Analysis of Belting Stiffness Transmission Impact on Rotating Mass Motion Law of Technological Machines

Transcription

1 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP. 5-0 Fist online: Apil 06 Analysis of Belting Stiffness Tansission Ipat on Rotating Mass Motion Law of Tehnologial Mahines D.A. Maatova, Shangyong Zhang *, A. Djuaev, M.A. Mansuova,, Theoetial an Applie Mehanis epatent, Tashkent Institute of Textile an Light Inusty, 5 Shohjohon st., Yakkasaay Distit, Tashkent, 0000, zbekistan Shool of Textile Siene an Engineeing, Wuhan Textile nivesity, No. Yangguang Roa, iangxia Distit, Wuhan, 000, hina * shangyong.zhang@wtu.eu.n Abstat-The ais of this eseah ae to evelop a new shee of belt tansission with an integal iven pulley an tensioning olle as well as to eteine the laws of otion fo the ain an botto shafts of the sewing ahine as they epen on the igiity of the elasti eleents of the iven belt pulley with justifiation of settings. The atile esibes a new iaga of a belt ive with a split iven pulley an eenti tension olle. The laws of the ive asses otion of the sewing ahine wee obtaine an analyze. Keywos- Belt Dive; Split Pulley; Tosion; Sewing Mahine; Rigiity; Toque I. INTRODTION Sewing-ahines have vaious estinations an ae poue in a nube of lasses. The ajoity of sewing-ahines have a ive in whih the otay otion fo the eleti oto is tansfee by a belt ive, an otion fo the ain shaft to the botto shaft is tansfee by a toothe belt ive (Fig. ) with the tansfe elation equal to. Suh ehaniss as the slie, thea take up, an wine eeive thei otion fo the ain shaft. The shuttle an tansfe ehanis obtain thei otion though the botto shaft. The toque oveent both on the ain an botto shafts have a opliate haate ue to the vaiability of ipats fo the oesponing ahines ehaniss. The poble ous espeially uing poessing of thik fabis. The iven belt usually expeienes geat shoks at stithing of lothing with high ensities. Diffeent types of belts with vaious values of stiffness as well as the ive of the ain shaft, Fig., have been esigne by ahine builing plants in eent yeas. Fig. Geneal view of the sewing ahine ive, -oto, -pulley, -belt, -iven oposite pulley, 5-tension pulley, 6-ain shaft, 7-ive pulley, 8-iven oposite pulley, 9-botto shaft, 0-toothe belt It is known that the iving belts tansfe tosion toque in the ives of ost tehnologial ahines an soe sewing ahines []. The belt tansission evens the flutuations of the otational oveent an the angula veloity uing the unning poess. Vaiation of spee an tosion toque on the shaft of the iven pulley will inease at high flutuations of tehnologial loas []. To eue the aplitue of these osillations, we eoen a new esign of a belt tansission []. Flutuations in the otational oents, M, an angula veloities,, of the woking shafts aise beause of the hangeable i tehnologial loas, as well as the vaiability of the inetial foes. This ay lea to stithing slips an alfuntions in looping togethe with inease thea beakage. Theefoe, we eoen using ou esign in the ive of the sewing ahine. II. ANALYTIAL METHOD A etho of ass eution was aopte to esign the shee, an Lagange s equations of the seon oe wee use to i - 5 -

2 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP. 5-0 analyse the syste of iffeential equations. In the seies of tehnologial ahines opeating une lage spee oes, sewing ahines in patiula, the loa vaiations shok absoption by the ive belt is not suffiient. We eoen belt ives, with split iven pulleys, with spinging eleents, whih allows onsieable eeasing of the loa vaiations peak values of the ain an botto shafts an sewing ahine s eleti ive shaft (Fig. ). The ive shaft (), though the belt (), ipats the otation to the iven pulley (), whih esults in otation of the tension olle (). The otational otion fo the i (5) though the ing-type sping bush (7) is ipate to the hub (6), whih is igily onnete to the iven pulley s shaft (). The iven pulley s shaft () is onnete to the ain shaft of the sewing ahine (not shown on the figue). Fig. Belt ive with split iven pulley an sping tension olle At the pefoane of the tehnologial poess on the sewing ahine by the ain shaft, the loa on the iven pulley s shaft () is hange. These vaiations in the oent of esistane ae tansitte to the i (5) though the ing-type sping bush (7) an, futhe, though the ive pulley () an to the eleti ive. Thus, the ing-type sping bush (7) absobs the peak values of the oent of esistane (loa). By hoosing the neessay sping-issipative popeties (ubbe ateial), it is possible to anage the extent of absoption in the peak loa values. Thus, the otation of the i (5) of the iven pulley () is suffiiently soothe out. onsie the shee on Fig., whih uses the eoene belt ive. Fig. The ynai oel of the sewing ahine s ive. I the ass of the eleti oto s oto with the ive pulley, II the pulley i s ass, III the ass of pulley hub with the ain shaft 6 with asses of segents of the neele ehanis an take up an ive pulley 7, IV the ass of the iven pulley s i 8, V the ass of the pulley hub 8 with the botto shaft an segents in the elevant sewing ahine s ehaniss At pattening of the ynai an atheatial otion oels of the sewing ahine s ehaniss, the given inetia oents of the ain an botto shaft wee taken as onstant, though they an vay in sall values on the segents of sewing ahine s toggle ehaniss []. The tension olle with a spinging eleent was use in the belt ive, fo the eleti oto to the ain shaft. Suh esign allows, to soe egee, a eease of the osillations of toques an spees on the oto oto s shaft. At the sae tie, taking into aount the tension olle s spinging eleent of the belt ive an hanging loas, the tansission atio of the ass is hange. The atio,,, between the angula spees of the sewing ahine s ive asses, i, will be: i j, ;, 0, ;, 0, ;, 0,5 5 () Fo the given equations in () is seen that only, has a vaiable value. The othe tansission atios, to soe egee, have thei ean values equal to one. The eleti oto, in the atheatial oel of the ive, was taken into aount as the ynai ehanial haateisti aoing to [, 5]. Applying the Lagange equations [6, 7] the equations of otion fo the sewing ahine s ive wee obtaine with onsieation of the toque oent, M, itial toque oent, M, on the oto, itial sliing value, S, an itial angula veloity, : M t M () SсM 0 t 0-6 -

3 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP Moent of inetia fo the fist ehanis of the sewing ahine onsies the oent of inetia, ot, of the oto an the oent of inetia, pul, of the ive pulley, as well as thei igiity,, issipation of the belt,, an the hange in the angle,,, of thei otation. t atg atg t atg atg atg atg M t p u l o t sin () The oent of inetia, 0,, fo the i of the iven pulley of the sewing ahine is esibe by the following equation.,0 atg atg t atg atg sin atg t t atg atg t atg atg t,, () The oent of inetia fo the thi ehanis of the sewing ahine takes into aount the oent of inetia, n, of the neele ehanis, the oent of inetia, s, of the ain shaft, the oent of inetia, h, of the iven pulley s hub, the oent of inetia, t, of the thea take up ehanis, an the oent of inetia, s, of the ive shaft of the toothe belt ive. (5) The oent of inetia, 0,, of the iven pulley s i in the toothe belt ive onsies its igiity,. t t t t t 5,5 5,5,,,,,0 (6) sin,,,,,,, s t n h s M t t t t t

4 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP. 5-0 The oent of inetia fo the fifth ehanis of the sewing ahine takes into aount the oent of inetia, 5sh, of the shuttle ehanis, the oent of inetia, 5pb, of the push ba ehanis, the oent of inetia, 5h, of the iven pulley s hub in the toothe belt ive, the oent of inetia, 5bs, of the botto shaft, an the oent of inetia, 5t, of the tansfe ehanis sh 5 pb 5h 5bs 5t,5,55,5,5 M 5 t (7) t t III. ALLATION RESLTS The solution of the poble was ae une the following values of the ive paaetes, taking into aount the oto powe apaity, N, voltage, v, uent fequeny, f, angula spee of the oto s oto, ω, otational spee of the oto s oto, n, otational spee of iven pulley, n, the noinal toque oent, M n, the itial toque oent, M, itial sliing, S,, an the oent of the oto inetia ot. The alulate oents of inetia fo iffeent ehaniss, in kg, ae given below. 5 pul ; ot pul 0.0 ; 0.00 ; 0. 0 ; 0.0 ; ; 0.0 ; 0.90 ; 0.90 ; 0.80 ; 0.0 ; 0.0 ; 0.0 ; s s 0.50 ; 0.60 ; 5bs 5 5 pb h 5sh ; s sh 5pb 5h 5bs 5t h n t s t 5h n 5t IV. EXPERIMENT In geneal, we wee inteeste in eseah on hanges in the sping (ubbe) bushes igiity of the iven pulleys in the sewing ahine s belt ives. The inease igiities of the iven pulleys sping bushes allow soe eeasing of the osillation aplitue of angula spees an loas on the ive shafts. The igiity fatos, i, wee obtaine with espet to the aius an elastiity of the segents in the ehaniss. =60 N/a; =60 N/a; =60 N/a; =60 N/a; Dissipation of the belts, i, was eteine with espet to the s setional aea of the belt an its length. = 5. Ns/a; = 6. Ns/a; = 5. Ns/a; = 6.0 Ns/a. The atio between the pats of the ive an the itial toque oent fo the an 5 oponents ae given by the following values., =.75;, =.0;, =.0;,5 =.0. M 0.75sin t ( )N; M 0.sin 5t ( )N. 5 The solution was alulate taking into aount the following initial onitions at t=0. 0; 0; M.N; M M n 5 The onsieable eease of igiity in the sping bushes pulleys esults in an inease of the osillation aplitue of angula spees an loas on the shafts. The gaphi egulaities of the angula spee s hange an the flutuations of aeleation an toque on the sewing ahine botto shaft ae pesente in Fig.. Fig. a, b, Regulaities in the hange of the angula spee, angula aeleation an toque une igiity vaiation atio fo the split iven pulley s sping - 8 -

5 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP. 5-0 bush of the toothe belt ive in the sewing ahine Fig. 5 a an b show the elationships between hanges to the osillation aplitue in spee, aeleation an toques fo the botto an ain shafts une an inease of igiity of the pulleys sping bushes. Fig. 5 The gaphi elations of the osillation aplitue s hange of angula spee, aeleation, an toque on the botto (a) an ain (b) shafts fo the hange of the igiity atios of the iven pulley s sping bushes in the sewing ahine s belt ives, the hange egulaities of toque s ean values, on the sewing ahine s botto an ain shafts, fo the hange of iula igiity atios of the belt ives sping bushes () Aoingly, the inease of igiity of the iven pulley s sping bush, whih aeleates the belt ive, esults in a eease of the osillation aplitue of spee, aeleation, an toque on the sewing ahine s ain shaft as well. The figues show that an inease of fo 50N/a to 0 N/a esults in eeases of the angula spee s aplitue of the botto shaft fo 8 s - to 5 s -, the angula aeleation s aplitue fo 05 s - to s -, an the toque s aplitue on the botto shaft fo 0. N to 0.05 N. It shoul be note that aplitues of Δ, Δ an ΔM, as ineases, has non-linea featues too, but iffes in the values, though the ean angula spee of both the botto an ain shaft is the sae. Thus, with an inease of fo 50 N/a to 705 N/a, the angula spee s aplitue eeases fo 5 s - to 8 s -, the angula aeleation s aplitue eeases fo 0 s - to s -, an ΔM eeases fo 0, 76 N to 0, 05 N. This is explaine by the fat that the ain shaft akes opliate oveents as well as, atually, all opeating tehnologial loas, inluing the esistanes at otion an elivey of the botto thea. Fo osillation aplitues less than = s -, the eoene values of the igiities fo the iven pulleys sping bushes of the = s - an Δ 5 Δ sewing ahine s belt ives ae = 95-5 N/a an = N/a. A futhe inease in the atios of igiity an esults in an inease of the ean loa values, whih is not esiable. At the sae tie, the ean value of M 5 ineases fo N, an M eeases fo N (see iagas an on Fig. 5). The eseah, une the hange of the belt ives paaetes (,,, ), shows that with an inease of an, the syste tansient tie in the poess ineases onsieably, an the loa on the sewing ahine s ive shafts ineases up to - 9 -

6 ounal of Mahiney Manufatuing an Autoation 06, Vol. 5 Iss., PP %. This is explaine by the fat that the syste opeates (shafts otation) une vaying loas an osillations in the angula spees une whih the absoption enegy in the syste s sping eleents is peulia. Besies that, the signifiant inease of an is onsiee unesiable at the high otational spees of the ain an botto shafts of the sewing ahine, as it an esult in quik failue of the ive belts (enlage belt efoation yle). Howeve, eeasing of the ive belts iula igiities up to 0-0 N/a esults in an inease of the ives sliing along the ive pulleys. Theefoe, the eoene paaete values of the sewing ahine s belt ives ae = 80-0N/a, = 0-60 N/a, = Ns/a, = Ns/a. V. ONLSION The egulaities in the otation of the ain an botto shafts of the sewing ahine wee obtaine uing this eseah by the eteination of the values fo eoene paaetes in the ive esign. Moents of inetia fo the iffeent asses of the syste have been efine with onsieation of the fatos of stiffness fo the elasti belt tensioning olle an elasti (ubbe) bush in the ive pulley fo the belt tansission. Intenal fition fatos wee taken into aount at iula efoations of the hub in the ive pulley an the elasti belt tansission. The aiuses fo the ive an the iven pulleys have been also obseve in this stuy, as well as the shifting of the tensioning olle axis ue to the efoation of the elasti bush. In aition, a new shee with the split belt iven pulley an tensioning olle was evelope to oenize the sewing ahine s ive. The ipat of the igi-issipative paaetes in belt ives on the evie s otion oe was stuie. The elationships in the hange of the sewing ahine s ain an botto shafts loa aoing to the hange of the belt ives igiity wee also obtaine. The eoene igiity values of the paaetes in the belt ives wee establishe to be: = (.9.) 0 N/a, = (..6) 0 N/a, = ( ) 0 Ns/a, = ( ) 0 Ns/a. REFERENES [] I.I. Voobyov, Belt Tansission, M. Engineeing, E. Mosow, Russia, pp. 68, 979. [] A. uaev, R. Maksuov, D. Maatova, S. Èlonov, I. uaev, an M. Muinov, Belt tansission, zbekistan Patent FAP0065, 8, 0. [] I.S. Pinhuk, Tansient poesses in the inution otos une the altenate loa, Eletiity, Mosow, vol. 9, pp. 7-0, 957. [] A. uaev, V.M. Tualiev, an R.Kh. Maksuov, Кineati an ynai analysis of belt tansissions with vaiable gea atio, Monogaph, E. Tashkent, zbekistan: Fan vatexnologiya, pp. 60, 0. [5] S.D. Baubekov, et., Dynais of ahines an ehaniss, E. Alaty, Kazakhstan, Eveo, pp. 00, 0. [6] I.I Atobolevskiy, Theoy of ehaniss an ahines, I.I. Atobolevskiy Publishing House of Siene, Eition of atheatial physis liteatue, E. Mosow, Russia, pp. 68, 975. [7] A. uaev, et., Theoy of ehaniss an ahines, E. Tashkent, zbekistan, pp. 59,