Asme b89 3 7 2013 (american society of mechanical engineers)

ASME B89.3.7-2013 Granite Surface Plates A N A M E R I C A N N AT I O N A L S TA N D A R D ASME B89.3.7-2013 Granite Surface Plates A N A M E R I C A N N AT I O N A L S TA N D A R D Two Park Avenue • New York, NY • 001 USA Date of Issuance: June 26, 201 This Standard will be revised when the Society approves the issuance of a new edition ASME issues written replies to in quiries cern in g in terpretations of tech nical aspects of th is Standard Periodically certain actions of the ASME B89 Committee may be published as Code Cases Code Cases and interpretations are published on the ASME Web site under the Committee Pages at http://cstools.asme.org/ as they are issued Errata to codes and standards may be posted on the ASME Web site under the Committee Pages to provide corrections to incorrectly published items, or to correct typographical or grammatical errors in codes and standards Such errata shall be used on the date posted The Committee Pages can be found at http://cstools.asme.org/ 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American Society of Mechanical Engineers Two Park Avenue, New York, NY 001 6-5990 Copyright © 201 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All rights reserved Printed in U.S.A CONTENTS Foreword Committee Roster Correspondence With the B89 Committee Introduction iv v vi vii General Definitions References General Requirements Figures Exaggerated View of a Surface Plate With Twist Surface Plate, Style 1, No Ledge, Rectangular or Square Surface Plate, Style 2, Two-Ledge, Either Direction, Rectangular or Square Surface Plate, Style 3, Four-Ledge, Rectangular or Square Surface Plate, Style 4, No Ledge, Round Support Layout for Rectangular Surface Plate Support Layout for Round Surface Plate Tables Common Sizes and Flatness Tolerances Tolerances for Local Variations in Flatness Using a Repeat Reading Gage Restrictions on Surface Area for Flatness and Twist Mandatory Appendix I Testing Nonmandatory Appendices A B C D E F G Mineralogical and Physical Properties Thickness Supports Factors Distorting the Work Surface Care of Granite Surface Plates Guidance to Estimating Uncertainty in Surface Plate Measurement Traceability iii 3 3 5 6 14 15 20 21 24 25 31 FOREWORD This ASME Standard is a revision of the 1973 Federal Specification GGG-P-463c which has been used extensively in American industry since its publication Although the measurement methods for surface plates had already been in use some decades prior to the Federal Specification, it did serve to document these methods In addition, it provided common language and terms of classification for surface plate manufacturing and commerce While little has changed with regard to measurement methods and the flatness tolerances of the various plate grades are still relevant today, ASME B89 Division decided an effort was justified to modernize the document Most notably, a more complete glossary was added with currently accepted definitions, metric units were added where appropriate, and a new format was used that should be more familiar to current users of the Standard This Committee also recognized the need for updates to a surface plate specification to incorporate modern concepts, such as traceability and measurement uncertainty, that have undergone considerable development since 1973 This new document under ASME B89 ownership will provide the platform for these and other updates periodically through the revision process This edition of B89.3.7 was approved by ANSI on April 12, 2013 iv ASME B89 COMMITTEE Dimensional Metrology (The following is the roster of the Committee at the time of approval of this Standard.) STANDARDS COMMITTEE OFFICERS B Parry, Chair S Phillips, Vice Chair F Constantino, Secretary STANDARDS COMMITTEE PERSONNEL M P Krystek, Physikalisch-Technische Bundesanstalt M Liebers, Professional Instruments Co E P Morse, University of North Carolina B Parry, The Boeing Co P H Pereira, Caterpillar, Inc S D Phillips, National Institute of Standards and Technology J G Salsbury, Mitutoyo America Corp D Sawyer, National Institute of Standards and Technology B R Taylor, Honorary Member, Renishaw R L Thompson, U.S Air Force Metrology Lab K L Skinner, Alternate, U.S Air Force Metrology Lab D E Beutel, Honorary Member, Caterpillar, Inc J B Bryan, Honorary Member, Bryan and Associates T E Carpenter, Honorary Member, U.S Air Force Metrology Lab T Charlton, Jr., Charlton Associates D J Christy, Mahr Federal, Inc F Constantino, The American Society of Mechanical Engineers G A Hetland, International Institute of Geometric Dimensioning and Tolerancing R J Hocken, Honorary Member, University of North Carolina R B Hook, Honorary Member, Metcon SUBCOMMITTEE 3: GEOMETRY J D Meadows, Chair, James D Meadows & Associates, Inc J B Bryan, Bryan and Associates M Liebers, Professional Instruments Co J Raja, University of North Carolina PROJECT TEAM 3.7/8: SURFACE PLATES D H Rahn, Chair, Consultant R Barta, Barta Precision Granite Surface Plates E W Blackwood, The Boeing Co D J Christy, Mahr Federal, Inc J D Drescher, Pratt and Whitney K J Haynes, Electro Rent Corp K W John, U.S Air Force Metrology Lab R L Knake, American Association for Laboratory Accreditation D A Lorenzen, The Boeing Co E V Lundquist, AA Jansson v CORRESPONDENCE WITH THE B89 COMMITTEE General ASME Standards are developed and maintained with the intent to represent the consensus of concerned interests As such, users of this Standard may interact with the Committee by requesting interpretations, proposing revisions, and attending Committee meetings Correspondence should be addressed to: Secretary, B89 Standards Committee The American Society of Mechanical Engineers Two Park Avenue New York, NY 10016-5990 http://go.asme.org/Inquiry Proposing Revisions Revisions are made periodically to the Standard to incorporate changes that appear necessary or desirable, as demonstrated by the experience gained from the application of the Standard Approved revisions will be published periodically The Committee welcomes proposals for revisions to this Standard Such proposals should be as specific as possible, citing the paragraph number(s), the proposed wording, and a detailed description of the reasons for the proposal, including any pertinent documentation Proposing a Case Cases may be issued for the purpose of providing alternative rules when justified, to permit early implementation of an approved revision when the need is urgent, or to provide rules not covered by existing provisions Cases are effective immediately upon ASME approval and shall be posted on the ASME Committee Web page Requests for Cases shall provide a Statement of Need and Background Information The request should identify the Standard, the paragraph, figure or table number(s), and be written as a Question and Reply in the same format as existing Cases Requests for Cases should also indicate the applicable edition(s) of the Standard to which the proposed Case applies Interpretations Upon request, the B89 Committee will render an interpretation of any requirement of the Standard Interpretations can only be rendered in response to a written request sent to the Secretary of the B89 Standards Committee The request for interpretation should be clear and unambiguous It is further recommended that the inquirer submit his/her request in the following format: Subject: Edition: Question: Cite the applicable paragraph number(s) and the topic of the inquiry Cite the applicable edition of the Standard for which the interpretation is being requested Phrase the question as a request for an interpretation of a specific requirement suitable for general understanding and use, not as a request for an approval of a proprietary design or situation The inquirer may also include any plans or drawings that are necessary to explain the question; however, they should not contain proprietary names or information Requests that are not in this format may be rewritten in the appropriate format by the Committee prior to being answered, which may inadvertently change the intent of the original request ASME procedures provide for reconsideration of any interpretation when or if additional information that might affect an interpretation is available Further, persons aggrieved by an interpretation may appeal to the cognizant ASME Committee or Subcommittee ASME does not “approve,” “certify,” “rate,” or “endorse” any item, construction, proprietary device, or activity Attending Committee Meetings The B89 Standards Committee regularly holds meetings that are open to the public Persons wishing to attend any meeting should contact the Secretary of the B89 Standards Committee vi Introduction One primary purpose of specifying values for surface plate parameters such as flatness, or for measuring these parameters, is to predict or estimate the level of accuracy that may be accomplished in measurements when the surface plate serves as a reference for those measurements, i.e., the measurement errors will tend to be smaller when a flatter (higher grade) surface plate is used as a reference, and measurement errors will generally be larger when a lower grade surface plate is used Although, in general, it is difficult to quantitatively relate surface plate flatness to measurement errors, for specific applications, a certain flatness parameter may correlate very well with measurement errors, e.g., a measurement task involving a height stand with support spacing the same as that of a repeat reading gage may have measurement errors that are close to the repeat readings from the gage It is safe to say, in general, the correlation will be useful but qualitative The definitions and procedures in this Standard can also allow fair comparisons between surface plates, and they can help to identify and quantify changes in a given surface plate that occur over time, either from use or from changes in the environment vii I N TE N TI O N ALLY LE FT B LAN K viii ASME B89.3.7-2013 NONMANDATORY APPENDIX C SUPPORTS C-1 NONSTANDARD SUPPORTS (0 031 in ) If shimming is required, put the shims between the bottom of the wedge and the foundation This is necessary, as the wedges generally only have mm (0 25 in.) total adj ustment, and all possible adjustment should be conserved for leveling and final tolerance The next operation is to lower the granite plate on the wedges, keeping the projection on all four sides as per the layout print supplied by the manufacturer Precise leveling is not important However, if checking involves checking the part with an optical level mounted on the floor, then the leveling must be more accurate The first step in leveling is accomplished with the four corner wedges only It is very important to use a torque wrench for this operation and to have each of the four corner wedges to exactly the same torque at the point of level This prevents any possibility of twist or strain in the plate that would interfere with final tolerance The next step is to bring the other wedges up to final torque This should be done by moving from one to the other, raising each wedge only about N·m (5 ft-lb) of torque at a time until all are equal There are working and loading conditions where more than the standard three point supports are desirable These cases should be individually engineered The foundation should be engineered for minimum deflection under load since any movement will affect the surface of the surface plate Even changes in the moisture content of a supporting concrete foundation may cause a change in the surface as the foundation shifts When four or more supports are used, shims or adj usting screws are necessary to make all supports receive their share of the load If a plate is used for a particularly heavy load, adjustable supports, which indicate the lift they are applying, may be considered The supports could be spotted under the loading points and set to approximately equal the loading Sometimes the work surface flatness can be improved by shifting support positions Fulcrum, air, and hydraulic supports are available Whenever nonstandard supports are used, the surface plate should be calibrated at the site for compliance to the flatness tolerance When supports at their permanent location are not attached to the plate, a diagram should be supplied showing the proper location of supporting points for calibration purposes When using wedges and a torque wrench, the spacing of each support should be such that each one supports an equal volume of granite Wedges should be placed under each support point Before the granite is placed on the wedges, each wedge should be in a “down” or retracted position The next step is the most important: The tops of the wedges should be surveyed, so that the top of each antifriction plate is in the same level plane within 0.8 mm C-2 RESILIENT SUPPORTS Resilient supports may be used on surface plates They are necessary where there is excessive vibration present in the area The use of resilient supports (an isolation system) reduces the effects of vibrations in the floor The percentage of the reduction will be a function of the vibration frequency and the natural frequency of the isolation system, i.e., the lower the natural frequency, the greater the isolation 20 ASME B89.3.7-2013 NONMANDATORY APPENDIX D FACTORS DISTORTING THE WORK SURFACE D-1 HOLES, SLOTS, AND INSERTS The values of the deformation (bow) are calculated from a simple model that assumes that the material properties are uniform through the plate and that the plate bends uniformly The following equation is used: Holes, slots, or inserts are not recommended on the work surface of grade AA surface plates because their use may cause the surface contour to change They may be used on grades A and B plates with caution bow Do not exceed the maximum torque values given in Table D-1 Use a torque wrench to limit distorting the work surface and pulling the insert D-3 CLAMPING LEDGES ON GRADE AA SURFACE PLATES In metric units [length units in millimeters and temperature units in degrees Celsius (°C)], the units of bow are in millimeters In U.S Customary units [length units in inches and temperature units in degrees Fahrenheit (°F)], the units of bow are in inches The value for the coefficient of thermal expansion of granites varies with the exact granite composition Values from 4.7 to 8.0 ? 10 −6 mm/mm/°C (2.6 to 4.4 ? 10−6 in./in./°F) are found Users are recommended to contact the manufacturer of the particular surface plate to determine the particular value that applies to their own surface plate The value of 6.3 ? 10 −6 mm/mm/°C (3.5 ? 10 −6 in./in./°F) is used in the following examples There is danger of distorting the work surface flatness beyond tolerance when a heavy item rests on the ledge or an item is clamped to the edge D-4 SPATIAL THERMAL GRADIENTS Changes in thermal gradients between the top and bottom surfaces of a granite plate will cause changes in the work surface If the temperature at the top of the granite plate is hotter, the work surface moves toward convex, and if it is colder, the work surface moves toward concave EXAMPLE (Metric): Grade A granite plate size 600 mm ? 900 mm ? 150 mm with temperature gradient of 1°C and with work surface at the higher temperature Its diagonal is 082 mm The work surface diagonal is 082 − (2 ? 25) p 032 mm (see Table 3) Substituting these values into the equation gives Table D-1 Permissible Torque on Threaded Inserts Torque, N·m M6 ? M8 ? M1 ? 25 M1 ? 25 M1 ? 50 10 20 27 34 41 Thread Size, in Torque, ft-lb 0.2500 0.31 25 0.3750 0.5000 0.6250 0.7500 L 2? ?T/8 H where H p the thickness of the surface plate L p the length of the diagonal of the working surface of the plate ?T p the temperature difference between the top and bottom of the plate ? p the coefficient of thermal expansion of the granite D-2 TORQUE ON THREADED INSERTS Thread Size, mm p (1 032 mm ? 032 mm) ? 6.3 ? 10 −6 mm/mm/°C ? 1°C)/(8 ? 150 mm) p 0.0056 mm p 5.6 ?m EXAMPLE (U.S Customary): Grade A granite plate size ft ? ft ? in with temperature gradient of 2°F and with work surface at the higher temperature Its diagonal is 43.3 in The work surface diagonal is 43.3 − (2 ? 1.0) − 41.3 in (see Table 3) Substituting these values into the equation gives (41.3 in 15 20 25 30 35 ? 41.3 in.) ? 3.5 ? 10−6 in./in./°F ? ? in.) p 0.000249 in p 249 ?in 2°F)/(8 Temperature gradients can be caused by heat due to lighting; using cleaning agents that evaporate, chilling the surface; air currents (drafts) in the room, both hot or cold; radiant heat affecting one surface more than the 21 ASME B89.3.7-2013 NOTE: As RTO/ ?T is a dimensionless ratio, temperature can be in either degrees Fahrenheit (°F) or degrees Celsius (°C) others; stratification of temperature, particularly during the winter due to heated air rising and cool air sinking to the floor; and insufficient space between the bottom of the plate and its supporting table, which restricts air flow to the bottom of the plate, causing ambient temperature changes to affect the top more than the bottom EXAMPLE (Metric): Given a surface plate that is subjected to a change in environmental temperature of 10°C, how much time must elapse before inspection can proceed if the temperature of the plate is to be within 1°C of the final temperature? The dimensions of the plate are 600 mm 150 mm Solution: H p 0.15 m L p 0.6 m RTO p 1°C RTO/?T p 0.1 w p 0.9 m ?T p 10°C ? D-5 TEMPERATURE SOAKING TIME Before granite surface plates are used or calibrated, the granite should remain in the calibration area until it has reached room temperature Large plates require more soak-out time than smaller ones The following will help in estimating the soak-out time Soak-out time p K[ C1 /(1/ L + 1/ w + 1/ H)] hr for rectangular plates K [ C2/(1/2H + 1/ D)] hr for round plates where D H L w p p p p and diameter of surface plate height of surface plate length of surface plate width of surface plate C2 p Kp RTO p T1 p T2 p p Residual Temperature Offset or required closeness to final temperature temperature of granite before soak-out time temperature of granite at time of measurement T2 − T1 p temp erature change of environment Calculate RTO/ ?T, and then calculate from the chart in Fig D-1 2.3 [53.1/(1/0.6 + 1/0.9 The dimensions of the plate are 18 in Solution: H p 13 ft L p 32 ft RTO p 1°F RTO/?T p 0.02 w p 32 ft ?T p 50°F 16.2 if the plate dimensions are in feet and 53.1 if the plate dimensions are in meters 8.1 if the plate dimensions are in feet and 26.6 if the plate dimensions are in meters −ln( RTO/ ?T) given p 900 mm EXAMPLE (U.S Customary): Given a surface plate that is subjected to a change in environmental temperature of 50°F, how much time must elapse before inspection can proceed if the temperature of the plate is to be within 1°F of the final temperature? K is a multiplier determined as follows: C1 p ?T From Fig D-1, K p 2.3 Estimated soak-out time + 1/0.15)] p 12.9 h ? K, From Fig D-1, K p 3.8 Estimated soak-out time 3)] p 14.2 hr p ? 18 in ? in 3.8 [16.2/(2/3 + 2/3 + D-6 SUPPORTS Plates supported at more than three points or other than as sp ecified b y the manufacturer will cause distortion or read it 22 ASME B89.3.7-2013 Fi g D-1 Resi d ual Tem perature Offset Over Tem perature Ch an ge K y ? = ln( x ) 0 01 RTO ?T / 23 ASME B89.3.7-2013 NONMANDATORY APPENDIX E CARE OF GRANITE SURFACE PLATES E-1 CLEANING AND MOISTURE whereas plates used in the laboratory may be recalibrated every year Frequent monitoring of the work surface by scanning it with the repeat reading gage is desirable When these results differ significantly from those recorded at the previous calibration, one should recalibrate the plate For more information, ILAC-G24 or NCSLI RP-1 address methods for determining appropriate recalibration intervals Plates should be cleaned thoroughly and given adequate time to dry and stabilize before being used or calibrated (This time can be included in the temperature soak-out time.) Water-based cleaners that have not dried out will make iron parts rust if left in contact on the surface overnight E-2 SCRATCHES AND NICKS E-5 DOWNGRADING, RESURFACING, OR REPLACEMENT LEVELS Whenever scratches and nicks appear on granite plates, the resulting burrs should be removed with a flat silicon carbide stone or a diamond impregnated cast iron block Any bump that shatters the surface raises fractured material at the rim of the crater At recalibration period, it is suggested that surface plates that deviate from the work surface flatness tolerance, which show repeat readings that exceed in-house requirements or which have objectionable scratches and nicks in the work area, shall be downgraded, resurfaced, or replaced E-3 WEAR DISTRIBUTION When a specific work area receives hard usage, it is suggested that the plate be rotated 180 deg on a periodic basis to increase wear life, or at least use different areas The production of a contour map during calibration is particularly helpful in locating the parts of the plate that should be given most use E-6 REFERENCES ILAC-G24:2007/ OIML D 10:2007, Guidelines for the determination of calibration intervals of measuring instruments Publisher: International Laboratory Accreditation Cooperation (ILAC) , P O Box 7507, Silverwater, NSW 2128, Australia (www.ilac.org) E-4 PERIODIC RECALIBRATION Periodic recalibration of granite surface plates is recommended to determine resurfacing or replacement needs The interval between calibrations will vary with the grade of the plate, wear resistance, and conditions and frequency of use Surface plates used in manufacturing departments might be recalibrated every mo, NCSLI RP-1 — 2010, Establishment and Adjustment of Calibration Intervals Pub lisher: The National Conference of Standards Laboratories (NCSL International), 2995 Wilderness Place, Suite 107, Boulder, CO 80301 (www.ncsli.org) 24 ASME B89.3.7-2013 NONMANDATORY APPENDIX F GUIDANCE TO ESTIMATING UNCERTAINTY IN SURFACE PLATE MEASUREMENT F-1 GENERAL F-2.1 Examples This Nonmandatory Appendix provides guidance for estimating measurement uncertainty by listing and discussing the factors that should be considered Examples are provided for reference The underlying assumptions for the example analyses should be carefully considered as these may not apply to individual circumstances The acceptable analysis procedures are well documented and are assumed to b e well known b y the user of this Standard [1, 2] F-2.1.1 Metric Units The displacement transducer of the repeat reading gage is calibrated and certified to have a 5:1 accuracy ratio to the requirements of any grade A or less surface plate, i.e., 1.5 ? m/5 p 0.3 ? m A test for repeatability of the gage was conducted Two nest positions were created on a Grade B 24-in ? 24-in surface plate diagonally opposed and with maximum practical separation distance The repeatability test consisted of the initial step of zeroing the displacement transducer at an arbitrary position near the center of the plate, and the following steps were repeated 25 times: (a) sliding the gage into nest (b) recording reading (1,i) (c) sliding the gage into nest (d) recording reading (2,i) The operator was instructed to read the dial indicator by estimating to the closest 0.1 ? m, which is one-fifth the 0.5-? m graduation of the gage dial In normal use of the gage, the instructions require the operator to read to the nearest graduation Therefore, in this analysis, the resolution is not considered to be included in the repeatability test results The resulting 50 readings were analyzed by statistical means with the result of a standard deviation for repeatability of 0.21 ? m For a point reading, the standard uncertainty is estimated as the combination of resolution, accuracy, and repeatability Standard uncertainty due to resolution, u ( res ), is estimated using Type B evaluation with the assumption of a uniform distribution with bounds equal to ±0.5 resolution F-2 REPEAT READING TEST The result of this test is the range of indicator readings, or full indicator movement (FIM) The uncertainty budget for this parameter should consider the following: (a) Meas urem en t Res olutio n The resolution may be determined by the specified least graduation of the meter or dial, any electrical noise if applicable, vibration, analog-to-digital conversion resolution if applicable, etc (b) Accuracy The accuracy may be determined as the deviation compared with known standards of length within the measuring range used in the repeat reading test (c) Repeatability/Reproducibility A well-designed and -executed study might of repeatability/reproducibility include the effects of resolution, as well as environmental factors and operator influences As such, the results may encompass a large percentage of the measurement uncertainty for this test The uncertainty analysis for the repeat reading is therefore relatively simple as long as the measurand is clearly stated as the FIM value If the results were stated as an estimate of flatness, then many other uncertainty terms would be necessary This is not in the scope of this Nonmandatory Appendix EXAMPLE: A repeat reading gage is used to measure the FIM repeat reading parameter according to the test described in Mandatory Appendix I The measurand for purposes of the uncertainty estimate is defined as the total range of surface deviations that a perfectly rigid and stable repeat reading gage having perfect accuracy and infinite resolution would measure along the lines specified for the test in the absence of any deflections, thermal effects, dirt, etc The measurement procedure results in an estimate of this measurand, the FIM parameter, which is the difference between maximum and minimum readings from the actual gage The uncertainty in this measurement may be estimated as follows ( u res ) p 0.5 ? m ?3 p 0.14 ? m Standard uncertainty due to accuracy, u ( acc), is estimated using Type B evaluation with the assumption of a uniform distribution with bounds equal to the certified accuracy To this is added in quadrature the standard uncertainty of the calibration 25 ASME B89.3.7-2013 Table F-1 Uncertainty Analysis for Repeat Reading FIM Measurement (?m) Uncertainty Factor Displacement transducer resolution Displacement transducer accuracy Point measurement repeatability Combined standard uncertainty for a point Combined standard uncertainty for FIM (max.–min.) Expanded uncertainty estimate (95% CI) ( u acc ) 0.3 p ?? ?3 ? ? p 0.09 ? m Standard uncertainty due to repeatability, u ( rep ), is estimated using Type A evaluation beginning with the sample standard deviation from the repeatability test ( u rep ) p 0.21 ? m The combined standard uncertainty of the point measurement, u ( p ), is the combination of the three independent factors ( ) u p p p p ?u (res ) + u (acc) + u (rep) ?0.142 + 0.09 + 0.21 0.27 ?m The measurement result is the difference of two independent point measurements, max – Therefore, the standard uncertainty of the measurement is the combination of the uncertainty for each point u (FIM) p p p ?2 ? u (p) ?2 ? (0.27) 0.39 ? m Note that this includes a simplifying assumption, i.e., the uncertainty associated with both the max and function is equal to the uncertainty of the maximum and minimum indicated values, respectively There may be actual higher maxima or lower mimima that were not visited This source of uncertainty is not included, and due to the nonsystematic portion of the uncertainty, the point where the maximum (or minimum) indicated value is found is not necessarily the point of actual maximum (or minimum), even among the points that are visited More advanced treatment of this uncertainty component is possible but is not included within this example Finally, the uncertainty of the repeat reading FIM measurement is stated at the 95% confidence interval as u (FIM), where is the coverage factor (FIM) U p Combined Expanded 0.1 0.09 0.21 0.27 0.39 0.77 F-2.1 U.S Customary Units The displacement transducer of the repeat reading gage is calibrated and certified to have a 5:1 accuracy ratio to the requirements of any Grade A or less surface plate, i.e., 60 ? in./5 p 12 ? in The uncertainty of the calibration is stated at the 95% confidence interval as ±6.0 ? in (Standard uncertainty of the calibration is 3.0 ? in.) A test for repeatability of the gage was conducted Two nest positions were created on a Grade B 24-in ? 24-in surface plate diagonally opposed and with maximum practical separation distance The repeatability test consisted of the initial step of zeroing the displacement transducer at an arbitrary position near the center of the plate, and the following steps were repeated 25 times: (a) sliding the gage into nest (b) recording reading (1,i) (c) sliding the gage into nest (d) recording reading (2,i) The operator was instructed to read the dial indicator by estimating to the closest millionths, which is onefourth the 20 millionths graduation of the gage dial In normal use of the gage, the instructions require the operator to read to the nearest graduation Therefore, in this analysis, the resolution is not considered to be included in the repeatability test results The resulting 50 readings were analyzed by statistical means with the result of a standard deviation for repeatability of 8.1 ? in For a point reading, the standard uncertainty is estimated as the combination of resolution, accuracy, and repeatability Standard uncertainty due to resolution, u ( res ), is estimated using Type B evaluation with the assumption of a uniform distribution with bounds equal to ±0.5 resolution 1/2 Standard ( u res ) p 20.0 ? in ?3 p 5.8 ?in Standard uncertainty due to accuracy, u ( acc ), is estimated using Type B evaluation with the assumption of a uniform distribution with bounds equal to the certified accuracy To this is added in quadrature the standard uncertainty of the calibration 0.77 ? m The analysis is summarized in Table F-1 26 ASME B89.3.7-2013 Table F-2 Uncertainty Analysis for Repeat Reading FIM Measurement (?in.) Uncertainty Factor Standard Combined Expanded Displacement transducer resolution Displacement transducer accuracy Point measurement repeatability Combined standard uncertainty for a point Combined standard uncertainty for FIM (max.–min.) Expanded uncertainty estimate (95% CI) 5.8 3.5 8.1 0.6 4.9 29.9 ( u acc ) p 12.0 2 ?? ?3 ? ? F-3 MOODY (UNION JACK) METHOD F-3.1 Uncertainty Due to Flatness Definition 1/2 p 3.5 ? in Flatness of a surface is the separation of two parallel planes that encompass the measured points of the surface Also, the planes must be chosen to minimize the perpendicular distance between them The analysis of the Moody method establishes a reference plane by equalizing computed deviations at the corners of the measured area Two additional planes, parallel to the reference plane, are established to encompass all computed surface height deviations The perpendicular distance between these two planes is taken as the flatness of the surface The Moody analysis therefore overestimates the flatness value giving a conservative estimate of the surface plate quality This Committee has reviewed results [3] from a reasonable sampling of surface plate measurements For each, the Moody “flatness” was compared with the minimum zone flatness as determined by a Chebychev plane fit analysis of the same measured data Fig F-1 shows a histogram of the results In Fig F-1, the two calculated percent differences shown as “More” had values of 20% and 32% Uncertainty principles generally assume that known sources of measurement bias in the measurement are corrected If this is done, then there is no uncertainty due to the definition Standard uncertainty due to repeatability, u ( rep ), is estimated using Type A evaluation beginning with the sample standard deviation from the repeatability test ( u rep ) p 8.1 ? in The combined standard uncertainty of the point measurement, u ( p ), is the combination of the three independent factors ( ) u p p p p ?u (res ) + u (acc) + u (rep) ?5.8 + 3.5 + 8.1 10.6 ?in The measurement result is the difference of two independent point measurements, max – Therefore, the standard uncertainty of the measurement is the combination of the uncertainty for each point u (FIM) p p p ?2 ? u (p) ?2 ? (10.6) 14.9 ? in Note that this includes a simplifying assumption, i.e., the uncertainty associated with both the max and function is equal to the uncertainty of the maximum and minimum indicated values, respectively There may be actual higher maxima or lower mimima that were not visited This source of uncertainty is not included, and due to the nonsystematic portion of the uncertainty, the point where the maximum (or minimum) indicated value is found is not necessarily the point of actual maximum (or minimum), even among the points that are visited More advanced treatment of this uncertainty component is possible but is not included within this example Finally, the uncertainty of the repeat reading FIM measurement is stated at the 95% confidence interval as u (FIM), where is the coverage factor u (FIM) p F-3.2 Uncertainty Due to Angular Measurement Several effects combine for the uncertainty of each angular measurement [2] (a ) calib rated accuracy of the angle -measuring instrument (b) thermal effects on the angle-measuring instrument (c) inexact placement of the instrument along each line of measurement (d) inexact initial setting of the sled foot spacing (e) actual contact area vs assumed knife-edge sled contact Guidelines for analysis of these elements may be found in the referenced document and is beyond the scope of this Nonmandatory Appendix Other elements of uncertainty may be appropriate for the particular measurement procedure followed and specific measuring instrument used 29.9 ? in The analysis is summarized in Table F-2 27 ASME B89.3.7-2013 Fig F-1 Percent by Which the Value of a Moody Analysis Out-of-Flatness Result Exceeds the Value of the Minimum Zone Out-of-Flatness Result Calculated From the Same Set of Height Deviations 12 10 Frequency 2 10 14 18 More Percent Difference GENERAL NOTE: For out of 25 sets of data from actual m easurements, the percen t differen ce was greater than 0% F-3.3 Combined Uncertainty Due to Angular Measurement its path does not indicate what deviations may have occurred along the way By the same reasoning, for a given set of equipment and a given measurement procedure, the range of closure values from many measured plates may be a reasonable indicator of the maximum uncertainty in height deviation measurements The uncertainty in the flatness could then be estimated as a combination of two such values: the uncertainty of the minimum value and the uncertainty of the maximum value Care should be taken with this approach, mainly because procedures usually allow (or require) that large values for closure not get recorded, i.e., when the closure is greater than some limit, the entire measurement is repeated A general formula for the standard uncertainty due to angular measurement uncertainty may be found [3], which is a function of plate size and foot spacing Given an uncertainty estimate for the individual angle measurements, the uncertainty in measured surface deviations varies for each line of measurement as a function of distance along the line from the datum In the Moody analysis, after the fitting, the overall datum is at the center at the intersection of the two diagonals Uncertainty of height deviations increases from the center to the corners along the diagonals (see Fig F-2) It increases from the corners to the midpoint of the perimeters and from the midpoint of perimeters back to the center along the bisectors The uncertainty of height deviations is therefore a function of the angle measurement uncertainty, the line lengths (or plate size), and the foot spacing along each line It is a maximum at the center of the plate It might be intuitive, therefore, that the closure value is a good estimate of uncertainty for the plate flatness However, this may not be the case In statistical terms, the uncertainty of height deviations along the line, from center to corner to midpoint perimeter and back to center, is a “random walk” in one dimension In two dimensions, it is analogous to the path of a knuckle ball (neglecting the nominal arc due to gravity) It has a seemingly random deviation in two dimensions perpendicular to the path along the way Odds are highest that the target will be missed, but occasionally, the ball will end up near the target path The location at the end of u (h) where 28 l p m n p p Sd S lp p p p ?(? ) ? m ( S sp ) + l(S lp) + n (S d) 2? 1/2 (1) number of measurement steps along second side number of measurement steps along first side number of measurement steps along the diagonal foot spacing along diagonal foot spacing along second side ASME B89.3.7-2013 Fig F-2 Unscaled Picture of Uncertainty Due to Uncertainty in Angle Measurement as a Function of Location Along the Lines of Measurement After the Fitting Is Applied S sp ( ) u h u (? ) p p p 0.3 arcseconds p 0.3 arcseconds arcsecond p 1.5 e−6 mm/mm foot spacing along first side standard uncertainty of height deviations due to angular measurement uncertainty standard uncertainty of angular measurement ( ) u h to a 900-mm ? 200-mm area of a surface plate Differential electronic levels are used, and the standard uncertainty for angle measurement is determined to be 0.30 arcseconds The measurand for the uncertainty analysis is defined as the actual flatness of the surface plate at the time of evaluation as analyzed by the Moody data-fitting algorithm and measurement procedure when measured by the perfect operator with perfect equipment The measurement result is an estimate of this measurand In practice, the measurement result may also be considered an estimate for the flatness of the surface plate for the duration of the calibration interval, but the uncertainty analysis of this example applies only to the measurand as defined Equation (1) simplifies in this case to ( ) where l m n S ( ) u h u (? ) p p p p p p p Su(? ) p p 150 mm 0.55 ?m ? 1.5 e−6 mm/mm [6 + + 10] 1/2 This represents the worst case standard uncertainty of height deviation that applies at the center of the measured area As stated, the uncertainty of height deviation depends on location within the measured area Therefore, an individual flatness uncertainty statement may take into account the shape of the surface profile and the location of the measured maximum and minimum values In general, for the 36 ? 48 surface plate using this equipment, it may be appropriate to estimate the uncertainty in flatness measurement conservatively as the combination of two standard uncertainties (one for the measured maximum and one for the measured minimum), both having the worst case value Then u [ m + l + n ] 1/2 (5 e−6 mm/mm)/ Then F-3.4 Examples F-3.4.1 Metric Units The Moody method is applied u h ? (2) (flatness) p ?2 u ( h ) p ?2 ? 0.55 ? m p 0.78 ? m and the expanded uncertainty for the flatness measurement stated at the 95% confidence interval would be number of measurement steps along second side p number of measurement steps along first side p number of measurement steps along the diagonal p 10 foot spacing p 150 mm standard uncertainty of height deviations due to angular measurement uncertainty standard uncertainty of angular measurement p 0.30 arcseconds (flatness) U p ±1.56 ?m F-3.4.2 U.S Customary Units The Moody method is applied to a 36-in ? 48-in area of a surface plate The diagonal is 60 in., and the foot spacing of in may conveniently be used for all lines Differential electronic levels are used, and the standard uncertainty for angle measurement is determined to be 0.30 arcseconds The measurand for the uncertainty analysis is defined as the actual flatness of the surface plate at the time of evaluation as analyzed by the Moody data-fitting algorithm and measurement procedure when measured by the perfect operator with perfect equipment The measurement result is an estimate of this measurand First, convert u ( ? ) to the unitless equivalent angular quantity in radians (or in./in.) 29 ASME B89.3.7-2013 In practice, the measurement result may also be considered an estimate for the flatness of the surface plate for the duration of the calibration interval, but the uncertainty analysis of this example applies only to the measurand as defined Equation (1) simplifies in this case to ( ) u h where l m n S ( ) u h u (? ) p p p p p p p Su(? ) [ m + l + n ] 1/2 variables of material thermal properties, size, thickness, etc., are too numerous for the Standards committee to p rovide a general p rescrip tive app roach in this Nonmandatory Appendix Several things should be noted Temperatures may be considered approximately constant for the duration of the measurement process This assumption may apply when (a) the surface plate is large and thick (b) the surface plate is of low conductivity material (c) the change in air temperature is minimal When temperature is considered constant for the duration of the measurement, uncertainty from temperature effects only arises because the true flatness may be defined for the condition of uniform, standard temperature In this case, it may be safe to assume the measured flatness is higher than it would be at standard conditions For surface plates produced in very good environments and that have not been reworked, this approach would be reasonable It is not recommended to measure surface plate flatness for evaluation or to rework surface plates based on the measurements in extreme temperature conditions or when air temperature is changing by more than 1°C/h (2) number of measurement steps along second side p number of measurement steps along first side p number of measurement steps along the diagonal p 10 foot spacing p in standard uncertainty of height deviations due to angular measurement uncertainty standard uncertainty of angular measurement p 0.30 arcseconds First, convert u ( ? ) to the unitless equivalent angular quantity in radians (or in./in.) 0.3 arcseconds p 0.3 arcseconds ? (5 e − in./ in )/ arcsecond p 1.5 e−6 in./in Then ( ) u h p p in ? 22 ? in 1.5 e−6 in./in [6 + + 10] 1/2 F-4.2 Humidity This represents the worst case standard uncertainty of height deviation that applies at the center of the measured area As stated, the uncertainty of height deviation depends on location within the measured area Therefore, an individual flatness uncertainty statement may take into account the shape of the surface profile and the location of the measured maximum and minimum values In general, for the 36 ? 48 surface plate using this equipment, it may be appropriate to estimate the uncertainty in flatness measurement conservatively as the combination of two standard uncertainties (one for the measured maximum and one for the measured minimum), both having the worst case value Then u (flatness) p ?2u(h) p ?2 ? 22 ?in p Some surface plate materials may be sensitive to humidity and changes in humidity Uncertainty in flatness measurement due to humidity should be assessed when app ropriate However, as with temperature effects, if conditions during flatness evaluation are worse than the conditions during initial production or the most recent rework, it may be safe to neglect this uncertainty term with the assumption that the uncertainty would bias toward a better flatness result F-4.3 References [1] BIPM Evaluation of measurement data guide to the exp ression of uncertainty in measurement, JCGM 100:2008 31 ? in and the expanded uncertainty for the flatness measurement stated at the 95% confidence interval would be (flatness) U p ±62 ? in [2] ASME Guidelines for the evaluation of dimensional measurement uncertainty, B89.7.3.2 F-4 UNCERTAINTY DUE TO ENVIRONMENTAL FACTORS F-4.1 Temperature [3] Drescher, J.D Analytical estimation of measurement uncertainty in surface plate calibration by the Moody method using differential levels In: Precision Engineering 27 (2003) Pp 323-332 Uncertainty in flatness measurement due to temperature can be estimated and should be included in uncertainty budgets when considered important, although the 30 ASME B89.3.7-2013 NONMANDATORY APPENDIX G TRACEABILITY G-1 GENERAL TRACEABILITY ISSUES plates Information on evaluating the uncertainty of the flatness results is given in Nonmandatory Appendix F This Standard employs the interpretation of traceability described in ASME B89.7.5 In this Standard, traceability issues arise in calibration of repeat reading gages (see section I-4) used to evaluate the short wavelength out-of-flatness of a surface plate and in the calibration of measurement instruments, such as electronic levels, autocollimators, and laser interferometers used to evaluate the long wavelength out-of-flatness In addition to the measurement equipment exhibiting traceability, it is important that any algorithms used to process individual measurements of these devices be properly qualified to ensure that the algorithms are correctly treating the measured data It is also critical in situations where multiple datapoints are combined into one numeric result, to ensure that the measurement process used to collect that data is documented and is being followed correctly The reference standard (repeat reading gage, laser interferometer, etc.) used for evaluation of flatness of the surface plate should satisfy the traceability requirements of section G-2 of this Nonmandatory Appendix This requirement provides the connection back to the SI meter and allows a comparison of the flatness errors with the specified MPE values The traceability of the reference standard must be documented The documentation traceability requirement describes how the connection to the SI meter is achieved The documentation traceability is the calibration certificate of the repeat reading gage, electronic level, autocollimator, or other instrument showing an unbroken chain of comparisons back to an appropriate metrological terminus (see section G-3), either a calibration certificate or documentation describing the means of realizing the SI meter (see ASME B89.7.5, Section 2) EXAMPLE: Repeat Reading Gage (a) State the quantity under measurement, e.g., the indicated value of the repeat reading gage (b) Identify the measurement system or standard used, e.g., a set of gage blocks identified as set ABCDEF (c) State the expanded uncertainty ( k p 2) associated with the gage blocks used to calibrate the repeat reading gage NOTE: This includes both the uncertainty on the calibration certificate and effects such as the prevailing thermal conditions at the time of the calibration, resolution of the repeat reading gage, and repeatability of the process during calibration (d) Provide an uncertainty budget describing the uncertainty components used to compute the statement of uncertainty For the repeat reading gage, the typical uncertainty components are the calibration uncertainty of the gage blocks, resolution of the gage, repeatability of the process, and temperature effects (e) Provide documentation of traceability back to an appropriate terminus of the standards used for the calibration of the repeat reaching gage (see section G-3 for an appropriate metrological terminus), e.g., if the repeat reading gage is calibrated using gage blocks, a copy of the calibration certificate of the gage block set would suffice, assuming the certificate is from an appropriate metrological terminus (f) Show evidence of an internal quality assurance program, so that the measurement uncertainty statement for the reference standard is assured This may be a simple procedure to ensure that the reference standard is periodically recalibrated, any fixturing is in accordance with the calibration requirements, and that any other effects are taken into account either in the process or in the uncertainty budget EXAMPLE: Angle-Measuring Instruments: levels, autocollimators, laser interferometer angle measurements For these measurements, typically the measuring device measures an angle of inclination, and the surface plate is profiled, generating a dataset that is then processed to calculate the out-offlat condition of the surface plate The individual angle measurements can be shown to be traceable to an appropriate metrological terminus These values must then be combined in a suitable fashion to result in an out-of-flatness determination for the entire surface plate (a) State the quantity under measurement, e.g., the indicated value of the angle measurement device (b) Identify the measurement system or standard used, e.g., a set of gage blocks identified as set ABCDEF, and an identified sine plate (c) State the expanded uncertainty ( k p 2) associated with the gage blocks used to calibrate the measurement system and the uncertainty associated with the separation of the rolls on the sine plate G-2 REFERENCE STANDARD TRACEABILITY Each measurement system used in the calibration, e.g., a sine plate and gage blocks used to establish a reference angle in the calibration of electronic levels or autocollimators, and measuring instruments used to verify the foot pad spacing on these instruments, or gage blocks used to establish the calibration of the repeat reading gage, should be traceable per ASME B89.7.5 Supplying the information below for each measurement system employed will satisfy the traceability requirements for the calibration of the flatness of surface NOTE: This includes both the uncertainty on the calibration certificate and effects such as the prevailing thermal conditions at the 31 ASME B89.3.7-2013 G-3 METROLOGICAL TERMINUS time of the calibration, resolution of the instrument being used, and repeatability of the process during calibration (d) Provide an uncertainty budget describing the uncertainty components used to compute the statement of uncertainty For sine plate measurements, the typical uncertainty components are the calibration uncertainty of the gage blocks and sine plate, resolution of the measuring instrument, repeatability of the process, and temperature effects (e) Provide documentation of traceability back to an appropriate terminus of the standards used for the calibration of the measuring instrument (see section G-3 for an appropriate metrological terminus), e.g., if the instrument is calibrated using gage blocks and a sine plate, a copy of the calibration certificates of these tools would suffice, assuming the certificate is from an appropriate metrological terminus (f) Show evidence of an internal quality assurance program so that the measurement uncertainty statement for the reference standard is assured This may be a simple procedure to ensure that the reference standard is periodically recalibrated, any fixturing is in accordance with the calibration requirements, and that any other effects are taken into account either in the process or in the uncertainty budget An appropriate metrological terminus for the documentation traceability is any one of the following sources (see ASME B89.7.5 for further details): (a) A calibration report from a national measurement institute (NMI) for the reference length (artifact or instrument) used in the testing (b) A calibration report from a competent laboratory fulfilling section 5.6 of ISO 17025 for the reference standard used in the testing documentation describing an independent realization of the SI meter used to generate the reference standard, e.g., a laser interferometer This documentation will include the measurement uncertainty of the calibration and evidence that the stated uncertainty is achievable, e.g., participation in a round robin or comparison against another independently calibrated length standard 32 ASME B89.3.7-2013 L0891