oo o PREFACE This workbook is for the purpose of testing the user's knowledge of geometric dimensioning and tolerancing as part of an educational or training progr¿rm. The workbook may also be used as an independent reference, thus providing a learning mechanism for review of the subject matter o¡ to extend existing knowledge. The author ¿ìssumes the user has some familiarity with basic engineering drawing practices. This workbook builds upon such knowledge and extends the learning experience into detailed study of geometric dimensioning and tolerancing as based upon the national standard Aì{SI/ASME Y14.5M-1994. This workbook, and its associated answe¡book, are designed as companion materials for the author's full text'Geo-Metrics III." The workbook contains avariety of materialwhich can be used in a number of ways appropriate to both the academic classroom and the in-industry training progam. Contained within the workbook is a series of questions and exercises, and some problem examples. The problern example pages are found at the rear of the workbook as indicated in the appropriate questions as the user proceeds. The answer to the questions and problems are contained in a separate answer bookwhich may be dist¡ibuted to the at his discretion. particþant alongwith this workbook or retained by the instructor ( Fundamentals................. FortR, Orientation, ....................... 1 Runout Tolerances hofile, and .,......... 10 Location Tolerances. ....,...25 Figures ..........65 QTIESTIONS . - FOR NOTES OR CALCULATIONS - . r¡.?þ F key words toåäemUerfor guiOance le r. 3 requirements and applicatioq^ù. method tt¡al provides best uniformiry For delineating tlrese requirements on a drawing. Place the correct symbol desigoæion Here are ttre fonræen variedes of geometric cha¡acæ¡istics.ï'*niãJq** 4..) symbolicallY by noæ GEOIYÍEIRIC CHARÀCIERXSflC SYI{BOIS 5...Furdcnrentqls GENERAI AI'FSTTOI{S provides numerous advantages' List foru of them' 1.. to control part configuration or specific relationships ullùe. beside each one- Ci¡cularrunout Total rutout ProfiIe of a sr¡rface Profrle of a line Position ConcentricitY Symmetry . Geometric Dimensioning and Tolerancing (1) (2) (3) (4) 2. Where The fi¡st magninrde of conuol on any pan is its of fea't¡¡res.¡L'¡wDvr-------5-r..rv¿rg¿J ' .or_rtolerancgsargused .:ryo In deærmining geometric dimensioning and tolerancing and ll Êc4'. þlerances. the National Standard AI'{SI Y14'5' is: and efñciency -¿ is ¡ecãmmended by the (Check one..r ce^/s ê. COI¡DITIONS 6. - MODIFIERS In using certain geomeuic rclerance characæristics, as applied to size featues, the "marerial condition" under which the tolerance applies must be considered. The th¡ee "marerial conditions" h^(also loown as modifiers where applicable) are , r\C-. L .a¡d R.rs 7. The symbols rsed to indicate two of these maærial conditions or modifte¡s are: is impted by Rule lt2 on all size feæues The third material condition, where the other maærial condition (modifien) symbols ¿ìre not specified- IYÍ¡üKIMITM I\TÍAIERIAI COI{DITION 8. 9. In the case of a hole, the MA)ilMUM IvIAIERIAL CONDHON MMC) is its (which: size? In the case of a pin, ttre MMC size is its minimum or maximum) 'w c^,r -r u,n u^ (minimum or maximum) r-' + --= ,-n ' sizg? The MMC size of the pins below is ó, Ld o Ø.zoo 1:838 size of the pins above is two opposiæ points of ø.198 size be The MMC size of the holes below The IÀfC o.lq) . What would a distance measured between calleÜ! *c 1¿4L ( oc Ì'¿ 5.7 tE ts 0 . zo 5 2x ø.2o5 ::333 The LMC size of the holes above is IVhat would a disunce meæued between two opposite poina of Ø.206 size be calleüt +<:Tt/K\ Loc¡-L lr?t. What would a maximum cylinder of Ø.207 size be gt Vr-'c cP C ' ¡r q'r Y¡V called? Sct- u o.zoE rrr tr 2 10. 11. When MMC is used as a design basis for functional inærrelationship of featrues of size of inærchangeability, the form, orientadon or position tolerance (increæes/decreases) with the fea¡ure acftal mating size deparnue from MMC' Where the MMC condition is not desirable to the design requirement and size of the conposition cemed features is to remain independent of any affect on the form, orientation or aPPliedtolerance, the condition BASIC OR EKACT DIMEI{SION 12. A basic (or exact) dimension speciñed on adrawing ¡ value used to describe the exact size, shape, or location of a feature. 13. ^ T Ll t:¿kLT -is r<-ru?- € É+<-T' A basic or exact dimension (e.g. .750) is shown symbolicalty. Show the .750 basic dimension below. 14. Where numefous basic or exact dimensions are required' a general on the drawing maY be used- il e-lc- 15. 16. associæed with the Use of a bæic or exact dimension requires also a or feau¡es involved stating the permissible variæion from the basic or exact orientation,lnofile position dimensions. or Circte the associaæd tolerances which provide ttre permissible variation from the basic exact orientation or position dimensions. ø .25O t.005 +lø.019 A qrl,rE, r1,?r,.ú tsl, Ç7,1L t7. A datum is a theoretically exact P,t' ..derived from the tn¡e geometric counæ¡part of a specrfi datum fearu¡e. 18. Dæums on parrs are idendfied by letæn of the alphabet (do not use I, 0, or Q) and placed in a squarc frame wittrg leade¡ and triangle direcæd to the fean¡re. This is known as a symbot. 1p-ø>,,,<- $ t*--+ 19. *A ";identify ttre hole as dæum "D." (IJse datum Identify the lower single edge as datum fean¡re synbols here and in questions 20 nd2L.) 20. Identify ttre outside ç{dth featu¡e as datum "A." 2l.Identify the small diameær as datum "A." 22. Adanrm is an acn¡al feær¡¡e of a part which is used to establish a daurm- 4 FENfl RE CONTROT FRÀtYfE 23. List the fou¡ elements of geometric control ttrat may be used in making up a compleæ Featr¡re Control Frame. (1) (2) (3) (4) 24. at feanue conuol frame which indicaæs 'þrpendicularity" of a hole wittún Ø.005' ûximum material condition, relative to daum plâne "B.'' Draw a CoMBINED TEATTTRE CONIROT TRAME ÀI.TD DÀfl'M TE¡III'RE STMBOT 25. a dan¡m Duplicaæ the feature control frame dr¿wn for the preceding question and add fearu¡e symbol ("C") to make a combined symbol' 26. Which of ttrese nr¡mbered sÉæmenß is correct? In the combined symbol shown in answer to question 25: l. Danrm *C. is a part of the datum reference fo¡ the perpendicularity requiremenr 2. Danrm..C- is compleæly identifies the featr¡re for separate from the perpendicutarity requirement and only othe¡ relationships. DÀn'MREFERENCEFRAME.oRDERoFPRECEDENCE 27. established In these feature control frames th¡ee datum references are used- According to n¡les, which a¡e the primary, secondary, afid tertiary datusts? a) ( Ø .oto 6D A B G b) Ø.oro €D F DIM 28. l\l 0 In the preceding symbols is the atphabetic order signiñcant? leuen reading Dan¡m order otþcedence is established by placing the danrm reference (1T G inttrefeatruecontrolframe' LE - É- @ üt n .E.) Orienation tolerances relaæs to the following characæristics: (Show their symbols below. (form) For this illustration.002 tolerance.ERANCE 30. which statement below most correctly describes the geometic conuoi on the part? ----. Form tolerances rela¡e to the following characæristics.) p¡oñle tolerances relaæ to the following characæristics: (Show their symbols below-) Runout tolerances relaæ to the foltowing cha¡acæristics: (Show their symbols below-) Locarion tolerances relare to the following characærisircs: (Show their symbols below. 3L. lerers A and B. 33. The toleranced dimensions for the size of a featrue conuols the form as well as size. Fea¡r¡re sizes shall not exceed 500 diameær and 1. RI'NOUT AI{D IOCAÍION TOI. PROFII.) FORM.IDARD RII.0O2 (l) Ø 36. .i.tq Illustraæ how datum idenrification letters are shown in the fean¡re control frame when no danm (Use the runout characteristic (or equal danrm) precedence is desiredsymUóf. datum r.) STÀ¡. (Show their symbols below.510 lengtþ- What is the basis for the corect answer in question 35? L Lf^^€f5 óF õs?8. and place them in a fea¡ure conuol frame below. 32. . ORIENTArION. 34.r.ES À¡{D PRINCIPLES 35. No element of rhe acgal featu¡e shall exænd beyond the specified higb or low limis of size or the boundary of perfect form at MMC. such as bars. Does the interpnetation of Rule I apply to commercial stock.fgan¡rgsandnot¡9¡þg r^ w+ offeanues. Rule 2 applies in conjunction with the fearu¡e control f¡ame and can be applied only 45. .. sheets. The inærpretation prescribiirg a boundary of perfect forrr at MMC applies only tl LL\-¡ !iê''''"-'"J''. 3?.geometry. and nrbing? Rule 1 may be removed from the application by anoæ such as placed on the drawing.\ ¿5lþ !i 39.. Rule# to fea¡r¡¡es of 44. Refeaing to the illustræion in question 35. 42. Which of these would be a feanue of "size'?' (1) A hole (2) A flat sr¡rface ..L.'-tt Lf1. Where size control gives inadequaæ control of part tolerances are sPecified- 3g. ( [' ("'' :14'r¿(' 'r i!' 40.. Whæ common qpe of geomeric relæionship of feanues ß not controlled by ttre condidons of Rule 1? 4I. draw a representation of the "boundary of perfectform æ MMC" of the Parr o' Soo l+--. ^'¡-.i .'/¿t. oos@lB trJ 48. Whæ is the virn¡al condition of the shaft and hole below? Sh. or a datum feature. Lqo . of size is controlled by is ttre collecúve effect of the sta¡ed separa¡e olerance of form. pirch diameter would be Show on these symbols how a gear or spline geomeric relæionship to ttre specified- Ø. K¡ c TòL(.aft o .46.hoie 0. dæum reference The Pirch Diameter Rute: Each tolerance of orientation or position a¡d qpecified for a screw thead applies to the 47. or location tolerance.S LS . It Of the feanue COnand the ¡wq'U ot.&fr¡. 0lø. geometric tolerance and On the symbols shown below. orientation. add ttre notadon ¡o indicaæ that Ûre dailm feæure basis is an exception to the Søew Th¡ead Rule and applies at the major dianeær.^ <-ífeæures a¡¡d in ttre clearance or worst case condition between mating part sidered in deærmining establishing gage feanue sizes- 50.ooz @lc H 49.l¿ryc' tTè{6Ío wt'. a A virn¡al condition exists where a featue. a-) Whe¡e the fean¡¡e Ðds is to be controlled and the desired tolerance zone shape is cylin- drical. (3) Is universally understood through ISO inæmational standards and practices. Place a check mark beside the most significant reasons for stating the maærial conditions (modiñen) under Rule 2. Whæ is the resultant condition of ttre Ø. . the sYmbol is sPecified' b.51.302? TOIER...AI{CE ZONE SHAPE 53.) True or False? Where rhe fean¡re is non+ylindrical and its center plane or axis is to be controlled within a total wide tolerance zone. (1) It is required- (2) Staæs the condition under which the design requirement applies.3001:38ånof" under question 50 if the hole is produced to the acn¡al mating envelope size of Ø. no shape of olerance zone is designaæd . 52. Suppoæ the lower part surface of Figure 1 was produced as shown here. ORIENTATION. It is time to test your ability to apply these principles in actual application. nomenclan¡re. 55. are not to be depended upon. PROFILE AND RUNOIJT TOLERANCE contols.rimum) tolerance for bow and other surface inaccuracies of .002 total (maximum) tolerance to the lower surface. 54. Add this requirement to Figure 1. sþrch in the tolerance zone applicable. a¡d nomenclan¡¡e of geometric dimensioning and tolerancing. l0 .FORM. speafy the accuracy of the lower surface (lower extremity of 1. PROFIIÆ AI{D RI'NOITT TOLERÀI{CING You have now progressed ttrough the steps necessary to learn the fundamenmls. 57.002. and inærpretation. Documents establishing suitable are either not specified or are (3) (4) do not provide the necessary control.610 dimension) is required in the pan functiot¡" o be in a parallel orientation of . ORIENTAIION. rules. Referring to Figrue 1 (found at rear of book). The upper surface (upper exuemiry of the 1. Use letter "A" for the datum. Using the form tolerance control selecæd in question 55. Geometric tolerances should be specified for all feanues criticat to function and interchangeability and whe¡e: (1) (2) Established practices c¿ìnnot be relied upon to provide the required accurÍrcy. The nex¡ series of questions and examples æe designed to exercise yor:r knowledge of proper FORM.610 dimension) to allow a total (ma. in a squarc In Figrue 1 (lower figrue). 1-6101'005 Assuming rhe .5g. ttre . suppose the vertical 1. lt . on the produced Show below (sþrch) how the tolerance zone and rhe dan¡m are established as part (Figrue l) for ttre requiremenr of question 57. Figue orientæion ro ttre lower surfacó wfthin . Assume ttre produced Pan surfaces irregutu. as in question 56. what is the boundary of perfect form at MMC size 60. and the Rule 1)? (remember size rcle¡ance. Add this requirement to requirement of quesdon Show below (skercÐ how rhe tolerance zone is established for the 60.002 flamess þlerance. Sg. 61.003.610 surface is required to be 1.002 parallelism tolerance. Assume thar in Figure theØ. the vertical 1.) (1) Perpendiculariry of a sr¡rface should be specified in the view reladonship with iu specific datum. this orientation control with reqpect to datum l t2 .62.500 sr¡rface is required to be in a squarc orientæion to the lowe¡ surface (of the 1. Specify on Figrre 1 that *4" is Ø. 64. Use letter "B" for the datum. Suppose that in Figure 1 (upper view).376 hole has been located witÌt position dimensions and tolerance (do nor yer concern yoruself wittr ttre method).376hole musr be maintained to a finer degree than the position tolerance. Add this requirement to Figrue 1.003 total' RFS. Why are two seParaæ qpecifications required? (Choose most significantteasons from below statements. 63. (2) Perpendicularity controls form as most ctearly showing is well a-s orientæion.610 by 1.500 end face surface was conEolled in its perpetOcutarity (squareness) in ¡vo directions from separaæ dæums. In questions 60 and 62the 1. but the orientation of the Ø.500 dimension) within.003. If the hole is produced arØ. what is the total AtØ-3782 tolerance permissible wittr hole size produced atØ3767 The answers to question 66 a¡e de¡ived because: (Selea the moæ conect answer. of Figure I (referSuppose the perpendiculariry tolerance of Ø. what is the ma¡rimum permissible perpendiculariry tolerance? If the hole is produced atø.003 on the ence also question 64) was required by the pan ñrnction to be on an MMC basis.378. The tolerance is implied or staæd as RFS r¡nder Rule 2AIl tolera¡rces smred a¡e totals. Show below (skerch) how the tolerance zone is established for ttre requirement of quemion &. How would the fea¡¡¡re control fras¡e be shown? ø376!'ffilot. 67.65. Referring to tbe perpendiculariry tolerance used in question 65 on Figrne 1. 66.) (1) Ø 68. whæ is the maximum perpendicularity olerance? t3 .376 (MMC). 002 to dan¡m "4. In Figure 1." ttle base sr¡rface. t4 . (gains/loses) production tolerance yet assur€s fi¡nction and inærchangeabitity. 1. tbe 25" and 30o angles æe critical o úe extent of a. when appropriare to the desig requirement." Show these requiremens on Figrre 1. From the response to question 68. From questions 64 tbrough 68 we see thæ whenever a fea¡rue of size such as a hole is involved. are desired as a designrequirement conditions 70. 71. we see that use of the MMC principle.69.010 maximr¡m olerance as they relaæ to tbeirrespective danms'4" and'8. the surface identified as datum'B" (in quesion 62) is to be square in orientation within . In the lower space on the Figrue sheeL skerch an end view and sþsw this requiremenr In Figure I 72. \ile mr¡st consider whether the or . 73. Also. t-" l5 .Flutn ss. for¡r types of Reviewing the Figure 1 questions and applications. it can be noæd that of the geometric form and orientation characæristics used' th¡ee require a datum reference. 75. does not re4vre a datum because the 'telationship" of the specified tially to a perfect counterPart of itself. show how the anguiar tolerance zone reliaæs to the '500 '005 t dimension. and 76. for exarnple as seen in the Figure is essensurface tion. Dæusr references a¡e used wherever a specific I applicaof one fearr¡re to another is required. requirement of question Show below (skeæh) how the tolerance zone is established for the 72 onthe 30o angle. dimension at the veflex end must þ within the 74. acÍ¡al PaÍ comef Referring to the 30" angle requirement of Figrue 1 (see question 12)'the and tolerance. and that the "boundary of perfect form æ MMC" (Rule 1) does rct apply. 80.0L5 rclaL RFS. ^/V ( 1 78. sraightness of the pan is conrolled tq maximum.0003 total as a refinement of ttre size control (see questions 77 and 78). to a maximum of Ø. Whæ is the ma. ló . What is the bæis for this answer? Assume on Figrue 2b ttræ ttre pan is to mount into bearings. :r0 *\t) U ^ Referring to Figure 2a(atb longinrdinal elements of the and the "boundary of perfectform at which will represent a critical size control for bearing mounting of the M t. 79. Spectfy this requirement on Figure 2c.77.ffi paÍ at each end- Specified as shown in Figrue 2a. and also that the straighmess of the longinrdinal elements of the cylindrical surface is critical to the design requirements and musr þ wirhin .rimum permissible snaighmess tolerance of Figue 2b? Assume on Figure 2c ¡ha¡ the part is to mount into bearings on the ends but staightness of tlre longitudinal axis of the cylindrical surface is less critical. Specfy this requirement on Figure 2b). 81. 0L5 æ MMC exceeding the boundary of perfect form æ MMC. what is Ø. Where interchangeabiüty of parts of this tpe is required.0L5 straightness olerance of question 81 was speciñed on an RFS basis. the condition often desirable. Show this requirement on Figue 2d.6t0? ttre suaightness tolerance permissibte if the pan size is at atØ599? 84. we will assume P{t2d can be perrrined a straighmess tolerance of Ø.6A0? 11æØ.82. rwhæ is the virrual condition of part 2dandthus the minimum (also perrrissible boundary of clea¡ance of the hole of part 2e? virual condition) What is the straightness tolerance permissible with ttre pin (pan 2d) size æ Ø. 85. Assume the pin shown in Figure 2d is to æsemble with the hole shown in Figure 2e.597?- t7 . Since the ø. With less critical assembly as the criterion. The collective effect ofthe size and form error on Figure 2c (question 81) results in a size of possible Il 83. 86. In Figrge ?Å. andthe responses to quesúons 84 and 85. it is seen that the deviation from tolerance equal to the deparure MMC size resulted in from MMC. other than cylindrical. 88. elemens could be applied 90. Suppose the circular cross sections of a cylindrical part (Figrue 3a.502. upon which a straightness of surface . gL. Sraighmess tolerance is applicable only to cylindrical parts. Wh¿t type of form control Show the proper symbolic conuol on Figure 3 a using would be used? a total olerance of . 89. (added/less) 8i. æ rear of book) are critical to a finer degree ttran the size tolerance would control.002. Tnre False A straighmess rolerance is normally specified in the drawing view in which the tolerance applies. True- False Name one rype of surface. Show below (sketch) how a tolerance zone would appea¡ if the maximum dia¡neær at ùat ctoss-section was Ø. l8 . 001 totat. T\oofoical part conngruations lariry tolerurce may be specified are of circularity is 93. Is adarum reference used with circularity olerarrcing? rer¡son fs¡ this Erplain Your l9 . add to the parr illustrations the requirement wfthin.92. which circularity olerancing can be qpecified on any part configruation (other than cylindricar) upon which circuin cross section. Refening to Figures 3b and 3c. on the Figrue 3b and 3c parts' Show below (sketches) how the tolerance zones would appeü 95. 94. of ttrem each force necessary to 20 .(Assume the ma:rimum produced size is-ø502 ) 98. Vee block analysis of critical circularity or cylindricity requirements must be wary of the and vee block angle effect of pafi 100. any daturr and the features in control may require specifiorthe naximum cation of their allowable to drawing Olerance. More r¡ccruaæ analysis methods for deæcting circularity or cylindriciry requirements utilize techniquæ which simulæe pan æris criteria. 101. Assume rtrat composiæ surface control of the entire cylindrical surface of the part shown in Figure 3d is required. Parts which distort due to their weight or flexibility or due to intemal stesses released in parts and are subject fabricæion are known as Where contol of this kind is necessary.001 total. such as methods. Is a da¡um ¡eference required with cylin&icity tolerancing? \ilhich th¡ee form tolerurce controls are included in composiæ in cylindricity olerancing? 99.96. Show below (sþrch) how the tolerance zone is developed. 9'1.Add to Figure 3d ttre proper speciñcæion to control the cylindrical surface within . attd 105. and equalty dþosed about the basic profile berween X and Y and relative þ datums C. Profrle of a surface conuol is normally a combination control. 103. tolerancing is an effective method of controlling an irregular curve' is desi¡ed" profrle of a ¿1¡c. 2L . of LO7. B. The surface profile on Figure 4 (at rear of book) is to be connolled to a total of . Show this on the drawing. 106. A profile toleiance is shown in the profile appears. or other unusual pan surface contour Where total surface control conuol is used. The desired profile is dimensioned by dimensions. of ttre drawing in which the desired 104. profile of a control is used. Profile of a line control is normally used as a refinement of other controls. where line element conuol is desired.t02.010 A. The profile of any line toleranæ zone must be contained within the profite of any surface control shown in Figure 4. Tn¡e False 22 . Show by hand skerch below how the tolerance zone is deærmined in the preceding example. ia form variation is affecæd- (2) Accuracy of the surface profile and its desi¡ed shape is normally not affected by Pan size va¡iation.108. Can aprofile of surface tolerance be modified to MMC? Which of these statements suPPorts your answer? (1) As the pan size varies. Add to Figure 4 rh¿t the profile line elements shown in the plan (left) view a¡e to be maintained m a fine¡ tolerance (of . 111.003) than the total surface profile. 110. 109. and Runout tolerance is considered as a unique category of geometrical dimensioning md tolerance but is u.tLz.002 total (FM) relæive to mounr into bealngs and the other diamerers arc to be the part axis of rotationregardless of feanne size' tolerancingshouldbeused. tolerance relaæs sr¡rfaces surfaces may be or (perpendicular/tadiat) 113. and a means or a-) Total runout includes such form errors Also. assume ttrat the within . ör .xis for siderable lengfh. (cylinder) a nrnout tolerance may be established by a diameær wo diameters having a. A n¡nout tolerance establishes ef ss¡trslling the funcdonal relationship of two r ryPe urd may be applied (complex/composite) is a tolerance of type This part more fea¡¡res of a æ one of ¡vo different t1ryes of nrnoul These two tyPes nrnouL n¡nout. 116. -' l 15. when applied to surfaces constn¡cted at right ¡ngles (or other) rc a danrm a¡ris. A nrnout of (cenraVcoaxial) The condition (RFS/ÀÆvf C) These to a th the datum datum the to is always used in runout tolerancing' - lL4.xial separæion' or a diameter and a which is at of con- a angle to it 23 .) Circula¡ nrnout includes such form errors at of the sr¡rface when applied to surfaces consm¡cæd and as ' circular right angles to a daom æris..tuJrv ã-ðótnui*tion tolerance controls. A darum a. b.ShowtherequirementsonFigure5. part diameærs o1:a9h end are to Referring to Figrue 5 (æ rear of book). Size + form. orientation or locaúon error = 24 . L20. 118. Specfy the datums with properprecedenceandthe Ø.4995 rli¡mgþ¡ is to be the secondary datum and provide the a.890 diameær wæ required only . to Figue 6 (at rear of book). orientation or location error = (shafrThole) (shaffiole) vimral condition virrual condition size - form. Referring to ttre ø. how would this be indicaæd by for symbology? Add to figure 6. 119.150 from the right face of the Ø1. Referring assume ttrat the left face of rhe part (left end of . The pan mounts into a bearing.0005 total. whatis the virrual condition of the hole? The virn¡al condition of a fean¡¡e is the size of the boundary that must be considered in deærmining clearance between mæing parß or features.030diameærswirhintotalrunoutof . Add ttris requirement to Figure 6.0300 diameær.ris of rotation.376 hole of Figure t held in perpendiculariry of Ø.001 total runout on the Ø.L77. Assume ttræ ttre circular elements of the 45o angular surface of Figure 6 are required to be contolled in rotation within .003 to danrm A (see question 65).001 with rcspect to the darum axis.890 andØ1. If it was desired that the.700 dim) is to be the primary datum and the Ø. IOCANON TOI. profiIe and Rrurout torerance controls. Ir is now bæic fundamentals as exænded to Location tolerance' ise yoru knowtedge in selection of In addition. tolerances relaæ to of 25 . of L23.sr your ability in using these orientation.-:**ples of time to . Tolerances of locæion involve the use of geometric characæristics and and 122.ERÀNCING Form' you have now successfully progressed ttEough the series of questions -9.. an emPhasis lzl. Locadon tolerances involve feanues a be must between two or more features. I-ocation featu¡es. At least one of the featu¡es feature. the position tolerance is the of the feanue must lie. Position tolerance is a cumulæive/non-cumulæive (which?) of control in which each feanne relæes to its own desired exrict (m¡e) position method 130. sloa and tabs) the position tolerance is the of the tolerance zone within which the center plane of the feature must lie. 129. The shape of the tolerance zone is implied as lotal wide in the absence of the symbot and by the placement of the dimension line and 128. A position tolerance is based on the as it relaæs to the size of the concerned fea¡ure part feature. Position olerancing is a method used to sPecify L26.g. principle ensures interchangeabiJity and provides gea. Ln. size of the mating 26 .test tolerance advan- L25.and or inærchangeability of mæing part features is involve4 the principles of tolerancing may be ued.g. holes and bosses). perrrissible variation in the locæion of a feature about its desired or ex¿rct (tue) posiúon. Where function The tages.L24. For cylindrical fean¡res (e. . A position tolerurce is the the location of an of a featue in relationship to a dan¡m reference or other feature. For noncylindrical features in the desired direction.. The of the tolerance zone within which the shape of the tolerance zone is specified wittl the symbol (e. Posirion rolerance apanern. 134. Which rwo of the th¡ee staæments below (1) (2) (3) Position tolerancing recognizes the permissible va¡iæion of a cylindrical fean¡¡e locæion in 360o of movemenl Position tolerurcing is a more convenient way þ relaæ mating feanres than plus and minus coordinaæ tolerancing. what is the MMC Specify on size of tlßØ. mat- L32.010 diameter at MMC. 2t .250 holes are to be locæed within a positional tolerance of .131. True in 133. the tolerance on the as the acftal actually produced fearure (increases/deøeases) ing size depans from MMC size. In this drawing. (at MMC) is ideally suiæd to multiple muing pan cylindrical fearu¡es False mosr support the answer to question 132.250 holes? the drawing that ttre four Ø. The position tolerance is developed directly from the relationship of the mating feanue MMC sizes. When position tolerance on an MMC basis is applied to a feæue. 247? question 134.253? tolerance zones at L36. skerch in the position MMC size of the hole and at IÀ{C size of the hole. Ø . suppose that the upper surface on the front view is the mounting surface and the other two surfaces are important to ttre hole patærn positional tolerance.tso 1. what is the position tolerurce of the hole if it is atø. On the below part. On this layout of the part under question 134.005 Ø. 137. add three datums with precedence indicated. 138. On the figr¡re shown under produced atØ. Dæum fearures or surfaces æ the basis for position relationships should be- on the drawing.oto @ 28 .135. 140. Now ren'n hole to show to Figure 1 and revise ttre specifications on the Ø. preceding question as Make a skerch below showing the inærpretation of the paft under the bæed uPon Your answer.139.376 it located at (venic¿l) and -940 (horizontal) basic dimensions' 29 . this will be taken up in succeeding exanples.l4l. However.138 screws (floæing fasæners) will assemble. Disregard hole Pauern locæion with reqpect to ouaide surfaces for this example. Assume thæ these rwo parts are mæing paru with the fou¡ holes in each to coincide so that fou. select appropriaæ prima¡y (orientation) datum feærues æ the Part's correqponding inærface sr¡rfaces. t5 I 1. Calculaæ the position olerances and compleæ the position dimensioning and tolerancing on the npo pars.003 30 . 4X ø. 33? --:.-J I t.oo¿ G) .400 r. t30 I I I I .416 (3t . I¿ I ' -6q lltRË. in toCing establishing th¡ee n the be- the danrms' ï ---------) . r48:'3? .#!) ?'15 ?5 1 P rnlS ù< øJ25 :.250 .?Jã--'ì --=Jt ___J -.3501 .600 .¡zg!'ononï þ ø .with ¡vo '1 142. Calculaæ position dimensioning aûd tolerancing. 138 -32 UNC-28 r.fi' i''ã@l{ßE] 2X .003 ø. to be assembled fastenef" two dowel bosses and mating holes. These two pafs are mæing P¿¡fts.3 00 2X ø. This is a "fxed positio ttre come fixed in their location æ æsembly. the position tolerance zone exænds to thq I44.752 2. the following measurements from the specified dan¡m surfaces and the hole sizes. Tbe cenæring effect of the inseræd screw may negarc added tolerance due to size deviation from MMC.138 thrcaded hole different in this regard? Select most appropriaæ answer: a) 146. b. Unless otherwise specifie{ of the fean¡re.001 inch.746 2.L25 boss if produced at actual mating size of Ø.749 . #3 (upper right). Make the necessary calculations and plot (use doa) the results on the graph using the zero (0) point as ttre rr¡e (exact) posiúon and origin for the X and Y differentials. Referring to the "answer" illustration of question L42. could the distribution of the position tolerance To suppon your a$¡wer.7454 32 .L235? The Ø. 148 hole if produced ar Ø. The total position tolerance calculaæd may be distributed as desired be¡veen the corresponding mæing part featues. make an analysis of the part shown on the given nextpage. an exercise Measurement X Direction Hole #1 Hole #2 Hole #3 Hole #4 .L43. in position tolerance principles.whæis ttre position tole¡ance of the Ø.) 145. and #4 Qower righÐ. The graph scale is I square = . In the exarrple shown unde¡ question 142.) Tæped holes usually have close size tolerances.fit2 (lower þft).L51? Why is the position rolerance of the . Imagine the concentric circles as a transparcnt overlay chart of the sane scale as the graph and as applied after plouing the hole centers or shown as concentic circles on the FaptL. Number the holes #1 (upper lefr). which on each part have been different? of the below staæments is most appropriaæ? a-) Position tolerance is calculæed on the basis of relationship of size of the corresponding mating paft feat¡res. As b. 6.300:333 Fas.Sçe-c¿- J.rsrzE- S t#. 7-12 o @ *= @l (x) Õ.7rs/ Y= ' 7fS Z srzE- o ..7 .013 -z-' ¡{ouL a .ú. TOL E aù X= o.so ¿:f @ \= . t oC tQ4 M\¡-t L .STLS-rr^.u--re -..f. ACTUAL LOC.014 . SIZE.I ØiçC ? S = \gOrô/øS T"ÒL. '' . oo ft l:t{g --:t-) soÒ stzE- a @ X = Z.7q 7 Y= Z.ft C-TU !>-.rC sz?Ë:.soe . O 1Dù --:d0 ¿ s--- Q 'aaLS ..ztzJ roL.ø'.. POS.010 ) ø .le -O 1cco.OtZ r.011 ..t-..o1o @ A B c HOLE NO.30? + coc <L. 4x ø. has hole #1 met the requirements? Has hole #2? What consideration was given to some holes to make the determination of question 147? Which is the most appropriate answer? (1) (2) r49. and calculation methods shown Hole #3 Hole #4 in your reference materials. xlf no calculator is available to you.30t Ø.303 Ø. (b) Measurement Hole Size Hole Hole Hole Hole #1 Y Direction 2. From the analvsis made on the part shown under question 146.Indicate at right acceptånce or rejection of each hole.302 #2 #3 #4 ) . Actual hole size deparnre from MMC adds position tolerance for that hole equal to the the departure. 148.746 )\¿. (yes or no) Hole #1 Hole #3 Hole Hole #4 #2- (c) Is the part acceptable? 150. All holes in the pattern may shift together within the position tolerance assigned. Hole #1 Hole #2 do the best you can with the tables. deærmine from the inspection results of another part (produced to the same drawing as shown under question 146) if the part is acceptable. Ø. graphs. Under the function and advantages of position tolerancing.752 . what further determinations could be made? (Write an answer. Is tlre part analyzed under questions 146 and 147 acceptable? (a) Using your calculator*.248 Ø.) Using-ody your calculator*.) 151. Has the part now met the position requirements in terms of the design specifications? Has it met the production requiremens within tolerance? Are the quality control or inspection requirements clearly stated? 4 . Fill in the derived diametical (cytindrical) values calculaæd for each hole (show at least to the fifth decimal place). confrm your a¡swer to question 146 mathematicatly.303 FüI in the derived diametrical (cylindrical) values calculaæd for each hole (show at least to the fifth decimal place).I47. 380 holes locaæ ¡ ke o¡ieutation (squareness) from? : take orienution from? 35 . if ø .ß2.75 !. what Is this a positional tolerance strift of the hole panem (as a unit) exiss? hole-hoþ added oþrance? I54. 380 hole position tolerance at MMC size? Wha¡ is üe virn¡al condition of the ' Ø. a) b) c) d) e) Ð s) h) Whu is the da¡un hole position tolerance æ MMC size? Whu is the datum hole position tolerance æ LMC stzÊ? Whü is the da¡um hole perpendicularity tolerance at MMC size? What is the da¡um hole perpendicularity tolera¡ce æ LMC size? Whû is the Ø. note that a featr¡re of size (a hole) has been used as a dat¡¡m.Ø502.0æ @ D the daa¡m D fea¡ne is produced at acn¡al mating slzn.382? 4x ø.380 holes? Whû is the virn¡al condition of the da¡um D hole? Whæ is the resulant condition of the Ø-380 hole if profuccd to acu¡al matine sze of Ø.014 @ A B A c Ø. which dailms does the datr¡m D hole tocaæ from? Which da¡uns does the ø.O1 :560 !.OO5 .913 o I 153. The da¡un hote has been locaæd by position tolerance with its orienta¡ion.75+.01 Ø .5oo:. refined to a þsser tolerance.o1o @ A D@ B 2. of.380:'m8 o 1. In the prcceding figuæ. In the preceding figure. Refecing to this figure. orlrrpendiculariry. Functional gâFng = Ø.) 159. Gage pin size for Ø.380 hole patærn under question 152.500 dau¡m *Do'hole =Ø How derived? 157. Erplain how you derived the gage pin sizes.155. Can functional gaging of ttre variety rlisst¡ssed in questions 156 both datum and featrues in control are on an RFS basis? though l5g be used whe¡e 3ó . what would the size of the gage pin be? \ryha¡ would the gage pin size be for the perpendiculariry requirement? can also be used to evaluue the position of the ø. Add the nominal gage pin sizes to this illustation of apin gage. If a ñ¡nctional gage similar to tbat shown under question 156 were to be use( but where in conrol remain on an MMC basis. whæ difference would exist generally in ttre gage desig¡. How derived? Gage pin size for Ø. RfS basis? position toleranced paüern of fea¡¡res be relaæd to an RFS daarm? Show the fea¡¡re control frame stffing this requirement here: This is based upon which rule? Can position tolerancing be applied on an Can an MMC 158.380 holes If a functional 156. gage were desired to evaluate the locæion of the datum D hole of the figure shown under question 152 which dan¡ms would be picked up and in what precedence? Would MMC be applicable to the dau¡ms? In the functional gage. and fr¡nction? (Descdbe in words or by the dau¡m is on an RFS basis and the feau¡¡es skerch below. Disregad conside¡ation of gage tolerances and the relæionship to daruÍi B for purposes of ttris question. Skerch below the parr shown unde¡ question 160 (above) and show the positional tolerance mîe. position olerancing may be used on functional or assemblabiliry requirements of noncylinùical feæues. On this prtt.ofy thæ the . 37 .003 161.120 1. rp.L20 width (at MMC) within -005 wide tolerance' 1.160.501 slot is to be locaæd al tn¡e position (at MMC) wittr respect to the 1. 9? Total ole¡ance at LMC size of flatanddarum = Total olerance a¡ LMC size of slot and = dan¡m MMC Size SIot(Part#2) = MMC Size Flæ (Pan *t¡ = 1-¡ MMC Size Daom Slot @an#Z) = MMC Size Dan¡m Flat (Part#1) = (-) NOTE: For the pu4)oses of this example andfor simpliciry of principles. EstaÞ lish position tolerances on the mating pans shown below. If you wish to corsider ttris additionally æ an optional exercise.L62. geometrical tolerance benveen the dan¡ms A and B on both parts has not been made a pan of the calculations. add here an explanation of the steps necess¡fy: 38 . Also calculate the ma:cimum permissible production tolerance that could be permitæd on each part if its fean¡re and datum actual mating envelope sizes were both to depan from MMC size to LMC size. Posirion tolerancing may be applied to relate noncylindrical featu¡es of mating pans. PART #1 PART +2 .503 *. 003 tolerance zone. On this parl specify that the Ø. 39 .o01 1&. Sketch below the parrshown r¡nder quesion 163 and show the positional tolerance zone.t63. ø . Posirion tolerancing may be used on ñmctional or assemblability requirements of coaxial features.305 t.305 fea¡r¡re is to be locaæd at tn¡e position (at MMC) wittr respect to the ø.500 featr¡re (at MMC) within ø. If you wish to consider this additionally as an optional exercise.881 ln-ø.300 t .oos ø. Position olerancing may be applied to relaæ coa.6r4:'333 1. Establish position tolerances on the rnating parts shown below. Also calculate the ftximum perrrissible production tolerance that could be permitæd on each part if its feanlre and datum ¿rctual mating envelope sizes were bottr to depart from MMC size to LMC size.7 4s::33Î Total tolerance at LMC size of hole and = datum Total tolerance æ IÀfC size of shaftanddan¡m = MMC Size Hole (Part*t¡ = MMC Size Shaft (Pa¡f2) - (-) MMC Size Datum Hole @art #1) MMC Size Dan¡m Shaft (Part f2) = (-) NOTE: For the purposes of this example and for simplicity of principleS.r'ul:BBå ø.sto1.L65. add here an explanation of the steps necessrrry: 40 .xial features of mating parrs. PART f 1 PART +2 . geometrical tolerance between the dæums A and B on both parts has not been made a part of the calculations.75'l:33å Ø. 500) are to establish ttre a:cis of rotation of ttre part with ttre Ø 1.005 ø.166. if t. which control is used? that part Assume below. 1. 4l . because the axis of the feature has not been deærmined.605 t. If ttre pan error exceeds the stated tolerance when the FIM method is use{ does this mean ttre pan has not met the concentricity requirement? Which statement supports yol¡r ânswer most appropriaæly? (1) ' Q) The surface may be out-of-circularity. within ø. Using conventional FIM methods of evaluæion. No. and the resultant error detected must þ compared to the cylindrical tolerance zone. Q) MMC methods or conventional surface criæria controls are more readily producible and economical. Where erors of form and location are considered on the basis of displacement of axis of two Establish or more basically coaxial feaû¡¡es. necessary dan¡ms and compleæ the featu¡e control frame for the ttre nvo diameærs (Ø.605 and Ø. Q) 168.000 diameærrelative to that atds. which other cha¡acæristics sidered first if possible? Which statement suppsrts your answer most appropriately? (1) Concenricity requirements ate encountered less frequently.soo 167.003 tolerance. has it met the concentricity requirement? Which of the answers below is most logicat? (1) Yes. which will influence the reading.OOl Ø.ool the pan checked at .. should be con- 169. Concentricity is a variety of locational tolerance control.000 1. Before a concentricity olerance is specifred.003 FIM. RFS. if the surface of rotation has been sufñciently sampled for mæcimum error. erc. but does not conclusively prove center (axis) dþlacement or eror. Specfy thæ ttre . Skeæh below the part shown under question 166 and show the concentricity tolerance zone ar¡d a representation as to how an acnrally produced dia. would be deærmined if in compliance witt¡ the requirement or DoL l7l.120 ! .170. RFS. a syrnmetry tolerance 1.005 wide total tolerance.120 widttr wirhin .501 widttr of ttris symmetrical part is to be locaæd using with reqpect to the 1.003 42 .OO3 +. and show ttre symmetry tolerance zone and a representation as to how an actually produced slot would be deærmined if in compliance with the requirement or not. Dæum targets have been panially shown on the part on ttre followingpage. select ttre tagets which appropriæely oonstruct these designated datum planes. whæ would the difference in mean L74.L72- Skerch below ttre part shown under question 171. Noting the feaore connol frames and their specified datums. RFS. f . tolerance. 173. If this part had been indicaæd as a positional ing be? Explain briefly. Then compleæ the danrm u¡get symbols and identify the targets according to your own selection. 0I0 t.020 is used for the relar. A refinement of ø. 9u!e! A.ionship of the patt.B.32 UNC - 28 174.7X.ern relative Èo the exErernity datum references. ø.138 . 4 .olerance in the pattern reLacive Eo datum D is used.C. Establish the dæum Érgets' dan¡m planes. hole pattern) with respect to the 176. In the space below design or sþrch t¡¡fgets. and show some feanre relationships (e.g. your own pan using datum Egets. Use a part similar to one from your own experience or esablish an imaginary one. add or modify with the necessary symbology to indicate that the tolerance zone is projected above the part for .190-32 45 .310. On the below part.175. 4X. Show the target locations using proper methodology but disregard determining the values. or. Select your own target locations as seems appropriate.32 46 . insert hypothetical values.164 . 8X . Add any necessary views to show your requirements. if you wish. On the following casting.I77. establish ttre datum planes for the parallelism and positional control relationships by dahrms and datum targets from the part surfaces. êlø.430 .o.dØ.z}iiroles) relarive to the dan¡m feattues D and E. There are a frames to ties but make your choice by adding in the appropriate modifiers in the feature control best achieve the following: (virnral Add material condition modifiers to relate to the danm features D and E on a functional condition) basis on the following figure.17g. pattems On the following part (shown twice) select the best methods to control the five hole possibiliof number (ø.oos (ù lA lB lc 47 . also ensure closer compatibility between ethods.179. lition indication to relate to the datum features . 2X Ø.ßo+'90-! 4x ø.250+'0^0-? Ø.205+'991 48 . 151 +.010 from LMC with respect to dìn¡m A (the bottom face of the part). diameter at Indicaæ on the below part that the 4 holes are located at tn¡e position within .lg0.003 49 . Disregard the pattern location the outside edges for purposes of this example' 4X Ø. - FOR NOTES OR CALCULATIONS - 50 . Ä fr.210:'.005 51 .ure Proper inærface.28 . Make the necessary determinacalculations and complete the drawings below' 6X. .190 .550 t.33.7gg 1.32 UNF .OtS \f 6x ø. Design (skeæh) a functional gage for the small part (one with clearance holes). 52 . to verify the inthe-paüern location controls only. as developed under question 181. but show the gage constn¡ction as based upon your answer to question 181.(NOTE: Question 182 is optional for those inærested in gagrng). You need only develop the nominal gage sizes. 182. 2!z HoIe 4 íoJ. From the below drawing (similar to one under Questions 181.996 ( .4. Is hole fr> good Is hole #6 good. has been used as the origin of the X and Y meastuements. (See pages 57 and 55). Graph paper and tracing paper with overlay circles to the graPh Paper scale.zt35 Persrissible position tol on hole /. 182) and given information.004 0 1 Actual hole size T !.010 at MMC requirement. The remaining holes. Is the part good ? 53 . .ztz fs hole #t Is hole #2 Yes good good Tq hole #3 good Is hole #4 good. 2. Hole #1. the lower left hole.ztz5 l. squ¿ue-uP origrn O Hole Hole 2 Hole 3 1 inX 0 inY 0 (.995 e 2 2 e e 2.1+925 /. Use the graphic analysis þaper gaging) method.zt3 l. ooo5 1 .e ) HoIe 6 . Use a scale of .183.5 and 6 have been measured from holes I and 3.).) .0032 .001 equals 2 squares. determine whether a produced part with the following measured results is acceptable to the positional Ø.9947 No f . are supplíed. the pattem has been squared-up with hole #3.4898 2.003 L. -FOR NOTES OR CALCULATIONS - 54 . 55 . - FOR NOTES OR CALCULATTONS - 56 . 25 0.35o.33 o.27 o.29 oi.REH0lfB FR.0 5 ( Datu¡n Bonus Tot Questlon 186 ) 5? .26 0.30 o.@f¡l EOO'K FOi USE 0N QIJESTIONS (For use on Questlons lg3 & lg6 ) o.32 o.3 I o.2a o. . . . optimum and inY: reference to the above answer.xes).e. The result of this calculation should give a di¡ect answer as to the accePtance of all the holes or noL The smallest circle (tolerance zone) size.184. Disregard the hole sizes (assume them RFS) for the initial calculation but consider their sizes as necessary (i. departure from MMC as bonus tolerance) in your final deærminations to verify the question 183 g¡aPhic analysisThe smallest circle (tolerance zone) sizn. is: @ (cenæroid) is in: and X: inÏ With reference to the above answer. optimum position of all 6 holes on all individual holes. in your calculations. write in your own words how you deærmined the part acceptable (or not) from your calculated results. 185. Veri$ yoru answer to question 183 mathematically with a computer or Programmed calculator. 59 . wriæ in your own words how you deærmined the part acceptable (or not) from yotu calculated results. Verify your answer to question 183 mathematically with a computer or programmed calculator. including the holes size departure from MMC (bonus tolerance). compensating for the MMC deparflue @onus tolerance) . (For information. Determine the smallest circle (tolerance zone) which will encompass all the measured hole centers (axes) simultaneously. is: Ø position of all 6 holes (centroid) is in X: 'With (For information. Determine the smallest circle (tolerance zone) which will encompass all the measured hole centers (a. 010.3715 I 2 J Actual Hole size ø.9948 . Use scale .003 4X Ø.9953 inY . (Graph paper and overlay ø. etc. From the below data given from an inspection process (i.994 .010 6iù A D ú\il) B 1. Use graphic (paper gagmg) methods. +.005 2. coordinate measuring) on this part.502 .001=2 squares.500+'991 Hole inX .e.500 hole? 60 .38O _.560 +.3825 ø.3726 .186.383 ø.9945 0 Has the part met the Ø.380 four-hole pattern met its requirement relative to the datum D ø.O1 ø. determine if it has met the positional tolerance requirements on the ø. 0 4 Danrm .376/.382 ø.380 holes and the pattern relationship to the ø.01 .382s ø.5N da¡¡m hole.380 hole to hole requirements relative to the tnre position of each hole? Has the ø.75 t. (Use page 57 overlay).377r .ooo e Ø. supplied).75 t. .:_. ..i-l -r.---.:f-r _-. :-f-..-¡¡¡i *i--. i---r.i. ..:-!:-...i-. :. -.-+-.-rr-t_l_i.--l--l- r-ri._--r--_1--iF----t__- +-++-+'-:-r-l ri I t ì I i' 1.' !..:'-*i.l:: I::: _:_..-L. .ri..--:-lLl ll_.1_ -r-i .t.....: : : l-:+-i._-..---:...r_i_r:i__:_i Ì-__.--. ...:.--i:-j-+-i -.:_l .1 - j....i--l -'i--i-.__'_ .-i-r-: J-.. .:. .:l-..-----] -a-j-t--..J+_. I _.: _:_ .::':::l.-:-....---:*--..t9 i-'r._ :..-:-.. .FOR NOTES OR CALCTILATTONS - 62 . 63 .tg?. From ttre data given under question 186. verify your answer to question 186 mathematically with a computer or programmed calculator. FOR NOTES OR CALCULATIONS - 64 .. FIGURES Figures 1 through 6 may be removed for convenience in doing the workshop exercises. 65 . 66 . FIGITRES in doing work on the related Figrues 1 through 6 may be removed if desired for convenience quesdons.376 +.bt ^ t.500 r.r¡r -i-o .005 / .005 tr@ t B tæFt 1.002 ñññ t'(ÎL h-4-t /- Þ //- ( + \ 1.rre I 67 .nt W. ùoilí 2 ræ. ø.*zW .005 Fig.500 +.610 ^(r\-r E ù. 68 . .ø. \ Figun 2 (VIRTUAL CONDITION)-) 69 .eoo_'.oool'!fo.. org ø..goo3 /. '10 . 005 Ø.500 t .oo3 (dl Figurc 3 7l ..soo t. 1a . 0300 t .ø 1.Asss rää Flgure 6 73 .0005 ø.