Some design questions of vertical screw conveyors

Transcription

1 Soe design questions of vetical scew conveyos Soe design questions of vetical scew conveyos DR. J. EKŐ Suay Vetical scew conveyos ae hadly entioned in the hoe technical liteatue They ae vey aely applied in pactice in spite of thei any advantages. The pobable eason of it that designing vetical scew conveyos equies uch expeience and theoetical knowledge. This pesentation deals with the explanation and calculation of two ipotant paaetes of the design naely the citical angula velocity and the conveying speed. Intoduction The hoe liteatue deals with the vetical scew conveyos unduly little and they ae aely used ateials conveying equipents in spite of thei seveal advantages. Thei application advantages ae the econoy sall space need hoizontally and vetically flexible unloading possibility (the chute can be connected at any height and angle to the housing wall cicufeence) as well as the light stuctue. A dawback can be ention that the opeation of the equipent needs the pesence of fiction. Theefoe it is not ecoended fo conveying highly abasive ateials. This study deals with two ipotant opeation paaetes of vetical scew conveyos: the citical angula velocity (p) and the convey ate including thei deteination. In the theoetical investigations the otion of a single gain is analysed. It can be ade because diffeent expeients poved that the application of paticle odel esults in negligible inaccuacies and the esults can be genealised. It is especially woth to ention that the theoetical eseach veified the phenoenon that afte a shot acceleation peiod a steady-state ateial flow is evolved in the scew conveyo. The equilibiu equations of the vetical scew conveyo fo steady-state otion can be deived fo the diffeential equation descibing the actions in an abitay alignent scew conveyo of angle to the hoizontal [] by substituting =/: (/a) g sin sin (/b) (/c) (/d) g cos cos sin cos cos cos (/e) cos cossin cos cos whee convolution adius ass angle between the vecto of absolute velocity and the binoal vecto

2 Hungaian Agicultual Engineeing /999 angula velocity of elative otion fiction coefficient between the ass point and the convolution suface fiction coefficient between the ass point and the housing constaint foce on the spial cuve constaint foce on the housing wall angula velocity of the scew conveyo axis g specific gavity. It is notewothy that the above syste of equations is only foally diffeent fo those esults published in papes [] [3] [4] about conveying scew conveyos theoy. In addition equations (/c) and (/e) ae altenates athe than independent expessions. otations can be undestood fo the Fig. whee the line in angle is the iage of the evolved angle helix in plane. In the figue v k is the cicufeential velocity ( v k ) of the helix and sis the speed of the ass point elative to the helix ( s / cos) v is the absolute velocity of the ass point. S and S ae the fiction foces on the convolution suface and on the housing wall. t and b vectos ae unit vectos of tihedal coodinate syste of suface. t b v st v k S S Fig. Velocity coponents of a ass point and the syste of foces while the ass point is oving on the convolution suface Citical value of angula velocity The conditions of the elative otion occuence ae fundaental question of design. Fo the investigation the initial values ( ) v=vk and =/belonging to the stat tie (t=) ae substituted into equation syste (). Then sin=cosand cos=sinhold. Theefoe the equilibiu equations afte substitution ae g sin cos g cos sin. It can be concluded fo the fist ow that the ass point oves in the diection t only if value of the positive sign te which is popotional to the squae of angula velocity is highe than the su of the absolute value of negative sign tes.

3 Soe design questions of vetical scew conveyos 3 Afte aanging and substituting one obtains: sin cos cos sin g and utilising the =tgidentity esults in g () tg( ) kit. Hence the citical angula velocity of scew conveyo axis can be coputed if the geoety and fiction coefficient data ae available. Deteination of the citical value is essentially ipotant fo the constuction and design pactice because it poduces the inial angula velocity below which value the conditions fo the elative otion do not exist and the scew conveying is ipossible. Consequently the initial data of ust be highe than the citical value. (It is entioned that the developed foula expesses the sae as the well known citical evolution speed elationship in the liteatue.) Conveying capacity of vetical scew conveyo Fo the deteination of the capacity it is assued that the ateial flows in concentic laye along helixes which have the sae coil pitch and diffeent adii. Utilisation of this eans that one can deteine the velocity of all gains if the agnitude and the diection of the velocity of a single paticle is known. Moeove since the axial displaceent of the layes ae the sae in accodance with the assuption all the paticles oves with the sae speed axially (i.e. in diection z). In shot it is enough to deteine the vz velocity of a single paticle to copute the z diectional conveying capacity. The conveying capacity: (3) Q 3 6Av z h [t/h] whee A conveying coss section [ ] v z conveying velocity of ateial in the axial dietion of scew conveyo (/s] h bulk ass density of conveyed ateial [kg/ 3 ] loading (filling) coefficient. The coss section of scew conveyo housing is A = D /4 whee D is the noinal diaete of the scew conveyo. A csigavályúban keesztetszete: A D / 4 ahol D a szállítócsiga névleges átéője. The conveying velocity One can ecognize in Fig. that the axis of scew conveyo is pependicula to the base of slope of angle so that the conveying velocity(v z ) is the vetical coponent of absolute velocity (v) which akes angle to the binoal vecto. As a esult of the hoizontal velocity coponent the path of the ateial is a helix of /(+) coil pitch [] [3]. The conveying velocity which decisively influences the conveying ate is intepeted as the axial coponent (vz) of the absolute velocity (v). This is (4) vz s sin sin tg vagy cos

4 4 Hungaian Agicultual Engineeing /999 cos( ) (5) v z s sin sin. cos Accoding to the expessions (4) and (5) the deteination of conveying velocity needs the knowledge of elative otion angula velocity ( ) o the conveying angle which chaacteise the diection of absolute velocity (v). They ae coputed fo the algebaic equation syste () by using a nueical pocedue. On the basis of () (4) and (5) vz v z ( ) thus the conveying velocity is function of coil pitch angle the fiction coefficients and the angula velocity of scew conveyo. Due to the sophisticated iplicite elationships the coputations need copute ipleentation. The application softwae developed in ou institution was elaboated piaily in ode to copute conveying velocity. The poga uses the evolution speed (n) noinal diaete (D) fiction coefficients ( ) and the s/d ate as input data fo which the conveying angle () the angula velocity of elative otion ( ) and the conveying velocity (vz) ae coputed. In addition the softwae is applicable to ake diffeent analyses and to constuct diagas that assist the design. 9 5 Velocity of tanspot [/s] =8 =6 =3 =4 = Velocity of tanspot [/s] 5 =6 D=5 n=6 f/in n=5 f/in n=4 f/in n=3 f/in 3 n=3 f/in D=5 5 n= f/in s/d nube s/d nube Figue. The conveying speed as function of s/d ate at diffeent fiction coefficients Figue 3. The conveying speed as function of s/d ate at diffeent evolution pe inute values As exaple Figs and 3 ae shown whee the conveying velocity cuves ae depicted as functions of s/d ate. In Fig. the effect of fiction coefficient can be analysed. The place of axiu of cuves can be consideed as optial s/d ates since the highest conveying velocities and ates belong to the which can be eached in the given conditions. The cuves in Fig. 3 exhibit velocity functions fo fixed fiction coefficient (=6) and diffeent evolution pe inute values. Obviously the chaacte of cuves is the sae as those peviously (Fig. ) and as it was expected the cuves ove upwad with inceasing evolution speed i.e. thee ae highe conveying velocities at highe p values. The design cannot change usually the fiction coefficient theefoe the selection of the coil pitch angle and the popotional (coil pitch/diaete) ate the angula velocity and the popo-

5 Soe design questions of vetical scew conveyos 5 tional evolution speed ay esult in the desied conveying velocity and the conveying ate. The diagas siila to Fig. and 3 can suppot this difficult couse of decision-aking. It is notewothy that the esults do not give a good account of the cuent design pactice. It is well known that the design enginees choose the s/d ate aound which coesponds nea coputed optiu values at quite low otation speed values (... p). Refeences [] EKŐ J.: Paticle odel fo desciption of opeation of scew conveyos. ulletin of the Univesity of Agicultual Sciences Volue Gödöllő [] ÉLAFALI J.: Függőleges szállítócsigák. A+CS 7. évf. 6. sz. 98. [3] Ö'TTCHER S - GALER H.: Untesuchungen zu Antiebsleistungs-beechnung senkechte Schnecken -föden Föden und Heben (6). [4] RADEMACHER F. J.: On the Chaacteistics of vetical scew conveyos fo fee flowing bulk ateial. VDI-Foschungsheft 59 VDI-Velag Düsseldof 979. [5] THÜSIG H. - FIK M.: Die Födeschnecke als stetige Senkechtfödee fü Schüttund Stückgut. Föden und Heben 958. (5). [6] VIERLIG A - EPHREMIDIS CH.: Untesuchungen zu Födevogang bein waageechten Senkechtfödee. Föden und Heben 7. k (9). Publikálva: Hungaian Agicultual Engineeing /999