Bend Forms of Circular Saws and Evaluation of their Mechanical Properties

Transcription

1 ISSN MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology, Kuns University of Technology, Studentų 56, LT-5144 Kuns, Lithuni Received 31 August 4; ccepted 19 Octoer 4 A circulr sw is le to operte properly only when its equilirium form is stle. Usully it is flt equilirium form. In most cses the loss of stility of circulr sw is relted to the loss of its dynmic stility. One of the resons re resonnce virtions of sws. With ppering resonnce phenomen, tiny forces cuse gret deformtions. The size of these deformtions depends on sw rigidity nd dmping vlue, therefore it is very importnt to know mechnicl properties of sws (strength, rigidity, coefficient of dmping, etc.). The elorted study methods nd equipment llow to evlute precisely mechnicl properties of sws, seprte end forms, resonnce frequencies nd dmping. Using resonnce frequencies, under which sw end forms re close to theoreticl, Young`s modulus ws estimted for ll four fstened sws (E = GP). Using mplitude-frequency chrcteristics of sw virtions, coefficient of dmping ws evluted (tgδ =.5.155). Bend forms of sws were lso studied chnging their fstening moment, respectively 5, 1 nd 15 Nm. The pper presents study methods, end forms of sws nd otined reltionships, reflecting the chnge of mechnicl properties of sws. Keywords: circulr sw, resonnce virtions of sws, coefficient of dmping, Young`s modulus. INTRODUCTION Circulr sws re widely pplied in wood processing industry. They cn operte relily only when their equilirium form is stle. Anlysis of technicl defects using circulr sws for swing shows, tht mjor prt of defects is cused y insufficient stility of sws [1]. Studies show, tht in most cses the loss of circulr sw stility is relted not to the loss of sttic stility of flt equilirium form, ut to the loss of dynmic stility. The reson for this re resonnce virtions of sws. These virtions led to worse wood processing qulity, incresed noise, fissures in the disc, etc. Under ppering resonnce phenomen, very smll forces cuse gret deformtions []. The size of these deformtions depends on sw rigidity nd dmping vlue, therefore it is very importnt to know mechnicl properties of sws (strength, rigidity, coefficient of dmping, etc.). The less is the dmping force of sw, the slower is stifling of virtions, the worse is swing qulity. Producing circulr sws, it is sought, tht dmping of the sw is s high s possile. The use of dmping mterils is n optiml wy to stifle virtions [3 5]. For this purpose virtion dmping rings re used [4, 6]. Owing to them, noise is reduced y 1 db, while in the cse of resonnce virtions y db. The mplitude of virtions decreses 1 nd more times, which leds to etter swing qulity. Mny studies re crried out seeking to reduce the noise cused y circulr sws. For this purpose, in the periphery of sws, cuts of different shpes re mde (circulr, zigzg, symmetricl, vrious holes etc.) [6 8]. These cuts my lso provide virtion dmping effect. The segments of these cuts my e filled with virtion dmping mteril. Corresponding uthor. Tel.: ; fx.: E-mil ddress: reference@emil.lt (K. Ukvlergienė) Studies re conducted lso chnging the construction of disc fstening flnges [9]. A lyer of virtion soring mteril my e ttched to one or oth of them. These studies llow to solve some prolems relted to sw form stility, however, in most cses sw end form is scertined only pproximtely, coefficient of dmping nd Young`s modulus re not evluted. Thus, the work is imed t precise mesurement of sw end forms nd evlution of its mechnicl properties y verstile form stility nlysis of circulr sws. THEORETICAL PART Theoreticlly, circulr sws re studied on the sis of round pltes fstened in the centre. In this cse the plte is nlysed s liner elstic system, where elstic nd viscid properties re uniformly distriuted in its whole volume. Anlysing virtions of such n elstic ody, it is ssumed, tht the mteril is monolithic nd isotropic, while its thickness is sufficiently smll s compred to other dimensions. Clssicl eqution of periodicl virtions of the plte is the following [1]: 4 ξ α ξ + = (1) t or ω ω + ξ =, () α α where α 4 Eh = 1 1 = ( µ ) ρ ρ D, (3) where µ is the Poisson s rtio (µ =.3); E is the Young`s modulus; h is the thickness of the plte; ζ is the function of eqution vriles; α is the coefficient; ω is the ngle frequency of free virtions; ρ is the density of plte mteril. 79

2 Solving the eqution of trnsverse virtions of plte firmly fstened in the centre, the otined frequency of its free virtions (end forms) is clculted s follows [11]: αh E f res =, Hz (4) πr 1( 1 µ )ρ where α is the prmeter, dependnt on the numer of knot circles; h is the thickness of circulr sw; R is the rdius of circulr sw; ρ is the density of sw disc mteril. Knowing the frequency of free virtions ƒ res, it is possile, using eqution (4), to clculte Young`s modulus E of the virting system. Interior friction (dmping) is evluted hving scertined mplitude-frequency chrcteristics of the sw [1]. Its form predetermines inner friction of the sw. Hving scertined resonnce frequency ƒ res nd mplitude A 1, dditionlly two other frequencies ƒ 1 nd ƒ re determined, under which the mplitude is thn resonnce mplitude (Fig. 1). times less Fig.. Study stnd of circulr sws: 1 circulr sw; shft; 3 flnges; 4 virtor; 5 sensor; 6 genertor of electric signls; 7 mplifier; 8 frequency mesurer; 9 phsometer; 1 virometer; 11 oscilloscope Fig. 1. Amplitude-frequency chrcteristics of the sw: A 1 resonnce mplitude, ƒ res resonnce frequency, ƒ 1 nd ƒ frequencies, under which mplitude is times less thn resonnce mplitude The rtio of frequency elt width ƒ = ƒ ƒ 1 nd resonnce frequency ƒ res is the mesure of inner friction of the sw: tgδ, (5) f f1 f res where tgδ is the coefficient of dmping. STUDY METHODS AND EQUIPMENT For the studies, specil virtion stnd ws used (Fig. ), which consists of circulr sw 1, fstened on shft with flnges 3, virtor 4, piezoelectric sensor 5, genertor of electric signls 6, n mplifier 7, frequency mesurer 8, phsometer 9, virometer 1 nd n oscilloscope 11. By fstening the sensor in chrcteristic points, mplitude-frequency chrcteristics of the sw is scertined, the vlues of resonnce frequencies nd virtion mplitudes s well s coefficient of dmping re evluted. For n ccurte sw form evlution, the whole sw is divided into seprte prts (96 points), otining certin numer of dimeters nd circles (Fig. 3). In the plces of their intersection the sensor is fstened nd resonnce Fig. 3. Circulr sw: 1 1, 1, 1 3 nd so on points, where mesurements re crried out, R 1, R, R 3 rdius of circles; A, B, C, D, E chrcteristic mesurement zones of sw virtions frequency, mplitude s well s the difference in the phses of signls etween the sensor 5 nd the genertor 6 re scertined. EXPERIMENTAL PART Four 9XФ steel type sws were studied. Their dimensions were: sw I dimeter D s = 1 mm, thickness s = 3.7 mm, flnge dimeter d f = 14 mm; sw II D s = 8 mm, s = 4. mm, d f = 14 mm; sw III D s = 5 mm, s =.6 mm, d f = 14 mm; sw IV D s = 4 mm, s =.8 mm, d f = 14 mm. Mesurements were crried out within Hz rnge. Mesuring virtions, resonnce frequencies nd mplitude-frequency chrcteristics of the sws were determined. The chnge of sw end forms nd mechnicl properties ws studied chnging the fstening moment of sws. Fig. 4 presents mplitude-frequency chrcteristics of sw I. Chrcteristic is the fct, tht the highest mplitudes re ttined y sw in the rnge of low frequencies (5 5 Hz). Anlogous mplitude-frequency chrcteristics were mesured for other sws too. Besides, these chrcteristics were otined under different sw fstening moments (5, 1 nd 15 Nm). 8

3 Amplitude, m/s * Frequency, Hz -fstening moment 5 Nm -fstening moment 1 Nm -fstening moment 15 Nm D s = 8 mm, ƒ res = 185 Hz, end form is lso with four knot dimeters, in Fig. 5c, under D s = 1 mm, ƒ res = 154 Hz end form is comined (with two knot dimeters nd one circle). Fig. 4. Amplitude-frequency chrcteristics of sw I, mesuring virtions in zone A Tle 1 presents otined resonnce frequencies of sws. It cn e seen, tht depending on sw dimensions under similr end form resonnce frequencies slightly differ, esides, dditionl resonnce frequencies occur, which in other sws were not recorded. Tle 1. Resonnce frequencies of sws Resonnce frequencies of sws, Hz (I) (II) (III) (IV) At the sme time sw end form ws scertined under ech of resonnce frequencies. It ws found, tht some end forms re close to theoreticl, while others significntly differ from theoreticl ones. It ws otined, tht nlogous end forms for sws with smller dimeter re oserved under higher frequencies. The disc of sw is system with n freedom degrees. It hs n endless multitude of virtion end forms. The following end forms re distinguished: without knot dimeters nd circles; with knot dimeters; with knot circles; comined (with knot dimeters nd knot circles) [1]. In sw I, sw II nd sw III end forms with knot dimeters nd comined ones re otined, while in sw IV only forms with knot dimeters re oserved. Some sw end forms re given in Fig. 5. In Fig. 5, under dimeter D s = 4 mm, frequency ƒ res = 48 Hz, end form is with four knot dimeters, in Fig. 5, under c Fig. 5. end forms: D s = 4 mm, ƒ res = 48 Hz, D s = 8 mm, ƒ res = 185 Hz, c D s = 1 mm, ƒ res = 154 Hz Using resonnce frequencies, under which sw end forms re close to theoreticl, in ccordnce with expression (4), Young`s modulus ws estimted for ll four sws (E = GP). Fig. 6 presents the chnge of sw I Young`s modulus chnging sw fstening moment, respectively 5, 1 nd 15 Nm. For this sw Young`s modulus ws estimted under resonnce frequency of 154 Hz. end form under this frequency is with two knot dimeters nd one knot circle. It cn e seen, tht with incresing frequency, Young`s modulus increses. Under fstening moment increment from 5 to 15 Nm, Young`s modulus respectively increses from 3 to 3 GP. E, GP fstening moment, Nm Fig. 6. Chnge of sw D s = 1 mm Young`s modulus, chnging sw fstening moment 81

4 Tle. Coefficient of dmping of sws fstening moment 5 Nm f res tgδ fstening moment 1 Nm f res tgδ fstening moment 15 Nm f res tgδ Using mplitude-frequency chrcteristics of sw virtions, coefficient of dmping ws lso evluted. Tle presents the vlues of sw I coefficient of dmping under chnging fstening moment nd frequency. Fig. 7 presents the dependence of coefficient of dmping, evluting sw end forms nd their frequencies. These dependencies were otined under different sw fstening moments (5, 1 nd 15 Nm). Fig. 7 shows, tht with incresing frequency, coefficient of dmping increses, when sw-fstening moments re 1 nd 15 Nm, nd decreses when swfstening moment is 5 Nm. Coefficient of dmping, r. u Nm -fstening moment 5 Nm -fstening moment 1 Nm -fstening moment 15 Nm 1 Nm 15 Nm mesurement points. Fig. 8 presents the chnge of coefficient of dmping on sw I plne under resonnce frequencies of 35 Hz nd 138 Hz. Under resonnce frequency of 35 Hz, coefficient of dmping is lower (tgδ =.45.89), ut it is more evenly distriuted on the sw plne thn under resonnce frequency of 138 Hz (tgδ = ). However, under oth resonnce frequencies zone CDE (Fig. 3) ws distinguished, in which coefficient of dmping is higher thn in the rest prt of the sw. It ws scertined, tht chnging sw fstening moment, end forms remin similr, however, the mplitude of virtions, frequency nd coefficient of dmping undergo chnges. Fig. 9 presents end forms of sw I, chnging sw fstening, respectively 5, 1 nd 15 Nm, when frequency is 154 Hz, while Fig. 1 shows corresponding chnges in the mplitude of virtions nd coefficient of dmping Frequency, Hz Fig. 7. Dependence of coefficient of dmping on frequency, D s = 1 mm Fig. 8. Chnge of coefficient of dmping on the plne of sw I: ƒ res = 35 Hz, ƒ res = 138 Hz Distriution of coefficient of dmping on the sw plne ws lso studied, i.e. it ws mesured in ech of 96 c Fig. 9. Chnge of sw I end forms, when ƒ res = 154 Hz, while fstening moment 5 Nm, fstening moment 1 Nm, c fstening moment 15 Nm 8

5 Amplitude, m/s Coefficient of dmping, r. u fstening moment, Nm fstening moment, Nm. It ws otined, tht only some sw end forms coincide with theoreticl ones. Anlogous end forms for sws with smller dimeter re oserved under higher frequencies. Besides, in sws with 1 mm, 8 mm nd 5 mm dimeters end forms with knot dimeters nd comined ones re otined, while in 4 mm dimeter sw only forms with knot dimeters re oserved. 3. Using resonnce frequencies, under which sw end forms re close to theoreticl, sw Young`s modulus ws clculted (E = GP). 4. It ws scertined, tht virtions of higher frequencies fde wy slower, i.e. their coefficient of dmping is higher thn tht of lower frequency virtions. Coefficient of dmping tgδ = ws clculted. 5. It ws determined, tht chnging sw fstening moment, end forms remin the sme, however, the mplitude of virtions, frequency nd coefficient of dmping undergo chnges. 6. It ws found, tht with incresing Young`s modulus of circulr sw, coefficient of dmping decreses. When Young`s modulus increses from 3 GP to 3 GP, coefficient of dmping decreses from.58 to.97. REFERENCES 1. Sthiyev, J. M. Workility of Flt Circulr s. Moscow, Lesny promyšlennostj, 1989: 38 p. (in Russin).. Voolis, J. Dignostics of Light Industry Mchinery. Kuns, Technology, 1996: 16 p. (in Lithunin). Fig. 1. Dependence of the mplitude () nd coefficient of 3. Yu, S. C., Hung, S. C. Virtion of Three-lyered Viscoelstic Sndwich Circulr Plte Interntionl Journl of Mechnicl Sciences 1: pp dmping () on sw I fstening moment 4. Noise Atement for Circulr s. Wellington. Occuptionl Sfety & Helth Service, 1989: p. Fig. 1 shows, tht with incresing fstening moment, the mplitude nd coefficient of dmping decresed respectively from.9 to.3 m/s nd from.58 to.97. Fig. 6 nd Fig. 1 show, tht with incresing Young`s modulus, coefficient of dmping decreses, i.e. with improving elstic properties of the system, its viscid properties ecome worse. Thus, hving scertined mplitude-frequency chrcteristics of the sw, nd knowing resonnce frequencies, it is possile to evlute mechnicl properties of such system, i.e Young`s modulus nd dmping. On the other hnd, these properties llow to evlute the qulity of circulr sws, forecst their workility nd swing precision. CONCLUSIONS 1. It ws found, tht the vlues of resonnce frequencies chnge depending on circulr sw dimensions, when D s = 4 mm, ƒ res = Hz, D s = 5 mm, ƒ res = 8.5 Hz, c D s = 8 mm, ƒ res = 5.9 Hz, D s = 1 mm, ƒ res = 3. Hz under the sme end form. 5. Wng, H. J., Chen, Y. R., Chen, L. W. Finite Element Dynmic Anlysis of Rotting Orthotropic Sndwich Annulr Pltes Composite Structures 3: pp Gorin, S. V. Circulr of Lowered Virtion nd Noise Wood Industry : pp. 5 6 (in Russin). 7. Sthiyev, J. M. On the Dynmic Coefficient (B) of Circulr s Wood Journl : pp (in Russin). 8. Circulr. Pt Russi, МКИ В7 В 33.8 Nosovskij, T. A., Beloshickij, V. I., Pishnik, I. M., Zuik, S. V. No /15 Appl..1.88; Pulished Device for Noise nd Virtion Reduction of Circulr s. Pt Russi МКИ В7 В 5/38 Bogchev, A. P., Bogchev, A. P., Bogchev, E. K. No 5394/15; Appl ; Pulished Skuchik, E. Simple nd Complex Virtion Systems. Moscow, Mir, 1971: 558 p. (in Russin). 11. Timoshenko, S. P. Virtions in Engineering. 1985: 47 p. (in Russin). 1. Voolis, J. Triology. Kuns, Technology, 1994: 187 p. (in Lithunin). 83