed at the50% packing ratio, it is expected that the damping

capacity varies with the structure size due to the weightchange of the packed balls and the vibration behavioralteration. Therefore, the effect of the structure size onthe damping capacity is examined next.

The effect of the structure size b on the vibration dis-sipation time T is shown in Fig. 6, for both glass andsteel ball packing. The packed ball size is d ¼ 5 mm. Inthe packing of both glass and steel balls, the vibrationdissipation time becomes shorter with the increase inthe structure size. The vibration dissipation time of glass ball packing is longer than that of steel ballspacking. However, the vibration dissipation time of

both types of ball packing becomes approximatelyequal at the structure size b ¼ 50 mm.

It is clear from the results presented in Fig. 6 that

damping capacity is affected remarkably by the struc-ture size. We investigated factors that have broughtabout such results. We first examined the effect of theweight of packed balls on damping capacity. Theweight of the structure changes according to the struc-ture size. The magnitude of the impulsive force is con-stant during the experiment, so the vibration energygiven to the structure is not changed by the structuresize. Thus we now examine the weight of packed balls.

The vibration dissipation time for various structuresizes in Fig. 6 is arranged according to the ball weightmB. In glass ball packing, the vibration dissipation timebecomes shorter rapidly with an increase in ball weightup to 1000 g. When the ball weight is greater than 1000 g,the vibration dissipation time decreases gradually. Incontrast, in steel ball packing, the vibration dissipationtime decreases almost linearly with the increase in thestructure size. Therefore, the vibration dissipation timedecreases with the increase in the weight of the packedballs and the damping capacity incremental improve-ment is remarkable. The results are given in Fig. 7. Itcan be understood from the figure that the damping

Fig. 5. Effect of impulsive force on damping ratio.

Fig. 6. Effect of model structure size on vibration dissipation time(packing ratio 50%).

Fig. 7. Effect of ball weight on vibration dissipation time (packingratio 50%).




capacity becomes saturated at a level when the ballweight is large. At approximately the 1000 g ballweight, a small difference is recognized between thevibration dissipation time for glass and steel ball pack-ing in spite of equal ball weight. The packed ballsweight is equal in both cases, but the structure size is

larger for glass ball packing. The small difference invibration dissipation time is induced from the differ-ence of the structure size.

At the 50% packing ratio, the natural frequency of the structure packed with balls is equal to that of square pipe without ball packing. The natural fre-quency becomes large with the increase of the structuresize. Thus, collisions between the packed balls andinner surface of the model structure become more fre-quent as the structure size increases. This tendency isevident in Fig. 7.

From the discussion in the previous section, thedamping capacity is remarkably influenced by the ballweight. In the non-obstructive particle damping(NOPD) technique [6], it is reported that the dampingcapacity can be improved with an increase in the spe-cific gravity of packed balls in the stable excitationstate. Details of the damping effect of the specific grav-ity of packed balls in impulsive excitation is not madesufficiently clear in such reports. Therefore, we investi-gated the damping capacity of model structures packedwith balls of different specific gravity by extensivelychanging the specific gravity. Moreover, noise gener-ation was also examined.

The effect of specific gravity c of packed balls on the

vibration dissipation time T and the maximum noiselevel LAmax is shown in Fig. 8 for the case d ¼ 5 mmand a 50% packing ratio. The vibration dissipationtime T decreases with the increase in the specific grav-ity of the packed balls. So, the damping capacity isimproved with the increase in the packed ball weight.In the case of the 50% packing ratio, packed balls havea considerable degree of freedom, and the damping

capacity is influenced by the motion of all the packedballs. The details are discussed in Section 5.1.

The magnitude of the maximum noise level LAmax ismeasured by a precision type noise meter positioned150 mm from the model structure. The maximum noiselevel is improved with the increase of the specific grav-

ity of packed balls. Therefore, when the specific gravityof packed balls is large, both the vibration dampingcapacity and the noise generation level are improvedsimultaneously.

In the above, the effect of the structure size and thespecific gravity of packed ball on damping capacitywere examined. When the structure size and the specificgravity of packed ball are large, a high dampingcapacity improvement is obtained and the dampingratio becomes approximately 0.1. This value is fairlyhigh compared with the damping ratio between 0.012and 0.018 obtained in the ferrocement machine tool

bed by Rahman et al. [9]. The structure, the excitationand the supporting method are similar to our study.Therefore, it is again ascertained that the application tothe machine tool bed of the balls packing is effectivefor the damping capacity improvement.

5. Considerations on damping capacity generation

5.1. Form of damping wave

It is found that the vibration dissipation time is shortand the damping capacity is improved with an increase

in the specific gravity of packed balls as shown inFig. 7. Further examination of the point elucidates thefollowing points. Fig. 9a,b shows the effect of specificgravity on the characteristic factors of the dampingwave shown in Fig. 2: initial amplitude a0, decrementfrom initial amplitude aD, residual amplitude aR, non-damping time T N, and damping time T D. With anincrease of the specific gravity, the initial amplitudedecreases linearly, and the decrement from the initialamplitude increases linearly. The residual amplitude isalmost constant irrespective of the specific gravity.With an increase in the specific gravity, the non-damp-

ing time shows a weak decreasing tendency. The damp-ing time shows a strong decrease c 4 at and a weakdecrease at c > 4. It is clear from these results that thedamping capacity is improved with an increase in thespecific gravity.

5.2. Measurements of repulsion coefficient and static friction coefficient of ball

In Section 5.1, it was found that the specific gravityis an important parameter influencing dampingcapacity. In this section, the effects of the repulsion

Fig. 8. Effect of specific gravity on vibration dissipation time andmaximum noise level (packing ratio 50%).




coefficient and the friction coefficient on the damping

capacity are examined.Table 2 gives the experimental results of the specific

gravity of packed balls, the friction coefficient againstthe SUS304 plate, and the repulsion coefficient withsquare pipe. From the table, the relation between therepulsion coefficient and the specific gravity is obtainedas shown in Fig. 10. The average repulsion coefficientdecreases with the increase of the specific gravity. How-ever, the tendencies of the aluminum and brass ballsdiffer from the average. The repulsion coefficient of thealuminum ball is extremely small for its specific grav-ity. Therefore, the damping capacity cannot be regu-

lated only by the magnitude of the repulsion

coefficient. The repulsion coefficient is determined bothby deformation of the model structure and the ball asshown in Fig. 11. The model structural deformationfrom the aluminum ball is large compared with theother type balls, judging from the values of Young’smodulus and Poisson’s ratio. Thus, it can be easilydeduced that the repulsion coefficient is small for itsspecific gravity.

The friction coefficients of polypropylene, aluminumand alumina balls are a little larger than those of ballsof other materials. The difference between themaximum and minimum values of the friction coef-

ficient is approximately 0.1. Moreover, the effect of thisdifference in the friction coefficient on the dampingcapacity is small, as a steady correlation between thefriction coefficient and the damping capacity does notappear. Thus, it is confirmed that the damping capacitygeneration can be reasonably understood by the spe-cific gravity of packed balls.

5.3. Observation of packed ball movement

The main factors generating the damping capacity bypacked balls are the collision and friction among the

packed balls and between the packed balls and the

Fig. 9. Effect of specific gravity on damping wave (packing ratio50%). (a) Initial amplitude, decrement from initial amplitude andresidual amplitude; (b) Non-damping time span and damping timespan.

Table 2Specific gravity, friction coefficient and repulsion coefficient of ball

Material Specificgravity

Frictioncoefficient

Repulsioncoefficient

Polypropylene 0.9 0.37 0.69Glass 2.5 0.28 0.40Aluminum 2.8 0.38 0.12Alumina 3.6 0.36 0.19Ferrite 5.0 0.30 0.15Steel 7.8 0.29 0.11Brass 8.5 0.33 0.15

Fig. 10. Relation between repulsion coefficient and specific gravity.

Fig. 11. Deformation of square pipe and ball by collision.




inner surface of the square pipe. It has been clarified ina previous report [7] that the damping ratio could besuccessfully regulated by the values of the repulsioncoefficient for glass balls of different diameters closelypacked in structures. However, the damping capacitycan be reasonably understood in terms of the specific

gravity of the packed balls, as seen when balls of thesame size and different material were packed at a 50%packing ratio. This result is thought to be due to differ-ences arising after the balls are packed. In close pack-ing or packing at the maximum damping capacity,small spaces remain between the packed balls and theinner surface of the square pipe. The collisions amongthe packed balls themselves and between the packedballs and the inner surface occur immediately after theimpulsive excitation. In contrast, at a 50% packingratio, there is approximately several millimeters of space between the packed balls and the inner surface.

The collisions between the packed balls and the innersurface do not occur immediately after the impulsiveexcitation. Therefore, the generation mechanism of thedamping capacity differs between close packing andthe 50% packing ratio. The packed ball movement atthe 50% packing ratio is now examined.

Fig. 12 briefly shows the measurement of the packedball movement. The model structure is supported byknife-edges, since the structure, hung by stainless steelwire, tended to swing from the force of the impulsiveexcitation. An 8 mm diameter hole was drilled at aposition 10 mm from the end of the model structure.

As a laser beam from a laser displacement meter witha response frequency of 16 kHz passes through thehole, the movement of the uppermost ball layers isobserved.

Fig. 13 shows the observed results of the aluminaball movement. The ball movement of the uppermostlayer does not follow the vibration of the fundamentalmode (650 Hz) of the structure. The balls movedupward once during the damped vibration of the struc-

ture. In close packing, the collision between the modelstructure inner surface and the packed balls produces agrate influence, since the space between the packedballs and the inner surface is very small. At the 50%packing ratio, however, this type of collision does notoccur due to the large space between the packed ballsand the inner surface of the model structure. Thevibration energy of the structure is transmitted to thepacked balls and the damping capacity is improved bythe upward movement of the packed balls. The relationbetween the maximum displacement Dmax and the spe-cific gravity is shown in Fig. 14. The maximum dis-

placement increases with the decrease in the specificgravity of the packed balls. Therefore, when the spe-cific gravity is small, the packed balls can easily moveupward and the friction among the packed ballsdecreases. Furthermore, the vibration energy is dissi-pated by the collision and, hence, the damping capacitydecreases, when the packed balls are light.

Fig. 12. Measurement of packed ball movement (packing ratio50%).

Fig. 13. Ball movement (alumina ball, d ¼ 5 mm).

Fig. 14. Effect of specific gravity on maximum displacement (pack-ing ratio 50%).




6. On effectiveness of balls packing in machine tool

structures

6.1. Damping characteristics of structure with three packing rooms

In Section 4.2, the effect of the structure size on the

damping characteristics is examined. However, when alarge structure is packed with balls at the 50% packingratio level, it is impractically heavy. Also, the machinetool structure as shown in Fig. 15 has many spaces andthe rib exists for reinforcement of the milling machineand the bed of lathe. Therefore, the damping character-istics of a structure that has three packing rooms isexamined.

Fig. 16 shows the section of the structure with threepacking rooms. The model structure has three packingrooms of stainless steel (SUS 304 in JIS) with the fol-lowing dimensions: outer size of 25 mmÂ 72 mm,

length 500 mm, and wall thickness of 1.5 mm. Theexperiments are carried out under various conditions,such as the number of the packed rooms, the packedroom position and the posture of the structure (verticalor horizontal). The packing ratio of the glass balls ineach packing room is 50%. As in the experiment in theprevious section, the magnitude of the impulsive forceis 150 N. The packing rooms are identified as 1, 2 and3 room in the case of vertical arrangement, and as A, Band C room in the case of horizontal arrangement.However, in the case of horizontal arrangement, theeffect of the packed rooms number on the damping

capacity is examined considering the weight balance.Fig. 17a,b shows the effect of the packed rooms

number on vibration dissipation time in the case of vertical and horizontal arrangement. It is confirmedthat the damping capacity can be improved with theincrease of the packed rooms number. However, inboth cases of vertical and horizontal arrangement, thedifference between the vibration dissipation time of tworooms packing and three rooms packing is small and

the damping capacity can effectively be improved bytwo rooms packing.

Moreover, from the experimental results of Fig. 17a,the largest damping capacity is obtained when the ballsare packed in the lowest room 3.

6.2. Damping characteristics of machine tool structuremodels

As an experiment related to actual machine toolstructure, two types of machine tool structure models

were constructed and the damping capacity improve-ment due to application of packed balls was examined.The radial boring machine has a construction that acolumn is fixed on a base and a moving radial arm ison the column. As another example, a milling machinehas a column and a head. In many cases, the machinetool base has T-type construction because the table andthe supporting column of cutting tool are connected.These machine tool structures are constructed by con-necting two cantilever beams. On these machine toolstructures, the damping capacity improvement isimportant.

Fig. 18 shows the machine tool structure model (typeA), constructed by two square pipes with an outer sideof 100 mm. One pipe is the column and the other is thehead or the radial arm. Packed ball size is d ¼ 5 mmand the material is glass, with 50 % packing ratio. Twopipes are connected by welding.

The damping characteristics of this machine toolstructure model were examined. Glass balls are packedin each part 1 or 2, or in both parts 1 and 2. Part 1 wasexcited. Fig. 19 shows the vibration waves in the casesof no packing (Fig. 19a) and the case of balls packingin both parts 1 and 2 (Fig. 19b). Fig. 20 is the obtainedFig. 15. Example of machine tool structure.

Fig. 16. Machine tool structure with three packing rooms; (a) Verti-cal arrangement; (b) Horizontal arrangement.




result of the damping characteristic in the type A

model. An accelerometer was bonded on the part 1.

Damping capacity can effectively be improved by balls

packing in the excited part 1. However, the damping

capacity improvement is small when balls are packed

only in the part 2.

Fig. 21 shows the machine tool T-type model (typeB), constructed by two perpendicularly intersecting

square pipes with an outer side of 100 mm. Fig. 22 is

the obtained result with the type B model. In the type

B model, an accelerometer was bonded on the part A,

which was excited. The damping capacity is effectively

improved by balls packing at the excited part. This is

the same tendency recognized in Fig. 20.From the above results, the damping capacity of

machine tool can be improved by application of balls

packing in the actual machine tool structures.

7. Conclusions

In this paper, an effective means is proposed to

improve the damping capacity of the machine tool

structures. Some experiments and considerations on the

damping capacity improvement of machine tool struc-

tures packed with balls are carried out by widely varying

Fig. 17. Effect of number of packing part on vibration dissipation time. (a) Vertical arrangement; (b) Horizontal arrangement.

Fig. 18. Machine tool structure model (type A).

Fig. 19. Free vibration response in type A model. (a) Without packed balls; (b) Balls packing in parts 1 and 2.




the packing ratio, the impulsive force, the structure sizeand the packed ball material.

The following results were obtained :

1. A packing ratio of approximately 50% is optimal,since the excitation process of structure is unnecess-ary and a high level of damping capacity isobtained.

2. At the 50% packing ratio, the damping capacity isaffected by the structure size and the packed ballweight. The damping capacity can be improved byincreasing the packed ball weight.

3. When the packed ball materials were changed, thedamping capacity improved remarkably by increas-

ing the specific gravity of the packed balls. Thedamping capacity at a 50% packing ratio was alsoaffected by the impulsive force.

4. Detailed observations of the damping waveformswere carried out and some characteristic parameterswere examined. Damping capacity generation couldbe evaluated more accurately by the specific gravityof the packed balls than by the frictional coefficientor the repulsion coefficient.

5. The damping capacity of a model structure that hasthree packing rooms was investigated through theeffects of the number of packed rooms and thepacked room position.

6. In two types of machine tool structure models, thatis, the column and head model and the T-typemodel, it was confirmed that the damping capacityis effectively improved by balls packing.

References

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[2] A. Papalou, S.F. Masri, Performance of ball damper under ran-dom excitation, Transactions of the ASME, Journal of Vibrationand Acoustics 118 (1996) 614–621.

[3] J.J. Moore, A.B. Palazzolo, R. Gadangi, T.A. Nale, S.A.Brown, G.V. Brown, A.F. Kascak, A forced response analysisand application of impact dampers to rotor dynamic vibrationsuppression in a cryogenic environment, Transactions of theASME, Journal of Vibration and Acoustics 117 (1995) 300–310.

[4] C. Cempel, G. Lotz, Efficiency of vibrational energy dissipationby moving shot, Journal of Structural Engineering 119 (9) (1993)2642–2652.

[5] L.A. Chen, S.E. Semercigil, A beam-like damper for attenuatingtransient vibrations of light structures, Journal of Sound andVibration 164 (1) (1993) 53–65.

[6] H.V. Panossian, Structural damping enhancement via non-obstructive ball damping technique, Transactions of the ASME,Journal of Vibration and Acoustics 114 (1992) 101–105.

[7] Y. Wakasawa, M. Hashimoto, E. Marui, Damping capacityimprovement of machine structures by close packing with balls,International Journal of Machine Tools and Manufacture 42(2002) 467–472.

[8] H.S. Kim, K.Y. Park, D.G. Lee, A study on the epoxy resinconcrete for the ultra-precision machine tool bed, Journal of Materials Processing Technology 48 (1995) 649–655.

[9] M. Rahman, M.A. Mansur, W.D. Ambrose, K.H. Chua,Design, fabrication and performance of a ferrocement machinetool bed, International Journal of Machine Tools and Manufac-ture 24 (1987) 431–442.

[10] R.K. McGeary, Mechanical packing of spherical balls, Journalof the American Ceramics Society 44 (10) (1961) 513–522.

Fig. 20. Measured damping capacity of the type A model.

Fig. 21. Machine tool structure model (type B).

Fig. 22. Measured damping capacity of the type B model.


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2004 Wakasawa Ball Packing Damping Test