U radu se prikazuje jednostavna metodologija utvrđivanja kritičnih frekvencija vrtnje kružnih pila. I proizvođači i korisnici trebali bi biti zainteresirani za informacije o stvarnim vrijednostima kritičnih (dopuštenih) frekvencija vrtnje. Naime, vrlo su često frekvencije vrtnje koje preporučuju proizvođači pila (katkad su naznačene
na listovima pila) veće od vrijednosti dobivenih eksperimentalnim putem.This paper presents a simple experimental methodology of determination of critical rotational speeds of circular saw blades. Both producers and users should be interested in getting information on the actual values of critical (permissible) speeds because very often rotational speeds recommended by producers (sometimes also
marked on saw blades) are larger than the values obtained experimentally

Kazimierz Orlowski

U radu se prikazuje jednostavna metodologija utvrđivanja kritičnih frekvencija vrtnje kružnih pila. I proizvođači i korisnici trebali bi biti zainteresirani za informacije o stvarnim vrijednostima kritičnih (dopuštenih) frekvencija vrtnje. Naime, vrlo su često frekvencije vrtnje koje preporučuju proizvođači pila (katkad su naznačene

na listovima pila) veće od vrijednosti dobivenih eksperimentalnim putem.This paper presents a simple experimental methodology of determination of critical rotational speeds of circular saw blades. Both producers and users should be interested in getting information on the actual values of critical (permissible) speeds because very often rotational speeds recommended by producers (sometimes also

marked on saw blades) are larger than the values obtained experimentally

Orlowski, Kazimierz

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Kazimierz A. Orlowski1Identification of criticalspeeds of clamped circularsaws*Odre|ivanje kriti~nih frekvencija vrtnje kru`nihpila pri~vr{}enih prirubnicama*Original scientific paper • Izvorni znanstveni radPrispjelo - received: 29. 9. 2005. • Prihva}eno - accepted: 25. 4. 2006.UDK: 630*822.332.6ABSTRACT • This paper presents a simple experimental methodology of determination of critical rotational spe-eds of circular saw blades. Both producers and users should be interested in getting information on the actual valu-es of critical (permissible) speeds because very often rotational speeds recommended by producers (sometimes alsomarked on saw blades) are larger than the values obtained experimentally.Key words: circular saw, critical rotational speed, methodology of determinationSA@ETAK • U radu se prikazuje jednostavna metodologija utvr|ivanja kriti~nih frekvencija vrtnje kru`nih pila. Iproizvo|a~i i korisnici trebali bi biti zainteresirani za informacije o stvarnim vrijednostima kriti~nih (dopu{tenih)frekvencija vrtnje. Naime, vrlo su ~esto frekvencije vrtnje koje preporu~uju proizvo|a~i pila (katkad su nazna~enena listovima pila) ve}e od vrijednosti dobivenih eksperimentalnim putem.Klju~ne rije~i: kru`na pila, kriti~na frekvencija vrtnje, metodologija utvr|ivanja1 INTRODUCTION1. UVODImprovement in sawing accuracy and sawn surfa-ce quality (roughness), operating noise level, tool lifeand reduction of kerf losses during cutting with circularsaws are inseparably connected with circular saw dyna-mic features such as: circular saw blade accuracy, wor-kpiece characteristic, static and dynamic properties ofthe machine tool.The effect of circular saw dynamics may be con-siderably amplified if the saw rotational speed is closeto the critical rotational speed due to the resonance phe-nomenon as exemplified by Stakhiev2 (Stakhiev, 1989;Stakhiev, 2000). The effect of the rotation speed ontransverse displacements of the idling circular saw du-ring gradual increase of the rpm is shown in Figure 1.Speed consists of the following distinguishedcomponents:DRVNA INDUSTRIJA 56 (3) 103-106 (2005) 103................... Orlowski: Identification of critical speeds of clamped circular saws1Author is associate professor at the Mechanical Engineering Faculty, Gdansk University of Technology, Poland.1Autor je profesor na Strojarskom fakultetu Tehnolo{kog sveu~ili{ta u Gdanjsku, Poljska.* Rad je pripremljen za sastanak Interkatedra 2005 „Woodworking technique”* The paper was prepared for meeting Interkatedra 2005 „Woodworking technique”2 Dr. Yury M. Stakhiev (1934 – 2004) was an acknowledged expert in the field of circular saws and a pioneer in the development of the criticalspeed theory (Schajer, 2004).Figure 1 Circular saw blade transverse displacements as afunction of rotational speed during idling (saw diameter: 510mm, clamping diameter: 125 mm), (reprinted from Stakhiev2,2000)Slika 1. Lateralno gibanje lista pile kao funkcija frekvencijevrtnje u praznom hodu (promjer pile 510 mm, promjer prirub-nica 125 mm) (Stakhiev2, 2000)1. universal rotational speed (univerzalna frekvencijavrtnje) nu,2. optimal rotational speed (optimalna frekvencijavrtnje) no,3. permissible rotational speed (dopu{tena frekvencijavrtnje) np,4. lowest critical rotational speed (najni`a kriti~nafrekvencija vrtnje) ncrmin ,5. lowest self-excited rotational speed (najni`a samo-uzbudna frekvencija vrtnje) nautmin ,6. destructive rotational speed (destruktivna frekven-cija vrtnje) ndesmin .The mechanism of saw blade instability was stu-died by many scientific publications (Mote and Szyma-ni, 1977; Li et al, 2000; Nishio and Marui, 2000; Scha-jer, 1986; Schajer, 1989; Siklienka and SvoreŒ, 1997;Stakhiev, 1989; Stakhiev 2000; Stakhiev 2004) whereinterest was focused on the theory of critical rotationalspeed of circular saws. Although this theory seems tobe well acceptable by the scientific community, itspractical implementation is rather limited. Moreover,the critical speed depends on some additional factorssuch as: internal stresses, tensioning level (Chabrierand Martin, 1999; Mote and Szymani, 1977; Li et al,2000; Schajer, 1985; Siklienka and Svorenf, 1997; Stak-hiev, 1989; Stakhiev 1989) temperature gradient (Moteand Szymani, 1977; Stakhiev, 1989; Siklienka andSvorenf), and saw design, i.e. the presence of slots (Ni-shio and Marui, 1996; Stakhiev, 1989; Svorenf, 2004).It is crucial for users to be well acquainted withthe critical rotational speed because in case the rotationspeed reaches its critical speed range, the clamped sawblade cannot resist transversal forces and becomes un-stable. Furthermore, it was confirmed that the maxi-mum (or permissible) rotational speed marked by toolproducers on the saw blade was occasionally higherthan the computed critical rotational speed of these in-vestigated saws (Stakhiev, 2004). For example, themark on the saw indicates 1500 rpm, where the calcula-ted speed was only 1173 rpm! As a result, in the speedrange between 1173rpm and 1500rpm, the circular sawwould easily become unstable (Stakhiev, 2004).Methodologies of critical speed determination fo-und in the reference literature are too specific to be ap-plied in industry (Nishio and Marui, 1996; Szymani,1984) and they mainly deal with computer aided desi-gning of solid saws. An alternative way for identifyingthe value of critical speeds is through an experiment.The aim of this paper is to present a simple expe-rimental methodology for identifying critical rotationalspeeds of circular saw blades.2 THEORETICAL BACKGROUND2. TEORIJSKE OSNOVEAccording to the theory of critical rotational spe-ed, the vibration of each sawblade is a superposition oftwo traveling waves moving in opposite directions aro-und the sawblade (the forward traveling wave and thebackward traveling wave, respectively). The naturalfrequency fn, for the nodal diameter number n, of therunning circular saw blade is influenced by the rotatio-nal speed of the saw blade. Thus, the frequency fn is afunction of the plate (blade) rotation speed N and itmay be expressed as f Nnf ( ). So, the frequencies of theforward and backward traveling waves may be expres-sed as follows (Mote and Szymani, 1977; Nishio andMarui, 1996; Schajer, 1985; Stakhiev, 1989):– forward traveling wave (val koji putuje prema napri-jed):f N f NnNnf nf( ) ( )= + 60(1)– backward travelling wave (val koji putuje unatrag):f N f NnNnb n( ) ( )= − 60(2)When the rotational speed of the circular saw in-creased, the frequency of the backward travelling wavebecomes zero at a definite rotational speed, which iscalled the critical (lowest) rotational speed n crmin (Moteand Szymani, 1977; Stakhiev, 1989). This is the reso-nance point where a small lateral force causes a largelateral deflection of the saw blade (Stakhiev, 1989;Stakhiev, 2004). There is no critical rotational speed incases where n = 0 and n = 1. In most cases the lowestcritical speed is for the nodal diameter n = 2 (Stakhiev,1989). Schajer (1986), however, reports that the modewhen the lowest critical speed is observed depends alsoon the collar diameter and sawblade outside diameterratio.The lowest critical speed may be calculated bythe following equation (Nishio and Marui, 1996; Scha-jer, 1986; Siklienka and SvoreŒ,1997; Stakhiev, 1989):nfn Kcrnmin( )=−60 02(3)where:• fn(0) Hz is the function of natural frequencyof saw blade at rest for the nodal diameter n(i.e. obtained from the impulse excitation test)fn(0) Hz funkcija je vlastite frekvencije kru-`ne pile koja miruje za broj ~vornih promjera n(dobiven iz testa impulsne pobude lista)• K is a constant independent of rotational speed.K konstanta je neovisna o frekvenciji vrtnje.Parameter K is a dimensionless value and it is cal-led centrifugal force coefficient (Nishio and Marui,1996; Schajer, 1986; Siklienka and SvoreŒ, 1997; Stak-hiev, 1989). Theoretical and experimental values of Kfor solid saw blades can be found in the reference litera-ture (Nishio and Marui, 1996; Stakhiev,1989). Unfor-tunately, there is a lack of K parameter data for somemore complex circular saws (such as saws with largernumber of slots).It should be emphasized that in the reference lite-rature (Stakhiev, 1989) data are given of f n ( )0 for most104 DRVNA INDUSTRIJA 56 (3) 103-106 (2005)Orlowski: Identification of critical speeds of clamped circular saws ...................commonly used dimensions of circular saws, which arealso the subject of the Russian Standards. Thus, criticalrotational speeds of solid circular saws may be easilydetermined.3 MATERIAL AND METHODS3. MATERIJAL I METODEExperimental determination of the critical rota-tional speed was carried out for a brand new circularsaw, delivered by the GASS Company, with the follo-wing characteristics: outside diameter D = 350 mm,hole diameter d = 30 mm, saw blade thickness s = 2.5mm, number of teeth z = 18, number of external slots 4,collar diameter A = 125 mm, clamping ratio A/D = 0.35(Figure 2a). The transverse displacements of thenon-rotating saw were measured with an eddy-currentdisplacement sensor mounted close the saw surface atthe radius close to gullets. The saw blade was excitedby hitting with a small hammer. Then, the Fourier tran-sform of the obtained signal was computed with “Ana-lizaDAQ.exe” software application.Additionally for comparison, natural frequencieswere evaluated of the solid saw of the same dimensionsas the tested saw, according to the data presented inStakhiev’s paper (Stakhiev, 1989).4 RESULTS AND DISCUSSION4. REZULTATI I DISKUSIJAThe critical rotational speeds of the examined sawwere determined by the Equation 3 based on the resultsof computed Fourier transform (Figure 2b) of the obtai-ned time signal for the saw with slots (number of slotsSL = 4). Furthermore, for the solid saw (number of slotsSL = 0) values of frequencies were taken from the Stak-hiev’s paper (Stakhiev, 1989). The mentioned speedswere calculated for the nodal diameters n = 2 and n = 3because of the value of the clamping ratio A/D = 0.35(Schajer, 1986). The constants K have values equal toK = 2.05 (n = 2 , SL = 4, (Nishio and Marui, 1996)) andK = 2.42 (n = 2 , SL = 0 (Stakhiev, 1989)), and K = 2.80(n = 3, SL = 4, (Nishio and Marui, 1996)) and K = 3.59(n = 3, SL = 0, (Stakhiev, 1989)). Additionally, permis-sible rotational speeds were calculated according toStakhiev (Stakhiev, 1989; Stakhiev, 2004):n np cr= ⋅085.min (4)The discussed results are presented in the bargraph (Figure 3).For both types of circular saw, with and withoutslots, minimum critical speeds have been observed fornodal diameter n = 3. The obtained minimum permissi-ble rotational speed np(min) = 5441 rpm (of the circularsaw with slots SL = 4) is slightly lower than the value ofrotational speed recommended by saw producers nr(vc= 100 m/s) = 5450 rpm (the latter is an example of theusual way to determine maximum rotational saw speedDRVNA INDUSTRIJA 56 (3) 103-106 (2005) 105................... Orlowski: Identification of critical speeds of clamped circular sawsa) b)Figure 2 (a) Circular saw general view and (b) Fast Fourier Transform (FFT) of the time data (Saw data: D = 350 mm,d = 30 mm, s = 2,5 mm, z = 18, SL = 4, A/D = 0,35)Slika 2. (a) Prikaz lista kru`ne pile i (b) Fast Fourierova transformacija (FFT) podataka o gibanju lista u vremenu (podaci okru`noj pili: D = 350 mm, d = 30 mm, s = 2,5 mm, z = 18, SL = 4, A/D = 0,35)Figure 3 Critical rotational speeds ncr, minimum permissiblerotational speeds np(min) and rotational speeds recommendedby saw producers nr(vc = 100 m/s)Slika 3. Kriti~ne frekvencije vrtnje ncr, minimalno dopu{tenefrekvencije vrtnje np(min.) i frekvencija vrtnje koju prepo-ru~uje proizvo|a~ kru`ne pile nr(vc =100 m/s)based on the value of maximum rim speed). It should beemphasized that inappropriate tensioning, hitting of thesaw during cutting and shrinking of the clamping ratiomay reduce the critical speed even more. Therefore,working with such a saw at the maximum rotationalspeed recommended by the producer might affect theproduct quality or, even worst, it could be dangerousfor the user.5 CONCLUSIONS5. ZAKLJU^CIBased on the results of this study following con-clusive remarks can be drawn:1. The presented methodology may be efficiently usedby producers and users for identifying permissiblerotational speeds of circular saw blades.2. Values of minimum critical rotational speeds ofsaws with external slots are lower than values of so-lid circular saws. Hence, in case of saw design withslots, the reduction in the constant K value shouldbe taken into account.3. The minimum permissible rotational speed np(min)= 5441 rpm (of the circular saw with slots SL = 4) isslightly lower than the value of the rotational speedrecommended by the saw producers nr(vc = 100m/s) = 5450 rpm.6 REFERENCES6. LITERATURA1. Chabrier P., Martin P. 1999: An overview of methods formonitoring circular saw blade preparation. Holz als Roh-und Werkstoff 57:157-163.2. Mote C.D., Szymani R. 1977: A review report on Princi-pal Development in Thin Circular Saw Vibration andControl Research. Part 1: Vibration of Circular Saws.Holz als Roh- und Werkstoff 35:189-196.3. Li L., Chao S., Baotian X. 2000: The restricting factors onthe limiting rotary speed of the circular saw. Forestry Stu-dies in China 2(2).4. Nishio S., Marui E. 1996: Effects of slots on the lateral vi-bration of a circular saw blade. Int. J. Mach. Tools Manu-fact. 36 (7): 771-787.5. Schajer G. S. 1985: Understanding saw tensioning. Holzals Roh- und Werkstoff 42, 11:425-430.6. Schajer G. S. 1986: Simple formulas for natural frequen-cies and critical speeds of circular saws. Forest Product J.36 (2): 37-43.7. Schajer G. S. 1989: Guided circular saw critical speedtheory. Proceedings of SawTech’89, Oakland, California,USA, October 2-3, 7-1 – 7-14.8. Schajer G. S. 2004: In Memoriam Dr. Yury M. Stakhiev(1934 – 2004). Wood Machining News, November/De-cember, S3.9. Siklienka M., SvoreŒ J.1997: Frekvencie vlastných tva-rov kmitov pílovych kotoú~ov pri statickom kmitaní.(Saw blade natural frequencies in conditions of static vi-brations. In Slovak). Vedecké {túdie, 10/1997/A. Tec-hnická univerzita vo Zvolene, Zvolen, p. 51.10. Stakhiev Y. M. 1989: Flat circular saws serviceability (InRussian). Forest Industry Publications, Moscow, p. 384.11. Stakhiev Y. M. 2000: Today and tomorrow circular saw-blades: Russian version. Holz als Roh- und Werkstoff 58:229-240.12. Stakhiev Y. M. 2004: Coordination of saw blade tensio-ning with rotation speed: myth or reality? Holz als Roh-und Werkstoff 62: 313-315.13. Svoreò J. 2004: Vplyv kompenza~ných dra`ok a nerov-nomerného rozstupu zubov pílového kotoú~a na hladinuhluku v procese rezania. (The influence of compensationslots and unbalance of tooth pitch of circular saw blade onnoise level in cutting process. In Slovak). Trieskové abeztrieskové obrábanie dreva ’04. Zborník predná{ok.14-16.10. Starý Smokovec. Technická univerzita vo Zvo-lene, Drev. Fakulta, Katedra Obrábania dreva, Zvolen,237-242.14. Szymani R. 1984: Using computers to design, operate andmaintain saws. World Wood, August, p. 4.Acknowledgement:Special thanks to GASS Company, Suwalki (Poland) forproviding the circular saw used in the experiment.Corresponding address:Assoc. Prof. KAZIMIERZ A. ORLOWSKI, PhD.Department of Manufacturing Engineeringand AutomationMechanical Engineering FacultyGdansk University of TechnologyNarutowicza 11/12, 80-952 Gdansk, Polande-mail: korlowskºpg.gda.pl106 DRVNA INDUSTRIJA 56 (3) 103-106 (2005)Orlowski: Identification of critical speeds of clamped circular saws ...................

Identification of critical speeds of clamped circular saws

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