TOOL WEAR AND ITS COMPENSATION IN SCREW ROTOR MANUFACTURING

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1 TOOL WEAR AND ITS COMPENSATION IN SCREW ROTOR MANUFACTURING Professor N. Sosic Cair i Posiive Displaceme Compressor Tecology Ciy Uiversiy, Lodo, EC1V 0HB, U.K. .sosic@ciy.ac.uk ABSTRACT Sice screw compressor roors are of a elical sape ad ool pois egaged i eir maufacurig pass differe cuig leg, e ools do o wear uiformly alog e roor profiles. Te ouiformiy depeds o a differece bewee e roor poi agle ad pressure agle ad o e roor elix agle. A differece i relaive moveme bewee e ool ad e roors wi ad wiou e cuig sock is used o quaify a relaive wear of e ool. Tis is ow i couerpar used as a basis for calculaio of a variable roor sock disribuio, wic resuls i a uiform wear of e fiisig ool we i is applied. Fially, e rougig or semi-fiisig ool is geeraed wic cus e roors wi suc a variable disribued sock. Applicaio of is procedure ca subsaially improve e overall ool ecoomy. 1 INTRODUCTION Screw compressors are posiive displaceme roary macies comprisig a mesig pair of elical roors coaied i a casig formig a camber wic volume depeds o eir roaio. Compressor efficiecy depeds o e roor profile ad clearaces bewee e roors ad bewee e roors ad compressor ousig. For suc macies o perform effecively e roors mus mee e mesig requiremes ad sould maiai a seal alog e eire roor coac. Fig 1. Roor ad ool coordiae sysems Te roor ad ool coordiae sysems are preseed i Fig 1. Roors are oday maily maufacured by e use of formed, millig or gridig ools. Tis meas a ools suiable for screw roor producio mus be calculaed by a appropriae mesig procedure. Te evelope meod, wic saes a wo surfaces are i mes if eac evelops e oer uder a specified relaive moio, is suiable for suc a purpose. Te procedure sars wi a give surface (1) wi is derivaives () ad (3), were x() ad y() are e roor (Fig ) coordiaes i e rasverse plae i e X,Y coordiae sysem for wic a

2 mesig ool surface is o be deermied. A family of suc surfaces is give i parameric form (4) ad eir derivaives i X Y Z roor ad X Y Z ool coordiae sysem respecively are give i (5) as preseed i Fig. 1, were C represes e axis disace, Σ saf agle ad idices ad are roor ad ool. Te evelope equaio of suc surfaces i respec of e roaio agle q is (6). Sice a geeraig surface is defied by e parameer, e evelope ca be used o calculae aoer parameer q, wic is e roor roaio agle, as a codiio o geerae a mesig surface. Te cross produc i e evelope equaio represes a surface ormal wile jr/j is a relaive velociy of wo surfaces i e commo poi, is a ool roaio agle ad p is a roor lead defied for a ui roaio agle. ρ = τ (, ϑ) = [ x, y, z ] = [ x cosϑ y siϑ, x siϑ + y cosϑ pϑ] r (1) r x =, y x y x y,,0 = cosϑ siϑ, siϑ + cosϑ,0 r = [ y, x, p] (3) ϑ ρ, ϑτ, = x, y, z = R cos τ, Rsi τ, ysiσ+ zcosσ = x C, y cosσ z si Σ, y si Σ+ z cosσ ( ) [ ] [ ] [ ] ρ τ [ y, x,0], = [ pϑ si Σ y cos Σ, ( x C) cos Σ, ( x C) si Σ] r r ρ = 0 ϑ τ y y ϑ (7) x x ( C x + p co Σ) x + y + p p C co Σ = 0 Evaluaed from (6) a codiio of mesig is preseed i (7), wic ca be solved by applicaio of a umerical meod. For a give parameer, e poi coordiaes ad eir derivaives are kow. A guessed value of parameer q is e used o calculae x, y ad jy /jx from (1) ad () for give x, y, jx/j ad jy/j. A revised value of q is e calculaed from equaio (7) ad e procedure repeaed uil e differece bewee wo cosecuive values becomes sufficiely small. For give rasverse coordiaes of e roor profile ad eir derivaives, coac agle q, deermied from (7) may be used o calculae e x, y ad z coordiaes of e roor elical surface from equaio (1). Te ool surface ad fially e ool rasverse poi coordiaes R ad z may e be calculaed from (4) as: ( x C) + ( y cosσ z si Σ), z = y si Σ + z Σ R = x + y = cos (8) Aloug derived ere for a screw roor ool geeraio, e mesig codiio, as sow, may be coveiely employed i geeral gearig pracice. Referece exbooks o gears cosider is applicaio oo complex ad oly a case of sraig-sided ools for ivolue geeraio is repored ere. However, Adreev 1961, [1], ad recely Xig 000, [5] i eir books o screw compressors give is full derivaio specifically for screw compressor ools. A similar approac as bee publised i Tag, (6) () (4) (5)

3 1995, [4], Zag, 1997, [6] ad i Sosic, 1998, [] were addiioally a reverse ool o roor rasformaio (10) was give, wic was laer used i Sosic, 1998, [3] o calculae iflueces of seig errors upo e screw roor maufacure. From e kow ool coordiaes, R ad z ad eir derivaive jz /jr, e roor profile pois x ad y ca be used o calculae e roor rasverse coordiaes x ad y of e roor wi give sock from iverse of e equaio (1) as: [ x, y ] [ x cosϑ + y siϑ, x siϑ + y cosϑ ] for e agle parameer q wic is obaied from: = (9) z z R + z cos ϑ + ( p + C co Σ) siϑ + p co Σ C = 0 (10) R R Oce calculaed, e disribuio of q alog e profile may be used o calculae e coordiaes of mesig ool ad roor pois, as well as o deermie e coac lies ad pas of coac bewee e roor ad ool. Te sealig lie of screw compressor roors is somewa similar o eir coac lie. Sice ere exiss a clearace gap bewee roors, e sealig lie is a lie cosisig of pois of e mos proximae roor posiio. Te mos coveie pracice o obai a clearace gap bewee e roors is o cosider e gap as e sores disace bewee e roors i a cross secio ormal o e roor elicoid. A rasverse clearace gap ca e be obaied from e ormal oe by a appropriae rasformaio. I is ieresig a a maufacurig sock, a surplus of maerial wic is o be removed by a ool acio, may be cosidered as a egaive clearace. I suc a case all rasformaios derived for clearaces ca be applied ad are valid for e sock calculaio. CALCULATION OF THE ROTOR AND TOOL COORDINATES.1 Roor Coordiaes for a Give Sock If a sock, wic is o be cu of e roors, d is give i e plae ormal o e roor elicoids surface, e firs par of e relaio (6), e cross produc of e r derivaives, wic defie e ormal direcio, ca be used o calculae e coordiaes of e roor elicoids wi e sock from e rasversal roor coordiaes wiou e sock ad e sock iself as: δ dy x = x + p, D d were e deomiaor D is give as: y y δ dx p, D d z δ dx = ( x D d = + dx dy dx dy D = p + p + x + y (1) d d d d dy y ) d (11) Tese serve o calculae e ew rasverse coordiaes x ad y of e roor wi sock from equaio (11) for e agle q =z /p. Te x ad y ad origial roor coordiaes x ad y serve ow o calculae e ool coordiaes, wic will cu e roors wi e sock, or rouged or semi-fiised roors ad

4 roors wiou e sock, or fial roors respecively. A differece bewee ese wo will somewa give a relaive measure of e ool wear.. Tool Wear A relaive moveme bewee e roor ad ool coais a simulaeous slidig ad rollig acio, because bo compoes ad o oly a age oe cou for e ool wear. Cuig process is deermied by e ool speed ad advace. However, if oly a relaive measure of e ool wear is cosidered, ese parameers will simulaeously be coaied i bo, e roug ad fie cuig. Terefore, e ool wear will be depede oly o e differece bewee e coordiaes eier of wo ools, wo roor elical coordiaes or wo roor rasverse coordiaes. Eier e roor or ool moio equally well deermie cuig roug e sock. As e simples, a differece of roor rasverse coordiaes x, y ad x, y is, ereby, preseed ere as relaive measure of e ool wear. s ( x x) + ( y y) = (13) A roor pair i cofiguraio of 5-6 lobes o e mai ad gae roor is used as a example ere. Te mai roor diameer is 18 mm. Te roor elix agle is 40 o. Roor cere disace is 90 mm. Fig. N Roors 5/6-18 mm Fig 3. Tool wear o cu uiform sock Te mesig roors i rasverse cross secio are preseed i Fig. A screw compressor roor ad is formed ool are mesed o o parallel ad o iersecig axes. Due o eir axes o beig parallel, ere is oly poi coac bewee em. Tis poi is a cuig poi. Te eed o saisfy equaio (7) leads o e roor - ool mesig requireme for e give fiised roor rasverse coordiae pois x ad y wi jy/jx. Te roor elical coordiaes x, y ad z are obaied from (1). Tese are sufficie o ge e ool rasverse poi coordiaes R ad z from (8). Te ideical procedure is applied for e x, y roor coordiaes wi 100 mm sock o obai eir cuig ools. I bo cases e roor-ool cere disaces were 105 ad 15 mm for e mai ad gae roor respecively. A saf agle was 45 o. Bo e ool coordiaes R ad z are ploed i Fig 3 as R ad z o visualize e ool wear wic is scaled 50 imes. I is obvious a e ool wear is o uiform alog e ool profile. I is miimal ad equal o e sock applied i all pois were e roor profile ad pressure agle are e same, ad i is larger i all oer cases. A disribuio of a relaive ool wear resulig from suc a cuig is preseed i deail i Figs 4 ad 5 for e mai ad gae roor respecively. Te ool poi umber i Figures 4 ad 5 represes e coordiae poi posiio alog e profile. For e roors preseed i e example e maximal ool wear was abou wice of e miimal oe for e mai roor ad abou 50 % i excess for e gae roor.

5 Fig 4. Tool wear, mai roor Fig 5. Tool wear, gae roor 3 APPLICATION OF VARIABLE CUTTING STOCK TO MINIMISE WEAR I is quie logical o expec a a variable sock applied aroud e roor profile will cause a differe ool wear alog e ool profile compared wi e uiform oe. If a disribuio of a sock is cose o be reciprocal o e wear caused by e uiform sock, a uiform ool wear ca be obaied. Tis is prove ere by applicaio of suc a sock o e roors, wic leads o e ew roor coordiaes x, y. Te ew coordiaes are compared wi e old oes, x, y ad preseed i Fig 6. Te scale of e roor coordiae differeces is agai 50 imes. Te ew coordiaes are ow used o calculae e ool coordiaes R ad z, preseed i Fig 7 as R ad z wic are compared wi e fiisig ool ad eir differece scaled 50 imes. Tis wear is preseed separaely for e mai ad gae roors i Fig 8 ad 9. I is visible a e ool wear is uiform ow. Te roor poi umber i Figures 8 ad 9 represes e coordiae poi posiio alog e profile. Fig 6. A roor sock for uiform ool wear Fig 7. Uiform ool wear

6 Fig 8. Sock for uiform wear, mai roor Fig 9. Sock for uiform wear, gae roor Te uiform ool wear appears o be e opimal oe for e ool ecoomy allowig e ool o be used for e loges period bewee wo ool codiioigs eier by dressigs or sarpeig. 4 CONCLUSION A ool wear is always prese i maufacurig of screw compressor roors. I is logical o expec a a variable macie sock wic is removed from e roor will cause a differe ool wear alog e ool profile compared wi e uiform oe. If a sock iversely proporioal o e wear caused by e uiform sock is o be cu off, a uiform ool wear could be obaied. Te evelope eory of gearig as bee applied ere as a mesig requireme for crossed elical gears o calculae e sock disribuio wic would resul i e uiform wear of a fiisig ool. REFERENCES [1] Adreev P.A, 1961: Viovie kompressorie masiii (Screw Compressio Macies), SUDPROM Leigrad, Russia [] Sosic N, 1998: O Gearig of Helical Screw Compressor Roors, Proc IMecE, Joural of Mecaical Egieerig Sciece, Vol 1, 587 [3] Sosic N, Smi I. K, ad Kovacevic A, 1998: Some Aspecs of Tool Desig for Screw Compressor Roor Maufacurig, I Desig Coferece -Desig 98, Dubrovik, Croaia [4] Tag Y, 1995: Compuer Aided Desig of Twi Screw Compressors, PD Tesis, Sraclyde Uiversiy, Glasgow, U.K. [5] Xig Z. W, 000: Screw Compressors: Teory, Desig ad Applicaio, (i Ciese), Cia Macie Press, Beijig, Cia [6] Zag Z, Li J, Si G ad Fu W, 1997: Geeral Program for Millig Cuer Profile Desig of Screw Compressor Roor, d I Compressor Tecique Coferece, Cegdu, Cia