DETERMINATION OF ERRANT RUN-OUT OF THE AXIS OF ROTATION OF OBJECTS, PERFORMING ACCURATE ROTATIONAL MOVEMENTS

Transcription

1 DETERMINATION OF ERRANT RUN-OUT OF THE AXIS OF ROTATION OF OBJECTS, PERFORMING ACCURATE ROTATIONAL MOVEMENTS Hrsto K. RADEV, Vassl J. BOGEV, Velzar A. VASSILEV Techncal Unversty of Sofa, Bulgara Abstract. Ths artcle dscusses problems of the accuracy of the axes poston of objects accomplshng rotary moton. Dfferent schemes to estmate the errant run-out of the axes and faces of object tables are proposed, as well as ther capabltes are estmated. Keywords: rotary moton, radal and axal run-out, errant radal and axal run-out 1. Introducton Constancy of the rotatonal axs s a basc requrement towards the objects, accomplshng accurate rotatonal movement (such as rotary tables of roundness measurng machnes, rotary modules of measurng systems and producton machnes, etc.). Ths volatlty s estmated by the so called Errant run-out (radal, axal and angular). The errant radal run-out (Δ rbb) s defned as volatlty of the poston of a pont from the nstantaneous axes of rotaton relatve to a vrtual reference axs n a plane perpendcular to that axs. The errant axal run-out (Δ abb) s defned as volatlty of the poston of ponts from the nstantaneous axes of rotaton relatve to a plane, whch s perpendcular to the vrtual reference axs. The errant angular run-out (Δ abb) s defned as volatlty of the angular poston of the nstantaneous axs of rotaton relatve to the vrtual reference axs. The vrtual reference axs s a straght lne n a xyz coordnate system, passng through the centrods of the ponts of the nstantaneous axs of rotaton n two dstant parallel planes xy []. The axs of rotaton s orented along the axs Z. A centrod s a pont wth coordnates, whch are arthmetc mean values of the coordnates of the ponts relatve to whch t s determned The errant run-out n a gven plane or drecton should be consdered as the locus of nstantaneous axes of rotaton of the object and accordngly represents a complex closed curve or a set of ponts, postoned along the lne of measurement (Fgure 1, a and b). The errant run-out can be quanttatvely estmated through the sze of the avalable area, or through the magntude of the devaton from the vrtual datum, or through the nstant postons of the nstantaneous axes relatve to the vrtual reference axs. For example, the errant radal run-out can be estmated by the dameter D of the crcle descrbed around the curve (Fgure 1a), or through the nstant devatons Δ relatve to the centrod, or through the spread of these devatons. max mn It should be noted that the dameter of the envelopng crcle D s affected by extreme devatons and s not suffcently nformatve, extr whch greatly lmts ts use. a) b) c) Fgure 1. The errant run-out n a gven plane or drecton The errant axal run-out s evaluated by the nstant postons of the nstantaneous axes of rotaton relatve to ther centrod, or the spread of ths poston n the drecton of the vrtual reference axs (the axs z) (Fgure 1b). The errant angular run-out s measured by the angle, whch th nstantaneous axs of rotaton makes wth the vrtual reference axs, or by the magntude of these angles ( ) (Fgure 1c). max mn The poston of the nstantaneous axs of rotaton, or respectvely the angle s a functon of the angle of rotaton of the object around the vrtual datum axs. 119

2 RECENT, Vol. 16, no. (45), July, 015 All three types of errant run-out have ther systematc and random component, whch can be evaluated by repeated measurement and by a correspondng statstcal processng of the measurement results.. Schemes of measurement - descrpton, nature and comparatve analyss.1. Scheme No. 1 Ths scheme s often used n the metrologcal practce to determne the errant radal and axal runout. But the methodology ncluded heren below makes t s possble to measure also the errant angular run-out. The procedure nvolves the measurement of both the radal and axal run-out of a reference glass hemsphere, located on the top of the turntable of the object under test (Fgure, a and b), by means of two measurng heads (MH), as well as by subsequent processng of ths prmary nformaton [4]. a) In the general case, the radal run-out ncludes the followng components: The devaton from roundness of the measured profle secton (EFK); The eccentrcty of the center of the assocated crcle of the measured profle (e); The errant run-out n a radal drecton (errant radal run-out Δ rbb). The axal run-out ncludes the followng components: The devaton from flatness of the measured profle EFE of the axal surface at a gven radus; Devaton from perpendcularty EPR of the assocated plane of the measured at a gven radus profle relatve to the axs of rotaton; Errant axal run-out Δ abb (nconstancy of the axal poston of the work-pece durng ts rotatonal movement); A component related to the parallelsm EPA of the nstantaneous axes of rotaton, respectvely the parallel msalgnment of the perpendcular to them planes, whch serve as a startng nstant datum -.e. a component assocated wth the angular errant run-out. In case a standard sphere s used, the component assocated wth ts own shape devaton, can be gnored and then the errant run-out occurs (results n) as the roundness devaton of the measurements hemsphere profle. The errant radal run-out on the graphs showng the results of the measured radal run-out s expressed as the roundness devaton relatve to the least squares assocated (LSQ) crcle, whose center s the centrod of the examned (obtaned) values, Fgure 3. The errant radal run-out s equal to the roundness devaton of the measured profle Δ. b) Fgure 3. The errant radal run-out expressed as the roundness devaton relatve to assocated LSQ crcle c) Fgure. The measurement of both the radal and axal run-out of a reference glass hemsphere When measurng the axal run-out wth a measurng head (MH) wth a flat stylus and a well centered hemsphere, all components except the errant axal run-out are neglgble. The latter can be measured drectly wth the MH. Smlarly to the errant radal run-out, the errant axal run-out 10

3 abb at a gven angle of rotaton φ, may be presented n the form of a graph, as the roundness devaton relatve to the LSQ assocated crcle. A measurng mandrel wth a ball s used for measurng the errant radal and axal run-out of the spndle of machne tools (Fgure c) [3]. Usually there s standardzaton of the heghts z 1 and z of the cross-secton, n whch the measurng of the sem-sphere s performed, or of the length z of the measurng mandrel, on whch the ball s located (Fgure b). It should be noted that the errant radal run-out s due to two factors: the parallel shft of the nstantaneous axs of rotaton and the angular devaton from ther vrtual datum axs. If necessary, these two components can be determned separately by assessng the angular errant run-out. In many cases, namely the evaluaton of angular errant run-out s essental n determnng the functonal and metrologcal capactes of certan measurng systems contanng rotary modules. The followng proposed methodology allows the determnaton of the angular errant run-out usng the results from the measurement of the radal run-out of dfferent hemsphere profles at dfferent heght z from the table top (Fgure, a and b). As s seen on Fgure 4a, the angle, whch makes the th nstantaneous axs of rotaton wth the vrtual datum axs, can be determned through the dfference between two sectons, located at dstance Δ z, usng the formula: z z1 arctg (1) z Analogcally to the errant radal and axal runout, the angular errant run-out can be presented n the form of a graph for assessng the devaton from roundness of whch represents the departure from roundness relatve to LSQ assocated crcle (Fgure 4b). The depcton of errant radal, axal and angular run-out as graphs to for assessng the crcularty devaton allows us to estmate both ther local values as a functon of the angle of rotaton, and ther maxmum dsspaton n the form of a spread. Plottng of graphs s performed by standard programs. The advantages of scheme No. 1 are: The possblty for determnaton of both errant radal and axal run-out, as well as errant angular run-out; Hgh precson of the orgnal measurement data; The smplcty of the measurng equpment; RECENT, Vol. 16, no. (45), July, The possblty for automatng the measurement, processng and presentaton of the results, whch allows measurement of the errant radal and axal run-out n both statc, as well as dynamc mode. Fgure 4. The angular errant run-out presented n the form of a graph The shortcomngs should refer the need for consecutve (non-smultaneous) measurement of the radal run-out of dfferent heghts of the measured hemsphere profles, whch hnders precse assessment of the random component of errant angular run-out... Scheme No. Ths scheme s nherently smlar to scheme No 1, but nstead of the reference glass hemsphere t uses a stepped reference shaft, two pns of whch have been pre-calbrated pursuant to EFK, and the face surface has been pre-calbrated accordng to EFE, usng a roundness measurng machne (Fgure 5). The axal run-out along a path wth radus R s measured wth the probes MH 1 and MH. Ths path s also used for the calbraton of EFE. The need for calbraton of EFE s elmnated, when an nterferental glass plate has been mounted on the face of the mandrel. The own devatons of the form (EFK of the

4 RECENT, Vol. 16, no. (45), July, 015 necks and EFE of the front surface) are excluded when measurng radal and axal run-out by ntroducng relevant correctons [3]. heads MH 1 and MH (Fgure 6a). In good centerng the measurement lne of MH 1 concdes approxmately wth the axs of rotaton.e. can be assumed R 1 0 and the errant axal run-out can be evaluated drectly by ts readng A 1. A graph s bult on the values of A on whch the local values of A abb and ther spread s assessed as the devatons from roundness smlar to schemes No. 1 and No.. Fgure 5. The axal run-out measured along a path wth radus R The axal run-out s determned by the halve values of the sums from the readngs and A A of MH 1 and MH at a specfc angle of rotaton φ,.e. A1 A A. () Thus, the nfluence of the perpendcularty of the shaft face relatve to the axs of rotaton s excluded. A graph s made by these values smlar to errant radal and angular run-out, and the local values of the errant axal run-out, as well as abb ther spread can be estmated by the roundness devatons wth respect to the LSQ assocated crcle. An advantage of the scheme No., besdes the aforementoned of scheme No. 1, s the possblty for smultaneous measurement of the radal and axal run-out of the calbrated radal and axal profles (surfaces) of the measurng mandrel, whch s essental for the assessment of the errant angular run-out under a dynamc mode. To the shortcomngs can be attrbuted the need for a measurng mandrel, calbrated accordng to EFK and EFE, whch complcates the measurement equpment and affects the accuracy of measurement..3. Scheme No. 3 Both the errant axal and angular run-out can be determned usng ths scheme (Fgure 6). The axal run-out of the glass nterferental plate lad on the object table s measured along paths wth rad R 1 and R usng two measurng A 1 Fgure 6. The measurement of the axal run-out of the glass nterferental plate l along paths wth rad R 1 and R The axal run-out, measured wth MH, ncludes both the errant axal run-out as well as the errant angular run-out of the axs. Then n analogcal manner to scheme No. 1, the current angle between the nstantaneous rotaton axes and the vrtual reference axs can be determned by the expresson (Fgure 6b): A A 1 90 arctg. (3) R where A are the current readngs of MH measurng the axal run-out of the path of radus R. Usng these values of a graph can be bult, on whch the current values of abb.e. should be presented as devatons relatve to LSQ assocated crcle (Fgure 6c). The major advantage of scheme No. 3 s the ablty to measure the axal and angular run-out wth the help of a relatvely smple measurng equpment and software. 1

5 RECENT, Vol. 16, no. (45), July, 015 The nablty to determne the errant radal runout can be referred to the defcences..4. Scheme No. 4 Ths scheme s typcally used to determne the errant axal run-out, as well as the devaton from perpendcularty of the table relatve to the axs of rotaton. An nterferental glass plate wth neglgble devaton from flatness s set on the table of the rotary module under test (Fgure 7a) [1]. Fgure 7. The measurement of the errant axal run-out, as well as the devaton from perpendcularty of the table relatve to the axs of rotaton The axal run-out of the plate along a path of radus R s measured usng two measurng heads MH 1 and MH located at 180. As has already been mentoned, the axal runout ncludes the flatness devaton of the plate (whch s neglgble), the devaton from perpendcularty of the assocated plane of the plate relatve to the axs of rotaton, the errant axal runout and the errant angular run-out of the axs of rotaton. Determnaton of the errant axal run-out The readngs of the two measurng heads and A A 1 are recorded smultaneously whle rotatng the object table at a relevant angle. The sem-sum of these readngs s calculated: A1 A A. (4) Ths sem-sum reflects only the errant axal run-out when the flatness devaton of the plate s neglgble. The current poston of the center of the plate n z-axs drecton can be evaluated usng the values of, relatve to ther centrod (average A value) and also the spread of these devatons ( ) (Fgure 1b). A A max mn Determnng the errant angular run-out Two ways to evaluate the errant angular runout are proposed as follows: 1 st way: Through the dfferences n the estmates of the devatons from the perpendcularty of the plate relatve to the axs of rotaton The sem-dfferences and n the readngs of the measurng heads are calculated at angles of rotaton and : A1, A, ' ; (5) A A1, 180 A, 180. (6) " A A' A" These values reflect the devatons from the plate perpendcularty relatve to the axs of rotaton and the errant angular run-out (shake of the object table). In the absence of errant angular run-out the A' A" wll be equal to the absolute values of and value, but wth opposte sgns (Fgure 7b),.e.. (7) A' A" The devaton from perpendcularty at a radus R s determned by the maxmum value of the ' " dfference Amax A A max. mn In the presence of errant angular run-out: " A A ; The A ' 1 A A ; ' A A. dfference A '' A A '' A 13

6 RECENT, Vol. 16, no. (45), July, 015 reflects the errant angular run-out as the angle between two nstantaneous axes of rotaton, located at 180 from each other -.e. angles and +180 A A (Fgure 7b): arctg. R When the dfference A ' A ' s postve, the angle s counterclockwse, and when t s a negatve - clockwse. The current values of the angle between the nstantaneous axes of rotaton and the vrtual reference axs cannot be determned by ths procedure, but nformaton for maxmum "shakng" of the object table s receved,.e. of max nd way: Through the devaton from snusodalty In the absence of errant axal and angular runout and n the presence of a devaton from plate perpendcularty relatve to the axs of rotaton, the local values of the axal run-out are descrbed by a sne wave. The presence of errant run-out wll nvolve а devaton from snusodalty EFS (Fgure 7c). In ths case, under devaton from snusodalty s meant the devaton of the real snusodal movements of a pont of the nterferental plate from the perfect sne-curve due to errant angular run-out. The devaton from snusodalty EFS at a gven rotaton angle of the table s determned wth regard to the deal sne-curve bult relatve to a perfect sne wave, usng the least squares method. Then the current values of angular errant runout expressed n angular unts s determned by the expresson: ' EFS arctg 90, R and the spread as a dfference between the maxmal and the mnmal values of : max mn. The major advantage of the scheme dscussed s the possblty of accessng not only the errant axal run-out but also the errant angular run-out, whle usng a smple measurement equpment, both n a statc and n a dynamc mode. The nablty to determne the errant radal runout may be allocated to the shortcomngs of the scheme..5. Scheme No. 5 Through a measurement under ths scheme the errant axal and angular run-out can be determned.. An nterferental glass plate wth neglgble devatons from flatness s set on the object table of the rotary module. Usng three measurng heads, whch are located on a crcle wth a gven radus R at 10 nterval from each other, the axal run-out of the plate s measured durng ts 360 rotaton (Fgure 8a). Fgure 8. The measurement of the errant axal and angular run-out Usng the readngs of measurng heads at a gven rotaton angle of the table -.e. by the coordnates of three ponts on the plate n a coordnate system xyz, usng a standard program and the poston of ts centrodal, the locaton of ts centrod along axs z (coordnate z ) s calculated, as well as the poston of the normal vector of ths plane relatve to the axs of rotaton. The axs of rotaton s orented along the axs z. The fluctuaton of the coordnate z of the centrod s the errant axal run-out, whle the varaton of the poston of the normal vector to the axs of rotaton reflects the errant angular run-out. Both types of run-out can be expressed wth ther current values relatve to the correspondng centrod, or through ther spread. The proposed by ths scheme approach can be successfully used for the assessment of the angular and axal poston of any object table (platform), performng lnear and angular dsplacements n the space (Fgure 9), both under statc and dynamc mode. Under a statc mode, the measured object can be placed wthn the workspace of a coordnate measurng machne (CMM) and the coordnates of the correspondng ponts n the coordnate system XYZ can be consequently determned. 14

7 RECENT, Vol. 16, no. (45), July, 015 measurng heads mounted on a stable fxed ntal datum (datum coordnate system) (Fgure 10). Fgure 9. The assessment of the angular and axal poston of any object table The man advantage of the scheme s the ablty to determne the errant axal and angular run-out under statc, as well as under dynamc mode. The proposed approach under ths scheme can be successfully appled to the assessment of the axal and angular poston of any object table (platform) performng axal and angular movements n the space under statc and dynamc mode. The complcated measurng equpment (several measurng heads) and software may be referred to the dsadvantages. The approach, proposed under ths scheme, can be successfully used for assessng the axal and angular poston of any object table (platform) carryng out axal and angular movements n the space both under a statc and under a dynamc mode. The measurement n statc mode nvolves the use of CMM. A measurement platform together wth the mounted on t prsmatc body s located wthn CMM workspace. The coordnates of sx pre-marked ponts of the cube n the coordnate system of the CMM (XYZ) are determned durng the dscrete movement of the platform (Fgure 9). For each statc poston, usng the three ponts 1, and 3, the defned by t planes are determned, the poston of the normal vector to the plane relatve to axs z s calculated, as well as the centrod of the three ponts -.e. the translaton z, rotatons x and y of the body relatve to axs x and axs y. Usng the coordnates of ponts 3 and 4, the translaton x along the axs and the rotaton about the axs z,.e. φ z are determned. Usng the coordnates of pont 6, the translaton y can be determned. In ths way complete nformaton of the platform poston can be obtaned durng ts dscrete movement wthn the workspace of CMM. Under dynamc mode the same effect s acheved wth smultaneous measurement of the coordnates of the respectve ponts, usng Fgure 10. The assessment of the platform poston under dynamc mode For small dsplacements, when the mpact of the change of the ponts postons on the cube surfaces can be consdered neglgble, measurements can be performed smultaneously wth the sx MH. When the dsplacement of the measured ponts s sgnfcant, t s approprate to determne the poston of each sde of the cube separately, based on three measured ponts. 3. Concluson 1. The constancy of the axs of rotaton measured by radal, axal and angular errant run-out s a basc requrement towards the objects, accomplshng accurate rotatonal movements.. The accomplshed survey and analyss of varous schemes for determnaton of ths nconstancy, allows the selecton of the most approprate way to measure the respectve errant run-out for each case. 3. Usng approprate automaton and software, all dscussed and analyzed schemes allow recevng and processng of the prmary measurement nformaton for the determnaton of errant run-out under statc, as well as under dynamc mode. References 1. Vasslev, V.: Measurng the dsplacement of a drll n machnng large hollow shafts. Proceedngs of the Natonal Symposum "Metrology and metrologcal 011", Bulgara. Radev, Hr.: Method for the measurement of the devatons of form and poston of surfaces and axes of rotatonal elements to vrtual ntal datum. Patent BG ISO 30-1:005 Test code for machne tools Part 1; Geometrc accuracy of machnes operatng under no-load or fnshng condtons 4. Vasslev, V.: Development and testng of a system for measurng geometrc parameters of large shafts. PhD thess, Techncal Unversty of Sofa, Bulgara, 014 Receved n May