Geometric error measurement and identification for rotational axes of five-axis CNC machine tool

Transcription

1 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd Geometrc error measurement and dentfcaton for rotatonal aes of fve-as CNC machne tool anbng N * - ance Lu - Bao hang 2 - hwen hang - Jnhe L School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna 2 Qngdao Hsense - Htach Ar Condtonng System Co. Ltd, Shandong, Chna It s dffcult to measure the atttude errors of fve-as machne tools, as t requres epensve nstruments. What s more, t s hard to measure and dentfy them n producton stes. Here, the B/C type of fve-as CNC machne tool s studed where the rotatonal aes are located n the cuttng tool movement chan and workpece movement chan respectvely. The method of geometrc error measurement and dentfcaton of the rotatonal aes s proposed based on use of a double ball bar (DBB). The geometrc error sources n two rotatonal aes are analysed. Then based on the homogeneous coordnate transformaton prncple, the relatonshps between the geometrc errors of each rotatonal as and the structure parameters of the machne tool are establshed on the C turntable and B swngng head respectvely. Identfcaton models for each as are bult by changng the nstallaton modes of the DBB n three coordnate drectons. The geometrc errors n the rotatonal aes are dentfed by the least-squares method. Fnally, the error measurement eperment of the machne tool s carred out for dfferent nstallaton modes of a DBB. The epermental results show that the dentfed error parameters are consstent wth actual condtons, and verfy the valdty and feasblty of the proposed method. Keywords: Fve-as CNC machne tool; Double ball bar; Error modellng; Error measurement and dentfcaton Hghlghts: A geometrc error measurement and dentfcaton method s proposed for the rotatonal aes of a B/C type of fve-as CNC machne tool based on DBB. The rotaton aes are located n the cuttng tool and workpece movement chans respectvely. Dfferent DBB nstallaton methods are desgned n three drectons. Seven measurements were accomplshed n three measurement modes and an dentfcaton model for each as establshed Eperments are carred out by DBB n dfferent measurng modes and the least-squares soluton of the system of over-determned equatons s obtaned. S geometrc errors of each rotaton as are dentfed. 0 INTRDUCTIN Fve-as CNC machne tools are wdely used n manufacturng ndustry. The accuracy s harder to be guaranteed snce rotatonal aes are nvolved n mult-as control. The basc geometrc accuracy of machne tools s the foundaton of ther comprehensve accuracy. So the geometrc errors must be controlled. Based on the establshed error models, error measurement and dentfcaton are the key to realsng error compensaton [-3]. Accordng to the dfferences n measurng nstruments and methods, error measurement s dvded nto sngle error measurement and comprehensve error measurement. Sngle error measurement s drect, but ts measurement perod s long and envronmental requrements are strct: n some cases such as calculatng errors n rotatonal aes, the sngle error measurement s relatvely dffcult. Hence n producton, comprehensve error s adopted to measure atttude errors that are not as accurate [4-6]. Based on the double ball bar (DBB) nvented by Bryan [7], scholars began to eplore the applcaton of DBB to the geometrc error measurement of rotatonal aes of CNC machne tools. Tsutsum, et al. [8] proposed a method of error measurement and dentfcaton based on DBB. Two translaton, and one rotatonal, aes were combned nto a measurement unt, and the senstve drecton of the DBB s kept constant. Then four dsplacement errors and four angular errors of the rotatonal aes of CNC machne tool wth two turntables were dentfed. After that, Tsutsum, et al. [9] proposed a two-step error measurement process and dentfcaton model accordng to the characterstcs of a mult-as * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn

2 control machne tool. Thus, four dsplacement errors and four angular errors of the rotatonal aes of the machne tool were obtaned. Amng at the turntable, Chen, et al. [0] put forward a method wth whch to measure the comprehensve geometrc errors of the rotatonal as by DBB. Two aes were smultaneously controlled and the crcle trajectores were planned n dfferent planes. Hence, there were nne error components measured from three mountng modes. The sources of error n the rotatonal as were dentfed by usng the error model. In addton, error measurement trajectores were found to nfluence the effcency of error dentfcaton []. Jang, et al. [2] establshed four paths wth whch to dentfy the poston ndependent geometrc errors n rotatonal aes. The dsplacement errors were measured frst and then the angular errors. Chen, et al. [3] proposed a four-nstallaton method whereby a DBB was nstalled parallel to the,, and -aes, and concally. A polynomal model of geometrc errors was establshed, and three dsplacement errors and two angular errors n the turntable were dentfed. Compared wth the former, ths method mproves the effcency of measurement. hang, et al. [4] planned measurement trajectores of the DBB. Two measurement trajectores of the DBB were desgned n dfferent horzontal planes so as to decouple dsplacement errors from angular errors. Three dsplacement errors and two angular errors of the rotatonal as were obtaned. Based on prevous studes, hu, et al. [5] regarded the CNC machne tool as a rgd mult-body system, and presented an ntegrated geometrc error dentfcaton model. S angular errors of the rotatonal aes on fve-as CNC machne tools wth two turntables were dentfed by usng DBB. Wth the help of standard parts, the effcency of geometrc error dentfcaton of rotatonal aes can also be mproved. Sharf Uddn, et al. [6] proposed a smulator dentfyng geometrc errors of a fve-as machne tool based on DBB. By comparng machnng geometrc errors generated n machnng a standard workpece wth the nomnal errors n the workpece, the geometrc errors n a CNC machne tool wth two turntables were dentfed. Nevertheless, how to select representatve standard parts needs further study. Furthermore, analysng the nfluence of error sources on the end effector s another way to solve the geometrc error source dentfcaton problem. Lasem and N, et al. [7-9] dvded error sources nto poston-ndependent and poston-dependent errors accordng to the dfference n the effects of geometrc error sources on the end effector by a DBB method. The dentfcaton model was establshed, and the geometrc errors were dentfed by senstvty analyss. In addton to DBB, a number of other methods have also been proposed to measure geometrc errors. Le, et al. [20] developed a devce called a probe-ball. The cuttng tool path was defned on a sphercal surface, and the overall postonng errors of a fve-as CNC machne tool were obtaned. However, ths devce makes t dffcult to separate each geometrc error n a fve-as machne tool, so t s not easy to use t to measure the geometrc errors of the rotatonal aes. Wekert, et al. [2] developed an R-test whch conssted of a hgh-precson ceramc sphere and a pedestal wth three or four dsplacement sensors. By usng ths devce, four geometrc errors of the rotatonal as on the fveas CNC machne tools wth two turntables were measured. Although the dsplacement errors n three drectons can be measured smultaneously and more nformaton can be obtaned n one test by ths devce, the manufacturng requrements of the precson sphere are relatvely hgh, so ncreasng the cost of measurement. Smlar to the prncple of the R-test, the CapBall was developed by argarbash, et al. [22] whch was a knd of measurng devce equpped wth a noncontact capactance sensor. In addton to the aforementoned methods, t s feasble to apply a laser to error measurement n rotatonal aes [23, 24]. Wang, et al. [25, 26] proposed a method to measure the geometrc errors of rotatonal aes by way of a laser tracker. Based on a sequental mult-lateral measurement prncple, the moton trajectores of rotatonal aes and the space coordnates of each measurng pont were measured at dfferent base statons. Then s geometrc errors of the rotatonal as were dentfed usng the error model. However, the nstallaton and commssonng of the devce are slow, and t s epensve. The research shows that error measurement and dentfcaton of rotatonal aes on fve-as CNC machne tools are relatvely 2 N, anbng. - Lu, ance. et al.

3 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd dffcult: t s therefore necessary to eplore a smple and convenent method to measure atttude errors n fve-as machne tools n producton ste. In terms of measurng nstruments, the DBB s the most wdely used due to ts low prce and smple nstallaton. Here, the B/C type of fveas CNC machne tool s studed where the rotatonal aes are located n the cuttng tool movement chan and workpece movement chan, respectvely. The geometrc error measurement and dentfcaton method of the rotatonal aes by Renshaw QC-20 DBB s studed. The geometrc error sources of two rotatonal aes on the machne tool are analysed. Then based on the homogeneous coordnate transformaton prncple, the mappng relatonshp between the geometrc errors of rotatonal aes and the structure parameters of the machne tool are establshed on the C turntable and B swngng head. The error dentfcaton model for the rotatonal aes s obtaned by changng the nstallaton modes of the DBB n three coordnate drectons on the machne tool. S geometrc errors n the rotatonal as are dentfed by usng the least-squares method. Fnally, the results are verfed by way of an error measurement eperment on a machne tool. METHDS. Establshment of coordnate system The machne tool shown n Fg. s a B/C type of fve-as CNC machne tool, whch conssts of three translaton aes (,, and ) and two rotatonal aes (B and C). system. In practcal stuatons, there are s atttude errors n each drecton between a knematc par of the machne tool. These errors are affected by some factors such as the devatons n manu-facture, nstallaton and abrason of parts. For the C turntable shown n Fg. 2, when the rotatonal as spns, there are errors n the drectons of s DFs ncludng three dsplacement errors and three angular errors, whch are the dsplacement error n the drecton, C the dsplacement error Cy n the drecton, the dsplacement error n the drecton of the - Cz as, the angular error about the -as, the C angular error about the -as, and the angular Cy error about the -as. Cz y z z y Fg.2. S errors of the C turntable Smlarly, for the B swngng head, there are also s errors: the dsplacement error n B the drecton, the dsplacement error n the By -as drecton, the dsplacement error n the Bz drecton, the angular error about the -as, B the angular error about the -as, and the By angular error about the -as. Bz B S T Cuttng tool movement chan W Fg.. Fve-as CNC machne tool Workpece movement chan C Accordng to the knematc prncple, the poston of an object n space s descrbed by three translatonal degrees of freedom (DFs) and three rotatonal DFs of three rectangular coor-dnate aes n the Cartesan coordnate R The bed of the machne tool Fg.3. artal coordnate system settng of the machne tool * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn 3

4 Ideally, the pont of the cuttng tool nose s the same as the pont to be machned on the workpece. In realty, there are devatons between them due to the errors n the machne tool. Therefore, the geometrc errors are predcted and controlled by establshng the error model for the machne tool. As shown n Fg. 3, there are two transmssons of movement chan from the bed of the machne tool. The cuttng tool movement chan s Bed -as -as -as B swngng head Cuttng tool. And the workpece movement chan s Bed C turntable Workpece. A partal coordnate system s developed for each part of the movement chan on the machne tool. As shown n Fg. 4, and 2 are coordnate systems fed on arbtrary adjacent parts. There are both translaton and rotaton transformatons of 2 relatve to. For the translaton transformaton, 2 respectvely moves through,, and y z n the,, and drectons relatve to transformaton, 2 through aes of, y, and. z 2 z. For the rotatonal respectvely rotates z about the,, and y y Fg.4. Schematc representaton of the homogeneous coordnate transformaton When 2 moves through only, the along the drecton of the -as of homogeneous coordnate transformaton of 2 relatve to s T Smlarly T y and T z are avalable. When 2 about the -as of () rotates through only, the homogeneous coordnate transformaton of 2 s relatve to cos sn 0 R 0 sn cos Smlarly R y and R z are avalable. (2) The error can be nterpreted as a small perturbaton and a frst-order lnear appromaton at the pont of measurement. Thus the appromate relatonshps are sn (3) cos (4) where s a varable that can be replaced by, y, z,, y, and z. Because of the multplcaton of varables, there wll be hgherorder nfntesmals. The hgher-order parts are omtted and only the frst-order varables reman, therefore the homogeneous coordnate transformaton of 2 relatve to s z y z y T T Ty Tz R Ry Rz y z (5).2 Geometrc error dentfcaton model The DBB s used as the measurng nstrument of whch the type s Renshaw QC20- W. It s used n connecton wth the lengthenng bar of dfferent szes. The measurement accuracy of the DBB s.25μm. The geometrc errors of each as are obtaned by changng the nstallaton postons of the DBB. The dentfcaton model s establshed n the measurng mode of the DBB to acqure the geometrc errors n each as..2. Identfcaton model on the C turntable As shown n Fg. 5, the DBB s nstalled parallel to the -as. ne end s connected wth the spndle, and the other end s fed on the machne tool table. A fed coordnate system s developed and t s assumed that the coordnate orgn s the ntersecton pont of the surface and the rotatonal as of the C turntable, L s the dstance between the centre and the rotatonal 4 N, anbng. - Lu, ance. et al.

5 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd as of the C turntable, and H represents the dstance between the centre and the surface of the C turntable n the -drecton. In the ntal state, the homogeneous coordnate of the pont n the fed coordnate system can be epr essed by L 0 H T. The change n bar length C turntable Spndle Fg.5. Installaton of the DBB of the C turntable Under deal condtons, when the rotaton angle of the C turntable about the -as s, the coordnates of pont can be epressed by: L R T L cos Lsn H (6) C cos sn 0 0 sn cos 0 0 R Where T C s the coordnate transformaton matr used to move from coordnate system C fed on the C turntable to the reference coordnate system R fed on the bed of the machne tool. The superscrpt denotes the th poston of the C turntable durng measurement. When C turntable moves, there are three dsplacement errors: C,, and Cy Cz along the,, and drectons and three angular errors C,, and Cy Cz about the,, and as. Based on the theoretcal dervaton of Eq. (5), the error matr generated by the rotaton of C turntable s: Cz Cy C R Cz C Cy E = C (7) Cy C Cz Due to the estence of these errors, pont s not n ts deal poston and ts actual coordnates can be epressed by H T R R e EC TC Lcos sn Cz H Cy C Lcos Cz sn H C Cy (8) L cos Cy sn C H Cz The dfference between the actual, and theoretcal, coordnates of pont can be epressed by e Lsn Cz HCy C L Cz cos HC Cy L Cy cos C sn Cz 0 0 (9) Where,, and are the components n three coordnate drectons of the changes n bar length. From Eq. (9), s errors n the C turntable can be obtaned ndrectly by measurng the value of. To acqure,, and n Eq. (9), the DBB needs to be nstalled separately n the radal, aal, and tangental drectons. To mprove the accuracy of dentfcaton, the values of H and L need to be changed to obtan the errors n the,, and drectons usng dfferent nstallaton methods. Therefore s geometrc errors generated durng the rotaton moton of the C turntable can be dentfed..2.. The frst combnaton method When the DBB s nstalled parallel to the -as (radal nstallaton) or -as (tangental nstallaton), gves L L (0) When the DBB s nstalled parallel to the -as (aal nstallaton), gves L 0 () In the two nstallaton methods, H s the value of H when the DBB s drectly nstalled on the worktable. The schematc dagrams of ths type of combnaton are llustrated n Fgs 6 and 7. From Eq. (9), L sn H Cz Cy C L cos H Cz C Cy L cos sn Cy C Cz (2) * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn 5

6 Where s the rotaton angle of the C turntable and subscrpt denotes the th measurement pont. C,, Cy Cz, C,, and Cy Cz are the geometrc errors correspondng to the C turntable at rotaton angle., and are the dfferences between the actual and the theoretcal coordnates of pont n the,, and drectons when the rotaton angle s. The followng meanngs are the same as those ndcated by the above symbols. C turntable Radal nstallaton Spndle L=L Tangental nstallaton H=H Fg.6. Frst combnaton: radal, and tangental, nstallatons L sn H L cos H Cz Cz Cy C Cz C Cy l cos l sn r t l sn + l cos r t l a (4).2..2 The second combnaton method When the DBB s nstalled parallel to the -as (radal nstallaton) or -as (tangental nstallaton), gves L L, L L (5) 2 2 H H, H H (6) 2 2 As Cz can be drectly obtaned under the frst combnaton, the nstallaton method parallel to the -as s unnecessary. The schematc dagram of ths type of combnaton s llustrated n Fg. 8. Spndle Spndle C turntable Radal nstallaton L=L2 Tangental nstallaton H=H2 C turntable H=H Fg.8. Second combnaton: radal, and tangental, nstallatons Fg.7. Frst combnaton: aal nstallaton and can be obtaned by the changes l r and l t n bar length when the DBB s nstalled n radal and tangental drectons. They can be epressed by cos sn l l r t (3) l sn + l cos r t s the change n bar length when the DBB s nstalled n the aal drecton, where l. a Eq. (2) can be wrtten as: From Eq. (9), L sn H 2 Cz 2 Cy C 2 (7) L cos H 2 Cz 2 C Cy 2 Smlarly, 2 and can be obtaned 2 by the changes l r 2 and l t 2 n bar length when the DBB s nstalled n the radal and tangental drectons. They can be epressed by: cos sn 2 l l r 2 t 2 (8) l sn + l cos 2 r 2 t 2 Eq. (7) can be wrtten as L sn H 2 Cz 2 Cy C L cos H 2 Cz 2 C Cy (9) l cos l sn r 2 t 2 l sn + l cos r 2 t 2 6 N, anbng. - Lu, ance. et al.

7 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd.2..3 The thrd combnaton method When the DBB s nstalled parallel to the -as (radal nstallaton) or -as (tangental nstallaton), gves L L, L L (20) 3 3 H H3, H3 H (2) H 3 s the value of H based on H when a magnetc fture or a cushon block s added between the DBB and the worktable. The schematc dagram of ths type of combnaton s shown n Fg. 9. From Eq. (9), L sn H 3 Cz 3 Cy C 3 (22) L cos H 3 Cz 3 C Cy 3 fgure. It was assumed that the coordnate orgn was the ntersecton pont of the swngng as of the B swngng head and spndle as. L s the dstance between the centre and the swngng as of B swngng head n the -drecton. In ts ntal state, the homogeneous coordnates of pont n the fed coordnate system can be epressed by 0 0 L T. Radal nstallaton C turntable Spndle L=L3 Tangental nstallaton H=H3 L Fg.0. Installaton method of the DBB on the B swngng head Fg.9. Thrd combnaton: radal, and tangental, nstallatons Smlarly, 3 and 3 can be obtaned from the changes l r 3 and l t 3 n bar length when the DBB s nstalled n the radal and tangental drectons. They can be wrtten as: cos sn 3 l l r3 t 3 (23) l sn + l cos 3 r 3 t 3 Eq. (22) can be wrtten as: L sn H 3 Cz 3 Cy C L cos H 3 Cz 3 C Cy (24) l cos l sn r3 t3 l sn + l cos r3 t3 Therefore, s geometrc errors at any angle can be calculated from Eqns (4), (9), and (24)..2.2 Identfcaton model for the B swngng head As shown n Fg. 0, the spndle of the machne tool s placed n the vertcal drecton. The DBB s nstalled parallel to the -as. ne end s connected wth the spndle, and the other end s fed on the machne tool table. The fed coordnate system s establshed as shown n the Under deal condtons, when the rotaton angle of the B swngng head about the -as s, the coordnates of pont can be epressed by: R T Lsn 0 Lcos (25) B cos 0 sn R Where T B sn 0 cos When B swngng head moves, there are three dsplacement errors: B,, and By Bz along the,, and drecton and three angular errors about the,, and aes. The error B,, By Bz matr generated by the rotaton of B swngng head s Bz By B R Bz B By E = B (26) By B Bz Because of the estence of errors, the actual coordnates of pont can be epressed by T * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn 7

8 E T L sn cos By B L sn cos L sn cos By Bz R R Bz B By e B B (27) The dfference between the actual, and theoretcal, coordnates of pont can be obtaned as e L By cos B L Bz sn B cos By L By sn Bz 0 0 (28) From Eq. (28), s errors n the B swngng head can be obtaned ndrectly by solvng the value of. To obtan,, and n Eq. (28), the DBB needs to be nstalled separately n the radal, tangental, and aal drectons. To mprove the accuracy of dentfcaton, the value of L needs to be changed to solve the error values n the,, and drectons under dfferent DBB nstallaton methods. Therefore the geometrc errors generated durng the rotaton moton of the B swngng head can be dentfed The frst combnaton method When the DBB s nstalled parallel to the -as (tangental nstallaton), -as (radal nstallaton), or -as (aal nstallaton), gves L L (29) Schematc representatons of ths type of combnaton are demonstrated n Fgs and 2. From Eq. (28), L cos By B L sn cos Bz B By L sn By Bz (30) Where s the rotaton angle of the B swngng head, B,, By Bz, B,, and By Bz are the geometrc errors correspondng to the B swngng head when the rotaton angle s ;,, and are the dfferences between the actual and the theoretcal coordnates of pont n the,, and drectons when the rotaton angle s. Subscrpt denotes the th measurement pont. The followng meanngs are the same as the above symbols. and can be obtaned from the changes l r and l t n bar length when the DBB s nstalled n the radal and tangental drectons. They can be epressed by: cos sn l l r t (3) l sn + l cos r t L=L Fg.. Frst combnaton: radal nstallaton L=L Aal nstallaton Tangental nstallaton Fg.2. Frst combnaton: aal, and tangental, nstallatons s the change n bar length when the DBB s nstalled n the aal drecton where l a. Eq. (23) can be wrtten as: L cos By B L sn cos Bz B By L sn By Bz (32) l cos l sn r t la l sn + l cos r t 8 N, anbng. - Lu, ance. et al.

9 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd.2.2. The second combnaton method When the DBB s nstalled parallel to the -as (tangental nstallaton), -as (radal nstallaton), or -as (aal nstallaton), gves L L2, L2 L (33) The schematc representatons of these types of combnaton are shown n Fgs 3 and 4. L=L2 2 s the change n bar length when the DBB s nstalled n the aal drecton where l. 2 a 2 Eq. (34) can be wrtten as: L cos 2 By B L2 sn cos Bz B By L sn 2 By Bz (36) l cos l sn r 2 t 2 la2 l sn + l cos r 2 t 2 Thus s geometrc errors, at any angle of the B as, can be calculated from Eqns (32) and (36). 2 EERIMENT AND RESULTS Fg.3. Second combnaton: radal nstallaton L=L2 Aal nstallaton Tangental nstallaton Fg.4. Second combnaton: aal, and tangental, nstallatons From Eq. (28): L cos 2 By B 2 L2 sn cos Bz B By 2 L sn 2 By Bz 2 (34) Smlarly, 2 and 2 can be calculated from the changes l r 2 and l t 2 n bar length when the DBB s nstalled n the radal and tangental drectons. They can be epressed by: cos sn 2 l l r 2 t 2 l sn + l cos 2 r 2 t 2 (35) 2. Error measurement eperment: the rotatonal as The parameters of the machne tool are as follows: the rotaton angle range of the C turntable s and the swngng angle range of the B swngng head s The dsplacement errors n the B as and C as are respectvely measured under dfferent nstallatons n the,, and drectons by the DBB when they are rotated through dfferent angles. The error measurements on the C as and the B as are shown n Fg. 5 and Fg. 6. S geometrc errors of each as are calculated by use of the dentfcaton model. In the process of the eperment, the bar length of the DBB s 50 mm. The rotaton angle of the C turntable s and the rotaton nterval s 20. The swngng angle of the B as s 00 0 and the rotaton nterval s 5. The errors are measured three tmes n each drecton (clockwse and counter clockwse). The geometrc errors of the translatonal aes can be drectly measured by the DBB and analysed by the software of Ballbar20. The measurements are conducted n the plane, plane and plane separately. And the results of the errors are shown n Fg. 7. The followng analyses can be obtaned accordng to Fg. 7. -as: The backlash errors are 0.2μm n the forward drecton and 0.μm n the reverse drecton. The straghtness error s.5μm. * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn 9

10 -as: The backlash errors are the forward drecton and drecton. The straghtness error s a) c) 0.μm n 0.2μm n the reverse b) d) 2.5μm. -as: The backlash errors are 0.4μm n the forward drecton. The straghtness error can not be analysed by the software because of the partal crcle measurement. It can be measured by other methods. The squareness error between the -as and the -as s.2μm m. The squareness error between the -as and the -as s 0.7μm m. The squareness error between the - as and the -as s 2.μm m. a) - 360deg 50mm e) f).0μm dv b) - 200deg 50mm Fg.5. The measurement on the C as a) b) μm dv c) d) c) - 200deg 50mm e) f) μm dv Fg.7. The epermental results of the translatonal aes n three planes Fg.6. The measurement on the B as The roundness errors are 6.μm, 8.6μm and 7.4μm n Fg.7a), b) and c), respectvely. 0 N, anbng. - Lu, ance. et al.

11 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd Thus, there are some proporton msmatches between each as. We found the servo msmatches are 0.02ms, 0.2ms and 0.8ms between each as durng the processes of measurement. Hence, the reason leadng to the proporton msmatches s probablely the adjustment devaton of servo parameters. Even so, the results can stll demonstrate the good accuracy of the machne tool. It can be seen from the above analyses that the process to get the geometrc errors of the translatonal aes s drect. However, the atttude errors of the rotatonal aes s harder to measure. Therefore, the dentfcaton model s necessary. The data collected n the process of the eperment ncluded the actual bar length of the DBB. After fnshng the data collecton for each measurement mode, we obtaned the changes n DBB bar length and calculated ther averages shown n Tables and 2. Table. The change values l of DBB bar length when measurng C turntable Angles [º] l [mm] Radal Tangental Aal Angles [º] l 2 [mm] l 3 [mm] Radal Tangental Radal Tangental Table 2. The change values l of DBB bar length when measurng B swngng head Angles [º] l [mm] Radal Tangental Aal Angles [º] l 2 [mm] Radal Tangental Aal * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn

12 Error value(rad) Error value(rad) Error value(mm) Error value(mm) Strojnšk vestnk - Journal of Mechancal Engneerng vol(yyyy)no, p-p Analyss of epermental results C z l can be drectly measured by a the error dentfcaton model for the C turntable. S equatons n the model nclude fve errors n the C turntable: the least-squares soluton to the system of over-determned equatons s obtaned by MATLAB, and each error s obtaned as shown n Fgs 8 and errors n the B swngng head at each angle are obtaned usng MATLAB (Fgs 20 and 2) drecton Aal drecton drecton Angle( ) Fg.20. Dsplacement error: B swngng head drecton drecton Aal drecton Angle( ) Fg.8. Dsplacement error: C turntable as as as as as as Angle( ) Fg.9. Angular error: C turntable Based on the errors obtaned from the dentfcaton model, the mamum, mnmum and average values of each as for the C turntable are shown n Table 3. Table 3. The mamum, mnmum and average values of each as for the C turntable Dsplacement errors [0-3 mm] Angular errors [0-5 rad] Aal Ma Mn Avg Then usng the dentfcaton model for the B swngng head, and the measured data, s Angle( ) Fg.2. Angular error: B swngng head Based on the errors obtaned from the dentfcaton model, the mamum, mnmum and average values of each as for the B swngng head are shown n Table 4. Table 4. The mamum, mnmum and average values of each as for the B turntable Dsplacement errors [0-3 mm] Angular errors [0-5 rad] Aal Ma Mn Avg The epermental results ndcate that the dsplacement errors of both the C turntable and B swngng head are the greatest n ther aal drectons, at 4.4μm and 22μm, respectvely; however, the dsplacement errors are smaller n the other drectons. In terms of the angular errors, the largest angular errors around the, and aes of the C turntable and the B swngng 5 5 head are rad, rad, rad. 2 N, anbng. - Lu, ance. et al.

13 Receved for revew: yyyy-mm-dd 205 Journal of Mechancal Engneerng. All rghts reserved. Receved revsed form: yyyy-mm-dd DI code rgnal aper Accepted for publcaton: yyyy-mm-dd Compared wth the translatonal aes, the atttude errors of the rotatonal aes s harder to measure drectly. Therefore, the proposed method can be used to measure and dentfy geometrc errors for rotatonal aes. 3 CNCLUSINS The geometrc errors of fve-as CNC machne tools usually need to be measured n producton.the method of the DBB s smple, convenent and effcent, so t s preferred to be used. However, ths nstrument cannot provde the measurement of the atttude errors for machne tools. In ths paper, the B/C type of fveas CNC machne tool was taken as the object. A method to dentfy the atttude errors of the machne tool was studed based on the DBB, whch was used to measure the errors of the machne tool n producton stes effcently. Dfferent nstallaton and combnaton methods of the DBB were desgned n three drectons. Seven measurements were mplemented under three measurement modes, respectvely. Then, the atttude errors of the machne tool were obtaned by the dentfcaton models. The straghtness, squareness and backlash errors of the machne tool could be obtaned drectly by the DBB measurement system. Accordng to the measurement results, The straghtness errors of each as are not greater than 2.5μm. The squareness errors between any two aes are less than 3μm m. The backlash errors of each as are less than 0.5μm. Addtonally, the roundness errors are 6.μm, 8.6μm and 7.4μm on three planes. The man geometrc accuraces of the machne tool are wthn the range of the accuracy requrements. The angular errors were dentfed by the method of the DBB. The largest angular errors around the, and aes of the C turntable and 5 the B swngng head are rad, rad and rad. Based on the measured and dentfed results, t ndcates that the method adopted n ths paper s effectve. Therefore, t can be used as a reference to evaluate the errors of the machne tool n future producton. 4 ACKNWLEDGEMENTS Ths work s supported by the Natonal Scence and Technology Major roject of Chna under grant REFERENCES [] Klobucar, R., Acko, B. (207). Automatc hgh resoluton measurement set-up for calbratng precse lne scales, Advances n roducton Engneerng & Management, Vol. 2, No., 88-96, [2] Hrelja, M., Klancnk, S., Irgolc, T., aulc, M., Jurkovc,., Balc, J., Brezocnk, M. (204). artcle swarm optmzaton approach for modellng a turnng process, Advances n roducton Engneerng & Management, Vol. 9, No., 2-30, /apem [3] Hrelja M., Klancnk S., Balc J., Brezocnk M. (204). Modellng of a Turnng rocess Usng the Gravtatonal Search Algorthm. Int. Journal of Smulaton Modellng, Vol. 3, No., p. 30-4, /IJSIMM3() [4] Schwenke, H., Knapp, W., Hatjema, H., et al. (2008). Geometrc error measurement and compensaton of machnes-an update. CIR Annals-Manufacturng Technology, vol. 57, no. 2, p , DI: 0.06/j.crp [5] Vgnat, F., Nguyen, D.S., Brssaud, D.A. (202). Method to Determne the Impact of Geometrcal Devatons on roduct erformance. Strojnsk Vestnk-Journal of Mechancal Engneerng, vol. 58, no. 9, p , DI: /svjme [6] ang, S., ang, J. (204). Usng a double ball bar to measure 0 poston-dependent geometrc errors for rotary aes on fve-as machne tools. The Internatonal Journal of Advanced Manufacturng Technology, vol. 75, no., p , DI: 0.007/s [7] Bryan, J.B. (982). A smple method for testng measurng machnes and machne tool. art : prncples and applcaton. recson Engneerng, vol. 4, no. 3, p. 6-69, DI: 0.06/ (82) [8] Tsutsum, M., Sato, A. (2003). Identfcaton and compensaton of systematc devatons partcular to 5-as machnng centers. Internatonal Journal of Machne Tools and Manufacture, vol. 43, no. 8, p , DI: 0.06/S (03) [9] Tsutsum, M., Sato, A. (2004). Identfcaton of * Corr. Author's Address: School of Mechancal Engneerng, Tanjn Unversty, Tanjn, Chna, nyb582@tju.edu.cn 3

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