RESEARCHES REGARDING THE RELATION FORCES DEFORMATIONS ON EXTENSIBLE ELASTIC DIAPHRAGM CHUCK WITH JAWS

Transcription

1 FASCICLE V, TECHNOLOGIES IN MCHINE BUILDING ISSN , 009 RESEARCHES REGARDING THE RELATION FORCES DEFORMATIONS ON EXTENSIBLE ELASTIC DIAPHRAGM CHUCK WITH JAWS Dragoş Florin Chitariu, Nicolae Seghedin, Nicolae Gherghel Gheorghe Asachi Technical University Iasi, Roania eail: ABSTRACT The paper presents an analysis, o plane stress and deoration, o elastic diaphrags that are used on elastic diaphrag chuck with jaws. A coparison, o induced stress and deorations, study was ade by using the relations ro dierent sources. In consideration o relations that describe induced stress and deoration on plan, circular, ebedded, plate, loaded with a concentrated orce and current knowledge regarding jaws, elastic, ebrane, echaniss. For the veriication o the results obtained, was used the Finite Eleent Method. The result obtained by using the inite eleent analysis, led on the conclusion that, the values or axiu stress calculated by using the atheatical odel or Fixtures are closer than the results obtained or odel KEYWORDS: ixtures, elastic diaphrag with jaws, stress, deoration. 1. THE OBJECTIVE OF THE PAPER The objective o the paper is the deterination o axiu stress and deoration that is eerging in the interior o the diaphrag, ro the structure o elastic diaphrag chuck with jaws, results o elastic deorations during the centering and gripping under the action o the acting orce.. GENERAL CONSIDERATIONS ON EXTENSIBLE ELASTIC DIAPHRAGM CHUCK WITH JAWS Fixtures can be deined as auxiliary coponents o technological systes, having the role o orienting and positioning o parts, tools, gauges, etc., in accordance with the requireents o cutting, inspection, assebly etc, and to aintain (preserve) this orientation in tie [], [9], [10]. Fixtures used in achinery construction can be deined as auxiliary coponents (eleents, links) o the technological systes, having the unctions, (role, purpose, destination), o orienting and positioning o parts (sei inished articles, asseblies, cutting tools, gauges), in accordance with the requireents o 405 cutting, inspection,assebly, and to ix it in order to aintain (preserve, conserve) this speciic position, used in achinery construction [], [9], [10]. Extensible elastic diaphrag devices or positioning and ixing are characterized by the existence, in the construction, o an elastic diaphrag, in which are ebedded a series o jaws, radial disposed. The jaws can eectuate the centering on short interior suaces (bolts, rods), or short exterior suaces (chucks). The centering and ixing is done by the elastic deoration o the diaphrag. The aterial and heat treatent used is the as in the case o springs. Fixtures, which contain this type o devices, are used or centering achined parts with tight tolerance, on inishing operation, where the stress is low. It has a siple construction and can be operated anually or echanized. Correctly anuactures and exploited, precision o 0.01 can be achieved [4]. Fixing orces S are realized in the absence o the acting orce Q, due to the reanent stress inside the diaphrag. In the case o the adjustable chucks, screws allow the adjustent o the device or various diaeters o the claping suaces and also allow the reodel o the centering precision by grinding, in case o wear. Copared to the centering and ixing echaniss with radial sliding jaws ovedthrough a channel provided with disk-shaped Arhiede spiral (universal

2 FASCICLE V three jaws chucks), the elastic diaphrag chuck presents a nuber o advantages, naely: centering and ixing accuracy, because o the higher nubers o centering eleents, reduced ties or claping (centering and ixing) and detaching (reoval and weakening) o the parts, constructive siplicity, easy to echanize, easy and convenient service [3]. Disadvantages, o the elastic diaphrag chucks, copared to the universal three jaws chucks are: the need or previous adjustents o the centering and claping eleents, the possibility o appearance o plastic strains o the ebrane, the construction o centering and claping eleents with screws, deterines the aendent o the initial adjustents because o the gae thread (which is increasing as use) [14]. 3. WORK METHODOLOGY For the achieveent o the objective the next ethodology was used: Identiication o bibliographical sources or Material strength and Fixtures doain and connected doains. Identiication and analyze o stress calculus relation ro Material strength regarding induced stress and deoration o plan, circular plane. Identiication and analyze o calculus relation ro Fixtures bibliography. Identiication and analyze o calculus odalities regarding stress and deoration o elastic diaphrag using inite eleent analysis. Coparative analysis, or a certain variant o echanis o centering and gripping, o induced stress and deoration by using calculus relation ro Material strength, Fixtures, inite eleent ethod. Forulating the conclusions. 4. CONDITIONS FOR RESEARCH A diaphrag with adjustable (Fig. 1.) jaws was investigated with the ollowing paraeter, ro the endowent, o Fixtures laboratory ro The Gheorghe Asachi Technical University o Iasi: r = 30 ; r = 95 ; r t = 16 ; a =,5 ; g = 5,5 ; n = 1; d p = r p = 30 ; T dp = 0,0 ; J in = 0,0. It was considered a orce or ixing the part S = 100 dan. Fig. 1. The operating principle o elastic diaphrag devices or positioning and ixing with jaws [19] 5. DETERMINATION OF THE DEFORMATION AND STRESS IN ELASTIC DIAPHRAGM BASED ON KNOWN CALCULATION RELATION 5.1. Relation between orces and deorations Matheatical odels or deterining the strains and tensions ro the literature o Material resistance Matheatical odel or deterining the strains and stresses that occur during deoration o elastic ebranes, because the driving orce, is described in the literature o Fixture. The source o these relations is the literature or Material resistance. Fro the Resistance o aterials Material resistance point o view, elastic ebranes are considered plane, circular, thin, ebedded plates, on which concentrated orces are applied through acting rods [1]. Plates, unlike bars, have two diensions length and width relatively high copared with the third thickness. Many coponents o achines or buildings have eleents in the or o plates, lat or curved, pistons, cylinders, tanks o various shapes, valves, pipes, loor, roo, etc. o various types [14]. The study o plates is ore coplicated than the bars and it is done in the Theory o elasticity. Geoetric eleents that characterize a plate are: the shape and size o the edian area and the width, easured perpendicular to the edian suace. The edian suace divides the plate in to two equal parts, in any section. Ater the area o edian section plates are divided into two ajor groups: lat plates and curved plates or coverings [14]. In ters o echanics, the plates resist any eorts. Very thin plates, which cannot only retrieve stretching eorts, wear the nae o diaphrags. Following the deoration o the plate, the edian area, takes o curve shape. The deoration ω o the plate, 406

3 FASCICLE V THE ANNALS OF DUNAREA DE JOS UNIVERSITY OF GALATI copared to the initial edian plane, is considered sall copared to plate thickness [1]. Ater the edian area, lat plates can be circular, rectangular, elliptical or other shapes. Plates which syetry can be lean and loaded syetrically which sipliies uch the calculations. Equations o strains or the axiu deoration in the ebrane ω, and angle o the jaw opening o φ are [1, 14]: Qr r Q = ln + 8πD r 16πD ( r r ) ω []; (1) Qr r Qr r ln = ln 8πD 4πD ϕ = [rad], () where the acting orce Q results: Q = [dan], (3) ln r Q the orce necessary or acting the diaphrag dan; r radius o the circle layout o jaws, ; r ebrane radius, easured ro its center to the restraint point, ; ϕ angle o the jaw opening, rad, which can be deterined by the relationship: ϕ = ϕ 1 + ϕ + ϕ 3 [rad], (4) ϕ 1 angle that ensures the achieveent o the necessary ixing orce due to elastic deoration ebrane: (1 [rad], (5) M speciic oent evenly distributed dan/; μ Poisson's coeicient or the ebrane aterial ; D cylindrical ebrane rigidity, which can be deterined by the relationship: 3 Eg D = [dan/ ], (6) 1(1 + μ ) E odulus o elasticity, noral o aterial diaphrag dan/ ; ϕ additional angle o the jaws opening, which takes into account the tolerances δ o the part in diaeter, which can be deterined by the relationship: T dp ϕ = [rad]. (7) a ϕ 3 additional angle o the jaws opening which takes into account the diaetral plays J in, necessary or the ree introduction and reoval o the part, which can be deterined by the relationship: J in ϕ 3 = [rad], (8) a where a length o the jaws. Maxiu stress inside the diaphrag is deterined by the ollowing relationship: Q(1 r σ ax = (0.485 ln + 0.5) [dan/ ], (9) g where g thickness o ebrane,. Maxiu displaceent inside the diaphrag is deterined by the ollowing relationship: Qr ω ax = []. (10) 16πD Matheatical odel or deterining the strains and tensions in the literature o Fixtures Speciic relationships ro Fixtures literature consider the acting orce or the diaphrag deoration ro the elastic diaphrag chuck the claping orce developed by the elastic diaphrag. The acting orce Q necessary to open the jaws on elastic extensible diaphrag devices or positing and ixing the part can be deterined by the relationship [3, 1, 19]: Q = 1 [dan]. (11) 3r ln r The equation or deterining the angle that ensures the achieveent o the necessary ixing orce due to elastic deoration ebrane, is: CMr CSar s = = [rad]; (1) D(1 πd(1 where C coeicient o proportionality depending o the ratio r r / s presented in table 1. The equation or axiu stress deterined by the action o the acting orce given the previous notation, is: 3Q(1 r σ ax = (ln + ) [dan/]. (13) πg r 4r 407

4 FASCICLE V Table 1. Coeicient o proportionality depending on the r / r [19] r r s 1,5 1,5 1,75 C 0,8 0,675 0,590 0,560 r r,5,5,75 3 C 0,555 0,565 0,575 0,585 Maxiu displaceent is deterined by the ollowing relationship: ωax = atgϕ []. (14) The analysis o knowledge and in particular the relations or available bibliographical sources, or Material resistance and Fixtures led on the conclusion that there are a series o dierences between the atheatical odel or deterination o orces, deorations and stress, dierences, naely the introduction o additional actor 1/3, in the orula or calculating the acting orce Q. Regarding the orula or calculating the angle o the jaw opening ϕ 1 presented in literature or Devices, it contains an additional coeicient o proportionality C. These coeicients take into account the shape o the elastic ebranes with jaws ro the structure o extensible, centering and ixing echaniss, that substantially diers to lat plates treated in the literature o Material resistance Calculation orulas or deterining axiu stress are copletely dierent. odel structure is in act, nuerical calculation veriication [11]. Thus, or a given deined diensional geoetry or a given loading and support conditions well speciied (restrictions), the results obtained are strains, tensions, reactions in supports and requencies. A coparison or the calculated values o stress and deoration was ade using, the inite eleent analysis odule Cosos Works ro Solid Works 007 coputer aid design sotware. In the irst step, the diaphrag was the odelled and the appropriate aterial was selected. To ipleent the inite eleent analysis, restrictions were applied on the outlines o the ebrane and a deoration orce applied in the center ebrane. By applying deoration orces, were calculated the axiu stress and axiu travel o the ebrane. 5.. Calculation o the acting orces, stresses and displaceent Given the atheatical odel presented or literature o Material resistance and Fixtures, the values or the orces, tensions, and displaceent were deterined, as shown in table. In Fig. and Fig. 3 are presented axiu displaceent on elastic diaphrag with jaws, axiu stress and stress distribution on elastic diaphrag with jaws, deterined with inite eleent analysis Analysis o deoration and tensions using inite eleents ethod Finite eleents ethod (FEM Finite Eleent Method) is one o the best existing ethods or achieving the various calculations and siulations in engineering. This ethod, and, o course, progras that incorporate it, becae a basic coponent o odern coputer-aided design [11]. In general, engineering, and particularly in the construction o achinery, equipent and installations, the basic coponent o a syste, the resistance structure, is analysed by FEM, deined as a group having a echanical unction very clearly established, such as taking o load, providing a certain unctionality or oveents between soe subasseblies, ensuring static/ dynaic stability and guaranteed rigidity iposed by the designer, etc. It should be noted that in the sequence: CAD FEM CAM exists an iterative process o design calculation peorance in this process is carried out successively, operations suary and analysis o prototype and odel or inite eleent calculation. At each iteration, o the process, iproveents are ade to the prototype or odel o coputation, to achieve desired peorance. Finite eleent analysis o a 408 Fig.. Maxiu displaceent on elastic diaphrag with jaws Fig. 3. Maxiu stress and stress distribution on elastic diaphrag with jaws

5 FASCICLE V THE ANNALS OF DUNAREA DE JOS UNIVERSITY OF GALATI Table. Calculated value or acting orce, stress, displaceent Paraeter Angle o jaw opening φ 1 [rad] Additional angle o the jaws opening, which takes into account the tolerances T dp o the part, φ [rad] Additional angle o the jaws opening which takes into account the diaetral plays, φ 3 [rad] Angle o jaw opening φ [rad] According to the literature Material resistance [1, 14] According to the literature o Fixtures [3, 1, 19] Relations Values Relations Value Mr Sar = = 0,00086 D(1 πd(1 T dp ϕ = a CMr CSa = = 0,0005 D(1 πd(1 T dp ϕ = a ϕ J in 3 = a ϕ J 3 = in a = + ϕ ϕ3 0,00174 ϕ + ϕ + ϕ3 ϕ + = 0,00139 Acting orce Q [dan] Q = r r ln r 03,75 Q = 3r ln r 53,97 Maxiu stress σ ax [dan/ ] σ Q(1 r = (0.485 ln g r ax + 0.5) 3Q(1 r r 9,41 σ ax = (ln + ) 1,96 πg r 4r Maxiu displaceent ω ax [] Qr ω ax = 0,11 ω tgϕ 16πD = a ax 0,031 Values deterined using the ethod o inite eleents Maxiu stress [dan/ ] The value o axiu stress deterined by applying a orce o [dan] 1,3 The value o axiu stress deterined by applying a orce o [dan] 0,359 Maxiu displaceent [] The value o axiu displaceent deterined by applying a orce o [dan] 0,008 The value o axiu displaceent deterined by applying a orce o [dan] 0,

6 FASCICLE V The value calculated using atheatical odel ro Fixture literature or opening angle o the jaw are lower than values calculated by using atheatical odel ro Material resistance because o the presence o a coeicient o proportionality C. The values or the acting orce calculated by using the orula ro Fixtures, is lower by 3,7 ties than the value calculated by using the orula ro Material resistance, because o the additional actor. Regarding the axiu stress value σ ax calculated according to the Fixtures literature, is 4,8 ties less than the axiu stress value calculated with the odel ro the literature o Material resistance, due to dierent values in ters o the acting orce and the dierence on the structure o the orulas. The value or the axiu displaceent calculated using the atheatical odel ro Material resistance is 7, tie greater than the value deterined by inite eleent analysis, the value or displaceent calculated using the atheatical odel ro Material resistance is 39, ties greater, than the value deterined by inite eleent analysis. The value or the axiu displaceent calculated using the atheatical odel ro Fixtures is 5,4 tie greater than the value deterined by inite eleent analysis, the value or displaceent calculated using the atheatical odel ro Fixtures is 40 ties greater than the value deterined by inite eleent analysis. 6. CONCLUSIONS The atheatical odel or deterining the orce, stress and displaceent presented in Fixtures literature is adjusted by introducing correction actors or reducing the degree o generality o these orulas, this results in reduced values or displaceent and stress, so constructive particularities o the diaphrag are taken into account. Literature or Fixtures does not present the reasoning o introducing these additional coeicients in these orulas. The result obtained by using the inite eleent analysis, led on the conclusion that, the values or axiu stress calculated by using the atheatical odel presented Fixtures literature are closer than the results obtained or odel described in Material resistance literature. The experient is the only one that can show with certainty which o the odels is closest to reality and the only one that can validate the presented results. REFERENCES [1] Buzdugan Gh., Rezistenţa aterialelor, Ed Acadeiei, Bucureşti, 1986, pag ; [] Gherghel N., Construcţia şi exploatarea dispozitivelor, vol. 1, Institutul Politehnic, Iaşi, 1981, pag. 4; [3] Gherghel N., Construcţia şi exploatarea dispozitivelor, vol., Institutul Politehnic, Iaşi, 1981; pag [4] Gherghel N., Gheorghe C., Mandrină cu ebrană elastică. Brevet de invenţie RO, nr / ; [5] Gherghel N., Îndruar de proiectare a dispozitivelor, vol.. Elaborarea scheelor optie de orientare în dispozitive. Institutul Politehnic, Iaşi, 199, pag. 76; 89 9; 93 96; ; 394; ; ; [6] Gherghel N., Îndruar de proiectare a dispozitivelor, vol. 3. Proiectarea eleentelor de orientare şi de orientare-strângere ale dispozitivelor. Institutul Politehnic, Iaşi, 199, pag. 6 13; 65 69; ; [7] Gherghel N., Hanganu A., Consideraţii privind etodologia de sinteză şi proiectare a andrinelor cu ebrane elastice. Ses. de co. şt. Concepte, tehnol. şi anage. în constr. de aş, secţ. 6. Aşch., sc. aşch., dispoz. şi veri., Iaşi, 3 ai 199, pag ; [8] Gherghel N., Seghedin N., Hanganu A., Proiectarea asistată de calculator a andrinelor cu ebrane elastice. Prograul PADA 11. Ses. de co. şt. Concepte, tehnol. şi anage. în constr. de aş, secţ. 6. Aşch., sc. aşch., dispoz. şi veri., Iaşi, 3 ai 199, pag. 1 19; [9] Gherghel N., Seghedin N., Proiectarea reazeelor dispozitivelor tehnologice, Ed. Tehnopress, Iaşi, 00, pag. 3 39; 78 84; ; ; 45 53; 74 99; ; ; ; ; ; [10] Gherghel N., Seghedin N., Concepţia şi proiectarea reazeelor dispozitivelor tehnologice, Ed. Tehnopress, Iaşi, 006, pag. 1 37; 77 84; ; ; 319; 333; ; 378; 49; 464; ; [11] Ghinea I.-G., Proiectare asistată în CATIA V5. Eleente teoretice şi aplicaţii, Ed. Bren, Bucureşti, 007, pag ; [1] Gojineţchi N., Îndruar pentru lucrări de laborator la construcţia şi exploatarea dispozitivelor, Institutul Politehnic, Iaşi, 1981, pag. 41 5; [13] Gojineţchi N., Gherghel N., Proiectarea dispozitivelor, vol. 1, Institutul Politehnic, Iaşi, 1983, pag ; [14] Mocanu D. R., Rezistenţa aterialelor, Ed. Tehnică, Bucureşti, 1980, pag ; [15] Stănescu I., Tache V., Dispozitive pentru aşini unelte. Proiectare, construcţie, Ed. Tehnică, Bucureşti, 1979, pag. 49; [16] Tache V., Ungureanu I., Brăgaru A., Gojineţchi N., Gherghel N., Marinescu I., Şuteu V., Druţu S., Construcţia şi exploatarea dispozitivelor, Editura Didactică şi Pedagogică, Bucureşti, 198, pag. 144; [17] Tache V., Ungureanu I., Stroe C., Eleente de proiectare a dispozitivelor pentru aşini-unelte. Bucureşti: Ed. tehn., 1985; [18] Tache V., Ungureanu I., Stroe C. Proiectarea dispozitivelor pentru aşini-unelte. Bucureşti: Ed. tehn., 1995; [19] Vasii-Roşculeţ S., Gojineţchi N., Gherghel N., Andronic C., Şelariu M., Proiectarea dispozitivelor, Editura Didactică şi Pedagogică, Bucureşti, 198, pag. 7 8; [0] *** Cosos Works Designer 008 Training Manual, pag