BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVI (LX), Fasc. 3, 2010 SecŃia TEXTILE. PIELĂRIE APPRECIATIONS REGARDING THE ROLE OF THE CONTROL MECHANISM WITH OSCILLATING CRANK LEVER OF THE OSCILLATING DOFFER COMB IN THE CARDING PROCESS BY FLORINA-LILIANA BUZESCU* and ADRIANA MUSTAłĂ** Abstract. The paper highlights the role of the control mechanism with oscillating crank lever of the oscillating doffer comb on the quality of the fiber web obtained in the process of carding. The kinematical study carried out in the paper led to the analysis of several operating parameters of the doffer comb, given that the action of the doffer comb correlated with the speed of the doffer and the quality of the processed fibers, namely fiber length, are necessary conditions to avoid the clogging with fibers of the doffer clothing and for the delivery of a uniform-thickness sequence. The results obtained in the paper allow the dynamic study of the respective mechanism, necessary for complying with conditions of rigidity, strength and vibration amplification by increasing the productivity of the card. Key words: oscillating doffer comb, doffer, crank, and kinematic study. 1. Introduction The oscillating doffer comb plays the role of removing the fibers web from the surface of the doffer during carding, [4], [6], and [7]. There are two types of control mechanisms for oscillating doffer combs: the mechanism with oscillating crank lever and the quadrilateral mechanism [1]. In terms of technology, the crank lever mechanism is more efficient, but has the disadvantage that at high work speeds there are difficulties related to the frictions between the crank lever and the block, which means higher power consumption, rapid wear. By increasing the oscillations, there are more mechanical difficulties, increased amplitude vibrations, rapid wear of the joints, etc. The analysis of the aforementioned aspects requires a dynamic study of the control mechanism of the oscillating doffer comb, preceded by a kinematic study.
10 Florentina Liliana Buzescu and Adriana MustaŃă 2. Kinematic Parameters of Crank Lever Mechanism Elements The crank lever mechanism is shown schematically in Fig. 1, in which O1A the crank (Mn) is, OB is the swing lever (Bl), OC is a comb fastening arm CD. The movement is transmitted from the crank (Mn), which performs a continuous and uniform rotation, by the sliding block (Pc), to the swing lever (Bl), which controls the rotation of the driving shaft of the doffer comb; on the oscillating shaft approximately 5-8 arms are fastened, at the end of which the oscillating doffer comb is screwed. The crank, the swing lever on which the sliding block glides, the oscillating shaft, the fastening arms of the oscillating comb, including the frame of the doffer comb, form a system of rigid bodies [5]. Fig. 1 Crank lever mechanism.
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 3, 2010 11 Table 1 presents five constructive versions from different manufacturing companies, and the values in the table have the following meanings: r = ŌĀ, crank length, a = ŌĀ 1, the distance between the crank joints and the swing lever, R = OD, the distance from the fabric of the doffer comb to the oscillating shaft, represented by joint O, and S, the stroke of the oscillating doffer comb. Table 1 Constructive Variants for the Crank Shaft No. r, [mm] a, [mm] R, [mm] S, [mm] 1. 10 67.5 107 22 2. 9.6 61.9 105 34 3. 8 40 108 44 4. 10 60 134 45 5. 14 120 116 21 The crank (Mn) performs a motion of uniform rotation around the fixed joint O 1, with a constant revolutions per minute comprised in the interval n = (1000-1500), [rot/min], with the corresponding angular velocity ω = (π n)/30, [s -1 ], and angular acceleration zero; as the rotation angle of the crank is expressed as. θ(t) = ω 0 t, it results θ(t) = ω 0 t and θ=ω 0 and θ=0... The sliding block (Pc), assimilated with the material point A, (Fig. 1), performs a circular uniform motion; vectors v, speed and ā, acceleration, shown in Fig. 1, will have the corresponding values of this particular case of motion v = r ω 0 and a = r ω 0 2 and the following analytical expressions: (1) 0 ( ) 2 0( ) v= rω sinθ i + cosθ j a = rω cosθ i + sinθj The swing lever (Bl), which controls the rotation of the driving shaft of the doffer comb, performs a motion of oscillating motion around the fixed joint O, its position being determined by rotation angle φ, with the expression obtained from relation: (2) rsin tg ϕ= θ a + rcos θ
12 Florentina Liliana Buzescu and Adriana MustaŃă where: (3) rsinθ ϕ( θ ) = arctg a + rcos θ The kinematic parameters of the swing lever are: angular velocity, ω dϕ dϕ dθ r+ a cosθ (4) ω= = = r ω 0 =Ω( θ) ω0 dt dθ dt a + r + 2ar cosθ with dϕ r+ a cosθ (5) Ω( θ ) = = r dθ a + r + 2ar cosθ angular acceleration, ε (6) 2 d ϕ dω a(r a )sinθ ε= = = r ω =Ε( θ) ω dt dt (r + a + 2ar cos θ) 0 0 with (7) 2 d Ω( θ) d ϕ a(r a )sinθ Ε( θ ) = = = r dθ d θ (r + a + 2ar cos θ) Values Ω(θ) and E(θ) given by relations (5) and (7) allow the calculation of the angular velocity ω, respectively of the angular acceleration ε of the swing lever, respectively of the oscillating doffer comb for any value of the revolutions per minute n of the crank. The dynamic study will take into account the two components of the composed motion of the sliding block [2] represented in the paper by point A: the relative component, the rectilinear oscillatory motion on the swing lever OB, with the position vector r " in marker Ox"y", relative velocity v r, relative acceleration ā r and the transportation component, the rotation motion with the swing lever in the case of the suppression of the relative motion, with transportation velocity v and transportation acceleration ā t. The velocity and acceleration vectors are represented in Fig. 2 and have the following expressions. t
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 3, 2010 13 Fig. 2 Velocity and acceleration vectors. (8) Relative motion position vector relative velocity r = OA= x i x ( θ ) = r + a + 2arcosθ arsinθ v = xɺ i = ω i = X ( θ) ω i r + a + 2ar cosθ (9) r 0 0 relative acceleration (10) ar(1+ cos θ ) + (r + a )cosθ r = ɺɺ = ω 3/2 0 = ɺɺ θ ω0 a x i ar i x ( ) i (r + a + 2ar cos θ)
14 Florentina Liliana Buzescu and Adriana MustaŃă Transportation motion transportation velocity (11) vt =ω t r =ωx ( θ ) j =Ω( θ) ω0x ( θ ) j transportation acceleration a =ε r ω r = ω x i +ε x j t t t (12) 2 rω0 at = r(r+ a cos θ ) i + a(r a )sinθ j 3/2 (a + r + 2ar cos θ) Absolute motion absolute velocity (13) rω 0 va = vr+ vt = asinθ i + (r+ a cos θ) j a + r + 2ar cosθ absolute acceleration (14) aa = ar+ at+ ac In mathematical relation (13), which expresses the Coriolis theorem, the complementary or Coriolis acceleration has the following expression [3]: (15) ac = 2ω t vr = 2ωɺ x j 3. Variation Limits of the Number of Oscillations of the Doffer Comb The problem of the uniformity of semi-products is a major concern of spinning specialists, machine designers and manufacturers. In this regard, attention will be paid to the fact that the action of the doffer comb correlated with the velocity of the doffer and the quality of processed fibers, respectively the fiber length, are necessary conditions to avoid the clogging with fibers of the doffer clothing and for the delivery of a uniform-thickness sequence of the fibers web. The oscillating doffer comb plays the role of completely removing the fibers from the clothing of the doffer. During the technological process, the doffer comb, with an oscillatory motion, returns with the needle clothing perfectly cleaned, to the work area in interaction with the doffer with fibers. The number of oscillations of the doffer comb n op, [oscillations/min], is calculated with relation: (16) n od πdpn = S p
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 3, 2010 15 where: D p the diameter of the doffer, [mm]; n p the revolutions per minute of the doffer, [rot/min]; S the stroke of the oscillating doffer comb, [mm]. The stroke of the oscillating doffer comb is determined by relation: π (17) S= RΦ 180 where: Φ represents the amplitude of the oscillatory motion of the oscillating comb, with an equal value to the amplitude of the oscillating motion of the swing lever. The extreme values, φ max and φ min, of angle φ correspond to the positions of the swing lever OB, tangent in A and A to the circle performed by point A (Fig. 1); for exemplification, by using the constructive data corresponding to version 3 of Table 1 (r = 8 mm, a = 40 mm and R = 108 mm), the following values are obtained: φ max = 11.537º and φ min = 11.537º, thus resulting Φ = 23.074º, which means that in the considered version the stroke of the doffer comb has the value S = 44 mm. Relation (3) allows the determination of the number of oscillations comb: (18) od n r(r+ a cos θ) = n a + r + 2ar cosθ The number of oscillations comb, which is equal to the expression in relation (15), leads to the following formula for calculating the speed n of the lever (Mn): (19) π D p a + r + 2ar cosθ n= n S r(r+ a cos θ) p Determining the revolutions per minute of the crank is required by the necessity of correlating the cyclical action of the oscillating doffer comb with the speed n p of the doffer. 4. Conclusions In this work we performed a kinematic study of the control mechanism with oscillating crank lever of the oscillating doffer comb in the card, determining both the kinematic parameters of the respective mechanism and implicitly of the doffer comb, and its amplitude, stroke and number of oscillations, depending on the constructive and functional parameters of the machine. Also, in view of a possible increase in the productivity of the card, either by increasing the work velocity or by increasing the quantity of supplied fiber, which will determine a corresponding increase in the number of
16 Florentina Liliana Buzescu and Adriana MustaŃă oscillations of the doffer comb, it is necessary to conduct a dynamic study based on the results obtained in this paper, as this increase is limited by the compliance with conditions of rigidity, strength and vibration amplification of the doffer comb. Received: September 26, 2010 Gheorghe Asachi Technical University of Iaşi, *Department of Theoretical Mechanics e-mail: florina_buzescu@yahoo.com **Department of Technology and Design of Textile Products e-mail: amustata@tex.tuiasi.ro R E F E R E N C E S 1. Avram D., Filatura de lână. Cardarea, Vol. II, Edit. Performantica, Iaşi (2004). 2. Buzescu F.L., Fetecău C., Elemente de mecanică teoretică. Edit. Performantica, Iaşi (2008). 3. Buzescu F.L., Avram D., Applications de la mécanique dans la technique textile. Edit. Tehnica-Info, Chişinău (2008). 4. Cuzic-Zvonaru C., MustaŃă A., Racu C., Manolache R., Zvonaru C., Filatura de liberiene. Compendiu, Edit. BIT, Iaşi (2001). 5. Mangeron D., Irimiciuc N., Mecanica rigidelor cu aplicańii în inginerie. Edit. Tehnică, Vol. I (1978), Vol. II (1980). 6. MustaŃă A., Procese şi maşini în filatura inului, cânepei, iutei. Partea I. Edit. Performantica, Iaşi (2007). 7. Sava C., Ichim M., Filatura de bumbac. Tehnologii şi utilaje în preparańie. Edit. Performantica, Iaşi (2005). APRECIERI PRIVIND ROLUL MECANISMULUI DE COMANDĂ CU CULISĂ OSCILANTĂ A PIEPTENELUI OSCILANT DETAŞOR ÎN PROCESUL DE CARDARE (Rezumat) Lucrarea evidenńiază rolul mecanismului de comandă cu culisă oscilantă a pieptenului oscilant detaşor asupra calităńii vălului de fibre obńinut în procesul de cardare. Studiul cinematic efectuat în lucrare a condus la analiza unor parametri de funcńionare ai pieptenului detaşor, dat fiind faptul că acńiunea pieptenelui detaşor corelată cu viteza cilindrului perietor şi cu calitatea fibrelor prelucrate, respectiv cu lungimea fibrelor, reprezintă condińii necesare pentru evitarea înfundării cu fibre a garniturii perietorului şi pentru debitarea unei înşiruiri uniforme ca grosime. Rezultatele obńinute în lucrare permit efectuarea studiului dinamic al mecanismului respectiv, necesar în respectarea condińiilor de rigiditate, de rezistenńă şi de amplificare a vibrańiilor, odată cu creşterea productivităńii cardei.