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Tool Life Testing With Single-Point I urning Tools ANSIIASME B94.55M - 1985 REAFFIRMED 2003 FOR CURRENT COMMITTEE PERSONNEL PLEASE E-MAIL CS@asme.org SPONSORED A N D PUBLISHED B 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 N e w York, N Y 1001 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 A AN M E R I C A N A T I O N A SL 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 to thisEdition 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 to assure that individuals from competent and concerned interests have had an opportunity to participate The proposed code or standard was made available for public review and comment whichprovides an opportunityforadditional public inputfromindustry, 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 mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability for infringement of any applicable Letters Patent, nor assume any such liability Users of a codeor standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility Participation by federal agency representative(s) or person(s) affiliated with industry is not to be standard interpreted as government or industry endorsementof this code or ASME accepts responsibility for only those interpretations issued in accordance with governing of interpretationsbyindividual ASMEproceduresandpolicies which precludetheissuance volunteers No part of this document may be reproduced any form, in in an electronic retrieval systemor otherwise, without the prior written permission of publisher the Copyright 1986 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All RightsReserved Printed inU.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 wh Date of Issuance: April 15, 1986 (This Foreword is not part of ANWASME B94.55M-1985.) This Standard is a slightly modified version of I S 3685-1977,Tool Life Testing With Single-Point Turning Tools Only several smallchanges have beenmade, such as replacing referenced I S materials specifications with ASTM and ANSI specifications It was felt that U.S users of the Standard wouldbe more familiar with the ASTM and ANSI specifications and have easier accessto them Following approval by the B94 Standards Committee and ASME, this Standard was submitted to ANSI and approved as an American National Standard on November 27, 1985 111 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 FOREWORD (The following is the roster of the Committee at the time of theofapproval the Standard.) OFFICERS E.J Czopor, Chairman W.R Daisak, Secretary COMMITTEE PERSONNEL AMERICAN SOCIETY OF MECHANICAL ENGINEERS, THE M.E Merchant, Metcut Research Associates, Inc., Cincinnati, Ohio G.F Wilson, Alternate, General Electric Co., Worthington, Ohio CUTTING TOOL MANUFACTURERS OF AMERICA E.J Czopor, Falcon Tool Co., Warren, Michigan C.W Jatho, Alternate, Cutting Tool Manufacturersof America, Birmingham, Michigan GENERAL SERVICESADMINISTRATION W.R Wacker, General Services Administration, Washington, DC HACK AND BAND SAW MANUFACTURERSASSOCIATION OF AMERICA R Schrade, Clemson Brothers, Inc., Middletown, NewYork C.M Stockinger, Alternate, Hack and Band Saw Manufacturers Association,Cleveland, Ohio METAL CUTTING TOOL INSTITUTE W.A Wagner, Cleveland Twist DrillCo., Cleveland, Ohio J.G Thirnrnig, Alternate, Metal Cutting Tool Institute, Cleveland, Ohio NATIONAL MACHINE TOOL BUILDERSASSOCIATION J.J Robinson Valeron Corp Troy, Michigan A.M Bratkovich, Alternate, National Machine Tool Builders Association, McLean, Virginia SOCIETY OF MANUFACTURING ENGINEERS G.L Spencer, Ford MotorCo., Detroit, Michigan UNITED STATES DEPARTMENT OF THEARMY D.L York, Liaison, Material Readiness Command, Rock Island, Illinois INDIVIDUAL MEMBERS A Ashburn, American Machinist, New York, New York H Cooper, Water Technology, Inc., Troy, Michigan R.T Koblesky, lngersoll Cutting ToolCo., Rockford, Illinois J.A Lang, Dayton Progress Corp., Dayton, Ohio L Storrer, Mohawk Tools, Inc., Montpelier, Ohio 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 wh ASME STANDARDS COMMITTEEB Standardization of Cutting Tools, Holders, Drivers, and Bushings M.E Merchant, Chairman, Metcut Research Associates, Inc., Cincinnati, Ohio R.M Byme, Trade Association Management, Inc., Tarrytown, New York D.D Jackson, Valeron Corp., Warren, Michigan J Johnston, General Electric Co.,Warren, Michigan J.F Kahles, Metcut Research Associates,Cincinnati, Ohio J.D Knox, Vermont American Corp., Louisville, Kentucky 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 wh PERSONNEL OF TECHNICAL COMMITTEE - LIFE TESTING WITH SINGLE-POINT TOOLS Foreword Standards Committee Roster 10 Introduction Scope and Field ofApplication References Workpiece Tool Cutting Fluid Cutting Conditions Tool Life Criteria and ToolWear Measurements Equipment Tool Life Test Procedure Recording and Reporting Results Figures ToolAngles 10 11 12 13 Details of Rounded Corner Tolerances on Squareness of Insert and Toolholder Location Insert Overhang and Chipbreaker Regrinding Tool After Testing Limits of Cutting Conditions Broken v.TCurve Combined Flank and Crater Wear Some Types of Wear on Turning Tools Development of Flank Wear for Different Cutting Speeds Development of Crater Depth for Different Cutting Speeds v-TCurvefor VBB= 0.3 mm v-TCurve for KT = 0.18 mm Number of Workpieces Produced as a Function of Spindle Speed 111 V 1 7 10 12 12 12 6 9 11 13 13 14 14 14 Tables Standard Tool Angles deg StandardCuttingConditions Limits of Other Cutting Conditions Geometric Series of Preferred Numbers for Cutting Speeds (m/min) Appendices A General Information B Grinding of High-speed Steel C Tool Wear and Tool Life Criteria D Datasheets vii 17 19 23 27 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 CONTENTS 31 33 49 Figures 14 15 16 17 Lines Fitted “By Eye” 18 Lines With Confidence Interval Fitted by Calculation 21 21 33 39 40 Tables Grinding Recommendations 20 10 11 12 Computation Schedule for Calculation of Regression Line y = a + k(x X) Computation Schedule for Assessment of Dispersion and Significance Computation Schedule for Calculation of Confidence Intervals Example Example Example ?-Distribution for 95% Confidence Level viii 41 42 43 44 45 46 47 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 Preliminary Tool Life Test Evaluation of Tool Life Data G Chip Forms E F AN AMERICAN NATIONAL STANDARD TOOL LIFE TESTING WITH SINGLE-POINT TURNING TOOLS INTRODUCTION If, for some reason, it is necessary to deviate from the specifications given in this Standard, this shall be reported in detail Tool life testing has been carried out for at least 75 years, in tremendously increasing volume, but under a variety of cutting conditions and methods having little in common with each other Thus, a need exists for standardization of tool life testing conditions applicable not only in laboratories but also in production plants The test conditions have been specified in such a way that the different factors which affect the results of tool life testing will all be under a reasonable and practical degree of control This Standard has been so framed that it can be NOTE: This Standard is not an acceptable test and it is not advisable to use it as such SCOPE AND FIELD OF APPLICATION This Standard establishes specifications for the following factors of tool life testing with single-point turning tools: workpiece, tool, cutting fluid, cutting conditions, tool wear and tool life, equipment, test procedures, recording and reporting and presentation of results Further general information is given in Appendix A directly applied to industrial testing and in research For research purposes, however, this Standard should be considered to be only a minimum set ofconditions, since greater attention may have to be givento the factors which affect thevariability of the tool life values Although the test parameters are standardized, any one or more of them may become variables in any giventestwhentheyarethequantitiesbeing examined The limits of the specification of the reference materials areleftrather wide for practical reasons It should be understood that results may vary from batch to batch If reproducibility is essential, special requirements should be discussed with the supplier of the work material The specifications for test conditions given in this Standard are primarily suited to testing on steel and castiron work materials.However, with suitable modification they can also be made applicable to testing on other materials The specifications for testconditionsarealso mainly applicable to tool life testing in which the tool wears at a conventional rate and in a conventional manner However, it is evident that they may also be applied to some types of accelerated tool life testing REFERENCES The latest issues of the following documents form a part of this Standard to the extent specified herein American Society for Testing andMaterials ASTM A 159-83, Standard Specification for Automotive Gray Iron Castings (Grade G3000) ASTM A 576-81, Standard Specification for Steel Bars,Carbon,Hot-Wrought, SpecialQuality (Grade G 10450) ASTM E 18-79, Standard Test Methods for Rockwell Hardness and Rockwell Superficial Hardness of Metallic Materials ASTM E 92-82, Standard Test Method for Vickers Hardness of Metallic Materials ASTM E 112-82, Standard Methods for Determining Average Grain Size 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 ANSI/ASME B94.55M-1985 AN AMERICAN NATIONAL STANDARD Nitrogen Content, (70 Source American National Standards ANSI B46.1-1978, Surface Texture ANSI B74.3-1982, Markings for Identifying Grinding Wheels and OtherBonded Abrasives ANSI B94.4-1976, Identification System for Indexable Inserts for CuttingTools ANSI B94.50-1975, Basic Nomenclature and Definitions forSingle-Point Cutting Tools Open hearth or converters Arc, 0.004 slag single 3.1 Work Material In all cutting tests in which the work material is not itself the test variable or is not itself an important parameter, the investigation shall be conducted on the appropriate oneof the reference materials indicated in paras 3.1.1, 3.1.2, and 3.1.3 Inthe exceptions quoted, however, it is desirable to conduct tests on a reference material for comparative purposes The provision of a well-defined reference work material shall be discussed withthe manufacturer The microstructure throughout theentire volume of each cast iron test bar shall consist essentially of a matrix of 100% pearlite with flake graphite within the following specification: hot-rolled medium carbon steel corresponding nominally to ASTM 1045 (A 576-81) but of the following controlled composition 0.50 0.02 0.50 0.40 0.80 0.035 to 0.008 3.1.2 Cast Iron The cast iron reference material shall correspond nominally to ASTM A 48, Class 25 (ASTM A 159-81), with a Brinell hardness of 200 to 220 HB If available, the following material shall be used 3.1.1 Steel The steel reference material shall be a 0.15 to 0.006 It will be necessary to analyze the steel for nitrogen The steel should be purchased to ASTM A 576-81 specifications, but special quality bars meeting the above criteria should be specified The limits of the elements and deoxidation practice shall be discussed with the steelmaker and analyses of C, Si, Mn, Ni, Cr, Mo, P, S, V, Cu, Al, and Nrequested at thetime of the order The minimum initial test bar diameter shall be 100 mm, but theactual initial diameter shall be reported The test bars, afterbeing cut to length, shall be normalized to a Brinell hardness of 180 to 200 HB The actual hardness shall be reported WORKPIECE 0.42 oxygen 0.003 Pearlite Free iron carbide Free ferrite Steadite (iron-iron phosphide eutectic) Graphite 100% 0070 5% max % max flake graphite only 3.1.3 Other Work Materials.Where the work material is not one of the reference materials, if possible, the grade, chemical composition, physical properties, microstructure, and complete details of theprocessing route of the work material (for example, hot-rolled, forged, cast, or cold drawn) and any heat treatment shall be reported The presence of the following elements in excess ofthe maximum values given belowshall disqualify the steel as areference test material Ni = 0.20% Cr = 0.15% MO = 0.05% v = 0.02% c u = 0.20% The steel shall be deoxidized with aluminum and the minimum aluminum content shall be 0.01 070 Special deoxidants shall not be used The nitrogen content, being to some extent dependent on thesteelmaking source, shall be as follows: 3.2 Standard Conditions for the Workpiece All mill scale or casting skin shall be removed by cleanup cuts before testing, except whenthe effect of the scale is beingtested 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 TOOL LIFE TESTINGWITH SINGLE-POINT TURNING TOOLS ANSVASME B94.55M-1985 AN AMERICAN NATIONAL STANDARD ANWASME B94.55M-1985 AN AMERICAN NATIONAL STANDARD The metal forming the surface of the shoulder,i.e., "the transient surface," and any other burnished or abnormally work-hardened surface on the workpiece which can come in contact with the test tool shall be removed with a sharp cleanup tool prior to testing in order to reduce as much as possible the residual subsurface deformations due to the previous test However, this does not include removal of the normally work-hardened surface on the test bar produced by the previous passes of the tool The length/diameter ratio of the workpiece shall be not more than the minimum ratio at which chatter occurs The test shall be stopped when chatter occurs A length/diameterratiogreaterthan 10 is not recommended The hardness of the work material shall be determined over the complete cross section of one end of each test bar The cutting test shall be conducted only on the bar in the range of diameters where the hardness lies withinthelimits given by theoriginalhardness specification Quantitative metallography (as regards microstructure, grain size, inclusion count, etc.)of the work material is recommended but when this is not practical, photomicrographs shall be included in the report.The magnification shall be in the range 100 to 0 ~ 4.1.1 High-speed Steel The composition of the reference tool material shall be as follows ponents, the fixing devices normally employed in the process shall be utilized The chuck and the spindle shall be stable and well balanced When fixing the workpiece between a chuck or a face plate and a center,special care shall be taken to prevent any bending loads on the workpiece A center hole of 6.3 mm diameter with 120 deg protecting chamfer is recommended proximate time at temperature shall be (d) Quenching The toolbits shall be quenched in oil or in a salt bath followed by air cooling (e) Tempering Temper between 550 and 560 "Cfor two periods of heach at full temperature Following a hardness test, the material shall be tempered a third time at a temperature suitable to obtain a hardness of 65 f HRC corresponding to 846 f23 H V and shall becheckedaccording to ASTM E 18-79 and ~~ CVO Si% Mn% 0.80 to 0.85 0.10 to 0.40 0.10 to 0.40 Cr% Mo% w 070 4.0 to 4.25 4.75 to 5.25 6.0 to 6.5 v 070 Pvo s070 1.7 to 2.1 0.03 max 0.03 m a ~~~ ~ The heat treatment of the preground toolbits shall be as follows (a) Annealing The tool material shall be annealed from a temperaturenot exceeding 850 "C, followed by furnace cooling (where possible, the cooling rate should not exceed 30 OC/h) (b) Preheating Preheat at 850°C When desired, a prior preheat at 650 "Cis permitted (c) Hardening Harden between 220 and 240 "C The holding time shall be adjusted according to batch size andfurnace size Where possible, neutral salt In machining tests carried out on production com- baths should be used as the heating media The ap- ASTM E 92-82 If the required hardness is achieved after the second temper, then the third temper shall be carried out at 550 "C After heat treatment, thegrain size shall be approximately intercept No 12 ASTM E 112-82 The actual value shall be recorded TOOL 4.1 Tool Material 4.1.2 Sintered Carbide The use of sintered carbide from "tool material banks"' is recommended If this is not possible, the carbidegrades to be used shall belong to USA application groups C-7 or C-6 for machining steel and C-3 or C-2 for machining cast iron In all cutting tests in which the tool material is not itself the test variable or is not itself an important parameter, theinvestigation shall be conducted with the appropriate one of the reference tool materials indicated in paras 4.1.1, 4.1.2, 4.1.3, and 4.1.4 In the exception quoted, however, it is desirable to conduct tests with a reference tool material for comparative purposes 'For example, indexable inserts manufactured especially for testing purposes 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 TOOL LIFE TESTINGWITH SINGLE-POINTTURNING TOOLS Calculation: Fromthe values, the mean value - observed number n of Tshould be calculated as: Tl+T2+T3+T4+ n T =CT/n = .+ Tn Moreover, if: (a) the observations are statistically independent; (b) randomization has been carried out; (c) the sample of the observed T-values may be regarded as drawn from a population with normally distributed T-values (Sometimesa normal distribution' may be obtained by taking log T instead of the T values.) The confidence interval for the calculated mean tool life can be obtained from: and a substitution in equation Corresponding limit values for log C and finally C may be obtained Again, Table suggests a method for recording the values obtained Example3: Obtain a measure for thedispersion about the regression line treated in Example (F2.2) Also, carry out atest of significance and set up confidence interval limits (a) Dispersion The calculations are shown in Table 10, part (b) Significance The calculations are shown in Table 10, parts and When the F-value is taken from the tableof the F-distribution,note that thedegree of freedom is n - for thesmaller sum of squares and for thegreater sum of squares and thus thecorrect F-value is taken from then - row and the first column As the variance ratio = 131 and F = 4.96, there exists a high degree ofsignificance (c) Confidence interval limits ( I ) Confidence Interval Limits for the Line asa Whole The calculations are shown in Table 1 The results can be shown graphically Note that if a log-log paper with scale modulus 100 mmis used, then x = 2.25 corresponds to a distance of 225.5 mm from x = 0.0 (v = m/min) Thus, a confidence interval width of Ay = 0.082 corresponds to a distance (above or below the mean regression line) of 8.2 mm In Fig 18 the regression line with confidence intervals limits corresponding to a confidence level of 95% is shown (2) Confidence Interval for k The calculations are shown in part of Table 11 (3) ConfidenceIntervalfor C.In part4 of Table 11the minimum and maximum values are shown - T=T+s- t J;; c where s is the standard deviation of the n observed values of tool life s = and t denotes Student's t-value for n - degrees of freedom for the desired level of confidence - a% (Table 12) Example 4: The difference between the wear resistance of two tool materials was investigatedby practical industrial tests in a machine tool group, where three machine tools of the same model and year of manufacture were in use underidenticalcutting conditions As the material for the workpieces was delivered from more than onestock, it was decidedto divide the material up in 20 lots The orderof the machining of each lot was determined by means of a table of random numbers The workpieces where then machined with toolbits made of materials A and B, and the number of workpieces that could be machined by each tool edge was recorded.(The tool lifecriterion was VB, = 0.8 mm.) ' Atest of normality should be usedfor confirmation 36 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 F5 EVALUATION OF TOOL LIFE TESTS AT A SINGLE SPEED Table suggests a method for recording the values obtained Input data may be obtained from part of Table The confidence interval for the constant a is obtained from Tool Life (Number of Workpieces for Each Tool Edge) Material A Material B 14 15 16 17 15 18 19 20 21 10 16 18 10 18 20 20 14 22 23 24 25 8 Sum n = = 20.0 f 0.4 Number of ObservedTool Lives The confidence interval is lessthan the difference between the mean tool lives for the tested materials Thus, themean tool life for material B is greater than that formaterial A under the,test conditions If there is no factor other than material tool that might explain the test result, it is justified to generalize that thetool material B has a greater wear resistance than material A, under conditions similar to those of the test However, in this case the formulationof the text of the problem indicates that there exist some factors (besides tool material) that might resultin a difference in tool lifein the two sets of observations These factors are the machine tools involved, their operators, and the orderof testing A andB If the influence of these factors had been controlled, for example by randomization, theabove conclusion could have beendrawn Example 5: The difference in the wear resistance of two kinds of high-speed steeltool materials was investigated For this purpose, the number of workpieces produced by one tool until tool failure occurred was recorded for anumber of tools made from,both kinds of high-speedsteel All workpieces wereidentical and made from colddrawn steel bars from onedelivery As there might be some influence of variation of the properties of the work material between the bars,tools were changed in a random sequence each time a workpiece was finished All tests were carried out by the same operator ona semiautomatic lathe with a constant spindle speed This means that these results not necessarily apply when cutting conditions, tool geometry, or work material are changed In order to achieve reasonably safe production, tools made of material A should be changed after 12 products have been made For tool material B this number is 15 Approximately 20% of the tools will fail before this number is reached If tools are changed after 11 and 14 products respectively, the risk of early failure is reduced to about 10% 101 100 Solution and discussion: The mean tool life for tool material A is - TA = x + ~ + ~ + 4+5+6+ = 19.0 The mean tool life for toolmaterial B is - TB = 20.0 The standarddeviation for material A is = f 4(14 + - + 19)’ 5(15 - 19)* + + + .- ~~ = 2.5 and forsteel B SB = 2.0 The confidence interval for material A is (witha confidence level of 95 To) TA = 19.0 * 1.984 X 2.5/ = 19.0 A 0.5 37 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 For material B the corresponding interval is The following tool life data were obtained: Tool Number Tool Life T 15 10 17 14 10 11 12 13 1.5 11 14 12 16 13 12 14 15 13 14 2.25 12.25 12.25 0.25 0.25 6.25 0.25 2.25 6.25 0.25 2.25 0.25 2.25 - 3.5 13 7.8 ( r - n2 r- I 3.5 0.5 - 0.5 - 2.5 0.5 - 1.5 2.5 - 0.5 - 1.5 0.5 1.5 -0.5 Tool Number 1 10 11 12 2- L I 14 12 10 16222018 Confidence level : 95 7’0 Number of degrees of freedom : n - Material A : n - = 13, f value = 2.160 Material B : n - = 11, f value = 2.201 r =r * -6 J;; rA= 13.5 = Tool Life T r- T (r- Tl2 14 - 2.6 6.76 1.96 0.16 12.96 0.36 1.96 0.16 11.56 0.36 0.36 2.56 5.76 18 17 13 16 18 17 20 16 16 15 19 - - 1.4 0.4 3.6 0.6 1.4 0.4 3.4 0.6 0.6 1.6 2.4 As it is felt that all factors which may affect tool life were kept under a reasonable degree of control, it i s justified to conclude that tool material B has a greater wear resistance than tool material A for the conditions of thesetests r, Tool Material B 16.62 2.16 X 1.97 = 13.5 f 1.1 fi 2.2 x 2.02 fi Difference significant = 16.6f1.3 Yes N O D 38 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 Tool Material A E 'c - 60 - 50- -1 I- 40 - 30 - 25 - 20 - 15 o CRITERION K T = 0.14 mm = - 4.2 k=- -loo 24 c = 300 CRITERION VBB = 0.3 mm x - - 100 k=-=- 31 3.2 C = 405 10 - - 87, 6, - u - 2- lp100 I \ \ I \ 300 160 200 140 180 125 FIG 17 I \ 400 500 600701D Cutting Speed v , mlmin LINES FITTED "BY EYE" 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 wh -c CRITERION KT = 0.14 mm k = - 4.27 C = 296 X CRITERION V B , = 0.3 mm k = - 3.10 C = 427 '9 VB, = 0.3 K T = 0.14* I ' ' \ I I tg&=- t g a* = - 4.27 i I u 1 FIG 18 3.10 200 \ 294 296 300 J \ 400427 400-4271 600 600 700 700 500 Cutting Speed Y, m/rnin LINES WITH CONFIDENCE INTERVAL FITTED BY CALCULATION 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 w o V T x =logv 10 11 12 13 14 15 Sum Number of observations n = X = Zxln = v = Cyln = a= mlmin 41 y = log T 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 1 Observation No + k(x - y ) TABLE COMPUTATION SCHEDULE FOR CALCULATION OF REGRESSION LINE y = a Part : Mean-Square Sum Due t o Deviation From theRegression Line (Residual Variation) Read from Table k = xxy = Zx.Lyln = Compute L x y - Z x X y / n = Part 2: Mean-Square Sum Due to Variation Explained by Regression (Explained Variation) Read from part of Table Part 3: Calculation of Variance Ratio and Comparison with F-value Source of Variation Mean-Square Sum Degrees of Freedom (d.f ) Ratio Regrssslon s2 R = Restduals n-2= 53 = Confldence level : ?/o Read F-value from Fisher’s F-table for d.f = 1, n - = Sigrificant No 42 ”.= 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 w TABLE COMPUTATION SCHEDULE FOR ASSESSMENT OF DISPERSION AND SIGNIFICANCE Part : Input Data Read from Table Read f r o m Table - Part n= s: = x - ( Z x ) z / n= Calculate a= s, = x= k= Confidence level % t-value for d.f = n - : ~~~ Part ~ 2: Confidence Interval Length (Besides Mean Value y ) Part 3: Confidence Interval f o r k k, = k ts,/JZx2 - ( Z x ) / n = k,,, = Part 4: Confidence Interval for a and C 43 kmax = I 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 TABLE COMPUTATION SCHEDULE FOR CALCULATION OF CONFIDENCE INTERVALS Calculation of Regression Line y = a + k ( x V mlmin T x = log 1ao 160 140 140 125 160 125 10 18.5 24 20 36 13 44 160 125 140 1ao 15.5 40 25 6.5 2.255 2.204 2.146 2.146 2.097 2.204 2.097 2.255 2.204 2.097 2.146 2.255 a a 1ao 10 11 12 13 14 15 Ex = jum Y y = log T 1.000 1.267 I,380 1.301 1.556 1.1 14 1.643 0.903 1.190 1.602 1.398 0.81 26.106 X y = Zx,Zyln = ( L x ) / n= 32.996 56.794 CRITERION K T = 0.14 rnrn Number of observations n = 12 26.106 = Z x l n = -+ 2.176 12 a= k= =Iy/n = 15.167 = 1.264 12 Z x v - ? ; x Z y / n - 32.821 - 32.996 Z x - (Ex)21n 56.835 - 56.794 - 0.1 75 _-=- 0.041 4.27 - llk = 0.234 = 2.176 a XY X2 Y2 2.255 2.792 2.961 2.799 3.263 2.455 3.445 2.036 2.623 3.359 3.000 1.833 5.085 4.858 4.605 4.605 4.397 4.858 4.397 5.085 4.858 4.397 4.605 5.085 1.000 1.605 1.904 1.693 2.421 1.241 2.699 0.815 1.416 2.566 1.954 0.661 15.167 Zxy = Zx.Zy = 395.950 X A Observation No + 1.264 4.27 44 -x ) 32.821 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 TABLE EXAMPLE Assessment of Dispersion and Significance Part : Mean-Square Sum Due to Deviation From the Regression Line (Residual Variation) Read from Table T y = 19.995 k = - 4.27 cxy= 32.821 = 1.264 S y = 15.167 C x S y l n = 32.996 Compute Z x y - C x C y / n = 32.821 - 32.996 = - 0.175 Compute residual variation sz = cy2 -YCy r - k ( C x y - X x C y / n ) - 19.975 - 1.264 x - - = 0.0057 15.167 - 4.27 x 0.1750.057 - n-2 12-2 10 Part 2: Mean-Square Sum Due to Variation Explained by Regression (Explained Variation) Read from part of Table 10 :s = k ( C x y - C x C y / n ) = 4.27 x 0.175 = 0.747 Part 3: Calculation of Variance Ratio and Comparison With F-Value I Source of Variation I Degrees of Freedom (d.f.1 Regression Residuals I I I n-2=10 Mean-Square Sum S i Read F-value from Fisher's F-table for d.f = 1, n - = 10 : 4.96 Significant 45 = 0.747 s3 = 0.0057 Confidence level : 95 YO Ratio I sg - 0.747 131 s: 0.0057 A I 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 TABLE 10 EXAMPLE Calculation of Confidence Intervals Part 1: Input Data Read from Table Read from part of Table 10 n = 12 53 x = 0.0057 = 2.176 2x2 - (Sx)2/n = 56.835 = 0.041 Calculate - 56.794 S, = 0.076 a = 1.264 k = - 4.27 Confldence level 95 % f-value for d.f =n - : 2.23 Part 2: Confidence Interval Length (Besides Mean Value y ) 0.169 2.255 2.204 2.146 2.097 0.079 0.083 0.028 - 0.030 - 0.079 0.1 52 0.01 0.022 0.1 52 0.082 0.054 0.055 0.082 Average: 0.068 Part 3: Confidence Interval fork km = k _+ ts,lJLx2 - ( Z x ) / n= 4.27 f l G I k, I = - 5.11 Part 4: Confidence Interval for a and C a = i ?E,/&= a = 7.264 0.169 1.264 f-= m = 0.049 (log C ,,) = X -,,,,.k,/r (log C), = X - i/km,,, 1.215 1.264 = 2.176+-= 2.545 3.43 1.264 = 2.176+ 5.1 - 2.424 46 amax = 1.313 I 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 TABLE 11 EXAMPLE Number of Degrees of Freedom TwoSided Interval r95 12.706 4.3 03 3.182 2.776 2.571 2.447 2.365 2.306 2.262 10 11 12 2.228 2.201 2.179 13 14 15 2.160 2.145 2.131 16 17 2.120 2.1 10 18 19 20 2.101 2.093 2.086 21 22 23 2.080 2.074 2.069 24 25 26 2.064 2.060 2.056 27 28 29 2.052 2.048 2.045 30 40 60 2.042 2.021 2.000 100 120 1.984 1.980 1.960 00 BIBLIOGRAPHY Hald, A Statistical Theory With Engineering Applications London, 1957 Leslie, R.T., and Lorenz, G Tool Life Exponents in the Light of Regression Analysis National Standards Laboratory Technical PaperNo 20, CSIRO, Australia, 1964 Natrella, G Experimental Statistics NBS Handbook 91 Washington, 1966 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 12 t-DISTRIBUTION FOR 95% CONFIDENCE LEVEL CHIP FORMS (This Appendix, which is placed after the main text for convenience, is an integral part of ANWASME B94.55M-1985.) Chip form follows on the next page, 49 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 G dinit 1.1 Long 2.3 Snarled 2.2 Short I in the direction workpieceandopposite the direction offeed motion Away from the to Towards the workpiece and opposite to the direction 01 feed motion of feed motion Towards the workpiece and Away from the workpiece and in the direction of feed motion lshown in the sketch) direction t 3.2 Conical 4.2 Short 4.1 Long from Away workpiece t 5.1 Long 5.2 Short I I r 6.2 Loom ELEMENTAL CHIPS Broken against machined surface Broken against work surface Broken against tool flank Broken against major cut surface is characterized b y the 6.1 Connrcted ARCCHIPS" * * Furthersubdivision third as follows : HELICAL CHIPS' CONICAL digit HELICAL CHIPS' WASHER-TYPE Towards workpiece SPIRALCHIPS The direction of the chip is characterized b y the third as follows : I CHIPS' TUBULAR r- RIBBON CHIPS' I' i I I I NEEDLECHIPS 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 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 FOR CUTTING TOOLS AMERICANNATIONALSTANDARDS