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3) Compute measurement, Me, over pins: 计算跨棒距，Me For even numbers of teeth: 对于偶数齿： Me = Db sec Φe + de

For odd numbers of teeth: 对于奇数齿： Me = (Db cos 90°/N) sec Φe + de where de = 1.9200/P for all external splines 所有外花键De=1.9200/P

（以下为美国标准ANSI B92.2M-1980 渐开线花键，米制部分，一并摘录做参考。）

American National Standard Metric Module Splines.— ANSI B92.2M-1980 (R1989) is the American National Standards Institute version of the International Standards Organization involute spline standard. It is not a “soft metric” conversion of any previous, inch- based, standard,* and splines made to this hard metric version are not intended for use with components made to the B92.1 or other, previous standards. The ISO 4156 Standard from which this one is derived is the result of a cooperative effort between the ANSI B92 committee and other members of the ISO/TC 14-2 involute spline committee.

* A “soft” conversion is one in which dimensions in inches, when multiplied by 25.4 will, after being appropriately rounded off, provide equivalent dimensions in millimeters. In a “hard” system the tools of production, such as hobs, do not bear a usable relation to the tools in another system; i.e., a 10 diametral pitch hob calculates to be equal to a 2.54 module hob in the metric module system, a hob that does not exist in the metric standard.

Many of the features of the previous standard, ANSI B92.1-1970 (R1993), have been retained such as: 30-, 37.5-, and 45-degree pressure angles; flat root and fillet root side fits; the four tolerance classes 4, 5, 6, and 7; tables for a single class of fit; and the effective fit concept.

Among the major differences are: use of modules of from 0.25 through 10 mm in place of diametral pitch; dimensions in millimeters instead of inches; the “basic rack”; removal of the major diameter fit; and use of ISO symbols in place of those used previously. Also, pro- vision is made for calculating three defined clearance fits.

The Standard recognizes that proper assembly between mating splines is dependent only on the spline being within effective specifications from the tip of the tooth to the form diameter. Therefore, the internal spline major diameter is shown as a maximum dimension and the external spline minor diameter is shown as a minimum dimension. The minimum internal major diameter and the maximum external minor diameter must clear the specified form diameter and thus require no additional control. All dimensions are for the finished part; any compensation that must be made for operations that take place during processing, such as heat treatment, must be considered when selecting the tolerance level for manufacturing.

The Standard provides the same internal minimum effective space width and external maximum effective tooth thickness for all tolerance classes. This basic concept makes possible interchangeable assembly between mating splines regardless of the tolerance class of the individual members, and permits a tolerance class “mix” of mating members. This arrangement is often an advantage when one member is considerably less difficult to pro- duce than its mate, and the “average” tolerance applied to the two units is such that it satisfies the design need. For example, by specifying Class 5 tolerance for one member and Class 7 for its mate, an assembly tolerance in the Class 6 range is provided.

If a fit given in this Standard does not satisfy a particular design need, and a

specific clearance or press fit is desired, the change shall be made only to the external spline by a reduction of, or an increase in, the effective tooth thickness and a like change in the actual tooth thickness. The minimum effective space width is always basic and this basic width should always be retained when special designs are derived from the concept of this Standard.

Spline Terms and Definitions: The spline terms and definitions given for American National Standard ANSI B92.1-1970 (R1993) described in the preceding section, may be used in regard to ANSI B92.2M-1980 (R1989). The 1980 Standard utilizes ISO symbols in place of those used in the 1970 Standard; these differences are shown in Table 12.

Dimensions and Tolerances: Dimensions and tolerances of splines made to the 1980

Standard may be calculated using the formulas given in Table 13. These formulas are for metric module splines in the range of from 0.25 to 10 mm metric module of side-fit design and having pressure angles of 30-, 37.5-, and 45-degrees. The standard modules in the system are: 0.25; 0.5; 0.75; 1; 1.25; 1.5; 1.75; 2; 2.5; 3; 4; 5; 6; 8; and 10. The range of from 0.5 to 10 module applies to all splines except 45-degree fillet root splines; for these, the range

of from 0.25 to 2.5 module applies.

Fit Classes: Four classes of side fit splines are provided: spline fit class H/h having a minimum effective clearance, cv = es = 0; classes H/f, H/e, and H/d having tooth thickness modifications, es, of f, e, and d, respectively, to provide progressively greater effective clearance cv, The tooth thickness modifications h, f, e, and d in Table 14 are fundamental deviations selected from ISO R286, “ISO System of Limits and Fits.” They are applied to the external spline by shifting the tooth thickness total tolerance below the basic tooth thickness by the amount of the tooth thickness modification to provide a prescribed mini- mum effective clearance cv.

Table 12. Comparison of Symbols Used in ANSI B92.2M-1980 (R1989) and Those in ANSI B92.1-1970, R1993 （B92.1和B92.2符号区别） Symbol B92.2M B92.1 c … theoretical clearance cv cv effective clearance cF cF form clearance D D pitch diameter DB Db base diameter pin contact diameter, dce Dce external spline pin contact diameter, dci Dci internal spline DEE DEI DFE DFI DIE DII DRE DRI hs Do Dri DFe DFi Dre Di de di … major diam., ext. spline major diam., int. spline form diam., ext. spline form diam., int. spline minor diam., ext. spline minor diam., int. spline pin diam., ext. spline pin diam., int. spline see Figs. 6a, 6b, 6c, and 6d Symbol B92.2M B92.1 m … … P … Ps Pb … p p π rfe rfi Ebsc Emax Emin Ev Sbsc Smax smin SV π rf rf Svmin s s Sv tvmax t t tv module diametral pitch stub pitch = 2P base pitch circular pitch 3.141592654 fillet rad.,ext.spline fillet rad., int. spline basic circular space width max. actual circular space width min. actual circular space width effective circular space width basic circular tooth thickness max. actual circular tooth thick min. actual circular tooth thick effective circular tooth thick. λ INV a KE KI g gw gγ T MRE MRI Z λ … Ke Ki L … … m Me Mi N effective variation involute α=tan α? arc α change factor, ext. spline change factor, int. spline spline length active spline length length of engagement machining tolerance meas. over 2 pins, ext. spline α αD αci αce αi αe αFe αFi es Φ ΦD Φci Φce Φi Φe ΦF ΦF … meas. bet. 2 pins, int. spline h,f,e,or d … number of teeth H … pressure angle standard pressure angle press. angle at pin contact diameter, internal spline press. angle at pin contact diameter, external spline press. angle at pin center, internal spline press. angle at pin center, external spline press. angle at form diameter, external spline press. angle at form diameter, internal spline ext. spline cir. tooth thick.modifi- cation for required fit class=cvmin (Table 14) tooth thick, size modifiers (called fundamental deviation in ISO R286), Table 14 space width size modifier (called fundamental deviation in ISO R286), Table 14

Table 13. Formulas for Dimensions and Tolerances for All Fit Classes—

Metric Module Involute Splines Formula Term Symbol 30-Degree Flat Root 0.5 to 10 module Pitch Diameter Base Diameter Circular Pitch Base Pitch Tooth Thick Mod Min Maj. Diam. Int Max Maj Diam. Int. Form Diam, Int. Min Minor Diam, Int Max Minor Diam,Int Cir Space Width, Basic Min Effective Max Actual Min Actual Max Effective Max Major Diam,Extd Min Major Diam.Ext Form Diam, External D DB p pb es DEI min DEI max DFI DII min DII max Ebsc EV min E max E min EV max DEEmax DEEmin DFE mZ mZ cos αD πm πm cos αD According to selected fit class, H/h, H/f, H/e, or H/d (see Table 14) m(Z + 1.5) m(Z + 1) + 2cF m(Z + 1.8) m(Z + 1)+2cF m(Z + 1.4) m(Z+0.9)+2cF m(Z + 1.2) m(Z+0.8)+2cF DEI min + (T + λ)/tan αD (see Footnote a) DFE + 2cF (see Footnote b) DII min + (0.2m0.667 ? 0.01m?0.5) (see Footnote c) 0.5πm 0.5πm EV min + (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) EV min + λ (see text on page 2181 for λ) E max ?λ (see text on page 2181 for λ) m(Z+1)-es/tanαD m(Z+1)-es/tanαD m(Z+0.9)-es/tanαD m(Z+0.8)-es/tanαD DEE max ? (0.2m0.667 ? 0.01m?0.5)c 30-Degree Fillet Root 0.5 to 10 module 37.5-Degree Fillet Root 0.5 to 10 module 45-Degree Fillet Root 0.25 to 2.5 module 2?(0.5Db)2?[0.5Dsin?D?hs?((0.5es)/tan?D)2]sin?DMax Minor Diam,Extd Min Minor Diam,Ext Cir Tooth Thick, Basic Max Effective Min Actual Max Actual Min Effective Total Tolerance on Circular Space Width or Tooth Thickness Machining Toler- ance on Circular Space Width or Tooth Thickness Effective Variation Allowed on Circu- lar Space Width or Tooth Thickness Form Clearance Rack Dimension DIE max DIE min Sbsc SV max S min S max SV min (T + λ) m(Z ?1.5)-es/tanαD 0.5πm Sbsc ? es m(Z ?1.8)?es/tanαD m(Z ?1.4)?es/tanαD m(Z ?1.2)?es/tanαD DIE max ? (T + λ)/tan αD (see Footnote a) SV max ? (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) SV max ?λ (see text on page 2181 for λ) S min + λ (see text on page 2181 for λ) See formulas in Table 15 T T = (T + λ) from Table 15 ?λ from text on page 2181. λ cF hs See text on page 2181. 0.1m 0.6m(see Fig. 6a) 0.6m(see Fig. 6b) 0.55m(see Fig. 6c) 0.5m(see Fig. 6d) a Use (T + λ) for class 7 from Table 15

b For all types of fit, always use the DFE value corresponding to the H/h fit.

c Values of (0.2m0.667 ? 0.01m?0.5) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 mod- ule, 0.66; for 5 module, 0.58; for 4 module, 0.50; for 3 module, 0.41; for 2.5 module, 0.36; for 2 mod-ule, 0.31; for 1.75 module, 0.28; for 1.5 module, 0.25; for 1.25 module, 0.22; for 1 module, 0.19; for0.75 module, 0.15; for 0.5 module, 0.11; and for 0.25 module, 0.06.d See Table 17 for values of es/tan α D.

Table 14. Tooth Thickness Modification, es, for Selected Spline Fit Classes External Splinesa External Splinesa Selected Fit Class Selected Fit Class Pitch Pitch d e f h d e f h Diameter in Diameter in Tooth Thickness Modification Tooth Thickness Modification mm, mm, (Reduction) Relative to Basic (Reduction) Relative to Basic D D Tooth Thickness at Pitch Tooth Thickness at Pitch ≤ 3 0.020 0.014 0.006 0 > 120 to 0.145 0.085 0.043 0 > 3 to 6 0.030 0.020 0.010 0 180 0.170 0.100 0.050 0 > 6 to 10 0.040 0.025 0.013 0 > 180 to 0.190 0.110 0.056 0 > 10 to 18 0.050 0.032 0.016 0 250 0.210 0.125 0.062 0 > 250 to > 18 to 30 0.065 0.040 0.020 0 0.230 0.135 0.068 0 > 30 to 50 0.080 0.050 0.025 0 315 0.260 0.145 0.076 0 > 315 to > 50 to 80 0.100 0.060 0.030 0 0.290 0.160 0.080 0 > 80 to 120 0.120 0.072 0.036 0 400 0.320 0.170 0.086 0 > 400 to a Internal splines are fit class H and have space width modification from basic space width

equal to zero; thus, an H/h fit class has effective clearance cv = 0.

Note: The values listed in this table are taken from ISO R286 and have been computed on the basis of the geometrical mean of the size ranges shown. Values in boldface type do not comply with any documented rule for rounding but are those used by ISO R286; they are used in this table to comply with established international practice.

Basic Rack Profiles: The basic rack profile for the standard pressure angle splines

are shown in Figs. 6a, 6b, 6c, and 6d. The dimensions shown are for maximum material condition and for fit class H/h.

Spline Machining Tolerances and Variations.— The total tolerance (T + λ), Table 15, is the sum of Effective Variation, λ, and a Machining Tolerance, T.

Table 15. Space Width and Tooth Thickness Total Tolerance, (T + λ), in Millimeters Spline Formula for Spline Tolerance Total Tolerance, Tolerance Class T + λ) Class Formula for Total Tolerance, (T + λ) In these formulas, i* and i** are tolerance units based upon pitch diameter and tooth thickness, respectively: (√ is radication) i?= 0.001 (0.45 *3√D+0.001D) for D≤500 mm i?= 0.001 (0.004D + 2.1 ) for D > 500 mm i??= 0.001 (0.45 *3 √(Sbsc) + 0.001 Sbsc ) 4 5 10i* + 40i** 16i* + 64i** 6 7 25i* + 100i** 40i* + 160i** Effective Variation: The effective variation, λ, is the combined effect that total index variation, positive profile variation, and tooth alignment variation has on the effective fit of mating involute splines. The effect of the individual variations is less than the sum of the allowable variations because areas of more than minimum clearance can have profile, tooth alignment, or index variations without changing the fit. It is also unlikely that these variations would occur in their maximum amounts simultaneously on the same spline. For this reason, total index variation, total profile variation, and tooth alignment variation are used to calculate the combined effect by the following formula:

millimeters

The above variation is based upon a length of engagement equal to one-half the pitch diameter of the spline; adjustment of λ may be required for a greater length of engagement. Formulas for values of Fp, ff, and Fβ used in the above formula are given in Table 16.

Table 16. Formulas for Fp, ff , and Fβ used to calculate λ

Spline Total Index Variation, in mm, Total Profile Variation, in mm, Total Lead Variation, in Tolerance Fp ff mm,Fβ Class 4 5 6 7 0.001(2.5*√(mZπ/2)+6.3) 0.001(3.55*√(mZπ/2)+9) 0.001(5*√(mZπ/2)+12.5) 0.001(7.1*√(mZπ/2)+18) 0.001[1.6m(1+0.0125Z)+10] 0.001[2.5m(1+0.0125Z)+16] 0.001[4m(1+0.0125Z)+25] 0.001[6.3m(1+0.0125Z)+40] 0.001(0.8*√g+4) 0.001(1.0*√g+5) 0.001(1.25*√g+6.3) 0.001(2*√g+10) ??0.6(Fp)2?(ff)2?(F?)2g = length of spline in millimeters. Table 17. Reduction, es/tan αD, of External Spline Major and Minor

Diameters

Required for Selected Fit Classes

Pitch Diameter D in mm ≤3 >3 to 6 30 37.5 d 0.035 0.052 0.026 0.039 0.02 0.03 45 Standard Pressure Angle, in Degrees 30 37.5 45 30 Classes of Fit e es/tan αD in millimeters 0.024 0.018 0.014 0.01 0.035 0.026 0.02 0.017 37.5 f 0.008 0.013 0.006 0.01 45 All h 0 0