© ISO 2015 Test code for machine tools — Part 7 Geometric accuracy of axes of rotation Code d’essai des machines outils — Partie 7 Exactitude géométrique des axes de rotation INTERNATIONAL STANDARD IS[.]
INTERNATIONAL STANDARD ISO 230-7 Second edition 2015-05-15 Test code for machine tools — Part 7: Geometric accuracy of axes of rotation Code d’essai des machines-outils — Partie 7: Exactitude géométrique des axes de rotation Reference number ISO 230-7:2015(E) © ISO 2015 ISO 230-7:2015(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2015, Published in Switzerland All rights reserved Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country o f the requester ISO copyright o ffice Ch de Blandonnet • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org ii © ISO 2015 – All rights reserved ISO 230-7:2015(E) Page Contents Foreword v Introduction vi Scope Normative references Terms and definitions 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 General concepts Error motion terms Consequences of axis of rotation error motion Directional decomposition of axis of rotation error motion 10 Decomposition of measured axis of rotation error motion based on rotational frequency 11 Terms for axis of rotation error motion polar plots 12 Terms for axis of rotation error motion polar plot centres 14 Terms for axis of rotation error motion values 15 Terms for structural error motion 17 Terms for axis shift 17 4.1 4.2 4.3 4.4 Measuring units 18 Reference to ISO 230-1 18 Recommended instrumentation and test equipment 18 Environment 19 Rotary component to be tested 19 Rotary component warm-up 19 Structural error motion tests 19 4.7.1 General 19 4.7.2 Test procedure 19 4.7.3 Analysis o f results 19 Preliminary remarks 18 4.5 4.6 4.7 Error motion test methods for machine tool spindle units 20 5.1 5.2 5.3 5.4 General 20 Test parameters and specifications 20 Spindle axis of rotation tests — Rotating sensitive direction(s) 20 5.3.1 General 20 5.3.2 Radial error motion 20 5.3.3 Tilt error motion 23 5.3.4 Axial error motion 25 Spindle tests — Fixed sensitive direction 26 5.4.1 General 26 5.4.2 Test setup 26 5.4.3 Radial error motion 27 5.4.4 Axial error motion 29 5.4.5 Tilt error motion 30 Error motion test methods for machine tool rotary tables/heads 31 6.1 6.2 6.3 General 31 Axial error motion 32 6.2.1 Test setup 32 6.2.2 Test procedure 32 6.2.3 Data analysis 33 Radial error motion 33 6.3.1 Test setup 33 6.3.2 Test procedure 33 6.3.3 Data analysis for rotating sensitive direction 33 6.3.4 Data analysis for fixed sensitive direction 34 © ISO 2015 – All rights reserved iii ISO 230-7:2015(E) 6.4 Tilt error motion 34 6.4.1 Test setup 34 6.4.2 Test procedure 34 f 34 f 35 Annex A (informative) Discussion of general concepts 36 Annex B (informative) Elimination of reference sphere roundness error 55 Annex C (informative) f f f 59 Annex D (informative) f D ata analys is o r ro tating s ens itive directio n 4 D ata analys is o r fixed s ens itive directio n T e r m s a n d d e f i n i t i o n s o r c o m p l i a n c e p r o p e r t i e s o a x i s o r o t a t i o n rotation of spindle and rotary tables/heads 60 T e r m s a n d d e f i n i t i o n s o r t h e r m a l l y - i n d u c e d e r r o r s a s s o c i a t e d w i t h (informative) Static error motion tests 61 Annex F (informative) Measurement uncertainty estimation for axis of rotation tests 62 Annex G (informative) f f 67 Annex H (informative) Linear displacement sensor bandwidth and rotational speed 69 Annex E A l p h a b e t i c a l c r o s s - r e e r e n c e o t e r m s a n d d e f i n i t i o n s Bibliography 72 iv © ISO 2015 – All rights reserved ISO 230-7:2015(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work o f preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the di fferent types o f ISO documents should be noted This document was dra fted in accordance with the editorial rules of the ISO/IEC Directives, Part (see www.iso.org/directives) Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f patent rights ISO shall not be held responsible for identi fying any or all such patent rights Details o f any patent rights identified during the development o f the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents) Any trade name used in this document is in formation given for the convenience o f users and does not constitute an endorsement For an explanation on the meaning o f ISO specific terms and expressions related to formity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT), see the following URL: Foreword — Supplementary in formation The committee responsible for this document is ISO/TC 39, Machine tools, Subcommittee SC 2, Test conditions for metal cutting machine tools This second edition cancels and replaces the first edition ( ISO technically revised 230–7:2006), which has been ISO 230 consists of the following parts, under the general title Test code for machine tools: — Part 1: Geometric accuracy of machines operating under no-load or quasi-static conditions — Part 2: Determination of accuracy and repeatability of positioning of numerically controlled axes — Part 3: Determination of thermal effects — Part 4: Circular tests for numerically controlled machine tools — Part 5: Determination of the noise emission — Part 6: Determination ofpositioning accuracy on body and face diagonals (Diagonal displacement tests) — Part 7: Geometric accuracy of axes of rotation — Part 8: Vibrations [Technical Report] — Part 9: Estimation ofmeasurement uncertainty for machine tool tests according to series ISO 230, basic equations [Technical Report] — Part 10: Determination of the measuring performance of probing systems of numerically controlled machine tools — Part 11: Measuring instruments suitable for machine tool geometry tests [Technical Report] © ISO 2015 – All rights reserved v ISO 0-7: 015(E) Introduction T h i s I nternationa l Standard s b e en revi s e d b as e d on the com ments re ceive d from i ndu s tr y and ac adem i a relate d to the appl ic ation s o f a xi s o f ro tation error mo tion s to ro tar y table s , a nd o ther m i l l i ng and drilling operations where more than one sensitive direction can be of critical importance In this revi s ion, the term s and defi n ition s were up date d a nd the s p e c ia l c as e s , where s t order harmon ic o f rad ia l error mo tion d i ffers i n d i fferent d i re c tion s , were add re s s e d T hey are a l s o re ordere d b a s e d on a mo d i fie d s tr uc tu re for b e tter cl ari fyi ng the genera l concep ts and thei r appl ication s T he c as e s where there are multiple sensitive directions as well as the consequence of axis of rotation error motion in radial location of parts (2D sensitive direction) are described vi © ISO 2015 – All rights reserved INTERNATIONAL STANDARD ISO 230-7:2015(E) Test code for machine tools — Part 7: Geometric accuracy of axes of rotation Scope T h i s p ar t o f I S O i s me d at s tanda rd i z i ng me tho d s o f s p e ci fic ation and te s t o f the ge ome tric acc u rac y o f a xes o f ro tation u s e d i n mach i ne to ol s Spi nd le un its , ro tar y he ad s , and ro ta r y a nd s wivel l i ng table s o f machine tools constitute axes of rotation, all having unintended motions in space as a result of multiple sources of errors T h i s p a r t o f I S O covers the fol lowi ng prop er tie s o f ro ta r y a xe s: — axis of rotation error motion; — speed-induced axis shifts T he o ther i mp or tant prop er ties o f ro tar y a xe s , s uch as therma l ly i nduce d a xi s s h i fts and envi ron menta l temperature variation-induced axis shifts, are dealt with in ISO 230-3 This part of ISO 230 does not cover the following properties of spindles: — a ngu l ar p o s ition i ng acc u rac y (s e e I S O -1 a nd I S O -2 ) ; — run-out of surfaces and components (see ISO 230-1); — to ol holder i nter face s p e c i fic ation s; — inertial vibration measurements (see ISO/TR 230-8); — noise measurements (see ISO 230-5); — ro tationa l s p e e d range and acc urac y (s e e I S O 10 79 1- a nd I S O 41- 6) ; — balancing measurements or methods (see ISO 1940-1 and ISO 6103); — idle run loss (power loss); — thermal effects (see ISO 230-3) Normative references T he fol lowi ng i nd i s p en s able c uments , i n whole or i n p ar t, a re normatively re ference d i n th i s c u ment and a re for its appl ic ation For date d re ference s , on ly the e d ition cite d appl ie s For u ndate d re ference s , the late s t e d ition o f the re ference d c u ment (i nclud i ng any amend ments) appl ie s ISO 230-1:2012, Test code for machine tools — Part 1: Geometric accuracy of machines operating under no-load or quasi-static conditions © ISO 2015 – All rights reserved ISO 230-7:2015(E) Terms and definitions For the purposes o f this document, the following terms and definitions apply NOTE They are presented in this sequence to help the user develop an understanding o f the terminology o f axes o f rotation The alphabetical cross-re ferences for these definitions are given in Annex G 3.1 General concepts 3.1.1 spindle unit tool or workpiece carrying device providing a capability to rotate the tool or the workpiece around an axis of rotation Note to entry: A machine tool may have one or more spindle units 3.1.2 rotary table swivelling table component o f a machine tool carrying a workpiece and providing a capability for changing angular orientation of the workpiece around an axis of rotation Note to entry: I f a rotary table o f a machining centre can be used for turning operations, the rotary table can be seen as a spindle unit for these operations 3.1.3 rotary head swivelling head component o f a machine carrying a tool holding spindle unit and providing a capability for changing the angular orientation of the spindle unit around an axis of rotation Note to entry: Sometimes multiple axes o f rotations may be combined in a machine component 3.1.4 spindle rotor rotating element o f a spindle unit (or rotary table/head) 3.1.5 spindle housing stator stationary element o f a spindle unit (or rotary table/head) 3.1.6 bearing element o f a spindle unit (or rotary table/head) that supports the rotor and enables rotation between the rotor and the stator 3.1.7 axis of rotation line segment about which rotation occurs [SOURCE: ISO 230-1:2012, 3.5.2] Note to entry: See Figure a) Note to entry: In general, during rotation, this line segment translates (in radial and axial directions) and tilts within the reference coordinate frame due to inaccuracies in the bearings and bearing seats’ structural motion or axis shifts, as shown in Figure a) and b) © ISO 2015 – All rights reserved ISO 230-7:2015(E) 3.1.8 positive direction in accordance with ISO 841, the direction of a movement that causes an increasing positive dimension of the workpiece 3.1.9 perfect spindle (or rotary table/head) spindle or rotary table/head having no error motion o f its axis o f rotation relative to its axis average line 3.1.10 perfect workpiece rigid body having a per fect sur face o f revolution about a centreline 3.1.11 functional point cutting tool centre point or point associated with a component on the machine tool where cutting tool would contact the part for the purposes of material removal [SOURCE: ISO 230-1:2012, 3.4.2] 3.1.12 axis average line straight line segment located with respect to the reference coordinate axes representing the mean location of the axis of rotation Note to entry: See Figure a) Note to entry: The axis average line is a use ful term to describe changes in location o f an axis o f rotation in response to load, temperature, or speed changes Note to entry: Unless otherwise specified, the position and orientation o f the axis average line should be determined by connecting the calculated least-squares centres o f two data sets o f radial error motion taken at axially separated locations (see 3.4) Note to entry: ISO 841 defines the Z-axis o f a machine as being “parallel to the principal spindle o f the machine” This implies that the machine Z-axis is parallel to the axis average line o f the principal spindle However, since axis average line definition applies to other spindles and rotary axes as well, in general, not all axes o f rotation are parallel to the machine Z-axis An axis average line should be parallel to the machine Z-axis only i f it is associated with the principal spindle of the machine 3.1.13 axis shift quasi-static relative angular and linear displacement, between the tool side and the workpiece side, of the axis average line due to a change in conditions Note to entry: See Figure c) Note to entry: Causes o f axis shi ft include thermal influences, load changes, as well as speed and direction changes Axis of rotation error motion measurements are carried out over a period of time (number of revolutions) and conditions that avoid axis shift 3.1.14 structural loop assembly o f components which maintains the relative position and orientation between two specified objects (i.e between the workpiece and the cutting tool) Note to entry: A typical pair o f specified objects is a cutting tool and a workpiece on a machine tool (e.g lathe) In this case, the structural loop would include the workpiece holding fixture (e.g chuck), spindle, bearings and spindle housing, the machine head stock, machine bed, the machine slideways, carriages, and the tool holding fixture © ISO 2015 – All rights reserved ISO 230-7:2015(E) a) Reference coordinate axes, axis of rotation, axis average line, and error motion of a spindle b) Error motions of axis of rotation c) Position and orientation errors (axis shift) of axis average line Key spindle (rotor) EAC EBC tilt error motion of C around X-axis tilt error motion of C around Y-axis axis average line axis of rotation (at a given angular position of the spindle) spindle housing (stator) EXC radial error motion of C in X-axis direction ECC EXOC angular positioning error motion of C error of the position of C in X-axis direction erro r mo tio n traj ecto ry o f axis o f ro tatio n at varying angular p o s itio ns o f the s p indle EYC radial error motion of C in Y-axis direction E axial error motion of C Reference axis a ZC error of the position of C in Y-axis direction error of the orientation of C in A-axis direction; squareness of C to Y EB(OX)C error of the orientation of C in B-axis direction; squareness of C to X EC0C zero position error of C-axis EYOC EA(OY)C Figure — Reference coordinate axes, axis average line, and error motions of an axis of rotation shown for a C spindle or a C rotary axis © ISO 2015 – All rights reserved ISO 230-7:2015(E) Annex D (informative) T e r m s a n d d e f i n i t i o n s f o r t h e r m a l l y - i n d u c e d e r r o r s a s s o c i a t e d with rotation of spindle and rotary tables/heads D.1 thermally-induced radial error sh i ft i n the a xi s me as u re d p erp end ic u lar to the Z re ference a xi s D.2 thermally-induced tilt error ti lt s h i ft o f the a xi s relative to the Z re ference a xi s c au s e d by the therma l e ffe c ts D.3 thermally-induced axial error sh i ft o f the a xi s co a xia l with or p ara l lel to the Z re ference a xi s D.4 thermally-induced face error combi nation o f a xia l and ti lt s h i fts o f the a xi s me as u re d at a s p e ci fie d rad ia l lo c ation D.5 thermal error plot ti me -b as e d re cord o f therma l ly-i nduce d error D.6 thermal error value d i fference b e twe en the ma xi mum and m i n i mu m va lue s over a s p e c i fie d p erio d o f ti me, at a s p e c i fie d speed (or speeds) and with a measured temperature change 60 © ISO 2015 – All rights reserved ISO 230-7:2015(E) Annex E (informative) Static error motion tests E.1 General The purpose of these tests is to separate spindle-bearing errors from spindle error motion caused b y dynam ic e ffe c ts o f the s pi nd le d rive s ys tem I t i s i mp or tant to i s ol ate the errors c au s e d by s pi nd le b e ari ngs T hey a re o ften b lame d for problem s c au s e d by the s pi nd le d rive s ys tem E.2 Test procedure The test setup is similar to the ones described in 5.3 and 5.4 Put the spindle drive into neutral If the spindle has a non disengageable belt drive, the belt tension should be removed, if possible, so that the spindle is free of all external forces Ro tate the s p i nd le b y h a nd at a m i n i mu m o f two re vo lutio n s , s to p p i n g at a m i n i mu m o f ei ght p o i nts per revolution Release all hand forces and record the average sensor reading at each point Averaging the readings eliminates the effect of structural motion with the spindle stopped E.3 Data analysis T he d ata are ana lys e d for the rad i a l, ti lt a nd a xi a l error mo tion u s i ng me tho d s de s crib e d i n © ISO 2015 – All rights reserved 5.3 and 5.4 61 ISO 230-7:2015(E) Annex F (informative) Measurement uncertainty estimation for axis of rotation tests F.1 Estimation of the measurement uncertainty T he e s ti mation o f the me as u rement u ncer tai nty fol lows the pro ce du re s a nd e quation s o f I S O/ T R -9 The measurement uncertainties U are calculated for a coverage factor of k = T he me a s u rement u ncer tai nty shou ld be s tate d for l i ne a r me a s u rements (i e for rad i a l a nd a xi a l movements) in micrometres (µm) and for angular measurements (i.e for tilt movements) in micrometres per metre (µm/m) Me as u rement u ncer tai ntie s a l s o d i ffer F.2 for d i fferent for rad ia l a nd a xia l movements may d i ffer M e a s urement uncer ta i ntie s ca n fre quenc y nge s , i e for d i fferent s pi nd le s p e e d range s Contributors to the measurement uncertainty F.2.1 General I n genera l, the mai n contributors to the me a s urement u ncer tai nty measurement device and the environmental variation error (EVE ) The following assumptions are made: me a s urement device used corre c tly accord i ng to the a xi s o f ro tation te s ts are the gu idel i ne of — the — a l l ne ce s s ar y a l ignment a nd adj u s tment pro ce du re s a re c arrie d out corre c tly; — any leng th me a s u rement device s , i f appl ic able, are a l igne d s quare to the s ur face touche d; — the me as u rement e qu ipment i s mou nte d s tatic a l ly u nd dynamic a l ly s ti ff and without any b ackla sh; manufacturer/supplier; is for the e qu ipment — the machine components holding the measurement equipment behave as rigid bodies; — the measurement equipment is placed on the machine tool with a maximum deviation of 10 mm from the position stated on the test report, fre quenc y nge — the me as u rement e quipment i s u s e d with i n the a l lowable — the u ncer tai nty o f the s o ftwa re eva luation i s i nclude d i n the me as u rement u ncer ta i nty o f the manufacturer/supplier; measurement equipment I f the s e a s s u mp tion s a re no t be taken into account 62 s tate d by the e qu ipment fu l fi l le d, add itiona l contribution s to the me a s urement u ncer tai nty have to © ISO 2015 – All rights reserved ISO 230-7:2015(E) F.2.2 Uncertainty due to the measurement device, UDEVICE T he u s e o f a c a l ibrate d me a s urement device i s re com mende d I f the ca l ibration cer ti fic ate s tate s the u ncer ta i nty i n [µm] for l i ne ar and i n [μm/m] for angu lar me a s urements , Formu la (F.1) appl ie s (F.1) U DEVICE = UCALIBRATION where UDEVICE UCALIBRA- TION i s the u ncer tai nty due to the me as u rement device i n m icrome tre s (µm) in micrometres per metre (µm/m) for angular measurement; for l i ne ar a nd i s the u ncer tai nty o f the c a l ibration accord i ng to the c a l ibration cer ti fic ate i n m icro metres (µm) for linear and in micrometres per metre (µm/m) for angular measurements with coverage factor k = - I f no c a l ibration cer ti fic ate i s ava i l able and the m anu fac tu rer s tate s an error range i n m ic rome tre s (µm) and i n m icrome tre s p er me tre (µm/m) , then Formu la ( F ) s hou ld b e u s e d T he i n fluence o f the re s olution of the measurement device is in general negligible and can be checked according to ISO/TR 230-9:2005, Formula (C.3) U DEVICE = , R DEVICE (F.2) where UDEVICE RDEVICE i s the uncer ta i nty due to the me a s u rement device i n m ic rome tre s (µm) for l i ne a r and i n micrometres per metre (µm/m) for angular measurement, coverage factor k = 2; i s the error range given b y manu fac tu rer o f device i n m icrome tres (µm) for l i ne ar and in micrometres per metre (µm/m) for angular measurement If the measurement equipment is assembled from different components, at least the following contributors s hou ld b e u s e d — for the e s ti mation o f the me a s u rement u ncer tai nty o f the device: rou nd ne s s a nd s u r face fi n i s h o f the me ch an ic a l a r te fac t; — alignment of the artefact on the spindle under test, if relevant; — me a s urement u ncer tai nty o f the l i ne ar d i s placement s en s or; — resolution of the linear displacement sensor; faci a l me a s urements for eva luati ng the — d i s ta nce b etwe en the rad i a l or — eva luation o f the me as u rement re ad out ( p arame ters u ncer tai nty o f ti lt movement measurements; — alignment of the linear displacement sensor to the surface of the artefact; from me an va lue s , centre defi nition, e tc ) f f — All other assumptions as listed in F.2 f factor of k = This estimation can differ for different speed ranges of the axis under test shou ld b e u ncer tai nty o F.2.3 u l fi l le d T he e s ti mation o the me a s u rement the device c a n u s e I S O/ T R -9 : 0 , Formu lae (1) to (7 ) and s hou ld u s e a coverage Uncertainty due to the environmental variation error (E VE , or thermal drift), UEVE D u ri ng mo s t me as u rements , temp eratu re ch ange s a nd vibration s c an b e ob s er ve d th at m ight i n fluence the mach i ne to ol and the me as u rement device T he s e e ffe c ts , a nd e s p e ci a l ly any d ri ft, ne e d to b e kep t to a minimum T he e ffe c ts are che cke d b y a s i mple te s t, a d ri ft te s t © ISO 2015 – All rights reserved 63 ISO 230-7:2015(E) Before starting the measurements according to this part of ISO 230, the axis of rotation under test is stopped During the approximate time needed for an axis of rotation measurement the readout of the measurement device is recorded The range of the readout, EVE , is the remaining environmental variation error that is used to estimate the corresponding uncertainty according to Formula (F.3), based on ISO/TR 230-9:2005, Formula (C.9) U EVE = , E VE (F.3) where UEVE is the measurement uncertainty due to environmental variation in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement, coverage factor k = 2; EVE F.3 F.3.1 is the range from drift test in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement Uncertainty estimation for error motion plots and error motion values General Asynchronous error motion, inner error motion, and outer error motion [see Figure b) and c)] are based on maxima or minima o f single measurement, synchronous error motion [see Figure a)] is based on mean values of several error motion plots For error motion values two extreme values of an error motion plot are used, as shown in Figure The following assumptions are made: — the evaluation o f error motion centres is executed correctly, — the correct error motion centre is used for the evaluation of error motion values, — the main contributors to the measurement uncertainty are the measurement device and the environmental variation error, — the environmental variation error is uncorrelated for different plots and for different angles, — the plots are available over a 360° rotation of the axis under test I f these assumptions are fulfilled, ISO/TR 230-9:2005, Formulae (1), (3), and (A.7) can be applied to estimate the uncertainty o f error motion plots and error motion values 64 © ISO 2015 – All rights reserved ISO 230-7:2015(E) F.3.2 Uncertainty estimation for total error motion plot, asynchronous error motion polar plot, inner error motion polar plot, outer error motion polar plot, U(single plot) All plots, except the synchronous error motion plot, are based on maxima o f several single plots There fore just the uncertainties o f the two main contributors, which are assumed to be uncorrelated, are summed according to ISO/TR 230-9:2005, Formula (1): U( single plot ) = U DEVICE + U E2 VE (F.4) where U(single plot) UDEVICE UEVE F.3.3 is the uncertainty o f total error motion plot, asynchronous error motion polar plot, inner error motion polar plot, outer error motion polar plot, coverage factor k = 2, in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular error motion plots; is the uncertainty due to the measurement device in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement; is the measurement uncertainty due to environmental variation in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement Uncertainty estimation for synchronous error motion plots, U(synchronous plot) For synchronous error motion plots, several plots are used to calculate a mean plot There fore, the influence o f the environmental variation error can be reduced according to ISO/TR 230-9:2005, Formulae (A.7) and (1) together, this results in Formula (F.5): U2 U(synchronous plot) = U DEVICE + EVE n where (F.5) U(synchronous is the uncertainty o f synchronous error motion polar plot, coverage factor k = 2, UDEVICE is the uncertainty due to the measurement device in micrometres (µm) for linear UEVE is the measurement uncertainty due to environmental variation in micrometres n is the number o f polar plots to calculate synchronous error motion polar plot plot) in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement; and in micrometres per metre (µm/m) for angular measurement; (µm) for linear and in micrometres per metre (µm/m) for angular measurement; I f a large number o f plots are taken to calculate the synchronous error motion polar plot, the environmental variation error should be taken from a drift test lasting for at least as long as the measurement time for the plots taken F.3.4 Uncertainty of total error motion value, asynchronous error motion value, inner error motion value, outer error motion value, U(single plot value) The error motion values are based on the difference of the maximum and the minimum radial deviation o f a polar plot As maximum and minimum generally appear at di fferent angles o f the axis o f rotation, the © ISO 2015 – All rights reserved 65 ISO 230-7:2015(E) contributors to the uncertainty are regarded as not correlated With ISO/TR 230-9:2005, Formula (1), this results in Formula (F.6): (F.6) where U(single plot is the uncertainty o f total error motion plot value, asynchronous error motion plot U(single plot) is the uncertainty o f total error motion plot, asynchronous error motion polar plot, value) value, inner error motion plot value, outer error motion plot value, coverage factor k = 2, in micrometres (µm) for linear and in micrometres per metre (µm/m) for angular measurement; inner error motion polar plot, outer error motion polar plot Uncertainty of synchronous error motion value, U(synchronous plot value) F.3.5 The synchronous error motion values are based on the di fference o f the maximum and the minimum radial deviation o f a synchronous polar plot As maximum and minimum generally appear at di fferent angles o f the axis o f rotation, the contributors to the uncertainty are regarded as not correlated With ISO/TR 230-9:2005, Formula (1), this results in Formula (F.7): U (s ynch ro n o us p lo t valu e ) where U(synchronous plot value) = U 1, (s ynch ro n o us p lo t) (F.7) is the uncertainty o f synchronous error motion value, coverage factor k = 2, in micrometres (µm) for linear and in in micrometres per metre (µm/m) for angular measurement; U(synchronous plot) is the uncertainty o f synchronous error motion plot 66 © ISO 2015 – All rights reserved ISO 230-7:2015(E) Annex G (informative) A l p h a b e t i c a l c r o s s - r e f e r e n c e Term 2D effect of axis of rotation error motion a s ynch ro nou s er ror mo tio n a s ynch ro nou s er ror mo tio n p ol a r p lo t a s ynch ronou s er ror mo tio n va lue axial error motion axial shift axis average line axis of rotation axis of rotation error motion axis shift bearing bearing error motion error motion polar plot error motion polar plot centre error motion value face error motion face shift fi xe d s en s itive d i re c tion functional point fundamental axial error motion value fundamental error motion fundamental error motion polar plot hys tere s i s inner error motion polar plot inner error motion value least-squares circle (LSC) centre maximum inscribed circle (MIC) centre minimum circumscribed circle (MCC) centre minimum radial separation (MRS) centre non-sensitive direction outer error motion polar plot outer error motion value perfect spindle perfect workpiece p l ay © ISO 2015 – All rights reserved o f t e r m s a n d d e f i n i t i o n s No 3.3.6 3.5.5 3.6.4 3.8.4 3.4.4 3.10.3 3.1.12 3.1.7 3.2.1 3.1.13 3.1.6 3.2.3 3.6.1 3.7.1 3.8.1 3.4.5 3.10.4 3.3.3 3.1.11 3.8.5 3.5.3 3.6.5 3.1.21 3.6.7 3.8.7 3.7.4 3.7.6 3.7.7 3.7.5 3.3.2 3.6.8 3.8.8 3.1.9 3.1.10 3.1.20 67 ISO 230-7:2015(E) polar chart (PC) centre Term p ol a r p ro fi le centre positive direction pure radial error motion radial error motion radial shift rad i a l th row o f a ro ta r y a xi s at a given p o i nt re s idu a l s ynch rono u s er ro r mo tion re s idu a l s ynch ro no u s error mo tion p ol a r p lo t re s idu a l s ynch rono u s er ro r mo tion va lue ro ta r y (or s wivel l i ng) tab le ro ta r y (or s wivel l i ng) he ad rotating sensitive direction run-out of a functional surface at a given section sensitive direction speed-induced axis shift value speed-induced axis shift plot spindle spindle housing spindle unit Squareness error between a linear axis of motion and an axis average line squareness error between two axis average lines static error motion s tation a r y p o i nt r u n- out structural error motion structural error motion plot structural error motion with non-rotating spindle structural error motion with rotating spindle structural loop structural error motion value s ynch rono u s er ro r mo tion s ynch rono u s er ro r mo tion p ol ar p lo t s ynch rono u s er ro r mo tion va lue tilt error motion tilt shift total error motion total error motion polar plot total error motion value va r yi n g s en s iti ve d i re c tio n 68 No 3.7.2 3.7.3 3.1.8 3.4.2 3.4.1 3.10.1 3.1.15 3.5.4 3.6.6 3.8.6 3.1.2 3.1.3 3.3.4 3.1.16 3.3.1 3.10.6 3.10.5 3.1.4 3.1.5 3.1.1 3.1.19 3.1.18 3.2.4 3.1.17 3.2.2 3.9.3 3.9.2 3.9.1 3.1.14 3.9.4 3.5.2 3.6.3 3.8.3 3.4.3 3.10.2 3.5.1 3.6.2 3.8.2 3.3.5 © ISO 2015 – All rights reserved ISO 230-7:2015(E) Annex H (informative) Linear displacement sensor bandwidth and rotational speed H.1 General Machine tool spindle axis of rotation error motion measurements are made with non-contact linear displacement sensors such as capacitive or inductive displacement transducers Such sensors measure displacements o f a rotating target along one direction as the target moves towards and away from the sensor as it rotates The bandwidth o f the measurement system should be capable o f accommodating the frequency o f the motion o f the target along that direction This annex provides some background information and guidance in selecting the displacement sensor with adequate bandwidth H.2 Bandwidth of linear displacement sensors In general, many displacement sensors respond to changing target position by varying output voltage corresponding to the amount o f motion However, as the frequency o f the target motion increases, the response o f the sensor starts decreasing beyond a frequency threshold This behaviour is shown in Figure H.1 In this example, the sensor output is considered “flat” up to 10 kHz The bandwidth specification o f any sensor is the frequency at which the output voltage is reduced to 70,7 % (−3 db) o f lower frequency (or DC) output levels In the example given in Figure H.1, the sensor bandwidth is 15 kHz This means that a target moving at 15 kHz with a displacement o f 10 µm will only be measured as µm , Figure H.1 — Example frequency response of a linear displacement sensor with a bandwidth of k H z , h a v i n g a f l a t r e s p o n s e u p t o k H z H.3 Considerations for the frequency of target motion H.3.1 The fundamental frequency Due to radial throw, all rotating targets will exhibit one cycle o f error motion per revolution This establishes a “ fundamental frequency.” A linear displacement sensor that has a flat frequency response up to 10 kHz can accurately measure fundamental error motions o f targets at speeds up to 600 000 r/min A sensor with 15 kHz bandwidth can measure rotational speeds of 900 000 r/min at 70 % of the actual displacement amplitude © ISO 2015 – All rights reserved 69 ISO 230-7:2015(E) H.3.2 Non-fundamental frequencies Frequencies other than the fundamental frequency are also present in the error motions o f a spindle Imperfections in bearing components, mounts, motors, drives, structural vibration, and other factors each contribute a unique frequency These error motions occur at integer and non-integer multiples o f the fundamental frequency H.3.3 Stator and rotor shape errors Stators and rotors are not per fectly round These imper fections create additional frequencies in the spindle error motion, which are always synchronous with the fundamental frequency Two- and three- lobe shapes are common out-of-roundness errors These form errors create error motion frequencies two and three times higher than the fundamental frequency Higher number o f lobes require sensor with higher bandwidth for accurate measurements, otherwise, spindle speeds have to be reduced For example, to accurately measure a three lobed error motion, sensor with a flat response to 10 kHz can only be used at spindle speeds o f up to 200 000 r/min H.3.4 Mounting induced errors Mounting of the spindle can create stresses in the bearing structure resulting in slight deformities These create synchronous error motions and are essentially the same as stator and rotor shape errors Theoretically, each mounting fastener could add another lobe to the synchronous error motion H.3.5 Motor pole print-through The magnetic poles in motors create a normal force on the motor’s rotor that is different at the poles than between the poles This varying force cycles on every rotation Depending on the sti ffness o f the spindle bearing, this changing force can appear as error motions in the spindle This motion is synchronous with the fundamental frequency The number of poles in the drive motor determines the shape of the print-through error For example, an eight-pole motor creates an 8-lobe pattern and would be accurately measured at speeds up to 75 000 r/min by a sensor with a flat response to 10 kHz A typical drive motor has 4, 6, or poles Very large motors can have more poles, but due to their size, they run at much slower speeds keeping the error motion frequencies comparatively low H.3.6 Structural vibration The machine structure itself will have natural resonant frequencies that can appear in the spindle error motion Because o f the size and mass o f the machine structure, these frequencies are usually low (10 Hz – 30 Hz) and might or might not be synchronous with the fundamental frequency H.3.7 Rolling-element bearings Rolling-element bearings have four basic components: the rolling element itself (ball or roller), inner inherent imperfections cause deviations in bearing forces and the axis of rotation which result in spindle error motions Each bearing component has its own shape errors which produce error motions in the spindle The ratio of the diameters of the bearing components and the contact angle of the rolling element determine the race, the outer race, and the cage As the bearing turns, these components interact mechanically; their relationships to the fundamental frequency To prevent resonances within the spindle, bearings are intentionally selected so that these frequencies are not synchronous with the spindle rotor; there fore, these errors occur at non-integer multiples o f the fundamental frequency H.3.8 Bearing frequencies The frequency distribution o f a bearing consists o f cage frequency, inner and outer race (ballpass) requencies and ball spin frequency and their harmonics They are represented as the multiples o f f 70 © ISO 2015 – All rights reserved ISO 230-7:2015(E) the fundamental frequency Table H.1 shows an example o f typical bearing frequencies shown as the multiples o f the fundamental frequency The highest frequency shown is 8,32 times the fundamental frequency Accurate measurements o f error motions can be made with spindle speeds up to 70 000 r/min using a sensor with a flat response to 10 kHz Table H.1 — Example bearing frequencies for a typical rolling-element bearing Number of balls 15 Ball diameter Pitch diameter BallPass outer BallPass inner Cage Ball spin [mm] [mm] [multiples of [multiples of [multiples of [multiples of fundamental fundamental fundamental fundamental © ISO 2015 – All rights reserved 72,5 requency] f 6,68 requency] f 8,32 requency] f 0,45 requency] f 4,52 71 ISO 230-7:2015(E) Bibliography [1] ISO 230-2, Test code for machine tools — Part 2: Determination of accuracy and repeatability of [2] [3] [4] ISO 230-5, Test code for machine tools — Part 5: Determination of the noise emission ISO/TR 230-8, Test code for machine tools — Part 8: Vibrations ISO/TR 230-9:2005, Test code for machine tools — Part 9: Estimation of measurement uncertainty [5] ISO 1940-1, Mechanical vibration — Balance quality requirements for rotors in a constant (rigid) [6] ISO 6103, Bonded abrasive products — Permissible unbalances of grinding wheels as delivered — [7] ISO 10791-6, [8] [9] positioning numerically controlled axes for machine tool tests according to series ISO 230, basic equations state — Part 1: Specification and verification o f balance tolerances Static testing interpolations Test conditions for machining centres — Part 6: Accuracy of feeds, speeds and ISO 13041-6, Test conditions for numerically controlled turning machines and turning centres — Part 6: Accuracy o f a finished test piece Unification Document Axes o f Rotation, ME Annals o f the CIRP, 2/1976 [10] TLUSTY J System and Methods of Testing Machine Tools Microtechnic 1959, 13 p 162 [11] BRYAN J., CLOUSER R., HOLLAND E Spindle Accuracy, American Machinist, Spec Rpt No 612, Dec 4, 1967 [12] PETERS J, & VANHERCK P An Axis of Rotation Analyser, Proceedings of the 14th International MTDR Conference, Manchester 1973 [13] DONALDSON R A Simple Method for Separating Spindle Error from Test Ball Roundness Error CIRP Ann 1972, 21 (1) p 125 [14] Lu X., & J am ali an A A new method for characterizing axis of rotation radial error motion: Part Two-dimensional radial error motion theory Precis Eng 2011, v35 [15] ISO/TR 230-11, Test code for machine tools — Part 11: Measuring Instruments and their application to machine tool geometry tests [16] ISO 230-3, Test code for machine tools — Part 3: Determination of thermal effects [17] ISO 841, Industrial automation systems and integration — Numerical control of machines — Coordinate system and motion nomenclature 72 © ISO 2015 – All rights reserved ISO 0-7: 01 (E) ICS 080.01 Price based on 72 pages © ISO 2015 – All rights reserved