Tiêu chuẩn iso 04156 1 2005

INTERNATIONAL STANDARD ISO 4156-1 First edition 2005-10-01 Straight cylindrical involute splines — Metric module, side fit — Part 1: Generalities Cannelures cylindriques droites flancs en développante — Module métrique, centrage sur flancs — Partie 1: Généralités `,,```,,,,````-`-`,,`,,`,`,,` - Reference number ISO 4156-1:2005(E) Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 Not for Resale ISO 4156-1:2005(E) PDF disclaimer This PDF file may contain embedded typefaces In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing In downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy The ISO Central Secretariat accepts no liability in this area Adobe is a trademark of Adobe Systems Incorporated Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing Every care has been taken to ensure that the file is suitable for use by ISO member bodies In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below © ISO 2005 All rights reserved Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body in the country of the requester ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.org Web www.iso.org Published in Switzerland ii `,,```,,,,````-`-`,,`,,`,`,,` - Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) Contents Page Foreword iv Introduction v Scope Normative references Terms and definitions 4.1 4.2 4.3 Symbols, subscripts and abbreviated terms General symbols Subscripts Formulae for dimensions and tolerances for all fit classes Concept of side fit splines 12 Effective fit concept 14 Basic rack profiles for spline 22 Spline fit classes 24 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Space width and tooth thickness tolerances 26 Total tolerance T + λ 26 Deviation allowance, λ 27 Total pitch deviation, Fp 27 Total profile deviation, Fα 28 Total helix deviation, Fβ 29 Machining tolerance, T 29 Effective clearance tolerance, Tv 30 Use of effective and actual dimensions for space width and tooth thickness .30 10 10.1 10.2 Minor and major diameters .31 Tolerances 31 Adjustment to minor diameters (Die), form diameters (DFe) and major diameters (Dee) of external splines 32 11 11.1 11.2 11.3 Manufacturing and design considerations .32 Radii 32 Profile shifts 32 Eccentricity and misalignment 33 12 12.1 12.2 12.3 12.4 Spline data 34 Basic dimensions 34 Combination of types 34 Designation 34 Drawing data 35 Annex A (informative) Drawing data example calculations 40 Bibliography 59 iii © ISO 2005 – All rights reserved `,,```,,,,````-`-`,,`,,`,`,,` - Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work of preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights ISO shall not be held responsible for identifying any or all such patent rights ISO 4156-1 was prepared by Technical Committee ISO/TC 14, Shafts for machinery and accessories This first edition of ISO 4156-1, together with ISO 4156-2 and ISO 4156-3, cancels and replaces ISO 4156:1981 and ISO 4156:1981/Amd 1:1992, of which it constitutes a technical revision The values and tables are the same as in ISO 4156:1981; however, some explanations and definitions have been clarified ISO 4156 consists of the following parts, under the general title Straight cylindrical involute splines — Metric module, side fit:  Part 1: Generalities  Part 2: Dimensions  Part 3: Inspection iv Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale `,,```,,,,````-`-`,,`,,`,`,,` - The main task of technical committees is to prepare International Standards Draft International Standards adopted by the technical committees are circulated to the member bodies for voting Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote ISO 4156-1:2005(E) Introduction ISO 4156 provides the data and indications necessary for the design, manufacture and inspection of straight (non-helical) side-fitting cylindrical involute splines Straight cylindrical involute splines manufactured in accordance with ISO 4156 are used for clearance, sliding and interference connections of shafts and hubs They contain all the necessary characteristics for the assembly, transmission of torque, and economic production The nominal pressure angles are 30°, 37,5° and 45° For electronic data processing purposes, the form of expression 37,5° has been adopted instead of 37°30’ ISO 4156 establishes a specification based on the following modules:  for pressure angles of 30° and 37,5° the module increments are 0,5; 0,75; 1; 1,25; 1,5; 1,75; 2; 2,5; 3; 4; 5; 6; 8; 10  for pressure angle of 45° the module increments are 0,25; 0,5; 0,75; 1; 1,25; 1,5; 1,75; 2; 2,5 `,,```,,,,````-`-`,,`,,`,`,,` - v © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale `,,```,,,,````-`-`,,`,,`,`,,` - Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale INTERNATIONAL STANDARD ISO 4156-1:2005(E) Straight cylindrical involute splines — Metric module, side fit — `,,```,,,,````-`-`,,`,,`,`,,` - Part 1: Generalities Scope This part of ISO 4156 provides the data and indications necessary for the design and manufacture of straight (non-helical) side-fitting cylindrical involute splines Limiting dimensions, tolerances, manufacturing errors and their effects on the fit between connecting coaxial spline elements are defined in the equations and given in the tables Unless otherwise specified, linear dimensions are expressed in millimetres and angular dimensions in degrees Normative references The following referenced documents are indispensable for the application of this document For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies ISO 286-1, ISO system of limits and fits — Part 1: Bases of tolerances, deviations and fits ISO 1101, Geometrical Product Specifications (GPS) — Geometrical tolerancing — Tolerances of form, orientation, location and run-out ISO 4156-2, Straight cylindrical involute splines — Metric module, side fit — Part 2: Dimensions ISO 4156-3:2005, Straight cylindrical involute splines — Metric module, side fit — Part 3: Inspection Terms and definitions For the purposes of this document, the following terms and definitions apply 3.1 spline joint connecting, coaxial elements that transmit torque through the simultaneous engagement of equally spaced teeth situated around the periphery of a cylindrical external member with similar spaced mating spaces situated around the inner surface of the related cylindrical internal member 3.2 involute spline member of spline joint having teeth or spaces that have involute flank profiles 3.3 internal spline spline formed on the inner surface of a cylinder © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) 3.4 external spline spline formed on the outer surface of a cylinder 3.5 fillet concave surface of the tooth or space connecting the involute flank and the root circle NOTE This curved surface as generated varies and cannot be properly specified by a radius of any given value 3.6 fillet root spline spline having a tooth or space profile in which the opposing involute flanks are connected to the root circle (Dei or Die diameter) by a single fillet 3.7 flat root spline spline having a tooth or space profile in which each of the opposing involute flanks are connected to the root circle (Dei or Die diameter) by a fillet 3.8 module m ratio of the circular pitch, expressed in millimetres, to the number π (or the ratio of the pitch diameter expressed in millimetres, to the number of teeth) 3.9 pitch circle reference circle from which all normal spline dimensions are derived, and the circle on which the specified pressure angle has its nominal value 3.10 pitch diameter D diameter of the pitch circle, in millimetres, equal to the number of teeth multiplied by the module 3.11 pitch point intersection of the spline tooth profile with the pitch circle `,,```,,,,````-`-`,,`,,`,`,,` - 3.12 circular pitch p length of arc of the pitch circle between two consecutive pitch points of left- (or right-) hand flanks, which has a value of the number π multiplied by the module 3.13 pressure angle α acute angle between a radial line passing through any point on a tooth flank and the tangent plane to the flank at that point 3.14 standard pressure angle αD pressure angle at the specified pitch point Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) 3.15 base circle circle from which Involute spline tooth profiles are generated 3.16 base diameter Db diameter of the base circle 3.17 base pitch pb arc length of the base circle between two consecutive corresponding flanks 3.18 major circle outermost (largest) circle of the external or internal spline 3.19 major diameter Dee, Dei diameter of the major circle 3.20 minor circle innermost (smallest) circle of the external or internal spline 3.21 minor diameter, Die, Dii diameter of the minor circle 3.22 form circle circle used to define the depth of involute profile control NOTE In the case of an external spline it is located near and above the minor diameter, and on an internal spline near and below the major diameter 3.23 form diameter DFe, DFi diameter of the form circle 3.24 depth of engagement radial distance from the minor circle of the internal spline to the major circle of the external spline, minus corner clearance and/or chamfer depth 3.25 basic (circular) space width or tooth thickness at the pitch diameter E or S for 30°, 37,5° and 45° pressure angle splines, half the circular pitch 3.26 actual space width practically measured circular space width, on the pitch circle, of any single space width within the limit values Emax and Emin `,,```,,,,````-`-`,,`,,`,`,,` - © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) 3.27 effective space width Ev space width where an imaginary perfect external spline would fit without clearance or interference, given by the size of the tooth thickness of this external spline, considering engagement of the entire axial length of the splined assembly NOTE The minimum effective space width (Ev min, always equal to E) of the internal spline is always basic, as shown in Table 3.28 actual tooth thickness practically measured circular tooth thickness, on the pitch circle, of any single tooth within the limit values Smax and Smin 3.29 effective tooth thickness Sv tooth thickness where an imaginary perfect internal spline would fit without clearance or interference, given by the size of the space width of this internal spline, considering engagement of the entire axial length of the splined assembly 3.30 effective clearance cv 〈looseness or interference〉 effective space width of the internal spline minus the effective tooth thickness of the external spline NOTE For looseness, cv is positive; for interference, cv is negative 3.31 theoretical clearance c 〈looseness or interference〉 actual space width of the internal spline minus the actual tooth thickness of the external spline NOTE It does not define the effective fit between internal and external spline, because of the effect of deviations 3.32 form clearance cF radial clearance between the form diameter of the internal spline and the major diameter of the external spline, or between the minor diameter of the internal spline and the form diameter of the external spline NOTE It allows eccentricity of their respective pitch circles 3.33 total pitch deviation Fp absolute value of the difference between the greatest positive and negative deviations from the theoretical spacing 3.34 total profile deviation Fα absolute value of the difference between the greatest positive and negative deviations from the theoretical tooth profile, measured normal to the flanks Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved `,,```,,,,````-`-`,,`,,`,`,,` - Not for Resale ISO 4156-1:2005(E) Emin = 1,571 + 0,049 = 1,620 Max effective space width Ev max = Emax − λ Ev max = 1,709 − 0,049 = 1,660 Measuring ball or pin diameter DRi (formulae taken from ISO 4156-3:2005, 8.5.2) ∩ DE i = E ⋅ cosα D + D b ⋅ invα D 2× π 2× π   inv αD = tanα D −  α D × = tan ( 30° ) −  30° × = 0,053 75  360°  360°    `,,```,,,,````-`-`,,`,,`,`,,` - where ∩ DE i = 1,571⋅ cos ( 30° ) + 21,650 64 ⋅ 0,053 75 = 2,524 25 BA = 21,650 64 × tan ( 30° ) D b × tanα D = 6,250 00 = 2 ∩   DE i   D b × tan  α D + invα D − D b     BO i =  2× π 2,524 25  360°  21,650 64 × tan  30° × + 0,053 75 −  × 360° 21,650 64  × π    BO i = = 5,373 62 Calculated From ISO R40 no series ( ) D Ri = ⋅ BA − BO i = ⋅ ( 6,250 − 5,373 62 ) = 1,752 76 DRi = 1,800 Maximum measurement between balls or pins MRi max (formulae taken from ISO 4156-3:2005, 8.6.1.2) From above formula DRi = 1,800 invα i = D  E  +  invα D − Ri  D  Db  E = Emax = 1,709 inv α i = 1,709  1,800  +  0,053 75 −  = 0,038 971 58 25,000  21,650 64  αi = 27,150 21° For odd numbers of teeth M Ri max = D b × cos 90° z −D Ri cosα i 46 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) M Ri max  90°  21,650 64 ⋅ cos    25  − 1,800 = 22,484 = cos ( 27,150 21° ) Min measurement between balls or pins MRi E = Emin = 1,620 inv α i = 1,620  1,800  +  0,053 75 −  = 0,035 411 58 25,000  21,650 64  αi = 26,347 37° M Ri  90°  21,650 64 × cos    25  − 1,800 = 22,313 = cos ( 26,347 37° ) Fillet radius ρ Fi = 0,4 × m (formula from Table 2) ρ Fi = 0,4 × 1,0 = 0,4 A.4 EXT 25z × 1,0m × 30P × 4h - ISO 4156 NOTE Unless otherwise stated all formulae are provided in Table Number of teeth z = 25 Module m = 1,0 Pressure angle αD = 30° Pitch diameter D = m ⋅ z = 1,0 ⋅ 25 = 25,000 Base diameter Db = m ⋅ z ⋅ cos αD = 1,0 ⋅ 25 ⋅ cos (30°) = 21,650 635 09 = 21,650 Major diameter D ee max = m ⋅ ( z + 1) + From Table es v tanα D esv = D ee max = 1,0 × ( 25 + 1) + = 26,00 tan(30°) Dee = 26,00 h11 (0/−0,130) Form diameter DFe max = ⋅ (0,5 ⋅ D b ) ,5 ⋅ es v  hs −  tanα D +  0,5 ⋅ D ⋅ sinα D −  sinα D         `,,```,,,,````-`-`,,`,,`,`,,` - 47 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) From Table hs = 0,6 × m = 0,6 × 1,0 = 0,6 From Table esv = 0,5 ×   0,6 −  tan (30°)   DFe max = × (0,5 × 21,650 64) +  0,5 × 25,0 × sin (30°) − sin (30°)       DFe max = 23,89 Maximum minor diameter (flat root) — not tabulated but necessary for calculating minimum minor diameter D ie max = m ⋅ ( z − 1,5 ) + es v = 1,0 ⋅ ( 25 − 1,5 ) + = 23,50 tanα D tan ( 30° ) D ie = D ie max − Minimum minor diameter (T + λ ) tanα D class (T + λ) = 40 ⋅ id + 160 iE From 9.1 id = 0,45 ⋅ D + 0,001 ⋅ D = 0,45 ⋅ iE = 0,45 ⋅ E + 0,001 ⋅ E 25,0 + 0,001 ⋅ 25,0 = 1,340 E = 0,5 ⋅ π ⋅ m = 0,5 ⋅ π ⋅ 1,0 = 1,571 iE = 0,45 ⋅ 1,571 + 0,001 ⋅ 1,571 = 0,524 T + λ = 40 ⋅ 1,340 + 160 ⋅ 0,524 = 137,584 µm = 0,138 mm D ie = 23,50 − 0,138 = 23,26 tan ( 30° ) Max effective tooth thickness Sv max = S + esv S = 0,5 × π × m = 0,5 × π × 1,0 = 1,571 Min actual tooth thickness `,,```,,,,````-`-`,,`,,`,`,,` - Sv max = 1,571 + = 1,571 S = S v max − (T + λ ) From 9.1 class (T + λ) = 10 ⋅ id + 40 ⋅ iE From above formula id = 1,340 et iE = 0,524 T + λ = 10 × 1,340 + 40 × 0,524 = 34,396 µm = 0,034 mm Smin = 1,571 − 0,034 = 1,537 Max actual tooth thickness Smax = Sv max − λ 48 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) NOTE λ can be calculated from total pitch deviation (Fp) total profile deviation (Fα) and total helix deviation (Fβ), see 9.2 , or λ can be obtained from Table 14 F p = 2,5 × L + 6,3 (formula from Table 7) Total pitch deviation where L =m× z× π π = 1,0 × 25 × = 39,269 908 17 2 F p = 2,5 × 39,269 908 17 + 6,3 = 21,97 µm = 0,022 mm Total profile deviation where ϕ f = m + 0,012 × m × z = 1,0 + 0,012 × 1,0 × 25 = 1,312 50 Total helix deviation where b= Fα = 1,6 × ϕ f + 10 (formula from Table 8) F β = 0,8 ⋅ b + b = length of spline (formula from Table 9) (assume to be one half of the pitch diameter) D 25 = = 12,50 2 F β = 0,8 × 12,50 + = 6,83 àm = 0,007 mm = 0,6 ì F p2 + Fα2 + F β2 Deviation allowance `,,```,,,,````-`-`,,`,,`,`,,` - λ = 0,6 × 0,022 + 0,012 + 0,007 λ = 0,016 Smax = 1,571 − 0,016 = 1,555 Min effective tooth thickness Sv = Smin + λ Sv = 1,537 + 0,016 = 1,553 Measuring ball or pin diameter DRe (formulae taken from ISO 4156-3:2005, 8.5.1) ∩ DE e = p b − ( S × cosα D + D b × invα D ) where and p b = m × π × cosα D = 1,0 × π × cos ( 30° ) = 2,720 70 2× π  2× π    inv αD = tanα D −  α D ×  = tan ( 30° ) −  30° × 360°  = 0,053 75 360 °     ∩ ( ) DE e = 2,720 70 − 1,571 × cos ( 30° ) + 21,650 64 × 0,053 75 = 0,196 45 BA = 21,650 × 64 × tan ( 30° ) D b × tanα D = 6,250 00 = 2 49 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) BO e ∩  DE e  D b × tan  α D + invα D + Db   =       2× π 0,196 45  360°  21,650 64 × tan  30° × + 0,053 75 +  × 360° 21,650 64  × π    BO e = = 7,192 20 Calculated ( ) D Re = ⋅ BO e − BA = ⋅ ( 7,192 20 − 6,250 00 ) = 1,884 40 From ISO R40 no series DRe = 1,900 Max measurement over balls or pins MRe max (formulae taken from ISO 4156-3:2005, 8.6.1.1) From above formula inv α e = DRe = 1,900 D π S  +  inv α D + Re −  D  Db z S = Smax = 1,555 inv α e = 1,555  1,900 π  +  0,053 75 + −  = 0,078 043 51 25,000  21,650 64 25  αe = 33,609 83° For odd numbers of teeth M Re max = M Re max D b ⋅ cos 90° z +D Re cosα e  90°  21,650 64 ⋅ cos    25  + 1,900 = 27,845 = cos ( 33,609 83° ) Min measurement over balls or pins MRe S = Smin = 1,537 invα e = 1,537  1,900 π  +  0,05375 + − = 0,077 323 51 25,000  21,65064 25  αe = 33,516 11° Fillet radius ρ Fe = 0,2 × m (formula from Table 2) ρ Fe = 0,2 × 1,0 = 0,2 50 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved `,,```,,,,````-`-`,,`,,`,`,,` - Not for Resale ISO 4156-1:2005(E) A.5 EXT 25z × 1,0m × 30R × 6e - ISO 4156 NOTE Unless otherwise stated all formulae are provided in Table Number of teeth z = 25 Module m = 1,0 Pressure angle αD = 30° Pitch diameter D = m × z = 1,0 × 25 = 25,000 Base diameter Db = m × z × cos αD = 1,0 × 25 × cos(30°) = 21,650 635 09 = 21,650 Major diameter D ee max = m ⋅ ( z + 1) + es v tanα D From Clause 10, adjustment is made to the major, form and minor diameters for fundamental deviation e esv = −0,040 So, from Table  −0,040  D ee max = 1,0 ⋅ ( 25 + 1) +   = 25,930  tan(30°)  Dee = 25,93 h11 (0/−0,130) Form diameter ,5 × es v  hs −  tanα D DFe max = × (0,5 × D b ) +  0,5 × D × sinα D −  sinα D   From Table hs = 0,6 ⋅ m = 0,6 ⋅ 1,0 = 0,6 From Table esv = −0,040 DFe max = × (0,5 × 21,650 64)  ,5 × ( −0,040 )  0,6 −   tan(30°)  +  0,5 × 25,0 × sin(30°) −   sin(30°)           2 DFe max = 23,83 Maximum minor diameter (fillet root) — not tabulated but necessary for calculating minimum minor diameter D ie max = m × ( z − 1,8 ) + Minimum minor diameter From 9.1 es v = 1,0 × ( 25 − 1,8 ) + ( −0,069 ) = 23,13 tanα D D ie = D ie max − (T + λ ) tanα D class (T + λ) = 40 ⋅ id + 160 ⋅ iE 51 `,,```,,,,````-`-`,,`,,`,`,,` - © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) id = 0,45 ⋅ D + 0,001 ⋅ D = 0,45 ⋅ iE = 0,45 ⋅ E + 0,001 ⋅ E 25,0 + 0,001 ⋅ 25,0 = 1,340 E = 0,5 ⋅ π ⋅ m = 0,5 ⋅ π ⋅ 1,0 = 1,571 iE = 0,45 ⋅ 1,571 + 0,001 ⋅ 1,571 = 0,524 T + λ = 40 ⋅ 1,340 + 160 ⋅ 0,524 = 137,584 µm = 0,138 mm D ie = 23,13 − Max effective tooth thickness 0,138 = 22,89 tan ( 30° ) Sv max = S + esv S = 0,5 × π × m = 0,5 × π × 1,0 = 1,571 Sv max = 1,571 + (−0,040) = 1,531 S = S v max − (T + λ ) From 9.1 class (T + λ) = 25 ⋅ id + 100 iE From above formula id = 1,340 et iE = 0,524 T + λ = 25 ⋅ 1,340 + 100 ⋅ 0,524 = 85,990 µm = 0,086 mm Smin = 1,531 − 0,086 = 1,445 Max actual tooth thickness Smax = Sv max − λ NOTE λ can be calculated from total pitch deviation (Fp) total profile deviation (Fα) and total helix deviation (Fβ), see 9.2 , or λ can be obtained from Table 14 F p = × L + 12,5 Total pitch deviation where L = m× z× (formula from Table 7) π π = 1,0 × 25 × = 39,269 908 17 2 F p = × 39,269 908 17 + 12,5 = 43,83 µm = 0,044 mm Fα = × ϕ f + 25 Total profile deviation where (formula from Table 8) ϕ f = m + 0,012 × m × z = 1,0 + 0,0125 × 1,0 × 25 = 1,312 50 Fα = × 1,312 50 + 25 = 30,25 µm = 0,030 mm Total helix deviation where F β = 1,25 × b + 6,3 (formula from Table 9) b = length of spline (assumed to be one half of the pitch diameter) 52 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale `,,```,,,,````-`-`,,`,,`,`,,` - Min actual tooth thickness ISO 4156-1:2005(E) b= D 25 = = 12,50 2 F β = 1,25 × 12,50 + 6,3 = 10,72 µm = 0,011mm Deviation allowance λ = 0,6 ⋅ F p2 + Fα2 + F β2 λ = 0,6 × 0,044 + 0,030 + 0,0112 λ = 0,033 Smax = 1,531 − 0,033 = 1,498 Min effective tooth thickness Sv = Smin + λ Sv = 1,445 + 0,033 = 1,478 Measuring ball or pin diameter DRe (formulae taken from ISO 4156-3:2005, 8.5.1) ∩ DE e = p b − ( S × cosα D + D b × invα D ) p b = m × π × cosα D = 1,0 × π × cos ( 30° ) = 2,720 70 where 2× π  2⋅π    inv αD = tanα D −  α D ×  = tan ( 30° ) −  30° × 360°  = 0,053 75 360 °     and ∩ ( ) DE e = 2,720 70 − 1,571× cos ( 30° ) + 21,650 64 × 0,053 75 = 0,196 45 `,,```,,,,````-`-`,,`,,`,`,,` - BA = BO e 21,650 64 × tan ( 30° ) D b × tanα D = 6,250 00 = 2 ∩  DE e  D b × tan  α D + invα D + Db   =       2× π 0,196 45  360°  21,650 64 × tan  30° × + 0,053 75 +  × 360° 21,650 64  × π    = 7,192 20 BO e = Calculated ( ) D Re = × BO e − BA = × ( 7,192 20 − 6,250 00 ) = 1,884 40 From ISO R40 no series DRe = 1,900 Maximum measurement over balls or pins MRe max (formulae taken from ISO 4156-3:2005, 8.6.1.1) From above formula DRe = 1,900 53 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) inv α e = D S  π +  invα D + Re −  D  Db z S = Smax = 1,498 invα e = 1,498  1,900 π  +  0,053 75 + −  = 0,075 763 51 25,000  21,650 64 25  αe = 33,310 74° For odd numbers of teeth M Re max = M Re max D b ⋅ cos 90° z cos α e + D Re  90°  21,650 64 ⋅ cos    25  + 1,900 = 27,756 = cos ( 33,310 74° ) Min measurement over balls or pins MRe S = S = 1,445 inv α e = 1,445  1,900 π  +  0,053 75 + −  = 0,073 643 51 25,000  21,650 64 25  αe = 33,026 41° M Re  90°  21,650 64 × cos    25  + 1,900 = 27,672 = cos ( 33,026 41° ) Fillet radius ρ Fe = 0,4 × m (formula from Table 2) ρ Fe = 0,4 × 1,0 = 0,4 A.6 EXT 25z × 1,0m × 30P × 5js - ISO 4156 NOTE Unless otherwise stated all formulae are provided in Table Number of teeth z = 25 Module m = 1,0 Pressure angle αD = 30° Pitch diameter D = m ⋅ z = 1,0 ⋅ 25 = 25,000 Base diameter Db = m ⋅ z ⋅ cos αD = 1,0 ⋅ 25 ⋅ cos(30°) = 21,650 635 09 = 21,650 `,,```,,,,````-`-`,,`,,`,`,,` - 54 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) es v tanα D D ee max = m × ( z + 1) + Major diameter From Clause 10, no adjustment is applied to the major diameter, but adjustment is applied to the form and minor diameters for fundamental deviation js So, es v =0 tanα D D ee max = 1,0 × ( 25 + 1) + = 26,00 Dee = 26,00 h11 (0/−0,130) 0, × es v  hs −  tanα D DFe max = × (0,5 × D b ) +  0,5 × D × sin α D −  sin α D   Form diameter hs = 0,6 ⋅ m = 0,6 ⋅ 1,0 = 0,6 From Table es v = From Table 5, Footnote a From 9.1       T +λ class (T + λ) = 16 ⋅ id + 64 ⋅ iE id = 0,45 ⋅ D + 0,001 ⋅ D = 0,45 ⋅ iE = 0,45 ⋅ E + 0,001 ⋅ E 25,0 + 0,001 ⋅ 25,0 = 1,340 E = 0,5 ⋅ π ⋅ m = 0,5 ⋅ π ⋅ 1,0 = 1,571 iE = 0,45 ⋅ 1,571 + 0,001 ⋅ 1,571 = 0,524 T + λ = 16 ⋅ 1,340 + 64 ⋅ 0,524 = 55,03 µm = 0,055 mm es v = 0,055 = 0,028 ,5 × ,028   0, −  tan(30°)   DFe max = × (0,5 × 21,650 64) +  0,5 × 25,0 × sin(30°) − sin(30°)       Maximum minor diameter (flat root) — not tabulated but necessary for calculating minimum minor diameter D ie max = m × ( z − 1,5 ) + es v 0,028 = 1,0 × ( 25 − 1,5 ) + = 23,55 tanα D tan ( 30° ) 55 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS `,,```,,,,````-`-`,,`,,`,`,,` - DFe max = 23,93 Not for Resale ISO 4156-1:2005(E) D ie = D ie max − Min minor diameter (T + λ ) tanα D From 9.1 class (T + λ) = 40 id + 160 iE From above formula id = 1,3408 and iE = 0,524 T + λ = 40 ⋅ 1,340 + 160 ⋅ 0,524 = 137,584 µm = 0,138 mm D ie = 23,55 − Max effective tooth thickness 0,138 = 23,31 tan ( 30° ) Sv max = S + esv S = 0,5 × π × m = 0,5 × π × 1,0 = 1,571 Sv max = 1,571 + 0,028 = 1,599 Minimum actual tooth thickness S = S v max − ( T + λ ) From above formula class (T + λ) = 0,055 Smin = 1,599 − 0,055 = 1,544 Max actual tooth thickness Smax = Sv max − λ NOTE λ can be calculated from total pitch deviation (Fp) total profile deviation (Fα) and total helix deviation (Fβ), see 9.2, or λ can be obtained from Table 14 F p = 3,55 × L + Total pitch deviation where L = m× z× (formula from Table 7) π π = 1,0 × 25 × = 39,269 908 17 2 F p = 3,55 × 39,269 908 17 + = 31,25 µm = 0,031 mm Total profile deviation Fα = 2,5 × ϕ f + 16 where (formula from Table 8) ϕ f = m + 0,012 × m × z = 1,0 + 0,012 × 1,0 ⋅ 25 = 1,312 50 Fα = 2,5 × 1,312 50 + 16 = 19,28 µm = 0,019 mm Total helix deviation where Fβ = b + b = length of spline b= (formula from Table 9) (assume to be one half of the pitch diameter) D 25 = = 12,50 2 F β = 12,50 + = 8,54 µm = 0,009 mm `,,```,,,,````-`-`,,`,,`,`,,` - 56 Organization for Standardization Copyright International Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) λ = 0,6 ⋅ F p2 + Fα2 + F β2 Deviation allowance λ = 0,6 × 0,0312 + 0,019 + 0,009 λ = 0,022 Smax = 1,599 − 0,022 = 1,577 Min effective tooth thickness Sv = Smin + λ Sv = 1,544 + 0,022 = 1,566 Measuring ball or pin diameter Dre (formulae taken from ISO 4156-3:2005, 8.5.1) ∩ DE e = p b − ( S × cosα D + D b × invα D ) where and p b = m × π × cosα D = 1,0 × π × cos ( 30° ) = 2,720 70 2× π  2× π    inv αD = tanα D −  α D ×  = tan ( 30° ) −  30° × 360°  = 0,053 75 360 °     ∩ ( ) BA = BO e 21,650 64 × tan ( 30° ) D b × tanα D = 6,250 00 = 2 ∩  DE e  D b × tan  α D + invα D + Db   =      `,,```,,,,````-`-`,,`,,`,`,,` - DE e = 2,720 70 − 1,571× cos ( 30° ) + 21,650 64 ⋅ 0,053 75 = 0,196 45  2× π 0,196 45  360°  21,650 64 × tan  30° × + 0,053 75 +  × 360° 21,650 64  × π    = 7,192 20 BO e = Calculated ( ) D Re = × BO e − BA = × ( 7,192 20 − 6,250 00 ) = 1,884 40 From ISO R40 no series DRe = 1,900 Maximum measurement over balls or pins MRe max (formulae taken from ISO 4156-3:2005, 8.6.1.1) From above formula inv α e = DRe = 1,900 D S  π +  inv α D + Re −  D  Db z S = Smax = 1,577 57 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) inv α e = π  1,577  1,900 +  0,053 75 + −  = 0,078 923 51 25,000  21,650 64 25  αe = 33,723 47° For odd numbers of teeth M Re max = M Re max D b ⋅ cos 90° z +D Re cosα e  90°  21,650 64 ⋅ cos    25  + 1,900 = 27,880 = cos ( 33,723 47° ) Minimum measurement over balls or pins MRe S = Smin = 1,544 inv α e = 1,544  1,900 π  +  0,053 75 + −  = 0,077 603 51 25,000  21,650 64 25  αe = 33,552 63° `,,```,,,,````-`-`,,`,,`,`,,` - M Re Fillet radius  90°  21,650 64 ⋅ cos    25  + 1,900 = 27,828 = cos ( 33,552 63° ) ρ Fe = 0,2 × m (formula from Table 2) ρ Fe = 0,2 × 1,0 = 0,2 58 Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS © ISO 2005 – All rights reserved Not for Resale ISO 4156-1:2005(E) Bibliography `,,```,,,,````-`-`,,`,,`,`,,` - [1] ISO 3, Preferred numbers — Series of preferred numbers 59 © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale ISO 4156-1:2005(E) `,,```,,,,````-`-`,,`,,`,`,,` - ICS 21.120.30 Price based on 59 pages © ISO 2005 – All rights reserved Copyright International Organization for Standardization Reproduced by IHS under license with ISO No reproduction or networking permitted without license from IHS Not for Resale