适合螺杆压缩机转子滚削加工装备关键技术问题

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Sep．2013机 床 与 液 压Hydromechatronics Engineering Vo1．41 No．18DOI：10．3969／j．issn．1001-3881．2013．18．012Analysis and Discussion of the Key Technical Problems for theScrew Compressor Rotor Hobbing M achiningW ANG Xiaoming’
，TIAN Qingqing ，XIONG Guoliang ，HE Zhongyu ，WAN ChangbiaoJ．Mechanical and Electrical Engineering College，East China Jiaotong University，Nanchang 330013，China；2．Shenyang Railway Administration，Shenyang 110000，China1．IntroductionAbstract：In this paper，the reseamh status and the existing problems of screw compressor rotorprocessing and equipping technology were comprehensive reviewed．Screw rotor with sharp pointprofile-unilateral asymmetric cycloid arc screw realized hobbing machining was figured out，andthe key technical problems of the hobbing tooth equipment were studied，meanwhile，the re-search status and the existing problems of screw compressor rotor processing technology wereanalyzed and researched.

Key words：screw rotor，hobbing machining，tool edge design，gear hobbing machineScrew compressors feature the advantages of highreliability，compact size，and lower easy deactivatedspares，convenient in operation and maintenance，good dynamic balance，high adaptable，long lifetimeand so on． They have been applied extensively inmine，chemical，power， metallurgy，construction，mechanical and refrigeration industries，especially indeveloped countries．The screw compressor utilizationration in developed countries such as Japan and Unit—ed States has reached 60％ —-80％ of the total pro-duction．while less than 2％ in China．For the sakeof improving the overall utilization， it is need tostrengthen the research of screw compressor，effec—tively reduce the manufacturing cost，reduce the vi—bration and noise in the process of operation，and im-prove machining precision， so as to shorten thedifference between the developed countries and keepReceived：2013—03—26The Ministry of Science and Technology Personnel Action Pro-ject Service Enterprises(SQ2009GJC5005668)，Production—study·-research Cooperation Projects in Jiangxi Province De-partment of EducationTIAN Qingqing．E—mail：tianqingqing08###163．eomup with the international pace[1]．Screw rotor is thekey part of screw compressor，as its complicate pro—files and high processing requirements，so the totalcompression utilization，reliability，running stabilityand noise of screw compressor are depend on the ma—chining precision of screw rotor to a great extent.

Thus，seek an effective processing method to improvescrew rotor machining precision is one of the most im—portant task for the research of screw compressor[2].

2．Research status and existing problems ofscrew rotor machiningThe quality of screw rotor is the key of the wholecompressor performance and reliability， while thequality of screw rotor is depends Oll the following as—pects：① the performance of screw rotor profile，②the machining precision of screw rotor tooth profile，⑧ the rotor material and its way to heat treatment，and the first two aspects play dominant role． In asense，screw rotor profile is relate to tooth profileprocessing，the machining precision of screw rotortooth profile is determ ined by processing technology ，screw rotor profile and processing technology mutualpromote，and in the last promote the improvement ofthe whole performance of screw compressor[3].

At present time，methods used to the machiningHydromechatronics Engineeringof compressor rotor including disc cutter milingmethod，generating method and grinding method．A-mong them，milling method belongs to discontinuousprocessing，if there are 4 —6 teeth need to be ma—chined，it must index milling one by one，this causebig index error．The milling method with the charac—ters of low machining precision，low production rateand so on，it afects the reliability and eficiency ofcompressor，and increases the noise of rotor in work—ing situation． The grinding method overcomes thedisadvantage of miling method，it possesses the ad.

vantages of high grinding precision，surface rough—ness value Ra can reach 0．4m，tooth eror can up to5 m；good molding process stability； it can obtainreasonable rotor meshing clearance and possessesdeep grinding function．However，grinding also hasits own limitation．If there is concave point in pro—file，it is hard to realize grinding．In the other hand，the grinding processing equipment is very expensive；it will bring economic pressure for most screw con—presser manufacture factory． Besides， the indexproblem still exists． Compared with milling methodand grinding method，hobbing manufacture has manyadvantages，it realizes multi-teeth machining comple·ted by one time feeding，it doesn’t need index，anddoesn’t exist index eror． Accordingly， hobbingmanufacture owns the features of high productionrate，high tooth machining precision and low pitcheror．This method is applicable for producing con—presser rotors with small outer diameter and largebatch[4—5].

Hobbing manufacture can not only improve rotormachining precision，but also save machining time，but realize the screw rotor processed by hobbing inour country at present need to solve the following twokey technical problems：the first one is to developand improve the screw compressor in order to developrotor profile fit for hobbing processing；another way isfrom the point of cutting tool，there is no need tochange rotor profile，we only have to research hobcutting tool design theory ，the cutting tool is used tomanufacture screw of unilateral asymmetric cycloidwith sharp point- pin tooth circular arc tooth profile；the second is to research the associated special screwrotor gear hobbing machine bed．As the screw rotorwith less teeth and big helical angle，so it is difcultto process by general gear hobbing machine． Be—sides，because of the existing of gear hobbing machi—ning eror，the quality and precision of screw rotor isseverely affected3．Problems and solutions of the hob cut.

ting edge designFig．1 shows the transverse profile of the asym—metric Yin screw rotor，it consists of line“ab”，arc“bc”．extended epicycloid “cd” and radial line“de”．As there is no common tangent on the cross.

point d of line“de’and extended epicycloid“cd”.

so there is a sharp point at“d”．In solving axial cut—ting edge meshes with rotor，the result shows the hobcuting edge separate，in other words，the“dl’ and“d2”misalign．as show in Fig．2．In order to processthe corect screw rotor profile， it must ensure thesharp point“d”is not be cut of by hob．In this situ.

ation，academia put forward the folowing two designsfor hob cuting edge to solve the sharp point issue：one is precise calculation based on normal rack，theother is calculate based on meshing contact line.

J IFig．1 Transverse profile of Yin screw rotord1。

2／cla1Fig．2 Sketch of hob axial cuting edge3．1．Precise calculation based on normal rackDue to the big helical angle of screw compressorrotor，precise calculation method must be adopted todesign hob cutting edge，the normal rack is not fitta—ble，otherwise the error is big．Using the concept ofcommon rack to solve the separate part profile，that isto say，first find the track of sharp point’s detachcurve equation formed on rack cuter，then accordingto this equation calculate cutting edge equation of theseparate part profile meshed with hob cutting edge，this precise calculation makes the space meshingproblem change to plane meshing problem[6].

WANG Xiaoming，et al：Analysis and Discussion of the Key Technical Problems forthe Screw Compressor Rotor Hobbing MachiningDue to the existence of sharp point“d”，racktooth profile which is work out according to the gearshape normal theory will appear two detach curvessimilar to Fig．2，the two separation points’coordi—nates d ( 1，Y1)and d ( 2，Y2)can be work out inworkpiece transverse plane rack o 1． Apparently，sharp point d moves on the rack tooth form s the sepa-ration section when the workpiece does meshingmovement relative to rack．In order to make the racktooth profile meshes properly with workpiece，i．e.

the sharp point d can’t be cut of by rack cutter，thed'd”curve equation on the rack must be work out.

As show in Fig．3，the mesh of workpiece and trans—verse rack can be thought as workpiece pitch circledoes pure roll on the rack section line．When theworkpiece rolls from point o to point o 1，the move—ment path equation of sharp point d on rack cutter otlcan be writen as Eqs．(1).

1=rO—psin(0+ ) Y￡1=一r+pcos(0+ ) (1)Where P is the profile length of od，r is the pitch cir-cle radius of workpiece，0 is parametric variable，and01≤0≤02， is the radial angle of straight line oeand Y coordinate.

d，d (D fl一
。 e )一 Fig．3 Formation of d'd curve onworkpiece transverse tooth profilePlug the coordinates d ( 1，Y1)and d”( 2，Y2)in Eqs．(1)，then the points d and d”correspond-ing to the range value 0l and 02 can be calculated.

Eqs．(1)is the curve equation of d d”on therack．Set the helical angle of Yin screw rotor as left—handed angle 1，and set hob helical angle as right—handed angle 2
．
the meshing position of workpiece，hob and common rack is shown in Fig．4．Only whenthe curve equation of d d on the rack was work out，the cutting edge profile meshed with curve d d”canbe calculated，as shown in Fig．2．As shown in Fig.

4，xf1 and Y￡1 converse to hob transverse rack coordi-nate of can be writen as Eqs．(2).

￡= n co 1／co 2y￡ Y 1y yr1Fig．4 The coordinates and position relationshipsamong workpiece，hob and common rack(2)According to Eqs．(2)and gear shape normaltheory，hob basic worlTl tooth profile equation meshedwith hob transverse track can be calculated，as shownin Eqs．(3)．Where stands for the hob worln turn—ing angle when a point M in workpiece begins tomesh and changes to contact point，“is the angle oftangent on point M and coordinate 。when the pointM begins to mesh， l is the hob basic WOIqTI pitch cir—c】e radjl】s.

x3Y31(r1 l— f)cos(fll(Y 一 1)cos~,+(Yttgu + f)／rl+ (，， 一 1)sin~vl( ￡一r1 1)sin~1(3)一 】 d“ gSeries of coordinate points on separation sectionof CHI Ve can be calculated according to Eqs．(3)，then makes the points spiral movement around thehob basic worli axis，in this way，transverse equationof hob worm separation section can be obtained．Di—vide along its axial，cutting tool axial edge equationof coresponding hob separation section is work out.

3．2．Calculate based on meshing contact lineScrew rotor hobbing machining process，whoseessence is the screw rotor helical surface contact withhob helical space，and the space position of the form—ing contact line remains the same．According to theproperty that contact line’s space position remainsthe same，contact condition of hob cutting edge de-sign is deduced，then by the contact condition calcu—late hob cutting edge of machine screw62 Hydromechatronics Engineeringrotor tooth[7—8].

Establish the Cartesian coordinate system asshown in Fig．5．Where O1Xl YlZ1 and O2X2 Z2 arestatic coordinates，coordinates Xl and X2 are in thesame straight line，the distance between the two coor—dinate origin o1 and o2 is set as A， O1 1Y1 l andO2 2Y2 2are dynamic coordinates of screw rotor，eoor—dinate axis 1、z2 coincide with Z1、Z2，respectively.

y。

＼主 O．，(z2Fig．5 Right hand space Cartesian coordinate systemSet the helical surface of screw rotor 1 as right—handed，its parameter equation of transverse profilein dynamic coordinate O1 1 Y1 1 as shown in Eqs.

(4).

1 = l( )Y1 = Yl( )While helical surface parameterstatic coordinate O l 1 Y1 Z1 is shown inX1 1cos01一Y1 sin01Y1= 1 sin01+Y1cos01Z1 P101(4)equations inEqs．(5).

(5)Where P is the screw characteristic number of helicalsurface.

A point’s coordinate in static coordinateO l Xl Y1 Z1 in contact line can be expressed in theform of vector as shown in Eqs．(6).

r1 r1(t，01) [X1，Y1，Z1] lxICOS01一Yl sin0l， 1 sin01+Y1cos01，Pl01] (6)The corresponding two tangent vectors acrosscontact point in’coordinate system O1X1 Y1Z1 can beindicated as Eqs．(7)and Eqs．(8).

= [鲁cos 一 sifl —— l——C 1——S1． a af af ?
Ox1
． n ． 删 1 +警 ，OlosO ——C1． a 一 (7)Orl
= [一 sin -ylcos01,XlCOS01一Yl sin0 ，P1]=[一Y1，X1，P1] (8)The vector of contact point in coordinate systemO2X2 y2Z2can be indicated as Eqs．(9).

r2=r2( ，02)=【X2，y2，Z2]=[x2cos02+Y2sin02，一x2sin02+Y2sin02，P202] (9)By the use of coordinate transformation between coor—dinate systems O1X1 YI Z1 and O2X2 y2Z2as wel as therelationship between unit vectors．the tangent vectorin O1XlY1Zlis obtained in form of Eqs．(10).

Or2
= [Y1c。s +Zl sin ，(A— 1)c。s 一P1 sin ，P1cos~Z+(A—X．)sin ] (10)As the tangent vector across any contact point inthe same plane，in other word，the mixes volume ofthe above three tangent vectors is zero，as shown inEqs．(11).

×01"1
·Or2
=u (11) —— ——·—— a a a，、Substitute Eqs．(7)～(9)in Eqs．(11)，andthe helical surface space geometry equation is ob—tained，as shown in Eqs．(12).

[(A—X1)sin +(Pl+P2)eos~F]×( OX1+yl鲁)+ 鲁sin +p (p2sin 。s =0 (12)is the angle of coordinate Z1 and Z2，substitute thehelical surface parameter equation (5)in contactcondition equation(1 2)，the transcendental equationaimed to solve hob cutting edge can be gained，asshown in Eqs．(13)：[(A 一 1cos01+Y1 sin01)sin +(pl+ ? )+p2
,O／ol(sin 1+ cos 。)sinqZ+ 1 。 -P1(P2sinqt—A cos )(c0 一 Sin =。 (13)where A。is the space distance between axis Z1 andZ2，i．e． the installment center distance，which isknown as well as hob screw characteristic number P.

If a point in transverse plane tooth profile whose coor—dinate is( 1，Y1)and its derivative is dy1／dx1 areknown，then the coresponding point 0l can be ob·tained．Substitute the value 01 in Eqs．(6)，then thecontact point coordinate(Xl，Y1，Z1)in coordinatesystem O1X1 Yl Z1 was gained， by using coordinatetransformation the coordinate(X2，y2，Z2)in coordi—nate system O2X2 Z2 and the corresponding hob cut—ting edge coordinate(Z2，(X2 +y2 ) )can be ob—tained.

WANG Xiaoming，et al：Analysis and Discussion of the Key Technical Problems forthe Screw Compressor Rotor Hobbing Machining 634．Keygeartechnology research of conventionalhobbing machining4．1．The existing problems and solutions of con-ventionai gear hobbing machiningThe tooth number of screw rotor is less，usuallythe number is 4～8，and the helical angle is big，a—bout 30。～60。． Machining screw rotor using gearhobbing machining similar to Y3 150E will meet thefollowing three troubles：1)Adjust tool rest according to the requirementof the screw rotor helical angle．the left of tool rest orthe movable bearing will generate interference withworkbench．and the effective stroke length of tool restvertical feeding is limited.

2 1 Arc part in front active arm of outer bracketand arc part in the left of tool rest wil generates in—terference with tool rest left side，as a result，cuttingtool can’t close to the being processed gear billetouter circular surface of screw rotor.

3)Due to the less tooth number of being pro—cessed screw rotor，thus the relative speed of work.

bench is high，the abrasion of indexing worin gearpair is increased，and then the machining accuracy oftooth circle is affected『9]．To sum up，for machi—ning screw rotor with less tooth number and big heli—cal angle，conventional gear hobbing machining isnot suitable．and the efect is not obvious，so it isneed to develop or introduce special screw gear hob—bing machining equipment.

4．2．Analysis of gear hobbing machine machiningerrorWith the increase demand of high precise screwrotor applied in fields such as mining， chemical，power，metalurgy，construction，machinery and re·frigeration，the requirement for gear hobbing machineaccuracy and machining accuracy is higher．Howev—er，as the gear hobbing machine with high speed，high efficiency，long working time，and the machinetool part’s movement and transmission are complex，therefore，gear hobbing machining error has great in—fluence on machining quality．The greatest impactson machining eror mainly include three factors[10]，which are hobbing force，vibration and thermal de—formatjon.

1)thermal eror．Inmachining，a lot of heatthe process of gear hobbingwill generate， mainly in—cludes hobbing heat，friction heat and motor heat，these heat absorbed by machine tool key parts afterconduction，radiation and convection，which makeuneven heat in parts，as a result temperature differ—enee form s among the parts，and causes the uprightbecome bend， the bed elongation and thermal de—form ation． Moreover， positional deviation betweenhob and workpiece spindle center distance is form ed，and then the machining eror of screw rotor is genera-ted.

2)Bed machining eror caused by hobbingforce．Hobbing force makes the hob and the work—piece spindle bending deformation， spindle centerdistance position ofset，the most affected is X direc—tion position，then the machining eror form ed，thiskind of eror called force—induced error． Besides，hobbing force increases the bearing reaction force ofhob spindle on both ends，makes the bearing load sit-uation worse，aggravates the wear and tear，reducesor affects the machining accuracy of machine too1.

3)Screw rotor machining eror caused by hob—bing vibration．In high speed cutting process，pro—cessing work is not stable，hobbing force makes thecutter and the workpiece self — induced vibratestrongly，which leads to the position of center dis—tance produces vibration displacement or slightchange，affects the machining precise，and then cau—ses the screw rotor machining error.

5．ConclusionsThe processing of compressor screw rotor is oneof the most important issues in the manufacture ofcompressor，it is difcult and has high accuracy re—quirement．At present，most screw compressor manu—facture factories in our country stil adopt milling ma—chining with low accuracy and low eficiency，this isseriously affect the quality of the screw compressor.

As a new kind of machining method for screw con—presser rotor，though hobbing machining possessesmany advantages over milling method，the realizationof bobbing machining still has many technical prob—lems need to solve，mainly includes the design of hobcuting edge，deep research of hobbing process anddevelop special screw gear bobbing machine.

To sum up，it is important to research hob cut—ring edge design methods，bobbing process and spe—cial screw gear hobbing machine aimed to solve theproblem that screw rotor with less tooth and big heli—Hydromechatronics Engineeringcal angle．At the same time，set up screw rotor ma-chining thermal error compensation models for difer·ent types of gear hobbing machines and diferent sea—sons； meanwhile， develop compensation model ofhobbing machining error caused by the hobbing forceand hobbing vibration is the inevitable trend of tech—nology development． In the near future，advancedhobbing machining process will become the mainmethod for the machining of screw compressor rotor，and play a positive role on the quality improvement ofscrew compressor.

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适合螺杆压缩机转子滚削加工装备关键技术问题王小明 ，田青青 ，熊国良 ，贺忠宇 ，万长标1．华东交通大学 机电工程学院，南昌 330013；2．沈阳铁路局，沈阳 110000摘要：论述了螺杆压缩机转子滚削加工及装备技术现状及存在的问题，对具有尖点廓形的螺杆转子——单边非对称摆线圆弧螺杆实现滚削加工及其滚齿设备的关键技术进行 了分析 ，对其研究现状及存在的问题进行了讨论。

关键词：螺杆转子；滚削加工；刃形设计；滚齿机中图分类号：TH12