Asme b89 3 4m 1985 (1992) (american society of mechanical engineers)

Axes of Rotation Methods for Specifying and Testing ANSllASME B89.3.4M - 1985 REAFFIRMED 1992 FOR CURRENTCOMMllTEE PERSONNEL PLEASE SEE ASME MANUALAS11 S P O N S O R E DA N DP U B L I S H E DB Y T H EA M E R I C A NS O C I E T Y United Engineering Center OF M E C H A N I C A LE N G I N E E R S East 47th Street New York, N Y 10017 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe A AN M E R I C A N A T I O N ASL T A N D A R D This Standard will be revised when the Society approves the issuance of a new edition There will be no addenda or written interpretations of the requirements of this Standard issued t o this Edition This code or standard was developed under procedures accredited as meeting the criteria for American National Standards The Consensus Committee that approved the code or standard was balanced t o assure that individuals from competent and concerned interests have had an opport u n i t y t o participate The proposed code or standard was made available for public review and comment which provides an opportunity for additional public input from industry, academia, regulatory agencies, and the public-at-large ASME does not "approve," "rate," or "endorse" any item, construction, proprietary device, or activity ASME does not take any position with respect to the validity of any patent rights asserted in connection with any items mentionedin this document, and does not undertake t o insure anyone utilizing a standard against liability for infringement of any applicable Letters Patent, nor assume any such liability Users of a code or standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely theirown responsibility Participation by federal agency representative(s1 or person(s) affiliated with industry is not t o be interpreted as government or industry endorsement of this code or standard ASME accepts responsibility for only those interpretations issued in accordance with governing ASME procedures and policies which preclude the issuance of interpretations by individual volunteers No part of this document may be reproduced in any form, in an electronic retrieval systemor otherwise, without the prior written permission of the publisher Copyright 1986 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in U.S.A Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe Date of Issuance: January 31, 1986 (This Foreword is not a part of ANWASME 889.3.4M-1985) The testing of axes of rotation is at least as old as machine tools since most forms of machine tools incorporate such an axis One of the more widely distributed European works on testing machine tools' devotes considerable attention to the problems encountered Consideration of principles, equipment, and methods were included in the work Other European work' was carried forward and was published, in part, in 1959 As a result, a variety of terms came into use throughout the world to describe and explain the various phenomena found during testing and subsequent use of machine tool spindles In the United States, work published in 19673 represented a new viewpoint both in definitions and methods of testing This work also underscored the lack of standardization of the entire subject of rotational axes When the American National Standards Subcommittee B89.3, Geometry, was formed in February 1963, axes of rotation were not initially considered as a separate topic This Standard, which was initiated by J K Emery in August 1968 as a part of the Geometry Subcommittee work, is the result of recognizing the need for uniform technology and methods of testing for axes of rotation The goal in preparing the present Standard has been to produce a comprehensive document for the description, specification, and testing of axes of rotation Because this is both a new and a comprehensive Standard, extensive advisory material has been provided in the Appendices as an aid to the user It is recommended that this material be studied before putting the Standard to use While the examples of the Appendices involve machine tools and measuring machines, the terminology and the underlying concepts are applicable to any situation in which the performance of a rotary axis is of concern This Standard was adopted as an American National Standard by the American National Standards Institute (ANSI) on May 17, 1985 'Schlesinger, G , Testing Machine Tools Machinev Publishing Co 'Tlusty, J System and Methods of Testing Machine Tools, Microtechnic, 13 162 (1959) 'Bryan J B.,Clouser R W and Holland E., Spindle Accuracy American Machinisr Dec 1967 iii Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe FOREWORD (The following is the Roster of the Committee at the time of approval of this Standard.) OFFICERS E.G Loewen,Chairman M Fadl,Vice Chairman J A Hall, Vice Chairman C.E Lynch,Secretary COMMITTEE PERSONNEL AEROSPACE INDUSTRIES ASSOCIATION OF AMERICA, INCORPORATED T Mukaihata, Hughes Aircraft Co., Culver City, California AMERICAN MEASURING TOOL MANUFACTURERS ASSOCIATION R P Knittle, Glastonbury Gage/REB Industries, Inc., Glastonbury, Connecticut C W Jatho, Alrernare, Cutting Tool Manufacturers Association, Birmingham, Michigan NATIONAL MACHINE TOOL BUILDERS ASSOCIATION A M Bratkovich, National Machine Tool Builders Association, McLean, Virginia J B Deam, Alrernafe, National Machine Tool Builders Association, McLean, Virginia SOCIETY OF MANUFACTURING ENGINEERS W E Drews, Rank Precision Industries, Inc., Des Plaines, lllinios UNITED STATES DEPARTMENT OF THE AIRFORCE J E Orwig, AGMC/MLDE, Newark, Ohio UNITED STATES DEPARTMENT OFTHE ARMY F L Jones, USATSG, Redstone Arsenal, Alabama UNITED STATES DEPARTMENT OF THE NAVY D B Spangenberg, Navy Primary Standards Department, Washington, D.C INDIVIDUAL MEMBERS P E Bitters, TRW Greenfield Tap & Die Division, Greenfield, Massachusetts J B Bryan, University of California, Livermore, California A K Chitayat, Anorad Corp., Hauppauge, New York A M Dexter, Old Lyme, Connecticut C G Erickson, Sterling Die Operation, West Hartford, Connecticut M Fadl, Scientific Columbus, Columbus, Ohio M Gross, Gould, Inc., Cleveland, Ohio J A Hall, Rockwell International, Anaheim, California R B Hook, Brown & Sharpe Manufacturing Co., North Kingstown, Rhode Island R W Lamport, The Van KeurenCo., Watertown, Massachusetts R G Lenz, G M Corp., Warren, Michigan A A Lindberg, Moore Special Tool Co., Inc., Bridgeport, Connecticut E.E Lindberg, Hewlett Packard Laboratories, Palo Alto, California E Loewen, Bausch & Lomb, Inc., Rochester, New York W B McCallum, General Electric Co., Schenectady, New York V Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe ASME STANDARDS COMMITTEE B89 Dimensional Metrology PERSONNEL OF SUBCOMMITTEE - GEOMETRY R G Lenz, Chairman, G M Corp., Warren, Michigan J B Bryan, Universityof California, Livermore, California E E Lindberg, Hewlett Packard Laboratories, Palo Alto,California J H Soutar, Jr., Rock of Ages Corp., Barre, Vermont J M Worthen Durham (RFD Lee), New Hampshire PERSONNEL OF WORKING GROUP 889.3.4 - AXES OF ROTATION E E Lindbera - Chairman, Hewlett Packard Co., Palo Alto,California H Arneson, Professional Instruments Co., Ft Myers Beach, Florida J B Bryan, LawrenceLivermoreNational Laboratory, Livermore, California R R Donaldson, LawrenceLivermoreNational Laboratory, Livermore, California E S Roth, Productivity Services, Inc., Albuquerque, NewMexico G J Siddall, Hewlett Packard Co., Palo Alto,California L G Whitten Jr Union Carbide Corp.,Oak Ridge, Tennessee vi Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe F J Meyer, Jr., Machine Tool Engineer Associates International, Forestdale, Rhode Island A Miller, IBM, Endicott, New York D Pieczulewski, A G Davis Gage & Engineering Co., Hazel Park, Michigan El J Taylor, Bendix Measurement Systems Division, Dayton, Ohio E L Watelet, Warwick, Rhode Island G B Webber, L S Starrett Co., Cleveland, Ohio J H Worthen, Durham (RFD Lee), New Hampshire A Detailed Contents Precedes Each Appendix Foreword Standards Committee Roster iii v Definitions Specification or Description of an Axis of Rotation Figures ReferenceCoordinateAxes.Axis of Rotation.andErrorMotion 2 scope of aSpindle Plan View of a Spindle Showing Error Motion and Axial Face Radial and Tilt Motion PolarPlotsofErrorMotionand Its Components Error Motion Polar Plot, Showing PC Center and MRS Center and Error Motion Values About TheseCenters Tables Motion Type PreferredCenter Combination of Error MotionTerms Appendices A Discussion of General Concepts B C Elimination of Master Ball Roundness Error References vii 37 43 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled when CONTENTS AN AMERICAN NATIONAL STANDARD AXES OF ROTATION Methods for Specifying and Testing workpiece with its center line coincident with the axis of rotation Error motions are specified as to location This document is primarily intendedfor, but not limand direction as shown in Fig 2, sketch (a) and not ited to, the standardizationof methods of specifying and include motions due tothennal drzj? testing the axesof rotation of spindles used in machine 2.7 sensitive and nonsensitive directions - the sensitools and measuring machines This Standard does not the idealgenerated include the subjectof angular positioning accuracy Ap- tivedirectionisperpendicularto of pendices are attached which provide advisory informa- workpiece surface through the‘ instantaneous point machining or gaging (refer to Fig 2) A nonsensitive tion for the interpretation and useof the Standard The direction is any direction perpendicular to the sensitive Appendices are not partof this Standard direction Two types of sensitive direction are recognized: DEFINITIONS (a) fixed sensitive direction, in which the workpiece is rotated by the spindle and the point of machining or The definitions in this Standard have been arranged gaging is fixed; and numerically to help the user develop an understanding (6) rotating sensitive direction, in which the workof the terminology of axes of rotation piece is fixed and the point of machining or gaging rotates with the spindle 2.1 axis of rotation - a line about which rotation ocCOMMENTS: curs SCOPE (I) A lathe has a fixed sensitive direction; a jig borer has a rotating sensitive direction (2) With a fixed sensitive direction, the reference coordinates are fixed; with a rotating sensitive direction, the reference coordinates rotate with the spindle COMMENT: In general this line translates and tilts with respect to the reference coordinate axes, as shown in Fig 2.2 spindle - a device which provides an axis of tation ro- 2.8 error motion t e r n - the following terms are used for special casesof error motion: (a) radial motion - error motion in a direction normal to the Z reference axis and at a specified axial location [Fig 2, sketch (d)]; COMMENT: Other-named devices such as rotary tables, trunnions, live centers, and so on are included within this definition 2.3 reference Coordinate axes - mutually perpendicular X, Y, and Z axes, fixed with respect to a specified object COMMENTS: ( I ) For simplicity, the axis is chosen to lie along the axis of rotation, as in Fig (2) Examples of a specified object are “tool holder” and “indicator bracket.” (3) The specified object may be jixed or roruting COMMENT: The term “radial runout” has an accepted meaning which includes errors due to centering and workpiece out-of-roundness and hence is not equivalent to radial motion (6)axial motion - error motion colinear with theZ reference axis [Fig 2, sketch (b)]; COMMENT: “Axial slip, “end-camming,” and “drunkenness” are nonprefemd terms for axial motion 2.4 perfect spindle - a spindle having no motion of its (c) face motion - error motion parallel to the Z reference axis at a specified radial location [Fig 2, sketch axis of rotation relative to the reference coordinate axes 2.5 perfect workpiece - a rigid body having a perfect surface of revolution abouta center line (41; COMMENT: The term “face runout” has an accepted meaning analogous to “radial runout” [see (a) above] and hence is not equivalent to face motion 2.6 error motion - changes in position, ielative to the reference coordinate axes, of the surface of a.perfect Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe ANSllASME B89.3.4M-1985 AN AMERICAN NATIONAL.STANDARD AXES OF ROTATION bearings and housing, the machine slideways and frame, and the tool workholding fixtures See Appendix A, paras A and A4 Z Reference Errormotionof axis of rotation (prior to time r) &I laxis Axis of rotation (at time r) 2.1 error motion sources - the sources of error motion are: I I I I I I I I (a) bearing error motion, due to imperfect bearings; and (b) structural error motion, due to internal or external excitationandaffected by elasticity,mass,and damping of the structural loop Y Reference axis I COMMENT: See Appendix A, paras A3, A4, and A7.4 2.12 error motion polar plot - a polar plot of error motion made in synchronization with the rotation of the spindle The following terms apply to the error motion polar plot‘and its components (see Fig.3): (a) total error motion polar plot - the complete error motion polar plot as recorded; (b) average error motionpolar plot- the mean contour of the total error motion polar plot averaged over the number of revolutions, which can be further divided into: ( ) fundamental error motion polar plot - the best fit referencecircle fitted to the average error motion polar plot; (2) residual error motion polar plot - the deviation of the average error motion polar plot from the fundamental error motion polar plot FIG REFERENCE COORDINATE AXES, AXIS OF ROTATION, AND ERROR MOTION OF A SPINDLE COMMENTS: (i) Various reference circle centers are defined in para 2.13 and are discussed in Appendix A, para AI (2) Strictly speaking, the fundamental error motion polar plot of an eccentric workpiece is a limacon This has a negligible deviation from a circle if the eccentricity is small See Appendix A, para A7.5 (3) The division of average error motion into fundamental and residual components is not applicable to radial and tilt motions because the fundamental component is nonexistent ( ) The term “synchronous error motion” is a nonpreferred term for average error motion since the latter includes asynchronous error motions which not necessarily average out to zero - error motion in an angular direction relative to the Z reference axis [Fig.2, sketch (e)]; ( d ) tilt motion COMMENTS: ( I ) Tilt motion about the Y axis is in the sensitive direction; tilt motion about the X axis is in the nonsensitive direction This comment is equally applicable to both fixed and rotating sensitive directions (2) “Coning,” “wobble,” and “swash” are nonpreferred terms for tilt motion See Appendix A, para A7.6 (3) Theterm “tilt motion” rather than “angular motion” was chosen to avoidconfusion with rotation about the axis or with angular positioning error of devices such as rotary tables (c) asynchronous error motion polar plot - the deviations of the total error motion polar plot from the 2.9 error motion measurement - a measurement reaverage error motion polar plot; cord of error motion, which shall include all pertinent information regarding the machine, instrumentation, and COMMENT: In this context the term “asychronous” means nonrepetitive from revolution to revolution of the spindle The previously test conditions as detailed in para 3.1.1 usedterm “random error motion” is now nonpreferred because of (a) static error motion measurement- a special case confusion with the statistical meaning of the word “random” of error motion in which the error motion is sampled ( d ) inner error motion polar plot - the contour of with the spindle at rest at a series of discrete rotational the inner boundary of the totalerror motion polar plot; positions (e) outer error motion polar plot - the contour of 2.10 structural loop - the assembly of physical comthe outer boundaryof the total error motion polar plot ponentswhichmaintain the relativepositionbetween 2.13 error motion centers - the following centersare two specified objects defined for the assessment of error motion polar plots COMMENT: A typical pair of specified objects is the cutting tool and the workpiece; the stmctural loop would include the spindle shaft, (refer to Fig 4): Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh ANSllASME B89.3.4M-1985 AN AMERICAN NATIONAL STANDARD (a) General Case of Error Motion (e) Face Motion (e) Tilt Motion Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe ANWASME 889.3.4M-1985 AN AMERICAN NATIONAL STANDARD AXES OF ROTATION (b)Axial Motion (d) Radial Motion AXES OF ROTATION (a) Total Error Motion (b)Average Error Motion (e) Asynchronous Error Motion FIG POLARPLOTS (c) Fundamental Error Motion (d) (f)Error Inner Motion Residual Error Motion ( ) Outer Error Motion OF ERROR MOTION AND ITS COMPONENTS Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh ANSVASME B89.3.4M-1985 AN AMERICAN NATIONAL STANDARD A9 MASTER TEST ERRORS Thus far it has been assumed that a geometrically perfect master test ballor equivalent was being used in the various error motion measurement examples It is clear that the geometry errors in a master will causeerroneous error motion measurements, and it cannot always be assumed that the master has negligibleerrors, since high quality axes of rotationmay have error motions of the order of l pin (0.025 pm) Appendix B describes methodsfor separating the errors of the master from the average error motion component ofthe a x i s of rotation A11.1 Minimum Radial Separation Center The concept of the minimum radial separation censo as ter is, as the name implies, that of a center chosen to make the difference in radii of the two concentric cirA10 ERROR MOTION VERSUSRUNOUT cles which contain the error motion polar plot an absoORT.I.R lute minimum By definition, the MRS center yields the It should be noted that error motion measurements smallest possible number for the error motion value differ from measurements of runout or T.I.R (total inThere is no direct method of locating this center and dicator reading) in several respects It is important to some form of iterative trial and error must be used In understandthesedifferences, since runouttestshave unusual cases, more than one such centermay exist Figbeen used extensively in the past in assessing the accuure A16 shows three successive trials using a bow comracy of rotational axes Runout is defined as “the total pass; further reductionis still possible as the reader may displacement measuredby an instrument sensing against wish to verify In general, the minimum has not been a moving surface or moved with respect to a fixed surfound until the inner and outer circles both touch the face.” Under this definition, a radial runout measurepolar profile at two points; in unusual cases more than ment includes both the roundness error and the centering two points percircle may occur In the commoncase of error of the surface that the gagehead senses against, two points per circle, the points must also alternate beand hence radial runout will be identical to radial motion tween the inner andouter circles The time required for only if both of these errors are zero As noted previtrial and error searching can be reduced by use of a ously, neither of theseconditionsiseasilyaccomtransparent template having engraved concentric circles plished While centering error unavoidably makes the Further reductions in time, together with improved acxunout larger than the error motion, it is possible for curacy, can be obtained with computer-aided systems roundness errors to make the runout either larger or (see Section A15) using iterative algorithms smaller than the error motion The latter situation can The MRS center has been chosen as the preferred arise if the surface against which the displacement trans- polar plot center for error motion assessment in the presducer is sensing was machinedin place on the a x i s bearent Standard and is to be understood as the method to ings, as discussedpreviouslyinpara.A7.2.Similar be used if no methodis specified.Any of the other three comments applyto face motion versus face runout; the methods can be used provided that the method is speclatter measurement includes nonsquareness and circular ified flatness errors (seealso para A7.5) A11.2 Least Squares Circle Center A l l ’ ERROR MOTION VALUES The least squares circle cenrer is based on the mathematical approachof choosing a center which will minimize the sum of the squares of the polardeviations plot from a circle about thatcenter The error motion values obtained by the LSC method canbe expected tobe about 10% larger than the MRS values on the average Since In most cases, an error motion value is equal to the difference in radii of two concentric circles that will just enclose the corresponding error motion polar plot, and the value obtaineddependsuponthelocation of the common center of these twocircles The followingfour 28 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh methods are recognized inthis Standard for locating polar plot centers: (a) minimum radial separation (MRS) center; (b) least squarescircle (LSC)center; (c) inscribed circle (MIC) center; maximum ( d )minimum circumscribed circle(XlCC) center These centersare the sameas those recognizedby ANSI B89.3.1 [para.Cl(a)] which is logical in view ofthe previously discussed relationship between radial motion and roundness In addition, a fifth center, the polar chart (PC) center, is used in establishing error motion values which include fundamental axial motion(see para A1 1.4) tion of the wheel spindle automatically becomes asynchronous motion with respectto the work spindle FIG A16 Third Trial DETERMINATION OF MINIMUM RADIALSEPARATION it canbedefinedmathematically,the LSC center is unique and can be found without trial and error methods The method is well suited to digital computer analysis and the LSC center can also be located by analog electroniccircuits For handcalculations,the LSC method is slower and more subjectto gross errors than the MRS method Figure A17 is a description of the LSC method, abstracted from Section A3 of the British Standard 3730: 1964 [para Cl(f)] A proof of the formulae and guidance on the effect ofthe number of radial ordinates used canbe.found in the same reference analogous to centeringe m r As a consequence, the total and average axial motion values are always measured using concentric circles drawn from the polar chart (PC) center If it is desired to break the average axial motion values into fundamental and residual axial motion components, thenany of the above four methods can be used to find the best fit center of the residual axial motion polar plot The radial distance between this best-fit center and the PC center is the fundamental axial motion value (also referred to as the axial motion center offset) The MRS center is the preferred center and is to be assumed unless another centeris specified Since face motioninvolvesthesamefundamental A11.3 Maximum Inscribed and Minimum component as axial motion, it follows that total and avCircumscribed Circle Centers erage face motion should also be based on the PC center However, if face motion is measured directly from These items are self-explanatory The error motion value is the difference in radii to a second circle drawn amasterflatmountedontheaxisofrotation,then about the same centerso as to just contain the polar plot squareness error of the fiat to the axis of rotation will This introduce a second fundamental motion component These centers are sometimes used in roundness measurement andare included in this Standard for complete- component cannot be separated from that due to the axis unless the fundamental axial motion value is known.If ness in view of the relationship already discussed bethe latter is known, the simplest procedure isto assess tween radial motion and part roundness For example, the residual portion of the face motion polar plot from assume a circular parthas a machined profile in accordance with the total radial motion polar plot and that it the appropriate polar plot center and then addthe fundamental axial motion value to obtain the desired result is placed in a perfectly round ring gage of the smallest In the general case of error motion at an arbitrary diameter that will acceptthe part Then the total radial motion value aboutthe MCC center represents the larg- angle to the Z reference axis, the fundamental error motion is equal to cos times the fundamental axial est gap between the part and gage, and, if the part is motion Therefore the addition procedure of the precedrotated in the ring gage, it will rotate about the MCC ing paragraph canbe used, except that the added quancenter tity is the fundamental axial motion times cos4 Finally, for tilt motion, the nonexistence of fundaA11.4 Polar Chart Center mental tilt motion requires the use of one of the four polar plot centers, with the polar chart center never being As noted previously, fundamental axial motion is a used red property of an axis of rotation rather than an error 29 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh Second Trial First Trial Least squares circle Least squares X 10 Y Determination of Least Squares Centerand Circle From the center of the chart, draw a sufficient even number of equally spaced radial ordinates In the illustration they are shown numbered 1-1 Two of these at right angles are selected to provide a system of rectangular coordinates X-X and Y-Y The distances of thepoints of intersection ofthe polar graph with these radial ordinates, P1 to P,,, are measured from the axes X-X and Y-Y, taking positive and negative signs into account The distances a and b of the least squares center from the center of the paper are calculated from thefollowing approximate formulae: a = X sum of x values number of ordinates b= n x sum of y values - 2Cy number of ordinates n The radius R of theleast squares circle, if wanted, is calculated as the average radial distance of thepoints P from thecenter; that is: R= Er sum of radial values numbers of ordinates n In practice, if it is required to know only the radial width of the zone enclosing the curve, there is no point in finding R, and it is sufficient to draw the inscribing and circumscribing circles from theleast squares center FIG A17 DETERMINATION OF LEAST SQUARESCENTER AND CIRCLE [para C l ( f 11 lExtrsa horn BS 3730:1964.b p o d u e e dby parmiuionof the British Standards Instinkh.NOTE BS 37301964h s been wpMseded by BS 37301982.) 30 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled w In determining the least squares center and circle, the position of the center of the least squares circle and the value of its radius can be calculated from simple approximate formulae Referring t o the figure below, the practical procedure is as follows: The asynchronous motion value if found from the total error motion polar plot as the maximum radial width of the “cloud band” at any angular position around the circumference It is the only measurement which does not employ concentric circles, since it involves the radial variation at a particular angle rather than the radial variation around the full circumference To be strictly correct, the asynchronous error motion value should be measured along a radial line from the polar chart (PC)center rather than from a best-fit center, even though this is contrary to what seems intuitively correct Figure A18 illustrates this point by means of a computer generated plot of a high frequency sinusoid of uniform amplitude which is superimposed on a limacon The sinusoid amplitude is constant if it is measured radially from the PC center, as it should be, but is up to 8% smaller (in this case) if it is measured radially from the MRS center A12 AXIS AVERAGE LINE FIG A I ASYNCHRONOUS MOTION ASSESSMENT - CONSTANT-AMPLITUDE SINUSOIDWITH CENTERING ERROR, SHOWING PROPER MEASUREMENT ALONG RADIUS FROM PC CENTER The definition given in para 2.1 for an axis of rotation is descriptive rather than technical, serving as a starting point in developing a more rigorous set of definitions for e m r motions and their measurement However, a definition that specifies the precise location of an axis of rotation is desirable For this purpose, the axis average line is defined as the line passing through two axially separated radial motion polar plot centers (see para 2.16) Axial motion is the only measurement which is independent of whether the sensitive direction is fixed or rotating, and hence is most easily measured by a fixed gagehead sensing along the Z reference axis For low speed rotary axes such as rotary tables, trunnions, etc., both fixed and rotating sensitive direction cases can be dealt with by use of a polar recorder whose angular drive is mechanically or electrically synchronized to the axis of rotation For the rotating sensitive direction, the master test ball is supported from the machine frame and the gagehead is supported on the axis of rotation For one or a few revolutions of the axis, it is usually possible to coil the gagehead cable around the axis in a noninfluencing manner; for continuous rotation, slip rings or their equivalent are necessary For high speed axes, the frequency response of polar recorders is usually inadequate since the polar plot may contain frequencies that are orders of magnitude higher than the axis rotational frequency The oscilloscope with a camera attachment is a more suitable instrument, but since it employs rectilinear rather than polar coordinates, means must be provided to generate a base circle and to cause the error motion to appear as a radial deviation from the base circle A13 ROTATING SENSITIVE DIRECTION MEASUREMENTS As noted inpara A2.3, the sensitive direction rotates with respect to the machine frame in those cases in which the workpiece is supported from the machine frame and the tool or gagehead is supported from the axis of rotation Boring machines and certain roundness measuring instruments are examples of machines having a rotating sensitive direction In principle, the same concepts regarding error motion of an axis of rotation apply for a rotating sensitive direction as for a fixed sensitive direction This can be understood by placing the observer on the tool or gagehead, so that the workpiece appears to rotate It will be assumed that the reader is already familiar with these concepts from the preceding Sections of this Appendix, and this Section deals with the differences involved in measuring and displaying the error motion polar plot 31 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe A11.5 Asynchronous Error Motion Value TEST METHOD FOR RADIAL MOTIONWITH AROTATING SENSITIVEDIRECTION [TLUSTY, para C1(dl1 The use of the oscilloscopeis simplest in the case of directions, are sensed by comparatively low magnificaradial motion measurement with a rotating sensitive dition gageheads to generate sine and cosine signals for rection, using a method described by Tlusty [see para 90 deg the basecircle; a single cam with the gageheads C 1(d)] FigureA19 is a schematic diagram showing hori-apart could also be used Radial motion is detected by zontalandverticalgageheadswhich-senseradially a third high magnification gagehead sensing against a against a master test ball The gagehead signalsare amas possible) master test ball which is centered (as closely plified and fed to the respective horizontal and vertical on the Z reference axis The sine and cosine signals are axes of the oscilloscope By use of a wobble plate, the each multiplied by the radial motion signal using Hallmaster ball is made eccentric to the Z reference axis effect multipliers and are then fed into the two axes of For a perfectaxis of rotation,the result would be a perthe oscilloscope The modulation of the base circle by fect circle as the axis rotates For an imperfect axis, rathe signal from the fixed radial motion gagehead yields dial motion in the direction of the master ball eccentrica polar plotof radial motion versus the angular position ity alters the shape of the oscilloscope display Motion of the axis of rotation Vanherck [see para Cl(g)] has at right angles to the master ball eccentricity moves the tested a modification in which a small (2 oz.) commeroscilloscope pip along a tangent to the base circle, causcial synchro unit is physically attached to the axis of ing a negligible effect on the shape Thus the arrangerotation to replace the eccentric cams andlow magnifiment yields a measurementof radial motion along arocation gageheadsas the sinecosine signal generator The tating sensitive direction which is parallel to aline from advantages are lower cost, less difficulty in obtaining an the Z reference axis to the geometric center of the ecaccurately round base circle, and simplification of the centric master ball If the tool or gage can be mounted test setup, with negligible influence on the axis from the on the a i s in only one angular orientation, the master synchro attachment except in the most exacting situaball must be eccentric in this direction If the orientation tions is arbitrary, then the axis shouldbe tested with the ball eccentric in a numberof different directions A15 CONSIDERATIONS ONTHE USE OF THE TWO-GAGEHEAD SYSTEM FOR AFIXED SENSITIVEDIRECTION A14 FIXEDSENSITIVEDIRECTION MEASUREMENTS Use of an oscilloscope for radial motion measurement with a fixed sensitive direction requires a separate means for generating the basecircle Figure A20 shows amethoddescribedbyBryanetd [seepara Cl(e)] Two circular cams, eccentric by 0.005 in in perpendicular 32 Since the oscilloscope test method of Fig A20 requires special electronic equipment thatis not commercially available, it is natural to consider substituting the two gagehead system of Fig A19 for measuring radial motion with a fixed sensitive direction If this substitution is made, the resulting radial motion polar plot will Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh FIG A19 Circle generating cams Spherical master f Summing amplifier MultiplierDemodulator FIG A20 TEST METHOD FOR RADIAL MOTIONWITH A FIXED SENSITIVE DIRECTION [BRYAN, ET AL., para Cl(e)l (Courtesy of University of California, Lawrence Livermore National Library and U.S Department of Energy) not be representative of the potential part out-of-roundness as discussed in para A7.2 If = deg is the fixed sensitive direction, then the polar plot reflects radial motion in this direction only in the vicinity of = deg and = 180 deg Moreover,if a given localized movement of the axisof rotation occuring at8 = deg appeam as a peak onthe polar plot, the same movement occumng at = 180 deg will have an undesired sign reversal and will appearas a valley At = 90 deg and = 270 deg the same movement will not register on the polar plot Despite the above observations, it still appears intuitively plausible that the radial motion value should be roughly the same for both fixed and rotating sensitive directions, even if the details of the polar plot are different This view appears reasonable if the factor of concern is asynchronous radial motion However, for’averageradialmotion,Donaldson[seepara Cl(h)] has notedacasegivingpreciselytheopposite result, in which an axis which exhibits an elliptical pattern when tested in a fixed sensitive direction isfree of radial motion when tested in a rotating sensitive direction The case occursfor the following motions: 33 AX(@ = A COS 28 (AS) AY(8) = (A9) A28sin whel): the coordinate system is that of Fig A9, sketch (a) With a fixed sensitive direction along the X axis, the radial motion polar plot has the equation where r, is the base circle radius Eq A10 represents an elliptical shape, having a value r, + A at = deg and = 180 deg and a value of r, - A at = 90 deg and = 270 deg The radial motion value based on any of the polar profile centersis A If the sensitive direction rotates with angle 8, the radial motion is given by the equation r(8) = r, + AX(@ COS + AY(8) sin (All) Figure A21 shows the resolution AX(@ of and AY(8) into components along the rotating sensitive direction Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe /- Wobble plate \ \ = AX(0) cos B awe) A VECTOR DIAGRAM FOR ROTATING SENSITIVEDIRECTION FIG A21 \ \ \ \ 34 D’ 1’ / F \ + AY(8) sin \ AB = AX@) cos AD = AY ( ) sin B = A’D’ A F = A B + ~ \ Y Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh Sensitive direction sin CY sin = - COS(^ A16 DIGITAL COMPUTER MEASUREMENT SYSTEM A digital computer provides an alternative basis for a system to collect, manipulate, and present data from axis of rotation measurements Vanherck and Peters [see para Cl(g)] describe a system in which the signal from a radially sensing gagehead [as in Fig A9, sketch (a)] is sampled at closely spaced angular intervals, using a perforated disk mounted on the axis and a photoelectric trigger The samples are converted to digital form and stored for subsequent calculation and display of the total, average, and asynchronous radial motion polar plots with elimination of the centering error; location of the MRS, LSC, MIC, and MCC centers, and the radial motion values from these centers In addition, three-dimensional representation (in the form of a helix over successive revolutions), master ball roundness error storage and automatic correction (after measurement by one of the methods of Appendix B), frequency content of the radial motionsignal by the Fast-Fourier transform method, and zero-phase-shift filtering are features of the digital measurement system which would be difficult to incorporate in an analog system Another potential advantage of the digital system is the ease with which it can deal with arbitrary fixed or rotating sensitive directions By adding a second radially sensing gagehead at 90 deg to the first, similar to that shown in Fig A19, the radial motion along a sensitive direction at any angle to the first gagehead can be calculated by the computer from the equation 0) - COS (a + 0>] the result is r(0) = r, + A-2 [cos + cos 381 Equation A14 is the equation of a circle which is offset from the origin by a distance A (aside from a secondorder limacon distortion as discussed in para A7.5), and hence the axis would be perfect if tested by the two gagehead system Two additional comments can be made on the above finding First, it can be argued that if the offset circle is assessed by concentric circles from the polar chart (PC) center, then a value of A is obtained, as with the fixed sensitive direction However, there is no way to carry out the initial electronic zeroing to locate the PC center, since the base circle cannot be generated independently of the polar profile using the test method of Fig A19 Secondly, the view might be taken that the above example is a mathematical oddity which is unlikely to occur in practice In this regard it can be noted that radial motion polar plots commonly exhibit an elliptical pattern, and that to the extent that the overall patterns in the X and Y directions contain components as given in Eqs A8 and A9, these components will not contribute to the measured radial motion value r(0) = r, + AX(@ cos + AY(8) sin d, (A15) where AX(@ and AY(8) are the two gagehead signals For a rotating sensitive direction having any angle d, relative to = 0, the radial motion using the same signals is given by r(8) = r, + AX(@ cos (8 + 4) By adding a second pair of 90 deg gageheads in a different axial plane, a similar generality is obtained in the measurement of tilt motion; with a fifth gagehead sensing axially, the error motion can be calculated in any direction at any location (refer to Fig A7) 35 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled when that leads to Eq A l l Combining Eqs A8 and A9 with Eq A1 and using the trigonometric identities (This Appendix is not a part of ANSllASME B89.3.4M -1985 but is included for information purposes only.) B1 B2 B3 B4 The Reversal Method B2.1 ProcedureP B2.2 Procedures The Multistep Method Practical Considerations Introduction Figures B1 B2 B3 Table B1 Schematic Test Setups Error Separation by ProfileAveraging The Multistep Method Procedure P andProcedure S 37 39 39 39 41 41 41 40 40 42 41 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh APPENDIX B ELIMINATION OF MASTER BALL ROUNDNESS ERROR (This Appendix is notpart of ANSllASME 689.3.4M-1985 but is included for information purposes only.) B1 INTRODUCTION B2.1 Procedure P Measurements of radial motion are directly influenced by the out-of-roundness of the test ball or other circular master against which the gagehead senses This Appendix describes methods for separating the out-ofroundness of the master from the radial motion of the axis of rotation These methods can be described as “multi-orientation” error separation techniques since they involve taking two or more measurements with differing relative orientations between master and spindle When correctly applied, they are a very effective means of accurately determining test ball errors The two most widely used techniques, the “reversal” and “multistep” methods, are described here Procedure P begins by recording an initial polar plot; the deviations from the base circle will be designated at T,(8) Figure B1, sketch (a) shows a schematic diagram of the test arrangement with the arbitrary initial positions being marked as = deg by coincident marks on the master, the gagehead, the shaft, and the housing of the axis of rotation The recorded value of Ti(@is the sum of the master roundness profile P ( ) and the radial motion S(8) It is assumed that the sign convention for roundness measurement is used so that hills and valleys on the polar plot correspond to hills and valleys on the master The second step of Procedure P is to make a second polar plot T @ ) using the arrangement of Fig B1, sketch (b), in which the shaft and housing marks are coincident at = deg., but the master and gagehead positions are reversed (rotated 180 deg about the axis of rotation) The same sign convention must be used as for TI(@.Comparison of Figs B1, sketch (a) and B1, sketch (b) shows that theout-of-roundness of the master is recorded in the same manner since the relative position of the gagehead and the master is unchanged However, radial motion is recorded with a reversed sign in Fig B1, sketch (b) since a movement of the spindle toward the gagehead in Fig B1, sketch (a) becomes a movement away from the gagehead in Fig B1, sketch (b) Expressed as an equation, B2 THE REVERSAL METHOD The reversal method has been described by Donaldson [ para C1@) ] and is also contained in Appendix D2.5 of ANSI B89.3.1 [para Cl(a)] The methodrequires two profile measurements to be taken, in the secthe orientations of both the part and the gagehead are reversed by 180 deg relative to the spindle The relative position of part and gagehead is unchanged while the effect of the spindle radial motion on the gagehead at any position is equal and opposite Thus the part or master ball roundness error can be extracted as the mean of the two traces while the difference gives the spindle radial motion The method is described in detail below In the interest of consistency, the same notation is used here as in AppendixD2.5 of ANSIB89.3.1,with P ( ) (for part) representing the out-of-roundness of the master and S(8) (for spindle) representing the radial motion Itis assumed that the axis of rotation is free of asynchronous radial motion; means of dealing with asynchronous motion will be discussed in Section EM The method canbe divided into two procedures: Procedure P , which yields the roundness error of the master, and Procedure S, which yields the radial motion Adding Eqs (BI) and (B2) causes S(8) to cancel Solving for P ( ) gives 39 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled when APPENDIX B ELIMINATION OF MASTER BALL ROUNDNESS ERROR 40 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh ERROR SEPARATION BY PROFILE AVERAGING FIG B2 (b)Radial Motion, S (8) (e) (a) Master Out-of-Roundness, P p(e’ f T2P T1 SCHEMATIC TEST SETUPS FIG B1 (e) (b) For T W ( ) and Ta (e) (a) For TI Procedure Master P B2.2 Procedure S S Procedure S begins by recording an initial profile T,(0) as in Procedure P The second step of Procedure S is also identical to the second step of Procedure P except that the sign convention must be reversed Calling the second polar plot T2S(6)it follows that Reverse for Record Master, gagehead Master, gagehead, sign Average out-of-roundness Radial motion the case of the reversal method, the technique can, in principle, be applied to either rotating workpiece (fixed sensitive direction) or rotating stylus (rotating sensitive direction) roundness instruments If Eqs (Bl) and (B4)are added, P ( ) cancels; solving for S(0) gives B4 PRACTICAL CONSIDERATIONS Several practical considerations arise in obtaining accurate results with error separation techniques A crucial assumption in these techniques is that the part and spindle error profiles are highly repeatable In the case of the part profile, this involves ensuring that the plane of measurement remains constant in each orientation without axial shift or tilt of the measurement track Sensitivity to track iocation can be tested by examining the repeatability of the measured profile as the track is shifted by small amounts in the first setup of each.method In the presence of asynchronous radial motion, the spindle error must be interpreted as the average radial motion polar plot, and the resulting accuracy depends upon being able to obtain a repeatable average radial motion in each orientation This can be tested by successive recordings of the measured profile in the first setup Repeatability over a single revolution is sometimes improved by turning the spindle backward to the same starting point, particularly with rolling element bearings With digital computer-aided measurement systems, averaging over several profiles in each orientation can be used to minimize the effects of asynchronous spindle motion Both the reversal and multistep methods have their respective advantages and disadvantages The reversal method may require modification of some commercial instruments and only works for radial error motions Other error motions can be computed by measuring axial motion and tilt motion as well and then combining the three error profiles according to Eq A4, which is practical only with the aid of a digital computer The multistep method is directly applicable to any error mo- Equation B5 states that a third polar plot drawn halfway between T,(0)and T2S(0)will be the radial motion polar plot s(e) Table B1 summarizes the above two procedures Both procedures are equally valid with either a fixed or a rotating sensitive direction B3 THE MULTISTEP METHOD The multistep method [Spragg and Whitehouse, para Cl(i)] entails taking a whole series of roundness profile measurements in each of which the part is stepped through equal angles relative to the spindle The most effective way of implementing the method is to take n separate but equi-angled orientations adding up to 360 deg as illustrated schematically in Fig B3 It is then possible to separate the part error, which rotates with each step, from the spindle error, which remains stationary To obtain the part error, it is necessary to pick one angle of the spindle’s rotation and to identify the changes in gagehead signal at this angle for all the different orientations in sequence To obtain spindle errors, a fixed angle on the part has to be chosen instead Before the error separation can be carried out, the profile sets from each orientation have to be normalized, i.e., they have to be adjusted so that the profile eccentricity and radius are always the same Because of the large amount of data processing, the method is much more conveniently carried out using a digital computer As in 41 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled whe TABLE B1 PROCEDURE P AND PROCEDURE S Equation B3 states that the out-of-roundness profile of the master, P ( ) , is the average of the first and second polar plots If T,(@and T2p(0)are recorded on the same polar chart, P ( ) can be obtained by drawing a third polar plot halfway between the first two as shown in Fig B2, sketch (a) Step / / FIG B3 n THEMULTISTEPMETHOD tion but requires a digital computer for effective implementation It also suffers to some extent from harmonic distortions and is therefore limited to errors involving only low numbers of undulations per revolution Both methods are, however, capable of giving excellent results A comparison of the two methods, using computer-aided roundness equipment [see para Cl(i)], has given agreement to within 0.04 pin (0.001 pm) standard deviation Once the test ball e m r s are known it is a simple matter, in a digital system, to store them in memory By subtracting them point-for-point from the measurement, the spindle radial motion can be evaluated accurately in one step 42 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh Gaaehead (This Appendix is not a pan of ANWASME B89.3.4M-1985 but is included for information purposes only.) ( f ) British Standard 3730:1964, Assessment of Departures from Roundness C1 REFERENCES In the case of ANSI Standards, referto the most recent edition (g) Vanherck, P., and Peters, J., Digital Axis of Rotation Measurements, CZRP Annals, vol 22/1, 1973 (a) ANSI B89.3.1, Measurement of Out-of-Roundness (h) Donaldson, R , A Simple Method for Separating Spindle Error from Test Ball Roundness Error, CZRP Annals, VOl 21/1, 1972 (b) ANSI B89.6.2, Temperature and Humidity Environment for Dimensional Measurement (e) Schlesinger, G., Testing Machine Tools, Machinery Publishing Co ( i ) Spragg, R., and Whitehouse, D., Procedures of the Institute of Mechanical Engineers, 182, 1968 ( d ) Tlusty, J., System and Methods of Testing Machine Tools, Microtechnic, vol 13, 1959 ( j ) Chetwynd, D G and Siddall, G.,Improving the Accuracy of Roundness Measurement, Journal of Physics,'E:Sci Instrum 9, 1976 (e) Bryan, J B., Clouser, R W., and Holland, E., Spindle Accuracy, American Machinist, Dec 4, 1967 43 Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh APPENDIX C REFERENCES Measurement of Qualified Plain Internal Diameters for Use as Master Rings and Ring Gages B89.1.6M-1984 Precision Gage Blocks for Length Measurement B89.1.9M-1984 (Through 20in and 500 mm) DialIndicators (for LinearMeasurements) B89.1.10-1978 Methods for Performance Evaluation of Coordinate Measuring Machines B89.1.12M-1985 Measurement of Out-of-Roundness B89.3 1.1972(R1979) Axes of Rotation B89.3.4M-1985 Temperature and Humidity Environmentfor Dimensional Measurement B89.6.2-1973(R1979) Gages and Gaging for Unified Inch Screw Threads 81.2-1983 Gages and Gagingfor Metric M Screw Threads B1.16 M.1984 Preferred Limits and Fits for Cylindrical Parts B4.1-1967(R 1979) B46.1-1978 Surface Texture (Includes ANSI Y14.36-1978) The ASME Publications Catalog shows a complete list of all the Standards published by the Society The catalog and bindersfor holding these Standardsare available upon request Copyrighted material licensed to Stanford University by Thomson Scientific (www.techstreet.com), downloaded on Oct-05-2010 by Stanford University User No further reproduction or distribution is permitted Uncontrolled wh AMERICAN NATIONAL STANDARDS RELATED TO DIMENSIONAL METROLOGY